Book of Proof 3rd Edition by Richard Hammack (PDF)

Description

This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions, calculus proofs and infinite cardinality.

User’s Reviews

Editorial Reviews: Review This is a wonderful book. Written as a text for a one-semester “transition to higher mathematics” course, it introduces the undergraduate to logic and proofs and to the basic objects and language used in higher mathematics. It is ideal for the many American undergraduates who come to college with little or no experience with proof or formal reasoning and need to be brought up to speed quickly in order to succeed in upper-level mathematics courses. — Mathematical Association of America, maa.org/press/maa-reviews/book-of-proof About the Author Richard Hammack is a professor of mathematics at Virginia Commonwealth University.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐It is. Good textbook. It belongs to.my library.

⭐This is by far the best-written math textbook AND most useful math text in it’s particular content area which I have ever read. I’m a certified High School Math Teacher in Texas, and I personally wrote a letter to the author of this book after reading it to praise his great achievement.Phenomenol – this should be on every math student’s shelve, and not just as a reference. This is the type of math book which one can read cover to cover WHILE LEARNING REAL, RIGOROUS MATH. I have read a lot of books, looking for one like this, and I’ve yet to find another anywhere near as good, though some books seem to have such a lofty ambition (though fail).This book far exceeded my expectations of what a math textbook could achieve.Buy this book. I bought two, and plan to buy more copies soon.

⭐As an M.Sc. in Electrical Engineering, I had to get a pretty extensive background in applied math, but almost nothing in theoretical math. I’ve lately taken an interest in various types of algebras, but I realized I didn’t have the theoretical background.In preparation for a (live) class in Abstract Algebra, I needed to learn to do formal proofs, and I didn’t want to sit through a full semester of that. So I looked for a self-study book, and “Book of Proof” turned out to be the book. It’s tailor-made for self-study, and as a bonus, it’s very affordable.Dr. Hammack literally starts at the beginning, with the basics of notation, sets, logic, etc. He introduces proofs gently enough to allow a determined self-student stay with it. There are plenty of exercises with odd-numbered solutions and these of course should not be skipped.Dr. Hammack then works through what amounts to a survey of various formal proof types, with plenty of examples and sufficient discussion. All of the major types are covered. My one minor criticism is that I think proof by induction could have used more attention, but you can supplement that elsewhere if you have the need or the urge.I wouldn’t call this book either “deep” or “comprehensive” but that’s not a criticism. The book is what it should be, a survey course, and it’s at least enough to prepare a student for the next steps. Combined with a course in Linear Algebra, Abstract Algebra will come within reach, as will other higher-level, deeper, and more specialized courses.Of course, it almost goes without saying that if you elect self-study, you’ve got to pay attention and work at things. No skimming! But I’m finding the payoff is high. This is clearly the right book for home use. It’s lucid, literate, well-constructed, and affordable. Hats off to Dr. Hammack for his contribution to the determined learner.

⭐I am an undergraduate freshman student majoring in maths and physics. This year I am taking a course of Discrete mathematics and I shall say it is one of the easiest courses I ever had. This is the book we use for our class and I truly enjoy it.The book is chaptered in a great, organized way. Every chapter has its subchapters and exercises after each subchapter. It is quick and easy studying with this book and all odd numbered problems have the solutions in the back, which is a nice way to check yourself. The author has a suggestion for professors or individual students to use as a study plan the schedule that he presented in the beginning of the book. The book is progressing through chapters and sometimes lack of the knowledge of previous chapters can become an obstacle in learning next ones.Discrete mathematics is the first steps of introduction of formal proof to maths students. This is one of the most important areas of mathematics and very fundamental. It is necessary to grasp the material of this course well to successfully progress further in mathematics.This is probably the best and most well-structured maths textbook I came across (it is also superlight) and I just love it!Online free copy is also available if you prefer to have it that way (brief google search will help you find it).Overall, regardless if you are a professor or a curious student, I definitely recommend this book for studying discrete maths.

