100 Best Mathematical Physics Books of All Time (Updated for 2026)

1

"Surely You're Joking, Mr. Feynman!": Adventures of a Curious Character

Richard P. Feynman

5.0

A series of anecdotes, such as are included in Surely You're Joking, Mr Feynman, shouldn't by rights add up to an autobiography, but that's just one of the many pieces of received wisdom that Nobel Prize-winning physicist Richard Feynman (1918-88) cheerfully ignores in this engagingly eccentric book. Fiercely independent (read the chapter entitled "Judging Books by Their Covers"), intolerant of st

Recommended by Larry Page, Mark Zuckerberg, Sergey Brin, and 12 others.

Larry Page

Co-Founder/Google

Google co-founder has listed this book as one of his favorites. [source]

Sergey Brin

Co-Founder/Google

Brin told the Academy of Achievement: "Aside from making really big contributions in his own field, he was pretty broad-minded. I remember he had an excerpt where he was explaining how he really wanted to be a Leonardo da Vinci, an artist and a scientist. I found that pretty inspiring. I think that leads to having a fulfilling life." [source]

Naval Ravikant

CEO & Co-Founder/AngelList

Learn about the inner mindset and external state of someone who was absolutely brilliant. [source]

2

Cosmos

Carl Sagan

4.8

Preview Summary

Cosmos has 13 heavily illustrated chapters, corresponding to the 13 episodes of the Cosmos television series. In the book, Sagan explores 15 billion years of cosmic evolution and the development of science and civilization. Cosmos traces the origins of knowledge and the scientific method, mixing science and philosophy, and speculates to the future of science. The book also discusses the underlying

Recommended by Richard Branson, Ante Shoda, Anurag Ramdasan, and 1 others.

Richard Branson

Founder/Virgin Group

Today is World Book Day, a wonderful opportunity to address this #ChallengeRichard sent in by Mike Gonzalez of New Jersey: Make a list of your top 65 books to read in a lifetime. [source]

Ante Shoda

It explains 14 billion years of the evolution of the universe, a sort of engineering experiment on the largest possible scale. It spans all scales of space and time, describing everything from the largest scales of the universe to the smallest scales of molecules and atoms. It’s a good book for putting everything in perspective. [source]

Anurag Ramdasan

This book helped draft a great perspective on the world and the universe at large and made me a fan of the Cosmos!

3

A Brief History of Time

Stephen Hawking

4.8

Preview Summary

In the ten years since its publication in 1988, Stephen Hawking's classic work has become a landmark volume in scientific writing, with more than nine million copies in forty languages sold worldwide. That edition was on the cutting edge of what was then known about the origins and nature of the universe. But the intervening years have seen extraordinary advances in the technology of observing bot

Recommended by Richard Branson, Adam Hart-Davis, Anurag Ramdasan, and 2 others.

Richard Branson

Founder/Virgin Group

Today is World Book Day, a wonderful opportunity to address this #ChallengeRichard sent in by Mike Gonzalez of New Jersey: Make a list of your top 65 books to read in a lifetime. [source]

Adam Hart-Davis

When Stephen Hawking wrote A Brief History of Time..his publisher told him that every equation he left in would halve the number of readers [source]

Anurag Ramdasan

My first intro into the world of physics and this got me completely hooked!

4

The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory

Brian Greene

4.5

The international bestseller that inspired a major Nova special and sparked a new understanding of the universe, now with a new preface and epilogue.

Brian Greene, one of the world's leading string theorists, peels away layers of mystery to reveal a universe that consists of eleven dimensions, where the fabric of space tears and repairs itself, and all matter—from the smallest quarks to the most ga

Recommended by Mark Kurlansky, Steven Gubser, and Tom Clarke.

Mark Kurlansky

I love this book. Brian Greene makes quantum physics and Einstein’s theory of relativity really make sense, so you can understand something which nobody seems to understand [source]

Steven Gubser

The book works at many levels – I gave a copy to my mom when it came out, and I also received very positive impressions about the book from Norman Ramsey, who is a Nobel Prize physicist at Harvard. So it’s a great achievement, and part of why it’s a great achievement is that it covers not only string theory but also the accepted pillars of 20th-century theoretical physics, namely, quantum mechanics and relativity. [source]

Tom Clarke

This book is perhaps the public debut of string theory – an attempt to explain how the best of the big and the small theories might be linked to explain the entire universe. [source]

5

The Three-Body Problem (Remembrance of Earth’s Past #1)

Cixin Liu, Ken Liu

4.5

The Three-Body Problem is the first chance for English-speaking readers to experience the Hugo Award-winning phenomenon from China's most beloved science fiction author, Liu Cixin.

Set against the backdrop of China's Cultural Revolution, a secret military project sends signals into space to establish contact with aliens. An alien civilization on the brink of destruction captures the signal and plan

Recommended by Barack Obama, Mark Zuckerberg, Adam Savage, and 7 others.

Barack Obama

Former USA President

As a devoted reader, the president has been linked to a lengthy list of novels and poetry collections over the years — he admits he enjoys a thriller. [source]

Mark Zuckerberg

Founder/Facebook

It's a Chinese science fiction book that has gotten so popular there's now a Hollywood movie being made based on it. This will also be a fun break from all the economics and social science books I've read recently. [source]

Adam Savage

I felt like I was getting a Chinese version of Chinese culture. And that frame felt unique. [source]

6

Gödel, Escher, Bach: An Eternal Golden Braid

Douglas R. Hofstadter

4.5

Douglas Hofstadter's book is concerned directly with the nature of “maps” or links between formal systems. However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. If life can grow out of the formal chemical substrate of the cell, if consciousness can emerge out of a formal system of firing neurons, then so too will computers at

Recommended by Steve Jurvetson, Seth Godin, Cory Zue, and 2 others.

