Math is a unique subject, based on logic, axiom and definitions.there are few tips to do better in it.

1..at research one should be clear in its research topic and future research plan.if you some research papers, try to mention journel rating.

2..geometry , figures and graph are the tool to describe math,soyou have commend on it.one should well prepared for graph of simple curve trignometrical ratio, mod fuction, greatest and least integer fuction, logarithem and exponential fuctions.

3..you should have at least famaliar with mathmatica and matlab software.if your are opting N.A or O.R , then it is nesseary.

4..if you trying for faculty position,then do some practice on lcd screen also.

5..for ph.d selection interview, one should make a good mix of pure and applied subjects for broad spectrum.

6..try to mention, with example , if converse of theorem is not true.converse of theroms are important concept in maths, because they test the limit of generilisation.

7.stess on definations, b/c there are pillars of mathematical structure.never discuss the proof of defination.also clear the concept of axiom.

8.. LINEAR ALGEBRA is safe bet for ph.d interview.it bridges pure and applied maths.students are well aware of matrix notation, so it is easy for them to comprehand linear algebra.every matrix represents a linear transformations.

## Sunday, December 31, 2006

### CFD

Computational Fluid Dynamics (CFD) is one of the branches of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows.The fundamental basis of any CFD problem is the Navier-Stokes equations, which define any single-phase fluid flow. These equations can be simplified by removing terms describing viscosity to yield the Euler equations. Further simplification, by removing terms describing vorticity yields the Full Potential equations.The most fundamental consideration in CFD is how one treats a continuous fluid in a discretized fashion on a computer. One method is to discretize the spatial domain into small cells to form a volume mesh or grid, and then apply a suitable algorithm to solve the equations of motion (Euler equations for inviscid, and Navier-Stokes equations for viscous flow.

### data mining

Data mining derives its name from the similarities between searching for valuable business information in a large database — for example, finding linked products in gigabytes of store scanner data — and mining a mountain for a vein of valuable ore. Both processes require either sifting through an immense amount of material, or intelligently probing it to find exactly where the value resides.Data mining, the extraction of hidden predictive information from large databases, is a powerful new technology with great potential to help companies focus on the most important information in their data warehouses. Data mining tools predict future trends and behaviors, allowing businesses to make proactive, knowledge-driven decisions. The automated, prospective analyses offered by data mining move beyond the analyses of past events provided by retrospective tools typical of decision support systems.

Data mining techniques are the result of a long process of research and product development. This evolution began when business data was first stored on computers, continued with improvements in data access, and more recently, generated technologies that allow users to navigate through their data in real time. Data mining takes this evolutionary process beyond retrospective data access and navigation to prospective and proactive information delivery.How exactly is data mining able to tell you important things that you didn't know or what is going to happen next? The technique that is used to perform these feats in data mining is called modeling. Modeling is simply the act of building a model in one situation where you know the answer and then applying it to another situation that you don't.

## Saturday, December 30, 2006

### math olampiyad

The first International Mathematical Olympiad (IMO) was held in 1959 in Romania. It was originally intended for Eastern Bloc countries only, but since then the list of participating countries has grown to over 80 from all over the world. The site of the competition changes each year, and past locations include such diverse venues as Finland, India, Cuba, Argentina, and Bulgaria. The United States first competed in the IMO in East Germany in 1974 and, in addition to hosting this year, also hosted the competition in 1981. The competition has been held every year except 1980. When the IMO first began, each country was allowed up to eight participants. In 1982 this was scaled back to four members, but in 1983 the number was increased to six, which is where it still stands. The contestants must be no more than 20 years old and must not have any postsecondary-school education. There is no limit to how many times a person may participate in the IMO, provided the individual meets the age and schooling requirements. Even though the contestants represent their countries in the Olympiad, there are no official teams and all scoring is done on an individual basis only. Although the particular way the representatives are chosen differs from country to country, each country requires a great deal of hard work and mathematical skill from its members.

Bringing math and students together is an age-old idea. Mathematical competitions have played important roles in the tradition of many countries for centuries, surely dating as far back as the Greeks competing to solve geometry problems. In the XVI century, the Italians competed to resolve cubic polynomials, the French held competitions in the XVIII century, and Hungary organized the Eotvos competitions since 1894, which is most likely the closest antecedent to the Mathematical Olympiad held today. The first Mathematical Olympiad took place in Leningrad (now San Petersburg) in 1934, organized by B.N. Delone and G.M. Frijtengolts. In 1959, Romania organized the first International Mathematical Olympiad as an eastern European regional competitmtion with seven countries.

Bringing math and students together is an age-old idea. Mathematical competitions have played important roles in the tradition of many countries for centuries, surely dating as far back as the Greeks competing to solve geometry problems. In the XVI century, the Italians competed to resolve cubic polynomials, the French held competitions in the XVIII century, and Hungary organized the Eotvos competitions since 1894, which is most likely the closest antecedent to the Mathematical Olympiad held today. The first Mathematical Olympiad took place in Leningrad (now San Petersburg) in 1934, organized by B.N. Delone and G.M. Frijtengolts. In 1959, Romania organized the first International Mathematical Olympiad as an eastern European regional competitmtion with seven countries.

## Friday, December 29, 2006

### Questions for math interview

1..Define projective geometry.

ANS..There are two geometries between them: similarity and affine. To see the relationships between these different geometries, consult Figure 1. Projective geometry models well the imaging process of a camera because it allows a much larger class of transformations than just translations and rotations, a class which includes perspective projections. Of course, the drawback is that fewer measures are preserved -- certainly not lengths, angles, or parallelism. Projective transformations preserve type (that is, points remain points and lines remain lines), incidence (that is, whether a point lies on a line), and a measure known as the cross ratio.

2..if the value of a third order determinent is 11,then the square of the determinent formed by the cofactors will be

ANS..121

3..Find the interval for theinitial value problem dy/dx=y*2 ,y(1)=-1.

ANS..(1/4, 5/4).

4..Define singular solution of a diffential equation.

ANS..A singular solution ys(x) of an ordinary differential equation is a solution that is tangent to every solution from the family of general solutions. By tangent we mean that there is a point x where ys(x) = yc(x) and y's(x) = y'c(x) where yc is any general solution.

5..A group G has subgroups of order 4 and 10.order of G is less than 50.what you conclude about order of G.

ANS..IT IS EITHER 40 or 2o.

6..If D IS AN INTERGRAL domain, what we can say about characteristic of D.

ANS...Eithre 0 or a prime.

7..HOW MANY homomorphism possible from Z[2]to Z[3].

ans..only one.

8..How many subgroups are possible for Z[2]*Z[4].

ANS..EIGHT

9.Find the soution of sin(dy/dx)=a with y(0)=1.

ANS..sin{(y-1)/x}=a

10..THE numbers of all possible triplets(a,b,c), such that a+bcos2x+csin*2(x)=0.

ANS--INFINITE.

11..Provide geometrical interpretation of all two-rowed orthogonal matrices.

ANS..Every two rowed orthogonal matrix corresponds either to a rotation about origin or to a reglection in a line through the origin.

12..provide some contexts in which the quardatic form appear.

ANS..1..STUDY OF CONICS AND QUADRICS.

2.investigation of max. and mini..of serval variable.

3.stability of equilibrium in mechanics.

13..LET A be 2-rowed square matrix and det(I+A)=1+detA. WHAT IS TRACE OF A,\.

ANS..zero.

14.if completeness preserved under homeomorphism.

ANS...No.we have R and ]0,1[, which are homeomorphic to each other.one of which complete and other is not.

## Thursday, December 28, 2006

### JAM

Jam is for admission to two-year M.Sc. programmes in IITs, three-year post-B.Sc. programmes (M.Tech. in applied geology / applied geophysics and MCA) at IIT Roorkee and M.Sc.-Ph.D. dual degree programmes in physics at IIT Bombay and IIT Kanpur. For the M.Sc. programmes, biotechnology, chemistry, applied geology, geological sciences, geophysics, mathematics, applied mathematics/industrial mathematics and informatics, applied statistics and informatics, statistics and informatics, physics, statistics disciplines are available.

Admission Test to M.Sc. – JAM is conducted by the Indian Institute of Technologies – IITs for admission to Master of Science ( M.Sc.) and other post–B.Sc. programmes offered at the 7 different Indian Institutes of Technology (IITs). In a given academic year, any one of the 7 IITs take the responsibility for the conduct of JAM test. IITs offer high quality post graduate education in different disciplines of basic and applied sciences which are comparable amongst best in the world. IITs have begun conducting JAM test from the Academic Session 2004-2005 for admission to M.Sc. and other Post B.Sc. Programmes.The key objective of the JAM test is to stimulate and fuse 'Science' as a Career Option. JAM test provides a single step opportunity for admission to the postgraduate programmes offered at the IITs for students across the country. Within due course of time, JAM test is expected to become a benchmark for normalizing the undergraduate level science education in the country.IITs have well operational contemporary laboratories, well-organized computer networks and state of the art libraries. The curriculum for Master of Science - M.Sc. and other post - B.Sc. programmes are designed to provide the students opportunities to develop academic talent

leading to demanding and meaningful professional career. The curriculum at each IIT is regularly updated. Interdisciplinary content of the curriculum equips the students to make use of scientific knowledge for practical applications. The teaching method is controlled to endorse close and continuous contact between the faculty and the students.

IITs offer credit based academic structure which allows students the flexibility to pursue the programme at their own pace, though a minimum level of performance is expected. The medium of instruction in all the programmes is English only. A number of financial assistantships and freeships are available to schedule cast (SC), schedule tribe (ST) and other deserving and meritorious students at all the 7 IITs.

Admission Test to M.Sc. – JAM is conducted by the Indian Institute of Technologies – IITs for admission to Master of Science ( M.Sc.) and other post–B.Sc. programmes offered at the 7 different Indian Institutes of Technology (IITs). In a given academic year, any one of the 7 IITs take the responsibility for the conduct of JAM test. IITs offer high quality post graduate education in different disciplines of basic and applied sciences which are comparable amongst best in the world. IITs have begun conducting JAM test from the Academic Session 2004-2005 for admission to M.Sc. and other Post B.Sc. Programmes.The key objective of the JAM test is to stimulate and fuse 'Science' as a Career Option. JAM test provides a single step opportunity for admission to the postgraduate programmes offered at the IITs for students across the country. Within due course of time, JAM test is expected to become a benchmark for normalizing the undergraduate level science education in the country.IITs have well operational contemporary laboratories, well-organized computer networks and state of the art libraries. The curriculum for Master of Science - M.Sc. and other post - B.Sc. programmes are designed to provide the students opportunities to develop academic talent

leading to demanding and meaningful professional career. The curriculum at each IIT is regularly updated. Interdisciplinary content of the curriculum equips the students to make use of scientific knowledge for practical applications. The teaching method is controlled to endorse close and continuous contact between the faculty and the students.

IITs offer credit based academic structure which allows students the flexibility to pursue the programme at their own pace, though a minimum level of performance is expected. The medium of instruction in all the programmes is English only. A number of financial assistantships and freeships are available to schedule cast (SC), schedule tribe (ST) and other deserving and meritorious students at all the 7 IITs.

### math interview

Q 1...State relation between the rank of a matrix and its adjoint matrix.

ANS..If A is a n*n matrix of rank n-1 ,then its adjoint is of rank 1.

Q2..IS {0,1,+}IS A GROUP.

ANS.. no,1+1=2, hence clousre property does not hold.

Q3..State a example of a fuction,which is continuous every where and nondifferentiable at two points only.

ANS..f(x)=mod(x)+mod(x-1).

Q4..IF A, B are n-rowed square matrices ,what will be same for AB and BA.

ANS..they have same characteristic equation.

Q5..What you can say about rank of skew-symmetric matrix.

ANS..It will be even.

Q6..WHAT IS MEANT BY ORDER OF CONVERGENCE OF A ITERATIVE METHOD.

