Book of Proof Richard Hammack 9780982406205 Books
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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 and infinite cardinality.
Book of Proof Richard Hammack 9780982406205 Books
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.
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Book of Proof Richard Hammack 9780982406205 Books Reviews
My first encounter with this book was before I started my master's in CS. I wanted to review my math and found this book. This book has opened my mind to the way I understood numbers. It is extremely well written and has a great flow to it. Best math book I ever read.
Very clear, lots of examples of different types of proofs with some helpful, general ways to think through trickier proofs. Easy read. Lots of exercises with a lot of worked out answers in the back (odds).
I give five stars only for clarity. The author hits a very nice spot between rigor and understanding. The content does not claim any comprehensiveness, nonetheless the presentation leaves almost nothing to be desired. Kudos to the author. If you have read this lovely book and feel you still need to know more about proof, then the next step would be 'How To Prove It' by Velleman. That is a beast of a book.
For a student of physics who has very little knowledge of abstract mathematics, this book really worked wonders.
First things first, it has very clear and detailed notions. Every theorem, definition, and concept is explained through an example. Also, the author shows exceptional command over his area of experties, i.e., mathematic.
Now to the cons, the paper quality is below average for a paper back. I personally do not like concepts, especially abstract concepts, to be explained with an example. They tend to muddle things. Moreover, sometimes the author tries a little too hard to explain a concept and instead ends up leaving the reader in a glorified puddle of confusion.
All in all, a good book if you are willing to accept the above mentioned short comings. However, for a novice, this should be a good buy.
Excellent book. I'd never done any maths beyond year 10 (jr high school) and was given this as a supplemental text for a Discrete Mathematics course I was doing for computing. Needless to say I was completely out of my depth in the course. This book saved me and I passed. Since then my confidence with mathematics has grown and I have drawn on the principles in this book to understand other areas of mathematics not covered in the book such as Calculus.
What the book does best is reason. It presumes almost nothing of the reader and builds concepts from the very basic points incorporating formal definitions and proofs naturally as they are encountered.
I cannot recommend this book any more highly to people who are new to Mathematics.
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.
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.
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