Understanding Mathematical Proof
Auteurs : Taylor John, Garnier Rowan
The notion of proof is central to mathematics yet it is one of the most difficult aspects of the subject to teach and master. In particular, undergraduate mathematics students often experience difficulties in understanding and constructing proofs.
Understanding Mathematical Proof describes the nature of mathematical proof, explores the various techniques that mathematicians adopt to prove their results, and offers advice and strategies for constructing proofs. It will improve students ability to understand proofs and construct correct proofs of their own.
The first chapter of the text introduces the kind of reasoning that mathematicians use when writing their proofs and gives some example proofs to set the scene. The book then describes basic logic to enable an understanding of the structure of both individual mathematical statements and whole mathematical proofs. It also explains the notions of sets and functions and dissects several proofs with a view to exposing some of the underlying features common to most mathematical proofs. The remainder of the book delves further into different types of proof, including direct proof, proof using contrapositive, proof by contradiction, and mathematical induction. The authors also discuss existence and uniqueness proofs and the role of counter examples.
Date de parution : 04-2014
15.6x23.4 cm
Date de parution : 06-2018
15.6x23.4 cm
Thème d’Understanding Mathematical Proof :
Mots-clés :
Proposition P1; Propositional Function; Techniques To Prove Mathematical Results; Consecutive Positive Integers; Constructing Mathematical Proofs; Jx1 X2j; Proof Using Contrapositive; Positive Integers; Proof By Contradiction; Venn Euler Diagram; Mathematical Induction; Odd Integer; Existence And Uniqueness Proofs; Direct Proof; Structure Of Mathematical Proof; Deduction Rules; Proving Mathematical Theorems; Surjective Functions; Proofs In Linear Algebra; Group Theory; And Real Analysis; Non-empty Subset; Innite Sets; Truth Table; Induction; Inductive Step; Compound Proposition; Axiom System; Existentially Quantied; Metric Space; Inductive Hypothesis; Jy1 Y2j; Pigeonhole Principle; Background Knowledge; Great Internet Mersenne Prime Search; A12 A13a21 A22 A23 A31