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portada Fundamentals of Mathematical Proof
Type
Physical Book
Publisher
Year
2018
Language
English
Pages
166
Format
Paperback
ISBN13
9781717176707

Fundamentals of Mathematical Proof

Charles A. Matthews (Author) · Createspace · Paperback

Fundamentals of Mathematical Proof - Charles A. Matthews

New Book Imported to New Zealand
Delivery: 19 Aug - 01 Sep Shipping: 16 to 20 business days.
NZ$ 82.81
Import costs and 15% GST included in the price ✅
NZ$ 82.81

Synopsis "Fundamentals of Mathematical Proof "

This mathematics textbook covers the fundamental ideas used in writing proofs. Proof techniques covered include direct proofs, proofs by contrapositive, proofs by contradiction, proofs in set theory, proofs of existentially or universally quantified predicates, proofs by cases, and mathematical induction. Inductive and deductive reasoning are explored. A straightforward approach is taken throughout. Plenty of examples are included and lots of exercises are provided after each brief exposition on the topics at hand. The text begins with a study of symbolic logic, deductive reasoning, and quantifiers. Inductive reasoning and making conjectures are examined next, and once there are some statements to prove, techniques for proving conditional statements, disjunctions, biconditional statements, and quantified predicates are investigated. Terminology and proof techniques in set theory follow with discussions of the pick-a-point method and the algebra of sets. Cartesian products, equivalence relations, orders, and functions are all incorporated. Particular attention is given to injectivity, surjectivity, and cardinality. The text includes an introduction to topology and abstract algebra, with a comparison of topological properties to algebraic properties. This book can be used by itself for an introduction to proofs course or as a supplemental text for students in proof-based mathematics classes. The contents have been rigorously reviewed and tested by instructors and students in classroom settings.

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The book is written in English.
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