TIPS FOR MATH INTERVIEW

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.

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.

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.

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.

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.

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

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!

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

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.

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.

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.

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.

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 .