HandWiki:Math

Mathematics

Mathematics (from Greek "knowledge, study, learning") includes the study of such topics as quantity (number theory), structure (algebra), space (geometry), and change (mathematical analysis).     [Add article].

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1. Up Series
2. Timeline of European exploration
3. Quality Management Maturity Grid
4. Open catalogue
5. JACKPHY
6. Cohort study
7. Proportional reasoning
8. Insight phenomenology
9. Reptation Monte Carlo
10. Binary choice
11. The Project on Forward Engagement
12. Systemic design
13. Spectral Hash
14. Argument from analogy
15. Rank reversals in decision-making
16. Panel Study of Income Dynamics
17. Low Fertility Cohorts Study
18. Defensive pessimism
19. Wollheim's paradox
20. Religious Orders Study
21. Delta debugging
22. Journal of Behavioral Decision Making
23. Global Alliance for Peace and Prosperity
24. Field trip
25. Family tree photographs
26. Eco-costs value ratio
27. Casa de Contratación
28. Survey of Income and Program Participation
29. Reversal test
30. Inductionism

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Main topics

1. 0 (number)
2. 1 (number)
3. 10 (number)
4. 10-polytopes
5. 2 (number)
6. 3 (number)
7. 3-manifolds
8. 4 (number)
9. 4-manifolds
10. 4-polytopes
11. 5 (number)
12. 5-polytopes
13. 6 (number)
14. 6-polytopes
15. 7 (number)
16. 7-polytopes
17. 8 (number)
18. 9 (number)
19. 9-polytopes
20. Abelian varieties
21. Additive combinatorics
22. Additive functions
23. Adjoint functors
24. Analysis of variance
25. Analytic functions
26. Apeirogonal tilings
27. Aperiodic tilings
28. Applied mathematics
29. Approximation algorithms
30. Approximations
31. Archimedean solids
32. Argument mapping
33. Arithmetic
34. Arithmetic functions
35. Articles containing proofs
36. Asymptotic analysis
37. Automorphic forms
38. Axiom of choice
39. Banach spaces
40. Bayesian estimation
41. Bayesian inference
42. Behavior selection algorithms
43. Bilinear operators
44. Binary arithmetic
45. Binary operations
46. Binary relations
47. Boundary conditions
48. Cache coherency
49. Cardinal numbers
50. Catalan solids
51. Causal diagrams
52. Chaotic maps
53. Characteristic classes
54. Classes of prime numbers
55. Classification algorithms
56. Closure operators
57. Clustering criteria
58. Cohomology theories
59. Combinatorial algorithms
60. Combinatorial optimization
61. Combinatorics
62. Combinatory logic
63. Compactification (mathematics)
64. Compactness (mathematics)
65. Complex analysis
66. Complex distributions
67. Complex dynamics
68. Complex manifolds
69. Complex numbers
70. Complex surfaces
71. Computational fields of study
72. Computer arithmetic
73. Conceptual modelling
74. Conditionals
75. Conformal mapping
76. Conformal mappings
77. Conformal projections
78. Conic sections
79. Conjectures
80. Conjugate prior distributions
81. Connection (mathematics)
82. Conservation equations
83. Constructible polygons
84. Constructivism (mathematics)
85. Continued fractions
86. Continuous distributions
87. Continuous integration
88. Continuous mappings
89. Continuous wavelets
90. Convergence (mathematics)
91. Convex analysis
92. Convex hull algorithms
93. Convex optimization
94. Coordinate systems
95. Covariance and correlation
96. Covering lemmas
97. Curvature (mathematics)
98. Cyclotomic fields
99. Decomposition methods
100. Definitions of mathematical integration
101. Deltahedra
102. Design of experiments
103. Determinants
104. Deterministic global optimization
105. Dichotomies
106. Differential calculus
107. Differential equations
108. Differential forms
109. Differential operators
110. Differential systems
111. Differentiation rules
112. Digit-by-digit algorithms
113. Dimension reduction
114. Dimensionless numbers
115. Diophantine approximation
116. Diophantine equations
117. Directed graphs
118. Discrete distributions
119. Discrete mathematics
120. Discrete transforms
121. Divergent series
122. Division (mathematics)
123. Divisor function
124. Dynamical systems
125. E (mathematical constant)
126. Educational technology
127. Elementary arithmetic
128. Elementary mathematics
129. Elementary shapes
130. Elementary special functions
131. Elliptic curves
132. Elliptic functions
133. Elliptic partial differential equations
134. Enumerative combinatorics
135. Equal-area projections
136. Equations of fluid dynamics
137. Equivalence (mathematics)
138. Error detection and correction
139. Errors and residuals
140. Estimation of densities
141. Euclidean symmetries
142. Euclidean tilings
143. Exchange algorithms
144. Exponential family distributions
145. Exponentials
146. Factor analysis
147. Factorial and binomial topics
148. Fibonacci numbers
149. Field (mathematics)
150. Fields of mathematics
151. Finite automata
152. Finite differences
153. Finite element method
154. Finite fields
155. Finite rings