ANS..convergence of a iterative method shows at each iteration absolute error is proportional to which ratio of the previous value.

Q7..PROVIDE EXAMPLE OF HAUSDROFF SPACE.

ANS..Real space.

Q8.IF z LIES ON mod(z)=1, then locus of 2/z.

ANS..LOCUS IS Circle with center at origin with radius 2.

Q9.THE order of a diff. equation. whose general solution is (a+b)cos(x+c)-d*e*(x+e).

ANS..3

ANS..If A is a n*n matrix of rank n-1 ,then its adjoint is of rank 1.

Q2..IS {0,1,+}IS A GROUP.

ANS.. no,1+1=2, hence clousre property does not hold.

Q3..State a example of a fuction,which is continuous every where and nondifferentiable at two points only.

ANS..f(x)=mod(x)+mod(x-1).

Q4..IF A, B are n-rowed square matrices ,what will be same for AB and BA.

ANS..they have same characteristic equation.

Q5..What you can say about rank of skew-symmetric matrix.

ANS..It will be even.

Q6..WHAT IS MEANT BY ORDER OF CONVERGENCE OF A ITERATIVE METHOD.

ANS..convergence of a iterative method shows at each iteration absolute error is proportional to which ratio of the previous value.

Q7..PROVIDE EXAMPLE OF HAUSDROFF SPACE.

ANS..Real space.

Q8.IF z LIES ON mod(z)=1, then locus of 2/z.

ANS..LOCUS IS Circle with center at origin with radius 2.

Q9.THE order of a diff. equation. whose general solution is (a+b)cos(x+c)-d*e*(x+e).

ANS..3

## Wednesday, December 27, 2006

### math and nature

If you wish to understand The Nature of Universe, we can do it! We, ourselves, are small copies of Universe, we have got this answer! ....J. Boivin

How can we understand Math’s nature and her beauty? How did Nature design the beautiful trees? Its forces are unlimited. Can we try it help of the computer? We want to offer an extremely useful and spectacular tool for learning and studying. Technical speaking, the most powerful facilities offered by the actual programming languages are explored by natural using of recursive method. We try to make a correlation between technique, art and nature. Our contribution is focussing on important pedagogical objectives, develops the procedural thinking, the recursive approach of the problems. We hope you will enjoy our new experiment!

## Tuesday, December 26, 2006

### Today Questions

1.Idea to create YOUTUBE.COM orginatd in...may 2005.

1..Members in sixth pay commission...1 chairman, 3 members.

3..High courts in india...22

4..Pending cases in all High Courts..53 lakhs.

5..Unskillled labour in 20-24 age group...95 percent.

6..Projected urban population in 2030...45 percent.

7.Winter season of Himachal Pradesh was heald..dhramshala.

8.Highest wheat producing state...Uttar Pradesh

1..Members in sixth pay commission...1 chairman, 3 members.

3..High courts in india...22

4..Pending cases in all High Courts..53 lakhs.

5..Unskillled labour in 20-24 age group...95 percent.

6..Projected urban population in 2030...45 percent.

7.Winter season of Himachal Pradesh was heald..dhramshala.

8.Highest wheat producing state...Uttar Pradesh

## Monday, December 25, 2006

### what is Abstract Algebra

Abstract algebra is the field of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. Most authors nowadays simply write algebra instead of abstract algebra.The term abstract algebra now refers to the study of all algebraic structures, as distinct from the elementary algebra ordinarily taught to children, which teaches the correct rules for manipulating formulas and algebraic expressions involving real and complex numbers, and unknowns. Elementary algebra can be taken as an informal introduction to the structures known as the real field and commutative algebra.

Abstract Algebra deals with many structures other than groups. What happens if we two operations called "addition" and "multiplication" that behave in ways simiar to the usual addition and multiplication of integers? We then have a structure that mathematicians call a ring. How about if the addition and multiplication behave like they do on fractions (so that we can divide, unlike in the integers)? This leads to a structure called a field. The investigation of these 3 types of structures (groups, rings, and fields) form the cornerstone of the field that mathematicians call Abstract Algebra. The term "abstract" refers to the perspective taken in the subject, which is very different from that of high school algebra. Rather than looking for the solutions to a particular problem, abstract algebra is interested in such questions as: When does a solution exist? If a solution does exist, is it unique? What general properties does a solution possess.

## Sunday, December 24, 2006

### INTERNET 2.0

Web 2.0 is the network as platform, spanning all connected devices; Web 2.0 applications are those that make the most of the intrinsic advantages of that platform: delivering software as a continually-updated service that gets better the more people use it, consuming and remixing data from multiple sources.The Web, though, is becoming the first piece of the bigger network as it meshes with new technologies that started from disparate corners of the industry — such as Wi-Fi wireless broadband connections, the Global Positioning System (GPS) and radio frequency identification tags (RFID).Web creator Tim Berners-Lee has been talking about a version of such a system for a couple of years. "The Web can reach its full potential only if it becomes a place where data can be shared and processed by automated tools as well as by people,".

Life span of Net

1994:

38 million Internet users; 3,000 Web sites worldwide; 35% of U.S. schools wired

GPS satellites fully functional

Web grows at a 341,634% annual rate

1995:

eBay and Yahoo founded.

The first macro virus is discovered in a Word document.

1996:

The number of Net hosts exceeds 9 million.

1997:

71,618 Usenet newsgroups.

1998:

Google officially opens its doors, about two years after founders Larry Page and Sergey Brin begin developing a search engine.

1999:

Online retailers register $5.3 billion in sales.

2000:

304 million people have access to the Net.

2001:

30 million Web sites exist.

Osama bin Laden No. 1 searched on Google in October.

Apple unveils the iPod.

2002:

Verizon launches first high-speed 3G cell network.

Friendster social networking site founded.

2003:

Wal-Mart tells its suppliers to put RFID tags on all pallets by 2005.

Hewlett-Packard ships 1 million digital cameras each quarter, double the previous year.

2004:

One millionth BlackBerry e-mail device sold.

Google indexes 4.2 billion Web pages.

800 million Internet users, 100 million songs downloaded from iTunes; 99% of U.S. public schools wired.

In the year and a half since, the term "Web 2.0" has clearly taken hold, with more than 9.5 million citations in Google. But there's still a huge amount of disagreement about just what Web 2.0 means, with some people decrying it as a meaningless marketing buzzword, and others accepting it as the new conventional wisdom.

### Questions of the day

1..WRITER OF THE BOOK.THE END OF POVERTY..IS..Jaffery Sachs.

2..REVERSE RAPO RATE...7.25

3..NO OF UNIVERSITIES IN INDIA...241

4..RASTIPATI BAHAWAN WAS BUILD IN YEAR...1931,desined by Lutyens

5.LARGESR DISTRCT IN AREA...Laddakh

6..LARGEST MANGROVE FOUND IN...Sunder van

7..India,s annual requirement of Uranium..4000ton

8..Singur belongs to.Hugli discrict

9..How much land area proposed to give Tatas in Singur...997 acre

10.Womens in IT Work Force..30 percent.

2..REVERSE RAPO RATE...7.25

3..NO OF UNIVERSITIES IN INDIA...241

4..RASTIPATI BAHAWAN WAS BUILD IN YEAR...1931,desined by Lutyens

5.LARGESR DISTRCT IN AREA...Laddakh

6..LARGEST MANGROVE FOUND IN...Sunder van

7..India,s annual requirement of Uranium..4000ton

8..Singur belongs to.Hugli discrict

9..How much land area proposed to give Tatas in Singur...997 acre

10.Womens in IT Work Force..30 percent.

## Saturday, December 23, 2006

### QUESTION OF DAY

1..Let a, b, c be real numbers. Given the equation for cos x:

a cos2x + b cos x + c = 0,

form a quadratic equation in cos 2x whose roots are the same values of x. Compare the equations in cos x and cos 2x for a=5 b=1, c=-1.

a cos2x + b cos x + c = 0,

form a quadratic equation in cos 2x whose roots are the same values of x. Compare the equations in cos x and cos 2x for a=5 b=1, c=-1.

### IIT JEE

After 10+2, IIT-JEE exam considered as benchmark in india.after High School or pre calculas level math olampiyad is a milestone in it.Math olampiyad included geometry, trignometry, number theory and algebra.Syalbii of school in 10+2 and diffculty level of IIT-JEE is much debated issue in india.IIT-JEE exam is totally objective type now. about few years ago, there are no special books for this exam.i recall the days, when there are only HALL AND KNIGHT and few russian books for math preprations.now there are plenty.in school also student read one side book beside main course book.<

### networking and math

DesiMartini.com, an SMS-based online social networking site for Indians around the world, launched by Pahwa KBS last month, says it has plans to beat the competition and reach a registered user base of 1 million members in six months.Started by 25-year-old Vivek Pahwa, a recent graduate from the Indian School of Business, and the University of Michigan, Ann Arbor, the site lets users create their own customisable homepages, send in updates (what they are doing) via SMS wherever they are, upload and share pictures, join groups and communities, chat with other members, and stay in touch with old friends and discover new ones.

Social networking has been one of the hottest areas of interest since Web 2.0 took off as a concept and media buzzword. In one of the most high profile media deals of 2005, Rupert Murdoch’s News Corporation bought MySpace for $580 million, a staggering amount at the time. This year, viral video has become the latest hot category with the defining Internet deal of 2006 being the sale of YouTube to Google for $1.76 billion.

math theorem...1.A (presumably autobiographical) character in one of astrophysicist Fred Hoyle's novels opined the following. "I figure that if to be totally known and totally loved is worth 100, and to be totally unknown and totally unloved is worth 0, then to be totally known and totally unloved must be worth at least 50."

2..Dunbar's number is a value significant in sociology and anthropology. Proposed by British anthropologist Robin Dunbar, it measures the "cognitive limit to the number of individuals with whom any one person can maintain stable relationships". The so-called rule of 150, states that the size of a genuine social network is limited to about 150 members ( called Dunbar's number). Dunbar supports this hypothesis through studies by a number of field anthropologists. These studies measure the group size of a variety of different primates; Dunbar then correlate those group sizes to the brain sizes of the primates to produce a mathematical formula for how the two correspond

### math news

Maths papers hailed as breakthrough of the year 2006.First proposed by French scientist Henri Poincare in 1904, the theory about "rubbery sheet geometry" and surfaces that can be stretched remained in the ether until reclusive mathematician Grigori Perelman published the first of three papers on the subject in 2002.The global mathematic community universally concluded that Mr Perelman had not only proved the Poincare theorem but also alluded to something more ambitious.

### GRE MATH SECTION

The The Education Testing Service (ETS) directs The Graduate Record Examination (GRE) on behalf of the Graduate Record Examinations Board and the Council of Graduate Schools. GRE Test is chiefly a multiple-choice test. The GRE test scores have to be submitted by students aspiring for admission in international graduate school for Graduate program. Apart from the general GRE test there are about 12 GRE subject test offered by the program to help determine a students success in specific fields. In addition to this the GRE program also offers a variety of services and publications to help students transfer to their respective graduate program. The GRE quantitative section is often referred to as the Mathematics section. It tests your basic understanding of arithmetic, algebra and geometry. Knowledge of more advanced mathematics is not required in this section of the GRE. Most of the questions in the Quantitative Ability section are of high school level and are intended to just show how well you understand elementary mathematics. Types of questions in GRE Math section that you'll come across are :

GRE Math - Quantitative Comparisons

GRE Math - Problem Solving

GRE Math - Data Interpretation

Arithmetic Questions involve

1.Arithmetic operations

2.Powers

3.Operations on radical expressions

4.Estimation

5.Percent

6.Absolute value

7.Properties of numbers (e.g. divisibility, prime numbers, odd and even integers)

8.Factoring

Algebra Questions involve

1.Rules of exponents

2.Factoring and simplifying algebraic expressions

3.Understanding concepts of relations and functions

4.Solving first and second degree equations and inequalities

5.Solving simultaneous equations

6.Setting up equations to solve word problems

7.Applying basic algebra skills to solve problems

Geometry

Questions involve properties of

1.Parallel lines

2.Circles and their inscribed central angles

3.Triangles

4.Rectangles Other polygons

5.Area

6.Perimeter

7.Volume

8.Pythagoras theorem

9.Angle measure in degrees

10.Simple coordinate geometry (including slopes, intercepts, and inequalities)

Data Analysis Questions involve

1.Elementary probability

2.Basic descriptive statistics

3.Mean

4.Median

5.Mode

6.Range

7.Standard deviation

8.Percentiles

9.Interpretation of data in graphs and tables

10.Line graphs

11.Bar graphs

12.Circle graphs

13.Frequency distributions

TIPS..1.Read the question well. Be sure to select the best answer for the variable, value, or expression that is requested!

