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Cover: 9780387946177 | An Accompaniment to Higher Mathematics | George R. Exner | Taschenbuch
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An Accompaniment to Higher Mathematics
Taschenbuch von George R. Exner
Sprache: Englisch

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Beschreibung
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.
Zusammenfassung
Designed 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.
Inhaltsverzeichnis
1 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.
Details
Erscheinungsjahr: 1996
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Undergraduate Texts in Mathematics
Inhalt: xvii
200 S.
ISBN-13: 9780387946177
ISBN-10: 0387946179
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Exner, George R.
Hersteller: Springer New York
Springer US, New York, N.Y.
Undergraduate Texts in Mathematics
Maße: 235 x 155 x 13 mm
Von/Mit: George R. Exner
Erscheinungsdatum: 05.01.1996
Gewicht: 0,347 kg
Artikel-ID: 102547333
Zusammenfassung
Designed 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.
Inhaltsverzeichnis
1 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.
Details
Erscheinungsjahr: 1996
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Undergraduate Texts in Mathematics
Inhalt: xvii
200 S.
ISBN-13: 9780387946177
ISBN-10: 0387946179
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Exner, George R.
Hersteller: Springer New York
Springer US, New York, N.Y.
Undergraduate Texts in Mathematics
Maße: 235 x 155 x 13 mm
Von/Mit: George R. Exner
Erscheinungsdatum: 05.01.1996
Gewicht: 0,347 kg
Artikel-ID: 102547333
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