ler totalmente Prove It?: The Beginning

Prove It?: The Beginning

A friendly introduction to mathematical proofs written by and for students and math competition enthusiasts.

I wrote this book because math is more than numbers. In my school system (US), and many more around the world, mathematics is taught as a subject in which the primary goal is to solve for some variable x. Yet, mathematical proofs are a cornerstone of the field that students learn far too late.

This book is meant to serve as a friendly introduction to mathematical proofs without the need to take an Analysis class. It covers some basic techniques from logic and sets, to methods of direct and indirect proof, and ends with a Potpourri of Proofs.

Mathematics competitions further inspired me. Specifically, while earlier stages are primarily calculation-based, the USA(J)MO (and the outlier USAMTS) and further competitions are primarily proof-based. As such, I have made an attempt to demonstrate concepts of mathematical proof while also proving some common theorems and strategies used in competition mathematics.

If you are making the transition from solving mathematical problems to constructing mathematical proofs, this book is for you. This transition happens at different stages for different people, so it is very difficult to pin down a specific age group or other demographic. If you are interested in mathematical proofs and want to learn more in an accessible way, this book is for you.

• 238 pages
• 100+ Worked Examples and Problems
• 88 Hints
• Full solutions

A Rough Sketch of the Table of Contents:

• Introduction / Why Proofs?
• Logic and Sets
• Direct Proof Techniques
• Indirect Proof Techniques
• Many Mixed Examples
• Appendices, including Hints, Solutions to Problem Sets, and Extra Resources

Above all, I hope it serves as a starting point to inspire you to learn about proof-based mathematics, enjoy it, and ultimately continue forward in your journey. I hope it brings challenges and encourages you to pursue proof-based math, whether in research, competitions, class, or simply as a hobby for fun.

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