Genetic Algorithm

Genetic programming (GP) is one of the most useful, general-purpose problem solving techniques available to developers. It has been used to solve a wide range of problems, such as symbolic regression, data mining, optimization, and emergent behavior in biological communities.GP is one instance of the class of techniques called evolutionary algorithms, which are based on insights from the study of natural selection and evolution. Living things are extraordinarily complex, far more so than even the most advanced systems designed by humans. Evolutionary algorithms solve problems not by explicit design and analysis, but by a process akin to natural selection.An evolutionary algorithm solves a problem by first generating a large number of random problem solvers (programs). Each problem solver is executed and rated according to a fitness metric defined by the developer. In the same way that evolution in nature results from natural selection, an evolutionary algorithm selects the best problem solvers in each generation and breeds them.Genetic programming and genetic algorithms are two different evolutionary algorithms. Genetic algorithms involve encoded strings that represent particular problem solutions. These encoded strings are run through a simulator and the best strings are mixed to form a new generation. Genetic programming, the subject of this article, follows a different approach. Instead of encoding a representation of a solution, GP breeds executable computer programs

Genetic Algorithm

An algorithm (pronounced AL-go-rith-um) is a procedure or formula for solving a problem. The word derives from the name of the mathematician, Mohammed ibn-Musa al-Khwarizmi, who was part of the royal court in Baghdad and who lived from about 780 to 850. Al-Khwarizmi's work is the likely source for the word algebra as well.
A computer program can be viewed as an elaborate algorithm. In mathematics and computer science, an algorithm usually means a small procedure that solves a recurrent problem.
Physics, Biology, Economy or Sociology often have to deal with the classical problem of optimization. Economy particularly has become specialist of that field1. Generally speaking, a large part of mathematical development during the 18th century dealt with that topic (remember those always repeated problems where you had to obtain the derivative of a function to find its extremes).A genetic algorithm (or short GA) is a search technique used in computing to find true or approximate solutions to optimization and search problems. Genetic algorithms are categorized as global search heuristics. Genetic algorithms are a particular class of evolutionary algorithms that use techniques inspired by evolutionary biology such as inheritance, mutation, selection, and crossover.Genetic algorithms make it possible to explore a far greater range of potential solutions to a problem than do conventional programs. Furthermore, as researchers probe the natural selection of programs under controlled an well-understood conditions, the practical results they achieve may yield some insight into the details of how life and intelligence evolve in the natural world.A 'fitness' function evaluates each solution to decide whether it will contribute to the next generation of solutions. Then, through operations analogous to gene transfer in sexual reproduction, the algorithm creates a new population of candidate solutions."

mca entrance

MCA (Master of Computer Applications) is a 3-year postgraduate program in computers (some institutes have 2 year programs). It is also called PGDCA or PGDIT. They all refer to the same postgraduate program, MCA. It can be either a degree or diploma. MCAs generally are concerned with the SOFTWARE field. A great career for those having a mathematical or analytical mindset.Despite the recent slowdown in IT, an MCA still remains a sought after career option. MacroByte helps you to prepare and consequently crack the entrances of prestigious universities/institutes like Delhi University, Pune University, Jawaharlal Nehru University among many other. Learning is a life long experience and no matter how old you are or what you do or how many people you teach, you can always improve and upgrade yourself. Knowledge or Gyan is a one of the few things in this world that increases when you share it with others. In this section, what you will find is a series of articles related to your area of interest. In addition to this, we invite you to join in in the chat sessions, opinion polls and discussion forums, which will not only enrich you but also enrich us. All the best.

math study

"The essential quality for a mathematician is the habit of thinking things out for oneself. That habit is usually acquired in childhood. It is hard to acquire it later." Professor W.W. Sawyer, mathematician
children are taught maths in alphanumeric language through written numbers. "Both writing and numbers are abstract skills, which are new and unfamiliar. This is the main reason why kids fail in maths. Knowledge is monopolised and distorted today, particularly with the greater commercialisation of education. Ours is a systematic attempt to break knowledge monopolies

news

"What good will this do me?" asks the 10th grader picking at an algebra problem.It's a pointed, timeless question that doesn't always have a quick answer. When parents and teachers are hounded by students wanting to know the practical applications of math, answers have to go beyond balancing the checkbook and grocery shopping.Many teachers agree that the biggest problems in math education have to do with motivating two very different groups of kids. Some students need convincing that all the headaches associated with math are for a good reason. And for others, the ones with a natural hunger for those brain tugging problems, it's a matter of challenging them.