Steve Jurvetson

Steve Jurvetson recommended this book on the podcast "The Tim Ferriss Show". [source]

Seth Godin

Author, Marketer, Entrepreneur

In the last week, I discovered that at least two of my smart friends hadn't read Godel, Escher, Bach. They have now. You should too. [source]

Cory Zue

More recently books like Godel, Escher, Bach and Sapiens have influenced my thinking a lot. [source]

7

Gravitation

Charles W. Misner, Kip S. Thorne, John Archibald Wheeler, David I. Kaiser

4.5

First published in 1973, Gravitation is a landmark graduate-level textbook that presents Einstein's general theory of relativity and offers a rigorous, full-year course on the physics of gravitation. Upon publication, Science called it "a pedagogic masterpiece," and it has since become a classic, considered essential reading for every serious student and researcher in the field of relativity. This

Recommended by Eric Weinstein, Kirk Borne, and Seamus Blackley.

Eric Weinstein

Managing Director/Thiel Capital

Eric Weinstein recommended this book on Twitter. [source]

Kirk Borne

#Gravity is the only one of the four fundamental forces of #Physics that doesn’t (yet) have a quantum explanation — learn how our understanding of Gravity has evolved, from Newton’s great insight to Einstein’s: https://t.co/DZJz9OJ9Lv 👇See this gravitationally heavy 3-kg book👇 https://t.co/9whUOUJqxi [source]

Seamus Blackley

A couple things saved me. One of them I found the other day, slipped into my all time favorite physics book. It was a simple note from my dad, still in it’s envelope. It said that he believed in me, and that things would work out. https://t.co/z48r12w6m6 [source]

8

Finite and Infinite Games a Vision of Life as Play and Possibility

James Carse

4.4

A fascinating meditation on life as a contest of games to be completed and games to be continued--and on what lies beyond winning and losing.

Recommended by Andra Zaharia, Ashley Hathaway, Graham Duncan, and 5 others.

Andra Zaharia

While I was thinking of the best books to add to this short list, I realized that not even half of them are directly related to digital marketing. This is because I believe that the best marketers are people who understand human nature deeply and aim to bring out the best in it. Call me naive, but that’s how I see it. If I were to want to pursue a career in marketing, I’d read … Finite and Infinite Games. [source]

Ashley Hathaway

I’d say Finite & Infinite games was my favorite & quite impactful. They were all impactful, actually. I read my altMBA books on a beach in Kauai (highly recommended). It was odd though because I was by myself and it was just- total knowledge bombs all over the place. Reading the altMBA books in rapid succession like that took a few months to digest honestly. [source]

Graham Duncan

I like this book which has been going around a lot. [source]

9

Infinite Powers: How Calculus Reveals the Secrets of the Universe

Steven Strogatz

4.4

Without calculus, we wouldn’t have cell phones, TV, GPS, or ultrasound. We wouldn’t have unraveled DNA or discovered Neptune or figured out how to put 5,000 songs in your pocket.

Though many of us were scared away from this essential, engrossing subject in high school and college, Steven Strogatz’s brilliantly creative, down‑to‑earth history shows that calculus is not about complexity; it’s about

Recommended by John Urschel, Kirk Borne, and Nigel Shadbolt.

John Urschel

I hope they enjoy it as much as I did. If you or someone you know is studying Calculus, this book is highly recommended. https://t.co/s2yVt6SwTx [source]

Kirk Borne

"Infinite Powers: How Calculus Reveals the Secrets of the Universe" book by @stevenstrogatz https://t.co/wy91xAEqlS Great #Mathematics book that explores the History of Modern Science from this amazing perspective! https://t.co/M4obTvpnbe [source]

Nigel Shadbolt

Infinite Powers is a wonderful motivational for anyone taking a course in calculus. For those readers who remember calculus with dread from maths classes of yore, here is a text that explains just why the material has always had such a key place in our curricula. It charts a history of ideas that sought to make sense of the world through mathematics—to develop methods that find the deep laws and patterns that govern nature and enable us to build everything from computers to jet engines, televisions to microwaves. [source]

10

The Feynman Lectures on Physics

Richard P. Feynman

4.4

The legendary introduction to physics from the subject's greatest teacher
"The whole thing was basically an experiment," Richard Feynman said late in his career, looking back on the origins of his lectures. The experiment turned out to be hugely successful, spawning a book that has remained a definitive introduction to physics for decades. Ranging from the most basic principles of Newtonian physics

Recommended by Bill Gates and David Bainbridge.

Bill Gates

CEO/Microsoft

You don't have to take a course to learn physics. If you're hardcore, read the Feynman book and do the problems. [source]

David Bainbridge

I think that he is one of the most intelligent people to live in the 20th century. Yet at the same time, surprisingly, he is an amazingly good teacher. This is quite an unusual combination. [source]

11

Mathematical Methods in the Physical Sciences

Mary L. Boas

4.4

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12

An Introduction to Statistical Learning: With Applications in R

Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani

4.4

An Introduction to Statistical Learning provides an accessible overview of the field of statistical learning, an essential toolset for making sense of the vast and complex data sets that have emerged in fields ranging from biology to finance to marketing to astrophysics in the past twenty years. This book presents some of the most important modeling and prediction techniques, along with relevant a

Recommended by Roger D. Peng.

Roger D. Peng

This book is written by a powerhouse of authors in the machine learning community, true authorities in the field. But beyond that, they’re also great writers. [source]

13

Mathematical Methods for Physics and Engineering: A Comprehensive Guide

K. F. Riley, M. P. Hobson, et al.

4.3

The third edition of this highly acclaimed undergraduate textbook is suitable for teaching all the mathematics for an undergraduate course in any of the physical sciences. As well as lucid descriptions of all the topics and many worked examples, it contains over 800 exercises. New stand-alone chapters give a systematic account of the 'special functions' of physical science, cover an extended range

14

The Drunkard's Walk: How Randomness Rules Our Lives

Leonard Mlodinow

4.3

Recommended by David Spiegelhalter and Gabriel Coarna.