2..Learn in advance all of the critical definitions, formulas, and concepts that appear in common questions.

3.Remember to use the test booklet for scratch work, as well as for marking up any diagrams/graphs.

4..Early questions in this section are easier. Spend less time on them.

5.Don't get carried away with detailed calculations. Look for a trick or a shortcut if the question seems time consuming.

6..When a question contains a weird symbol, just substitute the accompanying definition when figuring out the best answer choice.

### Iwasawa theory.

This years Ramanujan,s awards was back in his country.it was given on the work on Iwasawa theory.This theory joints thread between geometry, algebra and number theory.It is too difficult to explain it in layman language.IKenkichi Iwasawa attended elementary school in the town of his birth but went to Tokyo for his high school studies which were at the Musashi High School. In 1937 he entered Tokyo University where he was taught by Shokichi Shokichi Iyanaga and Zyoiti Suetuna. At this time Tokyo University had become a centre for the study of algebraic number theory as a result of Teiji Takagi's remarkable contributions.n number theory, Iwasawa theory is a Galois module theory of ideal class groups, initiated by Kenkichi Iwasawa, in the 1950's, as part of the theory of cyclotomic fields. In the early 1970's, Barry Mazur considered generalizations of Iwasawa theory to Abelian varieties

### QUESTIONS OF DAY

1..Total work force in india..40 crore.

2..Work force in IT sector...13 lakh.

3..K.G.BALAKISHAN WILL be chief justice of India..37th.

4..World wide reservation for the seventh book of Harry Potter..300 million.

5..FDI LIMIT IN INSURANCE SECTOR...26 PERCENT.

6..ORGANISED RETAIL SECTOR..3 percent.

7.World wide death annully due to tobacco...5 million.

8.Trafic handled by indian port in 2006-06..573 MT.

9..Inflation in week ended 9 dec...5.32

10.Projected agri growth rate in current year..4 percent.

2..Work force in IT sector...13 lakh.

3..K.G.BALAKISHAN WILL be chief justice of India..37th.

4..World wide reservation for the seventh book of Harry Potter..300 million.

5..FDI LIMIT IN INSURANCE SECTOR...26 PERCENT.

6..ORGANISED RETAIL SECTOR..3 percent.

7.World wide death annully due to tobacco...5 million.

8.Trafic handled by indian port in 2006-06..573 MT.

9..Inflation in week ended 9 dec...5.32

10.Projected agri growth rate in current year..4 percent.

## Friday, December 22, 2006

### jobs for math student

Mathematicians apply mathematical principles to solve problems in all areas of the sciences, technology, social sciences, business, industry and commerce.

A mathematician may perform the following tasks:

1..apply geometry and calculus to design objects as in architecture, computer graphics and robotics.

2..analyse statistics to find models for traffic flow, insurance risks, consumer research, market analysis and clinical trials.

3..develop models for financial markets and products for financial risk management

analyse processes from chemical, mining or agricultural industries by translating them into mathematical models.

4..develop computer modelling for industrial design.

5..develop and improve mathematical models to describe natural phenomena, such as soil erosion, the weather, ocean currents or biological behaviour.

6..develop computer programs for use in mathematical modelling and problem solving

design computer programs to make and break complex security codes, or investigate and develop schemes for information security.

7..carry out network analysis for the study of road systems, airline routes, transport and communication systems.

8..use linear programming for urban and regional planning.

engage in image and signal processing for astronomy, cartography, and medical and radar imaging .

9..analyse problems from the service, engineering or manufacturing sectors.

10..develop communications technology and information theory .

11..develop new mathematical relationships ranging across the areas of pure and applied mathematics, statistics, computing, operations research, commerce and industry .

12..teach mathematics .

### math joke

What is "pi"?

Mathematician: Pi is the ratio of the circumference of a circle to its diameter.

Engineer: Pi is about 22/7.

Physicist: Pi is 3.14159 plus or minus 0.000005

Computer Programmer: Pi is 3.141592653589 in double precision.

Nutritionist: You one track math-minded fellows, Pie is a healthy and delicious dessert!

Mathematician: Pi is the ratio of the circumference of a circle to its diameter.

Engineer: Pi is about 22/7.

Physicist: Pi is 3.14159 plus or minus 0.000005

Computer Programmer: Pi is 3.141592653589 in double precision.

Nutritionist: You one track math-minded fellows, Pie is a healthy and delicious dessert!

### contemporary mathematicians of india

Narendra Karmakar, now at TIFR formerly of UC Berkeley and AT&T Bell Labs. Read about him here: http://en.wikipedia.org/wiki/narendra_ka...

Madhu Sudan, Professor, MIT, read about him here: http://en.wikipedia.org/wiki/madhu_sudan...

Rajiv Motwani, Professor of Computer Science at Stanford University, read here: http://theory.stanford.edu/~rajeev/...

Prabhakar Raghavan, Professor of Computer Science at Stanford and Head of Yahoo! Research at US, as you can find out here:

http://theory.stanford.edu/~pragh/...

Among the ones who are alive, I can think of Abhyankar who is a famous algebraic geometer.Shreeram Shankar Abhyankar (born 1930)in an Maharashtrian koknastha Brahmin family is an Indian mathematician known for his contributions to singularity theory. His name is associated with Abhyankar's conjecture of finite group theory.Read;http://en.wikipedia.org/wiki/Shreeram_Shankar_Abhyankar

Manjul Bhargava (born 1974) is a professor of mathematics at Princeton University. His research interests span algebraic number theory, combinatorics, and representation theory. He graduated from Harvard University in 1996 and received his doctorate from Princeton in 2001, working under Andrew Wiles.read;http://en.wikipedia.org/wiki/Manjul_Bhargava

Madhu Sudan, Professor, MIT, read about him here: http://en.wikipedia.org/wiki/madhu_sudan...

Rajiv Motwani, Professor of Computer Science at Stanford University, read here: http://theory.stanford.edu/~rajeev/...

Prabhakar Raghavan, Professor of Computer Science at Stanford and Head of Yahoo! Research at US, as you can find out here:

http://theory.stanford.edu/~pragh/...

Among the ones who are alive, I can think of Abhyankar who is a famous algebraic geometer.Shreeram Shankar Abhyankar (born 1930)in an Maharashtrian koknastha Brahmin family is an Indian mathematician known for his contributions to singularity theory. His name is associated with Abhyankar's conjecture of finite group theory.Read;http://en.wikipedia.org/wiki/Shreeram_Shankar_Abhyankar

Manjul Bhargava (born 1974) is a professor of mathematics at Princeton University. His research interests span algebraic number theory, combinatorics, and representation theory. He graduated from Harvard University in 1996 and received his doctorate from Princeton in 2001, working under Andrew Wiles.read;http://en.wikipedia.org/wiki/Manjul_Bhargava

### Poincare conjecture

Grigory Perelman's proof of the century-old Poincare Conjecture has caused a sensation, and not just because of the brilliance of the work.In August, the Russian became the first person to turn down a Fields Medal, the highest honour in mathematics. He also seems likely to turn down a $1m prize offered by a US maths institute. For several years he worked, for the most part, alone on the Poincare Conjecture. Then, in 2002, he posted on the internet the first of three papers outlining a proof of the problem.

The Poincare is a central question in topology, the study of the geometrical properties of objects that do not change when they are stretched, distorted or shrunk. The surface of the Earth is what topology describes as a two-dimensional sphere. If one were to encircle it with a lasso of string, it could be pulled tight to a point. On the surface of a doughnut, however, a lasso passing through the hole in the centre cannot be shrunk to a point without cutting through the surface.

The Poincare Conjecture says that a three-dimensional sphere is the only enclosed three-dimensional space with no holes. Proof of the Conjecture eluded mathematicians until Perelman posted his work on the website arXiv.org.In 2005, a Chinese team consisting of Huai-Dong Cao of Lehigh University and Xi-Ping Zhu of Zhongshan University published what they claimed was "the first written account of a complete proof of the Poincare Conjecture".

### math and ramanujan

in 1913, the English mathematician G. H. Hardy received a strange letter from an unknown clerk in Madras, India. The ten-page letter contained about 120 statements of theorems on infinite series, improper integrals, continued fractions, and number theory .at first glance Hardy no doubt put this letter in desk . But something about the formulas made him take a second look, and show it to his collaborator J. E. Littlewood. After a few hours, they concluded that the results "must be true because, if they were not true, no one would have had the imagination to invent them".

Thus was Srinivasa Ramanujan (1887-1920) introduced to the mathematical world. Born in South India, Ramanujan was a promising student, winning academic prizes in high school. But at age 16 his life took a decisive turn after he obtained a book titled A Synopsis of Elementary Results in Pure and Applied Mathematics. The book was simply a compilation of thousands of mathematical results, most set down with little or no indication of proof. It was in no sense a mathematical classic; rather, it was written as an aid to coaching English mathematics students facing the notoriously difficult Tripos examination, which involved a great deal of wholesale memorization.

As a college dropout from a poor family, Ramanujan's position was precarious. He lived off the charity of friends, filling notebooks with mathematical discoveries and seeking patrons to support his work. Finally he met with modest success when the Indian mathematician Ramachandra Rao provided him with first a modest subsidy, and later a clerkship at the Madras Port Trust. During this period Ramanujan had his first paper published, a 17-page work on Bernoulli numbers that appeared in 1911 in the Journal of the Indian Mathematical Society.

Hardy wrote enthusiastically back to Ramanujan, and Hardy's stamp of approval improved Ramanujan's status almost immediately. Ramanujan was named a research scholar at the University of Madras, receiving double his clerk's salary and required only to submit quarterly reports on his work. But Hardy was determined that Ramanujan be brought to England.

Ramanujan's arrival at Cambridge was the beginning of a very successful five-year collaboration with Hardy. In some ways the two made an odd pair: Hardy was a great exponent of rigor in analysis, while Ramanujan's results were (as Hardy put it) "arrived at by a process of mingled argument, intuition, and induction, of which he was entirely unable to give any coherent account.

One remarkable result of the Hardy-Ramanujan collaboration was a formula for the number p(n) of partitions of a number n. A partition of a positive integer n is just an expression for n as a sum of positive integers, regardless of order. Thus p(4) = 5 because 4 can be written as 1+1+1+1, 1+1+2, 2+2, 1+3, or 4.

Ramanujan's years in England were mathematically productive, and he gained the recognition he hoped for. Cambridge granted him a Bachelor of Science degree "by research" in 1916, and he was elected a Fellow of the Royal Society (the first Indian to be so honored) in 1918. But the alien climate and culture took a toll on his health.

Besides his published work, Ramanujan left behind several notebooks, which have been the object of much study. The English mathematician G. N. Watson wrote a long series of papers about them. More recently the American mathematician Bruce C. Berndt has written a multi-volume study of the notebooks.

### Questions of the day

1.. Goverenment pick up amount from drive out from Maruti..Rs 27,000 crore.

2..BSNL offered broadband connectivity at speed..2 mbps.

3..No. of SEZ..237.

