Wikipedia:Requested articles/Mathematics

From Wikipedia, the free encyclopedia
Jump to: navigation, search
Add your request in the most appropriate place below.

Before adding a request please:


By convention, Wikipedia article titles are not capitalized except for the first letter and proper names -- write your request as This and such theorem instead of This And Such Theorem. Also, when adding a request, please include as much information as possible (such as webpages, articles, or other reference material) so editors can find and distinguish your request from an already-created article.

See also: User:Mathbot/Most wanted redlinks.

Abstract algebra[edit]

Algebraic geometry[edit]

Algorithms[edit]

Wolf and Pate correlation (capillary tubes)
L-PLS (extends Partial Least Squares regression to 3 connected data blocks)
OPLS (Orthogonal projections to latent structures) (currently link does not go to the right article)
OPLS-DA (Orthogonal Projections to Latent Structures - Discriminant Analysis) (Partial Least Squares with discrete variables)

Applied mathematics[edit]

Approximation theory[edit]

Arithmetic geometry[edit]

Books[edit]

Calculus of variations[edit]

Category theory[edit]

Coding theory[edit]

Combinatorics[edit]

Complex analysis[edit]

Complexity theory[edit]

Convex analysis / Optimization[edit]

Cryptography[edit]

Deformation theory[edit]

Differential equations[edit]


Please make a page on linearization of ordinary differential equations. More precisely, consider the system x dot = f(x,u,t) wherex and u are vectors. Then it is a standard result used in the theroy of control systems (in engineering disciplinnes) that it can be linearized as x dot = Ax + Bu where A = partial f / partial x and B = partial / partial u. However, in the engineeiring books or web resources no proof is offered for it. Many textbooks cite the following book [*] as a reference for its proof, but unfortunately I do not have access to it. In the engineering dield many researchers will benefir from its proof.

[*] H. Amann. Ordinary Differential Equations: An Introduction to Nonlinear Analysis, volume 13 of De Gruyter Studies in Mathematics. De Gruyter, Berlin - New York, 1990. —  Preceding unsigned comment added by 151.238.150.222 (talkcontribs) 20:12, 11 October 2015‎

This is a simple application of the concept of a Total derivative. Whether there is justification for having a whole article on the specific application you have in mind I am not sure. The editor who uses the pseudonym "JamesBWatson" (talk) 14:59, 13 October 2015 (UTC)

Differential geometry and topology[edit]

Dynamical systems[edit]

Elementary arithmetic[edit]

1+1(Elementary arithmetic)(ja:1+1)

Functional analysis[edit]

Field theory[edit]

Galois theory[edit]

Game theory[edit]

Geometry[edit]

Graph theory[edit]

Group theory[edit]

Harmonic analysis[edit]

History of mathematics and other cultural aspects[edit]

History of mathematics Journals[edit]

Homological algebra[edit]

Integrable systems[edit]

K theory[edit]

Lie groups, Algebraic groups / Lie algebras[edit]

Linear algebra[edit]

Mathematical analysis[edit]

Mathematics education[edit]

Mathematical logic[edit]

Requests for articles about mathematical logic are on a separate page, and should be added there.

Mathematical physics[edit]

Mathematicians[edit]

Prior to creating an article, any biographical details can be added to: Wikipedia:WikiProject Mathematics/missing mathematicians.

A–G[edit]

H–N[edit]

O–Z[edit]

Matrices[edit]

Measure theory[edit]

Number theory[edit]

[91] [92]

Elementary number theory[edit]

Algebraic number theory[edit]

Analytic number theory[edit]

Numerical analysis[edit]

Order theory[edit]

Organisations[edit]

Probability theory[edit]

Quantum stochastic calculus[edit]

Real analysis[edit]

Recreational mathematics[edit]

Representation theory (incl. harmonic analysis)[edit]

Semigroup theory[edit]

Special functions[edit]

Statistics[edit]

Topology[edit]

Algebraic topology[edit]

General topology[edit]

Geometric topology[edit]

Knot theory[edit]

Stable homotopy theory[edit]

Uncategorized[edit]

Please try to classify these requests.

