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Goodreads helps you keep track of books you want to read. Want to Read saving…. Want to Read Currently Reading Read. Other editions. Enlarge cover. Error rating book. Refresh and try again. Open Preview See a Problem? Details if other :. Thanks for telling us about the problem. Return to Book Page. 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 brea 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. 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 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. Get A Copy. Paperback , 2nd Edition , pages. More Details Original Title. Other Editions Friend Reviews. To see what your friends thought of this book, please sign up.
To ask other readers questions about How to Prove It , please sign up. Lists with This Book. Community Reviews. Showing Average rating 4. Rating details. More filters. Sort order. Nov 30, Simon Vindum rated it it was amazing Shelves: computer-science.
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 fiel This is how math should be thought. The chapter on induction is especially useful if your field of practice is computer science. I would have liked it if solutions where available for a larger amount of the exercises.
Since there are a lot of them it would have been helpful if the author had marked a selected subset as being the most important ones.
Dec 14, Jessica Austin rated it it was amazing Shelves: robotics. Jun 28, 0vai5 rated it really liked it. 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 se Highly recommended for beginners as it helps tremendously in understanding the mathematical rigour. Later when armed with all the proofing techniques all of those proofs were revisited and reader can clearly see the difference in his understanding for reading and writing proofs.
All the techniques of proofs except induction are covered in chapter Post that, book introduced other topics like relations and functions and employs proof techniques for proving theorem in these topics. It was a great way to demonstrate that techniques learned for writing proofs are independent of any area and can be applied anywhere in mathematics. I loved the treatment of proof by contradiction and mathematical induction. Cracking the corresponding exercises was a very rewarding experience.
In many proofs when no approach seems to be working, proof by contradiction comes to the rescue. Similarly power of proof by induction was on display in solving many humongous problems.
All exercises were ordered from easy to moderate preparing the reader along the way to learn writing proofs for easier to challenging ones. Many exercises are built on top of the theorems from earlier exercises. This is a good thing as it helped me in two ways: revising the older chapters and discovering errors in my proofs. There were many exercises asking the reader if the given proof is correct.
Many times proof looked correct but turned out wrong because of a conceptual mistake. This helped tremendously in clearing many misconceptions. In most of the sections, author also explains about how he arrived at a solution which helped in understanding how to approach a problem.
Finally in the last chapter author picked up a relatively advanced topic and employs all the proof techniques learned. In this chapter author does not go into explaining the proof structure but writes in a mathematical rigour so that reader should be able to read those proofs and gets an overall idea about reading and writing proofs by giving more focus to the topic than the proof technique.
One small thing that could have been better is the treatment of empty sets. I got confused while solving many exercises and felt like missing on some concepts regarding empty sets specially while dealing with family of sets. To summarise, - Quantifiers are everywhere. Overall it was a great endeavour and an enriching experience. Originally written on my blog Sep 23, Benjamin Schneider rated it it was amazing. 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.
Jan 11, Achmed rated it it was amazing. 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. Oct 05, Eryk Banatt rated it really liked it.
The writing is clear, and I would recommend it to someone who had never encountered proofs before. The use I got out of it was more about practicing proofs rather than learning how to do them, but whenever I forgot something basic I could just go back and look and the explanations were not terribly bogged down by jargon.
Nov 30, THN rated it really liked it Shelves: maths-for-science. The author is very patient in explaining the details to readers, but sometimes it gets too lengthy and confusing. The content is correct and rigorous, but there are some small inaccuracies notation typos or nuances, in second edition.
Overall, this is a good book to start getting familiar with mathematical proofs without too much intimidation of reading a full proof by oneself. It would be better if some parts get more concise. Jul 11, Anthony James rated it really liked it Shelves: resume , stem. I should have read something like this years ago, at the end of secondary school or start of university.
I intend on returning to it as I skipped more and more of the exercises as I moved through the text. Highly recommend to people who don't like proofs! Oct 10, Ege Onur rated it really liked it. A book that teaches you how to construct well-typed formulas. Use some other book instead, and read this book as a complementary source. Jul 25, Mahdi Dibaiee rated it it was amazing Shelves: science , academic.
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. Sep 04, Henry Cooksley rated it really liked it.
How to Prove It: A Structured Approach
How to prove it : a structured approach / Daniel J. Velleman.