David Spiegelhalter

This is a general introduction to the history of probability and the way it comes into everyday life. It intersperses the historical development with modern applications, and looks at finance, sport, gambling, lotteries and coincidences. [source]

Gabriel Coarna

Leonard Mlodinow's "The Drunkarkd's Walk" -more precisely, the section on the "Monty Hall" problem- totally changed how I look-at/think-about probabilities and choices in general; this has impacted almost every real-life choice I've made since I read this book. [source]

15

The Fabric of Reality: The Science of Parallel Universes--and Its Implications

David Deutsch

4.3

For David Deutsch, a young physicist of unusual originality, quantum theory contains our most fundamental knowledge of the physical world. Taken literally, it implies that there are many universes “parallel” to the one we see around us. This multiplicity of universes, according to Deutsch, turns out to be the key to achieving a new worldview, one which synthesizes the theories of evolution, comput

Recommended by Chris Anderson, Chris Anderson, Chris Anderson, and 1 others.

Chris Anderson

I honestly think it was reading this book that finally gave me the courage, 18 years ago, to leave my company and take over leadership of TED. [source]

Chris Anderson

I honestly think it was reading this book that finally gave me the courage, 18 years ago, to leave my company and take over leadership of TED. [source]

Chris Anderson

I honestly think it was reading this book that finally gave me the courage, 18 years ago, to leave my company and take over leadership of TED. [source]

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16

The Large Scale Structure of Space-Time

Stephen W. Hawking, G. F. R. Ellis, P. V. Landshoff, D. R. Nelson, D. W. Sciama, S. Weinberg

4.3

Einstein's General Theory of Relativity leads to two remarkable predictions: first, that the ultimate destiny of many massive stars is to undergo gravitational collapse and to disappear from view, leaving behind a 'black hole' in space; and secondly, that there will exist singularities in space-time itself. These singularities are places where space-time begins or ends, and the presently known law

Recommended by Eric Weinstein.

Eric Weinstein

Managing Director/Thiel Capital

Eric Weinstein recommended this book on Twitter. [source]

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17

Mathematical Tools for Physics

James Nearing

4.3

Having the right answer doesn't guarantee understanding. Encouraging students' development of intuition, this original work begins with a review of basic mathematics and advances to infinite series, complex algebra, differential equations, and Fourier series. Succeeding chapters explore multivariable and vector calculus, partial differential equations, numerical and complex analysis, tensors, comp

18

Lost in Math: How Beauty Leads Physics Astray

Sabine Hossenfelder

4.3

A contrarian argues that modern physicists' obsession with beauty has given us wonderful math but bad science.

Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones. This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in th

Recommended by Barbara Kiser.

Barbara Kiser

This is a firecracker of a book—a shot across the bows of theoretical physics. Sabine Hossenfelder, a theoretical physicist working on quantum gravity and blogger, confronts failures in her field head-on. [source]

19

Six Easy Pieces: Essentials of Physics By Its Most Brilliant Teacher

Richard P. Feynman

4.3

Six Easy Pieces: Essentials of Physics Explained by Its Most Brilliant Teacher is a publishing first. This set couples a book containing the six easiest chapters from Richard P. Feynman's landmark work, Lectures on Physics—specifically designed for the general, non-scientist reader—with the actual recordings of the late, great physicist delivering the lectures on which the chapters are based. Nobe

Recommended by Kate Lee (St Paul's Girls' School).

Kate Lee (St Paul's Girls' School)

Feynman could write about difficult physics and teach it in a way that no one else could. He is widely regarded as one of the best physics teachers of all time. His discussions of Newtonian gravitation and how we came to it, phenomena like tides, and how you can measure the speed of light by observing Jupiter’s moons are described with such humour and clarity. He conveys the excitement of physics [source]

20

The Feynman Lectures on Physics Vol 1

Richard P. Feynman, Robert B. Leighton, Matthew Sands

4.3

Recommended by Bill Gates.

Bill Gates

CEO/Microsoft

You don't have to take a course to learn physics. If you're hardcore, read the Feynman book and do the problems. [source]

21

Lost in Space: 5,000 Facts for Navigating the Universe

Neil deGrasse Tyson, Lindsey Nyx Walker

4.2

Prepare for liftoff with a sweeping new book on the universe from the world's most celebrated astrophysicist, brimming with wit, authority, and laugh-out-loud humor. Filled with 5,000 tantalizing facts and more than 300 charts, maps, and photographs, this book offers a dazzling look at the cosmos from our home planet to the farthest reaches of outer space.Strap in for a thrilling journey through o

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22

Local Quantum Physics: Fields, Particles, Algebras

Rudolf Haag

4.2

The new edition provided the opportunity of adding a new chapter entitled "Principles and Lessons of Quantum Physics." It was a tempting challenge to try to sharpen the points at issue in the long lasting debate on the Copenhagen Spirit, to assess the significance of various arguments from our present vantage point, seventy years after the advent of quantum theory, where, after ali, some problems

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23

Gauge Fields, Knots and Gravity

John Baez, Javier P Muniain

4.2

This is an introduction to the basic tools of mathematics needed to understand the relation between knot theory and quantum gravity. The book begins with a rapid course on manifolds and differential forms, emphasizing how these provide a proper language for formulating Maxwell's equations on arbitrary spacetimes. The authors then introduce vector bundles, connections and curvature in order to gene

24

The Road to Reality: A Complete Guide to the Laws of the Universe

Roger Penrose

4.2

Roger Penrose, one of the most accomplished scientists of our time, presents the only comprehensive and comprehensible account of the physics of the universe. From the very first attempts by the Greeks to grapple with the complexities of our known world to the latest application of infinity in physics, The Road to Reality carefully explores the movement of the smallest atomic particles and reaches

25

Quantum Mechanics: The Theoretical Minimum

Leonard Susskind

4.2

From the bestselling author of The Theoretical Minimum, a DIY introduction to the math and science of quantum mechanics.

