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Pythagoras' Legacy: Mathematics in Ten Great Ideas [Hardback]

3.67/5 (16 ratings by Goodreads)
(Full Professor of Anthropology, University of Toronto)
  • Formāts: Hardback, 182 pages, height x width x depth: 233x161x16 mm, weight: 470 g
  • Izdošanas datums: 03-Feb-2020
  • Izdevniecība: Oxford University Press
  • ISBN-10: 019885224X
  • ISBN-13: 9780198852247
Citas grāmatas par šo tēmu:
  • Hardback
  • Cena: 47,55 €
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  • Formāts: Hardback, 182 pages, height x width x depth: 233x161x16 mm, weight: 470 g
  • Izdošanas datums: 03-Feb-2020
  • Izdevniecība: Oxford University Press
  • ISBN-10: 019885224X
  • ISBN-13: 9780198852247
Citas grāmatas par šo tēmu:
In this book, Marcel Danesi presents a historical overview of the ten greatest achievements in mathematics, and dynamically explores their importance and effects on our daily lives.

As the famous Pythagorean statement reads, 'Number rules the universe', and its veracity is proven in the many mathematical discoveries that have accelerated the development of science, engineering, and even philosophy. A so called "art of the mind", mathematics has guided and stimulated many aspects of human innovation down through the centuries.

In this book, Marcel Danesi presents a historical overview of the ten greatest achievements in mathematics, and dynamically explores their importance and effects on our daily lives. Considered as a chain of events rather than isolated incidents, Danesi takes us from the beginnings of modern day mathematics with Pythagoras, through the concept of zero, right the way up to modern computational algorithms.

Loaded with thought-provoking practical exercises and puzzles, Pythagoras' Legacy allows the reader to apply their knowledge and discover the significance of mathematics in their everyday lives.

Recenzijas

A pleasant read, with a number of interesting asides * Alan Stevens, Mathematics today * ...this book is a good one. * Andrew J. Simoson, The Mathematical Intelligencer * Marcel Danesi's depth and breadth of knowledge of the history of mathematics, his innate narrative talent, and his uncanny knack for explaining complex notions in simple terms make this book about mathematical notions a true delight to read * Frank Nuessel * Pythagoras' legacy certainly is a gentle introduction to some paramount ideas of mathematics and can be considered as an appetizer for the reader eager to learn a bit more about one of the greatest endeavors of humanity: Mathematics. It is recommended reading for curious people without mathematical background and also for those professional mathematicians who love enjoying a pleasurable book on the science they are passionate about. * Luis Giraldo Gonzalez, MathSciNet *

Preface ix
1 The Pythagorean theorem: The birth of mathematics
1(21)
Prologue
1(2)
The Pythagorean theorem Proof
3(8)
Discovery of √2
11(2)
Practical uses
13(1)
Pattern
14(3)
Fermat's Last Theorem
17(1)
Epilogue
18(2)
Explorations
20(2)
2 Prime numbers: The DNA of mathematics
22(15)
Prologue
22(2)
The infinity of primes
24(2)
The Fundamental Theorem of Arithmetic
26(2)
Searching for the primes
28(4)
The Riemann Hypothesis
32(1)
Epilogue
32(2)
Explorations
34(3)
3 Zero: Place-holder and peculiar number
37(19)
Prologue
37(3)
Negative numbers
40(3)
Analytic geometry
43(3)
Division by zero
46(4)
The zero exponent
50(1)
Binary digits
51(2)
Epilogue
53(1)
Explorations
54(2)
4 π (Pi): A ubiquitous and strange number
56(13)
Prologue
56(2)
Value
58(2)
Transcendental numbers
60(1)
Manifestations
61(3)
Epilogue
64(2)
Explorations
66(3)
5 Exponents: Notation and discovery
69(13)
Prologue
69(2)
Exponential notation
71(2)
Exponential arithmetic
73(2)
Pascal's Triangle
75(2)
Logarithms
77(2)
Epilogue
79(1)
Explorations
80(2)
6 E: A very special number
82(11)
Prologue
82(2)
Mathematical connectivity
84(4)
Euler's identity
88(1)
Epilogue
89(1)
Explorations
90(3)
7 I: Imaginary numbers
93(11)
Prologue
93(2)
Quadratic equations
95(2)
Complex numbers
97(2)
Fundamental Theorem of Algebra
99(1)
Epilogue
100(2)
Explorations
102(2)
8 Infinity: A counterintuitive and paradoxical idea
104(11)
Prologue
104(1)
Zeno's paradoxes
105(2)
The Liar Paradox
107(1)
Galileos and Cantor's paradoxes
108(4)
Hilbert's infinite hotel paradox
112(1)
Epilogue
112(1)
Explorations
113(2)
9 Decidability: The foundations of mathematics
115(11)
Prologue
115(1)
Consistency
116(2)
Axiomatic structure
118(1)
Undecidability
119(3)
Epilogue
122(1)
Explorations
123(3)
10 The algorithm: Mathematics and computers
126(11)
Prologue
126(1)
Algorithms
127(2)
Computability
129(2)
Epilogue
131(2)
Explorations
133(4)
Answers 137(26)
References and Bibliography 163(6)
Index 169
Marcel Danesi is Full Professor of Linguistic Anthropology at the University of Toronto and a Co-Director of the Cognitive Science Network of the Fields Institute of Mathematical Research. He has published extensively in the field of mathematical cognition and in the theory of mathematical puzzles. He also writes a blog for Psychology Today that explore the nature of the puzzling mind.