4..Revenue purplus by indian railways...Rs 13,000 crore.

5..According NSSO ,

student studying at private unadided institutes...17 percent.

6..Chandrayaan-1 stated by ISRO in...march 2008.

7..Proposed iits in...bihar, andra, rajasthan.

8..Public sector profits..Rs 85,000 crore.

9..India,s expending on infrastructure..$ 36 b.

10..Projected india,s GDP in 2015..$ 1.6 trillion.

11...India,s annual air passenger volume..10-15 million.

12..HARRY POTTER tranlated into..63 languages..-

2..BSNL offered broadband connectivity at speed..2 mbps.

3..No. of SEZ..237.

4..Revenue purplus by indian railways...Rs 13,000 crore.

5..According NSSO ,

student studying at private unadided institutes...17 percent.

6..Chandrayaan-1 stated by ISRO in...march 2008.

7..Proposed iits in...bihar, andra, rajasthan.

8..Public sector profits..Rs 85,000 crore.

9..India,s expending on infrastructure..$ 36 b.

10..Projected india,s GDP in 2015..$ 1.6 trillion.

11...India,s annual air passenger volume..10-15 million.

12..HARRY POTTER tranlated into..63 languages..-

## Thursday, December 21, 2006

### MERSENNE PRIMES

A positive integer n is called a perfect number if it is equal to the sum of all of its positive divisors, excluding n itself.For example, 6 is the first perfect number because 6=1+2+3. The next is 28=1+2+4+7+14. The next two are 496 and 8128.

Theorem One: k is an even perfect number if and only if it has the form 2n-1(2n-1) and 2n-1 is prime

Theorem Two...If 2n-1 is prime, then so is n.

Theorem Three: Let p and q be primes. If q divides Mp = 2p-1, then

q = +/-1 (mod 8) and q = 2kp + 1

for some integer k.

THEOREM Four.. Let p = 3 (mod 4) be prime. 2p+1 is also prime if and only if 2p+1 divides Mp.

### Fractals and Nature

Ever wonder what causes the leaves to change color in the fall? Or how you can time claps of thunder to calculate your distance to a nearby storm? Believe it or not, math can help you to investigate these and other natural phenomena, such as earthquakes, hurricanes, and seasonal changes. In the collection of activities below, you'll also learn how you can use periodic trigonometric curves to represent cyclical patterns in nature. With a little help from the

mathematics, you'll be able to apply basic sine and tangent curves to such things as the beating of your heart, phases of the moon, and the path of the sun across the sky.

A fractal is a mathematical object that is self-similar, where each part resembles to the whole. Most fractals are generated by a relatively simple equation where the

are fed back into the equation until it grows larger than a certain boundary. Some fractals are just a graph of an equation using complex numbers. The mathematicians kept on asking themselves about some paradoxes, since 100 years ago. Thus, Sierpinski, a Polish mathematician, created some fractals, without knowing their meaning: The Curve, The Triangle and The Carpet. In the same time, in Sweden, Herge Von Koch invented “The Snowflakes’ Curve” or “Coast Line”.

Fractals were not discovered in a single instant, but knowledge of them grew quickly in the computer age. The first real fractal were discovered by a French mathematician named Gaston Julia. In his time there were no computers, so serious study of fractal objects was not practical at all.

In March 1980 the French mathematician Mandelbrot saw appearing on his computer screen something that would change his life completely. Many compare his discovery to Newton's discovery of the universal laws of mechanics. This discovery introduced a completely new field in Mathematics: Fractal Geometry. The application of fractal geometry is a subject of study in many scientific fields: medical science, meteorology, Biology and telecommunication benefit from this new science.

### Paper Folding

Paper Folding

Origami is an ancient Chinese and Japanese art of paper folding.This was the first usage of the word "origami" so far traced in Japan. The word "origami" came to be used occasionally for another kind of ceremonial folding, namely for "tsutsumi", or formal wrappers, by the beginning of the 18th century. However, its use for recreational origami of the kind with which we are familiar did not come until the end of the nineteenth century or the beginning of the twentieth. Before that, paperfolding for play was known by a variety of names, including "orikata", "orisue", "orimono", "tatamgami" and others.In the geometry of paper folding, a straight line becomes a crease or a fold. Instead of drawing straight lines, one folds a piece of paper and flattens the crease. Folding paper is analogous to mirroring one half of a plane in a crease. Thus folding means both drawing a crease and mapping one half of a plane onto another. As in the usual Geometry, the distinction is being made between experimentation with the physical paper and the abstract theory of "paper folding". "Abstract paper" may be folded indefinitely although in practice the number of folds is by necessity limited.

The most well-known construction is "straight edge and compass" construction, which refers to the geometric operations that can be formed with only those two instruments (note that the straight edge is not a ruler with length markings). It is well-known that SE&C constructions can be encompassed (no pun intended) by four basic axioms, first defined by Euclid, over 2000 years ago. It is also well known that there are certain operations that are impossible given just a straight edge and compass.

### india in math olympiad 2006

The 47th IMO was held in Ljubljana, Slovenia in 2006. The team leader was Dr. B.J. Venkatachala of the MO Cell (who had previously been the leader in 2002) and the Deputy Leader was Dr. Mahendra Datta.

1..Apurv Nakade from Nagpur won a Bronze medal with a score of 18 points.

2..Riddhipartim Basu from Kolkata won a Bronze medal with a score of 16 points.

3..Varun Suhas Jog from Pune, trained at the Bhaskaracharya Pratishthana, won a Bronze medal with a score of 15 points.

4..Ashay Arvind Burungale from Maharashtra won a Bronze medal with a score of 15 points.

5..Manas Rajendra Joglekar from Pune, trained at the Bhaskaracharya Pratishthana, won a Bronze medal with a score of 15 points.

6..Abhishek H. Dang from Pune, trained at the Bhaskaracharya Pratishthana, won an Honourable Mention with a score of 13 points.

With a total score of 92 points, India ranked 35th.

1..Apurv Nakade from Nagpur won a Bronze medal with a score of 18 points.

2..Riddhipartim Basu from Kolkata won a Bronze medal with a score of 16 points.

3..Varun Suhas Jog from Pune, trained at the Bhaskaracharya Pratishthana, won a Bronze medal with a score of 15 points.

4..Ashay Arvind Burungale from Maharashtra won a Bronze medal with a score of 15 points.

5..Manas Rajendra Joglekar from Pune, trained at the Bhaskaracharya Pratishthana, won a Bronze medal with a score of 15 points.

6..Abhishek H. Dang from Pune, trained at the Bhaskaracharya Pratishthana, won an Honourable Mention with a score of 13 points.

With a total score of 92 points, India ranked 35th.

### math news

A mathematician from India has been presented with the Ramanujan Prize, which honours young maths researchers from developing countries.

Ramdorai Sujatha, from the Tata Institute of Fundamental Research in Mumbai, picked up up the award at a ceremony in Trieste, Italy.

The prize was set up last year, so 44-year-old Professor Sujatha is the second recipient of the $10,000 award.Professor Sujatha has received all her university education in India and has been with the Tata Institute since 1985, where she is currently associate professor in the school of mathematics.

She was presented with the prize by Professor Lennart Carleson in a ceremony at the Abdus Salam International Centre for Theoretical Physics (ICTP) in Trieste, Italy.The Nobel Foundation currently has no award for mathematics, and the Abel Prize was set up to fill this vacuum.

The Ramanujan prize, meanwhile, was established by the ICTP as part of its mandate to strengthen science in developing countries.She was honoured for her work on the "arithmetic of algebraic varieties" and her substantial contributions to a mathematical framework known as Iwasawa theory.

### QUESTIONS FOR NET

1..which one is not uniformly continous in (R-0)...e*x,1/x,1/x*2, sinx.

2..check truthness...let Q be set of rationalnumbers, there is no one-one fuction between Q and [0.1].

3..Let f,g be two convex fuction.then which one is convex..f+g,f-g,fg,f/g.

4..Ths set of all real numbers with decimal expression contaning only even numbers has cardinality equal to...

5..In M/M/2 queue with arrival and service rates,the steady state probabitity the system is empty is..

2..check truthness...let Q be set of rationalnumbers, there is no one-one fuction between Q and [0.1].

3..Let f,g be two convex fuction.then which one is convex..f+g,f-g,fg,f/g.

4..Ths set of all real numbers with decimal expression contaning only even numbers has cardinality equal to...

5..In M/M/2 queue with arrival and service rates,the steady state probabitity the system is empty is..

### Questions of day

1..How many medals india won in doha...54-1=53.

2..In doha indian hockey team got..fifth position.

3..New king of bhutan..Jigme khesar namgyal wangchuck

4...Poverty level in india--28 percent

5..International diabetes day..14 nov.

6..Size of indian retail market..250 billion dollar

7..Time person of year..You

8..telecommunication growth in 2000-2005...27.1 percent

9..Regestred NGOs in india...13 lakhs.

10..Tower in place of World Trade Tower..Freedom Tower( 1776feet)

11..FDI limit in telecom sector ..74 percent

12..Export target for 2007-07..124 billon dollar

13..IT,ITes services contrabution in GDP..4.8 PERCENT

2..In doha indian hockey team got..fifth position.

3..New king of bhutan..Jigme khesar namgyal wangchuck

4...Poverty level in india--28 percent

5..International diabetes day..14 nov.

6..Size of indian retail market..250 billion dollar

7..Time person of year..You

8..telecommunication growth in 2000-2005...27.1 percent

9..Regestred NGOs in india...13 lakhs.

10..Tower in place of World Trade Tower..Freedom Tower( 1776feet)

11..FDI limit in telecom sector ..74 percent

12..Export target for 2007-07..124 billon dollar

13..IT,ITes services contrabution in GDP..4.8 PERCENT

## Wednesday, December 20, 2006

### classroom control

1..Discipline problems are common for new teachers. Even after many years of teaching, all teachers have discipline challenges.

2..1) Look at yourself: Do you fully understand the material that you are teaching and have anticipated the problems that students may have? Are you presenting material that is too hard? Too easy? Are you connecting with your students? Do you have enough structure?

3..2) Are you allowing time to explain the new material? Or are you constantly going over homework for most of the period, barely having time to present the new lesson, assigning new homework at the last minute thus creating a cycle where students are truly frustrated?

4..Talk to your department head or someone you can trust. Have this person visit your class and give you ideas about seating arrangements, your lesson structure, your presentation, etc. Don't try to deal with everything alone. Get a support system you can trust.

5.. Never overlook calling home. Most parents or guardians are supportive. In most cases, I let the student know I plan to call home. If you suspect the child's parent or guardian may be uncooperative, or abusive, check with the counselor or with an administrator who may know the family

6..Never make promises or threats you won't or can't follow. It will only make everything worse in the classroom if you lose the respect of your students.

7..Discipline problems that involve one or two students are best solved by finding out as much as possible about each student. Some students respond best by being talked to outside of class.

8... Never lose it! You can raise your voice but never engage in shouting matches with your students. Never say: Shut up!. Never, never, try to physically remove a student. In fact, never touch a student. You can be liable for touching a student unless it is in self defense or you are trying to stop a fight

9..Giving an important job to an unruly student (not when they are being unruly, of course), such as asking them to be a teacher assistant

10..Having the student sign a behavior contract and having a conference with the student and the

principal to find ways to correct the problem

11..there are behaviors that cannot be tolerated in the classroom and call for immediate action. If you or any of your other students are physically threatened you must act immediately. Seek help immediately if you cannot handle the situation on your own.

12..Structure and fairness combined with clear expectations and a clear lesson in a caring non-threatening environment are the key elements of good teaching. Teaching is not easy. It does get better.

2..1) Look at yourself: Do you fully understand the material that you are teaching and have anticipated the problems that students may have? Are you presenting material that is too hard? Too easy? Are you connecting with your students? Do you have enough structure?

