Here are 100 books that Fantasia Mathematica fans have personally recommended if you like
Fantasia Mathematica.
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As a full professor of mathematics for over 30 years, I have been engaged in research and teaching. Research can be difficult to describe to non-experts, but some important advances in mathematics can be explained to an interested public without the need for specialist knowledge, as I have done.
Frenkel came from the Soviet Union, where discrimination against Jews made it impossible for him to get into Moscow State University. During the oral exam they sent two graduate students to question him, pick holes in his responses, and ensure he failed. He turned to an informal network of Soviet mathematicians for help.
Like him, they were denied serious employment in the field, but after the 'cold war' against the Soviet Union, Harvard invited him to take a fellowship that later turned into a permanent job. Years later, when his old tormentor from Moscow State arrives to give a talk, he confronts the man in a lecture room with first-hand evidence of allegations against the system. Faced with a victim, the Russian mathematician's denials rang hollow.
This book reaches beyond mathematics to anyone of independent thought in an environment where it is not permitted to step out of line or,…
A New York Times Science BestsellerWhat if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren't even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry.In Love and Math , renowned mathematician Edward Frenkel reveals a side of math we've never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel…
A moving story of love, betrayal, and the enduring power of hope in the face of darkness.
German pianist Hedda Schlagel's world collapsed when her fiancé, Fritz, vanished after being sent to an enemy alien camp in the United States during the Great War. Fifteen years later, in 1932, Hedda…
As a full professor of mathematics for over 30 years, I have been engaged in research and teaching. Research can be difficult to describe to non-experts, but some important advances in mathematics can be explained to an interested public without the need for specialist knowledge, as I have done.
It provides an engaging description of the work that went into proving a famous result, first mentioned by the French mathematician Pierre de Fermat in the margin of a book.
The question was whether a sum of two nth powers of whole numbers could be the nth power of a whole number. It is certainly true for n = 2 but was not known for any n greater than 2. Fermat thought he had a proof that this was the case but later wrote proofs when n was 3 or 4, so his earlier claim was not taken seriously.
The general result turned out to be much harder than anyone imagined, and 350 years later, its truth was implied by another conjecture that was finally proved by Andrew Wiles, as this book explains. I admire the fact that the author distills some essential points from what turned out to be…
'I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain.'
It was with these words, written in the 1630s, that Pierre de Fermat intrigued and infuriated the mathematics community. For over 350 years, proving Fermat's Last Theorem was the most notorious unsolved mathematical problem, a puzzle whose basics most children could grasp but whose solution eluded the greatest minds in the world. In 1993, after years of secret toil, Englishman Andrew Wiles announced to an astounded audience that he had cracked Fermat's Last Theorem. He had no idea of the nightmare that…
As a full professor of mathematics for over 30 years, I have been engaged in research and teaching. Research can be difficult to describe to non-experts, but some important advances in mathematics can be explained to an interested public without the need for specialist knowledge, as I have done.
This book presents excerpts from original contributions to mathematics by scholars of the past. It includes principal developments from Neolithic times, from Mesopotamia, and from the ancient Greeks, right up to the modern world.
The extensive and well-chosen quotations make this a unique book. I found the excerpts from original sources rendered it a mine of valuable information for me or anyone else interested in the long history of mathematics.
In 1922 Barnes Wallis, who later invented the bouncing bomb immortalized in the movie The Dam Busters, fell in love for the first and last time, aged 35. The object of his affection, Molly Bloxam, was 17 and setting off to study science at University College London. Her father decreed that the two could correspond only if Barnes taught Molly mathematics in his letters.
Mathematics with Love presents, for the first time, the result of this curious dictat: a series of witty, tender and totally accessible introductions to calculus, trigonometry and electrostatic induction that remarkably, wooed and won the girl.…
Separating the true stories from the myths, The Duty of Memory provides a deeper understanding of the diverse motivations that drove ordinary people to join an underground network of French Resistants despite terrible odds and horrifying consequences.
This book takes the reader inside the true story of men and women…
As a full professor of mathematics for over 30 years, I have been engaged in research and teaching. Research can be difficult to describe to non-experts, but some important advances in mathematics can be explained to an interested public without the need for specialist knowledge, as I have done.
Hermann Weyl was one of the most influential mathematicians in the twentieth century. Born in North Germany, he worked for many years in Zürich and later moved to the Institute of Advanced Study in Princeton.
He was a colleague of Einstein in both places, and his book on Symmetry is a classic. This slim volume was a stimulus to me when I wrote my book.
