An Introduction to the Language of Mathematics

by Frederic Mynard

This is a textbook for an undergraduate mathematics major transition course from technique-based mathematics (such as Algebra and Calculus) to proof-based mathematics. It motivates the introduction of the formal language of logic and set theory and develops the basics with examples, exercises with solutions and exercises without. It then moves to a discussion of proof structure and basic proof techniques, including proofs by induction with extensive examples. An in-depth treatment of relations, particularly equivalence and order relations completes the exposition of the basic language of mathematics. The last chapter treats infinite cardinalities. An appendix gives some complement on induction and order, and another provides full solutions of the in-text exercises. The primary audience is undergraduate mathematics major, but independent readers interested in mathematics can also use the book for self-study.

Genres: Mathematics

197 pages, Hardcover

Published December 10, 2018

Reviews

[Alvaro E. · Rating 5 out of 5]

A non-mathematician gets an effective flying start. The work was very accessible for a independent student like myself.