Transition to Proofs

This textbook is aimed at transitioning high-school students who have already developed proficiency in mathematical problem solving from numerical-answer problems to proof-based mathematics. It serves to guide students on how to write and understand mathematical proofs. It covers proof techniques that are commonly used in several areas of mathematics, especially number theory, combinatorics, and analysis. In addition to just teaching the mechanics of proofs, this book showcases key materials in these areas, thus introducing readers to interesting mathematics along with proof techniques.Readership: High-school students with some problem-solving background, for example, at the level of being able to qualify for the American Invitational Mathematics Exam. It can also be used as a textbook for an undergraduate introduction to proofs for honors students, and it may be of interest to mathematical hobbyists who just want to learn more mathematics rigorously. Read more