⭐For a while I have developed an increasing interest in math. I am an active engineer with an advance degree. As such the curriculum mandated basic college level math (calculus, ordinary differential equations, linear algebra). Over time I realized that curriculum limited exposure to sufficient mathematics background needed to understand mathematics text. Consequently I find it difficult to understand mathematics text and perform my own proofs unless they are distilled and simplified by somebody into “engineering math”.This book wonderfully helps to fill some of the gap and perfect for self-study. The concepts are well organized and logically explained. The only minor downside is the exercises are generally rather simple. This often means the practice is somewhat mechanical. For most sections I would like to see a small set of challenge problems that step a outside of the material introduced in the section. Otherwise of you have none to little background in proofs (and few other foundational mathematics concepts) this book is a perfect tool to get you up to speed.

⭐Can’t commend this book enough; if you’ve heard of the vague but all too-cited term “mathematical maturity”, this book is exactly what you need to start developing it. Really, highly suggest this book for anyone transitioning to pure math. Hammack’s explanations for each concept are clear and intuitive, and the detailed solutions provided at the back of the book are immensely helpful.

⭐After 58 years I decided to revisit proofs (as in mathematical). I wish this book was available back then.

⭐This book covers a lot of material in a very readable way. It eschews a formal axiomatic approach in favour of introducing important ideas intuitively and using them to construct proofs. It gives a good overview to various mechanisms of proof and a bit of background on the history and development of the ideas that you won’t usually find in more formal texts on logic or set theory. It also includes exercises with solutions to the odd numbered ones.I’m not an academic and although it was my degree subject it’s a while since I’ve studied maths in a formal setting, but I’d say that this book would serve well as preparation for studying “proper” maths (I’d happily recommend it to someone who’s just finished their A levels and is about to embark on a degree) or even as an introduction pending further study in the foundations of mathematics.

⭐For any student who wants to read mathematics at undergraduate level should purchase this book. It is an introduction to mathematical proof and at its present price of approximately £8 is a good buy. I think you can download it free from the authors’ personal webpage.It has a large number of exercises to reinforce your understanding and some good illustrations.I do not know who published this book but it lacks a polished output and gives the impression that it has been printed on a local printer and bounded together; maybe this is why it can be sold at such a cheap price. Additionally it only gives solutions to odd numbered questions which can be off putting to a student who wants to use this book for self-learning.

⭐Clear explanations and well written. Lots of exercises and thoroughly worked examples. I expected it to be a very dry read, but not at all.

⭐Ich habe ein Buch gesucht um den Einstieg in die theoretische Mathematik (vor allem den Umgang mit Beweisen) zu lernen. In meinem Informatik Studium (Fokus ML) an einer FH liegt der Fokus weniger auf theoretischen Beweisen, da ich aber auf Dauer in die Forschung möchte und mich für Beweise interessiere brauchte ich ein Buch um den Einstieg zu schaffen (im Selbststudium) und schwerere Literatur verstehen zu können.Habe das Buch gekauft, um Bücher wie “Linear Algebra Done Right” besser zu verstehen, um damit die Grundlage für schwere Kost im ML Bereich zu schaffen wie z.B Bishop.Das Buch schafft es die theoretischen Grundlagen sehr leicht und vor allem VERSTÄNDLICH bei zu bringen. Habe das Gefühl, dass so etwas wie Beweise oft völlig unverständlicherweise viel zu kompliziert gelehrt werden, weil das Prinzip dahinter nicht erklärt wird. Dieses Buch schafft das aber grandios.Das Buch besitzt zahlreiche Aufgaben. Alle Aufgaben mit ungeraden Nummern haben dabei die Lösungen hinten im Buch stehen. Damit ist das Buch auch für das Selbststudium geeignet und ist nicht ausschließlich für die Durchführung eines Uni Kurses gedacht.Kann ich nur jedem empfehlen der den Einstieg von der anwendungsorientierten in die theoretische Mathematik sucht.Escribo la reseña despues de 4 meses de utilizar el libro y puedo decirles que es excelente.Abarca los temas de una manera comprensible para el lector y los ejercicios propuestos incluyen la respuesta con procedimiento, lo cual es bueno para verificar.Si eres estudiante de lic en matematicas no dudes en adquirir este libro.

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