3..2) Are you allowing time to explain the new material? Or are you constantly going over homework for most of the period, barely having time to present the new lesson, assigning new homework at the last minute thus creating a cycle where students are truly frustrated?

4..Talk to your department head or someone you can trust. Have this person visit your class and give you ideas about seating arrangements, your lesson structure, your presentation, etc. Don't try to deal with everything alone. Get a support system you can trust.

5.. Never overlook calling home. Most parents or guardians are supportive. In most cases, I let the student know I plan to call home. If you suspect the child's parent or guardian may be uncooperative, or abusive, check with the counselor or with an administrator who may know the family

6..Never make promises or threats you won't or can't follow. It will only make everything worse in the classroom if you lose the respect of your students.

7..Discipline problems that involve one or two students are best solved by finding out as much as possible about each student. Some students respond best by being talked to outside of class.

8... Never lose it! You can raise your voice but never engage in shouting matches with your students. Never say: Shut up!. Never, never, try to physically remove a student. In fact, never touch a student. You can be liable for touching a student unless it is in self defense or you are trying to stop a fight

9..Giving an important job to an unruly student (not when they are being unruly, of course), such as asking them to be a teacher assistant

10..Having the student sign a behavior contract and having a conference with the student and the

principal to find ways to correct the problem

11..there are behaviors that cannot be tolerated in the classroom and call for immediate action. If you or any of your other students are physically threatened you must act immediately. Seek help immediately if you cannot handle the situation on your own.

12..Structure and fairness combined with clear expectations and a clear lesson in a caring non-threatening environment are the key elements of good teaching. Teaching is not easy. It does get better.

### math job..(Financial Analysist)

Financial analysts help people decide how to invest their money. They work for banks, insurance companies, mutual funds, and securities firms. They often meet with company officials to learn more about the firms in which they want to invest. After the meetings, the analysts write reports and give talks about what they found out. Then, they suggest buying or selling that firm's stock.

Financial analysts may specialize. Those in investment banking study the companies that want to sell stock to the public for the first time. They also might study the pros and cons of a merger (when two companies join together) or a takeover (when one company buys another). Some financial analysts are ratings analysts who find out if companies can pay their debts.

Most financial analysts have a college degree in business, accounting, statistics, or finance. A master's degree in business administration (MBA) is desirable.

Math, computer, and problem-solving skills are vital. Working with clients requires good people skills. Confidence, maturity, and the ability to work on your own are important, too. Analysts also need good communication skills to explain complex financial ideas using simple words

Employment of financial analysts should grow faster than average for all occupations through 2025. Banks and mutual fund companies will need more financial analysts to recommend which stocks and bonds they should buy or sell. But competition is expected for jobs, because many people want them.

Financial analysts may specialize. Those in investment banking study the companies that want to sell stock to the public for the first time. They also might study the pros and cons of a merger (when two companies join together) or a takeover (when one company buys another). Some financial analysts are ratings analysts who find out if companies can pay their debts.

Most financial analysts have a college degree in business, accounting, statistics, or finance. A master's degree in business administration (MBA) is desirable.

Math, computer, and problem-solving skills are vital. Working with clients requires good people skills. Confidence, maturity, and the ability to work on your own are important, too. Analysts also need good communication skills to explain complex financial ideas using simple words

Employment of financial analysts should grow faster than average for all occupations through 2025. Banks and mutual fund companies will need more financial analysts to recommend which stocks and bonds they should buy or sell. But competition is expected for jobs, because many people want them.

### math job..(Cost Estimator)

Cost estimators figure out how much a project or product will cost. This helps business owners and managers decide whether to build a structure or manufacture a product. If a business doesn't think it can make enough money, it will not do it. Cost estimators also find out which jobs are making a profit. The exact method of figuring out the cost varies, depending on the industry in which you work.

They study information on all of the things that can change the cost of a project. This includes supplies, labor, location, and special equipment, like computer hardware and software.

In construction, they look at drawings and visit the site of the project. They determine the amount of materials and labor the firm will need. They also consider the costs of things like unused materials, delays due to bad weather, and shipping delays. They tell the architect, construction manager, or owner if they think the project will be profitable or not, and write their findings in a detailed report. In large companies, they may specialize. For example, one may estimate only electrical work and another may focus on concrete.

In manufacturing and other firms, they are assigned to the engineering, cost, or pricing departments. They estimate the cost of making products, including materials and labor. They make a list of parts to see if it is better to make or purchase the parts. The cost of computer software development is one of the fastest growing and hardest to estimate. Some specialize in this.

Estimators use computers a lot to do all of the necessary paperwork. This allows them more time to study and analyze potential projects or products

2..How to prepare for this occupation depends on the industry in which you want to work in. In construction, employers want people with a college degree in building construction, construction management or science, engineering, or architecture. In manufacturing, employers prefer to hire individuals with a degree in engineering, physical science, operations research, mathematics, or statistics. They can also have a degree in accounting, finance, business, economics, or a related subject.

Math and computer skills are very important. Strong communication and analytical skills are also important. Cost estimators must present their estimates to supervisors and others.

3..The number of cost estimators is expected to grow faster than the average for all occupations through the year 2020. Jobs should be best for those with work experience and a bachelor's degree in a related field. The expected increase in construction and repair projects on buildings, roads, airports, and other structures will lead to more jobs for estimators. This means that the best job opportunities will be in the construction industry.

They study information on all of the things that can change the cost of a project. This includes supplies, labor, location, and special equipment, like computer hardware and software.

In construction, they look at drawings and visit the site of the project. They determine the amount of materials and labor the firm will need. They also consider the costs of things like unused materials, delays due to bad weather, and shipping delays. They tell the architect, construction manager, or owner if they think the project will be profitable or not, and write their findings in a detailed report. In large companies, they may specialize. For example, one may estimate only electrical work and another may focus on concrete.

In manufacturing and other firms, they are assigned to the engineering, cost, or pricing departments. They estimate the cost of making products, including materials and labor. They make a list of parts to see if it is better to make or purchase the parts. The cost of computer software development is one of the fastest growing and hardest to estimate. Some specialize in this.

Estimators use computers a lot to do all of the necessary paperwork. This allows them more time to study and analyze potential projects or products

2..How to prepare for this occupation depends on the industry in which you want to work in. In construction, employers want people with a college degree in building construction, construction management or science, engineering, or architecture. In manufacturing, employers prefer to hire individuals with a degree in engineering, physical science, operations research, mathematics, or statistics. They can also have a degree in accounting, finance, business, economics, or a related subject.

Math and computer skills are very important. Strong communication and analytical skills are also important. Cost estimators must present their estimates to supervisors and others.

3..The number of cost estimators is expected to grow faster than the average for all occupations through the year 2020. Jobs should be best for those with work experience and a bachelor's degree in a related field. The expected increase in construction and repair projects on buildings, roads, airports, and other structures will lead to more jobs for estimators. This means that the best job opportunities will be in the construction industry.

### math job....(Actuary job)

1..Actuary...Actuaries deal with risk. They decide how likely things such as death, sickness, injury, disability, and loss of property are to occur, as well as the costs of these things.

Actuaries also decide how much money it will take in order to get a certain amount of retirement income. They help design insurance policies and pension plans and try to make sure that they are sound. Actuaries may need to explain their findings to company executives, government officials, and the public. They may also testify in court as an expert.

Most actuaries work for insurance companies. Some work in life and health insurance. Others work in property and casualty insurance. Actuaries make tables that show how likely it is that a claim will be made by a customer. They use these tables to decide how much the company will have to pay in claims. They make sure that the company charges enough to pay these claims. This amount must be enough for the company to make a profit. It must also be in line with what other insurance companies are charging.

2...

Actuaries need to know a lot about math and general business. Those just starting in the field often have a college degree in math, actuarial science, or statistics. Some have a degree in economics, finance, or accounting.

3...Employment for actuaries is expected to grow faster than the average for all jobs through 2020. Examinations to become an actuary are very difficult; those who pass have a good chance for a job. Actuaries working on health care issues will have good chances for a job because many more people will need health care in the future. Actuaries also will be needed to work on other issues

Actuaries also decide how much money it will take in order to get a certain amount of retirement income. They help design insurance policies and pension plans and try to make sure that they are sound. Actuaries may need to explain their findings to company executives, government officials, and the public. They may also testify in court as an expert.

Most actuaries work for insurance companies. Some work in life and health insurance. Others work in property and casualty insurance. Actuaries make tables that show how likely it is that a claim will be made by a customer. They use these tables to decide how much the company will have to pay in claims. They make sure that the company charges enough to pay these claims. This amount must be enough for the company to make a profit. It must also be in line with what other insurance companies are charging.

2...

Actuaries need to know a lot about math and general business. Those just starting in the field often have a college degree in math, actuarial science, or statistics. Some have a degree in economics, finance, or accounting.

3...Employment for actuaries is expected to grow faster than the average for all jobs through 2020. Examinations to become an actuary are very difficult; those who pass have a good chance for a job. Actuaries working on health care issues will have good chances for a job because many more people will need health care in the future. Actuaries also will be needed to work on other issues

### from teaching to industry

A mathematician working in industry must be an everyday problem solver and be willing to apply mathematical skills to any problem presented by the employer. In this article, I hope to give some direction to the teaching mathematician who desires to make a change to industry. I will try to give an assessment of the important factors to look for in a company and some insight into how companies conduct searches for technical staff.

I made the change from teaching and research after seven years of teaching. I moved to a matlab firm but I began my work atHow to Get Started

The first step in making a career change is to do some library research. Start by exploring employment information from the AMS, MAA, and SIAM, and specialized publications of IEEE. Many of these specialized publications contain articles on signal processing or satellite communications,investment, banking, share market for example, which can give an indication of areas which are currently of interest in industry and which may be of interest to you. Many of these articles are in fact written by mathematicians. Look at the biographies at the end of articles to determine the background of the authors contributing to the various specialized publications and their company and laboratory affiliations. Some of these articles are written by people working in industry-supported laboratories, and some are written by people supporting development projects directly for companies. If an area seems to match your interests, look in the business journals and supplements to see which companies are actively working in these areas. If the company is a government contractor, look up the recently awarded contract areas and contracts which are in the competition or pre-competition stage. If the company is doing commercial business, determine the customer base and extent of current and future sales possibilities. Once an area of interest is found, make a list of the candidate companies for further analysis.

Contact the company employment office and the career opportunity offices of both your current educational institution and the educational institution from which your last degree was obtained. Request all scientific and engineering openings and also request information about companies on your list to see if they have used the school's recruiting service in the past. At this point, geographical constraints can be applied as well as any other personal restrictions. Apply to those companies remaining on the list and emphasize the desire for a personal interview. Before the interview, expand your list of contracts and company activity for the last several years and of any pending contracts and future contract prospects using the business section of the library once again.

Most interviewers are used to interviewing people looking for their first job or people transferring within the industry. Having a good knowledge of company operations during the interview will help put you in the latter class and will put the interviewer, who is not used to interviewing people outside the industry with advanced degrees, at ease.

Company Structure

Understand the similarities and differences between the management structures in an educational institution, either teaching, research, or both, and the management structures in industry. The management structure in an educational institution is usually familiar to most mathematicians, who are exposed to it through their student years. Management structures in industry vary widely and can range from self-managing at the consultant level to a very structured chain of command as a member of a development team.

During a career as a mathematician in industry, generally two career tracks are available. One track is technical management; the other is the purely technical track. The two tracks are similar to the options a mathematician has in an educational institution. Most companies will advertise these options as separate but equal and indicate that an employee may move freely between tracks. While this is true at the lower ranks, the upper management and technical consultants in a company are usually very specialized and at some point in a career a decision must be made about which track to pursue. In both tracks, performance is the key to advancement, and as a new company member, the employee needs to be aggressive from the beginning to determine expectations of supervisors.