156. First order methods
157. Fixed points (mathematics)
158. Forcing (mathematics)
159. Formal sciences
160. Formal systems
161. Formal theories of arithmetic
162. Fourier analysis
163. Fourier series
164. Fractal curves
165. Fractional calculus
166. Fractions (mathematics)
167. Frequency distribution
168. Fréchet spaces
169. Function prefixes
170. Function spaces
171. Functional analysis
172. Functional calculus
173. Functional equations
174. Functions and mappings
175. Fuzzy logic
176. Gambling terminology
177. Gamma and related functions
178. Gaussian function
179. Gaussian quadratures
180. Generalizations
181. Generalizations of the derivative
182. Generalized convexity
183. Generalized functions
184. Generalized manifolds
185. Generating functions
186. Geodesic (mathematics)
187. Glossaries of mathematics
188. Glossary of areas of mathematics
189. Goldberg polyhedra
190. Golden ratio
191. Gradient methods
192. Grandi's series
193. Graph algorithms
194. Graph coloring
195. Graph connectivity
196. Graph data structures
197. Graph drawing
198. Graph enumeration
199. Graph families
200. Graph invariants
201. Graph operations
202. Graphical projections
203. Hamiltonian paths and cycles
204. Harmonic analysis
205. Harmonic functions
206. Heptagonal tilings
207. Heraldic charges
208. Hexadecimal numeral system
209. Hexagonal tilings
210. Hierarchy of functions
211. Higher-order functions
212. Hilbert space
213. Hilbert's problems
214. Historical treatment of quaternions
215. History of mathematics
216. Homeomorphisms
217. Homogeneous polynomials
218. Homogeneous spaces
219. Horizontal coordinate system
220. Hyperbolic knots and links
221. Hyperbolic partial differential equations
222. Hyperbolic tilings
223. Hypercomplex numbers
224. Hypergraphs
225. Immediate inference
226. Individual graphs
227. Inequalities
228. Infinite graphs
229. Infinite-order tilings
230. Information
231. Integer factorization algorithms
232. Integer sequences
233. Integrable systems
234. Integral calculus
235. Integral equations
236. Integral representations
237. Integral transforms
238. Integration on manifolds
239. Interpolation
240. Intersection classes of graphs
241. Invariant subspaces
242. Inverse functions
243. Irrational numbers
244. Isochoric 3-honeycombs
245. Isogonal 3-honeycombs
246. Isogonal tilings
247. Isohedral tilings
248. Isotoxal tilings
249. Iterated function system fractals
250. Johnson solids
251. Knot invariants
252. Knots and links
253. Knowledge representation
254. Lambda calculus
255. Laplace transforms
256. Large cardinals
257. Large integers
258. Large numbers
259. Lattice points
260. Lattice-based cryptography
261. Legendre polynomials
262. Limit sets
263. Limits (mathematics)
264. Linear logic
265. Linear operators
266. Linear operators in calculus
267. Lists of integrals
268. Lists of shapes
269. Lists of units of measurement
270. Localization (mathematics)
271. Logarithms
272. Logic symbols
273. Logical connectives
274. Logical expressions
275. Lorentzian manifolds
276. Loss functions
277. Lévy processes
278. Magic squares
279. Map projections
280. Maps of manifolds
281. Markov chain Monte Carlo
282. Markov models
283. Markov processes
284. Mathematical analysis
285. Mathematical and quantitative methods (economics)
286. Mathematical axioms
287. Mathematical classification systems
288. Mathematical concepts
289. Mathematical constants
290. Mathematical databases
291. Mathematical economics
292. Mathematical identities
293. Mathematical induction
294. Mathematical logic
295. Mathematical markup languages
296. Mathematical methods in general relativity
297. Mathematical modeling
298. Mathematical morphology
299. Mathematical notation
300. Mathematical optimization
301. Mathematical paradoxes
302. Mathematical physics
303. Mathematical principles
304. Mathematical problems
305. Mathematical proofs
306. Mathematical relations
307. Mathematical series
308. Mathematical structures
309. Mathematical symbols
310. Mathematical tables
311. Mathematical terminology
312. Mathematical tools
313. Mathematics
314. Mathematics education
315. Mathematics journals
316. Mathematics of infinitesimals
317. Mathematics of rigidity
318. Mathematics paradoxes
319. Mathematics timelines
320. Mathematics websites
321. Mathematics-related lists
322. Matrix decompositions
323. Matrix normal forms
324. Measures of complexity
325. Meromorphic functions
326. Metric tensors
327. Minimal surfaces
328. Minkowski spacetime
329. Modular arithmetic
330. Modular forms
331. Moment (mathematics)
332. Monte Carlo methods
333. Multiplication
334. Multivariable calculus
335. Multivariate continuous distributions
336. Multivariate interpolation
337. Necessity and sufficiency
338. Non-Newtonian calculus
339. Non-standard analysis
340. Non-standard positional numeral systems
341. Nonconvex polyhedra
