A Fields medalist recounts his lifelong effort to uncover the geometric shape—the Calabi-Yau manifold—that may store the hidden dimensions of our universe.Harvard geometer Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes, and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world’s most distinguished mathematicians. Beginning with an impoverished childhood in China and Hong Kong, Yau takes readers through his doctoral studies at Berkeley during the height of the Vietnam War protests, his Fields Medal–winning proof of the Calabi conjecture, his return to China, and his pioneering work in geometric analysis. This new branch of geometry, which Yau built up with his friends and colleagues, has paved the way for solutions to several important and previously intransigent problems.With complicated ideas explained for a broad audience, this book offers not only insights into the life of an eminent mathematician, but also an accessible way to understand advanced and highly abstract concepts in mathematics and theoretical physics.“The remarkable story of one of the world’s most accomplished mathematicians . . . Yau’s personal journey—from escaping China as a youngster, leading a gang outside Hong Kong, becoming captivated by mathematics, to making breakthroughs that thrust him on the world stage—inspires us all with humankind’s irrepressible spirit of discovery.” —Brian Greene, New York Times–bestselling author of The Elegant Universe“An unexpectedly intimate look into a highly accomplished man, his colleagues and friends, the development of a new field of geometric analysis, and a glimpse into a truly uncommon mind.” —The Boston Globe“Engaging, eminently readable. . . . For those with a taste for elegant and largely jargon-free explanations of mathematics, The Shape of a Life promises hours of rewarding reading.” —American Scientist Read more

An exquisite visual celebration of the 2,500-year history of geometryIf you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configurations involving infinity. The result is a delightful and informative illustrated tour through the 2,500-year-old history of one of the most important branches of mathematics. Read more

A comprehensive exploration of the captivating world of fractals, stretching from their origins in mathematical theory to their vast applications in the modern world. The book invites readers on a journey through the landscape of fractals, starting from their mathematical foundations, moving through their intricate connections with nature, the cosmos, and even human physiology, and concluding with the most recent advancements in fractal theory and its integration in fields such as machine learning and quantum physics. Told in an engaging, narrative style, the book is an accessible and enlightening read for anyone fascinated by the interplay of mathematics, nature, and the complexity of our universe. The book not only educates but also sparks awe and curiosity, revealing the hidden beauty of our world through the lens of fractals. Read more

This enlightening and gorgeously illustrated book explores the beauty and mystery of the divine proportion in art, architecture, nature, and beyond.From the pyramids of Giza, to quasicrystals, to the proportions of the human face, the golden ratio has an infinite capacity to generate shapes with exquisite properties. Author Gary Meisner has spent decades researching the subject, investigating and collaborating with people across the globe in dozens of professions and walks of life. In The Golden Ratio, he shares his enlightening journey. Exploring the long history of this fascinating number, as well as new insights into its power and potential applications, The Golden Ratio invites you to take a new look at this timeless topic. Read more

The bestselling book that has helped millions of readers solve any problemA must-have guide by eminent mathematician G. Polya, How to Solve It shows 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 help you attack any problem that can be reasoned out—from building a bridge to winning a game of anagrams. How to Solve It includes a heuristic dictionary with dozens of entries on how to make problems more manageable—from analogy and induction to the heuristic method of starting with a goal and working backward to something you already know.This disarmingly elementary book explains how to harness curiosity in the classroom, bring the inventive faculties of students into play, and experience the triumph of discovery. But it’s not just for the classroom. Generations of readers from all walks of life have relished Polya’s brilliantly deft instructions on stripping away irrelevancies and going straight to the heart of a problem. Read more

A comprehensive new illustrated guide to geometry—from New York Times bestselling cartoonist Larry GonickWhat's the point of points? Where do we draw the line? If there are two sides to everything, then what's up with triangles, squares, and polygons?Once again, mathematician-turned-cartoonist Larry Gonick uses his unique gift for witty, lively, and clear exposition to demystify another complex subject: geometry.Moving from the most basic geometrical concepts—planes, lines, and points—through elementary postulates and to elaborate proofs, The Cartoon Guide to Geometry is a comprehensive primer on all the essentials of plane geometry: angles, triangles, area, similarity, and, yes, the Pythagorean theorem. Carefully tailored to the curriculum standards and standardized testing guidelines of the subject, the book provides innovative visuals that develop proofs and constructions with sequential graphics rather than single illustrations. The reader emerges with a deep grasp of key ideas—and has fun getting there. Read more

The third volume in the bestselling physics series cracks open Einstein's special relativity and field theory Physicist Leonard Susskind and data engineer Art Friedman are back. This time, they introduce readers to Einstein's special relativity and Maxwell's classical field theory. Using their typical brand of real math, enlightening drawings, and humor, Susskind and Friedman walk us through the complexities of waves, forces, and particles by exploring special relativity and electromagnetism. It's a must-read for both devotees of the series and any armchair physicist who wants to improve their knowledge of physics' deepest truths. Read more

