Number Theory - Sailing on the Sea of Number Theory

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Contents:

• Convolutions of the von Mangoldt Function and Related Dirichlet Series
• Constructing New Non-congruent Numbers by Graph Theory
• Distribution of Units of an Algebraic Number Field Modulo an Ideal
• Sign Changes of Fourier Coefficients and Eigenvalues of Cusp Forms
• Shifted Convolution Sums of Fourier Coefficients of Cusp Forms
• Two Expositions on Arithmetic of Cubics
• Distribution of Points on Modular Hyperbolas
  

Math Puzzles and Games

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Contents:
Introduction

1. Number problems
2. Number patterns
3. Magic and party tricks with numbers
4. Magic squares and sliding-block puzzles
5. Illusions
6. Dominoes and dice
   

Math Proofs Demystified: A Self-Teaching Guide

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Contents:

Part One: The Rules of Reason

• The Basics of Proportional Logic
• How Sentences are Put Together
• Formalities and Techniques
• Vagaries of Logic
  

Key to Algebra_Book 4

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Contents:

• Polynomials
• Adding Polynomials
• Opposites of Polynomials
• Subtracting  Polynomials
• The Distributive Principle
• Factoring Out a Common Factor
• Monomials, Binomials and Trinomials
• Multiplying and Factoring Polynomials
• The Zero Product Rule

Everyday Math Demystified - A Self Teaching Guide

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Contents:

PART 1: EXPRESSING QUANTITIES

CHAPTER 1 Numbers and Arithmetic

• Sets
• Numbering Systems
• Integers
• Rational, Irrational, and Real Numb
• Number Operations
• More Principles Worth Memorizing
• Still More Principles
• Quiz

Elementary Number Theory, Group Theory, and Ramanujan Graphs

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Contents:

Chapter 1. Graph Theory

1.1. The Adjacency Matrix and Its Spectrum
1.2. Inequalities on the Spectral Gap
1.3. Asymptotic Behavior of Eigenvalues in Families of Expanders
1.4. Proof of the Asymptotic Behavior
1.5. Independence Number and Chromatic Number
1.6. Large Girth and Large Chromatic Number
1.7. Notes on Chapter 1

Encyclopedia of Mathematics

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Contents:

• “History of Equations and Algebra”
• “History of Calculus”
• “History of Functions”
• “History of Geometry”
• “History of Probability and Statistics”
• “History of Trigonometry”

Problems for the Mathematical Olympiads - From the First Team Selection Test to the IMO

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Contents:

I. Problems

• Chapter 1. GEOMETRY
• Chapter 2. NUMBER THEORY
• Chapter 3. COMBINATORICS
• Chapter 4. ALGEBRA

II. Solutions

• Chapter 1. GEOMETRY
• Chapter 2. NUMBER THEORY
• Chapter 3. COMBINATORICS
• Chapter 4. ALGEBRA

101 Problems in Algebra_From the Training of the USA IMO Team Enrichment Series Vol. 18

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Contents:
1. Introductory Problems
2. Advanced Problems
3. Solution to Introductory Problems.
4. Solution to Advanced Problems

104 Number Theory Problems - From the Training of the USA IMO Team

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Contents:

1 Foundations of Number Theory

• Divisibility
• Division Algorithm
• Primes
• The Fundamental Theorem of Arithmetic
• G.C.D.
• Euclidean Algorithm
• Bezout’s Identity
• L.C.M.
• The Number of Divisors
• The Sum of Divisors
• Modular Arithmetics
• Residue Classes