Problems from the book 2nd Edition Edition by Titu Andreescu, Gabriel Dospinescu ISBN 978-0979926907 0979926904
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Product details:
ISBN 10: 0979926904
ISBN 13: 978-0979926907
Author: Titu Andreescu, Gabriel Dospinescu
The authors provide a combination of enthusiasm and experience which will delight any reader. In this volume they present innumerable beautiful results, intriguing problems, and ingenious solutions. The problems range from elementary gems to deep truths. A trully delightful and highly instructive book, this will prepare the engaged reader not only for any mathematics competition they may enter but also for a life time of mathematical enjoyment. A must for the bookshelves of both aspiring and seasoned mathematicians.
Table of contents:
1 Some Useful Substitutions
1.1 Theory and examples
1.2 Problems for training
2 Always Cauchy-Schwarz…
2.1 Theory and examples
2.2 Problems for training
3 Look at the Exponent
3.1 Theory and examples
3.2 Problems for training
4 Primes and Squares
4.1 Theory and examples
4.2 Problems for training
5 T2’s Lemma
5.1 Theory and examples
5.2 Problems for training
6 Some Classical Problems in Extremal Graph Theory
6.1 Theory and examples
6.2 Problems for training
7 Complex Combinatorics
7.1 Theory and examples
7.2 Problems for training
8 Formal Series Revisited
8.1 Theory and examples
8.2 Problems for training
9 A Brief Introduction to Algebraic Number Theory
9.1 Theory and examples
9.2 Problems for training
10 Arithmetic Properties of Polynomials
10.1 Theory and examples
10.2 Problems for training
11 Lagrange Interpolation Formula
11.1 Theory and examples
11.2 Problems for training
12 Higher Algebra in Combinatorics
12.1 Theory and examples
12.2 Problems for training
13 Geometry and Numbers
13.1 Theory and examples
13.2 Problems for training
14 The Smaller, the Better
14.1 Theory and examples
14.2 Problems for training
15 Density and Regular Distribution
15.1 Theory and examples
15.2 Problems for training
16 The Digit Sum of a Positive Integer
16.1 Theory and examples
16.2 Problems for training
17 At the Border of Analysis and Number Theory
17.1 Theory and examples
17.2 Problems for training
18 Quadratic Reciprocity
18.1 Theory and examples
18.2 Problems for training
19 Solving Elementary Inequalities Using Integrals
19.1 Theory and examples
19.2 Problems for training
20 Pigeonhole Principle Revisited
20.1 Theory and examples
20.2 Problems for training
21 Some Useful Irreducibility Criteria
21.1 Theory and examples
21.2 Problems for training
22 Cycles, Paths, and Other Ways
22.1 Theory and examples
22.2 Problems for training
23 Some Special Applications of Polynomials
23.1 Theory and examples
23.2 Problems for training
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Tags: Titu Andreescu, Gabriel Dospinescu, the book