Books on Mathematical Proofs and Theory

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SUMMARY

The discussion centers on recommendations for books that effectively teach mathematical proofs and theory, particularly for students transitioning from multivariable calculus to differential equations. A notable suggestion is "Reading, Writing and Proving" by Ulrich Daepp and Pamela Gorkin, which is praised for its structured approach to proofs, starting with simple algebraic examples and progressing to more complex calculus-based proofs. The book is highlighted as beneficial for those struggling with the logical steps necessary for rigorous mathematical reasoning.

PREREQUISITES
  • Understanding of multivariable calculus concepts
  • Familiarity with differential equations
  • Basic knowledge of algebraic proofs
  • Experience with logical reasoning in mathematics
NEXT STEPS
  • Explore "Reading, Writing and Proving" by Ulrich Daepp and Pamela Gorkin
  • Research additional resources on rigorous mathematical proofs
  • Study techniques for improving logical reasoning in mathematics
  • Practice exercises in mathematical proof construction
USEFUL FOR

Students in mathematics, particularly those studying calculus and differential equations, educators seeking teaching materials, and anyone looking to enhance their skills in constructing and understanding mathematical proofs.

Lyuokdea
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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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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.
 

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