About this product

Product Identifiers

PublisherSpringer New York

ISBN-100387946179

ISBN-139780387946177

eBay Product ID (ePID)265790

Product Key Features

Number of PagesXvii, 200 Pages

Publication NameAccompaniment to Higher Mathematics

LanguageEnglish

SubjectTopology, Logic, Mathematical Analysis

Publication Year1996

TypeTextbook

Subject AreaMathematics

AuthorGeorge R. Exner

SeriesUndergraduate Texts in Mathematics Ser.

FormatTrade Paperback

Dimensions

Item Height0.2 in

Item Weight38.4 Oz

Item Length9.3 in

Item Width6.1 in

Additional Product Features

Edition Number2

Intended AudienceScholarly & Professional

LCCN95-044884

TitleLeadingAn

Dewey Edition21

Number of Volumes1 vol.

IllustratedYes

Dewey Decimal511.3

Table Of Content1 Examples.- 1.1 Propaganda.- 1.2 Basic Examples for Definitions.- 1.3 Basic Examples for Theorems.- 1.4 Extended Examples.- 1.5 Notational Interlude.- 1.6 Examples Again: Standard Sources.- 1.7 Non-examples for Definitions.- 1.8 Non-examples for Theorems.- 1.9 Summary and More Propaganda.- 1.10 What Next?.- 2 Informal Language and Proof.- 2.1 Ordinary Language Clues.- 2.2 Real-Life Proofs vs. Rules of Thumb.- 2.3 Proof Forms for Implication.- 2.4 Two More Proof Forms.- 2.5 The Other Shoe, and Propaganda.- 3 For mal Language and Proof.- 3.1 Propaganda.- 3.2 Formal Language: Basics.- 3.3 Quantifiers.- 3.4 Finding Proofs from Structure.- 3.5 Summary, Propaganda, and What Next?.- 4 Laboratories.- 4.1 Lab I: Sets by Example.- 4.2 Lab II: Functions by Example.- 4.3 Lab III: Sets and Proof.- 4.4 Lab IV: Functions and Proof.- 4.5 Lab V: Function of Sets.- 4.6 Lab VI: Families of Sets.- A Theoretical Apologia.- B Hints.- References.

SynopsisDesigned for students preparing to engage in their first struggles to understand mathematics independently, this book teaches in detail how to construct examples and non-examples to help understand a new theorem or definition, and how to discover the outline of a proof in the form of the theorem. It is intended to be used interactively, frequently asking the reader to pause and work on an example or a problem before continuing, and encouraging the student to learn from failed attempts at solving problems., For Students Congratulations You are about to take a course in mathematical proof. If you are nervous about the whole thing, this book is for you (if not, please read the second and third paragraphs in the introduction for professors following this, so you won't feel left out). The rumors are true; a first course in proof may be very hard because you will have to do three things that are probably new to you: 1. Read mathematics independently. 2. Understand proofs on your own.:1. Discover and write your own proofs. This book is all about what to do if this list is threatening because you "never read your calculus book" or "can't do proofs. " Here's the good news: you must be good at mathematics or you wouldn't have gotten this far. Here's the bad news: what worked before may not work this time. Success may lie in improving or discarding many habits that were good enough once but aren't now. Let's see how we've gotten to a point at which someone could dare to imply that you have bad habits. l The typical elementary and high school mathematics education in the United States tends to teach students to have ineffective learning habits, 1 In the first paragraph, yet. xiv Introduction and we blush to admit college can be just as bad., For Students Congratulations! You are about to take a course in mathematical proof. If you are nervous about the whole thing, this book is for you (if not, please read the second and third paragraphs in the introduction for professors following this, so you won't feel left out). The rumors are true; a first course in proof may be very hard because you will have to do three things that are probably new to you: 1. Read mathematics independently. 2. Understand proofs on your own. :1. Discover and write your own proofs. This book is all about what to do if this list is threatening because you "never read your calculus book" or "can't do proofs. " Here's the good news: you must be good at mathematics or you wouldn't have gotten this far. Here's the bad news: what worked before may not work this time. Success may lie in improving or discarding many habits that were good enough once but aren't now. Let's see how we've gotten to a point at which someone could dare to imply that you have bad habits. l The typical elementary and high school mathematics education in the United States tends to teach students to have ineffective learning habits, 1 In the first paragraph, yet. xiv Introduction and we blush to admit college can be just as bad., This text prepares undergraduate mathematics students to meet two challenges in the study of mathematics, namely, to read mathematics independently and to understand and write proofs. The book begins by teaching how to read mathematics actively, constructing examples, extreme cases, and non-examples to aid in understanding an unfamiliar theorem or definition (a technique famililar to any mathematician, but rarely taught); it provides practice by indicating explicitly where work with pencil and paper must interrupt reading. The book then turns to proofs, showing in detail how to discover the structure of a potential proof from the form of the theorem (especially the conclusion). It shows the logical structure behind proof forms (especially quantifier arguments), and analyzes, thoroughly, the often sketchy coding of these forms in proofs as they are ordinarily written. The common introductroy material (such as sets and functions) is used for the numerous exercises, and the book concludes with a set of "Laboratories" on these topics in which the student can practice the skills learned in the earlier chapters. Intended for use as a supplementary text in courses on introductory real analysis, advanced calculus, abstract algebra, or topology, the book may also be used as the main text for a "transitions" course bridging the gab between calculus and higher mathematics.

LC Classification NumberQA299.6-433