news

Performance of students in Mathematics at primary level remains a major area of concern across the country, according to a recent survey.The survey conducted by an NGO, Pratham, in which students were tested on arithmetic, writing, reading and comprehension, showed that about 60 per cent of students at Standard I and II could recognise numbers or do more mathematics. At Standard 3 to 5, only 65 per cent of the students could do substraction.The Annual Status of Education Report (Rural) 2006, which compiled the findings of the survey conducted across the country in 549 districts, said the performance of students was improving by only four to five per cent in the subject over the previous year's dismal figures.

harold widom

Harold Widom, professor emeritus of mathematics, will share the 2007 Norbert Wiener Prize in Applied Mathematics with UC Davis professor of mathematics Craig Tracy. Presented every three years by the American Mathematical Society and the Society for Industrial and Applied Mathematics, the Wiener Prize is awarded for outstanding contributions to applied mathematics in the highest and broadest sense.

math news

there is a good article about prime numbers.http://www.drobe.co.uk/riscos/artifact1779.html

CAT CUT-OFFS and IIM SELECTION

The overall cut-off is expected to be at the 98th percentile at a score of 120 this year, and 95% of the calls for Group Discussion (GD) and Personal Interview (PI) will happen above this.a section-wise cut-off expectation would be 35-40 marks in Maths and DI and 30-35 marks in Logic and 20-25 in English. Last year the overall cut-off was 45-55 marks. IIM-A’s cut-off is already out and it requires students to score 95.33 percentile in each section and an overall 98 percentile to get a call.
IIM Ahmedabad (IIM-A) has shortlisted over 820 students for around 280 seats, 30 more than last year, for the institute’s flagship PGP programme. A section-wise cut-off expectation would be 35-40 marks in Maths and DI and 30-35 marks in Logic and 20-25 in English.

news

1..The American Mathematical Society is presenting several prizes at the Joint Mathematics Meetings in New Orleans, including two prizes that are awarded jointly with two other mathematics organizations, the Mathematical Association of America and the Society for Industrial and Applied Mathematics.AMS Steele Prize for Mathematical Exposition: DAVID MUMFORD of Brown University for "his beautiful expository accounts of a host of aspects of algebraic geometry".AMS Steele Prize for a Seminal Contribution to Research: KAREN UHLENBECK, University of Texas at Austin "for her foundational contributions in analytic aspects of mathematical gauge theory".AMS Steele Prize for Lifetime Achievement: HENRY P. MCKEAN, Courant Institute of Mathematical Sciences, New York University, "for his rich and magnificent mathematical career".
2..A UGC sponsored three-day National Seminar on Graph Theory and Its Applications, was inaugurated here on Thursday 4 January at the Xavier block auditorium, St Aloysius College Mangalore.The seminar began with the rendition of the prayer song by the students. The event was inaugurated by Rev. Fr. Eugene Lobo, Principal, St. Aloysius College, an economist. The inaugural function was presided over by Vice Principal, Prof. Eric Patrao, who gave the welcome speech and gave some colorful anecdotes about mathematics and how important a role it plays in everyday life. Prof. Dr. M Abdul Rahiman former Vice Chancellor Kannur University and the Calicut University was the guest of honour. Prof. E. Sampath Kumar delivered the Keynote address and Dr. Parameshwara Bhat, the chairman, Dept of Mathematics, Mangalore University released the abstract and seminar proceedings.
3.What students need is better math instruction in elementary and junior high. If they don't receive a solid foundation in math in early years, it is very difficult to "catch up" in high school.A recent article in the National Council of Teachers of Mathematics newsletter stated the main reason why students are failing math in large numbers is that "U.S. mathematics curricula are a mile wide and an inch deep." In general, teachers in each grade level are accountable to teach a wide range of math standards. However, the large number of standards makes it virtually impossible to spend enough adequate time on each topic to ensure mastery of every skill by every student.

