Mathematics

• General Reference
  • Centre for Innovation in Mathematics Teaching (CIMT)
  • Interactive Mathematics Miscellany and Puzzles
  • Jean Daunizeau's useful resources (probability theory, matrices, calculus...)
  • Math Archives
  • Mathphysics.com - online textbooks
  • Maths - Martin Baker
  • Maths Tutorial
  • MathWorld
    • The Wolfram Functions Site
  • Metamath - Proof Explorer, Hilbert Space Explorer, Quantum Logic Explorer
  • Paul's Online Math Notes (Algebra & Calculus)
  • PlanetMath
  • ProofWiki
  • Sci.Math FAQ
  • S.O.S. Mathematics
  • Taschenbuch der Mathematik
  • The Connected Curriculum Project
  • The Mathematical Atlas
  • Theorem of the Day
  • WebMath
  • Wikibooks: Schulmathematik
    • Division
• Miscellaneous
  • The 12 Most Controversial Facts In Mathematics
  • The 17 equations that changed the course of history
• News
  • Proof claimed for deep connection between primes
• History and Definition
  • Definition - Encyclopaedia Britannica
  • The MacTutor History of Mathematics archive
    • An overview of the history of mathematics
    • Biographies
• Lists of Maths Sites
  • A Collection of Maths Web sites
  • Bachelor of Arts in Math: Math Resources
  • Maths Links
  • Yahoo maths links
• Humour
  • Maths/Science/Computer Jokes
  • Wert von x ein für alle Mal auf 5 festgesetzt
• Novels
  • A Certain Ambiguity: A Mathematical Novel
• People
  • Active Mathematicians
    • John Baez
      • John Baez's Stuff
    • David Marius Bressoud
    • John L. Casti
    • Gregory J. Chaitin
    • W. David Joyner
    • Dave Rusin
    • Ian Stewart
      • Wikipedia
        • Galois Theory Errata
    • Tadashi Tokieda
      • Modern Mathematics - International Summer School for Students 2014
  • Great Mathematicians
    • Paul Erdös
      • Paul Erdös - A Web site by Paul Hoffman
        • Book: The Man Whol Loved Only Numbers
      • The Erdös Number Project
        • Computing Your Erdös Number
        • Information about Paul Erdös (1913-1996)
      • Theoretical Computer Science at the University of Chicago salutes Paul Erdös
    • Kurt Gödel
      • The Kurt Gödel Society
    • Benoit Mandelbrot
      • A maverick's apprenticeship
  • Photos of Mathematicians
  • The Mathematics Genealogy Project
• Topics
  • Abstract Algebra
    • Abstract Algebra On Line
    • Elements of Abstract and Linear Algebra
  • Ackermann's Function
    • Susan Stepney's Ackermann page
  • Bayesian inference
    • Philosophy of Bayesian Inference
  • Big numbers
    • Notations
      • Conway's chained arrow notation
        • planetmath.org
        • Wikipedia
      • Knuth's up-arrow notation
        • planetmath.org
        • Wikipedia
    • Numbers
      • Graham's number
    • Surveys
      • Robert Munafo
      • Susan Stepney
  • Boolean Algebra
  • Borromean rings
  • Category Theory
    • A Categorical Primer
    • A Gentle Introduction to Category Theory - the calculational approach
    • Applied and Computational Category Theory
    • Basic Category Theory
    • Categories, Quantization, and Much More
    • Toposes, Triples and Theories by Michael Barr and Charles Wells
    • Stanford Encyclopedia of Philosophy
  • Continued Fractions
  • Cryptography
    • Public key cryptography
  • Curves
    • Cardioid
    • Conic Sections
      • Constructing Ellipses
      • Parabola
    • Famous Curves Index
  • Derivative
    • Existence of complex derivative implies the Cauchy-Riemann equations
  • Direct product
  • Euclidean Space
    • Definitions
      • Euclidean Space
      • Euclidean Vector Space
      • Inner Product
    • Distance
      • What is the geometric relationship between Eucledian distance, Eucledian norm and scalar product?
