What do you think?
Rate this book
Mathematical Proofs: Pearson New International Edition
Mathematical A Transition to Advanced Mathematics, 2/e, prepares students for the more abstract mathematics courses that follow calculus. This text introduces students to proof techniques and writing proofs of their own. As such, it is an introduction to the mathematics enterprise, providing solid introductions to relations, functions, and cardinalities of sets. KEY TOPICS : Communicating Mathematics, Sets, Logic, Direct Proof and Proof by Contrapositive, More on Direct Proof and Proof by Contrapositive, Existence and Proof by Contradiction, Mathematical Induction, Prove or Disprove, Equivalence Relations, Functions, Cardinalities of Sets, Proofs in Number Theory, Proofs in Calculus, Proofs in Group Theory. MARKET : For all readers interested in advanced mathematics and logic.
424 pages, Paperback
First published May 28, 2002
32 people are currently reading
797 people want to read
About the author
Gary Chartrand
29 books11 followersGary Theodore Chartrand is a professor emeritus of mathematics at Western Michigan University
Ratings & Reviews
Friends & Following
Create a free account to discover what your friends think of this book!
Community Reviews
Displaying 1 - 14 of 14 reviews
September 18, 2017
This is the book I should have been given for my introduction to theoretical math. Instead, I was taught to mechanically handle epsilon-delta proofs and struggled with proofs in later classes. This book provides a great number of concise but rigorous proofs that build confidence for tackling future subjects. Great read!
June 10, 2022
It is sooo good. Self-studying pure mathematics is a hard undertaking. Anyone who ever tried knows that. This book makes it easier than any university course I have ever taken. Working carefully and slowly through this book, doing all exercises and afterwards checking the solutions manual, honestly feels like having a really good teacher.
I recommend 4th edition though. It includes chapters for intermediate and fairly advanced topics like group theory, ring theory, metric spaces, topology, real analysis, linear algebra etc.
I recommend 4th edition though. It includes chapters for intermediate and fairly advanced topics like group theory, ring theory, metric spaces, topology, real analysis, linear algebra etc.
September 10, 2025
This was one of the best texts I've read in my career (while taking MTH 299 at Michigan State University). Really clearly explained (in tandem with my Prof. David Seal's teaching): direct proof, proof by contrapositive, proof by contradiction, and induction-based proofs (and concepts in set theory). Highly recommend, this text is game-changing.
Prof. Seal's website, which could be used alongside this book, is still active (as of 09/2025):
https://users.math.msu.edu/users/seal...
Prof. Seal's website, which could be used alongside this book, is still active (as of 09/2025):
https://users.math.msu.edu/users/seal...
December 28, 2022
Don't usually rate/review textbooks but I couldn't let this one slide.
To begin things, the book surely lives upto what it promises by providing a complete, comprehensive and swift introduction to everything it covers. It begins with Sets and Logics, and proceeds all the way to abstract algebra, covering alot of ground but while maintaining it's quality throughout, giving one the unfiltered essence of pure mathematics.
As a Physics Major, one would routinely encounter numerous math subjects but whenever I find a textbook and try to go through them, I commonly get lost in mathematical literature, rigorous notations and the author always assuming you know more than you would while leaving major theorems and lemmas as an exercise for the reader. The book provides solutions to all these problems, as for the proofs themselves, I rarely felt like referring to another source or googling the matter hand, as any proof out of the ordinary would either have a section of 'proof strategy' before the formal one or contain a 'proof analysis' afterwards. All in all, an engaging and fruitful book, would recommend to anyone (with a little background to basic math and single variable calculus) willing to dive deeper into advanced mathematics.
To begin things, the book surely lives upto what it promises by providing a complete, comprehensive and swift introduction to everything it covers. It begins with Sets and Logics, and proceeds all the way to abstract algebra, covering alot of ground but while maintaining it's quality throughout, giving one the unfiltered essence of pure mathematics.
As a Physics Major, one would routinely encounter numerous math subjects but whenever I find a textbook and try to go through them, I commonly get lost in mathematical literature, rigorous notations and the author always assuming you know more than you would while leaving major theorems and lemmas as an exercise for the reader. The book provides solutions to all these problems, as for the proofs themselves, I rarely felt like referring to another source or googling the matter hand, as any proof out of the ordinary would either have a section of 'proof strategy' before the formal one or contain a 'proof analysis' afterwards. All in all, an engaging and fruitful book, would recommend to anyone (with a little background to basic math and single variable calculus) willing to dive deeper into advanced mathematics.
