Geometry and Topology
DRAFT - WORK IN PROGRESS
PART I: INTRODUCTIONS AND HIGH DISCLOSURE
Geometry
- David Hilbert,S.Cohn-Vossen - Geometry and the imagination transl.it. Intuitive Geometry
- H.S.M. Coxeter - Introduction to Geometry - 2e (1961)
- John Stillwell - The Four Pillars of Geometry
- V.V. Prasolov, V.M. Tikhomirov - Geometry
- Irving Adler - A New Look at Geometry
- Saul Stahl - Geometry from Euclid to Knots
- Maciej Dunajski - Geometry. A Very Short Introduction (2022)
- Glen van Brummelen - Trigonometry. a Very Short Introduction (2020)
- Marco Andreatta - The shape of things. The alphabet of geometry (2019)
- Georg Glaeser - Geometry and Its Applications in Arts, Nature and Technology
- Eli Maor, Eugen Jost - Beautiful Geometry (2014) transl.it. The Art of Geometry
- Ferdinando Arzarello, C.Dané, L.Lovera, M.Mosca, N.Nolli, A.Ronco - From Euclid’s geometry to the geometry of the Universe
- John Barnes - Gems of Geometry - 2nd ed. (2012)
- Maria Dedò - Geometries
Geometry and Linear Algebra
- James Nearing - Mathematical Tools for Physics
- Byron, Fuller - Mathematics for Classic & Quantum Physics
- David A. Brannan, Matthew F. Esplen, Jeremy Gray - Geometry
- Gerald Farin, Dianne Hansford - Practical Linear Algebra.A Geometry Toolbox
Differential geometry
- Jeffrey R. Weeks - The Shape of Space 3ed (2019)
- Peter Collier - A Beginner’s Guide to Differential Forms (2021)
- Tristan Needham - Visual Differential Geometry and Forms: : A Mathematical Drama in Five Acts (2021)
- John McCleary - Geometry from a Differentiable Viewpoint (2012)
Topology
- Richard Earl - Topology: A Very Short Introduction
- H. Graham Flegg - From Geometry to Topology
- Robert Messer, Philip Straffin - Topology now (2006)
- David S. Richeson - Euler’s Gem: The Polyhedron Formula and the Birth of Topology
- V.V. Prasolov - Intuitive Topology
- Sue E. Goodman - Beginning Topology
- Paul Alexandroff - Elementary Concepts In Topology
- Bradford H. Arnold - Intuitive Concepts in Elementary Topology
- Stephen Barr - Experiments in Topology
Nodes and Graphs between topology and discrete mathematics
- Colin Adams - The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots
- David W. Farmer, Theodore B. Stanford - Knots and surfaces
- Alexei Sossinsky, Giselle Weiss - Knots: Mathematics with a Twist
- Gary Chartrand - Introductory Graph Theory
- Nora Hartsfield, Gerhard Ringel - Pearls in Graph Theory: A Comprehensive Introduction
- Peter M. Higgins - The mathematics of social networks. introduction to graph theory
Geometry and Physics
- Hermann Weyl - Space Time Matter (1952)
- George F. R. Ellis - Flat and Curved Space-Times (2001)
- Roger Penrose - The Road to Reality. A Complete Guide to the Laws of the Universe (2007)
- Pietro G. Frè - A Conceptual History of Space and Symmetry. from Plato to the Superworld (2019)
Carriers and Tensors
- Feynman’s Lectures on Physics, vol. I ch. 11,20 vol. II ch. 31,42
- James Nearing - Mathematical Tools for Physics
- Altland, von Delft- Mathematics for Physicists
- Nadir Jeevanjee - Introduction to Tensors & Group Theory For Physicists
- Daniel Fleisch - A Student’s Guide to Vectors and Tensors
- H. M Schey - Div, Grad, Curl, and All That: An Informal Text on Vector Calculus
- James G. Simmonds - A Brief on Tensor Analysis
Articles, lecture notes and online resources:
- Feynman’s Lectures on Physics https://www.feynmanlectures.caltech.edu/II_31.html https://www.feynmanlectures.caltech.edu/II_42.html
