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Discrete Structures

Andreas Klappenecker Hyunyoung Lee

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Hardback

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English
Springer International Publishing AG
19 February 2025
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.
By:   ,
Imprint:   Springer International Publishing AG
Country of Publication:   Switzerland
Edition:   2024 ed.
Dimensions:   Height: 235mm,  Width: 155mm, 
ISBN:   9783031734335
ISBN 10:   3031734335
Series:   Undergraduate Texts in Mathematics
Pages:   423
Publication Date:  
Audience:   College/higher education ,  Primary
Format:   Hardback
Publisher's Status:   Active
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.

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