Finalist for the PEN/E.O. Wilson Literary Science Writing Award"What a fun escape! Reminds me of math books I read when I was coming of age." —Neil deGrasse TysonAn "exhilarating" (Steven Strogatz) tour through the fundamental mathematical concepts—from arithmetic to infinity—that form the building blocks of our universe.Our universe has multiple origin stories, from religious creation myths to the Big Bang of scientists. But if we leave those behind and start from nothing—no matter, no cosmos, not even empty space—could we create a universe using only math? Irreverent, richly illustrated, and boundlessly creative, The Big Bang of Numbers invites us to try.In this new mathematical origin story, mathematician and novelist Manil Suri creates a natural progression of ideas needed to design our world, starting with numbers and continuing through geometry, algebra, and beyond. He reveals the secret lives of real and imaginary numbers, teaches them to play abstract games with real-world applications, discovers unexpected patterns that connect humble lifeforms to enormous galaxies, and explores mathematical underpinnings for randomness and beauty. With evocative examples ranging from multidimensional crochet to the Mona Lisa’s asymmetrical smile, as well as ingenious storytelling that helps illuminate complex concepts like infinity and relativity, The Big Bang of Numbers charts a playful, inventive course to existence. Mathematics, Suri shows, might best be understood not as something we invent to explain Nature, but as the source of all creation, whose directives Nature tries to obey as best she can.Offering both striking new perspectives for math aficionados and an accessible introduction for anyone daunted by calculation, The Big Bang of Numbers proves that we can all fall in love with math. Read more

The Quadrivium consists of the four Liberal Arts of Number, Geometry, Music, and Cosmology, studied from antiquity to the Renaissance as a way of glimpsing the nature of reality. They synthesize number, space, and time. Geometry is number in space, music is number in time, and the cosmos expresses number in space and time. Number, music, and geometry are metaphysical truths, good and beautiful everywhere at all times. Life across the universe investigates them. They foreshadow the physical sciences. This is the first volume to bring together the Quadrivium for many hundreds of years Read more

The Shape of Space, Third Edition maintains the standard of excellence set by the previous editions. This lighthearted textbook covers the basic geometry and topology of two- and three-dimensional spaces—stretching students’ minds as they learn to visualize new possibilities for the shape of our universe.Written by a master expositor, leading researcher in the field, and MacArthur Fellow, its informal exposition and engaging exercises appeal to an exceptionally broad audience, from liberal arts students to math undergraduate and graduate students looking for a clear intuitive understanding to supplement more formal texts, and even to laypeople seeking an entertaining self-study book to expand their understanding of space.Features of the Third Edition:Full-color figures throughout "Picture proofs" have replaced algebraic proofs Simpler handles-and-crosscaps approach to surfaces Updated discussion of cosmological applications Intuitive examples missing from many college and graduate school curricula About the Author:Jeffrey R. Weeks is a freelance geometer living in Canton, New York. With support from the U.S. National Science Foundation, the MacArthur Foundation and several science museums, his work spans pure mathematics, applications in cosmology and—closest to his heart—exposition for the general public. Read more

Linear algebra is growing in importance. 3D entertainment, animations in movies and video games are developed using linear algebra. Animated characters are generated using equations straight out of this book. Linear algebra is used to extract knowledge from the massive amounts of data generated from modern technology.The Fourth Edition of this popular text introduces linear algebra in a comprehensive, geometric, and algorithmic way. The authors start with the fundamentals in 2D and 3D, then move on to higher dimensions, expanding on the fundamentals and introducing new topics, which are necessary for many real-life applications and the development of abstract thought. Applications are introduced to motivate topics.The subtitle, A Geometry Toolbox, hints at the book’s geometric approach, which is supported by many sketches and figures. Furthermore, the book covers applications of triangles, polygons, conics, and curves. Examples demonstrate each topic in action. This practical approach to a linear algebra course, whether through classroom instruction or self-study, is unique to this book. New to the Fourth Edition: Ten new application sections.A new section on change of basis. This concept now appears in several places. Chapters 14-16 on higher dimensions are notably revised.A deeper look at polynomials in the gallery of spaces. Introduces the QR decomposition and its relevance to least squares.Similarity and diagonalization are given more attention, as are eigenfunctions. A longer thread on least squares, running from orthogonal projections to a solution via SVD and the pseudoinverse. More applications for PCA have been added.More examples, exercises, and more on the kernel and general linear spaces.A list of applications has been added in Appendix A.The book gives instructors the option of tailoring the course for the primary interests of their students: mathematics, engineering, science, computer graphics, and geometric modeling. Read more

