Topology

Möbius strips, which have only one surface and one edge, are a kind of object studied in topology.

In mathematics, topology is concerned with the properties of space that are preserved under continuous deformations, such as bending, twisting, stretching, and squashing, but not tearing or gluing.

Quotes

  • Presentday topology consists of two distinct parts: point set topology and algebraic topology. The first has mainly been the prerogative of Poland plus a strong American component: the school of R. L. Moore (of Austin, Texas).
    • I. M. James (24 August 1999). History of Topology. Elsevier. p. 544. ISBN 978-0-08-053407-7. 
  • Topologists are interested not only in finite-dimensional spaces (for example, subspaces of Rn), but also in infinite-dimensional ones, such as the spaces occurring in quantum field theory.
    • Albert S. Schwarz (16 July 1996). Topology for Physicists. Springer Science & Business Media. p. 23. ISBN 978-3-540-54754-9. 



Mathematics
Mathematicians
(by country)

Abel • Anaxagoras • Archimedes • Aristarchus of Samos • Averroes • Arnold • Banach • Cantor • Cartan • Chern • Cohen • Descartes • Diophantus • Erdős • Euclid • Euler • Fourier • Gauss • Gödel • Grassmann • Grothendieck • Hamilton • Hilbert • Hypatia • Lagrange • Laplace • Leibniz • Milnor • Newton • von Neumann • Noether • Penrose • Perelman • Poincaré • Pólya • Pythagoras • Riemann • Russell • Schwartz • Serre • Tao • Tarski • Thales • Turing • Weil • Weyl • Wiles • Witten

Numbers

1 • 23 • 360 • e • π • Fibonacci numbers • Irrational number • Negative number • Number • Prime number • Quaternion • Octonion

Concepts

Abstraction • Algorithms • Axiomatic system • Completeness • Deductive reasoning • Differential equation • Dimension • Ellipse • Elliptic curve • Exponential growth • Infinity • Integration • Geodesic • Induction • Proof • Partial differential equation • Principle of least action • Prisoner's dilemma • Probability • Randomness • Theorem • Topological space • Wave equation

Results

Euler's identity • Fermat's Last Theorem

Pure math

Abstract algebra • Algebra • Analysis • Algebraic geometry (Sheaf theory) • Algebraic topology • Arithmetic • Calculus • Category theory • Combinatorics • Commutative algebra • Complex analysis • Differential calculus • Differential geometry • Differential topology • Ergodic theory • Foundations of mathematics • Functional analysis • Game theory • Geometry • Global analysis • Graph theory • Group theory • Harmonic analysis • Homological algebra • Invariant theory • Logic • Non-Euclidean geometry • Nonstandard analysis • Number theory • Numerical analysis • Operations research • Representation theory • Ring theory • Set theory • Sheaf theory • Statistics • Symplectic geometry •

Applied math

Computational fluid dynamics • Econometrics • Fluid mechanics • Mathematical physics • Science

History of math

Ancient Greek mathematics • Euclid's Elements • History of algebra • History of calculus • History of logarithms • Indian mathematics • Principia Mathematica

Other

Mathematics and mysticism • Mathematics education • Mathematics, from the points of view of the Mathematician and of the Physicist • Philosophy of mathematics • Unification in science and mathematics


This article is issued from Wikiquote. The text is available under Creative Commons Attribution-Share Alike 4.0 unless otherwise noted. Additional terms may apply for the media files.