342. Nonlinear functional analysis
343. Nonlinear systems
344. Nonstandard analysis
345. Normal distribution
346. Norms (mathematics)
347. Numeral systems
348. Numerical analysis
349. Numerical differential equations
350. Numerical function drawing
351. Numerical integration
352. Numerical integration (quadrature)
353. Obfuscation
354. Operations research
355. Optimal decisions
356. Optimization algorithms and methods
357. Optimization in vector spaces
358. Optimization of ordered sets
359. Order-2 tilings
360. Order-3-n 3-honeycombs
361. Order-4 tilings
362. Order-4-n 3-honeycombs
363. Order-5 tilings
364. Order-5-n 3-honeycombs
365. Order-6 tilings
366. Order-6-n 3-honeycombs
367. Order-7 tilings
368. Order-7-n 3-honeycombs
369. Order-8-n 3-honeycombs
370. Order-n-2 3-honeycombs
371. Order-n-3 3-honeycombs
372. Order-n-4 3-honeycombs
373. Order-n-5 3-honeycombs
374. Order-n-6 3-honeycombs
375. Order-n-7 3-honeycombs
376. Order-n-8 3-honeycombs
377. Ordinal numbers
378. Ordinary differential equations
379. Orthogonal coordinate systems
380. Orthogonal polynomials
381. Orthogonal wavelets
382. Oscillation
383. Parabolic partial differential equations
384. Paradoxes of infinity
385. Parametric families of graphs
386. Parity (mathematics)
387. Partial differential equations
388. Pentagonal tilings
389. Pentagrammic-order tilings
390. Perfect graphs
391. Permutation patterns
392. Permutations
393. Pi algorithms
394. Planar graphs
395. Platonic solids
396. Point processes
397. Poisson distribution
398. Poisson point processes
399. Polyhedral combinatorics
400. Polyhedral compounds
401. Polynomial functions
402. Polynomials
403. Positional numeral systems
404. Prime numbers
405. Prismatoid polyhedra
406. Problem structuring methods
407. Propositional calculus
408. Pseudorandomness
409. Pyramids and bipyramids
410. Quadratic forms
411. Quadratic irrational numbers
412. Quadratic residue
413. Quadrilaterals
414. Quality control tools
415. Quantification
416. Quasiregular polyhedra
417. Quaternions
418. Quotient objects
419. Random graphs
420. Random matrices
421. Randomized algorithms
422. Rational functions
423. Rational numbers
424. Real analysis
425. Real closed field
426. Real numbers
427. Real transcendental numbers
428. Recurrence relations
429. Regression analysis
430. Regular 3-honeycombs
431. Regular graphs
432. Regular polyhedra
433. Regular tessellations
434. Regular tilings
435. Riemann surfaces
436. Riemannian manifolds
437. Root-finding algorithms
438. Rotation in three dimensions
439. Rotational symmetry
440. Rules of inference
441. Runge–Kutta methods
442. Scaling symmetries
443. Scientific method
444. Self-dual polyhedra
445. Self-dual tilings
446. Self-organization
447. Semiregular tilings
448. Separation axioms
449. Sequence spaces
450. Sequences and series
451. Series expansions
452. Set families
453. Set indices on mathematics
454. Sets of real numbers
455. Several complex variables
456. Shift-and-add algorithms
457. Simplicial sets
458. Singular integrals
459. Singular value decomposition
460. Smooth functions
461. Smooth manifolds
462. Snub tilings
463. Sobolev spaces
464. Sources of knowledge
465. Space-filling polyhedra
466. Spanning tree
467. Sparse matrices
468. Spatial data analysis
469. Spatial gradient
470. Spatial processes
471. Special functions
472. Spectral sequences
473. Spherical trigonometry
474. Spiric sections
475. Splines (mathematics)
476. Square tilings
477. Stable distributions
478. Star polygons
479. Stochastic calculus
480. Stochastic differential equations
481. Stochastic models
482. Stochastic processes
483. Strongly regular graphs
484. Structural analysis
485. Structures on manifolds
486. Summability methods
487. Survival analysis
488. Symmetric functions
489. Symmetric relations
490. Ternary operations
491. Theta functions
492. Three-dimensional coordinate systems
493. Time domain analysis
494. Time in science
495. Transcendental numbers
496. Transfer functions
497. Transformation (function)
498. Transforms
499. Transitive relations
500. Triangles of numbers
501. Triangular tilings
502. Trigonometric functions
503. Trigonometry
504. Truncated tilings
505. Two-dimensional coordinate systems
506. Types of databases
507. Types of functions
508. Unary operations
509. Undecidable conjectures
510. Unification (computer science)
511. Uniform polyhedra
512. Uniform spaces
513. Uniform tilings
514. Unitary operators
515. Units of area
516. Units of luminous intensity
517. Units of plane angle
518. Units of power
519. Unsolved problems in mathematics
520. Variables (mathematics)
521. Variants of random walks
522. Variational analysis
523. Variational principles
524. Vector bundles
525. Vector calculus
526. Vector spaces
527. Vectors (mathematics and physics)
528. Vertical position
529. Wiener process
530. Zeta and L-functions
531. Δ-hyperbolic space