Many companies have a written review process, which may occur more often during the initial years of employment. Some have incentive programs directly tied to goals which are determined and agreed to by employee and management. Be certain to discuss these policies during the interview and again with management immediately after joining a company. Many large companies use a point system, assigning points to technical experience and education. Discuss the point system with the human resources department of the company to be certain all eligible points are received. These points usually determine starting salary and are often awarded for specific technical experience, military duty, or specific teaching duties. Sometimes experience listed on an application is not complete or is misinterpreted by the department tallying the points, so ask. With these companies, specific point levels must be met as a minimum requirement for promotion, so obtain as much knowledge about how the specific system works before accepting employment.

Companies with opportunities for technical employment will generally have medical benefits similar to those found in teaching.

The companies providing funded pension plans are rare because of recent government regulations. On the other hand, the new retirement plans usually provide employment mobility for the employee with immediate vesting and ownership. The main area of difference is the number of days of vacation provided. The normal starting vacation time to expect is from two to three weeks per year plus some holidays and possibly several personal days. Vacation days are usually earned on a monthly or quarterly basis. Some companies increase vacation time by a day each year, some by a week at five years, and some a week at the end of 10 years.

a small facility away from the main company headquarters. Working in a smaller group allowed me more flexibility and greater visibility while still enabling me to interact with mathematicians and other scientists and engineers throughout the company.

There is another caution for those wishing to continue publishing in the open journals. Some company projects may be deemed company proprietary, and publication of scientific results may be delayed or even prohibited. Some government contracts also entail publication constraints; however, publication is usually possible if all the rules are followed.

After the Move

The previous teaching experience of the mathematician employed by an education institution can be a great asset both to the employee and to the company. In aerospace, for example, briefings in front of large audiences are common, and teaching experience, as well as technical expertise, play an important role. You will have a definite advantage if you can present a difficult technical topic so it can be understood by an audience with a wide spectrum of technical expertise. If you do the pre-employment planning and investigation well and a good technical match is made between you and your company, it may be possible to continue to work as a mathematician and become a recognized expert in a specialized area within the company or even within an industrywide community.

I made the change from teaching and research after seven years of teaching. I moved to a matlab firm but I began my work atHow to Get Started

The first step in making a career change is to do some library research. Start by exploring employment information from the AMS, MAA, and SIAM, and specialized publications of IEEE. Many of these specialized publications contain articles on signal processing or satellite communications,investment, banking, share market for example, which can give an indication of areas which are currently of interest in industry and which may be of interest to you. Many of these articles are in fact written by mathematicians. Look at the biographies at the end of articles to determine the background of the authors contributing to the various specialized publications and their company and laboratory affiliations. Some of these articles are written by people working in industry-supported laboratories, and some are written by people supporting development projects directly for companies. If an area seems to match your interests, look in the business journals and supplements to see which companies are actively working in these areas. If the company is a government contractor, look up the recently awarded contract areas and contracts which are in the competition or pre-competition stage. If the company is doing commercial business, determine the customer base and extent of current and future sales possibilities. Once an area of interest is found, make a list of the candidate companies for further analysis.

Contact the company employment office and the career opportunity offices of both your current educational institution and the educational institution from which your last degree was obtained. Request all scientific and engineering openings and also request information about companies on your list to see if they have used the school's recruiting service in the past. At this point, geographical constraints can be applied as well as any other personal restrictions. Apply to those companies remaining on the list and emphasize the desire for a personal interview. Before the interview, expand your list of contracts and company activity for the last several years and of any pending contracts and future contract prospects using the business section of the library once again.

Most interviewers are used to interviewing people looking for their first job or people transferring within the industry. Having a good knowledge of company operations during the interview will help put you in the latter class and will put the interviewer, who is not used to interviewing people outside the industry with advanced degrees, at ease.

Company Structure

Understand the similarities and differences between the management structures in an educational institution, either teaching, research, or both, and the management structures in industry. The management structure in an educational institution is usually familiar to most mathematicians, who are exposed to it through their student years. Management structures in industry vary widely and can range from self-managing at the consultant level to a very structured chain of command as a member of a development team.

During a career as a mathematician in industry, generally two career tracks are available. One track is technical management; the other is the purely technical track. The two tracks are similar to the options a mathematician has in an educational institution. Most companies will advertise these options as separate but equal and indicate that an employee may move freely between tracks. While this is true at the lower ranks, the upper management and technical consultants in a company are usually very specialized and at some point in a career a decision must be made about which track to pursue. In both tracks, performance is the key to advancement, and as a new company member, the employee needs to be aggressive from the beginning to determine expectations of supervisors.

Many companies have a written review process, which may occur more often during the initial years of employment. Some have incentive programs directly tied to goals which are determined and agreed to by employee and management. Be certain to discuss these policies during the interview and again with management immediately after joining a company. Many large companies use a point system, assigning points to technical experience and education. Discuss the point system with the human resources department of the company to be certain all eligible points are received. These points usually determine starting salary and are often awarded for specific technical experience, military duty, or specific teaching duties. Sometimes experience listed on an application is not complete or is misinterpreted by the department tallying the points, so ask. With these companies, specific point levels must be met as a minimum requirement for promotion, so obtain as much knowledge about how the specific system works before accepting employment.

Companies with opportunities for technical employment will generally have medical benefits similar to those found in teaching.

The companies providing funded pension plans are rare because of recent government regulations. On the other hand, the new retirement plans usually provide employment mobility for the employee with immediate vesting and ownership. The main area of difference is the number of days of vacation provided. The normal starting vacation time to expect is from two to three weeks per year plus some holidays and possibly several personal days. Vacation days are usually earned on a monthly or quarterly basis. Some companies increase vacation time by a day each year, some by a week at five years, and some a week at the end of 10 years.

a small facility away from the main company headquarters. Working in a smaller group allowed me more flexibility and greater visibility while still enabling me to interact with mathematicians and other scientists and engineers throughout the company.

There is another caution for those wishing to continue publishing in the open journals. Some company projects may be deemed company proprietary, and publication of scientific results may be delayed or even prohibited. Some government contracts also entail publication constraints; however, publication is usually possible if all the rules are followed.

After the Move

The previous teaching experience of the mathematician employed by an education institution can be a great asset both to the employee and to the company. In aerospace, for example, briefings in front of large audiences are common, and teaching experience, as well as technical expertise, play an important role. You will have a definite advantage if you can present a difficult technical topic so it can be understood by an audience with a wide spectrum of technical expertise. If you do the pre-employment planning and investigation well and a good technical match is made between you and your company, it may be possible to continue to work as a mathematician and become a recognized expert in a specialized area within the company or even within an industrywide community.

### maths for net

1..discuss the nature of solution;

a..dy/dx=sin(xy) , y(0)=3

b..xdy/dx=y+2 x*2 , y(o)=o

c..dy/dx=x*2+y*2 , Y(0)=0

d..2xdy/dx=3(2y-1) , y(0)=1/2

2...which can not be cardinality of a field 4 ,6, 7, 27.

3...which one is correct..

a..a computer can be used to sort out 10 lakh number in increasing order.

b..a computer can be used for factoring any integer.

4...which one is correct

a..every principal ideal domain is euclidean domain.

b..the groups of units in the ring Z/37Z is cyclic.

5..which one is software.word perfect,internet explorer, nt, lotous

6..in a non -abelian group , the element a has a order 108, the order of a * 42 is....

7..in a permutation group S6, THE NUMBER OF ELEMENTS conjugate to (123)(456) is...

a..dy/dx=sin(xy) , y(0)=3

b..xdy/dx=y+2 x*2 , y(o)=o

c..dy/dx=x*2+y*2 , Y(0)=0

d..2xdy/dx=3(2y-1) , y(0)=1/2

2...which can not be cardinality of a field 4 ,6, 7, 27.

3...which one is correct..

a..a computer can be used to sort out 10 lakh number in increasing order.

b..a computer can be used for factoring any integer.

4...which one is correct

a..every principal ideal domain is euclidean domain.

b..the groups of units in the ring Z/37Z is cyclic.

5..which one is software.word perfect,internet explorer, nt, lotous

6..in a non -abelian group , the element a has a order 108, the order of a * 42 is....

7..in a permutation group S6, THE NUMBER OF ELEMENTS conjugate to (123)(456) is...

### Questions of the week

1...The Mariana Trench is located in the Pacific Ocean, just east of the 14 Mariana Islands (11"21' North latitude and 142" 12' East longitude ) near Japan. As you probably already know, it is the deepest part of the earth's oceans, and the deepest location of the earth itself. It was created by ocean-to-ocean subduction, a phenomena in which a plate topped by oceanic crust is subducted beneath another plate topped by oceanic crust.

The deepest part of the Mariana Trench is the Challenger Deep, so named after the exploratory vessel HMS Challenger II; a fishing boat converted into a sea lab by Swiss scientist Jacques Piccard

2...Jupiter is the fifth planet from the Sun and is the largest one in the solar system. If Jupiter were hollow, more than one thousand Earths could fit inside. It also contains more matter than all of the other planets combined. It has a mass of 1.9 x 1027 kg and is 142,800 kilometers (88,736 miles) across the equator. Jupiter possesses 28 known satellites, four of which - Callisto, Europa, Ganymede and Io - were observed by Galileo as long ago as 1610.

3..Lake Van (Turkish: Van Gölü; Armenian: Վանա լիճ; Kurdish: Gola Wanê) is the largest lake in Turkey, in the far east of the country. It is a saline lake of volcanic origin with no outlet, receiving water from numerous small streams that descend from the surrounding mountains. It is 120 km long, 80 km wide and 457 metres deep. It has an area of 3,755 km² and is 1719 metres above sea level.

4...The Moon is 384,403 kilometers (238,857 miles) distant from the Earth. Its diameter is 3,476 kilometers (2,160 miles). Both the rotation of the Moon and its revolution around Earth takes 27 days, 7 hours, and 43 minutes. This synchronous rotation is caused by an unsymmetrical distribution of mass in the Moon, which has allowed Earth's gravity to keep one lunar hemisphere permanently turned toward Earth. Optical librations have been observed telescopically since the mid-17th century. Very small but real librations (maximum about 0°.04) are caused by the effect of the Sun's gravity and the eccentricity of Earth's orbit, perturbing the Moon's orbit and allowing cyclical preponderances of torque in both east-west and north-south directions.

5..In biology, a species is one of the basic units of biodiversity. A species generally consists of all the individual organisms of a natural population which are able to interbreed, generally sharing similar appearance, characteristics and genetics due to having relatively recent common ancestors.

6..

A famous land version of symbiosis is the relationship of the Egyptian Plover bird and the crocodile. In this relationship, the bird is well known for preying on parasites that feed on crocodiles which are potentially harmful for the animal. To that end, the crocodile openly invites the bird to hunt on his body, even going so far as to open the jaws to allow the bird enter the mouth safely to hunt. For the bird's part, this relationship not only is a ready source of food, but a safe one considering that few predator species would dare strike at the bird at such proximity to its host.

7..In chemistry, an amino acid is any molecule that contains both amine and carboxyl functional groups. In biochemistry, this shorter and more general term is frequently used to refer to alpha amino acids: those amino acids in which the amino and carboxylate functionalities are attached to the same carbon, the so-called α–carbon. These amino acids are used as the basic components of proteins. There are twenty "standard" amino acids used by cells in protein biosynthesis that are specified by the general genetic code.

8..

## Tuesday, December 19, 2006

### NET TOPICS

1..Prime numbers have intrigued mathematicians for centuries. It is an

important sub-branch of mathematics called "number theory". Despite the

efforts of the best mathematical minds over the centuries, there is no

general "formula" for generating prime numbers. There are some

approximations, and there are theorems predicting the number of prime

numbers less than a particular upper bound. As of 2003 the largest known

prime number is:

The 39th Mersenne prime

m39 = 213,466,917-1

is the largest known prime number (as of the time of this writing, May 23,

2003). In the decimal system it requires 4,053,946 digits to be written

fully. Most of this page is taken up by those digits.