First he taught you classical mechanics. Now, physicist Leonard Susskind has teamed up with data engineer Art Friedman to present the theory and associated mathematics of the strange world of quantum mechanics.

In this follow-up to the New York Times best-selling The Theoretical M

Recommended by Eric Weinstein.

Eric Weinstein

Managing Director/Thiel Capital

Eric Weinstein recommended this book on Twitter. [source]

26

The Holographic Universe: The Revolutionary Theory of Reality

Michael Talbot

4.2

"Awake-up call to wonder, an adventure in ideas." —Larry Dossey,M.D., author of Space, Time & Medicine

Now witha new foreword by Lynn McTaggart, author of TheField, Michael Talbot’s classic treatise on the latest frontiers of physicsreveals a revolutionary theory of reality, explaining the paranormal abilitiesof the mind, the unsolved riddles of brain and body, and the true nature of theuniverse. L

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27

Mathematical Physics: A Modern Introduction to Its Foundations

Sadri Hassani

4.2

This book is for physics students interested in the mathematics they use and for mathematics students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation tries to strike a balance between formalism and application, between abstract and concrete. The interconnections among the various topics are clarified both by the use of vector

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28

Operator Algebras and Quantum Statistical Mechanics 2: Equilibrium States. Models in Quantum Statistical Mechanics

Ola Bratteli and Derek William Robinson

4.2

For almost two decades this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. It describes the general structure of equilibrium states, the KMS-condition and stability, quantum spin systems and continuous systems.
Major changes in the new edition relate to Bose--Einstein condensation, the dynamics of the X-Y model and questions on phase trans

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29

Foundations of Mechanics

Ralph Abraham and Jerrold E. Marsden

4.2

This is a reference on symplectic geometry, analytical mechanics and symplectic methods in mathematical physics.

30

The Principia: Mathematical Principles of Natural Philosophy

René Descartes

4.2

In his monumental 1687 work Philosophiae Naturalis Principia Mathematica, known familiarly as the Principia, Isaac Newton laid out in mathematical terms the principles of time, force, and motion that have guided the development of modern physical science. Even after more than three centuries and the revolutions of Einsteinian relativity and quantum mechanics, Newtonian physics continues to account

Recommended by Alan Kay.

Alan Kay

I have never forgotten the combined shock and thrill of making my way through this in my 20s. [source]

31

The Geometry of Physics: An Introduction

Theodore Frankel

4.2

Theodore Frankel explains those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms essential to a better understanding of classical and modern physics and engineering. Key highlights of his new edition are the inclusion of three new appendices that cover symmetries, quarks, and meson masses; representations a

32

Mathematical Physics

Robert Geroch

4.2

Mathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space. Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics. Perhaps the most valuable feature of the book is the illuminating intuitive discussion of the "whys" of proofs and

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33

Classical Theory of Gauge Fields

Valery Rubakov, Stephen S. Wilson

4.2

Based on a highly regarded lecture course at Moscow State University, this is a clear and systematic introduction to gauge field theory. It is unique in providing the means to master gauge field theory prior to the advanced study of quantum mechanics. Though gauge field theory is typically included in courses on quantum field theory, many of its ideas and results can be understood at the classical

34

Scientific American September 2026

Scientific American

4.2

Scientific American covers the most important and exciting research, ideas and knowledge in science, health, technology, the environment and society. It is committed to sharing trustworthy knowledge and enhancing our understanding of the world .

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35

Quantization of Gauge Systems

Marc Henneaux, Claudio Teitelboim

4.2

This book is a systematic study of the classical and quantum theories of gauge systems. It starts with Dirac's analysis showing that gauge theories are constrained Hamiltonian systems. The classical foundations of BRST theory are then laid out with a review of the necessary concepts from homological algebra. Reducible gauge systems are discussed, and the relationship between BRST cohomology and ga

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36

Mathematics of Classical and Quantum Physics

Frederick W. Byron and Robert W. Fuller

4.2

This textbook is designed to complement graduate-level physics texts in classical mechanics, electricity, magnetism, and quantum mechanics. Organized around the central concept of a vector space, the book includes numerous physical applications in the body of the text as well as many problems of a physical nature. It is also one of the purposes of this book to introduce the physicist to the langua

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37

Differentiable Manifolds: A Theoretical Physics Approach

Gerardo F. Torres del Castillo

4.2

This textbook delves into the theory behind differentiable manifolds while exploring various physics applications along the way. Included throughout the book are a collection of exercises of varying degrees of difficulty. Differentiable Manifolds is intended for graduate students and researchers interested in a theoretical physics approach to the subject. Prerequisites include multivariable calcul

38

Physics of the Impossible

Michio Kaku

4.2

A fascinating exploration of the science of the impossible—from death rays and force fields to invisibility cloaks—revealing to what extent such technologies might be achievable decades or millennia into the future.

One hundred years ago, scientists would have said that lasers, televisions, and the atomic bomb were beyond the realm of physical possibility. In Physics of the Impossible, the renowned

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39

An Introduction to Tensors and Group Theory for Physicists

Nadir Jeevanjee

4.2

"An Introduction to Tensors and Group Theory for Physicists" provides both an intuitive and rigorous approach to tensors and groups and their role in theoretical physics and applied mathematics. A particular aim is to demystify tensors and provide a unified framework for understanding them in the context of classical and quantum physics. Connecting the component formalism prevalent in physics calc

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40

Supersymmetry and Equivariant de Rham Theory

Victor W Guillemin, Shlomo Sternberg, Jochen Brüning

4.2

Equivariant cohomology on smooth manifolds is the subject of this book which is part of a collection of volumes edited by J. Bruning and V.W. Guillemin. The point of departure are two relatively short but very remarkable papers be Henry Cartan, published in 1950 in the Proceedings of the "Colloque de Topologie." These papers are reproduced here, together with a modern introduction to the subject,