Theorems

1. Automated theorem proving
2. Central limit theorem
3. Compactness theorems
4. Fixed-point theorems
5. Fundamental theorems
6. Mathematical theorems
7. Probability theorems
8. Statistical theorems
9. Theorems about prime numbers
10. Theorems in Fourier analysis
11. Theorems in Riemannian geometry
12. Theorems in abstract algebra
13. Theorems in algebra
14. Theorems in algebraic geometry
15. Theorems in algebraic number theory
16. Theorems in algebraic topology
17. Theorems in analysis
18. Theorems in analytic number theory
19. Theorems in approximation theory
20. Theorems in calculus
21. Theorems in combinatorics
22. Theorems in complex analysis
23. Theorems in complex geometry
24. Theorems in computational complexity theory
25. Theorems in convex geometry
26. Theorems in differential geometry
27. Theorems in differential topology
28. Theorems in discrete geometry
29. Theorems in discrete mathematics
30. Theorems in functional analysis
31. Theorems in geometry
32. Theorems in graph theory
33. Theorems in group theory
34. Theorems in harmonic analysis
35. Theorems in linear algebra
36. Theorems in measure theory
37. Theorems in number theory
38. Theorems in plane geometry
39. Theorems in projective geometry
40. Theorems in real analysis
41. Theorems in representation theory
42. Theorems in statistics
43. Theorems in the foundations of mathematics
44. Theorems in topology
45. Theorems regarding stochastic processes