December 9, 2014
Yay! Finally finished reading this book - and teaching it to my students. I really liked it actually, and yes, although I didn't teach sections 12.5 or 12.6 or chapter 13, I did actually read those as well. :-)
This book is not for everyone. At all. Just letting you know.
This book is not for everyone. At all. Just letting you know.
December 9, 2021
This is a really nice text. It's written in an accessible and student-friendly style that doesn't sacrifice content or clarity. Highly recommended to anyone looking to build a strong foundation for proofs!
March 17, 2024
An absolute tour de force of a book! Covers the often cumbersome transition between elementary mathematics and university mathematics with a precise clarity as well as providing ample amounts of examples and exercises along the way which further aid the reader. The book also stands out in way of explaining proofs immediately after they are given allowing the reader less familiar with proofs to further appreciate the reasoning and logic behind proofs which has great pedagogical value.
The book while being large in scope none the less never feels dense to the reader as there is a great amount of clarity in the writing style as well as not rushing the reader at any point. I also like how the book starts with a discussion on mathematical writing (how to communicate mathematics) which certainly like all forms of writing encompasses certain tradition and styles. The all to easy trap of the overuse of mathematical symbols in proof writing is discussed for example as well as taking care not to mix words and symbols.
The book take great care to cover all proof types (direct proof, induction, proof by contradiction...) which proceeds by easing the reader into topics such as equivalence relations, functions, infinite sets before ending with related proofs in various fields such as calculus and number theory.
In all this would on top of my list of recommendations for transitioning from high school mathematics to university mathematics (or perhaps for the advanced high school student). Cannot recommend this book enough.
Note: I don't like the star rating and as such I only rate books based upon one star or five stars corresponding to the in my opinion preferable rating system of thumbs up/down. This later rating system increases in my humble opinion the degree to which the reader is likely to engage with a review instead of merely glancing at the number of stars of a given book.)
The book while being large in scope none the less never feels dense to the reader as there is a great amount of clarity in the writing style as well as not rushing the reader at any point. I also like how the book starts with a discussion on mathematical writing (how to communicate mathematics) which certainly like all forms of writing encompasses certain tradition and styles. The all to easy trap of the overuse of mathematical symbols in proof writing is discussed for example as well as taking care not to mix words and symbols.
The book take great care to cover all proof types (direct proof, induction, proof by contradiction...) which proceeds by easing the reader into topics such as equivalence relations, functions, infinite sets before ending with related proofs in various fields such as calculus and number theory.
In all this would on top of my list of recommendations for transitioning from high school mathematics to university mathematics (or perhaps for the advanced high school student). Cannot recommend this book enough.
Note: I don't like the star rating and as such I only rate books based upon one star or five stars corresponding to the in my opinion preferable rating system of thumbs up/down. This later rating system increases in my humble opinion the degree to which the reader is likely to engage with a review instead of merely glancing at the number of stars of a given book.)
September 22, 2020
While I have done an undergraduate course on proofs (HUL251 Intro to logic @ IIT Delhi), this book was a really helpful book for theory i.e. elements of mathematical proof (sets, relations, induction, contradiction, truth tables etc.) and practice i.e. the last half of the book on proofs in different branches of mathematics. Helped me a lot in beginning of a course on Numerical Linear Algebra.
January 25, 2022
I think this is an excellent book.
The proofs are brief and straight to the point. Sometimes, I had to find a few YouTube videos to help me grasp the concepts. But very good material and it will prove to be useful to make reference to when reading other Mathematics books.
The proofs are brief and straight to the point. Sometimes, I had to find a few YouTube videos to help me grasp the concepts. But very good material and it will prove to be useful to make reference to when reading other Mathematics books.
January 28, 2022
Topology proofs looking real tasty.
November 7, 2024
A great starting point for studying logic and proofs .
March 6, 2014
Clear, precise, and altogether excellent introduction of proofs and basic set theory. I'm glad historical context and facts about the development of logic were given (a move few maths textbooks have the balls to do). If you're looking to get into real maths, not the BS taught up to college, this is a great starting point.
February 10, 2015
I can't say enough good things about this textbooks -- it's definitely one of the best I have ever used. It's small and extremely concise and not burdened by tons of graphics and sidebars and sidenotes. Just exactly what you need to know, broken down into small pieces.
July 27, 2016
Muuuch better than Girls & Sex: Navigating the Complicated New Landscape!!
Displaying 1 - 14 of 14 reviews