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Mathematics Lovers Companion: Masterpieces for Everyone [Kõva köide]

  • Formaat: Hardback, 296 pages, kõrgus x laius x paksus: 235x165x25 mm, kaal: 635 g, 106 b-w illus.
  • Ilmumisaeg: 02-May-2017
  • Kirjastus: Yale University Press
  • ISBN-10: 0300223005
  • ISBN-13: 9780300223002
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  • Formaat: Hardback, 296 pages, kõrgus x laius x paksus: 235x165x25 mm, kaal: 635 g, 106 b-w illus.
  • Ilmumisaeg: 02-May-2017
  • Kirjastus: Yale University Press
  • ISBN-10: 0300223005
  • ISBN-13: 9780300223002
Teised raamatud teemal:
Twenty-three mathematical masterpieces for exploration and enlightenment

A mind-broadening experience.Paul J. Campbell, Mathematics Magazine

How can a shape have more than one dimension but fewer than two? What is the best way to elect public officials when more than two candidates are vying for the office? Is it possible for a highly accurate medical test to give mostly incorrect results? Can you tile your floor with regular pentagons? How can you use only the first digit of sales numbers to determine if your accountant is lying? Can mathematics give insights into free will?   Edward Scheinerman, an accomplished mathematician and enthusiastic educator, answers all these questions and more in this book, a collection of mathematical masterworks. In bite-sized chapters that require only high school algebra, he invites readers to try their hands at solving mathematical puzzles and provides an engaging and friendly tour of numbers, shapes, and uncertainty. The result is an unforgettable introduction to the fundamentals and pleasures of thinking mathematically.

Arvustused

"Twenty-three masterworks whose analysis Scheinerman presents with rigor and accessibility."James Ryerson, New York Times Book Review

"I recommend this book to anyone with an interest in mathematics, including those mathematicians who want to experience again the excitement and surprise to be found in the study of mathematics."Terence Morley, Mathematics Today

"This is undoubtedly one of the best popular mathematics books of recent years and it is strongly recommended, above all for teachers who would like to rekindle their enthusiasm for mathematics and as a gift for any teenager who loves the subject as the title suggests."Owen Toller, The Mathematical Gazette

"An accessible presentation of some of the most compelling and beautiful ideas of mathematics. Scheinerman demonstrates the diversity and liveliness of the subject in a friendly and inviting way."Susan Jane Colley, Oberlin College and Editor, The American Mathematical Monthly

"A great read for anyone who wants to learn what math really is, no prerequisites required. And those of us in the field are reminded of what first drew us to it."Maria Chudnovsky, Princeton University and 2012 MacArthur Fellow

"In this well-written book, the reader is taken on a fascinating journey across a broad landscape of beautiful mathematics."Ron Graham, author of Magical Mathematics

"A first-rate mathematician and expositor, Scheinerman takes us on a guided tour of great mathematical ideas. Written with clarity and humor, The Mathematics Lover's Companion will appeal to a wide audience."Arthur Benjamin, author of The Magic of Math: Solving for x and Figuring Out Why

"A clear and lively exposition that will entice non-mathematicians into the world of mathematics."Anna Lachowska, coauthor of Beautiful, Simple, Exact, Crazy: Mathematics in the Real World

