How to Read and Do Proofs: An Introduction to Mathematical Thought Processes

by Daniel Solow

This text makes a great supplement and provides a systematic approach for teaching undergraduate and graduate students how to read, understand, think about, and do proofs. The approach is to categorize, identify, and explain (at the student's level) the various techniques that are used repeatedly in all proofs, regardless of the subject in which the proofs arise. How to Read and Do Proofs also explains when each technique is likely to be used, based on certain key words that appear in the problem under consideration. Doing so enables students to choose a technique consciously, based on the form of the problem.

Genres: Mathematics, Nonfiction, Logic, Science, Textbooks, Computer Science, Stem

336 pages, Kindle Edition

First published January 1, 1982

Reviews

[Eno RoJo]

Reading Challenge 2020: 24. Un libro sobre un tema del que no sabes nada

Siempre había creído que las matemáticas no eran complicadas, hasta que llegué a tomar clases de análisis 😟

El problema es que nadie se toma la molestia en explicar como se hace una demostración ni la lógica que debe de seguir (lo que es valido, y lo que no es)😕

[Matt Young]

Most of the mathematics people are taught in school is simply calculation. Algebra, Trig, etc. all have their place but to get a real feel for what mathematics is and to glimpse its beauty you must get into abstraction. But first you'll need a primer on how to read and do proofs. This book is an excellent introduction to that. You'll be taking on Cantor in no time.

[Julie Moronuki]

This is a very solid introduction to proof techniques, well illustrated with examples and exercises. I particularly liked the extended examples in the appendices.

[Victoria Zabuzova]

Must read for high-school . Well, 'read' not so much as understanding of proofs with mathematics.

[Tuvalu]

Started reading in preparation for a proof writing class. While I cant say it prepared me a ton for the class, it was still a very interesting look at the logic behind proofs. The inclusion of proofs for other areas of mathematics is also very nice

[Aprilleigh]

I borrowed this from the university library to help me remember what I had learned about mathematical proofs years ago. It's surprisingly easy to read and takes a fairly direct approach to the material. I'm not sure how this approach would work for someone that wasn't already somewhat familiar with several of the proof methods, but the explanations were understandable even for those methods I had never encountered before.

He covers all the main proof methods and a couple others that are used only in specific circumstances. He includes an excellent summary of all the methods and where they are best used. Once you understand the various methods, that chart is a fantastic reference tool.

The examples used in the book cover a variety of mathematics courses: I saw proofs from elementary algebra, linear algebra, calculus, abstract algebra, etc. To be honest, I couldn't completely follow some of them without spending more time than I had to learn the necessary background, but I was still able to follow the explanations of how to use each proof method.

[Daniel Hoffman]

Very nice overview of various useful proof techniques and worked out examples in the back of the book. Read it in one sitting, and I would whip it out again as a reference material if I felt the need.

[Vasili]

Un libro muy bueno para entender de que van la partes de las matemáticas que no es sólo hacer cuentas. Sirve mucho para acomodar las idea si uno tiene ganas de realizar los ejercicios. Especialmente con el objetivo de programar.

[Francesca Fernandes]

a PHENOMENAL introduction to proof-writing. read it you won’t regret it!!!!

[Garrett]

The best introduction to proof writing out there.

[sbs transit]

Does what it says on the cover

[Orbeez eyeballs]

Structural and step by step. Best paired with Solow’s lectures on YouTube

[Tonatiuh Dávila]

Great book, easy to read / understand. The only problem that i had with it, is that if you've been trying to do proofs before reading it, the book is totally obsolete. Recommended for new Math students.

[Peter]

Very clear and simple - thank God.

[Adele]

Good, but hard to follow just with a reading at times.

[Vahid]

This book is a MUST read for anybody who wants to practice Logic, Math or even programming ..

[Michael Bond]

I wish I had this as an undergrad.

[Fatima]

CS103