Surds

When we can't simplify a number to remove a square root (or cube root etc) then it is a surd.

Example: √2 (square root of 2) can't be simplified further so it is a surd

Example: √4 (square root of 4) can be simplified (to 2), so it is not a surd!

Have a look at some more examples:

Number	Simplified	As a Decimal	Surd or not?
√2	√2	1.4142135...(etc)	Surd
√3	√3	1.7320508...(etc)	Surd
√4	2	2	Not a surd
√¼	½	0.5	Not a surd
3√11	3√11	2.2239800...(etc)	Surd
3√27	3	3	Not a surd
5√3	5√3	1.2457309...(etc)	Surd

The surds have a decimal which goes on forever without repeating, and are Irrational Numbers.

ALGEBRA - EQUATION AND FORMULA

Equations and Formulas

What is an Equation?

An equation says that two things are equal. It will have an equals sign "=" like this:

x

+

2

=

6

That equations says: what is on the left (x + 2) is equal to what is on the right (6)

So an equation is like a statement "this equals that"

(Note: this equation has the solution x=4)

What is a Formula?

A formula is a fact or rule that uses mathematical symbols.

It will usually have:

• an equals sign (=)
• two or more variables (x, y, etc) that stand in for values we don't know yet

                 WILLIAM  TIMOTHY  GOWERS

                              Sir William Timothy Gowers, FRS (born 20 November 1963) is a British mathematician. He is a Royal Society Research Professor at the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge, where he also holds the Rouse Ball chair, and is a Fellow of Trinity College, Cambridge. In 1998, he received the Fields Medal for research connecting the fields of functional analysis and combinatorics.
  
                             Gowers has written several works popularising mathematics, including
 Mathematics: A Very Short Introduction (2002), which describes modern mathematical research for the general reader. He was consulted about the 2005 film Proof, starring Gwyneth Paltrow and Anthony Hopkins. He edited The Princeton Companion to Mathematics (2008), which traces the development of various branches and concepts of modern mathematics. For his work on this book, he won the 2011 Euler Book Prize of the Mathematical Association of America.

             MICHAEL  ATIYAH  CONTRIBUTION  TO

                               MATHEMATICS

           “One of the world's greatest living mathematicians, Sir Michael Atiyah has made fundamental contributions to many areas of mathematics, but especially to topology, geometry and analysis. From his first major contribution—topological K-theory—to his more recent work on quantum field theory, Sir Michael has been influential in the development of new theoretical tools and has supplied far-reaching insights. He is a notable collaborator, with his name linked with other outstanding mathematicians through their joint research. A superb lecturer, he possesses the ability to explain sophisticated mathematics in a simple geometric way.”

From the Abel Prize Foundation:

“The second Abel Prize has been awarded jointly to Michael Francis Atiyah and Isadore M. Singer. The Atiyah-Singer index theorem is one of the great landmarks of twentieth-century mathematics . . . . the culmination and crowning achievement of a more than one-hundred-year-old evolution of ideas, from Stokes’s theorem, which students learn in calculus classes, to sophisticated modern theories like Hodge’s theory of harmonic integrals and Hirzebruch’s signature theorem. The problem solved by the Atiyah-Singer theorem is truly ubiquitous. In the forty years since its discovery, the theorem has had innumerable applications, first in mathematics and then, beginning in the late 1970s, in theoretical physics: gauge theory, instantons, monopoles, string theory, the theory of anomalies, etc.”

               TERENCE TAO- MATHEMATICIAN

WORKS IN MATHEMATICS:

                                Terence Tao has done work in many different fields of mathematics (although as you can assume from Paul's focus on Tao's number theory work, arguably his most profound contributions have been in that field). Terence Tao specializes in partial differential equations, analytic number theory, harmonic analysis, combinations, matrix theory and ergodic theory. The actual contributions he has made are mainly in number theory, like the Green-Tao theorem, but he has made many other advances in many of the aforementioned fields, they are just not as profound as the Green-Tao theorem and some of his other working in number theory. Terence Tao is a mathematical genius by all definitions (also a genius in most other fields of academia), he has mastered most of the concepts in mathematics and has done research for many years in an attempt to better our understanding of the world through mathematics. The only way that I can truly stress the influence he has had in mathematics, without you having to understand any of the mathematics is to say that he won the Fields Medal, which is considered the "Nobel Prize of Mathematics" and is only awarded every four years.

                              C.S. SESHADRI

                       C.S. Seshadri FRS (born 29 February 1932) is an eminent Indian mathematician. He is the founder and Director-Emeritus of the Chennai Mathematical Institute, and is known for his work in algebraic geometry. The Seshadri constant is named after him.
He is a recipient of the Padma Bhushan in 2009,the third highest civilian honor in the country. Research work:

                Seshadri's main work is in algebraic geometry. His work with M S Narasimhan on unitary vector bundles and the Narasimhan–Seshadri theorem has influenced the field. His work on Geometric Invariant Theory and on Schubert varieties, in particular his introduction of standard monomial theory, is widely recognized. Seshadri's contributions include the creation of the Chennai Mathematical Institute, an institute for the study of mathematics in India.

                   NARENDRA  KARMARKAR

Karmarkar’s Famous algorithm

                           Karmarkar’s algorithm solves the various linear Programming problems in the polynomial time. These problems are mostly represented by a “n” variables and a “m” constraints. The previous used method for solving these type of problems consisted a lot of problem representation by a “x” sided solid with a “y” vertices, where all the solution was then approached by traversing it from the vertex tovertex. Karmarkar’s novel method approaches all the solution by method of cutting through the all the above solid in all its traversal.        

                      Consequently, the complex optimization problems are also solved much faster using the method of Karmarkar algorithm. A practical example of this type of efficiency is the solution to a very complex problem in the communications network optimization where all the solution time taken was reduced from the weeks to some days. His algorithm thus enables the faster business and various policy decisions. Karmarkar’s algorithm has also stimulated all the development of the several other used interior point methods, some of which are now used in the current codes for solving the linear programs.