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Theorems, Corollaries, Lemmas, and Methods of Proof

Rossi, Richard J.

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ISBN 10: 0470042958 / ISBN 13: 9780470042953
Published by Wiley Interscience, Hoboken, New Jersey, 2006
Used Condition: Very Good - Hardcover
From Second Edition Books (Butte, MT, U.S.A.)

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Clean tight copy. Full number line on copyright page. Wear at corners and spine. Stamp across bottom of pages. Boards are lightly rubbed. Part of the Pure and Applied Mathematics series by Wiley. Successfully addressing the frustration many students experience as they make the transition from computational mathematics to advanced calculus and algebraic structures, this book equips the student with the needed tools while providing a firm foundation in the axiomatic structure of modern mathematics Author is Professor of Math at Montana Tech of University of Montana in Butte, MT 318 pp. Bookseller Inventory # 16979

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Bibliographic Details

Title: Theorems, Corollaries, Lemmas, and Methods ...

Publisher: Wiley Interscience, Hoboken, New Jersey

Publication Date: 2006

Binding: Hardcover

Book Condition:Very Good -

Dust Jacket Condition: No Jacket

About this title

Synopsis:

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

Successfully addressing the frustration many students experience asthey make the transition from computational mathematics to advancedcalculus and algebraic structures, Theorems, Corollaries, Lemmas,and Methods of Proof equips students with the tools needed tosucceed while providing a firm foundation in the axiomaticstructure 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 atheorem
* Presents the basic properties of real numbers
* Discusses how to use mathematical induction to prove atheorem
* Identifies the different types of theorems
* Explains how to write a clear and understandable proof
* Covers the basic structure of modern mathematics and the keycomponents of modern mathematics
A complete chapter is dedicated to the different methods of proofsuch as forward direct proofs, proof by contrapositive, proof bycontradiction, mathematical induction, and existence proofs. Inaddition, the author has supplied many clear and detailedalgorithms that outline these proofs.

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

Intended as a main text for mathematics courses such as Methods ofProof, Transitions to Advanced Mathematics, and Foundations ofMathematics, the book may also be used as a supplementary textbookin junior- and senior-level courses on advanced calculus, realanalysis, and modern algebra.

About the Author:

RICHARD J. ROSSI, PHD, is Professor in the Department ofMathematics at Montana Tech of The University of Montana in Butte,Montana. He served as President of the Montana Chapter of theAmerican Statistical Association in 1996 and 2001 and as anAssociate Editor for Biometrics from 1997–2000. He is amember of the American Mathematical Society, the Institute ofMathematical Statistics, and the American Statistical Association.Dr. Rossi received his PhD in statistics from Oregon StateUniversity in 1988.

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