- Math Insight on vector algebra https://mathinsight.org/thread/vector_algebra
- James Nearing - Mathematical Tools for Physics, 12, Tensors http://www.physics.miami.edu/~nearing/mathmethods/tensors.pdf
- Edmund Bertschinger - Introduction to tensor calculus for general relativity (1999) https://web.mit.edu/edbert/GR.html
- Sean Carrol - Lecture notes on general relativity https://www.preposterousuniverse.com/grnotes/
PART II: DISCLOSURE FOR ALL
Geometry and Topology
- Edwin Abbott - Flatland. multi-dimensional fantasy story
- Laura Catastini, Franco Ghione - Limitless Geometries: Non-Euclidean Worlds
- Dario Palladino, Claudia Palladino - Non-Euclidean geometries
- Paolo Freguglia - Geometry and numbers. History, elementary theory and applications of geometric calculus
- David Acheson - The Wonder Book of Geometry. A Mathematical Story (2020)
- Jordan Ellenberg - Form. Hidden geometry in data, society, politics, information, the universe and many other places (2022)
- Piergiorgio Odifreddi - There is room for everyone. The great tale of geometry (2011)
- Piergiorgio Odifreddi - An escape route. The great tale of modern geometry (2012)
- Piergiorgio Odifreddi - Down with Euclid! The great tale of contemporary geometry (2013)
Geometry and Physics
- Albert Einstein, “Relativity: popular exposition. With classical writings on space geometry physics,” 5th ed. (2010)
- Anthony Zee - On Gravity: A Brief Tour of a Weighty Subject (2018) transl.it. Gravity: A Brief Tour of a Weighty Subject
- Kip S. Thorne - Black Holes and Time Warps. Einstein’s Outrageous Legacy. translated it. black holes and time jumps
- Shing-Tung Yau, Steve Nadis - The Shape of Inner Space. String Theory and the Geometry of the Universe Hidden Dimensions
- Lisa Randall - Warped Passages: Unraveling the Mysteries of the Universe’s Hidden Dimensions
PART III: INSIGHTS
Geometry and Linear Algebra
- John Hubbard, Barbara Burke Hubbard - Vector Calculus, Linear Algebra, and Differential Forms. 5_Ed.(2015)
- Nadir Jeevanjee - Introduction to tensors and group theory for physicists
- Chris J. Isham - Groups and Vector Spaces for Physicists
Complex Analysis
- Tristan Needham - Visual Complex Analysis
- Ian Stewart, David Tall - Complex Analysis
Differential geometry
- Kristopher Tapp - Differential Geometry of Curves and Surfaces
- Bernard Schutz - Geometrical methods of mathematical physics
- Chris J. Isham - Modern Differential Geometry for Physicists, 2nd ed. (1999)
- Theodore Frankel - The geometry of physics
- Richard Bishop, Samuel Goldberg - Tensor Analysis on Manifolds
Topology
- Colin Adams, Robert Franzosa - Introduction to Topology - Pure and Applied
- John Stillwell - Classical topology and combinatorial group theory (1993)
- Peter Saveliev - Topology Illustrated
- Robert Ghrist - Elementary Applied Topology
- Charles Nash, Siddhartha Sen - Topology and Geometry for Physicists
Graphs
- Arthur Benjamin, Gary Chartrand, Ping Zhang - The Fascinating World of Graph Theory
- Jonathan L. Gross, Jay Yellen - Graph Theory and Its Applications
- John Trudeau - Introduction to Graph Theory
Geometry and Physics: insights
- Kip Thorne, Roger Blandford - Modern Classical Physics
- Vladimir Arnold - Mathematical methods of classical mechanics
- Jorge Jose, Eugene Saletan - Classical Dynamics
- Bernard Schutz - A First Course in General Relativity, 3rd ed. (2022)
- Sean Carroll - SpaceTime and Geometry
- John C. Baez, Javier P. Muniain - Gauge Fields, Knots, And Gravity
- Roderich Moessner, Joel E. Moore - Topological Phases of Matter (2021)
