EAN: 9783030006402

AN INTRODUCTION TO THE LANGUAGE OF MATHEMATICS ...

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.

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