Sign-In
Cart
Manifolds: The Foundations of General Relativity
Paperback
Publisher: Independently Published
Published: Apr 12 2026
Pages: 122
Weight: 0.38
Height: 0.29 Width: 6.00 Depth: 9.00
Language: English
Most calculus is taught as if the symbols are the mathematics.
This book takes the opposite view: the symbols are not the mathematics-they are just a coordinate system describing something deeper.
A point is not a pair of numbers. A function is not a formula. A coordinate system is not reality. These are descriptions layered on top of geometric objects that exist independently of how we label them.
The goal of this book is to rebuild calculus from that distinction upward.
It focuses on separating objects from their representations: what remains invariant when coordinates change, what survives different descriptions, and what it actually means for something to be geometric rather than symbolic.
Along the way, familiar ideas from calculus are reframed in a coordinate-independent way, leading naturally toward the language of manifolds and differential geometry.
This is not a procedural textbook. It does not begin with memorization or computation tricks. It begins with meaning.
You will learn to see:
- why coordinates are optional rather than fundamental
- what the same object means under different descriptions
- how calculus changes when symbols stop being mistaken for structure
- the geometric foundation behind manifolds and curvature
The aim is not to make calculus more complicated, but to make it impossible to unsee what it is really doing.
Also from
Cole, Jesse
Fans First: Change The Game, Break the Rules & Create an Unforgettable Experience
Cole, Jesse
Paperback
Also in
Physics
The Formative Years of Relativity: The History and Meaning of Einstein's Princeton Lectures
Gutfreund, Hanoch
Renn, Jürgen
Hardcover
Physics of the Future: How Science Will Shape Human Destiny and Our Daily Lives by the Year 2100
Kaku, Michio
Hardcover
How It All Works: All Scientific Laws and Phenomena Illustrated & Demonstrated
Dant, Adam
Clegg, Brian
Hardcover
Feynman's Lost Lecture: The Motion of Planets Around the Sun [With CDROM]
Goodstein, David L.
Paperback
Accessory to War: The Unspoken Alliance Between Astrophysics and the Military
Lang, Avis
Degrasse Tyson, Neil
Hardcover
The Edge of Space-Time: Particles, Poetry, and the Cosmic Dream Boogie
Prescod-Weinstein, Chanda
Hardcover
Lost in Space: 5,000 Facts for Navigating the Universe
Tyson, Neil Degrasse
Walker, Lindsey Nyx
Hardcover
5 Steps to a 5: AP Physics 1 2027: Practice AP Tests + AP Content Review + Digital Exams
Jacobs, Greg
Paperback
Just Visiting This Planet, Revised and Updated for the Twenty-First Century: Further Scientific Adventures of Merlin from Omniscia
Tyson, Neil Degrasse
Hardcover
What If? 10th Anniversary Edition: Serious Scientific Answers to Absurd Hypothetical Questions
Munroe, Randall
Hardcover
Astronomy 101, 2nd Edition: From Gravitational Waves and Merging Black Holes to New Exoplanets and Asteroid Samples, Key Theories, Discoveries, and Fa
Petersen, Carolyn Collins
Hardcover
Time's Second Arrow: Evolution, Order, and a New Law of Nature
Hazen, Robert M.
Wong, Michael L.
Hardcover
Six Easy Pieces: Essentials of Physics Explained by Its Most Brilliant Teacher
Leighton, Robert B.
Sands, Matthew
Feynman, Richard P.
Paperback
My Big TOE Awakening Discovery Inner Workings: The Complete My Big TOE Trilogy Unifying Philosophy, Physics and Metaphysics
Campbell, Thomas
Hardcover
What If? 2: Additional Serious Scientific Answers to Absurd Hypothetical Questions
Munroe, Randall
Hardcover
A New Science of Heaven: How the New Science of Plasma Physics Is Shedding Light on Spiritual Experience
Temple, Robert
Paperback
Beyond Darwin: How Epigenetics, Quantum Science, and Cooperation Shape Humanity's Future
Lipton, Bruce H.