PROPOSED IITS

In the 1950s Bihar Institute of Technology, Sindri, was to get converted into an IIT but then it was set up in Kharagpur due to then West Bengal chief minister B C Roy's friendship with Jawaharlal Nehru. The second new IIT will come up in the Telengana region of Andhra Pradesh most likely in Medak. Earlier, it was decided to have it in Adilabad. And the third will be in Rajasthan, the exact site having not yet been finalised. There is also a plan to have two new Indian Institutes of Science Education and Research, one likely in Madhya Pradesh and other in South India, and two new Schools of Planning and Architecture. Though the bulk of increase in the budget outlay would be to accomplish 56% increase in seats and related infrastructure over the next three years to accommodate 27% reservation for Other Backward Castes, it would also go towards setting up of three new IITs, two new IISERs and two new SPAs.An expenditure of Rs 600 crores would be incurred for establishing IIT institute while Rs 150 crores would be spent for opening IIIT institute .

IIT at ANDHRA PRADESH

The prestigious Indian Institute of Technology will come up in Andhra Pradesh on 600 acres of land near Patancheru in Medak district, near Hyderabad.Patancheru is infamous as the most polluted place in the state. Unregulated industrialization over the last two decades has polluted the air and groundwater in the area.Of the nearly 4000 students in IITs all over the country, students from Andhra Pradesh on an average bag 850 to 1000 seats, and IIT Medak may finally bring some cheer to the people of Patancheru.The government also plans to set up three water treatment plants in the area. Despite the controversy, the announcement of an IIT in Andhra Pradesh has also generated much euphoria among the student community. Experts say, with institutes like the ISB, a branch of the Bits Pilani, an annexe of the IIM being proposed, the IIT will put the state on the global education map.

"Martin Kruskal

Mr. Kruskal, one of the world's pre-eminent applied mathematicians and mathematical physicists, died Dec. 26 at Princeton Medical Center after suffering a stroke in mid-December. He was 81. He had suffered an earlier stroke in August, but had fought his way back to health and was working as an active scholar when he was felled again last month. Officials at Princeton University announced his death yesterday. Mr. Kruskal spent 38 years on the Princeton faculty before moving to Rutgers University in 1989.
Mr. Kruskal is best known for his work in the 1960s in which he pioneered the understanding of the soliton, a powerful energy wave. His mathematical analysis of solitons, conducted with colleague Norman Zabusky, proved that such waves were possible and brought them within the realm of practical use, including their use as boosters of the signals conveyed along long-distance, undersea, fiber optic communication cables.In the 1950s, Kruskal made a number of seminal contributions including Kruskal-Shafranov Instability, Bernstein-Greene-Kruskal ( BGK ) Modes and the MHD Energy Principle, which laid the theoretical foundations of controlled nuclear fusion and the then undeveloped field of plasma physics. In 1960, he developed the well-known Kruskal Coordinates ( also called Kruskal-Szekeres Coordinates ), used in the theory of relativity to explain black holes.
He is most famous for his role in starting the "soliton revolution," considered one of the great mathematical advances of the last half of the 20th century. He and Norman Zabusky discovered nonlinear waves that behave in many ways like linear waves, which they termed "solitons." Solitons are now known to be ubiquitous in nature, from physics to chemistry to biology. Their unique properties make them useful for communications, such as in undersea fiber optic cables, and they have been considered as a basis for computing.

news

Professor Alastair Gillespie, chairman of the Scottish Mathematical Council, believes that by introducing simple gambling games into Maths lessons, children will become more engaged and will likely to improve their mathematical skills.Gillespie claims that young children have problems with mathematical problems such as probability, a concept at the heart of gambling."Things like tossing coins and cutting cards are simple techniques which teach pupils about basic maths and I think it would catch the interest of students if we were to introduce that in schools. What you are trying to do is engage with pupils and present them with scenarios which interest them because it shows how maths can be relevant and we need to do more of that," Gillespie advised.Gillespie immediately came under fire for his comments from anti-gambling societies, claiming that his ideas would only serve to encourage children to gamble.

ramanujan award

An international prize for mathematics has been won by Ramdorai Sujatha, an Indian woman, according to a report on the Science and Development Network website (www.scidev.net). The $10 000 prize is named after Srinivasa Ramanujan, the Indian mathematics genius, a college dropout who ended up at the University of Cambridge in England during World War One.A movie about Ramanujan's passion for mathematics and his friendship with a cricket-loving university don who recognised his talent is being produced by Stephen Fry, the British actor-writer and Dev Benegal, the renowned Indian director.When your automated teller machines divide and arrange your money before coughing it up, they are all using Ramanujan's partition theory." The winner of the Ramanujan prize, was Ramdorai Sujatha, an associate professor from the Tata Institute of Fundamental Research in Mumbai. She was awarded the prize at a ceremony at the Abdus Salam International Centre for Theoretical Physics in Trieste, Italy.
The Centre was founded by Abdus Salam, the Pakistan-born physicist and Nobel prizewinner, who once said "scientific thought is the common heritage of mankind". The Ramanujan Prize is the only international prize honouring mathematicians from developing countries, including those in Africa, Latin America and Asia.

