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Conjecture and Proof

MAA Press: An Imprint of the American Mathematical Society
Available Formats:
Softcover ISBN: 978-1-4704-7241-2
Product Code: CLRM/15.S
List Price: $37.00 MAA Member Price:$27.75
AMS Member Price: $27.75 Electronic ISBN: 978-1-4704-5832-4 Product Code: CLRM/15.E List Price:$37.00
MAA Member Price: $27.75 AMS Member Price:$27.75
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List Price: $55.50 MAA Member Price:$41.63
AMS Member Price: $41.63 Click above image for expanded view Conjecture and Proof MAA Press: An Imprint of the American Mathematical Society Available Formats:  Softcover ISBN: 978-1-4704-7241-2 Product Code: CLRM/15.S  List Price:$37.00 MAA Member Price: $27.75 AMS Member Price:$27.75
 Electronic ISBN: 978-1-4704-5832-4 Product Code: CLRM/15.E
 List Price: $37.00 MAA Member Price:$27.75 AMS Member Price: $27.75 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$55.50 MAA Member Price: $41.63 AMS Member Price:$41.63
• Book Details

Classroom Resource Materials
Volume: 152001; 118 pp

The Budapest semesters in mathematics were initiated with the aim of offering undergraduate courses that convey the tradition of Hungarian mathematics to English-speaking students.

This book is an elaborate version of the course on Conjecture and Proof. It gives miniature introductions to various areas of mathematics by presenting some interesting and important, but easily accessible results and methods. The text contains complete proofs of deep results such as the transcendence of $e$, the Banach-Tarski paradox and the existence of Borel sets of arbitrary (finite) class. One of the purposes is to demonstrate how far one can get from the first principles in just a couple of steps.

Prerequisites are kept to a minimum, and any introductory calculus course provides the necessary background for understanding the book. Exercises are included for the benefit of students. However, this book should prove fascinating for any mathematically literate reader.

• Chapters
• Part I. Proofs of Impossibility, Proofs of Nonexistence
• 1. Proofs of Irrationality
• 2. The Elements of the Theory of Geometric Constructions
• 3. Constructible Regular Polygons
• 4. Some Basic Facts About Linear Spaces and Fields
• 5. Algebraic and Transcendental Numbers
• 6. Cauchy’s Functional Equation
• 7. Geometric Decompositions
• Part II. Constructions, Proofs of Existence
• 8. The Pigeonhole Principle
• 9. Liouville Numbers
• 10. Countable and Uncountable Sets
• 11. Isometries of $\mathbf {R}^n$
• 12. The Problem of Invariant Measures
• 14. Open and Closed Sets in $\mathbf {R}$. The Cantor Set
• 15. The Peano Curve
• 16. Borel Sets
• 17. The Diagonal Method

• Reviews

• I love this book! It's a very well designed problem driven course done in the splendid Hungarian tradition.

Michael Bert, MAA Online
• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 152001; 118 pp

The Budapest semesters in mathematics were initiated with the aim of offering undergraduate courses that convey the tradition of Hungarian mathematics to English-speaking students.

This book is an elaborate version of the course on Conjecture and Proof. It gives miniature introductions to various areas of mathematics by presenting some interesting and important, but easily accessible results and methods. The text contains complete proofs of deep results such as the transcendence of $e$, the Banach-Tarski paradox and the existence of Borel sets of arbitrary (finite) class. One of the purposes is to demonstrate how far one can get from the first principles in just a couple of steps.

Prerequisites are kept to a minimum, and any introductory calculus course provides the necessary background for understanding the book. Exercises are included for the benefit of students. However, this book should prove fascinating for any mathematically literate reader.

• Chapters
• Part I. Proofs of Impossibility, Proofs of Nonexistence
• 1. Proofs of Irrationality
• 2. The Elements of the Theory of Geometric Constructions
• 3. Constructible Regular Polygons
• 4. Some Basic Facts About Linear Spaces and Fields
• 5. Algebraic and Transcendental Numbers
• 6. Cauchy’s Functional Equation
• 7. Geometric Decompositions
• Part II. Constructions, Proofs of Existence
• 8. The Pigeonhole Principle
• 9. Liouville Numbers
• 10. Countable and Uncountable Sets
• 11. Isometries of $\mathbf {R}^n$
• 12. The Problem of Invariant Measures
• 14. Open and Closed Sets in $\mathbf {R}$. The Cantor Set