Proofs is the heart of mathematics. It is what differentiates mathematics from other sciences. In mathematical proofs, we can show that a statement is true for all possible cases without showing all the cases. We can be certain that the sum of two even numbers is even without adding all the possible pairs.
For those who are “non-math people,” the proof techniques below will help you, but the “math people” are probably those who are going to enjoy them more. Continue reading
If you are familiar with Polya’s How to Solve It, one of the most well-known classic books in mathematical problem solving, a similar book exists for learning mathematical proofs. Daniel Velleman’s How to Prove It: A Structured Approach is one of the good books available for learning the structure of proofs.
The books include topics onm Sentential logic, Quantification Logic, Proof Strategies, Relations, Functions, Mathematical Induction and Infinite Sets. It contains detailed explanation and numerous examples on different types of proofs and the logic behind them. It contains explanations on connectives, quantifiers, truth tables, countable and uncountable sets and more.
How to Prove It is a recommended book for undergraduate mathematics students as well as advanced high school students who plan to be mathematics majors.
I have written quite a number of articles on mathematical proofs, so I want to summarize them in this post. Most of these proofs are high school level, so students who are mathematically inclined are encouraged to read them.
I will update this list every time I have written proof-related posts, so you may want to book mark this post.