math music

Marcus du Sautoy, Professor of Mathematics at the University of Oxford, said that while the introduction of the numeracy strategy had enthused a generation of younger children about maths, too often this momentum was lost between the ages of 11 to 14.
“Pupils often get very bored with the first stage of secondary school maths. There is too much emphasis on numbers and sums. People think maths should be all about arithmetic, but that is wrong.
Professor du Sautoy, who often plays a trumpet during lectures to illustrate the similarities between harmonics and the sine waves used to predict prime numbers, suggested that maths teaching should be similar to music teaching.He also suggested that teenagers struggling with maths may benefit from learning a musical instrument. “There is evidence that if you play an instrument during the early teenage years it stimulates the mathematical side of your brain. Both music and maths are about searching for and recognising patterns,” he said.He also advocates mixed-age group teaching for maths, believing that the subject has to be taught as a pyramid from bottom to top

news

The 'There is no branch of mathematics, however abstract, which may not someday be applied to the phenomena of the real world.'
-– Nicolai Lobachevsky
'If you think the math isn't important, you don't know the right math.'
Chris.Ferguson. Theorists who first created the mathematics that describe the behavior of the recently announced "invisibility cloak" have revealed a new analysis that may extend the current cloak's powers, enabling it to hide even actively radiating objects like a flashlight or cell phone.Allan Greenleaf, professor of mathematics at the University of Rochester, working with colleagues around the globe, has announced a mathematical theory that predicts some strange goings on inside the cloak—and that what happens inside is crucial to the cloak's effectiveness.
In October, David R. Smith, associate professor of electrical and computer engineering at Duke University, led a team that used a circular cloaking device to successfully bend microwaves around a copper disk as if the disk were invisible. In 2003, however, Greenleaf and his colleagues had already developed the mathematics of invisibility.

CARTOGRAPHY

Globe is, of course, the only possible medium for showing all geograpical relationships in true perspective...But globes have a serious drawback:they are limited in scale. A globe which would show a continent on the same scale as most standard maps would have to be two, three, perhaps four meters in diameter."
John Noble Wilford from The Mapmakers.
Maps are the primary tools by which spatial relationships are depicted. Maps therefore become important documents. There are several key elements that should be included each time a map is created in order to aid the viewer in understanding the communications of that map. The recording of spatial data on maps is known as cartography.

math history

How different concerns of society influenced mathematics. How the development of the concept of number is reflected in language. How the concept of how many led to arithmetic. How the concept of how much led to geometry. Efforts to keep time led to trigonometry. Navigation and associated astronomical problems led to logarithms [and more trigonometry]. Problems in artillery led to graphs. Both required an understanding of motion. Analytic geometry and calculus were invented in part to better understand motion. Statistics developed to understand problems in the social sciences.Surveys some of Neugebauer's remarkable discoveries on Babylonian mathematics, at a time when many of these discoveries were just made. Discusses notation, tables of squares, cubes, and n3+n2. Also exponentials, approximations to compound interest problems where we would use logarithms, a sum of a finite geometric series and a finite sum of squares. Geometric results, including the Pythagorean theorem, proportionality of sides in similar right triangles, a perpendicular bisecting the base in an isosceles triangle, the angle in a semicircle being a right angle, formulas for the circumference and area of a circle (using pi = 3).

ph.d at HRI

Candidates who wish to apply for ph.d programme in at HRI and IMSc
NEED NOTsend in any application. However, they MUST apply for the PhD Scholarships of the National Board for Higher Mathematics (NBHM) and appear for that screening test. The advertisement of the NBHM PhD Scholarships examination is expected to appear in national newspapers in the last quarter of each year. IMSc and HRI will directly get the test scores and copies of the applications from the NBHM and will independently send call letters for interview to successful candidates.
Date of NBHM screeing test: 27 January 2007 , LINK =http://www.mri.ernet.in/~mathjest/