Need help transitioning from calculus to proof-based math? Check out this book!

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SUMMARY

The recommended resource for transitioning from calculus to proof-based mathematics is "An Introduction to Mathematical Reasoning" by Peter J Eccles. This book is specifically designed for individuals with no prior experience in mathematical proofs, including proof by induction. It covers a variety of mathematical fields and includes both questions and challenging problems to enhance understanding. A new edition of the book is forthcoming, ensuring its continued relevance for learners.

PREREQUISITES
  • Basic understanding of calculus concepts
  • Familiarity with mathematical terminology
  • Willingness to engage with proof techniques
  • Desire to improve logical reasoning skills
NEXT STEPS
  • Explore proof techniques such as proof by induction and contradiction
  • Study additional mathematical reasoning texts for broader perspectives
  • Practice solving problems from "An Introduction to Mathematical Reasoning"
  • Join study groups or forums focused on proof-based mathematics
USEFUL FOR

Students transitioning from calculus to higher-level mathematics, educators seeking teaching resources, and anyone interested in developing strong proof-writing skills.

ice109
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what's a good book to segue from a calc sequence to upper level proof based classes? i need something that presumes nothing about my mathematical reasoning abilities, like i don't even know how to do proof by induction.
 
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The best book in my opinion is An Introduction to Mathematical Reasoning by Peter J Eccles. It teaches you how do proofs, and covers a variety of mathematical fields. I myself learned to do proofs from this book. He is coming out without another edition later on. The book has questions and problems. The problems are harder than the questions, and some of them are challenging.
 

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