Mathematics and the Imagination


Edward Kasner - 1940
    But your pleasure and prowess at games, gambling, and other numerically related pursuits can be heightened with this entertaining volume, in which the authors offer a fascinating view of some of the lesser-known and more imaginative aspects of mathematics.A brief and breezy explanation of the new language of mathematics precedes a smorgasbord of such thought-provoking subjects as the googolplex (the largest definite number anyone has yet bothered to conceive of); assorted geometries — plane and fancy; famous puzzles that made mathematical history; and tantalizing paradoxes. Gamblers receive fair warning on the laws of chance; a look at rubber-sheet geometry twists circles into loops without sacrificing certain important properties; and an exploration of the mathematics of change and growth shows how calculus, among its other uses, helps trace the path of falling bombs.Written with wit and clarity for the intelligent reader who has taken high school and perhaps college math, this volume deftly progresses from simple arithmetic to calculus and non-Euclidean geometry. It “lives up to its title in every way [and] might well have been merely terrifying, whereas it proves to be both charming and exciting." — Saturday Review of Literature.

A Mathematician's Apology


G.H. Hardy - 1940
    H. Hardy was one of this century's finest mathematical thinkers, renowned among his contemporaries as a 'real mathematician ... the purest of the pure'. He was also, as C. P. Snow recounts in his Foreword, 'unorthodox, eccentric, radical, ready to talk about anything'. This 'apology', written in 1940 as his mathematical powers were declining, offers a brilliant and engaging account of mathematics as very much more than a science; when it was first published, Graham Greene hailed it alongside Henry James's notebooks as 'the best account of what it was like to be a creative artist'. C. P. Snow's Foreword gives sympathetic and witty insights into Hardy's life, with its rich store of anecdotes concerning his collaboration with the brilliant Indian mathematician Ramanujan, his aphorisms and idiosyncrasies, and his passion for cricket. This is a unique account of the fascination of mathematics and of one of its most compelling exponents in modern times.

Bad Astronomy


Philip Plait - 2002
    Plait created his popular web site: http://www.badastronomy.com/index.html, to debunk bad astronomy in popular culture. This website proved popular, which led to this first book by Plait, that carries on from the website and in a detailed and clear fashion criticises and disproves popular myths and misconceptions relating to astronomy, and promotes science as a means of explaining the skies. The work describes 24 common astronomical fallacies, including the beliefs that the Coriolis effect determines the direction that water drains in a bathtub, and that planetary alignments can cause disaster on Earth. The author sharply and convincingly dismisses astrology, creationism, and UFO sightings, and explains the principles behind basic general concepts (the Big Bang, why the sky is blue, etc.).

The Math of Life and Death: 7 Mathematical Principles That Shape Our Lives


Kit Yates - 2019
    But for those of us who left math behind in high school, the numbers and figures hurled at us as we go about our days can sometimes leave us scratching our heads and feeling as if we’re fumbling through a mathematical minefield. In this eye-opening and extraordinarily accessible book, mathemati­cian Kit Yates illuminates hidden principles that can help us understand and navigate the chaotic and often opaque surfaces of our world. In The Math of Life and Death, Yates takes us on a fascinating tour of everyday situations and grand-scale applications of mathematical concepts, including exponential growth and decay, optimization, statistics and probability, and number systems. Along the way he reveals the mathematical undersides of controversies over DNA testing, medical screening results, and historical events such as the Chernobyl disaster and the Amanda Knox trial. Readers will finish this book with an enlightened perspective on the news, the law, medicine, and history, and will be better equipped to make personal decisions and solve problems with math in mind, whether it’s choosing the shortest checkout line at the grocery store or halting the spread of a deadly disease.

The Heart of Mathematics: An Invitation to Effective Thinking


Edward B. Burger - 1999
    In this new, innovative overview textbook, the authors put special emphasis on the deep ideas of mathematics, and present the subject through lively and entertaining examples, anecdotes, challenges and illustrations, all of which are designed to excite the student's interest. The underlying ideas include topics from number theory, infinity, geometry, topology, probability and chaos theory. Throughout the text, the authors stress that mathematics is an analytical way of thinking, one that can be brought to bear on problem solving and effective thinking in any field of study.

What Is Life? with Mind and Matter and Autobiographical Sketches


Erwin Schrödinger - 1944
    The book was based on a course of public lectures delivered by Schrödinger in February 1943 at Trinity College, Dublin. Schrödinger's lecture focused on one important question: "how can the events in space and time which take place within the spatial boundary of a living organism be accounted for by physics and chemistry?" In the book, Schrödinger introduced the idea of an "aperiodic crystal" that contained genetic information in its configuration of covalent chemical bonds. In the 1950s, this idea stimulated enthusiasm for discovering the genetic molecule and would give both Francis Crick and James Watson initial inspiration in their research.

Einstein's Universe


Nigel Calder - 1979
    It far surpasses any previous explanation of Relativity for laypersons.

