Seduction is not just an end result, but a process — and in mathematics, both the end results and the process by which those end results are achieved are often charming and elegant. This helps to explain why so many people — not just those for whom math plays a key role in their day-to-day lives — have found mathematics so seductive. Math is unique among all subjects in that it contains end results of amazing insight and power, and lines of reasoning that are clever, charming, and elegant. This book is a collection of those results and lines of reasoning that make us say, "OMG, that's just amazing," — because that's what mathematics is to those who love it. In addition, some of the stories about mathematical discoveries and the people who discovered them are every bit as fascinating as the discoveries themselves. This book contains material capable of being appreciated by students in elementary school — as well as some material that will probably be new to even the more mathematically sophisticated. Most of the book can be easily understood by those whose only math courses are algebra and geometry, and who may have missed the magic, enchantment, and wonder that is the special province of mathematics.
Author(s): James D. Stein
Series: Problem Solving in Mathematics and Beyond, 28
Edition: 1
Publisher: World Scientific Publishing
Year: 2022
Language: English
Commentary: Has a banner on the left hand-side of every page.
Pages: 224
City: Singapore
Tags: Numbers; Arithmetic; Analytic Geometry; Mathematical Induction; Calculus; Complex Numbers; Infinite Series; Probability; Infinity
Contents
Preface — Just What Does She See in Him, Anyway?
About the Author
Introduction: Seduced by Mathematics
Seduced by Murder Mysteries
The World Series (and Other Best of … Competitions)
A Seductive Proof of the Pythagorean Theorem
Bibliography
Chapter 1 Seduced by Numbers
Size Matters
Prime Numbers
Seductive Numbers
2
Algebraic Numbers
π
e
Reciprocity
Bibliography
Chapter 2 Seduced by Arithmetic
Last Digit Standing
1,729
635,318,657
Taxicab Numbers
An Oldie But Goodie
1,089
Does the 1,089 Trick Work in Octal?
6,174
Beating the Averages in Investing
Bibliography
Chapter 3 Seduced by Patterns
Recursive and Explicit (Formulaic) Patterns
Fibonacci Numbers
Excel 101
Fun with Fibonacci — Excel 102
More about the Golden Ratio
The Quicksand of Mathematics
Seduced by Hidden Patterns
Last Marble in the Jar
A Different Last Marble Problem
Bibliography
Chapter 4 Seduced by Analytic Geometry
The Unexpected Parallelogram — Varignon’s Theorem
Morley’s Theorem
Covering Up
Homage to the Greeks
Descartes and the Birth of Analytic Geometry
But It Doesn’t Just Make Geometry Easier
Implicit Functions
The Moving Dot
Foxes and Rabbits — The Lotka–Volterra Equations
Bibliography
Chapter 5 Seduced by Mathematical Induction (and How to Avoid It)
The Principle of Mathematical Induction
March Madness, Classic Version
The GOAT — Candidate #1
The Sum of Odd Integers
The GOAT — Candidate #2
Bibliography
Chapter 6 Seduced by Calculus I
Simply the Best
Crossing a River
The L-Shaped Corridor
Two You Don’t Often See
Four Problems, One Diagram
Bibliography
Chapter 7 Seduced by Complex Numbers
Rene Descartes’ Imaginary Contribution
The Work of Man
The Complex Plane
Euler’s Formula
De Moivre’s Theorem
The nth Roots of 1
Partial Fractions
Complex Numbers and Differential Equations
A Cutie from Multivariable Calculus
The Residue Theorem
Bibliography
Chapter 8 Seduced by Infinite Series
Geometric Series
Questions
Tool #1 — The Thin Sub-sequence Test
Torricelli’s Tower
Taylor’s Theorem
Playing with Infinite Series
Offspring
Riemann’s Casino
John von Neumann and the Bumblebee
Bibliography
Chapter 9 Seduced by Probability
Playing Games
The Birthday Problem
The Monty Hall Problem
Bayes’ Theorem
Tennis, Anyone?
Tennish, Anyone?
Entanglement in Quantum Mechanics
Probabilistic Entanglement
Blackwell’s Bet
Bibliography
Chapter 10 Seduced by Infinity
Sleight of Hand
One-to-One Correspondences
Finite and Countable Sets: Hilbert’s Hotel
An Influx of Bynars
Cantor’s Theorem
The Continuum Hypothesis
The Axioms of Set Theory
The Axiom of Choice
Transfinite Induction
Zorn’s Lemma
Bibliography
Chapter 11 Seduced by Computers
Chaotic Phenomena
The Traveling Salesman Problem
Easy, Hard, and Nasty Problems
Temple of Benares/Tower of Hanoi
The Traveling Salesman Problem Returns
Monte Carlo Simulations
Making a Name for Yourself — with the Aid of a Computer and This Book
Bibliography
Chapter 12 Seduced by a Few of My Favorite Things
My Favorite Mathematical Joke
My Next Favorite Mathematical Joke
One Good Whack
To the Vector Belong the Spoils
Equivalence Relations
Mathematical Results with Amusing Names
Fixed-Point Theorems
Bibliography
Index
