D'Agostino Susan. How to Free Your Inner Mathematician. Notes on Mathematics and Life

Oxford University Press, 2020. — 368 p. — ISBN 978–0–19–884359–7.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.Why does this book exist?
Is this book for you?
What should you expect?
Mathematics for the body
Mix up your routine, as cicadas with prime number cycles
Grow in accessible directions, like Voronoi diagrams
Rely on your reasoning abilities, because folded paper may reach the moon
Define success for yourself, given Arrow’s Impossibility Theorem
Reach for the stars, just like Katherine Johnson
Find the right match, as with binary numbers and computers
Act natural, because of Benford’s Law
Resist comparison, because of chaos theory
Look all around, as Archimedes did in life
Walk through the problem, as on the Konigsberg bridges
Untangle problems, with knot theory
Consider all options, as the shortest path between two points is not always straight
Look for beauty, because of Fibonacci numbers
Divide and conquer, just like Riemann sums in calculus
Embrace change, considering non-Euclidean geometry
Pursue an easier approach, considering the Pigeonhole Principle
Make an educated guess, like Kepler with his Sphere-Packing Conjecture
Proceed at your own pace, because of terminal velocity
Pay attention to details, as Earth is an oblate spheroid
Join the community, with Hilbert’s twenty-three problems
Mathematics for the mind
Search for like-minded math friends, because of the Twin Prime Conjecture
Abandon perfectionism, because of the Hairy Ball Theorem
Enjoy the pursuit, as Andrew Wiles did with Fermat’s Last Theorem
Design your own pattern, because of the Penrose Patterns
Keep it simple whenever possible, since 0.999…=1
Change your perspective, with Viviani’s Theorem
Explore, on a Mobius strip
Be contradictory, because of the infinitude of primes
Cooperate when possible, because of game theory
Consider the less traveled path, because of the Jordan Curve Theorem
Investigate, because of the golden rectangle
Be okay with small steps, as the harmonic series grows without bound
Work efficiently, like bacteriophages with icosahedral symmetry
Find balance, as in coding theory
Draw a picture, as in proofs without words
Incorporate nuance, because of fuzzy logic
Be grateful when a solution exists, because of Brouwer’s Fixed Point Theorem
Update your understanding, with Bayesian statistics
Keep an open mind, because imaginary numbers exist
Appreciate the process, by taking a random walk
Fail more often, just like Albert Einstein did with E=mc2
Mathematics for the spirit
Get disoriented, on a Klein bottle
Go outside your realm of experience, on a hypercube
Follow your curiosity, along a space-filling curve
Exercise your imagination, with fractional dimensions
Proceed with care, because some infinities are larger than others