Fourier Series


Georgi P. Tolstov - 1976
    Over 100 problems at ends of chapters. Answers in back of book. 1962 edition.

On Growth and Form


D'Arcy Wentworth Thompson - 1917
    Why do living things and physical phenomena take the forms they do? Analyzing the mathematical and physical aspects of biological processes, this historic work, first published in 1917, has become renowned as well for the poetry of is descriptions.

Dancing Wu Li Masters: An Overview of the New Physics (Perennial Classics)


Gary Zukav - 1979
    Like a Wu Li Master who would teach us wonder for the falling petal before speaking of gravity, Zukav writes in beautifully clear language—with no mathematical equations—opening our minds to the exciting new theories that are beginning to embrace the ultimate nature of our universe...Quantum mechanics, relativity, and beyond to the Einstein-Podolsky-Rosen effect and Bell's theorem.At an Esalen Institute meeting in 1976, tai chi master Al Huang said that the Chinese word for physics is Wu Li, "patterns of organic energy." Journalist Gary Zukav and the others present developed the idea of physics as the dance of the Wu Li Masters--the teachers of physical essence. Zukav explains the concept further: The Wu Li Master dances with his student. The Wu Li Master does not teach, but the student learns. The Wu Li Master always begins at the center, the heart of the matter.... This book deals not with knowledge, which is always past tense anyway, but with imagination, which is physics come alive, which is Wu Li.... Most people believe that physicists are explaining the world. Some physicists even believe that, but the Wu Li Masters know that they are only dancing with it. The "new physics" of Zukav's 1979 book comprises quantum theory, particle physics, and relativity. Even as these theories age they haven't percolated all that far into the collective consciousness; they're too far removed from mundane human experience not to need introduction. The Dancing Wu Li Masters remains an engaging, accessible way to meet the most profound and mind-altering insights of 20th-century science. --Mary Ellen Curtin

The Calendar


David Ewing Duncan - 1998
    The year 2000 is alternatively the year 2544 (Buddhist), 6236 (Ancient Egyptian), 5761 (Jewish) or simply the Year of the Dragon (Chinese). The story of the creation of the Western calendar, which is related in this book, is a story of emperors and popes, mathematicians and monks, and the growth of scientific calculation to the point where, bizarrely, our measurement of time by atomic pulses is now more accurate than time itself: the Earth is an elderly lady and slightly eccentric - she loses half a second a century. Days have been invented (Julius Caesar needed an extra 80 days in 46BC), lost (Pope Gregory XIII ditched ten days in 1582) and moved (because Julius Caesar had 31 in his month, Augustus determined that he should have the same, so he pinched one from February).

We Have No Idea: A Guide to the Unknown Universe


Jorge Cham - 2017
    While they're at it, they helpfully demystify many complicated things we do know about, from quarks and neutrinos to gravitational waves and exploding black holes. With equal doses of humor and delight, they invite us to see the universe as a vast expanse of mostly uncharted territory that's still ours to explore.This entertaining illustrated science primer is the perfect book for anyone who's curious about all the big questions physicists are still trying to answer.

How to Solve It: A New Aspect of Mathematical Method


George Pólya - 1944
    Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be reasoned out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem.

Imagining the Tenth Dimension: A New Way of Thinking about Time and Space


Rob Bryanton - 2006
    Ten dimensions? Most of us have barely gotten used to the idea that there are four.Using simple geometry and an easygoing writing style, author Rob Bryanton starts with the lower dimensions that we are all familiar with, then uses those concepts to build one layer upon another, ultimately arriving at a way of imagining the tenth dimension.Part scientific exploration, part philosophy, this unique book touches upon such diverse topics as dark matter, Feynman's "sum over paths", the quantum observer, and the soul. It is aimed at anyone interested in leading-edge theories about cosmology and the nature of reality, but it is not about mainstream physics. Rather, Imagining the Tenth Dimension is a mind-expanding exercise that could change the way you view this incredible universe in which we live.

The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy


Sharon Bertsch McGrayne - 2011
    To its adherents, it is an elegant statement about learning from experience. To its opponents, it is subjectivity run amok.In the first-ever account of Bayes' rule for general readers, Sharon Bertsch McGrayne explores this controversial theorem and the human obsessions surrounding it. She traces its discovery by an amateur mathematician in the 1740s through its development into roughly its modern form by French scientist Pierre Simon Laplace. She reveals why respected statisticians rendered it professionally taboo for 150 years—at the same time that practitioners relied on it to solve crises involving great uncertainty and scanty information (Alan Turing's role in breaking Germany's Enigma code during World War II), and explains how the advent of off-the-shelf computer technology in the 1980s proved to be a game-changer. Today, Bayes' rule is used everywhere from DNA de-coding to Homeland Security.Drawing on primary source material and interviews with statisticians and other scientists, The Theory That Would Not Die is the riveting account of how a seemingly simple theorem ignited one of the greatest controversies of all time.