Here are 100 books that Alex Through the Looking-Glass fans have personally recommended if you like
Alex Through the Looking-Glass.
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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.
I have always liked the classical geometry of triangles and circles, but Matt Parker's book helped me go way beyond that and broaden my whole outlook. And the attractively hand-drawn diagrams and zany humour just added to the whole experience. After all, how many maths authors do you know who decide to build a computer out of 10,000 dominoes, just to calculate 6 + 4?
Stand-up mathematician and star of Festival of the Spoken Nerd, Matt Parker presents Things to Make and Do in the Fourth Dimension -- a riotous journey through the possibilities of numbers, with audience participation
- Cut pizzas in new and fairer ways! - Fit a 2p coin through an impossibly small hole! - Make a perfect regular pentagon by knotting a piece of paper! - Tie your shoes faster than ever before, saving literally seconds of your life! - Use those extra seconds to contemplate the diminishing returns of an exclamation-point at the end of every bullet-point! - Make a…
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.
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.
One way of enlivening any presentation of mathematics is by including some history of the subject, but this only really works if there is some serious scholarship behind it. I especially like Hollingdale's book, partly because of the concise writing style, and partly because of the unusually good balance between history and mathematics itself. The calculus, in all its various forms, with some aspects going right back to the Ancient Greeks, is treated especially well.
Fascinating and highly readable, this book recounts the history of mathematics as revealed in the lives and writings of the most distinguished practitioners of the art: Archimedes, Descartes, Fermat, Pascal, Newton, Leibniz, Euler, Gauss, Hamilton, Einstein, and many more. Author Stuart Hollingdale introduces and explains the roles of these gifted and often colorful figures in the development of mathematics as well as the ways in which their work relates to mathematics as a whole. Although the emphasis in this absorbing survey is primarily biographical, Hollingdale also discusses major historical themes and explains new ideas and techniques. No specialized mathematical knowledge…
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 book has haunted me for years. For what is it, exactly, that gives it such enduring popularity? After all, it was first published in 1936, yet is still in print today. In his autobiography, Hogben remarks on the importance of eye-catching illustrations but speculates that its success may instead be because the book contains – most unusually for a 'popular' work – exercises and answers, making it more suitable for self-teaching. Whatever the real answer, his book must surely have something to teach anyone – like myself – who aspires to bring mainstream mathematics to life for the general public.
I am a Research Assistant Professor of Computer Science at Stony Brook University learning/teaching/researching mathematics/algorithms/puzzles. In these fields, I have published a book, published 15+ papers in conferences/journals, been granted a US patent, won two Outstanding Paper Awards, taught 10+ courses in 25+ offerings, and have supervised 90+ master's/bachelor students. I am a puzzle addict involved in this field for 25 years and puzzles are my religion/God. Puzzles are the main form of supreme energy in this universe that can consistently give me infinite peace.
This book is full of beautiful puzzles on a mathematical topic called pursuit evasion. Its author Paul Nahin has written tens of books in physics and mathematics.
Nahin's writing can be described as a captivating reading experience pulling readers into his world like a whirlpool. His appreciation of mathematics, physics, and the people who discover them is unmatchable. It seems like the physics of motion and the mathematics of calculus is inseparable, as can be witnessed in the book.
The calculus used in this book is heavy. Nevertheless, Nahin makes his readers fall in love with this big beast. Almost every puzzle in this book is aesthetically beautiful and gives readers a deep sense of satisfaction. My favorites include Lady in the Lake, and Lion and Man.
We all played tag when we were kids. What most of us don't realize is that this simple chase game is in fact an application of pursuit theory, and that the same principles of games like tag, dodgeball, and hide-and-seek are also at play in military strategy, high-seas chases by the Coast Guard, and even romantic pursuits. In Chases and Escapes, Paul Nahin gives us the first complete history of this fascinating area of mathematics, from its classical analytical beginnings to the present day. Drawing on game theory, geometry, linear algebra, target-tracking algorithms, and much more, Nahin also offers an…
I have worked in scientific research and teaching for over 30 years, and maintained a love of art and music as well, but am saddened when I hear statements, especially from high-school pupils, that ‘there is no room for creativity or imagination in science.’ Like all working scientists, I know that imagination is the most important faculty for a scientist. The Poetry and Music of Science is my project to tease out the creative threads in the scientific process, and also to find the buried pathways that link science with the arts and humanities. The journey of discovery has been full of surprises and delights for me.
Visual representations are not the only pathway to creative acts in art and science, but they are responsible for large territories of creativity – including, and surprisingly, the mathematical. Arthur Miller shows how ‘seeing the unseen’ becomes possible from atoms to the conservation of energy in science, and from modernism to cubism in art. The book itself is as visually striking as its contents and helped me to think through why the visual metaphor – ‘Oh, I see!’ – becomes the standard description of the moment of insight.
