Putnam and Beyond 1st edition by Razvan Gelca 0387257659 9780387257655

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ISBN 10: 0387257659
ISBN 13:978-0387257655
Author:Razvan Gelca

Putnam and Beyond takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis in one and several variables, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. Using the W.L. Putnam Mathematical Competition for undergraduates as an inspiring symbol to build an appropriate math background for graduate studies in pure or applied mathematics, the reader is eased into transitioning from problem-solving at the high school level to the university and beyond, that is, to mathematical research.

Putnam and Beyond 1st Table of contents:

1.Methods of roof

argument by contradition

mathematical induction

the pigeonhole principle

invariants and semi-invariants

 

2.Algebra

identities and inequalities

polynomials

linear Algebra

abstract algebra

 

3.Real Analysis

Sequences and series

continuity, derivatives, and integrals

mutivariable differential and integral calculus

equations with functions as unkhows

 

4.Geometry and Trigonometry

Geometry

trigonometry

 

5.Number Theory

Integer-valued sequences and function

Arithmatic

diophantine equations

 

6.Combinatorial and Probability

combinatorials arguments in set theory

combinatorial geometry

graphs

binomial coefficients and counting methods

probability

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