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Undergraduate Texts in Mathematics Ser.: Mathematical Reflections : In a Room with Many Mirrors by Peter Hilton, Jean J. Pedersen and Derek Holton (1998, Hardcover)

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MATHEMATICAL REFLECTIONS: IN A ROOM WITH MANY MIRRORS (UNDERGRADUATE TEXTS IN MATHEMATICS) By Peter Hilton, Derek Holton, Jean Pedersen - Hardcover **BRAND NEW**.

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Focusing Your Attention The purpose of this book is Cat least) twofold. First, we want to show you what mathematics is, what it is about, and how it is done-by those who do it successfully. We are, in fact, trying to give effect to what we call, in Section 9.3, our basic principle of mathematical instruction, asserting that "mathematics must be taught so that students comprehend how and why mathematics is qone by those who do it successfully./I However, our second purpose is quite as important. We want to attract you-and, through you, future readers-to mathematics. There is general agreement in the (so-called) civilized world that mathematics is important, but only a very small minority of those who make contact with mathematics in their early education would describe it as delightful. We want to correct the false impression of mathematics as a combination of skill and drudgery, and to re- inforce for our readers a picture of mathematics as an exciting, stimulating and engrossing activity; as a world of accessible ideas rather than a world of incomprehensible techniques; as an area of continued interest and investigation and not a set of procedures set in stone.

Product Identifiers

Publisher
Springer New York
ISBN-10
0387947701
ISBN-13
9780387947709
eBay Product ID (ePID)
781966

Product Key Features

Author
Peter Hilton, Derek Holton, Jean J. Pedersen
Publication Name
Mathematical Reflections : in a Room with Many Mirrors
Format
Hardcover
Language
English
Publication Year
1998
Series
Undergraduate Texts in Mathematics Ser.
Type
Textbook
Number of Pages
Xvi, 352 Pages

Dimensions

Item Length
10in
Item Height
0.4in
Item Width
7in
Item Weight
72 Oz

Additional Product Features

Number of Volumes
1 Vol.
Lc Classification Number
Qa241-247.5
Table of Content
1 Going Down the Drain.- 1.1 Constructions.- 1.2 Cobwebs.- 1.3 Consolidation.- 1.4 Fibonacci Strikes.- 1.5 Dénouement.- 2 A Far Nicer Arithmetic.- 2.1 General Background: What You Already Know.- 2.2 Some Special Moduli: Getting Ready for the Fun.- 2.3 Arithmetic mod p: Some Beautiful Mathematics.- 2.4 Arithmetic mod Non-primes: The Same But Different.- 2.5 Primes, Codes, and Security.- 2.6 Casting Out 9's and 11's: Tricks of the Trade.- 3 Fibonacci and Lucas Numbers.- 3.1 A Number Trick.- 3.2 The Explanation Begins.- 3.3 Divisibility Properties.- 3.4 The Number Trick Finally Explained.- 3.5 More About Divisibility.- 3.6 A Little Geometry!.- 4 Paper-Folding and Number Theory.- 4.1 Introduction: What You Can Do With--and Without--Euclidean Tools.- 4.2 Going Beyond Euclid: Folding 2-Period Regular Polygons.- 4.3 Folding Numbers.- 4.4 Some Mathematical Tidbits.- 4.5 General Folding Procedures.- 4.6 The Quasi-Order Theorem.- 4.7 Appendix: A Little Solid Geometry.- 5 Quilts and Other Real-World Decorative Geometry.- 5.1 Quilts.- 5.2 Variations.- 5.3 Round and Round.- 5.4 Up the Wall.- 6 Pascal, Euler, Triangles, Windmills.- 6.1 Introduction: A Chance to Experiment.- 6.2 The Binomial Theorem.- 6.3 The Pascal Triangle and Windmill.- 6.4 The Pascal Flower and the Generalized Star of David.- 6.5 Eulerian Numbers and Weighted Sums.- 6.6 Even Deeper Mysteries.- 7 Hair and Beyond.- 7.1 A Problem with Pigeons, and Related Ideas.- 7.2 The Biggest Number.- 7.3 The Big Infinity.- 7.4 Other Sets of Cardinality ?0.- 7.5 Schröder and Bernstein.- 7.6 Cardinal Arithmetic.- 7.7 Even More Infinities?.- 8 An Introduction to the Mathematics of Fractal Geometry.- 8.1 Introduction to the Introduction: What's Different About Our Approach.- 8.2 Intuitive Notion of Self-Similarity.- 8.3The lént Map and the Logistic Map.- 8.4 Some More Sophisticated Material.- An Introduction to the Mathematics of Fractal Geometry.- 8.1 Introduction to the Introduction: What's Different About Our Approach.- 8.2 Intuitive Notion of Self-Similarity.- 8.3 The tent Map and and the Logistic Map.- 8.4 Some more Sophisticated Material.- 9 Some of Our Own Reflections.- 9.1 General Principles.- 9.2 Specific Principles.- 9.3 Appendix: Principles of Mathematical Pedagogy.
Copyright Date
1997
Topic
Geometry / General, General, Number Theory, Essays
Lccn
96-014274
Dewey Decimal
510
Intended Audience
Scholarly & Professional
Dewey Edition
20
Illustrated
Yes
Genre
Mathematics

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item 5 MATHEMATICAL REFLECTIONS: IN A ROOM WITH MANY MIRRORS By Peter Hilton & Derek
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Picture 1 of 1

Undergraduate Texts in Mathematics Ser.: Mathematical Reflections : In a Room with Many Mirrors by Peter Hilton, Jean J. Pedersen and Derek Holton (1998, Hardcover)

About this product

Product Information

Product Identifiers

Product Key Features

Dimensions

Additional Product Features

All listings for this product

item 1 Mathematical Reflections: In a Room with Many Mirrors (Undergraduate - VERY GOOD

item 2 Mathematical Reflections: In a Room with Many Mirrors (Undergraduate Text - GOOD

item 3 Mathematical Reflections: In a Room with Many Mirrors (Undergraduate Texts i...

item 4 Mathematical Reflections: In a Room ..., Pedersen, Jean

item 5 MATHEMATICAL REFLECTIONS: IN A ROOM WITH MANY MIRRORS By Peter Hilton & Derek

item 6 Mathematical Reflections: In A Room With Many Mirrors

item 7 Mathematical Reflections: In a Room with Many Mirrors by Peter Hilton: New

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