2..The system of quaternions is an extension of the complex number system in

the same way that the complex number system is an extension of the real

number system. Recall that you treat 2 + 3i algebraically just as you would

treat

2 + 3x except that when multiplying you replace any occurrence of i*i by -1.

You would treat a quaternion such as 2 + 3i + 5j - 2k algebraically just as

you would treat 2 + 3x + 5y - 2z except that you replace products of i, j,

and k according to the following rules:

i * i = -1, j * j = -1, k * k = -1, i * j = k, j * k = i, k * i = j,

j * i = -k, k * j = -i, and i * k = -j.

As you observed, this does make multiplication not commutative

, but is not any weirder than the i * i = -1 in the complex

numbers or the non-commutativity of matrix multiplication

3..If K is a prime and M(K) = 2^K-1 is also a prime (

called a Mersenne

prime) then P(K) =2^(K-1)*M(K) is a perfect number (the sum of all of its

proper divisors is equal to P(K)).

4.Christian Goldbach (1690-1764), in a letter to Euler dated February, 16,

1745, stated that every even number equal to or greater than 6 is the sum of

two odd primes in one or more ways. The first sentence is a direct quote

from THE LORE OF PRIME NUMBERS by G. P. Loweke, p 68. The conjecture

remains unsettled, but computers have verified the conclusion for all even N

below very large bounds (Loweke noted the bound of 100,000 but that is quite

old, I believe). A related conjecture is that every even number is a

difference of two primes in infinitely many ways! Loweke ascribes this

statement to A. de Polignac around 1849.

5.. Fermat's Last Theorem states that the equation

a^n + b^n = c^n

has no integer solutions for n > 2. The theorem can be easily proved for

some specific values of _n_, for example, n = 3. The hard part is proving

it in general.

6..

Two positive integers are "relatively prime" if their prime factorizations

have no common prime factors. For example, if you "reduce a rational

fraction to its lowest terms"

then the numerator and denominator must be relatively prime.

7..The ancient greeks decided (probably based on experiments: try using a cord

to estimate the circumference of some cylinders) that the perimeter of a

circle (and other symmetric objects) must be a constant multiple of its

diameter. A little later attempts were made to estimate the value of the

constant using the geometry of inscribed polygons. Much later, when

symbolism became more popular in mathematics, "pi" (the first letter in the

greek word for perimeter) started to gain acceptance for representing this

famous constant. Full details on how "they" get it are too long to type

here. Perhaps the earliest estimate for PI was 3. I believe that Archime-

des gets credit for using geometry to improve the estimate to 22/7. The

greeks at that time loved pure fractions and used nothing like our many

decimal representations.

important sub-branch of mathematics called "number theory". Despite the

efforts of the best mathematical minds over the centuries, there is no

general "formula" for generating prime numbers. There are some

approximations, and there are theorems predicting the number of prime

numbers less than a particular upper bound. As of 2003 the largest known

prime number is:

The 39th Mersenne prime

m39 = 213,466,917-1

is the largest known prime number (as of the time of this writing, May 23,

2003). In the decimal system it requires 4,053,946 digits to be written

fully. Most of this page is taken up by those digits.

2..The system of quaternions is an extension of the complex number system in

the same way that the complex number system is an extension of the real

number system. Recall that you treat 2 + 3i algebraically just as you would

treat

2 + 3x except that when multiplying you replace any occurrence of i*i by -1.

You would treat a quaternion such as 2 + 3i + 5j - 2k algebraically just as

you would treat 2 + 3x + 5y - 2z except that you replace products of i, j,

and k according to the following rules:

i * i = -1, j * j = -1, k * k = -1, i * j = k, j * k = i, k * i = j,

j * i = -k, k * j = -i, and i * k = -j.

As you observed, this does make multiplication not commutative

, but is not any weirder than the i * i = -1 in the complex

numbers or the non-commutativity of matrix multiplication

3..If K is a prime and M(K) = 2^K-1 is also a prime (

called a Mersenne

prime) then P(K) =2^(K-1)*M(K) is a perfect number (the sum of all of its

proper divisors is equal to P(K)).

4.Christian Goldbach (1690-1764), in a letter to Euler dated February, 16,

1745, stated that every even number equal to or greater than 6 is the sum of

two odd primes in one or more ways. The first sentence is a direct quote

from THE LORE OF PRIME NUMBERS by G. P. Loweke, p 68. The conjecture

remains unsettled, but computers have verified the conclusion for all even N

below very large bounds (Loweke noted the bound of 100,000 but that is quite

old, I believe). A related conjecture is that every even number is a

difference of two primes in infinitely many ways! Loweke ascribes this

statement to A. de Polignac around 1849.

5.. Fermat's Last Theorem states that the equation

a^n + b^n = c^n

has no integer solutions for n > 2. The theorem can be easily proved for

some specific values of _n_, for example, n = 3. The hard part is proving

it in general.

6..

Two positive integers are "relatively prime" if their prime factorizations

have no common prime factors. For example, if you "reduce a rational

fraction to its lowest terms"

then the numerator and denominator must be relatively prime.

7..The ancient greeks decided (probably based on experiments: try using a cord

to estimate the circumference of some cylinders) that the perimeter of a

circle (and other symmetric objects) must be a constant multiple of its

diameter. A little later attempts were made to estimate the value of the

constant using the geometry of inscribed polygons. Much later, when

symbolism became more popular in mathematics, "pi" (the first letter in the

greek word for perimeter) started to gain acceptance for representing this

famous constant. Full details on how "they" get it are too long to type

here. Perhaps the earliest estimate for PI was 3. I believe that Archime-

des gets credit for using geometry to improve the estimate to 22/7. The

greeks at that time loved pure fractions and used nothing like our many

decimal representations.

### TIPS FOR EVE OF EXAM

Increasing and Keeping Motivation

1..Think about the iit you want to join to (stay aware of it always)

1b..Keep your interest high

2...Use interests & goals to keep you determined (i.e. stduy, religion, music, sports, etc.)

3..Ask peers and family to encourage your strengths.

4..Come with a positive attitude; tell yourself.

" You can do it!"

5..Think about your life after you get your degree.

6..Stay focused on your goals; ones that success in math classes will allow you to achieve

### QUESTION FOR NET

1...If A ,B are two n- rowed sqaure matrices having ranks 1 and 2 respectively. find the rank of AB.

2..Constract a skew-symmetric matrix of rank 5.

3..if A is a non-zero coulmn and B is a non-zerorow matrix,then prove rank(A_B)=1.

4..State and prove navier-stroke,s equation.

5..Let X be the matric space whose points are the rational numbers, withthe metric d(x,y)=mod(x-y). what is the completion of this space.

2..Constract a skew-symmetric matrix of rank 5.

3..if A is a non-zero coulmn and B is a non-zerorow matrix,then prove rank(A_B)=1.

4..State and prove navier-stroke,s equation.

5..Let X be the matric space whose points are the rational numbers, withthe metric d(x,y)=mod(x-y). what is the completion of this space.

## Sunday, December 17, 2006

### Net Questions

1..green house effect mainly due to which gas.

2..which one is vector quantity ;time, temperature. pressure, stress.

3.. 1 bit consist how many bite.

4..prove that cantor ternary set is a perfect set with empty interior.

5..find the mobius transformation which maps 1,-i.2 onto 0,2 ,-i resectively.

6..prove the imageof a cachy sequence under a uniformly continuous mapping is a cauchy mapping.

7..constract a fuction f(z), which has real fuction u(x,y)=e*x(xcosy-ysiny).

8..in a vector space R*3,LET a=(1,2,1),b=(3,1,5) ,c=(3,-4,7).show that there exist more than one basis for the subspace spanned by theset S=(a, b,c).

9...let dy/dx=-xy,y(0)=1.find y(.2)using Runge-Kutta method.

### golden ratio

1..We will call the Golden Ratio (or Golden number) after a greek letter,Phi () here, although some writers and mathematicians use another Greek letter, tau (). Also, we shall use phi (note the lower case p) for a closely related value. The golden ratio, also known as the divine proportion, golden mean, or golden section, is a number often encountered when taking the ratios of distances in simple geometric figures such as the pentagon, pentagram, decagon and dodecahedron. It is denoted , or sometimes . The designations "phi" (for ) and "Phi" (for the golden ratio conjugate ) are sometimes also used (Knott).

2..

The arrangements of leaves is the same as for seeds and petals. All are placed at 0·618034.. leaves, (seeds, petals) per turn. In terms of degrees this is 0·618034 of 360° which is 222·492...°. However, we tend to "see" the smaller angle which is (1-0·618034)x360 = 0·381966x360 = 137·50776..°. When we look at properties of Phi and phi on a later page, we shall see that

1-phi = phi2 = Phi-2

If there are Phi (1·618...) leaves per turn (or, equivalently, phi=0·618... turns per leaf ), then we have the best packing so that each leaf gets the maximum exposure to light, casting the least shadow on the others. This also gives the best possible area exposed to falling rain so the rain is directed back along the leaf and down the stem to the roots. For flowers or petals, it gives the best possible exposure to insects to attract them for pollination.

The whole of the plant seems to produce its leaves, flowerhead petals and then seeds based upon the golden number.

And why do the Fibonacci numbers appear as leaf arrangements and as the number of spirals on seedheads?

3...

Botanists have shown that plants grow from a single tiny group of cells right at the tip of any growing plant, called the meristem. There is a separate meristem at the end of each branch or twig where new cells are formed. Once formed, they grow in size, but new cells are only formed at such growing points. Cells earlier down the stem expand and so the growing point rises.

Also, these cells grow in a spiral fashion, as if the stem turns by an angle and then a new cell appears, turning again and then another new cell is formed and so on.

These cells may then become a new branch, or perhaps on a flower become petals and stamens.

The amazing thing is that a single fixed angle can produce the optimal design no matter how big the plant grows. So, once an angle is fixed for a leaf, say, that leaf will least obscure the leaves below and be least obscured by any future leaves above it. Similarly, once a seed is positioned on a seedhead, the seed continues out in a straight line pushed out by other new seeds, but retaining the original angle on the seedhead. No matter how large the seedhead, the seeds will always be packed uniformly on the seedhead.

And all this can be done with a single fixed angle of rotation between new cells?

Yes! This was suspected by people as early as the last century. The principle that a single angle produces uniform packings no matter how much growth appears after it was only proved mathematically in 1993 by Douady and Couder, two french mathematicians.

4...The Rhind Papyrus of about 1650 BC is one of the oldest mathematical works in existence, giving methods and problems used by the ancient Babylonians and Egyptians. It includes the solution to some problems about pyramids but it does not mention anything about the golden ratio Phi.

The ratio of the length of a face of the Great Pyramid (from centre of the bottom of a face to the apex of the pyramid) to the distance from the same point to the exact centre of the pyramid's base square is about 1·6. It is a matter of debate whether this was "intended" to be the golden section number or not.

According to Elmer Robinson

using the average of eight sets of data, says that "the theory that the perimeter of the pyramid divided by twice its vertical height is the value of pi" fits the data much better than the theory above about Phi.

## Saturday, December 16, 2006

### Problems for NET 2006

1..Check the differentiability of arg(z)

2.Prove that if the primal problem has a unbounded solutaion,then duel problem has no feasible solution.

3...Show that sin(x)and cos(x) are of bounded variation over a finite interval.

4..Find the limit point of sequence (m+1/n),where m,n are natural numbers.

5..Determine the uniformly continuity of tan(inverse)x over R.

6..IF the set of all polynomials with rational cofficients is countable.

7..Suppose V is finite dimensionl vector space.suppose T is a linear operator ov V, such that rank(T)=rank(T*2).find the intersection of kernel(T) and imag (T).

8..How many homomorphism are there Z into Z.

9.Find the differential equation of all straight lines at a unit distance from the origin.

10..Find the differential equation arising of f(x+y+z,x*2+y*2-z*2).

