Discrete Structures : DE (Undergraduate Texts in Mathematics)

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Discrete Structures : DE (Undergraduate Texts in Mathematics)

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  • 製本 Paperback:紙装版/ペーパーバック版
  • 商品コード 9783031734366

Description

The aim of this text is to introduce discrete mathematics to beginning students of mathematics or computer science. It does this by bringing some coherency into the seemingly incongruent subjects that compose discrete math, such as logic, set theory, algebra, and combinatorics. It emphasizes their theoretical foundations and illustrates proofs along the way. The book prepares readers for the analysis of algorithms by discussing asymptotic analysis and a discrete calculus for sums. The book also deduces combinatorial methods from the foundations that are laid out. Unlike other texts on this subject, there is a greater emphasis on foundational material that leads to a better understanding. To further assist the reader in grasping and practicing concepts, roughly 690 exercises are provided at various levels of difficulty. Readers are encouraged to study the examples in the text and solve as many of the exercises as possible.

The text is intended for freshman or sophomore undergraduate students in mathematics, computer science, or similar majors. The assumed background is precalculus. The chapter dependency chart included is designed to help students, independent readers, and instructors follow a systematic path for learning and teaching the material, with the option to explore material in later chapters.

Preface.- Notation.- I. Discrete Structures.- 1. Introduction.-2. Mathematical Arguments.-3. Sets.- 4. Proof by Induction.- 5. Equivalence Relations.- 6. Partial Orders and Lattices.- 7. Floor and Ceiling Functions.- 8. Number Theory.- II. Summation and Asymptotics.- 10. Asymptotic Analysis.- III. Combinatorics.- 11. Counting.- 12. Generating Functions.- 13. Recurrence Relations.- 14. Graphs.- 15. Probability.- Bibliography.- Index.

Andreas Klappenecker is Professor in the Department of Computer Science & Engineering, Texas A&M University. His research interests include quantum computing, image processing, and cryptography.

 

Hyunyoung Lee is Senior Lecturer in the Department of Computer Science & Engineering, Texas A&M University. Her research interests include distributed and parallel algorithms and systems, wireless mobile computing, fault-tolerant computing and reliable computing.

The book under review can be considered to be a textbook for a first course in discrete mathematics at the undergraduate level, for students with precalculus.  ... It begins by motivating the subject via the problem of finding a closed knight s tour. It is possible to cover significant parts of the book in a one-semester course, and the book is a good addition to the flourishing literature on discrete mathematics textbooks. (Manjil Pratim Saikia, zbMATH 1570.68002, 2026)