Proofs play a central role in advanced mathematics and theoretical computer science, yet many students struggle the first time they take a course in which proofs play a significant role. This bestselling text’s third edition helps students transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. Featuring over 150 new exercises and a new chapter on number theory, this new edition introduces students to the world of advanced mathematics through the mastery of 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 an analysis of techniques that can be used to build up complex proofs step by step, using detailed ‘scratch work’ sections to expose the machinery of proofs about numbers, sets, relations, and functions. Assuming no background beyond standard high school mathematics, this book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and, of course, mathematicians.
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How to Prove It: A Structured Approach
Original price was: $83,95.$19,99Current price is: $19,99.
PDF 26,47 MB • Pages: 470
gabriel moreira gonçalves –
Todo estudante de engenharia devia estudar esse livro antes de entrar em cálculo e álgebra
Math Customer –
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.
opalqnka –
The book is written in a clear manner, the proofs and reasoning are accessible and help develop the mathematical skills of the reader.
kz –
I had lots of mathematics related courses during my university years, but they were mostly about solving engineering/physics problems. This book (along with ‘Proofs from the Book’) gave me a proper introduction to mathematical proofs. It is easy to follow, with interesting examples and problems. I highly recommend this book, if you are interested in this topic.
Ikechukwu U. –
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.
Kirk Peters –
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.
Michelle B. –
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.
Kleinbaker –
If you know your boolean then this is a great next step.
long nguyen –
very good
Math Customer –
Lots of problems with lots of solutions. Many over my head! Lots to learn but if you want to the info is there.
Wayne Caissie –
I am almost done the first chapter and I am really happy with the quality of this book. I would buy this book a thousand times again if I had to. Totally worth every cent.
Joseph Elsisi –
Bought it from a goodwill seller
Math Customer –
Good for self teaching.
Alisson de Abreu –
O livro é muito bom.
Filip –
I am working on a PhD degree in the field of computational chemistry. In particular, I am interested in applying existing theoretical and computational methodologies to develop novel and efficient approaches towards studying organic small-molecule catalysts and predicting their chemical properties. Since I am originally a physical chemist by profession, this book has taught me something I’ve always been lacking: The ability to think to think like a mathematician. Sometimes when a certain concept in science is muddled with ambiguity, you have to distill it down to basic building blocks of pure logic and reason. I’ve learned a lot from this book and I would definitely recommend it to anyone who is willing to sharpen their mathematical skills.
Thomas Deniffel –
Great Book. The solutions are on page 397 to 452 (55 pages!) in case you are wondering.
Christopher Scott Kopech –
Not The Best Text At Teaching How To Write Proofs. First, This Text Is Very Verbose. Second, Clarity Is Lacking In Some Explanations. Third, The Text Does A Mediocre Job of explaining how to write proofs. Fourth – Richard Hammack’s “Book Of Proof” Is Far Better, More Rigorous, And More Concise.
This Book Is A Good Reference, But If You Are Thinking Of Buying This Book, You Need To Buy “Book Of Proof” As Well – Best Math Text I’ve Ever Read, and I’m a Certified High School Math Teacher in Texas.
J.M. –
Came in great condition. Very useful book.
Carlitos salazar –
Awesome awesome!
Ahmed Deq Abdullahi –
I love it, clear and great writing. The author gives very good examples and even though there is not solutions to all exercises at the end of the book, you learn so well that you can almost always verify your answers to be correct with great certainty.
One of my favorites –
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
RB –
Used this book to supplement a college math course.
Explanations are very clear and to the point with ample examples. Book is a perfect size for reading in transit. Only wished that more solutions are provided in the exercises.
Andrei –
I’m having an applied math major, but always struggled with the proofs. The book really helped to see and understand why certain reasoning has right to be a “proof” of a concept, and then structures the reasonings, leading to theorem proofs. There’s enough exercises with hints or solution to some. (Solutions to everything can also be found online if you study alone and wish to double check if your solution is OK).
I simply don’t know a similar book or any resource about proofreading and math reasoning, so it definitely should be on your shelf.
John2959 –
Just as it stated, It allows a structured approach to problem solving.
José Marcelo Medina Camacho –
Muy claro y el tema bien explicado, diferente a lo que he visto en otros del mismo tema, superrecomendadisimo
Tarek1611 –
Isaac Wolford –
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.
Joe B. –
Lessons are concise and clear with many worked out examples. Writing style is to the point but not dry. Exercises are appropriately difficult with solutions to selected exercises.
I bought two other books and this is my pick for proofs and mathematical reasoning for self-study.
Lucas Cavalcanti Rodrigues –
Livro fascinante. Gostaria de ter lido ele antes na vida. Saber lidar com provas e formalismo matemático é uma habilidade fundamental para qualquer curso de matemática ou matemática aplicada. Recomendo.