11..Determine the dimension of vectorspaceW of the fllowing n*n matrices.

a..Symmetric matrices

b..Antisymmetric matrices

c...Diagonal matrices

d..Scalar matrices

### Question of the week

## Friday, December 15, 2006

### IIT-JEE

The Indian Institutes of Technology (Hindi: भारतीय प्रौद्योगिकी संस्थान), or IITs, are a group of seven autonomous engineering and technology oriented institutes of higher education established and declared as Institutes of National Importance by the Government of India. The IITs were created to train scientists and engineers, with the aim of developing a skilled workforce to support the economic and social development of India after independence in 1947. The students and alumni of IITs are colloquially referred to as IITians.

In order of establishment, the seven IITs are located at Kharagpur, Mumbai (Bombay), Chennai (Madras), Kanpur, Delhi, Guwahati, and Roorkee. Some IITs were established with financial assistance and technical expertise from UNESCO, Germany, the United States, and the Soviet Union. Each IIT is an autonomous university, linked to the others through a common IIT Council, which oversees their administration. They have a common admission process for undergraduate admissions, using the Joint Entrance Examination (popularly known as IIT-JEE) to select around 4,000 undergraduate candidates a year. Graduate Admissions are done on the basis of the GATE. About 15,500 undergraduate and 12,000 graduate students study in the seven IITs, in addition to research scholars.

IITians have achieved success in a variety of professions, resulting in the establishment of the widely recognised Brand IIT.[1] The autonomy of the IITs has helped them to create specialised degrees in technology at the undergraduate level, and consequently to award the Bachelor of Technology (B.Tech.) degree, as opposed to the Bachelor of Engineering (BE) degree awarded by most other Indian universities. The success of the IITs has led to the creation of similar institutes in other fields, such as the National Institutes of Technology, the Indian Institutes of Management, the Indian Institute of Information Technology & Management and the Indian Institute of Information Technology.

The Institutes

Quotes about Indian Institute of Technology

The seven IITs are located in Kharagpur, Bombay, Madras, Kanpur, Delhi, Guwahati, and Roorkee. All IITs are autonomous universities that draft their own curricula, and they are, with the exception of IIT Kanpur, members of LAOTSE, an international network of universities in Europe and Asia. LAOTSE membership allows the IITs to exchange students and senior scholars with universities in other countries.

### fellowship

Ford foundation international fellowship program 2007

Appicant should be indian graduate at least two years work experiance relevent to your proposed field of study.website; www.ifpsa.org

Appicant should be indian graduate at least two years work experiance relevent to your proposed field of study.website; www.ifpsa.org

## Thursday, December 14, 2006

### last years question in NET

1...mō´dem) (n.) Short for modulator-demodulator. A modem is a device or program that enables a computer to transmit data over, for example, telephone or cable lines. Computer information is stored digitally, whereas information transmitted over telephone lines is transmitted in the form of analog waves. A modem converts between these two forms.

2.. FM broadcasting is a broadcast technology invented by Edwin Howard Armstrong that uses frequency modulation (FM) to provide high-fidelity sound over broadcast radio.

3.... freshly polished, negatively charged zinc plate looses its charge if it is exposed to ultraviolet light. This phenomenon is called the photoelectric effect.

Careful investigations toward the end of the nineteenth century proved that the photoelectric effect occurs with other materials, too, but only if the wavelength is short enough. The photoelectric effect is observed below some threshold wavelength which is specific to the material. Especially the fact that light of large wavelengths has no effect at all even if it is extremely intensive, appeared mysterious for the scientists.

Albert Einstein finally gave the explanation in 1905: Light consists of particles (photons), and the energy of such a particle is proportional to the frequency of the light. There is a certain minimum amount of energy (dependent on the material) which is necessary to remove an electron from the surface of a zinc plate or another solid body (work function). If the energy of a photon is bigger than this value, the electron can be emitted. From this explanation the following equation results:

Ekin = h f – W

Ekin ... maximal kinetic energy of an emitted electron

h ..... Planck constant (6.626 x 10-34 Js)

f ..... frequency

W ..... work function

4...acid rain

Acid deposition is a general term that includes more than simply acid rain. Acid deposition primarily results from the transformation of sulphur dioxide (SO2) and nitrogen oxides into dry or moist secondary pollutants such as sulphuric acid (H2SO4), ammonium nitrate (NH4NO3) and nitric acid (HNO3). The transformation of SO2 and NOx to acidic particles and vapours occurs as these pollutants are transported in the atmosphere over distances of hundreds to thousands of kilometers. Acidic particles and vapours are deposited via two processes - wet and dry deposition. Wet deposition is acid rain, the process by which acids with a pH normally below 5.6 are removed from the atmosphere in rain, snow, sleet or hail. Dry deposition takes place when particles such as fly ash, sulphates, nitrates, and gases (such as SO2 and NOx), are deposited on, or absorbed onto, surfaces. The gases can then be converted into acids when they contact water.

5..A set is a collection of objects called elements of the set. Why not use the word ``collection'' and eliminate the word ``set'', thereby having fewer words to worry about? ``Collection'' is a common word whose generic meaning is understood by most people. The use of the word ``set'' means that there is also a method to determine whether or not a particular object belongs in the set. We then say that the set is well-defined. For example, it is easy to decide that the number 8 is not in the set consisting of the integers 1 through 5. After all, there are only five objects to consider and it is clear that 8 is not one of them by simply checking all five.

A basic problem here is now to indicate sets on paper and verbally. As seen above, a set could be described with a phrase such as ``the integers 1 through 5'' and the speaker hopes that it is understood. Symbollically, we use two common methods to write sets. The roster notation is a complete or implied listing of all the elements of the set. So and are examples of roster notation defining sets with 4 and 20 elements respectively. The ellipsis, `` '', is used to mean you fill in the missing elements in the obvious manner or pattern, as there are too many to actually list out on paper. The set-builder notation is used when the roster method is cumbersome or impossible. The set B above could be described by . The vertical bar, ``|'', is read as ``such that'' so this notation is read aloud as ``the set of x such that x is between 2 and 40 (inclusive) and x is even.'' (Sometimes a colon is used instead of |.) In set-builder notation, whatever comes after the bar describes the rule for determining whether or not an object is in the set. For the set the roster notation would be impossible since there are too many reals to actually list out, explicitly or implicitly.

6... Hydrogen bonding differs from other uses of the word "bond" since it is a force of attraction between a hydrogen atom in one molecule and a small atom of high electronegativity in another molecule. That is, it is an intermolecular force, not an intramolecular force as in the common use of the word bond.

When hydrogen atoms are joined in a polar covalent bondwith a small atom of high electronegativity such as O, F or N, the partial positive charge on the hydrogen is highly concentrated because of its small size. If the hydrogen is close to another oxygen, fluorine or nitrogen in another molecule, then there is a force of attraction termed a dipole-dipole interaction. This attraction or "hydrogen bond" can have about 5% to 10% of the strength of a covalent bond.

Hydrogen bonding has a very important effect on the properties of water and ice. Hydrogen bonding is also very important in proteins and nucleic acids and therefore in life processes. The "unzipping" of DNA is a breaking of hydrogen bonds which help hold the two strands of the double helix together

7...The equations of modern atomic theory are difficult to solve. Fortunately, many of the results can be obatined by following some simple rules. These rules are known as the Aufbau principle. However, we first need to discuss quantum numbers, shells, subshells and orbitals.

The principal quantum number n - the shell

Quantum numbers abound in quantum theory. These quantum numbers serve the purpose of keeping track of the various quantum possibilities that emerge. Perhaps the most important quantum number is the "principal" quantum number n. The principal quantum number n can take on the values 1, 2, 3, 4, 5, 6, ... . Associated with each n is a principle energy level known as a shell. Thus, shell 1 has n=1, shell 2 has n=2 etc. and so on associated with it.

Each shell has subshells associated with it

Depending upon its quantum number, each shell can have one or more subshells associated with it. For the n=1 shell there is only one subshell - the s subshell. For the n=2 shell there are two subshells - the s and p subshells and so on. The number of subshells within a shell is equal to n.The physical and chemical properties of elements is determined by the atomic structure. The atomic structure is, in turn, determined by the electrons and which shells, subshells and orbitals they reside in. The rules af placing electrons within shells is known as the Aufbau principle. These rules are:

1. Electrons are placed in the lowest energetically available subshell.

2. An orbital can hold at most 2 electrons.

3. If two or more energetically equivalent orbitals are available (e.g., p, d etc.) then electrons should be spread out before they are paired up (Hund's rule).

8..

When deciding how electrons are arranged in an orbital diagram for a given atom or ion, Hund's rule is used.

When several orbitals of equal energy are available, electrons enter singly with parallel spins

In other words, add one electron to each orbital of equal level (such as the five d orbitals) all with the same spin.

9...TotalInternal Reflection

An unusual observation - a discrepant event - was observed in a recent lab - the Index of Refraction lab. The refraction of light through a glass block in the shape of an isosceles triangle was investigated (at least, so we thought). In the lab, a ray of light entered the face of the triangular block at a right angle to the boundary. This ray of light passed across the boundary without refraction since it was incident along the normal (recall the Secret of the Archer Fish). The ray of light then traveled in a straight line through the glass until it reached the second boundary. Only instead of transmitting across this boundary, the entirety of the light seemed to reflect off the boundary and transmit out the opposite face of the isosceles triangle. This discrepant event bothered many as they spent several minutes looking for the light to refract through the second boundary. Then finally, to their amazement, they looked through the third face of the block and could clearly see the ray.

10....

Right-angled triangles

Here is a triangle. There are three angles inside it: one we've called "theta"; one is left empty and one has a small square drawn in it. This small square indicates that that angle is a right-angle, which is 900 or p/2 in radians. The triangle is therefore known as a right-angled triangle.

The longest side of a right-angled triangle is called the "hypotenuse" as shown. The other two sides are labelled in terms of their position to the angle q. (So if we were considering the other angle, rather than q, their labels would be swapped over).

We are going to define two new quantities called sine and cosine. They depend on the angle q: if q changes the they will also change.

The sine of q, written as sin(q), is defined as the length of the opposite side divided by the length of the hypotenuse.

Similarly, the cosine of q, written as cos(q), is defined as the length of the adjacent side divided by the length of the hypotenuse.

## Wednesday, December 13, 2006

### math job

1..Call it a resume, a CV or a bio-data, it is the most important tool you have when approaching employers. You will be trained and educated in various skills in institutions — and there are enough jobs out there that need your kind of skills. But then, you are not the only one. An employer will carefully compare and contrast you with the scores of others with similar skills before coming to a decision whom to employ. The employer- in this exercise of evaluating candidates- refers most often to the resume. Often, the decision to employ or reject a particular candidate is taken within 10 seconds after reading a resume.

2..A Resume or bio data is a tool that outlines a prospective employee's professional and personal achievements on the basis of which an employer decides to hire him/her.

A resume is extremely crucial for a person's job prospects because through it, first impressions are formed, and as they say- "the first impression is the last impression."

For example, if you are a sales or marketing professional, the potential employer will expect your resume and cover letter to reflect that type of expertise. In other words, the employer may decide that if you can’t sell yourself, how can you sell their product or service.

3...The crucial difference between your skills and your resume is that the latter has a purely temporary function. Once you land that plumb job- your skills and how you put them to practice are all that matter to employers. A well written resume is not a passport to permanent bliss. Just as a poor resume may restrict your chances of landing a job, a splendid resume may get you the job, but if you don't use your skills effectively, your professional growth will be stunted, or worse, you might get fired.

4... C.V. or curriculum vitae is a detailed description of all ur achievements, qualifications and other profile without any editing....therefore it may run into pages.......a Resume is created in response to a particular advertisment u plan to apply for whereas a bio-Data is a one page profile which gives ur personal details,qualification and experience.....it is general format and can be used for many purposes.

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