See also[edit]

References[edit]

  1. ^ Hazewinkel, Michiel, ed. (2001), "Akivis algebra", Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4 
  2. ^ Jacobson, Nathan (1968). Structure and Representations of Jordan Algebras. American Mathematical Society Colloquium Publications. 39. American Mathematical Society. p. 287. ISBN 0-8218-7472-1. 
  3. ^ J. Alexander and A. Hirschowitz (1995). "Polynomial interpolation in several variables". Journal of Algebraic Geometry. 1. pp. 201–222. 
  4. ^ Narkiewicz, Władysław (2004). Elementary and analytic theory of algebraic numbers. Springer Monographs in Mathematics (3rd ed.). Berlin: Springer-Verlag. p. 254. ISBN 3-540-21902-1. Zbl 1159.11039. 
  5. ^ Formanek, Edward (1991). The polynomial identities and invariants of n×n matrices. Regional Conference Series in Mathematics. 78. Providence, RI: American Mathematical Society. p. 27. ISBN 0-8218-0730-7. Zbl 0714.16001. 
  6. ^ Kaplansky, Irving (1972). Fields and Rings. Chicago Lectures in Mathematics (2nd ed.). University Of Chicago Press. ISBN 0-226-42451-0. Zbl 1001.16500. 
  7. ^ Garibaldi, Skip; Petersson, Holger P. (2011). "Wild Pfister forms over Henselian fields, K-theory, and conic division algebras". J. Algebra. 327: 386–465. Zbl 1222.17009. 
  8. ^ Loos, Ottmar (2011). "Algebras with scalar involution revisited". J. Pure Appl. Algebra. 215: 2805–2828. Zbl 1229.14002. 
  9. ^ Baur, Karin; King, Alastair; Marsh, Robert J. "Dimer models and cluster categories of Grassmannians". arXiv:1309.6524Freely accessible [math.RT]. 
  10. ^ Knus, Max-Albert; Merkurjev, Alexander; Rost, Markus; Tignol, Jean-Pierre (1998). The book of involutions. Colloquium Publications. 44. With a preface by J. Tits. Providence, RI: American Mathematical Society. p. 128. ISBN 0-8218-0904-0. Zbl 0955.16001. 
  11. ^ Reiner, I. (2003). Maximal Orders. London Mathematical Society Monographs. New Series. 28. Oxford University Press. pp. 294–298. ISBN 0-19-852673-3. Zbl 1024.16008. 
  12. ^ Rosenfeld, Boris (1997). Geometry of Lie groups. Mathematics and its Applications. 393. Dordrecht: Kluwer Academic Publishers. p. 91. ISBN 0792343905. Zbl 0867.53002. 
  13. ^ a b c Caenepeel, Stefaan (1998). Brauer groups, Hopf algebras and Galois theory. Monographs in Mathematics. 4. Dordrecht: Kluwer Academic Publishers. p. 184. ISBN 1-4020-0346-3. Zbl 0898.16001. 
  14. ^ McCrimmon, Kevin (1977). "Axioms for inversion in Jordan algebras". J. Algebra. 47: 201–222. Zbl 0421.17013. 
  15. ^ Racine, Michel L. (1973). The arithmetics of quadratic Jordan algebras. Memoirs of the American Mathematical Society. 136. American Mathematical Society. p. 8. ISBN 978-0-8218-1836-7. Zbl 0348.17009. 
  16. ^ Formanek, Edward (1991). The polynomial identities and invariants of n×n matrices. Regional Conference Series in Mathematics. 78. Providence, RI: American Mathematical Society. p. 51. ISBN 0-8218-0730-7. Zbl 0714.16001. 
  17. ^ Racine, Michel L. (1973). The arithmetics of quadratic Jordan algebras. Memoirs of the American Mathematical Society. 136. American Mathematical Society. p. 2. ISBN 978-0-8218-1836-7. Zbl 0348.17009. 
  18. ^ Schinzel, Andrzej (2000). Polynomials with special regard to reducibility. Encyclopedia of Mathematics and Its Applications. 77. Cambridge: Cambridge University Press. ISBN 0-521-66225-7. Zbl 0956.12001. 
