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E-raamat: Essentials of Mathematical Thinking [Taylor & Francis e-raamat]

(Washington University, St. Louis, Missouri, USA)
  • Formaat: 336 pages, 22 Tables, black and white; 174 Illustrations, black and white
  • Sari: Textbooks in Mathematics
  • Ilmumisaeg: 22-Sep-2017
  • Kirjastus: CRC Press
  • ISBN-13: 9781315116822
Teised raamatud teemal:
  • Taylor & Francis e-raamat
  • Hind: 240,04 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
  • Tavahind: 342,91 €
  • Säästad 30%
Essentials of Mathematical ThinkingSuurem pilt
  • Formaat: 336 pages, 22 Tables, black and white; 174 Illustrations, black and white
  • Sari: Textbooks in Mathematics
  • Ilmumisaeg: 22-Sep-2017
  • Kirjastus: CRC Press
  • ISBN-13: 9781315116822
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9781315116822
Essentials of Mathematical Thinking addresses the growing need to better comprehend mathematics today. Increasingly, our world is driven by mathematics in all aspects of life. The book is an excellent introduction to the world of mathematics for students not majoring in mathematical studies.

The author has written this book in an enticing, rich manner that will engage students and introduce new paradigms of thought. Careful readers will develop critical thinking skills which will help them compete in todays world.

The book explains:











What goes behind a Google search algorithm





How to calculate the odds in a lottery





The value of Big Data





How the nefarious Ponzi scheme operates



Instructors will treasure the book for its ability to make the field of mathematics more accessible and alluring with relevant topics and helpful graphics. The author also encourages readers to see the beauty of mathematics and how it relates to their lives in meaningful ways.
Preface xv
1 First Thoughts
1(4)
1.1 What Is Mathematical Thinking?
1(1)
1.2 How Does Mathematics Differ from Other Disciplines?
2(1)
1.3 A Sample Problem
2(3)
2 Diverse Mathematical Thoughts
5(44)
2.1 A Fraction of the Time
5(2)
2.2 How to Swindle on the Stock Market
7(2)
2.3 The Bible Code
9(2)
2.4 Winning on a Game Show
11(3)
2.5 Cutting the Cake
14(3)
2.6 A Lesson in Map Coloring
17(18)
2.6.1 Analysis
20(5)
2.6.2 Modern Developments
25(9)
2.6.3 Denouement
34(1)
2.7 The Complexity of Songs
35(6)
2.8 Bertrand's Paradox
41(8)
3 Strategy
49(12)
3.1 It's All in the Balance
49(3)
3.2 See and Say
52(2)
3.3 The Ponzi Scheme
54(1)
3.4 Ham Sandwich Theorems
55(6)
4 Focus
61(8)
4.1 The Erdos Number
61(2)
4.2 Time Out
63(2)
4.3 Days of the Week
65(4)
5 Science
69(16)
5.1 A Belt for the Earth
69(3)
5.2 Your Next Breath
72(2)
5.3 A Hairy Question
74(1)
5.4 The Motions of the Planets
75(4)
5.5 How Big Is Big Data?
79(6)
6 Counting
85(24)
6.1 Funny Numbers
85(1)
6.2 The Pigeon Flew the Coop
86(6)
6.3 Conditional Probability
92(6)
6.4 Benford's Law
98(7)
6.5 Puzzling Birthdays
105(4)
7 Games
109(22)
7.1 How to Count
109(4)
7.2 How to Beat the Lottery
113(4)
7.3 The Eudaemonic Pie
117(3)
7.4 A Dicey Bet
120(2)
7.5 The Game of Life
122(4)
7.6 The Tower of Hanoi
126(5)
8 Geometry
131(34)
8.1 Thoughts of Pythagoras
131(4)
8.2 Symmetry
135(4)
8.3 Buffon's Needle Problem
139(3)
8.4 Euler's Formula
142(4)
8.5 Sphere Packing
146(8)
8.6 The Platonic Solids
154(5)
8.7 Heron's Problem
159(2)
8.8 A Little Geometric Reasoning
161(4)
9 Practical Matters
165(46)
9.1 Strangers on a Plane
165(3)
9.2 You've Got My Vote
168(11)
9.2.1 The Plurality System
170(1)
9.2.2 The Hare System
170(5)
9.2.3 The Borda Count
175(2)
9.2.4 Cumulative Voting
177(1)
9.2.5 Approval Voting
178(1)
9.2.6 Conclusions
179(1)
9.3 Take Your Pill
179(3)
9.4 Geometric Analysis and Facial Structure
182(11)
9.4.1 Geometry and Facial Structure
183(1)
9.4.2 Conformal Mapping
183(1)
9.4.3 Wavelets and Filters
184(6)
9.4.4 Summary Remarks
190(3)
9.5 Beware the Raven
193(4)
9.6 The Prisoner's Dilemma
197(4)
9.7 The Eyes Have It
201(2)
9.8 A Sure Bet
203(2)
9.9 Hilbert's Hotel Infinity
205(6)
10 Breaking the Code
211(32)
10.1 Alan Turing and Cryptography
211(21)
10.1.1 Background on Alan Turing
211(2)
10.1.2 The Turing Machine
213(1)
10.1.3 What Is Cryptography?
214(7)
10.1.4 Encryption by Way of Affine Transformations
221(6)
10.1.5 Digraph Transformations
227(5)
10.2 RSA Encryption
232(11)
10.2.1 Basics and Background
232(2)
10.2.2 Preparation for RSA
234(1)
10.2.3 Modular Arithmetic
235(2)
10.2.4 Relatively Prime Integers
237(1)
10.2.5 The RSA System Enunciated
238(2)
10.2.6 The RSA Encryption System Explicated
240(3)
11 Discrete Problems
243(26)
11.1 Far-Reaching Dominoes
243(2)
11.2 Surreal Life
245(5)
11.3 A Problem with Marriage
250(4)
11.4 Euler's Bridges
254(9)
11.5 Scheduling Sporting Events
263(6)
12 Advanced Ideas
269(50)
12.1 Searching on Google
269(10)
12.1.1 The Mathematics of a Google Search
269(1)
12.1.2 The Directed Web Graph
270(1)
12.1.3 Passage to the Web HyperLink Matrix
270(1)
12.1.4 A Fix for Dangling Nodes
271(5)
12.1.5 The Ultimate Google Matrix
276(3)
12.2 A Needle Problem of Kakeya
279(8)
12.3 Euclidean and Non-Euclidean Geometry
287(13)
12.4 Archimedes and the Area of a Circle
300(19)
12.4.1 The Genius of Archimedes
300(4)
12.4.2 Archimedes's Calculation of the Area of a Circle
304(15)
13 Concluding Remarks
319(2)
13.1 The Final Word
319(2)
References 321(6)
Index 327
Steven G. Krantz is a professor of mathematics at Washington University in St. Louis. He has written more than 65 books and more than 175 scholarly papers and is the founding editor of the Journal of Geometric Analysis. An AMS Fellow, Dr. Krantz has been a recipient of the Chauvenet Prize, Beckenbach Book Award, and Kemper Prize. He received a Ph.D from Princeton University.
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