Books on Mathematical Proofs and Theory

In summary, the person is looking for a book that focuses on equations and proofs, specifically starting with simple algebraic proofs and progressing to more complex calculus-based proofs. They are currently finishing multivariable calculus and plan to study differential equations next quarter. They have received a suggestion for the book "Reading, Writing and Proving" by Ulrich Daepp and Pamela Gorkin, which they have read a third of and found helpful for learning how to do rigorous mathematical proofs. They are open to any other suggestions for books on this topic.
  • #1
Lyuokdea
154
0
I'm looking for a book that gives you many equations and goes through proofs etc. One of my weaknesses mathematically tends to be logically getting from one point to another when I'm not solving problems numerically and remembering what are and what are not legal steps to prove something. I'm currently in finishing multivariable calculus and am doing differential equations next quarter when I plan to be going through this stuff. However, I would like a book which kind of starts at the beginning with simple proofs that can be done algebraically and then moves through to more difficult calculus based proofs.

All suggestions are appreciated.

~Lyuokdea
 
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  • #2
I picked up "Reading, Writing and Proving", by Ulrich Daepp and Pamela Gorkin. I have read about a third of the book and wish I had the time to get back to the exercises. I too have had much trouble in learing how to do rigorous mathematical proofs (the only course I flunked at the university). It looks pretty good so far.
 
  • #3


One book that I highly recommend for learning mathematical proofs and theory is "How to Prove It: A Structured Approach" by Daniel J. Velleman. This book starts with the basics of logic and proof techniques and gradually builds up to more advanced topics such as set theory and combinatorics. It also includes plenty of exercises and examples to help you practice and solidify your understanding of the material.

Another great resource is "Mathematical Proofs: A Transition to Advanced Mathematics" by Gary Chartrand, Albert D. Polimeni, and Ping Zhang. This book covers a wide range of topics including number theory, combinatorics, and calculus, and provides clear explanations and step-by-step guidance on how to construct proofs.

Lastly, "The Art of Proof: Basic Training for Deeper Mathematics" by Matthias Beck and Ross Geoghegan is a fantastic book for beginners in proof writing. It covers the fundamentals of logic and proof techniques, and also includes interesting historical anecdotes and problems to keep you engaged.

I hope these suggestions help you in your search for a book on mathematical proofs and theory. Happy reading and best of luck in your studies!
 

1. What is the purpose of studying mathematical proofs and theory?

Studying mathematical proofs and theory allows us to understand the foundations of mathematics and how different concepts and theorems are derived. It also helps us to develop critical thinking and logical reasoning skills.

2. What are some popular books on mathematical proofs and theory?

Some popular books on mathematical proofs and theory include "How to Prove It: A Structured Approach" by Daniel J. Velleman, "Introduction to Mathematical Thinking" by Keith Devlin, and "The Art of Proof: Basic Training for Deeper Mathematics" by Matthias Beck and Ross Geoghegan.

3. Do I need a strong background in mathematics to read books on proofs and theory?

While a strong foundation in basic mathematics is helpful, many books on proofs and theory are written in a way that is accessible to beginners. As long as you have a willingness to learn and a basic understanding of algebra and geometry, you can benefit from reading these books.

4. How can studying mathematical proofs and theory benefit me in other fields?

Studying mathematical proofs and theory can help to develop logical thinking and problem-solving skills, which are valuable in many fields such as computer science, engineering, and economics. It can also improve analytical and critical thinking skills, which are helpful in any career.

5. Are there any online resources to supplement books on mathematical proofs and theory?

Yes, there are many online resources such as video lectures, practice problems, and interactive tutorials that can supplement books on mathematical proofs and theory. Some popular websites for this include Khan Academy, Brilliant, and Coursera.

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