Connecting Discrete Mathematics and Computer Science
Connecting Discrete Mathematics and Computer Science
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GBPComputer science majors taking a non-programming-based course like discrete mathematics might ask 'Why do I need to learn this?' Written with these students in mind, this text introduces the mathematical foundations of computer science by providing a comprehensive treatment of standard technical topics while simultaneously illustrating some of the broad-ranging applications of that material throughout the field. Chapters on core topics from discrete structures – like logic, proofs, number theory, counting, probability, graphs – are augmented with around 60 'computer science connections' pages introducing their applications: for example, game trees (logic), triangulation of scenes in computer graphics (induction), the Enigma machine (counting), algorithmic bias (relations), differential privacy (probability), and paired kidney transplants (graphs). Pedagogical features include 'Why You Might Care' sections, quick-reference chapter guides and key terms and results summaries, problem-solving and writing tips, 'Taking it Further' asides with more technical details, and around 1700 exercises, 435 worked examples, and 480 figures.
- Includes 1700 exercises (with an instructors' solutions manual), 435 worked examples, and 480 figures
- Covers all recommended topics for a Discrete Structures course in the ACM Curriculum Guidelines for Undergraduate Degree Programs in Computer Science
- Connects course material to programming, data structures, other core CS topics, and the real world by beginning each chapter with a 'why you might care' section and discussing how the material in each section is connected to CS through 60 'Computer Science Connections' pages
- Concludes each chapter with a quick-reference guide and summary of key terms and results
- Motivates students interested in more technical details with 'Taking it Further' asides, including alternate ways of thinking about a definition or why something is called the thing it's called
- Livens up the material with a conversational tone, and offers tips throughout for problem-solving and how to write up results
Reviews & endorsements
'Finally! I've spent years struggling to find a textbook that makes the topic of Discrete Structures relevant to Computer Science students, David Liben-Nowell has put forth a book that will make CS students invested in the material. He not only connects every topic to Computer Science but does so in a clear and entertaining way.' Dan Arena, Vanderbilt University
'Unlike most discrete math texts, here the computer science content and connections are woven extensively throughout, with “forward pointers” that can excite students about numerous computer science areas they will encounter in their future studies. In addition, the book is written TO students, not FOR faculty. It will be a joy to teach with!' Valerie Barr, Mount Holyoke College
'By foregrounding the connections between the fields, this outstanding textbook makes a compelling case for why computer science students should embrace the study of discrete mathematics. This is an approachable yet rigorous book, written with wit and verve, that I look forward to teaching from!' Raghuram Ramanujan, Davidson College
'David Liben-Nowell's Connecting Discrete Mathematics and Computer Science provides students with a beautifully motivated, clearly written, and accessible exploration of the mathematical foundations of computer science. The “Computer Science Connections” sections provide compelling applications of the mathematical content and the frequent “Taking in further” notes provide extra richness that add to the joy of the experience. This is a discrete math book that truly keeps the reader engaged!' Ran Libeskind-Hadas, Founding Chair of Integrated Sciences, Claremont McKenna College
'An inspired approach to the introductory discrete math course, illuminating the aesthetic appeal of the subject together with the profound and inextricable links that connect it to the core ideas of computing.' Jon Kleinberg, Cornell University
Product details
August 2022Hardback
9781009150491
690 pages
260 × 202 × 38 mm
1.77kg
Available
Table of Contents
- 1. On the point of this book
- 2. Basic data types
- 3. Logic
- 4. Proofs
- 5. Mathematical induction
- 6. Analysis of algorithms
- 7. Number theory
- 8. Relations
- 9. Counting
- 10. Probability
- 11. Graphs and trees
- 12. Looking forward.