Symmetry is a classic study of symmetry in mathematics, the sciences, nature, and art from one of the twentieth century's greatest mathematicians. Hermann Weyl explores the concept of symmetry beginning with the idea that it represents a harmony of proportions, and gradually departs to examine its more abstract varieties and manifestations--as bilateral, translatory, rotational, ornamental, and crystallographic. Weyl investigates the general abstract mathematical idea underlying all these special forms, using a wealth of illustrations as support. Symmetry is a work of seminal relevance that explores the great variety of applications and importance of symmetry.
Philosophy’s core questions have always obsessed me: What is real? What makes life worth living? Can knowledge be made secure? In graduate school at the University of Virginia I was drawn to mathematically formalized approaches to such questions, especially those of C. S. Peirce and Alain Badiou. More recently, alongside colleagues at Endicott College’s Center for Diagrammatic and Computational Philosophy and GCAS College Dublin I have explored applications of diagrammatic logic, category theory, game theory, and homotopy type theory to such problems as abductive inference and artificial intelligence. Philosophers committed to the perennial questions have much to gain today from studying the new methods and results of contemporary mathematics.
From a strictly philosophical perspective, the emergence of category theory as a unifying paradigm rivaling set theory is probably the most important development in mathematics in the last half-century.
But for philosophers without a lot of mathematical background, learning even its rudiments can be daunting. Among many introductory texts (Lawvere and Schanuel, Awodey, Riehl, Spivak), Cheng’s book stands out as perhaps the friendliest and most accessible.
She does not forego rigor, but she isn’t afraid to put aside precise formalism when necessary for intuition and clearer understanding. Her book takes the reader from mathematical beginnings through category theory’s core constructions to glimpses of higher-order categories (one of Cheng’s areas of expertise).
A mathematically novice philosopher who wants to understand the basics of category theory couldn’t do better.
Mathematician and popular science author Eugenia Cheng is on a mission to show you that mathematics can be flexible, creative, and visual. This joyful journey through the world of abstract mathematics into category theory will demystify mathematical thought processes and help you develop your own thinking, with no formal mathematical background needed. The book brings abstract mathematical ideas down to earth using examples of social justice, current events, and everyday life - from privilege to COVID-19 to driving routes. The journey begins with the ideas and workings of abstract mathematics, after which you will gently climb toward more technical material,…
I believe that knowledge is power. Understanding how something works leads to practical applications. In markets, I believe you should develop your own ideas on how to invest rather than being told. After all, how can you profit if you’re doing what everyone else is doing? Markets are efficient enough to give an opportunity to everyone but advantage to no one, unless you do something different than the crowd. My list is designed to give you information to develop investment strategies based on chaos theory, complexity, and fractals. It is not designed to tell you how to invest.
Readers of this list may be surprised that there are no books by Benoit Mandelbrot, the father of fractals. I found his books fascinating but frustrating. Feder’s book, by contrast, was readable and usable.
This book taught me how to do fractal analysis. While Feder’s book has nothing to do with markets, it has everything to do with applications. While I reuse much of Feder’s methodology in my books, readers will find it useful to see other practical applications of fractal analysis.
This lovely little book will take off and fly on its own power, but the author has asked me to write a few words, and one should not say no to a friend. Specific topics in fractal geometry and its applications have already benefited from several excellent surveys of moderate length, and gossip and preliminary drafts tell us that we shall soon see several monographic treatments of broader topics. For the teacher, however, these surveys and monographs are not enough, and an urgent need for more helpful books has been widely recognized. To write such a book is no easy…
What were America's first prisons like? How did penal reformers, prison administrators, and politicians deal with the challenges of confining human beings in long-term captivity as punishment--what they saw as a humane intervention?
The Deviant Prison centers on one early prison: Eastern State Penitentiary. Built in Philadelphia, one of the…
I've been teaching math and physics for more than 20 years as a private tutor. During this time, I experimented with different ways to explain concepts to make them easy to understand. I'm a big fan of using concept maps to show the connections between concepts and teaching topics in an integrated manner, including prerequisites and applications. While researching the material for my book, I read dozens of linear algebra textbooks and watched hundreds of videos, looking for the best ways to explain complicated concepts intuitively. I've tried to distill the essential ideas of linear algebra in my book and prepared this list to highlight the books I learned from.
In my opinion, Prof. Axler's book is the best way to learn the formal proofs of linear algebra theorems.
