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Help out$\mathsf{Pr} \infty \mathsf{fWiki}$ is a great resource for mathematical proofs but can not maintain itself. If you want to help $\mathsf{Pr} \infty \mathsf{fWiki}$ expand and grow check out the lists of things below. | ||
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A selection of links to some other sites which are more or less concerned with Mathematics:
On-line Text Books (School and Undergraduate Level)
- Free High School Science Texts (South Africa)
- The Maths Factor
- Math Open Reference
- Maths Unlocked: British A-level past papers solved -- video presentations
- Dictionary of Units
- Teacher Resources on Line
- Better Explained
- Maths Genie
- OpenStax
- Long(er)-Form Mathematics
Magazines
- http://plus.maths.org/
- https://www.stem.org.uk/resources/collection/4088/isquared-magazine
- http://www.maa.org/pubs/mathmag.html
- https://www.maa.org/press/periodicals/maa-focus
- https://chalkdustmagazine.com/
- https://link.springer.com/journal/283
- http://polymathprogrammer.com/singularity/
Forums and Online Communities
- The Math Forum
- http://www.mathhelpforum.com/math-help/
- http://www.thestudentroom.co.uk/
- http://physicsforums.com/ (Mathematics section)
- http://mathoverflow.net/
- http://math.stackexchange.com
- Math is Fun
- Math Is Fun Forum
- Natural Math
- Math Future
- Sangakoo
- Maths Centre for Professional Teachers
Books
- Bertrand Russell and Alfred North Whitehead: Principia Mathematica
- http://www-cs-faculty.stanford.edu/~knuth/taocp.html
Wikis and Encyclopedias
- Project Euclid: Mathematics and Statistics Online
- Scholarpedia
- ProvenMath
- Subject Wikis
- http://www.tricki.org/
- http://en.wikipedia.org/wiki/Wikipedia:WikiProject_Mathematics
- Math Wiki (on Wikia)
- MathPages
- http://mathworld.wolfram.com/
- http://planetmath.org/
- http://www.mathwords.com/
- nLab
- Art of Problem Solving
- Interactive Mathematics
- Mathemapedia
- Springer Online Reference Works: Encyclopaedia of Mathematics (recently wikified, now using the same technology as $\mathsf{Pr} \infty \mathsf{fWiki}$)
- Esolang (yes I know it's not mathematics)
- HandWiki: a wiki dedicated to articles on computing, science, technology and general knowledge
Blogs and other personal websites
- http://www.mathblogging.org/ (Aggregates from various math blogs)
- http://blog.tanyakhovanova.com/
- http://terrytao.wordpress.com/
- http://wildaboutmath.com/
- http://randmathfun.blogspot.com
- Math Accent
- Bee Bop Parade
- A Quantum Immortal: Stuff Ron Gross finds interesting
- AG from the Beginning: A blog about Algebraic Geometry at an accessible level
- Infinity Series; an introduction to ordinals
- Annoying Precision by Qiaochu Yuan
- Mathematical Enchantments by James Propp
- Yet Another Mathblog by David Joyner
- http://www.cadaeic.net by Mike Keith
- The Aperiodical
- The Mathematical Garden
- Fred Akalin
- ThatsMaths
- Ralph the triangle by Ralph Heiner Buchholz
- Mathstodon by John Carlos Baez
Software/Computing
- http://www.latex-project.org/
- http://www.w3.org/Math/Software/
- http://pari.math.u-bordeaux.fr/
- http://www.gnu.org/software/octave/
- http://www.sagemath.org/
- http://www.texmacs.org/
- http://www.lyx.org/
- http://www.mersenne.org/
- http://primegrid.com/
- http://www.geogebra.org/cms/en/info
- http://demonstrations.wolfram.com/index.html
- http://www.r-project.org/
- http://docs.latexlab.org/ (Free online $\LaTeX$ development environment - Requires a Google account)
- http://www.scribtex.com (Free online $\LaTeX$ development environment - Good for rapid previews)
- http://www.demonstranda.com
- TrianCal (Free online calculator triangles without advertising)
- Javascript Julia Set Generator by Mark McClure
- Javalab
Comics
- http://xkcd.com/
- http://brownsharpie.courtneygibbons.org/
- http://abstrusegoose.com/
- http://spikedmath.com/
- Saturday Morning Breakfast Cereal
Formalized Mathematical Proofs
- Mizar: "an attempt to reconstruct mathematical vernacular in a computer-oriented environment."
