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.

Great book for discrete mathematics. Many examples and answers to many of the homework problems.

I've been reading the online version of this textbook and it is a very good textbook. It is easily digestible and has tons of practice problems. However the physical version has not arrived yet and I ordered used. I will update my review based on the condition of the physical copy

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 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 student of physics who has very little knowledge of abstract mathematics, this book really worked wonders. First things first, it has very clear and detailed notions. Every theorem, definition, and concept is explained through an example. Also, the author shows exceptional command over his area of experties, i.e., mathematic. Now to the cons, the paper quality is below average for a paper back. I personally do not like concepts, especially abstract concepts, to be explained with an example. They tend to muddle things. Moreover, sometimes the author tries a little too hard to explain a concept and instead ends up leaving the reader in a glorified puddle of confusion. All in all, a good book if you are willing to accept the above mentioned short comings. However, for a novice, this should be a good buy.

I read this book the summer before starting a bachelor's in mathematics and it changed my life

Bom

I gave this book a five-star rating because I really appreciate what the author has done here in creating a high quality text at a low cost. This text would probably be most appropriate as a resource for a discrete math course. I am intending to use several sections of this text, as a resource for a math-literacy course for education majors that I teach. The tone of the book is somewhat casual for a pure math book, but the overall level of the book suggests it would be most appropriate for second or third year students majoring in math, or a closely related discipline such as physics or engineering, with a strong math concentration. It's inexpensive enough (freely available as a PDF download), approachable enough, and concise enough for an enterprising student, trying to improve their marks in a pure math course (or courses) to use independently as a supplementary resource.

This is a gorgeous book, it is a lovely introduction to proof based mathematics. Give it a month or two and you will be good to go.

Ich habe ein Buch gesucht um den Einstieg in die theoretische Mathematik (vor allem den Umgang mit Beweisen) zu lernen. In meinem Informatik Studium (Fokus ML) an einer FH liegt der Fokus weniger auf theoretischen Beweisen, da ich aber auf Dauer in die Forschung möchte und mich für Beweise interessiere brauchte ich ein Buch um den Einstieg zu schaffen (im Selbststudium) und schwerere Literatur verstehen zu können. Habe das Buch gekauft, um Bücher wie "Linear Algebra Done Right" besser zu verstehen, um damit die Grundlage für schwere Kost im ML Bereich zu schaffen wie z.B Bishop. Das Buch schafft es die theoretischen Grundlagen sehr leicht und vor allem VERSTÄNDLICH bei zu bringen. Habe das Gefühl, dass so etwas wie Beweise oft völlig unverständlicherweise viel zu kompliziert gelehrt werden, weil das Prinzip dahinter nicht erklärt wird. Dieses Buch schafft das aber grandios. Das Buch besitzt zahlreiche Aufgaben. Alle Aufgaben mit ungeraden Nummern haben dabei die Lösungen hinten im Buch stehen. Damit ist das Buch auch für das Selbststudium geeignet und ist nicht ausschließlich für die Durchführung eines Uni Kurses gedacht. Kann ich nur jedem empfehlen der den Einstieg von der anwendungsorientierten in die theoretische Mathematik sucht.

This book is highly recommended for self studies in Mathematics