  19. ^ Choie, Y.; Diamantis, N. (2006). "Rankin–Cohen brackets on higher-order modular forms". In Friedberg, Solomon. Multiple Dirichlet series, automorphic forms, and analytic number theory. Proceedings of the Bretton Woods workshop on multiple Dirichlet series, Bretton Woods, NH, USA, July 11–14, 2005. Proc. Symp. Pure Math. 75. Providence, RI: American Mathematical Society. pp. 193–201. ISBN 0-8218-3963-2. Zbl 1207.11052. 
  20. ^ http://arxiv.org/abs/alg-geom/9606004
  21. ^ Montgomery, Susan (1993). Hopf algebras and their actions on rings. Expanded version of ten lectures given at the CBMS Conference on Hopf algebras and their actions on rings, which took place at DePaul University in Chicago, USA, August 10-14, 1992. Regional Conference Series in Mathematics. 82. Providence, RI: American Mathematical Society. p. 164. ISBN 978-0-8218-0738-5. Zbl 0793.16029. 
  22. ^ Willerton, Simon (2013-02-18). "Tight spans, Isbell completions and semi-tropical modules". arXiv:1302.4370Freely accessible. 
  23. ^ Jech, Thomas (2003). Set Theory. Springer Monographs in Mathematics (Third Millennium ed.). Berlin, New York: Springer-Verlag. pp. 88–89. ISBN 978-3-540-44085-7. Zbl 1007.03002. 
  24. ^ Sikorski, Roman (1964). Boolean algebras (2nd ed.). Berlin-Göttingen-Heidelberg-New York: Springer-Verlag. MR 31#2178. Zbl 0123.01303. 
  25. ^ Chabert, Jean-Luc (1979). "Anneaux de Skolem". Arch. Math. (in French). 32: 555–568. Zbl 0403.13008. 
  26. ^ Snaith, Victor P. (1994). Galois module structure. Fields Institute monographs. 2. American Mathematical Society. p. 41. ISBN 0-8218-7178-1. 
    Taylor, Martin (1984). Classgroups of group rings. LMS Lecture Notes. 91. Cambridge University Press. p. 26. ISBN 0-521-27870-8. 
  27. ^ Berstel, Jean; Reutenauer, Christophe (2011). Noncommutative rational series with applications. Encyclopedia of Mathematics and Its Applications. 137. Cambridge: Cambridge University Press. p. 53. ISBN 978-0-521-19022-0. Zbl 1250.68007. 
  28. ^ Narkiewicz, Władysław (1990). Elementary and analytic theory of numbers (Second, substantially revised and extended ed.). Springer-Verlag. p. 37. ISBN 3-540-51250-0. Zbl 0717.11045. 
  29. ^ Gabber, Ofer; Ramero, Lorenzo (2003). Almost ring theory. Lecture Notes in Mathematics. 1800. Berlin: Springer-Verlag. doi:10.1007/b10047. ISBN 3-540-40594-1. MR 2004652. 
    Notes by Torsten Wedhorn
  30. ^ Bhargava, Manjul; Ho, Wei (2013). "Coregular spaces and genus one curves". arXiv:1306.4424v1Freely accessible [math.AG]. 
  31. ^ Khovanskiǐ, A.G. (1991). Fewnomials. Translations of Mathematical Monographs. 88. Translated from the Russian by Smilka Zdravkovska. Providence, RI: American Mathematical Society. ISBN 0-8218-4547-0. Zbl 0728.12002. 
  32. ^ a b Marcolli, Matilde (2010). Feynman motives. World Scientific. ISBN 978-981-4304-48-1. Zbl 1192.14001. 
  33. ^ Soulé, C.; Abramovich, Dan; Burnol, J.-F.; Kramer, Jürg (1992). Lectures on Arakelov geometry. Cambridge Studies in Advanced Mathematics. 33. Joint work with H. Gillet. Cambridge: Cambridge University Press. p. 36. ISBN 0-521-47709-3. Zbl 0812.14015. 
  34. ^ Timashev, Dmitry A. (2011). Invariant Theory and Algebraic Transformation Groups 8. Homogeneous spaces and equivariant embeddings. Encyclopaedia of Mathematical Sciences. 138. Berlin: Springer-Verlag. ISBN 978-3-642-18398-0. Zbl 1237.14057. 