Hardcover
Do Aliens Speak Physics?: And Other Questions about Science and the Nature of Reality
Whiteson, Daniel
Warner, Andy
Hardcover
Take Me to Your Leader: Perspectives on Your First Alien Encounter (Large Print Edition)
Tyson, Neil DeGrasse
Hardcover
The Disordered Cosmos: A Journey Into Dark Matter, Spacetime, and Dreams Deferred
Prescod-Weinstein, Chanda
Paperback
Strange Angel: The Otherworldly Life of Rocket Scientist John Whiteside Parsons
Pendle, George
Paperback
Princeton Review AP Physics 1 Premium Prep, 13th Edition: 5 Practice Tests + Digital Practice Online + Content Review
The Princeton Review
Paperback
American Prometheus (Pulitzer Prize Winner): The Inspiration for the Major Motion Picture Oppenheimer
Sherwin, Martin J.
Bird, Kai
Paperback
The Montauk Project - Experiments in Time: Silver Anniversary Edition
Moon, Peter
Nichols, Preston B.
Paperback
AP Physics 1 Premium, 2027: Prep Book with 4 Practice Tests + Comprehensive Review + Online Practice
Rideout, Kenneth, M. S.
Wolf, Jonathan, M. a. Ed M.
Paperback
Zinn and the Art of Mountain Bike Maintenance, 7th Edition: The World's Best-Selling Guide to Mountain Bike Repair
Zinn, Lennard
Paperback
AP Physics 1 Premium, 2026: Prep Book with 4 Practice Tests + Comprehensive Review + Online Practice
Rideout, Kenneth, M. S.
Wolf, Jonathan, M. a. Ed M.
Paperback
The Tao of Physics: An Exploration of the Parallels Between Modern Physics and Eastern Mysticism
Capra, Fritjof
Paperback
Graph Paper Notebook 1/4 inch squares: Graph Paper Composition Book For Children and Women 8 x 10 inch, 122 Pages
Warren, Leann S.
Paperback
Quantum Physics and Higher Consciousness: Unlocking the Mysteries of Reality and Awakening Your Inner Power
Silva, Mari
Hardcover
The Black Book of Manifestation: Hidden Secrets & Forbidden Techniques to Shape Your Reality
Sharma, Sagar
Paperback
Ways of Being: Animals, Plants, Machines: The Search for a Planetary Intelligence
Bridle, James
Paperback
Princeton Review AP Physics 1 Premium Prep, 12th Edition: 5 Practice Tests + Digital Practice Online + Content Review
The Princeton Review
Paperback
Why Nobody Understands Quantum Physics: The Story of the Science That Shapes Our World
Verstraete, Frank
Broeckaert, Céline
Hardcover
Rocket Dreams: Musk, Bezos, and the Inside Story of the New, Trillion-Dollar Space Race
Davenport, Christian
Hardcover
From Shiva to Schrödinger: Unravelling Cosmic Secrets with Trika Shaivism & Quantum Insights
Majumdar, Mrittunjoy Guha
Paperback
The Montauk Project - Experiments in Time: Silver Anniversary Edition
Nichols, Preston B.
Moon, Peter
Hardcover
Introduction to Live Sound Reinforcement: The Science, the Art, and the Practice
Boyce, Teddy
Paperback
Smithsonian Atlas of Space: A Map to the Universe from the Big Bang to the Future
Launius, Roger D.
Hardcover
Zinn & the Art of Road Bike Maintenance, 6th Edition: The World's Best-Selling Bicycle Repair and Maintenance Guide
Zinn, Lennard
Paperback
Do Your Ears Pop in Space? and 500 Other Surprising Questions about Space Travel
Mullane, R. Mike
Paperback
The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory
Greene, Brian
Paperback
A Brief Welcome to the Universe: A Pocket-Sized Tour
Tyson, Neil Degrasse
Gott, J. Richard
Strauss, Michael A.
Paperback
Six Not-So-Easy Pieces: Einstein's Relativity, Symmetry, and Space-Time
Sands, Matthew
Feynman, Richard P.