- Isabelle
- HOL light
- HOL4
- Coq
- HOL Zero
- ProofPower
- Metamath: A tiny language that can express theorems in abstract mathematics
Computational Knowledge Engines
Lecture Notes
Algebra
Abstract Algebra
- R.B. Ash: Abstract Algebra
- Paul Garrett: Abstract Algebra
- Paul Garrett: Intro to Abstract Algebra (Solutions)
- D. Surowski: A Workbook in Higher Algebra
Linear Algebra
- H. Connell: Elements of Abstract and Linear Algebra
- J. Hefferon: Linear Algebra
- A. Baker: Basic Linear Algebra
- W.W.L. Chen: Linear Algebra
Group Theory
- J.S. Milne: Group Theory
- P. Cvitanović: Group Theory: Birdtracks, Lie's and Exceptional Groups
- Paul Garrett: Buildings, BN-Pairs, Hecke Algebras, Classical Groups
- R.B. Howlett: Miscellaneous Facts About Coxeter Groups
- Introduction to Group Theory
- A. Baker: Groups and Symmetry
Representation Theory
- A. Baker: Representations of Finite Groups
- C. Teleman: Representation Theory
- P. Etingof, O. Golberg, S. Hensel, T. Liu, A. Schwendner, D. Vaintrob, and E. Yudovina: Introduction to representation theory
Universal Algebra
- G.M. Bergman: An Introduction to Universal Algebra
- S. Burris and H.P. Sankappanavar: A Course in Universal Algebra
- M. Valeritoe: Lectures on Universal Algebra
Lie Groups
- B.C. Hall: An Elementary Introduction to Groups and Representations
- Paul Garrett: Lie Algebras and Lie Groups
- I. Avramidi: Notes on Lie Groups
- R.L. Bryant: An Introduction to Lie Groups and Symplectic Geometry
- A. Cap: Lie Groups
Galois Theory
- J.S. Milne: Fields and Galois Theory
- D. Wilkins: Galois Theory
- A. Baker: An Introduction to Galois Theory
- J.P. Serre: Topics in Galois Theory
- M. Reid: Galois Theory
- S.R. Ghorpade: Notes on Galois Theory
Lattice Theory
Commutative Algebra
- R.B. Ash: Commutative Algebra
- Paul Garrett: Homological and Commutative Algebra
- D. Murfet: Matsumura: Commutative Algebra
- S.R. Ghorpade: Lectures on Commutative Algebra
Category Theory
- M. Fokkinga: A Gentle Introduction to Category Theory
- M. Bar and C. Wells: Toposes, Triples and Theories
- J. van Oosten: Basic Category Theory
- D. Turi: Category Theory Lecture Notes
- D.E. Rydeheard and R.M. Burstall: Computational Category Theory
Number Theory
- W.W.L. Chen: Elementary Number Theory
- W.W.L. Chen: Distribution of Prime Numbers
- J.S. Milne: Algebraic Number Theory
- R.B. Ash: Algebraic Number Theory
- J.S. Milne: Modular Functions and Modular Forms
- Paul Garrett: Modular Forms and L-Functions
- I.V. Dolgachev: Modular Forms
- J.S. Milne: Etale Cohomology
- J.S. Milne: Class Field Theory
- J.S. Milne: Complex Multiplication
- J.S. Milne: Abelian Varieties
- Paul Garrett: Number Theory
- Paul Garrett: Cryptography and Number Theory
- Paul Garrett: Coding Theory
- A. Baker: An Introduction to $p$-adic Numbers and $p$-adic Analysis
- A. Baker: Algebra and Number Theory
- I. Connell: An Elliptic Curve Handbook
Geometry
Algebraic Geometry
- J.S. Milne: Algebraic Geometry
- J.S. Milne: Algebraic Groups
- I.V. Dolgachev: Introduction to Algebraic Geometry
- I.V. Dolgachev: The McKay Correspondence
- I.V. Dolgachev: Topics in Classical Algebraic Geometry