  35. ^ Knutson, Allen; Lam, Thomas; Speyer, David (15 Nov 2011). "Positroid Varieties: Juggling and Geometry". arXiv:1111.3660Freely accessible [math.AG]. 
  36. ^ J.-Y. Welschinger, Invariants of real rational symplectic 4-manifolds and lower bounds in real enumerative geometry, Invent. Math. 162 (2005), no. 1, 195-234. Zbl 1082.14052
  37. ^ Itenberg, Ilia; Mikhalkin, Grigory; Shustin, Eugenii (2007). Tropical algebraic geometry. Oberwolfach Seminars. 35. Basel: Birkhäuser. pp. 86–87. ISBN 978-3-7643-8309-1. Zbl 1162.14300. 
  38. ^ Consani, Caterina; Connes, Alain, eds. (2011). Noncommutative geometry, arithmetic, and related topics. Proceedings of the 21st meeting of the Japan-U.S. Mathematics Institute (JAMI) held at Johns Hopkins University, Baltimore, MD, USA, March 23–26, 2009. Baltimore, MD: Johns Hopkins University Press. ISBN 1-4214-0352-8. Zbl 1245.00040. 
  39. ^ Machiel van Frankenhuijsen (2014). The Riemann Hypothesis for function fields. LMS Student Texts. 80. Cambridge University Press. ISBN 978-1-107-68531-4. 
  40. ^ Bartolome, Boris (2014). "The Skolem-Abouzaid theorem in the singular case". arXiv:1406.3233Freely accessible [math.NT]. 
  41. ^ Nisse, Mounir (2011). "Complex tropical localization, and coamoebas of complex algebraic hypersurfaces". In Gurvits, Leonid. Randomization, relaxation, and complexity in polynomial equation solving. Banff International Research Station workshop on randomization, relaxation, and complexity, Banff, Ontario, Canada, February 28–March 5, 2010. Contemporary Mathematics. 556. Providence, RI: American Mathematical Society. pp. 127–144. ISBN 978-0-8218-5228-6. Zbl 1235.14058. 
  42. ^ Ballico, E. (2011). "Scroll codes over curves of higher genus: Reducible and superstable vector bundles". Designs, Codes and Cryptography. 63 (3): 365. doi:10.1007/s10623-011-9561-6. 
  43. ^ Sanyal, Raman; Sturmfels, Bernd; Vinzant, Cynthia (2013). "The entropic discriminant". Adv. Math. 244: 678–707. Zbl 06264349. 
  44. ^ Björner, Anders; Ziegler, Günter M. (1992). "8. Introduction to greedoids". In White, Neil. Matroid Applications. Matroid applications. Encyclopedia of Mathematics and its Applications. 40. Cambridge: Cambridge University Press. pp. 284–357. doi:10.1017/CBO9780511662041.009. ISBN 0-521-38165-7. MR 1165537. Zbl 0772.05026. 
  45. ^ Park, Seong Ill; Park, So Ryoung; Song, Iickho; Suehiro, Naoki (2000). "Multiple-access interference reduction for QS-CDMA systems with a novel class of polyphase sequences". IEEE Trans. Inf. Theory. 46 (4): 1448–1458. Zbl 1006.94500. 
  46. ^ Ardila, Federico; Rincón, Felipe; Williams, Lauren (15 Sep 2013). "Positroids and non-crossing partitions". arXiv:1308.2698Freely accessible [math.CO]. 
  47. ^ Marcolli, Matilde (2005). Arithmetic noncommutative geometry. University Lecture Series. 36. With a foreword by Yuri Manin. Providence, RI: American Mathematical Society. p. 83. ISBN 0-8218-3833-4. Zbl 1081.58005. 
  48. ^ Marcolli, Matilde (2005). Arithmetic noncommutative geometry. University Lecture Series. 36. With a foreword by Yuri Manin. Providence, RI: American Mathematical Society. p. 83. ISBN 0-8218-3833-4. Zbl 1081.58005. 
  49. ^ *Fokas, A S (1997). "A unified transform method for solving linear and certain nonlinear PDEs". Proceedings of the Royal Society. A (Mathematical, Physical, and Engineering Sciences). 453. Royal Society. pp. 1411–1443. 
