Deliver toUnited Arab Emirates
Book of Proof

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.


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:

5.0 out of 5 stars Exceptionally easy to read, tons of examples, solutions to odd #'ed practice, Cheap/free online

J.G. · January 25, 2025

I am writing this review as a thank you to the author Hammack. This book is a great boon for the math self study community. I cannot recommend it enough. Another very good book on introductions to proofs is written by Jay Cummings and I recommend that as well, but this book by Hammack is better for a few reasons I'll describe below.I own a few books that are introduction to Proofs but this is by far the easiest to read and has multiple great examples as well as plenty of practice problems for each topic. It is such an easy read that I can pull it out while in bed which I rarely am capable of doing with a math textbook. There are also solutions to odd numbered problems "chef's kiss".There is a free PDF online but the book was very cheap to purchase and is still good quality and doesn't fall apart with heavy use.This is one of the most "readable" math books I own and perfect for self study. There are even youtube channel " MathMajor " that follow this book and give lectures so you really can teach this to yourself just as well as a 3000 level math majors class. I'd suggest starting this directly after a Calc 2 class so you have sequences and series fresh in your memory. It is very approachable.The new sections in the 3rd addition include basic analysis with definitions for derivatives and limits. This is a topic that is good to include in a book like this because it can be daunting to read this in an analysis class for the first time. This book includes plenty of pictures and examples to help with some of these very conceptual ideas.

5.0 out of 5 stars Easy to Understand

S. · June 6, 2025

I've been reading the online version of this textbook and it is a very good textbook. It is easily digestible and has tons of practice problems. However the physical version has not arrived yet and I ordered used. I will update my review based on the condition of the physical copy

5.0 out of 5 stars Great Discrete maths textbook, very well structured!

E. · April 11, 2017

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.

5.0 out of 5 stars Best Mathematics Book I've Ever Read (I'm a Certified High School Math Teacher)

C.S.K. · February 15, 2022

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.

5.0 out of 5 stars Great Book!

M.T. · October 19, 2025

Great book for discrete mathematics. Many examples and answers to many of the homework problems.

4.0 out of 5 stars Try Hard But Sometimes.

M. · June 26, 2018

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.

Bom

E.H.N. · July 29, 2025

Bom

An approachable and affordable text for pure math students.

A.C. · July 8, 2019

I gave this book a five-star rating because I really appreciate what the author has done here in creating a high quality text at a low cost. This text would probably be most appropriate as a resource for a discrete math course. I am intending to use several sections of this text, as a resource for a math-literacy course for education majors that I teach. The tone of the book is somewhat casual for a pure math book, but the overall level of the book suggests it would be most appropriate for second or third year students majoring in math, or a closely related discipline such as physics or engineering, with a strong math concentration. It's inexpensive enough (freely available as a PDF download), approachable enough, and concise enough for an enterprising student, trying to improve their marks in a pure math course (or courses) to use independently as a supplementary resource.

Good choice.

M. · November 24, 2020

This is a gorgeous book, it is a lovely introduction to proof based mathematics. Give it a month or two and you will be good to go.

more than proofs

d. · December 5, 2017

A very good book for a first or second semester course on foundations for math undergrads, with a nice mix of rigour and play. I have adopted it as the main text for such a course. Though it is available as a free download, I recommend a purchase of the printed version by anyone seriously interested in its topics.

Book of Mathematical Proofs

P.&.Y. · August 9, 2025

This book is highly recommended for self studies in Mathematics

Book of Proof

Product ID: U0989472124
Condition: New

4.7

AED22198

Price includes VAT & Import Duties
Type: Paperback
Availability: In Stock

Quantity:

|

Order today to get by 7-14 business days

This item qualifies for free delivery

Returns & Warranty policies

Imported From: United States

At BOLO, we work hard to ensure the products you receive are new, genuine, and sourced from reputable suppliers.

BOLO is not an authorized or official retailer for most brands, nor are we affiliated with manufacturers unless specifically stated on a product page. Instead, we source verified sellers, authorized distributors or directly from the manufacturer.

Each product undergoes thorough inspection and verification at our consolidation and fulfilment centers to ensure it meets our strict authenticity and quality standards before being shipped and delivered to you.

If you ever have concerns regarding the authenticity of a product purchased from us, please contact Bolo Support. We will review your inquiry promptly and, if necessary, provide documentation verifying authenticity or offer a suitable resolution.

Your trust is our top priority, and we are committed to maintaining transparency and integrity in every transaction.

All product information, images, descriptions, and reviews originate from the manufacturer or from trusted sellers overseas. BOLO is not affiliated with, endorsed by, or an authorized retailer for most brands listed on our website unless stated otherwise.

While we strive to display accurate information, variations in packaging, labeling, instructions, or formulation may occasionally occur due to regional differences or supplier updates. For detailed or manufacturer-specific information, please contact the brand directly or reach out to BOLO Support for assistance.

Unless otherwise stated, all prices displayed on the product page include applicable taxes and import duties.

BOLO operates in accordance with the laws and regulations of United Arab Emirates. Any items found to be restricted or prohibited for sale within the UAE will be cancelled prior to shipment. We take proactive measures to ensure that only products permitted for sale in United Arab Emirates are listed on our website.

All items are shipped by air, and any products classified as “Dangerous Goods (DG)” under IATA regulations will be removed from the order and cancelled.

All orders are processed manually, and we make every effort to process them promptly once confirmed. Products cancelled due to the above reasons will be permanently removed from listings across the website.