Here, distinguished science historian Arthur I. Miller delves into the connections between modern art and modern physics. He takes us on a wide-ranging study to demonstrate that scientists and artists have a common aim: a visual interpretation of both the visible and invisible aspects of nature. Along the way, we encounter the philosophy of mind and language, cognitive science and neurophysiology in our search for the origins and meaning of visual imagery. At a time when the media are overeager to portray science as a godless, dehumanising exercise undermining the very fabric of society, this sixth book by Professor Miller…
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…
I am a physics professor with a passion for teaching. When I was a graduate student, I took required courses in classical mechanics, classical electrodynamics, quantum mechanics, and statistical mechanics. Some of the textbooks assigned by my professors were good; some were not so good. In every case, it was extremely helpful to read what other authors had to say about these foundational subjects. Four of the five books I recommend below are my personal favorites among these serious physics books. My fifth book choice is less serious and does not teach physics, but it will improve your graduate student experience nonetheless.
I love this book! Of course, it teaches the mathematics of the Lagrangian and Hamiltonian approaches to classical mechanics. But its real uniqueness lies in how the author explains the basic concepts of the subject with a constant emphasis on intuitive physics. It was only after reading Lanczos that I finally understood what variational calculations were really about. Ditto for virtual work, non-holonomic constraints, Liouville’s theorem and Hamilton-Jacobi theory. I barely noticed that I was learning about the history and philosophy of classical mechanics at the same time.
Analytical mechanics is, of course, a topic of perennial interest and usefulness in physics and engineering, a discipline that boasts not only many practical applications, but much inherent mathematical beauty. Unlike many standard textbooks on advanced mechanics, however, this present text eschews a primarily technical and formalistic treatment in favor of a fundamental, historical, philosophical approach. As the author remarks, there is a tremendous treasure of philosophical meaning" behind the great theories of Euler and Lagrange, Hamilton, Jacobi, and other mathematical thinkers. Well-written, authoritative, and scholarly, this classic treatise begins with an introduction to the variational principles of mechanics including…
I studied Greek philosophy in college and graduate school and wrote my Ph.D. dissertation on Plato. In response to the environmental crisis, first widely recognized in the 1960s, I turned my philosophical attention to that contemporary challenge, which, with the advent of climate change, has by now proved to be humanity’s greatest. I taught the world’s first course in environmental ethics at the University of Wisconsin-Stevens Point in 1971 and, with a handful of other philosophers, helped build a literature in this new field over the course of the next decade—a literature that has subsequently grown exponentially. With Greek Natural Philosophy, I rekindled the romance with my first love.
MIT scientist Tegmark directly connects contemporary physics and cosmology with our story of the Presocratic natural philosophers.
In his view the universe is not only described in the language of mathematics, it is a huge purely mathematical object. This was precisely the view of the Pythagoreans. In the course of expounding his theory of a mathematical universe, Tegmark brings the lay reader up to date on the latest developments in natural philosophy (aka theoretical physics and cosmology) and demonstrates their continuity with those of their ancient predecessors.
Nature, said Galileo, is 'a book written in the language of mathematics'. But why should this be? How can mathematics be at the heart of our universe?
The great Hungarian physicist and Nobel laureate Eugene Wigner stressed that this 'unreasonable effectiveness' of mathematics at describing the world was a mystery demanding explanation. Here, Max Tegmark, one of the most original cosmologists at work today, takes us on an astonishing journey to solve that mystery.
Part-history of the cosmos, part-intellectual adventure, Our Mathematical Universe travels from the Big Bang to the distant future via parallel worlds, across every possible scale -…
My undergraduate physics textbook asked, “What is an electric field? Is it something real, or is it merely a name for a factor in an equation which has to be multiplied by something else to give the numerical value of the force we measure in an experiment?” Here, I thought, is a good question! But the textbook said that since electromagnetic theory “works, it doesn’t make any difference" what an electric field is! Then it said, "That is not a frivolous answer, but a serious one.” I felt ashamed. But my physics teacher helpfully suggested that I “speak to the philosophers.” I am very pleased that I decided to become one!
This is the most fun book that has ever been written about the famous philosophical challenges posed by the proper interpretation of quantum mechanics. It is extremely difficult to say what the real world could possibly be like considering that quantum mechanics is so accurate at predicting our observations of it. Albert is a wonderful guide to this problem. His book is genuinely funny and down-to-earth (yes, I mean it!) and it introduces only as much technical and scientific machinery as is absolutely necessary. There is no other quantum mechanics book quite like this one.
The more science tells us about the world, the stranger it looks. Ever since physics first penetrated the atom, early in this century, what it found there has stood as a radical and unanswered challenge to many of our most cherished conceptions of nature. It has literally been called into question since then whether or not there are always objective matters of fact about the whereabouts of subatomic particles, or about the locations of tables and chairs, or even about the very contents of our thoughts. A new kind of uncertainty has become a principle of science.