  50. ^ *Template:Http://mathworld.wolfram.com/FuchsianSystem.html
  51. ^ *Soulé, C. (1992). Lectures on Arakelov geometry. Cambridge Studies in Advanced Mathematics. 33. with the collaboration of D. Abramovich, J.-F. Burnol and J. Kramer. Cambridge University Press. ISBN 0-521-41669-8. MR 1208731. Zbl 0812.14015. 
  52. ^ Mirzakhani, Maryam (2008). Ergodic theory of the earthquake flow. Int. Math. Res. Not. 2008. doi:10.1093/imrn/rnm116. Zbl 1189.30087. 
  53. ^ Lapidus, Michel L.; van Frankhuijsen, Machiel (2006). Fractal Geometry, Complex Dimensions and Zeta Functions: Geometry and Spectra of Fractal Strings. Springer Monographs in Mathematics. Springer-Verlag. ISBN 0-387-33285-5. 
  54. ^ Sidorov, Nikita (2003). "Arithmetic dynamics". In Bezuglyi, Sergey; Kolyada, Sergiy. Topics in dynamics and ergodic theory. Survey papers and mini-courses presented at the international conference and US-Ukrainian workshop on dynamical systems and ergodic theory, Katsiveli, Ukraine, August 21–30, 2000. Lond. Math. Soc. Lect. Note Ser. 310. Cambridge: Cambridge University Press. pp. 145–189. ISBN 0-521-53365-1. Zbl 1051.37007. 
  55. ^ Dooley, Anthony H. (2003). "Markov odometers". In Bezuglyi, Sergey; Kolyada, Sergiy. Topics in dynamics and ergodic theory. Survey papers and mini-courses presented at the international conference and US-Ukrainian workshop on dynamical systems and ergodic theory, Katsiveli, Ukraine, August 21–30, 2000. Lond. Math. Soc. Lect. Note Ser. 310. Cambridge: Cambridge University Press. pp. 60–80. ISBN 0-521-53365-1. Zbl 1063.37005. 
  56. ^ Christian Bonatti; Lorenzo J. Díaz; Marcelo Viana (30 March 2006), Dynamics Beyond Uniform Hyperbolicity: A Global Geometric and Probabilistic Perspective, Springer Science & Business Media, p. 9, ISBN 978-3-540-26844-4 
  57. ^ Baake, Michael; Moody, Robert V., eds. (2000). Directions in mathematical quasicrystals. CRM Monograph Series. 13. Providence, RI: American Mathematical Society. p. 237. ISBN 0-8218-2629-8. Zbl 0955.00025. 
  58. ^ Walters, Peter (2000). An Introduction to Ergodic Theory. Graduate Texts in Mathematics. 79. Springer-Verlag. p. 207. ISBN 0-387-95152-0. ISSN 0072-5285. 
  59. ^ a b Azizov, T.Ya.; Iokhvidov, E.I.; Iokhvidov, I.S. (1983). "On the connection between the Cayley-Neumann and Potapov-Ginzburg transformations". Funkts. Anal. (in Russian). 20: 3–8. Zbl 0567.47031. 
  60. ^ e.g. Cwikel et al., On the fundamental lemma of interpolation theory, J. Approx. Theory 60 (1990) 70–82
  61. ^ Jacobson, Nathan (1996). Finite-dimensional division algebras over fields. Berlin: Springer-Verlag. ISBN 3-540-57029-2. Zbl 0874.16002. 
  62. ^ a b Whaples, G. (1957). "Galois cohomology of additive polynomial and n-th power mappings of fields". Duke Math. J. 24: 143–150. doi:10.1215/S0012-7094-57-02420-1. Zbl 0081.26702. 
  63. ^ McCarthy, Paul J. (1991). Algebraic extensions of fields (Corrected reprint of the 2nd ed.). New York: Dover Publications. p. 132. Zbl 0768.12001. 
  64. ^ Fried, Michael D.; Jarden, Moshe (2008). Field arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. 11 (3rd ed.). Springer-Verlag. p. 562. ISBN 978-3-540-77269-9. Zbl 1145.12001. 
  65. ^ Zinovy Reichstein. "Joubert's theorem fails in characteristic 2". arXiv:1406.7529Freely accessible [math.NT]. 
