Mathematical proofs a transition to advanced mathematics

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 ·  148 ratings  ·  11 reviews

Start your review of Mathematical Proofs: A Transition to Advanced Mathematics

Sep 17, 2017 Justin Ritter rated it really liked it

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!

Jun 10, 2022 Yannick rated it it was amazing

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

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.

...more

Aug 16, 2022 Nasir Ali rated it it was amazing

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 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. ...more

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.

Dec 09, 2021 Beth G rated it it was amazing

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! 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! ...more

Jan 25, 2022 Dayton Outar rated it it was amazing

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.

Topology proofs looking real tasty.

Feb 24, 2014 CR rated it liked it

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. 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. ...more

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. 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. ...more

Dec 08, 2014 Thomas Bell rated it really liked it

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.

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.

...more

Gary Theodore Chartrand is a professor emeritus of mathematics at Western Michigan University

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