How to Prove It: A Structured Approach

Nice structure overall, good quality and great illustrations.

This book is very well done and is quite engaging. It has good practice problems and is really quite thorough. Overall a very solid choice for learning proofs.

Wow, wow, wow. This is definitely the best math book I have ever read. I am currently starting chapter 3, and have worked through all the examples and exercises so far. This book covers everything one should learn in a discrete math/introduction to proofs course and a little bit more.There are plenty of examples, and the exercises are very accessible while still being nontrivial. There are solutions to some problems in the back of the book, but many of the exercises are written in such a way that you can verify the answers yourself.Physically, the book is flawless. Extremely high quality pages, large font size, and a smaller frame closer to the size of a novel.

If you study this book well, you will become highly skilled in doing mathematical proofs, but not just. After having only gone thoroughly through the first chapters, you will be so skilled that you can skip the material at the beginning of many math textbooks that review set theory, etc. For instance, Munkres, Topology. The material at the beginning of the book becomes an utter triviality. Your understanding of proofs in Real Analysis textbooks will be ameliorated. I can not fully explain how this will help you.I personally read How to Read and Do Proofs, Solow, but after going through that textbook then picking up this one. I would advise you to not bother with Solow's text. He makes up his own terminology for things that already exist, and it's kind of handwavy. You will find that you have to relearn what you're doing if you read his, but you will see where he was coming from on his techniques. His techniques are wrong, but there is a better way. Use this book. I never give anything 5 stars. 4 is the max I rate out of 5; it would be 9 stars, if it were up to 10, etc.Buy this book, study it, go back to the beginning of the book, and review it, just like you would if you were taking a college exam on the material. Ensure your mastery. You will not regret it.

It's a great introduction for math proofs, and not only that, it has a wide variety of exercises some of them pretty challenging. It's a great way to study and learn how to write mathematical proofs

Just as it stated, It allows a structured approach to problem solving.

This is a remarkable book! It focuses narrowly on mathematical logic, set theory, and the application of both to theorem-proving. In practice this works very well, provided the reader is willing to read the text and the examples carefully, and provided that he or she is willing to put the work into the provided exercises. This is the most useful math book I have ever opened, and I think it's rather accessible for what it is.

I discovered that this is an additional resource recommended by my Real Analysis professor. The book covers in depth several proof methods and structures at a graduate level.