  66. ^ Fried, Michael D.; Jarden, Moshe (2008). Field arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. 11 (3rd ed.). Springer-Verlag. pp. 463–464. ISBN 978-3-540-77269-9. Zbl 1145.12001. 
  67. ^ Leriche, Amandine (2011). "Pólya fields, Pólya groups and Pólya extensions: a question of capitulation". J. Théor. Nombres Bordx. 23: 235–249. Zbl 1282.13040. 
  68. ^ Lam, Tsit-Yuen (2005). Introduction to Quadratic Forms over Fields. Graduate Studies in Mathematics. 67. American Mathematical Society. p. 453. ISBN 0-8218-1095-2. MR 2104929. Zbl 1068.11023. 
  69. ^ Lam, Tsit-Yuen (2005). Introduction to Quadratic Forms over Fields. Graduate Studies in Mathematics. 67. American Mathematical Society. p. 463. ISBN 0-8218-1095-2. MR 2104929. Zbl 1068.11023. 
  70. ^ Coxeter, H.S.M.; Greitzer, S.L. (1967). Geometry Revisited. New Mathematical Library. 19. Washington, D.C.: Mathematical Association of America. p. 100. ISBN 978-0-88385-619-2. Zbl 0166.16402. 
  71. ^ Coxeter, H.S.M.; Greitzer, S.L. (1967). Geometry Revisited. New Mathematical Library. 19. Washington, D.C.: Mathematical Association of America. p. 95. ISBN 978-0-88385-619-2. Zbl 0166.16402. 
  72. ^ Erickson, Martin J. (2014). Introduction to Combinatorics. Discrete Mathematics and Optimization. 78 (2 ed.). John Wiley & Sons. p. 134. ISBN 1118640217. 
  73. ^ Imre, Sandor; Gyongyosi, Laszlo (2012). Advanced Quantum Communications: An Engineering Approach. John Wiley & Sons. p. 112. ISBN 1118337433. 
  74. ^ Oh, Suho; Postnikov, Alex; Speyer, David E (20 Sep 2011). "Weak Separation and Plabic Graphs". arXiv:1109.4434Freely accessible [math.CO]. 
  75. ^ Manjunath, Madhusudan; Sturmfels, Bernd (2013). "Monomials, binomials and Riemann-Roch". J. Algebr. Comb. 37 (4): 737–756. doi:10.1007/s10801-012-0386-9. Zbl 1272.13017. 
  76. ^ Ellis-Monaghan, Joanna A.; Moffatt, Iain (2013). Graphs on Surfaces: Dualities, Polynomials, and Knots. SpringerBriefs in Mathematics. Springer-Verlag. ISBN 1461469716. 
  77. ^ Fried, Michael D.; Jarden, Moshe (2008). Field arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. 11 (3rd ed.). Springer-Verlag. p. 613. ISBN 3-540-22811-X. Zbl 1055.12003. 
  78. ^ Fried, Michael D.; Jarden, Moshe (2008). Field arithmetic. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. 11 (3rd ed.). Springer-Verlag. p. 352. ISBN 3-540-22811-X. Zbl 1055.12003. 
  79. ^ Tao, Terence (2012). Higher-order Fourier analysis. Graduate Studies in Mathematics. 142. Providence, RI: American Mathematical Society. ISBN 978-0-8218-8986-2. Zbl 1277.11010. 
  80. ^ a b Tao, Terence (2012). Higher-order Fourier analysis. Graduate Studies in Mathematics. 142. Providence, RI: American Mathematical Society. p. 92. ISBN 978-0-8218-8986-2. Zbl 1277.11010. 
  81. ^ Montgomery, Susan (1993). Hopf algebras and their actions on rings. Expanded version of ten lectures given at the CBMS Conference on Hopf algebras and their actions on rings, which took place at DePaul University in Chicago, USA, August 10-14, 1992. Regional Conference Series in Mathematics. 82. Providence, RI: American Mathematical Society. p. 207. ISBN 978-0-8218-0738-5. Zbl 0793.16029. 
  82. ^ Kaplansky, Irving (1972). Fields and Rings. Chicago Lectures in Mathematics (2nd ed.). University Of Chicago Press. p. 135. ISBN 0-226-42451-0. Zbl 1001.16500. 
