Book of Proof

I am writing this review as a thank you to the author Hammack. This book is a great boon for the math self study community. I cannot recommend it enough. Another very good book on introductions to proofs is written by Jay Cummings and I recommend that as well, but this book by Hammack is better for a few reasons I'll describe below.I own a few books that are introduction to Proofs but this is by far the easiest to read and has multiple great examples as well as plenty of practice problems for each topic. It is such an easy read that I can pull it out while in bed which I rarely am capable of doing with a math textbook. There are also solutions to odd numbered problems "chef's kiss".There is a free PDF online but the book was very cheap to purchase and is still good quality and doesn't fall apart with heavy use.This is one of the most "readable" math books I own and perfect for self study. There are even youtube channel " MathMajor " that follow this book and give lectures so you really can teach this to yourself just as well as a 3000 level math majors class. I'd suggest starting this directly after a Calc 2 class so you have sequences and series fresh in your memory. It is very approachable.The new sections in the 3rd addition include basic analysis with definitions for derivatives and limits. This is a topic that is good to include in a book like this because it can be daunting to read this in an analysis class for the first time. This book includes plenty of pictures and examples to help with some of these very conceptual ideas.

I am an undergraduate freshman student majoring in maths and physics. This year I am taking a course of Discrete mathematics and I shall say it is one of the easiest courses I ever had. This is the book we use for our class and I truly enjoy it.The book is chaptered in a great, organized way. Every chapter has its subchapters and exercises after each subchapter. It is quick and easy studying with this book and all odd numbered problems have the solutions in the back, which is a nice way to check yourself. The author has a suggestion for professors or individual students to use as a study plan the schedule that he presented in the beginning of the book. The book is progressing through chapters and sometimes lack of the knowledge of previous chapters can become an obstacle in learning next ones.Discrete mathematics is the first steps of introduction of formal proof to maths students. This is one of the most important areas of mathematics and very fundamental. It is necessary to grasp the material of this course well to successfully progress further in mathematics.This is probably the best and most well-structured maths textbook I came across (it is also superlight) and I just love it!Online free copy is also available if you prefer to have it that way (brief google search will help you find it).Overall, regardless if you are a professor or a curious student, I definitely recommend this book for studying discrete maths.

For a while I have developed an increasing interest in math. I am an active engineer with an advance degree. As such the curriculum mandated basic college level math (calculus, ordinary differential equations, linear algebra). Over time I realized that curriculum limited exposure to sufficient mathematics background needed to understand mathematics text. Consequently I find it difficult to understand mathematics text and perform my own proofs unless they are distilled and simplified by somebody into "engineering math".This book wonderfully helps to fill some of the gap and perfect for self-study. The concepts are well organized and logically explained. The only minor downside is the exercises are generally rather simple. This often means the practice is somewhat mechanical. For most sections I would like to see a small set of challenge problems that step a outside of the material introduced in the section. Otherwise of you have none to little background in proofs (and few other foundational mathematics concepts) this book is a perfect tool to get you up to speed.

This is by far the best-written math textbook AND most useful math text in it's particular content area which I have ever read. I'm a certified High School Math Teacher in Texas, and I personally wrote a letter to the author of this book after reading it to praise his great achievement.Phenomenol - this should be on every math student's shelve, and not just as a reference. This is the type of math book which one can read cover to cover WHILE LEARNING REAL, RIGOROUS MATH. I have read a lot of books, looking for one like this, and I've yet to find another anywhere near as good, though some books seem to have such a lofty ambition (though fail).This book far exceeded my expectations of what a math textbook could achieve.Buy this book. I bought two, and plan to buy more copies soon.

I just got this book, and haven't read it through, but I have to say that just from looking it over, it's exactly what I was looking for. I take an intuitive approach to math... and as a result I'm kinda illiterate when it comes to proving things or following other peoples proofs. In the past I've skimmed over the rigorous parts to get to the parts connecting with my intuition. This has often left me with huge gaps in my understanding and difficulty communicating my understanding thoroughly.Lately I've been really motivated to fill those gaps and strengthen my overall mathematical literacy. I can tell this book is gonna be a huge help in grounding my intuition in basic mathematics!Imagine this: you're a physicist. like a lot of physicists you don't care as much about mathematical details. one day, suddenly and unexpectedly, you discover a deep mathematical result that mathematicians everywhere have been looking for!!! it's time to pick up this book and get that paper written ;)