دانلود کتاب The Best Writing on Mathematics 2010

فهرست مطالب :

Foreword xi Introduction xv @=30 The Role of the Untrue in Mathematics 3 Desperately Seeking Mathematical Proof 13 An Enduring Error 18 What Is Experimental Mathematics? 32 What Is Information-Based Complexity? 37 What Is Financial Mathematics? 43 If Mathematics Is a Language, How Do You Swear in It? 47 Birds and Frogs 57 Mathematics Is Not a Game But... 79 Massively Collaborative Mathematics 89 Bridging the Two Cultures: Paul Valéry 94 A Hidden Praise of Mathematics 99 Mathematics and the Internet: A Source of Enormous Confusion and Great Potential 109 The Higher Arithmetic: How to Count to a Zillion without Falling Off the End of the Number Line 134 Knowing When to Stop: How to Gamble if You Must \em The Mathematics of Optimal Stopping 145 Homology: An Idea Whose Time Has Come 158 Adolescent Learning and Secondary Mathematics 163 Accommodations of Learning Disabilities in Mathematics Courses 175 Audience, Style and Criticism 194 Aesthetics as a Liberating Force in Mathematics Education? 206 Mathematics Textbooks and Their Potential Role in Supporting Misconceptions 236 Exploring Curvature with Paper Models 247 Intuitive vs Analytical Thinking: Four Perspectives 260 Why Did Lagrange \l"Prove\r" the Parallel Postulate? 283 Kronecker's Algorithmic Mathematics 303 Indiscrete Variations on Gian-Carlo Rota's Themes 311 Circle Packing: A Personal Reminiscence 330 Applying Inconsistent Mathematics 346 Why Do We Believe Theorems? 358 Mathematicians Solve 45-Year-Old Kervaire Invariant Puzzle 373 Darwin: The Reluctant Mathematician 377 Loves Me, Loves Me Not (Do the Math) 380 The Mysterious Equilibrium of Zombies and Other Things Mathematicians See at the Movies 383 Strength in Numbers: On Mathematics and Musical Rhythm 387 Math-hattan 391 Contributors 395 Acknowledgments 403 Credits 405