"A complete introduction to the geometric code of nature, written and illustrated by the most perceptive of its modern investigators." —John Michell, from the Preface You need not be a philosopher or a botanist, and certainly not a mathematician, to enjoy the bounty of the world around us. But is there some sort of order, a pattern, to the things that we see in the sky, on the ground, at the beach? In A Beginner's Guide to Constructing the Universe, Michael Schneider, an education writer and computer consultant, combines science, philosophy, art, and common sense to reaffirm what the ancients observed: that a consistent language of geometric design underpins every level of the universe, from atoms to galaxies, cucumbers to cathedrals. Schneider also discusses numerical and geometric symbolism through the ages, and concepts such as periodic renewal and resonance. This book is an education in the world and everything we can't see within it.Contains numerous b&w photos and illustrations. “Once initiated into the ancient mysteries, the reader will recognize profound meanings—not merely scientific utility—in squares, triangles, and other common shapes. The reader needs no extraordinary expertise in mathematics to explore these pages, just a relish for intellectual adventure. Schneider helps us discover just how much mental energy can fit within the circle of new horizons.” —Booklist"Highly informative . . . [shows] Schneider's particular gift of transforming everyday experience into something magical . . . Highly recommended." —New Frontier Read more

“I love maps. I love math. And gosh, do I love this book, which so beautifully and clearly sounds the depths of both.” —Ben Orlin, author of Math with Bad DrawingsExplore the surprising connections between math and maps—and the myriad ways they’ve shaped our world and us.Why are coastlines and borders so difficult to measure? How does a UPS driver deliver hundreds of packages in a single day? And where do elusive serial killers hide? The answers lie in the crucial connection between maps and math.In Mapmatics, mathematician Paulina Rowińska leads us on a riveting journey around the globe to discover how maps and math are deeply entwined, and always have been. From a sixteenth-century map, an indispensable navigation tool that exaggerates the size of northern countries, to public transport maps that both guide and confound passengers, to congressional maps that can empower or silence whole communities, she reveals how maps and math have shaped not only our sense of space but our worldview. In her hands, we learn how to read maps like a mathematician—to extract richer information and, just as importantly, to question our conclusions by asking what we don’t see.Written with authority and compassion, wit and unforgettable storytelling, this is math exposition at its best. By unpacking the math behind the maps we depend on, Mapmatics illuminates how our world works and, ultimately, how we can better look after it. Read more

This engaging review guide and workbook is the ideal tool for sharpening your Geometry skills!This review guide and workbook will help you strengthen your Geometry knowledge, and it will enable you to develop new math skills to excel in your high school classwork and on standardized tests. Clear and concise explanations will walk you step by step through each essential math concept. 500 practical review questions, in turn, provide extensive opportunities for you to practice your new skills. If you are looking for material based on national or state standards, this book is your ideal study tool!Features:•Aligned to national standards, including the Common Core State Standards, as well as the standards of non-Common Core states and Canada•Designed to help you excel in the classroom and on standardized tests•Concise, clear explanations offer step-by-step instruction so you can easily grasp key concepts•You will learn how to apply Geometry to practical situations•500 review questions provide extensive opportunities for you to practice what you’ve learned Read more

"A must-read.”―Avi Loeb, New York Times–bestselling author of Extraterrestrial One of the preeminent mathematicians of the past half century shows how physics and math were combined to give us the theory of gravity and the dizzying array of ideas and insights that has come from it  Mathematics is far more than just the language of science. It is a critical underpinning of nature. The famed physicist Albert Einstein demonstrated this in 1915 when he showed that gravity—long considered an attractive force between massive objects—was actually a manifestation of the curvature, or geometry, of space and time. But in making this towering intellectual leap, Einstein needed the help of several mathematicians, including Marcel Grossmann, who introduced him to the geometrical framework upon which his theory rest.   In The Gravity of Math, Steve Nadis and Shing-Tung Yau consider how math can drive and sometimes even anticipate discoveries in physics. Examining phenomena like black holes, gravitational waves, and the Big Bang, Nadis and Yau ask: Why do mathematical statements, derived solely from logic, provide the best descriptions of our physical world?  The Gravity of Math offers an insightful and compelling look into the power of mathematics—whose reach, like that of gravity, can extend to the edge of the universe. Read more

