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1.

電子ブック
ＥＢ
1. Number Theory
Dorin Andrica, Titu Andreescu, Noam Elkies
出版情報: SpringerLink Books - AutoHoldings , Birkhäuser Boston, 2009
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Preface
Acknowledgments
Notation
Fundamentals / I：
Divisibility / 1：
Prime Numbers / 1.1：
The Greatest Common Divisor and Least Common Multiple / 1.3：
Odd and Even / 1.4：
Modular Arithmetic / 1.5：
Chinese Remainder Theorem / 1.6：
Numerical Systems / 1.7：
Representation of Integers in an Arbitrary Base / 1.7.1：
Divisibility Criteria in the Decimal System / 1.7.2：
Powers of Integers / 2：
Perfect Squares / 2.1：
Perfect Cubes / 2.2：
kth Powers of Integers, k at least 4 / 2.3：
Floor Function and Fractional Part / 3：
General Problems / 3.1：
Floor Function and Integer Points / 3.2：
A Useful Result / 3.3：
Digits of Numbers / 4：
The Last Digits of a Number / 4.1：
The Sum of the Digits of a Number / 4.2：
Other Problems Involving Digits / 4.3：
Basic Principles in Number Theory / 5：
Two Simple Principles / 5.1：
Extremal Arguments / 5.1.1：
The Pigeonhole Principle / 5.1.2：
Mathematical Induction / 5.2：
Infinite Descent / 5.3：
Inclusion-Exclusion / 5.4：
Arithmetic Functions / 6：
Multiplicative Functions / 6.1：
Number of Divisors / 6.2：
Sum of Divisors / 6.3：
Euler's Totient Function / 6.4：
Exponent of a Prime and Legendre's Formula / 6.5：
More on Divisibility / 7：
Congruences Modulo a Prime: Fermat's Little Theorem / 7.1：
Euler's Theorem / 7.2：
The Order of an Element / 7.3：
Wilson's Theorem / 7.4：
Diophantine Equations / 8：
Linear Diophantine Equations / 8.1：
Quadratic Diophantine Equations / 8.2：
The Pythagorean Equation / 8.2.1：
Pell's Equation / 8.2.2：
Other Quadratic Equations / 8.2.3：
Nonstandard Diophantine Equations / 8.3：
Cubic Equations / 8.3.1：
High-Order Polynomial Equations / 8.3.2：
Exponential Diophantine Equations / 8.3.3：
Some Special Problems in Number Theory / 9：
Quadratic Residues; the Legendre Symbol / 9.1：
Special Numbers / 9.2：
Fermat Numbers / 9.2.1：
Mersenne Numbers / 9.2.2：
Perfect Numbers / 9.2.3：
Sequences of Integers / 9.3：
Fibonacci and Lucas Sequences / 9.3.1：
Problems Involving Linear Recursive Relations / 9.3.2：
Nonstandard Sequences of Integers / 9.3.3：
Problems Involving Binomial Coefficients / 10：
Binomial Coefficients / 10.1：
Lucas's and Kummer's Theorems / 10.2：
Miscellaneous Problems / 11：
Solutions to Additional Problems / II：
Pythagorean Equations
Glossary
Bibliography
Index of Authors
Subject Index
Preface
Acknowledgments
Notation
2.

電子ブック
ＥＢ
2. Problems in Real Analysis
Teodora-Liliana Radulescu, Titu Andreescu, Vicentiu D. Radulescu
出版情報: SpringerLink Books - AutoHoldings , Springer New York, 2009
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Foreword
Preface
Acknowledgments
Abbreviations and Notation
Sequences, Series, and Limits / Part I：
Sequences / 1：
Main Definitions and Basic Results / 1.1：
Introductory Problems / 1.2：
Recurrent Sequences / 1.3：
Qualitative Results / 1.4：
Hardy's and Carleman's Inequalities / 1.5：
Independent Study Problems / 1.6：
Series / 2：
Elementary Problems / 2.1：
Convergent and Divergent Series / 2.3：
Infinite Products / 2.4：
Limits of Functions / 2.5：
Computing Limits / 3.1：
Qualitative Properties of Continuous and Differentiable Functions / 3.3：
Continuity / 4：
The Concept of Continuity and Basic Properties / 4.1：
The Intermediate Value Property / 4.2：
Types of Discontinuities / 4.4：
Fixed Points / 4.5：
Functional Equations and Inequalities / 4.6：
Qualitative Properties of Continuous Functions / 4.7：
Differentiability / 4.8：
The Concept of Derivative and Basic Properties / 5.1：
The Main Theorems / 5.2：
The Maximum Principle / 5.4：
Differential Equations and Inequalities / 5.5：
Applications to Convex Functions and Optimization / 5.6：
Convex Functions / 6：
Basic Properties of Convex Functions and Applications / 6.1：
Convexity versus Continuity and Differentiability / 6.3：
Inequalities and Extremum Problems / 6.4：
Basic Tools / 7.1：
Elementary Examples / 7.2：
Jensen, Young, Hölder, Minkowski, and Beyond / 7.3：
Optimization Problems / 7.4：
Antiderivatives, Riemann Integrability, and Applications / 7.5：
Antiderivatives / 8：
Main Definitions and Properties / 8.1：
Existence or Nonexistence of Antiderivatives / 8.2：
Riemann Integrability / 8.4：
Classes of Riemann Integrable Functions / 9.1：
Basic Rules for Computing Integrals / 9.4：
Riemann Iintegrals and Limits / 9.5：
Applications of the Integral Calculus / 9.6：
Overview / 10.1：
Integral Inequalities / 10.2：
Improper Integrals / 10.3：
Integrals and Series / 10.4：
Applications to Geometry / 10.5：
Appendix / 10.6：
Basic Elements of Set Theory / A：
Direct and Inverse Image of a Set / A.1：
Finite, Countable, and Uncountable Sets / A.2：
Topology of the Real Line / B：
Open and Closed Sets / B.1：
Some Distinguished Points / B.2：
Glossary
References
Index
Foreword
Preface
Acknowledgments
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