Geometria e Topologia

DRAFT - WORK IN PROGRESS

PARTE I: INTRODUZIONI ED ALTA DIVULGAZIONE

Geometria

  • David Hilbert,S.Cohn-Vossen - Geometry and the imagination
    trad.it. Geometria intuitiva
  • 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 - La forma delle cose. L’alfabeto della geometria (2019)
  • Georg Glaeser - Geometry and Its Applications in Arts, Nature and Technology
  • Eli Maor, Eugen Jost - Beautiful Geometry (2014)
    trad.it. L’arte della geometria
  • Ferdinando Arzarello, C.Dané, L.Lovera, M.Mosca, N.Nolli, A.Ronco - Dalla geometria di Euclide alla geometria dell’Universo
  • John Barnes - Gems of Geometry - 2°ed. (2012)
  • Maria Dedò - Geometrie

Geometria ed Algebra Lineare

  • 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

Geometria differenziale

  • 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)

Topologia

  • 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

Nodi e Grafi tra topologia e matematica discreta

  • 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 - La matematica dei social network. Introduzione alla teoria dei grafi

Geometria e Fisica

  • 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)

Vettori e Tensori

  • Feynman’s Lectures on Physics, vol. I cap. 11,20 vol. II cap. 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

Articoli, appunti di lezioni e risorse online:

PARTE II: DIVULGAZIONE PER TUTTI

Geometria e Topologia

  • Edwin Abbott - Flatlandia. Racconto fantastico a più dimensioni
  • Laura Catastini, Franco Ghione - Geometrie senza limiti: I mondi non euclidei
  • Dario Palladino, Claudia Palladino - Le geometrie non euclidee
  • Paolo Freguglia - Geometria e numeri. Storia, teoria elementare e applicazioni del calcolo geometrico
  • David Acheson - The Wonder Book of Geometry. A Mathematical Story (2020)
  • Jordan Ellenberg - Forma. La geometria nascosta nei dati, nella società, nella politica, nell’informazione, nell’universo e in molti altri posti (2022)
  • Piergiorgio Odifreddi - C’è spazio per tutti. Il grande racconto della geometria (2011)
  • Piergiorgio Odifreddi - Una via di fuga. Il grande racconto della geometria moderna (2012)
  • Piergiorgio Odifreddi - Abbasso Euclide! Il grande racconto della geometria contemporanea (2013)

Geometria e Fisica

  • Albert Einstein, “Relatività: esposizione divulgativa. Con scritti classici su spazio geometria fisica”, 5° ed. (2010)
  • Anthony Zee - On Gravity: A Brief Tour of a Weighty Subject (2018) trad.it. Gravità: Trattazione leggera di un soggetto pesante
  • Kip S. Thorne - Black Holes and Time Warps. Einstein’s Outrageous Legacy. trad. it. Buchi neri e salti temporali
  • 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

PARTE III: APPROFONDIMENTI

Geometria ed Algebra Lineare

  • 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

Analisi Complessa

  • Tristan Needham - Visual Complex Analysis
  • Ian Stewart, David Tall - Complex Analysis

Geometria differenziale

  • 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

Topologia

  • 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, Siddharta Sen - Topology and Geometry for Physicists

Grafi

  • 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

Geometria e Fisica: approfondimenti

  • Kip Thorne, Roger Blandford - Modern Classical Physics
  • Vladimir Arnold - Metodi matematici della meccanica classica
  • Jorge Josè, Eugene Saletan - Classical Dynamics
  • Bernard Schutz - A First Course in General Relativity, 3° 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)