My undergraduate studies were in engineering, so I never learned the proofs. This is why I chose this book to solidify my understanding of the material; it didn't disappoint! Already, in the first few chapters, I learned new things about concepts that I thought I understood.
The book contains numerous exercises which were essential for the learning process. I went through the exercises with a group of friends, which helped me stay motivated. It wasn't easy, but all the time I invested in the proofs was rewarded by a solid understanding of the material.
I highly recommend this book as a second book on linear algebra.
This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra.
The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have…
Philosophy’s core questions have always obsessed me: What is real? What makes life worth living? Can knowledge be made secure? In graduate school at the University of Virginia I was drawn to mathematically formalized approaches to such questions, especially those of C. S. Peirce and Alain Badiou. More recently, alongside colleagues at Endicott College’s Center for Diagrammatic and Computational Philosophy and GCAS College Dublin I have explored applications of diagrammatic logic, category theory, game theory, and homotopy type theory to such problems as abductive inference and artificial intelligence. Philosophers committed to the perennial questions have much to gain today from studying the new methods and results of contemporary mathematics.
Zalamea’s book is the perfect introduction and survey if you want to understand how developments in contemporary mathematics are relevant to current philosophy.
Zalamea’s own approach follows closely in the steps of Peirce, Lautman, and Grothendieck, merging pragmatism, dialectics, and sheaf theory, but he also engages the work of dozens of other key mathematicians and philosophers coming from different points of view, sometimes cursorily, always tantalizingly.
No philosopher can read this book without a quickened heartbeat and eager plans to clear shelf space for some of the many volumes of mathematics and philosophy of mathematics canvassed here by Zalamea.
A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest.
A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest, this book gives the inquisitive non-specialist an insight into the conceptual transformations and intellectual orientations of modern and contemporary mathematics.
The predominant analytic approach, with its focus on the formal, the elementary and the foundational, has effectively divorced philosophy from the real practice of mathematics and the profound conceptual shifts in the discipline over the last century. The first part discusses the…
I am an applied mathematician at Oxford University, and author of the bestseller 1089 and All That, which has now been translated into 13 languages. In 1992 I discovered a strange mathematical theorem – loosely related to the Indian Rope Trick - which eventually featured on BBC television. My books and public lectures are now aimed at bringing mainstream mathematics to the general public in new and exciting ways.
This is a sequel to Alex Bellos's bestseller Alex's Adventures in Numberland, but more focused on applications of mathematics to the real world, especially through physics. Many of these were known to me, particularly when they involved calculus, but I greatly enjoyed Alex's distinctive and novel way of putting across sophisticated ideas, in part by interspersing them with personal interviews with mathematicians of all kinds.
From triangles, rotations and power laws, to fractals, cones and curves, bestselling author Alex Bellos takes you on a journey of mathematical discovery with his signature wit, engaging stories and limitless enthusiasm. As he narrates a series of eye-opening encounters with lively personalities all over the world, Alex demonstrates how numbers have come to be our friends, are fascinating and extremely accessible, and how they have changed our world.
He turns even the dreaded calculus into an easy-to-grasp mathematical exposition, and sifts through over 30,000 survey submissions to reveal the world's favourite number. In Germany, he meets the engineer who…
Pioneer Paddles of the Colonial South
by
William D. Auman,
Award-winning novelist William Auman, author of If Trees Could Testify..., takes the reader on a time-traveling odyssey featuring 345 bodies of water in six states within the historical context through which they unfold.
Journey into remaining Colonial-era wilderness with stories of pirate treasure, epic frontiersmen, Indigenous Peoples, and Revolutionary…
I am an applied mathematician at Oxford University, and author of the bestseller 1089 and All That, which has now been translated into 13 languages. In 1992 I discovered a strange mathematical theorem – loosely related to the Indian Rope Trick - which eventually featured on BBC television. My books and public lectures are now aimed at bringing mainstream mathematics to the general public in new and exciting ways.
This may seem an odd choice, but as a maths popularizer I need to know all that I can about why some people find the main elements of the subject so difficult. I found Doug French's book exceptionally helpful in this respect, even though it is aimed principally at high school teachers. This is partly because he focuses throughout on the most important mathematical ideas and difficulties. Moreover, the scope is wider than the title suggests, for he also ventures imaginatively into both geometry and calculus.
Continuum has repackaged some of its key academic backlist titles to make them available at a more affordable price. These reissues will have new ISBNs, distinctive jackets and strong branding. They cover a range of subject areas that have a continuing student sale and make great supplementary reading more accessible. A comprehensive, authoritative and constructive guide to teaching algebra.
