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Mathematics - Major themes in mathematics | | Mathematics - Major themes in mathematics: Encyclopedia II - Mathematics - Major themes in mathematics | | An alphabetical and subclassified list of mathematics articles is available. The following list of themes and links gives just one possible view. For a fuller treatment, see areas of mathematics or the list of mathematics lists.
Mathematics - Quantity.
Quantity starts with counting and measurement.
Natural numbers
...
See also:Mathematics, Mathematics - History, Mathematics - Inspiration pure and applied mathematics and aesthetics, Mathematics - Notation language and rigor, Mathematics - Is mathematics a science?, Mathematics - Overview of fields of mathematics, Mathematics - Major themes in mathematics, Mathematics - Quantity, Mathematics - Structure, Mathematics - Space, Mathematics - Change, Mathematics - Foundations and methods, Mathematics - Discrete mathematics, Mathematics - Applied mathematics, Mathematics - Important theorems, Mathematics - Important conjectures, Mathematics - History and the world of mathematicians, Mathematics - Mathematics and other fields, Mathematics - Mathematical tools, Mathematics - Common misconceptions | | | Mathematics, Mathematics - Applied mathematics, Mathematics - Change, Mathematics - Common misconceptions, Mathematics - Discrete mathematics, Mathematics - Foundations and methods, Mathematics - History, Mathematics - History and the world of mathematicians, Mathematics - Important conjectures, Mathematics - Important theorems, Mathematics - Inspiration pure and applied mathematics and aesthetics, Mathematics - Is mathematics a science?, Mathematics - Major themes in mathematics, Mathematics - Mathematical tools, Mathematics - Mathematics and other fields, Mathematics - Notation language and rigor, Mathematics - Overview of fields of mathematics, Mathematics - Quantity, Mathematics - Space, Mathematics - Structure, Mathematical game, Mathematical problem, Mathematical puzzle, Puzzle | | |
| | | Mathematics: Encyclopedia II - Mathematics - Major themes in mathematics
Mathematics - Major themes in mathematics
An alphabetical and subclassified list of mathematics articles is available. The following list of themes and links gives just one possible view. For a fuller treatment, see areas of mathematics or the list of mathematics lists.
Mathematics - Quantity
Quantity starts with counting and measurement.
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| Natural numbers |
Integers |
Rational numbers |
Real numbers |
Complex numbers |
Number – Hypercomplex numbers – Quaternions – Octonions – Sedenions – Hyperreal numbers – Surreal numbers – Ordinal numbers – Cardinal numbers – p-adic numbers – Integer sequences – Mathematical constants – Number names – Infinity – Base
Mathematics - Structure
Pinning down ideas of size, symmetry, and mathematical structure.
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| Arithmetic |
Number theory |
Abstract algebra |
Group theory |
Order theory |
Monoids – Rings – Fields – Linear algebra – Algebraic geometry– Universal algebra
Mathematics - Space
A more visual approach to mathematics.
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| Geometry |
Trigonometry |
Differential geometry |
Topology |
Fractal geometry |
Algebraic geometry – Differential topology – Algebraic topology – Linear algebra – Combinatorial geometry – Manifolds
Mathematics - Change
Ways to express and handle change in mathematical functions, and changes between numbers.
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| Calculus |
Vector calculus |
Differential equations |
Dynamical systems |
Chaos theory |
Analysis – Real analysis – Complex analysis – Functional analysis – Special functions – Measure theory – Fourier analysis – Calculus of variations
Mathematics - Foundations and methods
Approaches to understanding the nature of mathematics.
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| Mathematical logic |
Set theory |
Category theory |
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Foundations of mathematics – Philosophy of mathematics – Mathematical intuitionism – Mathematical constructivism – Proof theory – Model theory – Reverse mathematics
Mathematics - Discrete mathematics
Discrete mathematics involves techniques that apply to objects that can only take on specific, separated values.
[1,2,3][1,3,2]
[2,1,3][2,3,1]
[3,1,2][3,2,1] |
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| Combinatorics |
Theory of computation |
Cryptography |
Graph theory |
Computability theory – Computational complexity theory – Information theory
Mathematics - Applied mathematics
Applied mathematics uses the full knowledge of mathematics to solve real-world problems.
Mathematical physics – Mechanics – Fluid mechanics – Numerical analysis – Optimization – Probability – Statistics – Mathematical economics – Financial mathematics – Game theory – Mathematical biology – Cryptography
Mathematics - Important theorems
These theorems have interested mathematicians and non-mathematicians alike.
See list of theorems for more
Pythagorean theorem – Fermat's last theorem – Gödel's incompleteness theorems – Fundamental theorem of arithmetic – Fundamental theorem of algebra – Fundamental theorem of calculus – Cantor's diagonal argument – Four color theorem – Zorn's lemma – Euler's identity – classification theorems of surfaces – Gauss-Bonnet theorem – Quadratic reciprocity – Riemann-Roch theorem.
Mathematics - Important conjectures
See list of conjectures for more
These are some of the major unsolved problems in mathematics.
Goldbach's conjecture – Twin Prime Conjecture – Riemann hypothesis – Poincaré conjecture – Collatz conjecture – P=NP? – open Hilbert problems.
