Theorems, Corollaries, Lemmas, and Methods of Proof

Richard J. Rossi

318 pages, parution le 15/08/2006

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Résumé

A hands-on introduction to the tools needed for rigorous and theoretical mathematical reasoning

Successfully addressing the frustration many students experience as they make the transition from computational mathematics to advanced calculus and algebraic structures, Theorems, Corollaries, Lemmas, and Methods of Proof equips students with the tools needed to succeed while providing a firm foundation in the axiomatic structure of modern mathematics.

This essential book:

Clearly explains the relationship between definitions, conjectures, theorems, corollaries, lemmas, and proofs
Reinforces the foundations of calculus and algebra
Explores how to use both a direct and indirect proof to prove a theorem
Presents the basic properties of real numbers
Discusses how to use mathematical induction to prove a theorem
Identifies the different types of theorems
Explains how to write a clear and understandable proof
Covers the basic structure of modern mathematics and the key components of modern mathematics

A complete chapter is dedicated to the different methods of proof such as forward direct proofs, proof by contrapositive, proof by contradiction, mathematical induction, and existence proofs. In addition, the author has supplied many clear and detailed algorithms that outline these proofs.

Theorems, Corollaries, Lemmas, and Methods of Proof uniquely introduces scratch work as an indispensable part of the proof process, encouraging students to use scratch work and creative thinking as the first steps in their attempt to prove a theorem. Once their scratch work successfully demonstrates the truth of the theorem, the proof can be written in a clear and concise fashion. The basic structure of modern mathematics is discussed, and each of the key components of modern mathematics is defined. Numerous exercises are included in each chapter, covering a wide range of topics with varied levels of difficulty.

Intended as a main text for mathematics courses such as Methods of Proof, Transitions to Advanced Mathematics, and Foundations of Mathematics, the book may also be used as a supplementary textbook in junior- and senior-level courses on advanced calculus, real analysis, and modern algebra.

Sommaire

Preface
Introduction to Modern Mathematics
An Introduction to Symbolic Logic
Methods of Proof
Introduction to Number Theory
The Foundations of Calculus
Foundations of Algebra
References
Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Wiley
Auteur(s)	Richard J. Rossi
Parution	15/08/2006
Nb. de pages	318
Format	16 x 24,5
Couverture	Relié
Poids	486g
Intérieur	Noir et Blanc
EAN13	9780470042953
ISBN13	978-0-470-04295-3