Essentials of Mathematical Thinking 1st Edition by Steven George Krantz 113819770X 9781138042575

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ISBN-10 :  113819770X 

ISBN-13 :  9781138042575

Author:   Steven George Krantz 

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 today’s 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.

Essentials of Mathematical Thinking 1st Table of contents:

1. First Thoughts
1.1 What Is Mathematical Thinking?
1.2 How Does Mathematics Differ from Other Disciplines?
1.3 A Sample Problem
2. Diverse Mathematical Thoughts
2.1 A Fraction of the Time
2.2 How to Swindle on the Stock Market
2.3 The Bible Code
2.4 Winning on a Game Show
2.5 Cutting the Cake
2.6 A Lesson in Map Coloring
2.6.1 Analysis
2.6.2 Modern Developments
2.6.3 Denouement
2.7 The Complexity of Songs
2.8 Bertrand’s Paradox
3. Strategy
3.1 It’s All in the Balance
3.2 See and Say
3.3 The Ponzi Scheme
3.4 Ham Sandwich Theorems
4. Focus
4.1 The Erdo˝s Number
4.2 Time Out
4.3 Days of the Week
5. Science
5.1 A Belt for the Earth
5.2 Your Next Breath
5.3 A Hairy Question
5.4 The Motions of the Planets
5.5 How Big Is Big Data?
6. Counting
6.1 Funny Numbers
6.2 The Pigeon Flew the Coop
6.3 Conditional Probability
6.4 Benford’s Law
6.5 Puzzling Birthdays
7. Games
7.1 How to Count
7.2 How to Beat the Lottery
7.3 The Eudaemonic Pie
7.4 A Dicey Bet
7.5 The Game of Life
7.6 The Tower of Hanoi
8. Geometry
8.1 Thoughts of Pythagoras
8.2 Symmetry
8.3 Buffon’s Needle Problem
8.4 Euler’s Formula
8.5 Sphere Packing
8.6 The Platonic Solids
8.7 Heron’s Problem
8.8 A Little Geometric Reasoning
9. Practical Matters
9.1 Strangers on a Plane
9.2 You’ve Got My Vote
9.2.1 The Plurality System
9.2.2 The Hare System
9.2.3 The Borda Count
9.2.4 Cumulative Voting
9.2.5 Approval Voting
9.2.6 Conclusions
9.3 Take Your Pill
9.4 Geometric Analysis and Facial Structure
9.4.1 Geometry and Facial Structure
9.4.2 Conformal Mapping
9.4.3 Wavelets and Filters
9.4.4 Summary Remarks
9.5 Beware the Raven
9.6 The Prisoner’s Dilemma
9.7 The Eyes Have It
9.8 A Sure Bet
9.9 Hilbert’s Hotel Infinity
10. Breaking the Code
10.1 Alan Turing and Cryptography
10.1.1 Background on Alan Turing
10.1.2 The Turing Machine
10.1.3 What Is Cryptography?
10.1.4 Encryption by Way of Affine Transformations
10.1.5 Digraph Transformations
10.2 RSA Encryption
10.2.1 Basics and Background
10.2.2 Preparation for RSA
10.2.3 Modular Arithmetic
10.2.4 Relatively Prime Integers
10.2.5 The RSA System Enunciated
10.2.6 The RSA Encryption System Explicated
11. Discrete Problems
11.1 Far-Reaching Dominoes
11.2 Surreal Life
11.3 A Problem with Marriage
11.4 Euler’s Bridges
11.5 Scheduling Sporting Events
12. Advanced Ideas
12.1 Searching on Google
12.1.1 The Mathematics of a Google Search
12.1.2 The Directed Web Graph
12.1.3 Passage to the Web HyperLink Matrix
12.1.4 A Fix for Dangling Nodes
12.1.5 The Ultimate Google Matrix
12.2 A Needle Problem of Kakeya
12.3 Euclidean and Non‐Euclidean Geometry
12.4 Archimedes and the Calculation of the
12.4.1 The Genius of Archimedes
12.4.2 Archimedes’s Calculation of the Area of a Circle
13. Concluding Remarks
13.1 The Final Word

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