Similar suggestions by Bolo

More from this brand

Similar items from “Discrete Mathematics”

Book of Proof

Product ID: U0989472124
Condition: New

4.7

Book of Proof-0
Type: Paperback

AED22198

Price includes VAT & Import Duties
Availability: In Stock

Quantity:

|

Order today to get by 7-14 business days

This item qualifies for free delivery

Returns & Warranty policies

Imported From: United States

At BOLO, we work hard to ensure the products you receive are new, genuine, and sourced from reputable suppliers.

BOLO is not an authorized or official retailer for most brands, nor are we affiliated with manufacturers unless specifically stated on a product page. Instead, we source verified sellers, authorized distributors or directly from the manufacturer.

Each product undergoes thorough inspection and verification at our consolidation and fulfilment centers to ensure it meets our strict authenticity and quality standards before being shipped and delivered to you.

If you ever have concerns regarding the authenticity of a product purchased from us, please contact Bolo Support. We will review your inquiry promptly and, if necessary, provide documentation verifying authenticity or offer a suitable resolution.

Your trust is our top priority, and we are committed to maintaining transparency and integrity in every transaction.

All product information, images, descriptions, and reviews originate from the manufacturer or from trusted sellers overseas. BOLO is not affiliated with, endorsed by, or an authorized retailer for most brands listed on our website unless stated otherwise.

While we strive to display accurate information, variations in packaging, labeling, instructions, or formulation may occasionally occur due to regional differences or supplier updates. For detailed or manufacturer-specific information, please contact the brand directly or reach out to BOLO Support for assistance.

Unless otherwise stated, all prices displayed on the product page include applicable taxes and import duties.

BOLO operates in accordance with the laws and regulations of United Arab Emirates. Any items found to be restricted or prohibited for sale within the UAE will be cancelled prior to shipment. We take proactive measures to ensure that only products permitted for sale in United Arab Emirates are listed on our website.

All items are shipped by air, and any products classified as “Dangerous Goods (DG)” under IATA regulations will be removed from the order and cancelled.

All orders are processed manually, and we make every effort to process them promptly once confirmed. Products cancelled due to the above reasons will be permanently removed from listings across the website.

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.


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:

5.0 out of 5 stars Exceptionally easy to read, tons of examples, solutions to odd #'ed practice, Cheap/free online

J.G. · January 25, 2025

I am writing this review as a thank you to the author Hammack. This book is a great boon for the math self study community. I cannot recommend it enough. Another very good book on introductions to proofs is written by Jay Cummings and I recommend that as well, but this book by Hammack is better for a few reasons I'll describe below.I own a few books that are introduction to Proofs but this is by far the easiest to read and has multiple great examples as well as plenty of practice problems for each topic. It is such an easy read that I can pull it out while in bed which I rarely am capable of doing with a math textbook. There are also solutions to odd numbered problems "chef's kiss".There is a free PDF online but the book was very cheap to purchase and is still good quality and doesn't fall apart with heavy use.This is one of the most "readable" math books I own and perfect for self study. There are even youtube channel " MathMajor " that follow this book and give lectures so you really can teach this to yourself just as well as a 3000 level math majors class. I'd suggest starting this directly after a Calc 2 class so you have sequences and series fresh in your memory. It is very approachable.The new sections in the 3rd addition include basic analysis with definitions for derivatives and limits. This is a topic that is good to include in a book like this because it can be daunting to read this in an analysis class for the first time. This book includes plenty of pictures and examples to help with some of these very conceptual ideas.

5.0 out of 5 stars Easy to Understand

S. · June 6, 2025

I've been reading the online version of this textbook and it is a very good textbook. It is easily digestible and has tons of practice problems. However the physical version has not arrived yet and I ordered used. I will update my review based on the condition of the physical copy

5.0 out of 5 stars Great Discrete maths textbook, very well structured!

E. · April 11, 2017

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.

5.0 out of 5 stars Best Mathematics Book I've Ever Read (I'm a Certified High School Math Teacher)

C.S.K. · February 15, 2022

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.

5.0 out of 5 stars Great Book!

M.T. · October 19, 2025

Great book for discrete mathematics. Many examples and answers to many of the homework problems.

4.0 out of 5 stars Try Hard But Sometimes.

M. · June 26, 2018

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.

Bom

E.H.N. · July 29, 2025

Bom

An approachable and affordable text for pure math students.

A.C. · July 8, 2019

I gave this book a five-star rating because I really appreciate what the author has done here in creating a high quality text at a low cost. This text would probably be most appropriate as a resource for a discrete math course. I am intending to use several sections of this text, as a resource for a math-literacy course for education majors that I teach. The tone of the book is somewhat casual for a pure math book, but the overall level of the book suggests it would be most appropriate for second or third year students majoring in math, or a closely related discipline such as physics or engineering, with a strong math concentration. It's inexpensive enough (freely available as a PDF download), approachable enough, and concise enough for an enterprising student, trying to improve their marks in a pure math course (or courses) to use independently as a supplementary resource.

Good choice.

M. · November 24, 2020

This is a gorgeous book, it is a lovely introduction to proof based mathematics. Give it a month or two and you will be good to go.

more than proofs

d. · December 5, 2017

A very good book for a first or second semester course on foundations for math undergrads, with a nice mix of rigour and play. I have adopted it as the main text for such a course. Though it is available as a free download, I recommend a purchase of the printed version by anyone seriously interested in its topics.

Book of Mathematical Proofs

P.&.Y. · August 9, 2025

This book is highly recommended for self studies in Mathematics

Similar suggestions by Bolo

More from this brand

Similar items from “Discrete Mathematics”