Theories

1. Abelian group theory
2. Additive number theory
3. Algebraic K-theory
4. Algebraic graph theory
5. Algebraic number theory
6. Analytic number theory
7. Approximation theory
8. Asymptotic theory (statistics)
9. Axioms of set theory
10. Basic concepts in infinite set theory
11. Basic concepts in set theory
12. Bifurcation theory
13. Category theory
14. Chaos theory
15. Class field theory
16. Classical control theory
17. Coding theory
18. Combinatorial game theory
19. Complex systems theory
20. Computability theory
21. Computational number theory
22. Computational problems in graph theory
23. Conformal field theory
24. Continuum theory
25. Density functional theory
26. Descriptive set theory
27. Dimension theory
28. Effective descriptive set theory
29. Elementary number theory
30. Ergodic theory
31. Estimation theory
32. Experiment (probability theory)
33. Extremal graph theory
34. Field theory
35. Free probability theory
36. Galois theory
37. Game theory
38. Geometric graph theory
39. Geometric group theory
40. Geometric transversal theory
41. Graph minor theory
42. Graph theory
43. Graph theory objects
44. Group theory
45. Hidden variable theory
46. Higher category theory
47. Homology theory
48. Homotopy theory
49. Independence (probability theory)
50. Infinite group theory
51. Information theory
52. Inner model theory
53. Intersection theory
54. Invariant theory
55. Knot theory
56. Large deviations theory
57. Lattice theory
58. Limits (category theory)
59. Martingale theory
60. Matching (graph theory)
61. Matrix theory
62. Matroid theory
63. Measure theory
64. Measures (measure theory)
65. Metatheory
66. Model theory
67. Module theory
68. Network theory
69. Number theory
70. Objects (category theory)
71. Operator theory
72. Order theory
73. Paradoxes of naive set theory
74. Paradoxes of set theory
75. Perturbation theory
76. Probability theory
77. Probability theory paradoxes
78. Queueing theory
79. Ramsey theory
80. Representation theory
81. Representation theory of Lie algebras
82. Representation theory of Lie groups
83. Representation theory of algebraic groups
84. Representation theory of finite groups
85. Representation theory of groups
86. Ring theory
87. Scheme theory
88. Semigroup theory
89. Set theory
90. Sheaf theory
91. Singularity theory
92. Spectral theory
93. Squares in number theory
94. Stability theory
95. Statistical theory
96. Structural complexity theory
97. Summability theory
98. Surgery theory
99. Systems of set theory
100. Systems theory
101. Theorems in algebraic number theory
102. Theorems in analytic number theory
103. Theorems in approximation theory
104. Theorems in computational complexity theory
105. Theorems in graph theory
106. Theorems in group theory
107. Theorems in measure theory
108. Theorems in number theory
109. Theorems in representation theory
110. Theory of computation
111. Theory of probability distributions
112. Topological graph theory
113. Topos theory
114. Trees (graph theory)
115. Type theory
116. Unitary representation theory

Algebra

1. Abstract algebra
2. Algebra of random variables
3. Algebraic K-theory
4. Algebraic combinatorics
5. Algebraic curves
6. Algebraic geometry
7. Algebraic graph theory
8. Algebraic groups
9. Algebraic homogeneous spaces
10. Algebraic logic
11. Algebraic number theory
12. Algebraic numbers
13. Algebraic structures
14. Algebraic surfaces
15. Algebraic topology
16. Algebraic varieties
17. Banach algebras
18. Boolean algebra
19. C-algebras
20. Clifford algebras
21. Commutative algebra
22. Composition algebras
23. Computer algebra
24. Diagram algebras
25. Differential algebra
26. Elementary algebra
27. Exceptional Lie algebras
28. Free algebraic structures
29. Geometric algebra
30. Homological algebra
31. Hopf algebras
32. Lie algebras
33. Linear algebra
34. Linear algebraic groups
35. Multilinear algebra
36. Non-associative algebra
37. Non-associative algebras
38. Nonlinear algebra
39. Numerical linear algebra
40. Ockham algebras
41. Operator algebras
42. Real algebraic geometry
43. Representation theory of Lie algebras
44. Representation theory of algebraic groups
45. Super linear algebra
46. Theorems in abstract algebra
47. Theorems in algebra
48. Theorems in algebraic geometry
49. Theorems in algebraic number theory
50. Theorems in algebraic topology
51. Theorems in linear algebra
52. Topological algebra
53. Topological methods of algebraic geometry
54. Universal algebra
55. Von Neumann algebras

