Mathematics of choice : or how to count without counting / by Ivan Niven.

Format:

Book

Author/Creator:

Niven, Ivan, 1915-1999.

Series:

Anneli Lax New Mathematical Library ; 15

Language:

English

Subjects (All):

Combinatorial analysis.

Mathematical analysis.

Physical Description:

1 online resource (xi, 202 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Washington, D.C. : Mathematical Association of America, 1965.

Language Note:

English

Summary:

Counting lies at the heart of much mathematics, and Niven's subtitle is — How to count without counting. This is the whole art of combinatorics: permutations, combinations, binomial coefficients, the inclusion-exclusion principle, combinatorial probability, partitions of numbers, generating polynomials, the pigeonhole principle, and much more.

Contents:

Front Cover

Mathematics of Choice or How to Count Without Counting

Copyright Page

Contents

Preface

Chapter 1. Introductory Questions

Chapter 2. Permutations and Combinations

2.1 The Multiplication Principle

2.2 Factorials

2.3 Permutations

2.4 Zero Factorial

2.5 Combinations

2.6 Permutations of Things in a Circle

2.7 Summary

Chapter 3. Combinations and Binomial Coefficients

3.1 A Path Problem

3.2 Permutations of Things Not All Alike

3.3 Pascal's Formula for C(n, r)

3.4 The Binomial Expansion

3.5 The Multinomial Expansion

3.6 Pascal's Triangle

3.7 The Number of Subsets of a Set

3.8 Sums of Powers of Natural Numbers

3.9 Summary

Chapter 4. Some Special Distributions

4.1 Fibonacci Numbers

4.2 Linear Equations with Unit Coefficients

4.3 Combinations with Repetitions

4.4 Equations with Restricted Solutions

4.5 Summary

Chapter 5. The Inclusion-Exclusion Principle

Probability

5.1 A General Result

5.2 Applications to Equations and to Combinations with Repetitions

5.3 Derangements

5.4 Combinatorial Probability

5.5 Summary

Chapter 6. Partitions of an Integer

6.1 Graphs of Partitions

6.2 The Number of Partitions

6.3 Summary

Chapter 7. Generating Polynomials

7.1 Partitions and Products of Polynomials

7.2 Change for a Dollar Bill

7.3 Summary

Chapter 8. Distribution of Objects Not All Alike

8.1 Objects Different, Boxes Different

8.2 Objects Different, Boxes Alike (Partitions of a Set)

8.3 Objects Mixed, Boxes Different

8.4 Summary

Chapter 9. Configuration Problems

9.1 The Pigeonhole Principle

9.2 Chromatic Triangles

9.3 Separations of the Plane

9.4 Summary

Chapter 10. Mathematical Induction

10.1 The Principle of Mathematical Induction

10.2 Notation for Sums and Products

10.3 Summary.

Chapter 11. Interpretations of a Non-Associative Product

11.1 A Recursion Relation

11.2 The Development of an Explicit Formula

11.3 Proof of the Conjecture

11.4 A Formula for F(n)

11.5 Summary

Miscellaneous Problems

Answers and Solutions

Bibliography

Index.

Notes:

Title from publisher's bibliographic system (viewed on 02 Oct 2015).

Bibliography: p. [199]

Description based on print version record.

ISBN:

0-88385-930-0

OCLC:

929120318