Feeling overwhelmed just thinking about the SAT®? Not sure where to start your prep but need a clear plan? Buried under a mountain of study material and want a way to cut through the clutter?You’re not alone. A lot of students feel exactly like you—anxious, unprepared, and feeling the weight of pressure from parents, friends, or even yourself. It’s easy to feel like you’re drowning in the fear of failing or not meeting expectations. And let’s not even mention those SAT® prep books—most are outdated, overly complicated, and just way too long. Just looking at them can make you want to quit before you start!But here’s the good news: there’s a solution.The trick is simple—study smarter, not harder. Focus on what really matters with a streamlined, up-to-date study plan that targets exactly what you need to know and cuts out all the fluff.That’s where Digital SAT Condensed Exam Prep comes in. This guide is the result of years of teaching experience, using the most effective study methods to help you learn faster. The innovative condensed format is easy to follow and will get you exam-ready, fast—reducing your stress and boosting your confidence along the way.This book is fully updated for 2025 and covers every SAT® topic you need. You’ll get a clear, straightforward approach that helps you fully prep for the exam without wasting time. No fluff, no stress—just results.With this condensed guide, you will:Master the Digital SAT® Format: Get comfortable with the new digital interface and learn how to ace the adaptive testing format.Cut Out test Anxiety: Discover the best tips and techniques to handle test day with total confidence, keep calm, and stay focused.Balance SAT Preparation with Your Commitments: Our value-packed, bite-sized lessons make it easy to balance SAT® prep with your already busy schedule.Overcome Subject-Specific Challenges: Get practical advice on how to confidently handle the areas where you feel least prepared, strengthening your knowledge across subjects.Develop Effective Test-Taking Strategies: Learn how to avoid common traps, manage your time like a pro, and maximize your score.And thanks to all of this, you’ll be able to ACHIEVE THE BEST POSSIBLE SCORE!✅ Includes 2 Full-Length Practice Tests to help you measure your progress and fine-tune your strategy—a must-have for checking your preparation.Are you ready to take control of your future and stop letting fear and stress hold you back?Imagine walking into test day feeling totally prepared and confident, without the fear of the unknown, and with the calm focus you need to perform at your best. Digital SAT Condensed Exam Prep gives you everything you need to succeed—and secure your spot at the college of your dreams!Don’t waste any more time—scroll up and BUY your copy today! Read more

"The Fourth Dimension" by Charles Howard Hinton explores the concept of higher dimensions beyond our usual perception. The book delves into the idea of a four-dimensional world, using poiographs to represent complex relationships and phenomena in higher-dimensional space. Through the visualization of tesseracts and rotations in four dimensions, the author provides a fascinating insight into the complexity of spatial dimensions and their implications on matter and physical phenomena. The book also introduces a space language for naming figures in multiple dimensions, emphasizing simplicity and ease of pronunciation in creating a system for understanding higher-dimensional space. Read more

This is the definitive edition of one of the very greatest classics of all time—the full Euclid, not an abridgement. Utilizing the text established by Heiberg, Sir Thomas Heath encompasses almost 2500 years of mathematical and historical study upon Euclid.This unabridged republication of the original enlarged edition contains the complete English text of all 13 books of the Elements, plus a critical apparatus which analyzes each definition, postulate, and proposition in great detail. It covers textual and linguistic matters; mathematical anayses of Euclid's ideas; classical, medieval, Renaissance, modern commentators; refutations, supports, extrapolations, reinterpretations, and historical notes, all given with extensive quotes."The textbook that shall really replace Euclid has not yet been written and probably never will be," Encyclopaedia Britannica. Read more

Learn how to improve your life by deepening your understanding of sacred geometry.Have you ever noticed how certain patterns and shapes are so prevalent in our society?Have you ever been curious about what these shapes might mean for you personally?Do you have a sneaky suspicion that there is a power behind these patterns and that you can use them to “shape” your world?If so, then this book is definitely for you. In it, you will:Learn the divine secrets of sacred geometryDiscover how these fascinating shapes are in every facet of human existenceLearn more about ancient structures that possessed sacred geometryUnderstand the science behind sacred geometry and how it affects us allDiscover the connection between numerology and sacred geometryUnderstand the true numerical value of every shape you’ve ever knownDiscover why the golden ratio is so importantDiscover the wonders of the Fibonacci sequence and prime numbersLearn more about the hidden shape behind every numberLearn how platonic solids present themselves in real lifeUnderstand the symbology of these sacred shapes and how they affect your lifeLearn everything you’ve ever wanted to know about MetatronDiscover the shapes responsible for our existenceUnderstand how to craft crystal grids using these sacred shapes for your prosperity and peaceMaster practical ways to work with sacred geometry every dayWith this book as your starting point, you will discover that there is a lot of magic you have not been paying attention to, and you will find out exactly how to take advantage of the shapes you see every single day.So click the “add to cart” button now and begin the process of shaping your life exactly as you want it using your newfound knowledge of sacred geometry. Read more

Clear explanations, an uncluttered and appealing layout, and examples and exercises featuring a variety of real-life applications have made this book popular among students year after year. This latest edition of Swokowski and Cole's ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY retains these features. The problems have been consistently praised for being at just the right level for precalculus students. The book also provides calculator examples, including specific keystrokes that show how to use various graphing calculators to solve problems more quickly. Perhaps most important--this book effectively prepares readers for further courses in mathematics.Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version. Read more