Preface xv
Joy xv
Overview xvii
How to read a mathematics book xviii
About the cover xviii
Acknowledgments xix
Prelude: Theorem and Proof 1(4)
The last words
4(1)
Part I Number
5(136)
1 Prime Numbers
7(12)
The integers
7(2)
Factoring
9(1)
How many?
10(3)
A constructive approach
13(1)
A different proof
14(2)
Two infamous problems
16(1)
Application to cryptography
17(2)
2 Binary
19(8)
When in Rome
19(1)
Unary
20(1)
A middle ground
21(1)
Calculation
22(3)
Extensions
25(2)
3 0.999999999999 ...
27(6)
The meaning of decimals
27(1)
Decimal numbers with infinitely many digits
28(2)
Let's be reckless
30(3)
4 √2
33(11)
Rational numbers
33(1)
The diagonal of a square
34(1)
Beyond the rational
35(3)
Constructible numbers
38(2)
Playing in tune
40(4)
5 i
44(8)
Another square-root conundrum
44(2)
Imaginary numbers
46(1)
Complex numbers
47(3)
The Fundamental Theorem of Algebra
50(2)
6 π
52(8)
What is π?
52(3)
Transcendence*
55(1)
Relatively prime
56(4)
7 e
60(11)
Leonhard Euler
60(1)
An "interesting" number
61(3)
The deranged hat check clerk
64(2)
The average gap between primes
66(3)
A miraculous equation
69(2)
8 ∞
71(15)
Sets
71(4)
Infinite sets of unequal size
75(5)
Transfinite numbers
80(1)
Weirdness in setland
81(5)
9 Fibonacci Numbers
86(16)
Squares and dominoes
86(2)
The Fibonacci numbers
88(1)
Sums of Fibonacci numbers
89(2)
Proof by induction
91(2)
Combinatorial proof
93(4)
Ratios of Fibonacci numbers and the golden mean
97(5)
10 Factorial!
102(7)
Books on the shelf
102(2)
Is there a formula?
104(3)
A puzzle
107(1)
What is 0!?
107(2)
11 Benford's Law
109(15)
Wild measurements
110(2)
Multiplication tables
112(3)
Catching crooks cooking books
115(1)
Refining the problem with scientific notation
115(2)
Yards or feet?
117(3)
What's logs got to do with it?
120(3)
Collecting the loose ends
123(1)
12 Algorithm
124(17)
Sorting
125(6)
Greatest common divisor
131(5)
Least common multiple
136(5)
Part II Shape
141(74)
13 Triangles
143(12)
It all adds up to 180
143(2)
Area
145(3)
Centers
148(3)
Lurking equilateral triangles
151(4)
14 Pythagoras and Fermat
155(10)
The Pythagorean Theorem
155(3)
Absolute value of complex numbers
158(1)
Pythagorean triples
159(3)
Fermat's Last Theorem
162(3)
15 Circles
165(10)
A precise definition
165(1)
An equation
166(1)
Triangles right inside
167(1)
Ptolemy's Theorem
167(1)
Packing
168(2)
Kissing circles
170(3)
Pascal's Hexagon Theorem
173(2)
16 The Platonic Solids
175(15)
Polyhedra
175(3)
Euler's polyhedral formula
178(5)
Is that all there is?
183(4)
Archimedian solids
187(3)
17 Fractals
190(14)
Sierpinski's triangle
190(2)
Between dimensions
192(2)
Box counting
194(4)
The dimension of Sierpinski's triangle
198(3)
Pascal and Sierpinski
201(1)
The Koch snowflake
202(2)
18 Hyperbolic Geometry
204(11)
Euclid's Postulates
204(3)
What is a line?
207(3)
An entire plane inside a disk
210(1)
Implications
211(4)
Part III Uncertainty
215(54)
19 Nontransitive Dice
217(6)
A game of two dice
218(1)
A challenger
219(1)
Triumph of the underdog
220(1)
Further examples
220(3)
20 Medical Probability
223(7)
Conditional probability*
226(4)
21 Chaos
230(15)
Functions
231(2)
Iterating the logistic map
233(4)
From order to chaos
237(5)
The Collatz 3x + 1 problem
242(3)
22 Social Choice and Arrow's Theorem
245(14)
Two-party elections
245(4)
Elections with more than two candidates
249(6)
The independence of irrelevant alternatives
255(4)
23 Newcomb's Paradox
259(10)
Newcomb's game
259(3)
Don't leave money on the table!
262(1)
Greed doesn't pay
263(2)
Conflict and resolution
265(2)
Computer as the Chooser
267(2)
Further Reading 269(2)
Index 271
Edward Scheinerman is professor of applied mathematics and vice dean for engineering education at Johns Hopkins University. He has twice won the Mathematical Association of Americas Ford Award for excellent mathematical writing.