How to Free Your Inner Mathematician: Notes on Mathematics and Life

by Susan D'Agostino

Overview

How to Free Your Inner Mathematician: Notes on Mathematics and Life offers readers guidance in managing the fear, freedom, frustration, and joy that often accompany calls to think mathematically. With practical insight and years of award-winning mathematics teaching experience, D'Agostino offers more than 300 hand-drawn sketches alongside accessible descriptions of fractals, symmetry, fuzzy logic, knot theory, Penrose patterns, infinity, the Twin Prime Conjecture, Arrow's Impossibility Theorem, Fermat's Last Theorem, and other intriguing mathematical topics.

Readers are encouraged to embrace change, proceed at their own pace, mix up their routines, resist comparison, have faith, fail more often, look for beauty, exercise their imaginations, and define success for themselves.

Mathematics students and enthusiasts will learn advice for fostering courage on their journey regardless of age or mathematical background. How to Free Your Inner Mathematician delivers not only engaging mathematical content but provides reassurance that mathematical success has more to do with curiosity and drive than innate aptitude.

Product Details

ISBN-13:	9780198843597
Publisher:	Oxford University Press
Publication date:	05/26/2020
Pages:	368
Product dimensions:	7.80(w) x 5.20(h) x 1.00(d)

About the Author

Susan D'Agostino, Council for the Advancement of Science Writing; Taylor/Blakeslee Fellow, Johns Hopkins University

Susan D'Agostino is a mathematician and writer whose essays have been published in Quanta Magazine, Scientific American, Financial Times, Nature, Undark, Times Higher Education, Chronicle of Higher Education, Math Horizons, Mathematics Teacher, and others. She earned her PhD in Mathematics from Dartmouth College, Master of Arts in Teaching Mathematics from Smith College, and BA in Anthropology from Bard College. She is a Council for the Advancement of Science Writing Taylor/Blakeslee Fellow at Johns Hopkins University. Her website is www.susandagostino.com and her Twitter handle is @susan_dagostino.

Table of Contents

1. Mix up your routine, as cicadas with prime number cycles2. Grow in accessible directions, like Voronoi diagrams3. Rely on your reasoning abilities, because folded paper may reach the moon4. Define success for yourself, given Arrow's Impossibility Theorem5. Reach for the stars, just like Katherine Johnson6. Find the right match, as with binary numbers and computers7. Act natural, because of Benford's Law8. Resist comparison, because of chaos theory9. Look all around, as Archimedes did in life10. Walk through the problem, as on the Konigsborg bridges11. Untangle problems, with knot theory12. Consider all options, as the shortest path between two points is not always straight13. Look for beauty, because of Fibonacci numbers14. Divide and conquer, just like Riemann sums in calculus15. Embrace change, considering non-Euclidean geometry16. Pursue an easier approach, considering the Pigeonhole Principle17. Make an educated guess, like Kepler with his Sphere-packing Conjecture18. Proceed at your own pace, because of terminal velocity19. Pay attention to details, as Earth is an oblate spheroid20. Join the community, with Hilbert's 23 problems21. Search for like-minded math friends, because of the Twin Prime Conjecture22. Abandon perfectionism, because of the Hairy Ball Theorem23. Enjoy the pursuit, as Andrew Wiles did with Fermat's Last Theorem24. Design your own pattern, because of the Penrose Patterns25. Keep it simple whenever possible, since26. Change your perspective, with Viviani's Theorem27. Explore, on a Mobius strip28. Be contradictory, because of the infinitude of primes29. Cooperate when possible, because of game theory30. Consider the less-travelled path, because of the Jordan Curve Theorem31. Investigate, because of the golden rectangle32. Be okay with small steps, as the harmonic series grows without bound33. Work efficiently, like bacteriophages with icosahedral symmetry34. Find the right balance, as in coding theory35. Draw a picture, as in proofs without words36. Incorporate nuance, because of fuzzy logic37. Be grateful when solutions exist, because of Brouwer's Fixed Point Theorem38. Update your understanding, with Bayesian statistics39. Keep an open mind, because imaginary numbers exist40. Appreciate the process, by taking a random walk41. Fail more often, just like Albert Einstein did with42. Get disoriented, on a Klein bottle43. Go outside your realm of experience, on a hypercube44. Follow your curiosity, along a space-filling curve45. Exercise your imagination, with fractional dimensions46. Proceed with care, because some infinities are larger than others

Editorial Reviews

"This is a popular book for those who want to learn about mathematics and mathematical thinking but have no mathematical background...Detailed solutions to the problems are provided" — Roman Murawski, zbMATH

"In an era of excellent books about mathematics for a popular audience, this book stands out, for its spirit, imagination, and liveliness." — Paul Campbell, Beloit College, The Hastings Center Report

"I never knew I could find math so entertaining! I loved not just bending my mind around concepts I can actually use in my life but learning about some of the mathematicians and history behind them. D'Agostino's clever illustrations are a big plus!" — Nancy Lord, former Alaska writer laureate & author of Fishcamp and Beluga Days

"Marvelous mathematical meditations. D'Agostino leads the reader to discover their mathematical selves through self-contained explorations. Appropriate for mathematical novices, enthusiasts, professionals, or anyone willing to reflect on the truth, beauty, and joy of mathematics." — Jennifer J. Quinn, President Elect of Mathematical Association of America 2021-2022, Professor of Mathematics, UW Tacoma, & author of Proofs That Really Count: The Art of Combinatorial Proof

"In life, as in mathematics, a fresh approach is sometimes warranted. D'Agostino intertwines life's lessons with those gleaned from a stunning array of mathematical gems to forge a vision of mathematics that is both personal and universal." — Rhonda Hughes, Professor Emerita of Mathematics, Bryn Mawr College

"This delightful book contains precious nuggets of mathematics rendered accessible to most by connecting them to real life and engaging the reader in artfully paced steps. What is truly unique about this book, however, is the way D'Agostino infuses it with her humanity, making it as fun and instructive as it is wise." — Christophe Gole, Smith College Professor of Mathematics & Statistics

"Few things are as beautiful, fascinating and revealing about life and important to its pursuit as mathematics. This elegantly written book makes mathematics alive and accessible, without compromise, with charm, clarity, grace, and wit. This book should fall into the hands not only of all students, but all adults. Readers will not only be grateful, but will smile along the way." — Leon Botstein, Bard College President, American Symphony Orchestra Conductor, & author of Jefferson's Children: Education and the Promise of American Culture

"This book is a great entry point for the curious student wondering about the world around them, a wonderful reference guide for the parent, a reminder for the working engineer, or an enjoyable read for anyone seeking to "update their understanding." It reminds us how elegantly math helps make sense of the world - and that success is in the eye of the beholder!" — Joseph J. Helble, Provost and Professor of Engineering, Dartmouth College

"I could describe the essays in this collection as inspiring and motivational, but that wouldn't quite communicate the validation I felt reading them... [the book] draws upon the theorems, applications, and history of mathematics to inspire lessons and advice for us along our mathematical (and other) pursuits. Delightful illustrations and an (honestly) enjoyable exercise accompany each essay. This book will appeal to aspiring mathematicians at any career stage, but its most important audience may be the latent mathematicians who have been discouraged from the discipline but are open to a fresh invitation." — Jason Cory Brunson, Research Assistant Professor, Laboratory for Systems Medicine, University of Florida, New Books Network

From the Publisher