- C. Weibel: An Introduction to Algebraic K-Theory
Differential Geometry
- B. Csikós: Differential Geometry
- G. Lugo: Differential Geometry
- M. Kazarian: Differential Geometry
- T. Shifrin: Differential Geometry: A First Course in Curves and Surfaces
- D. Zaitsev: Differential Geometry: Lecture Notes
- J.-P. Demailly: Complex Analytic and Differential Geometry
Analysis
Complex Analysis
- R.B. Ash: Complex Variables
- Paul Garrett: Complex Analysis
- G. Cain: Complex Analysis
- H.V. McIntosh: Complex Analysis
- W.W.L. Chen: Introduction to Complex Analysis
Real Analysis
- R.B. Ash: Real Variables with Basic Metric Space Topology
- S. Semmes: Elements of Linear and Real Analysis
- J. Orr: Analysis WebNotes
- I. Craw: Advanced Calculus and Analysis
- W.W.L. Chen: Fundamentals of Analysis
Functional Analysis
- W.W.L. Chen: Linear Functional Analysis
- W.W.L. Chen: Introduction to Lebesgue Integration
- T. Ward: Functional Analysis
- Paul Garrett: Functional Analysis
Differential Equations
Probability and Statistics
- R.B. Ash: Lectures on Statistics
- R.B. Ash: Basic Probability Theory
- C. Grinstead and J. Snell: Introduction to Probability
- N. Vaillant: Probability Tutorials
Complexity and Algorithms
- C. Yap: Fundamental Problems in Algorithmic Algebra
- C. Yap: Introduction to Complexity Classes
- C. Yap: Robust Geometric Computation
- C. Yap: Algorithmics
- W.W.L. Chen: Discrete Mathematics
Combinatorics
- M. Petkovsek, H. Wilf and D. Zeilberger: The Book A=B
- H. Wilf: Generatingfunctionology
- D. Feldman: Ramsey's Theorem and Ramsey Theory
- Dynamic Surveys in Combinatorics
Basic Algebra
- K. Kubota: College Algebra
- D. Joyce: A Short Course in Trigonometry
- T. Ward: Basic Mathematics
- W.W.L. Chen: Miscellaneous Topics in First Year Mathematics
- MathIsFun: College Algebra
Calculus
- G. Cain and J. Herod: Multivariable Calculus
- Harvey Mudd College Calculus Tutorials
- D. Sloughter: Difference Equations to Differential Equations
- P. Dawkins: Paul's Online Math Notes
- W.W.L. Chen and X.T. Duong: Elementary Mathematics
- W.W.L. Chen: First Year Calculus
- W.W.L. Chen: Multivariable and Vector Analysis
Graph Theory
Dynamical Systems
- G. Elert: The Chaos Hypertextbook
- P. Cvitanović, R. Artuso, R. Mainieri, G. Tanner, G. Vattay, N. Whelan and A. Wirzba: Chaos: Classical and Quantum
- J. Milnor: Dynamics in One Complex Variable
- P. Arnoux, V. Berthé, S. Ferenczi, S. Ito, C. Mauduit, M. Mori, J. Peyrière, A. Siegel, J.-I. Tamura and Z.-Y. Wen: Substitutions in Dynamics, Arithmetic and Combinatorics
- T. Ward: Entropy of Compact Group Automorphisms
- T. Ward: Valuations and Dynamics
Topology
Algebraic Topology
Logic
MIT Online Materials
Other random stuff
Video Media
Uncategorized (Wait...)
- http://www.cut-the-knot.org/
- http://nrich.maths.org/public/
- http://www.abstractmath.org/MM/MMIntro.htm
- http://radicaleye.com/lifepage/
- MSC2010
- Math Reference Project (Web-based notes on university-level mathematics.)
- The On-line Encyclopedia of Integer Sequences
- Theorem of the Day
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