In this book, Velleman does three things: Still, the part that I got through almost to proofs section was very insightful and fun. Introduction to the Representation Theory of Algebras. 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. Another chapter on functions.

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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 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,.

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## How to Prove It: A Structured Approach

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 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.

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## How to Prove It: A Structured Approach

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