Discrete Mathematics textbooks for undergraduates - MathOverflow

Discrete Mathematics textbooks for undergraduates

2012-08-01T11:59:17Z

For the first time, I will be teaching a course on Discrete Mathematics for electrical and computer undergraduates students.

I intend to focus on practical applications.

I would be grateful if people would suggest names of books/lecture notes on the subject. Thank you in advance!

Answer by Joel Reyes Noche for Discrete Mathematics textbooks for undergraduates

2012-08-01T12:42:53Z

Harold S. Stone's Discrete Mathematical Structures and their Applications (Science Research Associates, 1973) has applications of group theory to computer design (adders, dynamic memories) and applications of linear finite-state machines to linear feedback shift registers. You might want to use a newer text, though.

Answer by Joseph O'Rourke for Discrete Mathematics textbooks for undergraduates

2012-08-01T14:17:18Z

Discrete Mathematics and Its Applications, by Ken Rosen, 2012. Amazon link. Here is the publisher's description:

Discrete Mathematics and its Applications, Seventh Edition, is intended for one- or two-term introductory discrete mathematics courses taken by students from a wide variety of majors, including computer science, mathematics, and engineering. This renowned best-selling text, which has been used at over 500 institutions around the world, gives a focused introduction to the primary themes in a discrete mathematics course and demonstrates the relevance and practicality of discrete mathematics to a wide variety of real-world applications…from computer science to data networking, to psychology, to chemistry, to engineering, to linguistics, to biology, to business, and to many other important fields.

It is now in its 7th(!) edition. Here is a link to its table of contents. And here is a review (of the 5th edition) by Diane Spresser, which ends

... this is, overall, an excellent text, with an impressive supplemental package.

Answer by Stopple for Discrete Mathematics textbooks for undergraduates

2012-08-01T15:09:38Z

I like Concrete Mathematics by Graham, Knuth and Patashnik:

This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline.

Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study.

Answer by darij grinberg for Discrete Mathematics textbooks for undergraduates

2012-08-01T19:38:18Z

Lex Schrijver, who led a team redesigning the Dutch railway schedule, has a course in Combinatorial Optimization with a number of applications (although usually not at a very concrete level). I'm not always happy with the level of detail in the proofs in the text, but keep in mind that these are lecture notes and they're free. He also has a number of other texts on his website; it's a treasure trove.

This, of course, is "Hungarian" combinatorics. As for enumerative and algebraic combinatorics, I don't know of a source giving many applications (but then again, who needs applications if you can have universal properties?...).