Statistics

1. Applied probability
2. Asymptotic theory (statistics)
3. Bayesian statistics
4. Biostatistics journals
5. Computational statistics
6. Computational statistics journals
7. Directional statistics
8. Experiment (probability theory)
9. Free probability theory
10. Functions related to probability distributions
11. Independence (probability theory)
12. Infinitely divisible probability distributions
13. Location-scale family probability distributions
14. Logic and statistics
15. Multivariate statistics
16. Nonparametric statistics
17. Parametric statistics
18. Probabilistic arguments
19. Probabilistic inequalities
20. Probability
21. Probability and statistics
22. Probability assessment
23. Probability bounds analysis
24. Probability fallacies
25. Probability interpretations
26. Probability problems
27. Probability theorems
28. Probability theory
29. Probability theory paradoxes
30. Robust statistics
31. Sampling (statistics)
32. Statistical algorithms
33. Statistical approximations
34. Statistical data types
35. Statistical deviation and dispersion
36. Statistical hypothesis testing
37. Statistical inference
38. Statistical methods
39. Statistical paradoxes
40. Statistical parameters
41. Statistical randomness
42. Statistical ratios
43. Statistical theorems
44. Statistical theory
45. Statistics
46. Statistics journals
47. Statistics-related lists
48. Summary statistics
49. Theorems in statistics
50. Theory of probability distributions
51. Types of probability distributions

Geometry

1. Affine geometry
2. Algebraic geometry
3. Analytic geometry
4. Arithmetic geometry
5. Arithmetic problems of plane geometry
6. Birational geometry
7. Classical geometry
8. Computational geometry
9. Configurations (geometry)
10. Conformal geometry
11. Contact geometry
12. Convex geometry
13. Coordinate systems in differential geometry
14. Descriptive geometry
15. Differential geometry
16. Differential geometry of surfaces
17. Diophantine geometry
18. Discrete geometry
19. Elementary geometry
20. Euclidean geometry
21. Euclidean plane geometry
22. Euclidean solid geometry
23. Finite geometry
24. Four-dimensional geometry
25. Geometric algebra
26. Geometric algorithms
27. Geometric centers
28. Geometric dissection
29. Geometric graph theory
30. Geometric graphs
31. Geometric group theory
32. Geometric inequalities
33. Geometric measurement
34. Geometric shapes
35. Geometric topology
36. Geometric transversal theory
37. Geometry of divisors
38. Geometry of numbers
39. Geometry processing
40. Honeycombs (geometry)
41. Hyperbolic geometry
42. Hypergeometric functions
43. Incidence geometry
44. Integral geometry
45. Metric geometry
46. Multi-dimensional geometry
47. Non-Euclidean geometry
48. Noncommutative geometry
49. Orientation (geometry)
50. Projective geometry
51. Real algebraic geometry
52. Riemannian geometry
53. Special hypergeometric functions
54. Spherical geometry
55. Symplectic geometry
56. Systolic geometry
57. Theorems in Riemannian geometry
58. Theorems in algebraic geometry
59. Theorems in complex geometry
60. Theorems in convex geometry
61. Theorems in differential geometry
62. Theorems in discrete geometry
63. Theorems in geometry
64. Theorems in plane geometry
65. Theorems in projective geometry
66. Topological methods of algebraic geometry
67. Triangle geometry
68. Triangulation (geometry)

Topology

1. Algebraic topology
2. Computational topology
3. Differential topology
4. General topology
5. Geometric topology
6. Properties of topological spaces
7. Symplectic topology
8. Theorems in algebraic topology
9. Theorems in differential topology
10. Theorems in topology
11. Topological algebra
12. Topological graph theory
13. Topological groups
14. Topological methods of algebraic geometry
15. Topological spaces
16. Topological vector spaces
17. Topology of Lie groups
18. Topology of function spaces
19. Topology of homogeneous spaces
20. Trees (topology)

Groups

1. Abelian group theory
2. Algebraic groups
3. Braid groups
4. Coxeter groups
5. Discrete groups
6. Finite groups
7. Functional subgroups
8. Geometric group theory
9. Group actions (mathematics)
10. Group theory
11. Infinite group theory
12. Kleinian groups
13. Lie groups
14. Linear algebraic groups
15. Ordered groups
16. Permutation groups
17. Properties of groups
18. Quantum groups
19. Representation theory of Lie groups
20. Representation theory of algebraic groups
21. Representation theory of finite groups
22. Representation theory of groups
23. Semigroup theory
24. Solvable groups
25. Sporadic groups
26. Subgroup properties
27. Theorems in group theory
28. Topological groups
29. Topology of Lie groups