Combinatorics Discrete Mathematics and its Applications 2nd Edition by Nicholas Loehr ISBN 131515336X 9781498780261

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ISBN 10: 131515336X
ISBN 13: 9781498780261
Author: Nicholas Loehr

Combinatorics, Second Edition is a well-rounded, general introduction to the subjects of enumerative, bijective, and algebraic combinatorics. The textbook emphasizes bijective proofs, which provide elegant solutions to counting problems by setting up one-to-one correspondences between two sets of combinatorial objects. The author has written the textbook to be accessible to readers without any prior background in abstract algebra or combinatorics.

Part I of the second edition develops an array of mathematical tools to solve counting problems: basic counting rules, recursions, inclusion-exclusion techniques, generating functions, bijective proofs, and linear algebraic methods. These tools are used to analyze combinatorial structures such as words, permutations, subsets, functions, graphs, trees, lattice paths, and much more.

Part II cover topics in algebraic combinatorics including group actions, permutation statistics, symmetric functions, and tableau combinatorics.

This edition provides greater coverage of the use of ordinary and exponential generating functions as a problem-solving tool. Along with two new chapters, several new sections, and improved exposition throughout, the textbook is brimming with many examples and exercises of various levels of difficulty.

Combinatorics Discrete Mathematics and its Applications 2nd Table of contents:

Chapter 1: Fundamentals of Counting

Chapter 2: Basic Counting Principles

Chapter 3: Permutations and Combinations

Chapter 4: Binomial Coefficients and the Binomial Theorem

Chapter 5: Discrete Probability

Chapter 6: Discrete Random Variables and Probability Distributions

Chapter 7: Combinatorial Identities and Binomial Identities

Chapter 8: Generating Functions

Chapter 9: Recurrence Relations

Chapter 10: Graph Theory

Chapter 11: Trees

Chapter 12: Advanced Counting Techniques

Chapter 13: Applications of Combinatorics

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Nicholas Loehr,Combinatorics Discrete,Mathematics,Applications