An Introduction to the Language of Mathematics by Frédéric Mynard (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Engaging learn how to create proofs textbook. The set theory part is very approachable for a non-mathematician such as myself.

⭐Excellent book! So well written and clearly explained. Dr. Mynard presents every concept in interesting ways with mind-blowing examples that motivate students. He beautifully shows how mathematical reasoning can be related and applicable to many real-life situations, and succeeds leading the readers onto the path of thinking like mathematicians.I highly recommend this textbook for every undergraduate/graduate student who wants to develop a strong understanding of real Mathematics.

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