Book of Proof

Superb 👌

A very good book for a first or second semester course on foundations for math undergrads, with a nice mix of rigour and play. I have adopted it as the main text for such a course. Though it is available as a free download, I recommend a purchase of the printed version by anyone seriously interested in its topics.

Every definition, theorem & fact is substantiated with more than one example. Awesome book for beginners in abstract mathematics.

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.

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.

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.