41

Special Relativity and Classical Field Theory: The Theoretical Minimum

Leonard Susskind

4.1

A funny, insightful, and self-contained guide to Einstein's relativity theory and classical field theories--including electromagnetism

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 Friedm

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42

Gauge Theories in Particle Physics, Volume 2: Non-Abelian Gauge Theories: Qcd and the Electoweak Theory

I.J.R. Aitchison, A.J.G. Hey

4.1

This is the second volume of the third edition of a successful text, now substantially enlarged and updated to reflect developments over the last decade in the curricula of university courses and in particle physics research. Volume I covered relativistic quantum mechanics, electromagnetism as a gauge theory, and introductory quantum field theory, and ended with the formulation and application of

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43

Group Theory in a Nutshell for Physicists

A. Zee

4.1

A concise, modern textbook on group theory written especially for physicists

Although group theory is a mathematical subject, it is indispensable to many areas of modern theoretical physics, from atomic physics to condensed matter physics, particle physics to string theory. In particular, it is essential for an understanding of the fundamental forces. Yet until now, what has been missing is a moder

44

Differential Geometry of Curves and Surfaces

Kristopher Tapp

4.1

This is a textbook on differential geometry well-suited to a variety of courses on this topic. For readers seeking an elementary text, the prerequisites are minimal and include plenty of examples and intermediate steps within proofs, while providing an invitation to more excursive applications and advanced topics. For readers bound for graduate school in math or physics, this is a clear, concise,

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45

Dirichlet Branes And Mirror Symmetry (Clay Mathematics Monographs)

and P.M.H. Wilson Paul S. Aspinwall, Tom Bridgeland, Alastair Craw, Michael R. Douglas, Mark Gross, Anton Kapustin, Gregory W. Moore, Graeme Segal, Balazs Szendroi

4.1

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46

Geometry and Integrability

Lionel Mason, Yavuz Nutku

4.1

Based on courses held at the Feza GUrsey Institute, this collection of survey articles introduces advanced graduate students to an exciting area on the border of mathematics and mathematical physics. Including articles by key names such as Calogero, Donagi and Mason, it features the algebro-geometric material from Donagi as well as the twistor space methods in Woodhouse's contribution, forming a b

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47

Differential Geometry and Mathematical Physics: Part II. Fibre Bundles, Topology and Gauge Fields

Gerd Rudolph, Matthias Schmidt

4.1

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48

Flatland: A Romance of Many Dimensions

Edwin A. Abbott

4.1

This masterpiece of science (and mathematical) fiction is a delightfully unique and highly entertaining satire that has charmed readers for more than 100 years. The work of English clergyman, educator and Shakespearean scholar Edwin A. Abbott (1838-1926), it describes the journeys of A. Square [sic – ed.], a mathematician and resident of the two-dimensional Flatland, where women-thin, straight lin

Recommended by Bryan Johnson.

Bryan Johnson

Bryan Johnson recommended this book on Twitter. [source]

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49

Classical Solutions in Quantum Field Theory

Erick J. Weinberg

4.1

Classical solutions play an important role in quantum field theory, high energy physics and cosmology. Real-time soliton solutions give rise to particles, such as magnetic monopoles, and extended structures, such as domain walls and cosmic strings, that have implications for early universe cosmology. Imaginary-time Euclidean instantons are responsible for important nonperturbative effects, while E

50

Riemannian Geometry: Theory & Applications

Manfredo Perdigao do Carmo, Francis Flaherty

4.1

Riemannian Geometry is an expanded edition of a highly acclaimed and successful textbook (originally published in Portuguese) for first-year graduate students in mathematics and physics. The author's treatment goes very directly to the basic language of Riemannian geometry and immediately presents some of its most fundamental theorems. It is elementary, assuming only a modest background from reade

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51

Analysis, Manifolds and Physics, Part II - Revised and Enlarged Edition

Yvonne Choquet-Bruhat

4.1

Twelve problems have been added to the first edition; four of them are supplements to problems in the first edition. The others deal with issues that have become important, since the first edition of Volume II, in recent developments of various areas of physics. All the problems have their foundations in volume 1 of the 2-Volume set Analysis, Manifolds and Physics. It would have been prohibitively

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52

Probability Theory

E. T. Jaynes, G. Larry Bretthorst

4.1

Going beyond the conventional mathematics of probability theory, this study views the subject in a wider context. It discusses new results, along with applications of probability theory to a variety of problems. The book contains many exercises and is suitable for use as a textbook on graduate-level courses involving data analysis. Aimed at readers already familiar with applied mathematics at an a

53

The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics

Leonard Susskind

4.1

Recommended by Sean M Carroll.

Sean M Carroll

This book discusses some of the deepest features of the laws of nature. [source]

54

The Cosmic Landscape: String Theory and the Illusion of Intelligent Design

Leonard Susskind

4.1

In his first book ever, the father of string theory reinvents the world's concept of the known universe and man's unique place within it. Line drawings.

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55

A Student's Guide to Vectors and Tensors

Daniel Fleisch

4.1

Vectors and tensors are among the most powerful problem-solving tools available, with applications ranging from mechanics and electromagnetics to general relativity. Understanding the nature and application of vectors and tensors is critically important to students of physics and engineering. Adopting the same approach used in his highly popular A Student's Guide to Maxwell's Equations, Fleisch ex

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56

Relativity and the Nature of Spacetime

Vesselin Petkov

4.1

The most important question addressed in this book is "what is the nature (the ontological status) of spacetime?" or, equivalently, "what is the dimensionality of the world at the macroscopic level?" The answer to this question is developed via a thorough analysis of relativistic effects and explicitly asking whether the objects involved in those effects are three-dimensional or four-dimensional.

