Most of the students struggle while understanding mathematics, even some find it the most boring subject because of a couple of reasons. In most of the cases they've been taught very poorly, hence their fundamental concepts remain unclear. They lose their self-esteem and gradually start detesting this subject. In my opinion, its instructor’s responsibility to understand his student’s learning approach. Instructor must present his lecture in such a way that not only engage his students but motivate them to explore the subject on their own.
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D. Singh Brar is in online Education program on WIZIQ since 2007. He is a math instructor and a researcher who loves perfectionism. He is an innovative and laborious teacher and an expert in teaching all types of mathematics. But his basic teaching interests are in advance mathematics which covers Calculus, Real and Complex Analysis, Differential Equations, General Topology, Abstract Algebra (Group, Ring), Linear Algebra, Functional Analysis (Hilbert & Banach Spaces), Numerical Analysis, Probability and Statistics, Operation Research (Linear Programming), Number theory.

He also offer training classes for International Universities entrances: GMAT, GRE, SAT and CAT (Quantitative and Verbal sections). He has a quite good experience of teaching GMAT and GRE. He has worked with some online education institutes like TCY Learning Solution (P) Ltd., Grey Matters Pvt. Ltd., IBS etc.

FEEL FREE TO CONTACT HIM:
E-mail: siman.brar.pu@gmail.com
Cell Phone # +1 519-701-0212

You can also follow him on his Official fb Page: www.facebook.com/BrAr.SimAn



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HIS REFLECTION ON MATHEMATICS

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What I know about Mathematics:

I get fascination from the relations of mathematics and the study of Nature. I feel that, somewhere math and art have mysterious ties, because creative mathematicians are inspired by the art of mathematics rather than by any prospect of ultimate usefulness. I think the mathematician’s best work is, a high perfect Art, as daring as the most secret dream of imagination.
The process of starting from a simple set of axioms and deriving almost every mathematical truth (putting Gödel’s Incompleteness to one side) is the prominence of the subject also it rightly viewed, possesses not only the truth, but supreme beauty. In mathematics, everything to me looks like a piece of artistic work that possesses uttermost beauty. For instance, we can look at Dedekind’s construction of real line. A natural phenomenon, petals from flowers sometimes grow in the Fibonacci sequence. Moreover we can look at e^ιπ+1=0 (Euler’s identity) known as most beautiful equation in mathematics unites five of the most fundamental aspects in mathematics into one equation, π e (both transcendental numbers), ι (Imaginary no.), 0 (Additive identity) and 1 (multiplicative identity). It also unites the two most fundamental operations in mathematics (addition and multiplication).
I think beauty is the first and last test for mathematics. I believe one’s intellect and aesthetic life remained uncompleted unless it includes an appreciation of the power and the beauty of mathematics. These creative arts and principles that reside in mathematics allure me and motivate me to do something radical in this beautiful subject.

Mathematical proof always fascinates me; without it we face wave after wave of contradiction, and an endless spiral of arguments as to what is true and what is not. So poof provides a rigorous axiomatic justification and means to make new discoveries, new developments or new connections, such as the relationship forged between elliptic curves and number theory through Wile's proof of Fermat's Last Theorem (Taming the Infinite, Ian Stewart, 2008), which make it so important.

Mathematics and Goal of my life:

I found mathematics is the study of patterns of structure and space; formally it is the investigation of axiomatically defined abstract forms by using logic and mathematical notations. Mathematics evolved through all the Civilizations of the world by maturity of human thought process and awareness of specification and classification of features of nature and then logical reasoning developed its base structure.

I believe Mathematics is the chief source of the belief in eternal and exact truth as well as a sensible intelligible world. The essence of mathematics resides in its freedom. The mathematics presents the most brilliant example of how pure reason that is the product of human thought may successfully enlarge its domain without the aid of experience. So Mathematics is one of the primary manifestations of the creative powers of the human mind, and it is the universal organ for world-understanding through theoretical construction. Therefore, Mathematics will remain an essential element of the knowledge and abilities which we have to teach, of the culture we have to transmit, to the next generation.

I think it’s (mathematics) major reason to enjoy special esteem, above all other sciences, is that its propositions are absolutely certain and indisputable. The Ultimate dream and mission of the Mathematical Sciences is to achieve the absolute Truth of the Universe by unfolding all the manifolds and mysteries of Nature. It is mathematics that always commands all the missions of scientific discoveries by providing them necessary platform to establish their root structure, which leads to expose the secrets of Nature. Goal of my life is to play my best role in this mission. Math in 20th century performed its outstanding role in the most profound and prominent research work. For instance we can look at the Mathematics of Great theories of the century like STR (Special theory of relativity), GTR (General theory of relativity), Super string theory, GUT’s (Grand unified field theories), M theory and K theory which came into existence after rigorous use of mathematics.

Beauty that I perceive in mathematical Equations:

It is a rather peculiar beauty, known only to those who come sufficiently close to it, different to describe in a language other than its own, and impervious to the language of the poetry. Beautiful equation F=ma, is Sir Isaac Newton’s most important discovery, nearly all over classical mechanics can be derived from this simple equation. F=G M1M2/r^2 , is an equation for gravitational attraction, NASA needs nothing more than this equation and few others in Newtonian mechanics when they plan the trajectory of the rocket for moon landing. Equation S=(C^3 A)/4h, describe the entropy of the black hole and derived by Stephen Hawking, not only this equation explores some interesting aspects of black hole but it also manages to unify many of the different discipline to the physics in one equation. E=mc^2 Is likely most wonderful and recognizable equation of the world, it not only unifies the concept of mass and energy, but it is also behind all the developments of the modern world by providing Nuclear Energy, on the other hand it gives us dreadful thought of destruction (Atomic bomb) that is still resisting nations from war. (Here I want to add that, John von Neumann was a USA’s mathematician who contributed to the development of Atom Bomb).

My Work Plan and Research to me:

As Henri Poincaré said “To force the future of mathematics the true method is to study its history and its present state.” (In whole), my work plan in mathematics is to, understand the history, foundation and structure of the subject, and to provide it a new vision, or to open up new doors of possibilities by capturing new dimensions of the subject after reviving the old visions of Masters because I strongly believe that the outgrowth of any field is not possible without thorough understanding of it. We can see, The Prince of mathematics, Gauss who introduced many new branches to the subject by reviving old Greek thought similarly in 1899 David Hilbert revived 2000 years old axiomatic vision of Euclid and made it more fundamental and rigorous by putting geometry in a formal axiomatic setting and introduced 21 basic axioms to its foundation. In most sciences one generation tears down what another has built and what one has established another undoes but in mathematics alone each generation adds a new story to the old structure and enriches it. Like; Zeno was concerned with three problems the infinitesimal, the infinite, and continuity. The finest intellects of each generation turn attacked these problems, finally after a great exertion on its historical study; Weierstrass, Dedekind, and Cantor have completely solved them. Their solutions are so clear as to leave no longer the slightest doubt or difficulty. This achievement was probably the greatest. I love this tradition in mathematics and want to make it continue.

“Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.” David Hilbert