Mathematics - History and the world of mathematicians
See also list of mathematics history topics
History of mathematics – Timeline of mathematics – Mathematicians – Fields medal – Abel Prize – Millennium Prize Problems (Clay Math Prize) – International Mathematical Union – Mathematics competitions – Lateral thinking – Mathematical abilities and gender issues
Mathematics - Mathematics and other fields
Mathematics and architecture – Mathematics and education – Mathematics of musical scales
Other related archivesp-adic numbers, A Mathematician's Apology, Abacus, Abel Prize, Abstract algebra, Algebraic geometry, Algebraic topology, Analysis, Applied mathematics, Arithmetic, Base, British Isles, Calculators, Calculus, Calculus of variations, Cantor's diagonal argument, Cardinal numbers, Carl Friedrich Gauss, Category theory, Chaos theory, Collatz conjecture, Combinatorial geometry, Combinatorics, Commonwealth English, Complex analysis, Complex numbers, Computability theory, Computational complexity theory, Computer algebra systems, Cryptography, Differential equations, Differential geometry, Differential topology, Discrete mathematics, Dynamical systems, Euclid, Euclidean geometry, Eugene Wigner, Euler's identity, Fermat, Fermat's last theorem, Feynman, Feynman path integral, Fields, Fields medal, Financial mathematics, Fluid mechanics, Foundations of mathematics, Four color theorem, Fourier analysis, Fractal geometry, Functional analysis, Fundamental theorem of algebra, Fundamental theorem of arithmetic, Fundamental theorem of calculus, G. H. Hardy, Game theory, Gauss-Bonnet theorem, Geometry, Goldbach's conjecture, Graph theory, Greek, Group theory, Gödel's incompleteness theorem, Gödel's incompleteness theorems, Hilbert problems, Hilbert's program, History of mathematics, Hypercomplex numbers, Hyperreal numbers, Inca empire, Infinity, Information theory, Integer sequences, Integers, International Mathematical Union, Internet shorthand notation, Intuition, Isaac Newton, Kurt Heegner, Lateral thinking, Lie groups, Linear algebra, Manifolds, Mathematical abilities and gender issues, Mathematical beauty, Mathematical biology, Mathematical constants, Mathematical constructivism, Mathematical economics, Mathematical game, Mathematical intuitionism, Mathematical logic, Mathematical notation, Mathematical physics, Mathematical problem, Mathematical puzzle, Mathematicians, Mathematics and architecture, Mathematics and education, Mathematics competitions, Mathematics of musical scales, Measure theory, Mechanics, Mental calculation, Mersenne, Millennium Prize Problems (Clay Math Prize), Model theory, Monoids, Napier's bones, Natural numbers, Neolithic, Newton, North American English, Number, Number names, Number theory, Numeral systems, Numerical analysis, Octonions, Optimization, Order theory, Ordinal numbers, P=NP?, Philosophy of mathematics, Poincaré conjecture, Probability, Programming languages, Proof theory, Pseudomathematics, Puzzle, Pythagorean theorem, Pythagorean triples, Quadratic reciprocity, Quaternions, R programming language, Rational numbers, Real analysis, Real numbers, Reverse mathematics, Riemann hypothesis, Riemann-Roch theorem, Rings, Ruler, SAS programming language, SPSS, Sedenions, Set theory, Simplicity, Special functions, Statistics, Surreal numbers, The Unreasonable Effectiveness of Mathematics in the Natural Sciences, Theory of computation, Timeline of mathematics, Topology, Trigonometry, Twin Prime Conjecture, Universal algebra, Vector calculus, Zorn's lemma, abstract algebra, academia, accountancy, accounting, addition, aesthetics, algebra, algebraic geometry, analysis, analytic geometry, applied mathematics, areas of mathematics, arithmetic, arithmetical, astronomical, astronomy, automated theorem provers, axiomatic system, axiomatization, axioms, beauty, calculus, change, chaos theory, classification theorems of surfaces, commerce, compass, complex analysis, complex numbers, computability theory, computational complexity theory, computer science, computer-assisted proofs, computers, conjectures, count, days, deductive reasoning, definitions, deterministic, differential equations, differential geometry, division, dynamical systems, economics, electronic computers, engineering, experimentation, fast Fourier transform, fiber bundles, fields, formal theories, formal verification, foundations of mathematics, function, general relativity, generality, geometry, grammatically correct, groups, infinitesimal calculus, information theory, integers, khipu, land measurement, learned journal, linear algebra, list of conjectures, list of mathematics articles, list of mathematics history topics, list of mathematics lists, list of theorems, listing, literature, mathematical analysis, mathematical jargon, mathematical logic, mathematical papers, mathematical proof, mathematical rigour, mathematical structure, measuring, medicine, model theory, modular arithmetic, multiplication, natural numbers, natural sciences, non-Euclidean geometries, number theory, numbers, numerology, peer review, prehistoric, prime numbers, probability theory, proof theory, pseudoscience, pure mathematics, quantity, quantum mechanics, real analysis, real numbers, recursion theory, rings, rounding errors, science, seasons, sentences, set theory, slide rule, software, space, statistical analysis, statistics, string theory, structure, subtraction, tallies, the unreasonable effectiveness of mathematics, theorem proving, theoretical computer science, time, topological groups, topology, vector spaces, vectors, writing, years
 Adapted from the Wikipedia article "Major themes in mathematics", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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