57

Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life

Albert-Laszlo Barabasi

4.1

In the 1980's, James Gleick's Chaos introduced the world to complexity. Now, Albert-László Barabási's Linked reveals the next major scientific leap: the study of networks. We've long suspected that we live in a small world, where everything is connected to everything else. Indeed, networks are pervasive--from the human brain to the Internet to the economy to our group of friends. These linkages, it turns out, aren't random. All networks, to the great surprise of scientists, have an underlying order and follow simple laws. Understanding the structure and behavior of these networks will help us do some amazing things, from designing the optimal organization of a firm to stopping a disease outbreak before it spreads catastrophically.In Linked, Barabási, a physicist whose work has revolutionized the study of networks, traces the development of this rapidly unfolding science and introduces us to the scientists carrying out this pioneering work. These "new cartographers" are mapping networks in a wide range of scientific disciplines, proving that social networks, corporations, and cells are more similar than they are different, and providing important new insights into the interconnected world around us. This knowledge, says Barabási, can shed light on the robustness of the Internet, the spread of fads and viruses, even the future of democracy. Engaging and authoritative, Linked provides an exciting preview of the next century in science, guaranteed to be transformed by these amazing discoveries.From Linked:This book has a simple message: think networks. It is about how networks emerge, what they look like, and how they evolve. It aims to develop a web-based view of nature, society, and technology, providing a unified framework to better understand issues ranging from the vulnerability of the Internet to the spread of diseases. Networks are present everywhere. All we need is an eye for them...We will see the challenges doctors face when they attempt to cure a disease by focusing on a single molecule or gene, disregarding the complex interconnected nature of the living matter. We will see that hackers are not alone in attacking networks: we all play Goliath, firing shots at a fragile ecological network that, without further support, could soon replicate our worst nightmares by turning us into an isolated group of species...Linked is meant to be an eye-opening trip that challenges you to walk across disciplines by stepping out of the box of reductionism. It is an invitation to explore link by link the next scientific revolution: the new science of networks.

Recommended by Anne-Marie Slaughter and Bill Barhydt.

Anne-Marie Slaughter

Linked is about how to understand the world in terms of networks. To understand network science the first thing to do is to visualise the world the way you visualise the Internet or even the universe – hubs of infinitely intersecting networks. As the author says, everything can be reduced to links and nodes. This book is a very accessible introduction to the science of networks and to how to think about everything from anthills to traffic jams to complex conflict from the perspective of network science. [source]

Bill Barhydt

Written before Facebook, this book predicts what the world will look like with amazing precision. [source]

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58

Mirror Symmetry

Kentaro Hori, Sheldon Katz, Albrecht Klemm, Rahul Pandharipande, Richard Thomas, Cumrun Vafa, Ravi Vakil, Eric Zaslow

4.1

Suitable for those wishing to advance their understanding by exploring mirror symmetry at the interface of mathematics and physics, and for graduate students and research mathematicians interested in mathematical and theoretical physics.

59

The Variational Principles of Mechanics

Cornelius Lanczos

4.1

Philosophic, less formalistic approach to perennially important field of analytical mechanics. Model of clear, scholarly exposition at graduate level with coverage of basic concepts, calculus of variations, principle of virtual work, equations of motion, relativistic mechanics, much more. First inexpensive paperbound edition. Index. Bibliography.

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60

Gauge Theories in Particle Physics, Volume 1: From Relativistic Quantum Mechanics to QED

I.J.R. Aitchison, A.J.G. Hey

4.1

Provides a practical introduction to the three gauge theories of the standard model of particle physics, quantum electrodynamics, quantum chromodynamics and the electroweak theory. For each of them, the authors provide discussion of the main conceptual points, an exposition of many practical calculations of physical qualities and a comparison of these quantitive predictions with experimental resul

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61

Quantum Inverse Scattering Method and Correlation Functions

V Korepin

4.1

The quantum inverse scattering method is a means of finding exact solutions of two-dimensional models in quantum field theory and statistical physics (such as the sine-Gordon equation or the quantum nonlinear Schrodinger equation). This introduction to this important and exciting area first deals with the Bethe ansatz and calculation of physical quantities. The authors then tackle the theory of th

62

Love and Math: The Heart of Hidden Reality

Edward Frenkel

4.1

A New York Times Science Bestseller

What 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 re

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63

Equations of Mathematical Physics

A. N. Tikhonov and A. A. Samarskii

4.1

Thorough, advanced-undergraduate to graduate-level treatment of problems leading to partial differential equations. Hyperbolic, parabolic, elliptic equations; wave propagation in space, heat conduction in space, special functions, more. Emphasis on mathematical formulation of problems, rigorous solutions, physical interpretation of results obtained. Problems. Appendixes. Tables.

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64

Geometric Phases in Physics

F Wilczek

4.1

During the last few years, considerable interest has been focused on the phase that waves accumulate when the equations governing the waves vary slowly. The recent flurry of activity was set off by a paper by Michael Berry, where it was found that the adiabatic evolution of energy eigenfunctions in quantum mechanics contains a phase of geometric origin (now known as ‘Berry's phase’) in addition to

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65

Methods of Homological Algebra

Sergei I. Gelfand, Yuri I. Manin

4.1

This modern approach to homological algebra by two leading writers in the field is based on the systematic use of the language and ideas of derived categories and derived functors. It describes relations with standard cohomology theory and provides complete proofs. Coverage also presents basic concepts and results of homotopical algebra. This second edition contains numerous corrections.

66

Principles of Quantum Mechanics

Ramamurti Shankar

4.0

Reviews from the First Edition:

"An excellent text ... The postulates of quantum mechanics and the mathematical underpinnings are discussed in a clear, succinct manner." (American Scientist)

"No matter how gently one introduces students to the concept of Dirac's bras and kets, many are turned off. Shankar attacks the problem head-on in the first chapter, and in a very informal style suggests that th

Recommended by Eric Weinstein.