Leighton, Robert B.
Paperback
My Big TOE Awakening Discovery Inner Workings: The Complete My Big TOE Trilogy Unifying Philosophy, Physics, and Metaphysics
Campbell, Thomas
Paperback
Time Travel in Einstein's Universe: The Physical Possibilities of Travel Through Time
Gott, J. Richard
Paperback
The Fabric of Reality: The Science of Parallel Universes--And Its Implications
Deutsch, David
Paperback
The Theoretical Minimum: What You Need to Know to Start Doing Physics
Susskind, Leonard
Hrabovsky, George
Paperback
Welcome to the Universe: An Astrophysical Tour
Gott, J. Richard
Tyson, Neil Degrasse
Strauss, Michael A.
Hardcover
The Autobiography of Nikola Tesla and Other Works (Deluxe Leatherbound Edition)
Tesla, Nikola
Martin, Thomas Commerford
Hardcover
Signals from the Subatomic World: How to Build a Proton Precession Magnetometer
Hollos, Richard
Hollos, Stefan
Paperback
Quantum Mechanics Done Right: The Shortest Path from Novice to Researcher
Freericks, James K.
Hardcover
There Are Places in the World Where Rules Are Less Important Than Kindness: And Other Thoughts on Physics, Philosophy and the World
Rovelli, Carlo
Paperback
Fundamentals of Astrodynamics: Second Edition
Bate, Roger R.
Mueller, Donald D.
White, Jerry E.
Paperback
Collisions: A Physicist's Journey from Hiroshima to the Death of the Dinosaurs
Nevala-Lee, Alec
Hardcover
Cosmos and Transcendence: Breaking Through the Barrier of Scientistic Belief
Smith, Wolfgang
Paperback
Let's Review Regents: Physical Science- Physics, Sixth Edition (Barron's NY Regents)
Lazar, Miriam A., M. S.
Tarendash, Albert, M. S.
Paperback
Regents Exams and Answers Physical Science Physics Sixth Edition (Barron's New York Regents)
Lazar, Miriam, M. S. Ed
Paperback
The One Thing You Need to Know: The Simple Way to Understand the Most Important Ideas in Science
Chown, Marcus
Paperback
Unseen Universe: Space as You've Never Seen It Before from the James Webb Space Telescope
Harper, Caroline
Hardcover
Alchemy of Nine Dimensions: Activating the Full Spectrum of Consciousness
Clow, Barbara Hand
Paperback
The Sound Atlas: A Guide to Strange Sounds Across Landscapes and Imagination
Yuen, Isaac
Vieser, Michaela
Hardcover
Cosmic Queries: Startalk's Guide to Who We Are, How We Got Here, and Where We're Going
Tyson, Neil DeGrasse
Hardcover
Princeton Review AP Physics C Premium Prep, 19th Edition: 4 Practice Tests + Digital Practice Online + Content Review
The Princeton Review
Paperback
AP Physics C Premium, Eighth Edition: 4 Practice Tests + Comprehensive Review + Online Practice (2026)
Pelcovits, Robert A., PH. D.
Farkas, Joshua, M. D.
Paperback
Sciencia: Mathematics, Physics, Chemistry, Biology, and Astronomy for All
Tweed, Matt
Watkins, Matthew
Betts, Moff
Hardcover
The Universe Story: From the Primordial Flaring Forth to the Ecozoic Era--A Celebration of the Unfol
Swimme, Brian
Paperback
Analytic Idealism in a Nutshell: A Straightforward Summary of the 21st Century's Only Plausible Metaphysics
Kastrup, Bernardo
Paperback
Scale: The Universal Laws of Life, Growth, and Death in Organisms, Cities, and Companies
West, Geoffrey
Paperback
Relativity: The Special and the General Theory - 100th Anniversary Edition
Einstein, Albert
Paperback
Sounds Wild and Broken: Sonic Marvels, Evolution's Creativity, and the Crisis of Sensory Extinction
Haskell, David George
Paperback