Customer Reviews

Mathematics: A Discrete Introduction

5 star:		(8)
4 star:		(1)
3 star:		(0)
2 star:		(1)
1 star:		(3)

 

 

This book is very clear. It explains most of the fundamentals of discrete mathematics, including logic, combinatorics, graph theory, probability, number theory, cryptography, and more. Things are clearly explained, and students are taught the basics of proof writing. Proof templates give the reader a skeleton for different proofs (such as direct, contradiction, induction, contrapositive, etc.). A great book!

This book explains, with simple examples complex material. He includes proof templates, that are helpful in the understanding of the material.

I would not recommend for Below College level.

Discrete mathematics is now a keystone course in the computer science major and a fundamental course in the mathematics major. The mathematics covered in the course is still somewhat open to interpretation, but far less than it has been in the past. I examined this book for possible use as a textbook and ended up recommending that it be used. At this time, it is the book being used for the discrete mathematics class at the college where I am employed.
It begins with a short explanation of what a mathematical proof is and some simple examples are given. Chapter 2 is called collections and covers lists, the basics of set theory and quantifiers. The next chapter covers counting and relations and chapter four is a more complex examination of the nature of mathematical proof. The remaining chapters are:

Chapter 5: Functions
Chapter 6: Probability
Chapter 7: Number theory
Chapter 8: Algebra
Chapter 9: Graphs
Chapter 10: Partially ordered sets

The coverage is complete, the writing is understandable and there are plenty of exercises at the end of the chapters. Solutions to many of the problems are found in appendices.
A sound introduction to discrete mathematics, this is a book that I can heartily recommend for use as a textbook. It covers what we in the department feel must be covered.

I had this book for my first class in the number theory & combinatorics realm, and this has been the best book I've used since. To respond to an earlier review, the errors in the proofs serve a very important function: they make you actually read the proof. The templates teach you how to recognize when a particular method of proof is required. My only regret is that I have sold the book after taking the class, and $140 is too steep to buy a fresh copy.

I was assigned this book for a class, but instead of using it as merely a reference for the assigned problems, as I usually do, I read it nearly cover-to-cover, enjoying the author's clear, casual prose. I've never been as pleasantly surprised by a textbook.

Yup definitely much more readable and a pleasure to read compared to the Rosen Discrete math book I was forced to use. Has some great examples, like how to use the Inclusion-Exclusion for instance, using Venn-diagrams to boot. Rosen book doesn't even bother and leaves it all in the exercises. Some of the word choice is patronizing or childish at times like "a ghastly formula" for example? The proof templates littered throughout the book would've really helped me with proofs on my tests since they are like cliff notes on solving them. There is nothing like that in the Rosen book and you'd need to actually go to class/lecture and hope the instructor gave you tips like that. I like this book while it might not be as rigorous as others it's honest. The authors even say so on the section on planar graphs."Some proofs in this section are not rigorous. We shall be honest with you concerning where we are not using full rigor." You don't see any of that in the Rosen book either. So if your current Discrete math book is putting you to sleep or headaches give this book a look.

I have used this book for self reading, and it was very useful.

I don't think this book is suitable for computer science\Engineering students, it is mostly mathematical-oriented, for them Rosen's book is better

The material is actually put forth in a pretty easy to understand way, but the problem is that the material is very difficult - and the back of the book provides absolutely zero answers. This resulted in me, more than once, thinking that I had an idea or concept understood and completing my homework, only to find on quiz or test day that I had the wrong idea.

Teachers, please do not assign this book! Or if you absolutely must assign this book, at least make sure to go over the homework in class.

I can understand some of the bad reviews on this textbook, but in context of being an intro, it is outstanding.

What does intro mean? Well it is for those do not understand the fundamentals of proof or theorems, and most of the material in this book.

Most discrete math books fail at one major topic of instruction, and that is proofs and induction. The authors struggle on instructing the students both the language and how to write proofs. The authors expect a specific level of sophistication in the student. And in most cases this might be true, depending on where this course fits in the cirriculum and who the students are taking the course. Math and engineering majors have a different level of background and confidence.

This textbook is really a great intro because of the method employed by the author to instruct. He introduces each topic from a conversational level and then brings in the more formal proofs and examples. He does this with everything so it builds up the students understanding of both the how and why so that a student not only understands the topic, but understands how the proof is constructed.

His instruction on proofs and induction will teach students the language of math from a very elementary level to the point where they will be able to follow more rigourous texts.

His coverage of graphs is brilliant, his instruction really connects the students with the subtle differences in the various theorems.

Advanced students will find this a boring text, but most students will take away a profound understanding of how to think and speak like a mathematian.

I used this textbook during a Discrete math class, during which I worked through the vast majority it. I am impressed with Discrete: A Modern Introduction's elegance, clear prose, and the thought-provoking and interesting questions it posed for exercises.

The book is roughly split into thirds: one section is on combinatorics, one on number theory, and another on graph theory. Discrete also gives a step-by-step guide on mathematical proofs in parallel with the material, which was a refreshing way to learn the more interesting proof techniques. I also found Appendix A, which contained hints for most of the odd problems, to be of the utmost use.

The greatest strength of Mathematics: A Discrete Introduction was it's problems, especially the proof-based questions, which were different from the worked out examples in order to be interesting, but were similar enough to the material covered to not be insurmountable. A few of the challenge problems in each chapter will likely leave you stumped for a while- it's best to read the more challenging problems and turn them over for a day or two.

I also liked the punny title- "Mathematics: A Discrete Introduction" versus "Mathematics: A Discreet Introduction." Intentional? The product of my sleep deprived college mind? I'll never know.

An excellent Discrete book.