**By Daniel J. Velleman,**

__How to Prove It: A Structured Approach__

Geared to preparing students to make the transition from solving problems to proving theorems, this text teaches them the techniques needed to read and write proofs The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted These concepts are used as the basis for a step by step breaGeared to preparing students to make the transition from solving problems to proving theorems, this text teaches them the techniques needed to read and write proofs The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted These concepts are used as the basis for a step by step breakdown of the most important techniques used in constructing proofs To help students construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software No background beyond standard high school mathematics is assumed Previous Edition Hb 1994 0 521 44116 1 Previous Edition Pb 1994 0 521 44663 5

This is how math should be thought It is a very interesting book that explains how mathematical proofs works from the bottom up In the process of doing that it also teaches discrete math The learning curve was just right something that is no easy to achieve Velleman explains things in a way that is far from being dry yet understandable and precise I believe everyone who comes in contact with mathematical proofs should read the book The chapter on induction is especially useful if your field of p [...]

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Working through this book was tremendously rewarding The book very logically and lucidly explained how proofs work and guides the reader through interesting exercises in logic and useful topics such as set theory and countability This book is excellent preparation for any rigorous math class that contains proofs as opposed to just calculations and numerical examples.This book is very accessible and demands from the student little in the way of prerequisite math knowledge.

A great book on mathematical proofs for someone with very limited prior knowledge.The exercises are great, though they are plenty and can take a considerable amount of time to work through.

Highly recommended for beginners as it helps tremendously in understanding the mathematical rigour.Author does not expect much from the reader and begins with very basic concepts and slowly progresses towards quantifiers, then set theory, relation and functions, mathematical induction and finally, infinite sets.Inside introduction, author gives proof of few theorems in an intuitive way Later when armed with all the proofing techniques all of those proofs were revisited and reader can clearly see [...]

How to Prove It is a wonderful textbook on the different techniques one can use to prove mathematical theorems using first year logic It is very well written from the point of view of someone with little mathematical knowledge beyond high school math As someone who enjoys systematic thinking, precision and rigour, I truly enjoyed the journey from simple, ordinary proofs to proofs involving different sizes of infinities And though I didn t quite understand everything, that is because I read the b [...]

I picked this book up because I had zero experience with proofs, and was seriously struggling while trying to learn math This is a fantastic and gentle first exposure to proofs the book walks you through basic logic, set theory, proof methods, basic number theory, etc.If you do the exercises, you ll have found that what initially seemed like an arbitrary set of rules have become a set of tools that feel completely natural Also note that there is no shortage of exercises you can do as many, or as [...]

The book delivers what it promises a structured approach to proofs It can be a bit challenging, but develops the theory from the ground up and walks the reader through at the beginning Towards the end, Velleman moves pretty quickly through the material, assuming the reader as absorbed all of the earlier material, which is fine, but it makes for some challenging sections The progression from sets to relations to functions to cardinality flowed well There are also many useful interesting exercises [...]

Man, I wish I had read this book BEFORE undergrad In this book, Velleman does three things describes basic concepts in Logic gives common proof strategies, with plenty of examples dives into set theory, defining functions, etcHe does all this assuming the reader is NOT a mathematician in fact, he does an excellent job of explaining a mathematician s thought process when trying to prove something.I highly recommend this book if you feel uncomfortable reading and or writing proofs, since it will [...]

This book demonstrates proofs and shows the underlying logical machinery behind them It focuses especially on the language of mathematical logic This is a good thing since most of the symbols might as well be from an alien language It is split into seven chapters with two appendices, a section on suggested further reading, a summary of proof techniques mentioned, and an index The book also mentions Proof Building Software, but I did not check to see if the link still worked or not.

How to Prove It is a wonderful textbook on the different techniques one can use to prove mathematical theorems using first year logic It is very well written from the point of view of someone with little mathematical knowledge beyond high school math I truly enjoyed the journey from simple, ordinary proofs to proofs involving different sizes of infinities This text was a great introduction to set theory and mathematical induction.

Great introduction for writing proofs for mathematics Guides you step by step until you write a perfect proof, providing different methods Would be a 5 star book if all the exercises would have an answer, offline or online It matters whether you are right or wrong, right Also no proof methods that are common in logic and algebra, like Natural Deduction, sequent calculus or axiomatic proof sytems like Hilberts.

Along with proof methods, this is an excellent explanation of and introduction to symbolic logic I m not mathematician, but I am interested in the subject and this book was a key addition to my mathematics library The only downside is that, like other non text books, there are only selected answers to the many exercises throughout the book.

Intense, yet very educational If you are familiar with the basics of propositional logic, feel free to skip the first chapter The excercises provided were sometimes a little out of topic and could easily drown a casual reader, but overall a great book.

I used this book for an introductory class I took on logic and set theory, and I really enjoyed using it Easy to understand, a smooth read, and plenty of problems examples to work through and gauge understanding

This book should have been read by everyone who took calculus, before they took it Mathematical induction has been improperly given a sharp learning curve by crappy teachers at my school For myself and I m sure many others this book amounts to a course missing from the math curriculum.

Great book as Mathematical Thinking books go Comprehensive and readable Plenty of examples doesn t do what many books do, which is to sacrifice accessibility to achieve mathematical elegance.

Awesome I used it in his class.

Exercises are boring, examples are boring, no thrill of discovery.

Witty, sharp, and helpful for detecting the bologna in your own decision making and of course in others.

Heh, that was kind of intense.

Book seems Ok but I have not found anything new in it

This is a very great introduction to logic and method of proof The author exemplifies each method by several interesting and classical problems It suits the best for the beginners in logic.