    • Euclid's Elements of Geometry
    • Euclidean Space - Building a 3D World
  • Euclid's Algorithm
  • Euler's formula
    • Euler's identity
  • Fermat's Last Theorem
    • Book: Fermat's Last Theorem - Simon Singh
    • The Mathematics of Fermat's Last Theorem
      • The Proof
  • Fourier Transforms
    • Fourier Transform - MathWorld
    • Fourier Transform - Wikipedia
      • Multi-dimensional version
    • Mathematics of the Discrete Fourier Transform (DFT)
    • The Convolution Theorem
      • MathWorld
      • Wikipedia
      • The Two-Dimensional Convolution Theorem
        • Fourier analysis and imaging - by Ronald Newbold Bracewell
    • The Fast Fourier Transform (FFT)
  • Fractals
    • Fractint
    • Spanky Fractal Database
  • Fundamental Theorem of Algebra
  • Geometric Algebra & Geometric Calculus
    • Cambridge University Geometric Algebra Research Group
      • Chris Doran
        • Introduction to Geometric Algebra
    • Geometric Calculus
    • Timothy F. Havel
      • A Unified Model for the Classical Geometries with Geometric Algebra
      • Geometric Algebra: Parallel Processing for the Mind
  • Graph Theory
    • General Information
      • Daniel Sanders' Graph Theory Pages
      • Reinhard Diestel's online book
      • Stephen Locke's Graph Theory page
      • The Mathematical Atlas
    • Theorems
      • The Four Colour Theorem
      • The Strong Perfect Graph Theorem
  • Group Theory
    • ATLAS of Finite Group Representations - Version 3
    • Direct product of groups
    • GAP - Groups, Algorithms, Programming - a System for Computational Discrete Algebra
      • Analyzing Rubik's Cube with GAP
    • History of Group Theory
      • The abstract group concept
    • Introduction to Group Theory
      • Rubik's Cube
  • Hilbert's Hotel
    • Maths Thesaurus Entry
    • Reference to article in New Scientist by Ian Stewart
  • Hilbert Space
    • Direct Sum and Tensor Product
      • Nathan Urban, John Baez: Tensor Product and Direct Sum
      • Tensor (Direct) Products vs. Direct Sums
    • Notes on Hilbert Space by Prof. C-I Tan
    • Notes on Linear Algebra and Operators by M.A. Parker
    • Riesz-Frechet Theorem
    • Uncountably infinite dimensional Hilbert Spaces
  • Hopf Fibration
    • An Elementary Introduction to the Hopf Fibration - David W. Lyons
  • Hyperspheres
    • MathWorld
    • Wikipedia - n-sphere
      • Hyperspherical coordinates
    • Franz Vesely - From Hyperspheres to Entropy
  • Inner or Dot Product
    • Dot Product
    • Inner Product
      • Cauchy-Schwarz Inequality
      • Triangle Inequality
  • Knot Theory
  • Limits
    • One-Sided Limits
    • Infinite Limits
    • The Definition of the Limit
  • Linear Algebra
    • Elements of Abstract and Linear Algebra - Edwin H. Connell
    • Linear Algebra - Jim Hefferon
    • Linear Algebra and Applications Textbook - Thomas S. Shores
    • Norm
      • Euclidean norm
        • Euclidean distance
      • p-norm
        • L^p space
    • Schmidt Decomposition
      • Bipartite states and Schmidt decomposition
  • Linear Methods of Applied Mathematics
    • The geometry of functions
  • Mathematical Logic - Peter Smith
  • Matrices
    • Block matrices
      • Block Multiplication of Matrices
      • Multiplying block matrices
      • Multiplication of Partitioned Matrices
    • Kronecker product and the Vec operator
      • Notes
        • Jean Daunizeau
        • Steven L. Scott
      • Wikipedia
        • Kronecker product
        • Vectorization
    • Outer product
    • Singular Value Decomposition
      • Introduction to the Singular Value Decomposition - Todd Will