Eric Weinstein

Managing Director/Thiel Capital

Eric Weinstein recommended this book on Twitter. [source]

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67

Group Theory

Pierre Ramond

4.0

Group theory has long been an important computational tool for physicists, but, with the advent of the Standard Model, it has become a powerful conceptual tool as well. This book introduces physicists to many of the fascinating mathematical aspects of group theory, and mathematicians to its physics applications. Designed for advanced undergraduate and graduate students, this book gives a comprehen

68

A Guide to Feynman Diagrams in the Many-Body Problem: Second Edition

Richard D. Mattuck

4.0

Until this book, most treatments of this topic were inaccessible to nonspecialists. A superb introduction to important areas of modern physics, it covers Feynman diagrams, quasi particles, Fermi systems at finite temperature, superconductivity, vacuum amplitude, Dyson's equation, ladder approximation, and much more. "A great delight to read." — Physics Today. 1974 edition.

69

DIV, Grad, Curl, and All That: An Informal Text on Vector Calculus

H. M. Schey

4.0

Since the publication of the First Edition over thirty years ago, Div, Grad, Curl, and All That has been widely renowned for its clear and concise coverage of vector calculus, helping science and engineering students gain a thorough understanding of gradient, curl, and Laplacian operators without required knowledge of advanced mathematics.

70

Fourier Analysis, Self-Adjointness (Methods of Modern Mathematical Physics #2)

Michael Reed, Barry Simon

4.0

71

Course of Theoretical Physics: Vol. 1, Mechanics

L D Landau, E.M. Lifshitz

4.0

Devoted to the foundation of mechanics, namely classical Newtonian mechanics, the subject is based mainly on Galileo's principle of relativity and Hamilton's principle of least action. The exposition is simple and leads to the most complete direct means of solving problems in mechanics.
The final sections on adiabatic invariants have been revised and augmented. In addition a short biography of L D

72

A New Kind of Science

Stephen Wolfram

4.0

Recommended by Steve Jurvetson and Dan Sullivan.

Steve Jurvetson

A series of epiphanies from the author and others that the world is really interesting when you look at iterative algorithms applied millions and billions of times. [source]

73

A Student's Guide to Maxwell's Equations

Daniel Fleisch

4.0

Gauss's law for electric fields, Gauss's law for magnetic fields, Faraday's law, and the Ampere-Maxwell law are four of the most influential equations in science. In this guide for students, each equation is the subject of an entire chapter, with detailed, plain-language explanations of the physical meaning of each symbol in the equation, for both the integral and differential forms. The final cha

74

Geometrical Methods of Mathematical Physics

Bernard Schutz

4.0

In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers th

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75

Mathematical Methods of Classical Mechanics

V. I. Arnold, A. Weinstein, K. Vogtmann

4.0

This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic

76

The Character of Physical Law

Richard Feynman

4.0

In the Messenger Lectures, originally delivered at Cornell University & recorded for TV by the BBC, Feynman offers an overview of selected physical laws & gathers their common features into one broad principle of invariance. He maintains at the outset that the importance of a physical law isn't "how clever we are to have found it out, but...how clever nature is to pay attention to it" & tends his

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77

Mathematical Methods for Physicists

George B. Arfken, Hans J. Weber

4.0

Provides the essential mathematical tools and techniques used to solve problems in physics. This work includes differential forms and the elegant forms of Maxwell's equations, and a chapter on probability and statistics. It also illustrates and proves mathematical relations.

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78

Analysis of Operators (Methods of Modern Mathematical Physics #4)

Michael Reed, Barry Simon

4.0

BESTSELLER of the XXth Century in Mathematical Physics voted on by participants of the XIIIth International Congress on Mathematical Physics
This revision will make this book mroe attractive as a textbook in functional analysis. Further refinement of coverage of physical topics will also reinforce its well-established use as a course book in mathemtical physics.

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79

The Dawning of Gauge Theory

Lochlainn O'Raifeartaigh

4.0

During the course of this century, gauge invariance has slowly emerged from being an incidental symmetry of electromagnetism to being a fundamental geometrical principle underlying the four known fundamental physical interactions. The development has been in two stages. In the first stage (1916-1956) the geometrical significance of gauge-invariance gradually came to be appreciated and the original

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80

Manifolds, Tensors, and Forms

Paul Renteln

4.0

Providing a succinct yet comprehensive treatment of the essentials of modern differential geometry and topology, this book's clear prose and informal style make it accessible to advanced undergraduate and graduate students in mathematics and the physical sciences. The text covers the basics of multilinear algebra, differentiation and integration on manifolds, Lie groups and Lie algebras, homotopy

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81

Lie Groups, Lie Algebras, Cohomology and Some Applications in Physics

Josi A. de Azc¿rraga

4.0

Now in paperback, this book provides a self-contained introduction to the cohomology theory of Lie groups and algebras and to some of its applications in physics. No previous knowledge of the mathematical theory is assumed beyond some notions of Cartan calculus and differential geometry (which are nevertheless reviewed in the book in detail). The examples, of current interest, are intended to clar

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82

Symmetry and the Standard Model: Mathematics and Particle Physics

Matthew Robinson

4.0

While theoretical particle physics is an extraordinarily fascinating field, the incredibly fast pace at which it moves along, combined with the huge amount of background information necessary to perform cutting edge research, poses a formidable challenge for graduate students.

This book represents the first in a series designed to assist students in the process of transitioning from coursework to r

83

The Mathematical Theory of Communication

Claude E. Shannon, Warren Weaver

4.0

Scientific knowledge grows at a phenomenal pace--but few books have had as lasting an impact or played as important a role in our modern world as The Mathematical Theory of Communication, published originally as a paper on communication theory in the Bell System Technical Journal more than fifty years ago. Republished in book form shortly thereafter, it has since gone through four hardcover and si

84

Quanta and Fields: The Biggest Ideas in the Universe

Sean Carroll

4.0

85

Scientific American 20th January 2026

Scientific American

4.0

Scientific American covers the most important and exciting research, ideas and knowledge in science, health, technology, the environment and society. It is committed to sharing trustworthy knowledge and enhancing our understanding of the world .

