An Introduction to the Language of Mathematics
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Beschreibung
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.
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.
Includes both solved and unsolved exercises Includes informal discussions of aspects of philosophy of mathematics, and of the relation between certain mathematical notions and thought processes Helps engage students in a reflexion on the nature of mathematics and periodically breaks away from technicalities Provides a more extensive treatment of relations, including equivalence relations and order relations, than most comparable books Request lecturer material: sn.pub/lecturer-material
Autor*in
Frédéric Mynard
Themen in »An Introduction to the Language of Mathematics«
propositional logic set theory proofs mathematical induction relations equivalence relation order relation infinite cardinality