      • The Extraordinary SVD - Carla D. Martin and Mason A. Porter
    • Tensor product
      • Math3ma - The Tensor Product, Demystified
      • Wikipedia
    • The Matrix Reference Manual
    • Wikipedia
  • Methods of Theoretical Physics (PHY 501)
    • Lecture notes
  • Multiplication: different methods
    • Lattice Multiplication
    • Russian Peasant Multiplication
      • Ancient Egyptian Multiplication
  • Octonions
    • John C. Baez
      • This Week's Finds in Mathematical Physics (Week 59)
      • This Week's Finds in Mathematical Physics (Week 61)
      • Paper: The Octonions
    • Geoffrey M. Dixon
      • Book: "Division Algebras: Octonions, Quaternions, Complex Numbers and the Algebraic Design of Physics"
      • Octonions and other Division Algebras
  • Orientation entanglement
  • Penrose Tiling
  • Poincaré Conjecture
    • Poincaré Conjecture Proved - This Time for Real
    • The Daily Princetonial - Perelman explains proof to famous math mystery
  • Prime Numbers
    • PRIMES is in P - A 2200 year old math problem solved!
      • Manindra Agrawal
        • PRIMES is in P
    • The First 1,000 Primes
    • Ulam Spiral
  • Principal component analysis (PCA)
    • Relationship between SVD and PCA. How to use SVD to perform PCA?
    • A Tutorial on Principal Component Analysis
  • Probability Theory
    • Negative Probability
      • Half of a Coin: Negative Probabilities
      • Interpretations of Negative Probabilities
    • Non-Commutative Probability Theory
      • Non-Commutative Probability Theory, Paul D. Mitchener
      • Two Examples in Non-Commutative Probability, Dror Bar-Natan, Foundations of Physics 19 (1989) 97-104
    • Probability Theory As Extended Logic
  • Proof - Methods of Proof
  • Quantum Chaos
  • Quaternions
    • Biquaternions
    • Equivalence to 3D Rotations
    • Introduction to the Quaternions
    • Notes on Quaternions and Vectors
    • Quaternions and spatial rotation
    • Sir William Rowan Hamilton
      • On Quaternions
    • Using Quaternions to Represent Rotation
  • Rotations
    • Berkeley CS184: Computing Rotations in 3D - The Rodrigues Formula
    • Gimbal Lock
    • Rotation Matrices - Martin Baker
      • AxisAngle to Matrix conversion
      • Representing rotations as 2 reflections
        • Reflection
    • Rotations in Three Dimensions by Confuted and Silvercord
      • Part Three: Rotation About an Arbitrary Axis
    • The Mathematics of the 3D Rotation Matrix - Diana Gruber
      • Deriving the Rotation Matrix Around an Arbitrary Axis in R^3
  • Sets
    • Cartesian product
  • Spinors
    • Geometric Algebra Approach
      • A Unified Algebraic Framework for Classical Geometry
      • Majorana Spinors, a modern approach
      • Spinors Particle Mechanics
    • Spinors and Dirac matrices in three dimensions
    • Spinors - Fedja Hadrovic
    • Spinors in Geometry and Physics
    • The Nature of Spinors
    • Two-dimensional spinors
    • Wikipedia - Spinor
      • Three dimensions
        • Spinors in three dimensions
  • Statistics
    • Efficiently sampling vectors and coordinates from the n-sphere and n-ball
    • Elementary Statistical Java Applets and Tools
    • Monty Hall problem
    • Multivariate normal distribution
  • Sums
    • Some special sums
    • Sums of Powers
      • The Formula for the Sum of Squares
  • Topology
    • How To Turn A Torus Inside Out
    • Klein bottle
  • Trigonometric Identities
  • Twistors
    • Twistors - What Are They?
  • Unsolved Mathematics Problems
  • Vectors
    • Direct Rotations versus Passive Transformations

Last updated on
by Ian Glendinning