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86

Mirror Symmetry and Algebraic Geometry

David A. Cox

4.0

Mirror symmetry began when theoretical physicists made some astonishing predictions about rational curves on quintic hypersurfaces in four-dimensional projective space. Understanding the mathematics behind these predictions has been a substantial challenge.

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87

Partial Differential Equations of Mathematical Physics

S. L. Sobolev

4.0

This volume presents an unusually accessible introduction to equations fundamental to the investigation of waves, heat conduction, hydrodynamics, and other physical problems. Topics include derivation of fundamental equations, Riemann method, equation of heat conduction, theory of integral equations, Green's function, and much more. The only prerequisite is a familiarity with elementary analysis.

88

Foundations of Potential Theory

Oliver D. Kellogg

4.0

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89

A Relativist's Toolkit

Eric Poisson

4.0

This textbook fills a gap in the existing literature on general relativity by providing the advanced student with practical tools for the computation of many physically interesting quantities. The context is provided by the mathematical theory of black holes, one of the most successful and relevant applications of general relativity. Topics covered include congruences of timelike and null geodesic

90

Scientific American April 2026

Scientific American

4.0

Scientific American covers the most important and exciting research, ideas and knowledge in science, health, technology, the environment and society. It is committed to sharing trustworthy knowledge and enhancing our understanding of the world .

91

My Best Mathematical and Logic Puzzles

Martin Gardner

4.0

Over a period of 25 years as author of the Mathematical Games column for Scientific American, Martin Gardner devoted a column every six months or so to short math problems or puzzles. He was especially careful to present new and unfamiliar puzzles that had not been included in such classic collections as those by Sam Loyd and Henry Dudeney. Later, these puzzles were published in book collections,

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92

The Archetypal Imagination

James Hollis, David H. Rosen

4.0

93

Differential Geometry

Erwin Kreyszig

4.0

An introductory textbook on the differential geometry of curves and surfaces in 3-dimensional Euclidean space, presented in its simplest, most essential form, but with many explanatory details, figures, and examples, and in a manner that conveys the theoretical and practical importance of the different concepts, methods, and results involved. With problems and solutions. Includes 99 illustrations.

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94

Superstring Theory: Volume 1, Introduction

Michael B. Green, John H. Schwarz, Edward Witten

4.0

In recent years, superstring theory has emerged as a promising approach to reconciling general relativity with quantum mechanics and unifying the fundamental interactions. Problems that have seemed insuperable in previous approaches take on a totally new character in the context of superstring theory, and some of them have been overcome. Interest in the subject has greatly increased following a su

Recommended by Steven Gubser.

Steven Gubser

As a practitioner of the subject I am drawn to the serious accounts. The two volumes by Green, Schwarz and Witten are a wonderful early account of the subject. It was a subject that first fluoresced in the mid-80s. The notion of string theory was already present, even in the late 1960s, but only in 1984, with the work of Green and Schwarz, did people realise string theory could really be consistent with quantum mechanics, as well as including gravity, and could provide theories that looked very much like the standard model of particles. So there was this tremendous light-bulb moment, where everybody said, ‘Oh my God! This could work.’ And that book, Superstring Theory, captures that era in a very substantive way – as well as being a fairly readable account. In terms of readability, I would say even non-physicists could get something out of the first chapter, and then later chapters, they’re more for practitioners. [source]

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95

Lectures on Quantum Mechanics

Paul A. M. Dirac

4.0

Four concise, brilliant lectures on mathematical methods by the Nobel Laureate and quantum pioneer begin with an introduction to visualizing quantum theory through the use of classical mechanics. The remaining lectures build on that idea, examining the possibility of building a relativistic quantum theory on curved surfaces or flat surfaces.

96

Calculus with Multiple Variables Essential Skills Workbook: Includes Vector Calculus and Full Solutions

Chris McMullen

4.0

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97

Student Solutions Manual for Mathematical Methods for Physics and Engineering

K. F. Riley

4.0

Mathematical Methods for Physics and Engineering, Third Edition is a highly acclaimed undergraduate textbook that teaches all the mathematics for an undergraduate course in any of the physical sciences. As well as lucid descriptions of all the topics and many worked examples, it contains over 800 exercises. New stand-alone chapters give a systematic account of the 'special functions' of physical s

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98

The Trouble with Physics: The Rise of String Theory, the Fall of a Science and What Comes Next

Lee Smolin

4.0

In this groundbreaking book, the renowned theoretical physicist Lee Smolin argues that physics — the basis for all other sciences — has lost its way. For more than two centuries, our understanding of the laws of nature expanded rapidly. But today, despite our best efforts, we know nothing more about these laws than we knew in the 1970s. Why is physics suddenly in trouble? And what can we do about

Recommended by James Owen Weatherall.

James Owen Weatherall

Smolin’s argument is that string theory is both puzzling and hugely problematic. [source]

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99

Lecture Notes on Elementary Topology and Geometry

I.M. Singer, J.A. Thorpe

4.0

At the present time, the average undergraduate mathematics major finds mathematics heavily compartmentalized. After the calculus, he takes a course in analysis and a course in algebra. Depending upon his interests (or those of his department), he takes courses in special topics. Ifhe is exposed to topology, it is usually straightforward point set topology; if he is exposed to geom- etry, it is usu

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100

A Collection of Problems on Complex Analysis

L. I. Volkovyskii, G. L. Lunts, I. G. Aramanovich

4.0

Over 1500 problems on theory of functions of the complex variable; coverage of nearly every branch of classical function theory. Topics include conformal mappings, integrals and power series, Laurent series, parametric integrals, integrals of the Cauchy type, analytic continuation, Riemann surfaces, much more. Answers and solutions at end of text. Bibliographical references. 1965 edition.