  83. ^ Deligne, Pierre; Etingof, Pavel; Freed, Daniel S.; Jeffrey, Lisa C.; Kazhdan, David; Morgan, John W.; Morrison, David R.; Witten, Edward, eds. (1999). Quantum fields and strings: a course for mathematicians. Material from the Special Year on Quantum Field Theory held at the Institute for Advanced Study, Princeton, NJ, 1996–1997. 2. Providence, RI: American Mathematical Society. p. 884. ISBN 0-8218-8621-5. Zbl 0984.00503. 
  84. ^ Belavin, A.A. (1980). "Discrete groups and integrability of quantum systems". Funkts. Anal. Prilozh. 14 (4): 18–26. Zbl 0454.22012. 
  85. ^ Joao Caramalho Domingues (2014). "The repercussion of José Anastácio da Cunha in Britain and the USA in the nineteenth century". BSHM Bulletin. 20 (1): 32–50. doi:10.1080/17498430.2013.802111. 
  86. ^ Roquette, Peter (2013). "The remarkable career of Otto Grün". Contributions to the history of number theory in the 20th century. Heritage of European Mathematics. Zürich: European Mathematical Society. pp. 77–116. ISBN 978-3-03719-113-2. Zbl 1276.11001. 
  87. ^ Brualdi, Richard A. (2006). Combinatorial Matrix Classes,. Encyclopedia of Mathematics and its Applications. 108. Cambridge University Press. p. 401. ISBN 0-521-86565-4. ISSN 0953-4806. 
  88. ^ Formanek, Edward (1991). The polynomial identities and invariants of n×n matrices. Regional Conference Series in Mathematics. 78. Providence, RI: American Mathematical Society. p. 45. ISBN 0-8218-0730-7. Zbl 0714.16001. 
  89. ^ Guterman, Alexander E. (2008). "Rank and determinant functions for matrices over semirings". In Young, Nicholas; Choi, Yemon. Surveys in Contemporary Mathematics. London Mathematical Society Lecture Note Series. 347. Cambridge University Press. pp. 1–33. ISBN 0-521-70564-9. ISSN 0076-0552. Zbl 1181.16042. 
  90. ^ section 5.3. of http://arxiv.org/pdf/1203.2888.pdf
  91. ^ http://nuclearstrategy.co.uk/prime-number-distribution-series
  92. ^ http://www.codeproject.com/Tips/816931/Prime-Number-Distribution-Series/
  93. ^ Narkiewicz, Władysław (2004). Elementary and analytic theory of algebraic numbers. Springer Monographs in Mathematics (3rd ed.). Berlin: Springer-Verlag. p. 307. ISBN 3-540-21902-1. Zbl 1159.11039. 
  94. ^ * Narkiewicz, Władysław (1990). Elementary and analytic theory of numbers (Second, substantially revised and extended ed.). Springer-Verlag. p. 416. ISBN 3-540-51250-0. Zbl 0717.11045. 
  95. ^ Narkiewicz, Władysław (2004). Elementary and analytic theory of algebraic numbers. Springer Monographs in Mathematics (3rd ed.). Berlin: Springer-Verlag. p. 123. ISBN 3-540-21902-1. Zbl 1159.11039. 
  96. ^ Romanoff, N. P. (1934). "Über einige Sätze der additiven Zahlentheorie". Math. Ann. (in German). 109: 668–678. JFM 60.0131.03. 
  97. ^ Rosen, Michael (2002). Number theory in function fields. Graduate Texts in Mathematics. 210. New York, NY: Springer-Verlag. p. 157. ISBN 0-387-95335-3. Zbl 1043.11079. 
  98. ^ Bossert, Walter; Suzumura, Kōtarō (2010). Consistency, choice and rationality. Harvard University Press. p. 36. ISBN 0674052994. 
  99. ^ Gantmacher, F.R. (2005) [1959]. Applications of the theory of matrices. Dover. ISBN 0-486-44554-2. Zbl 0085.01001. 
  100. ^ a b c Turzański, Marian (1992). "Strong sequences, binary families and Esenin-Volpin's theorem". Comment.Math.Univ.Carolinae. 33 (3): 563–569. MR 1209298. Zbl 0796.54031. 
  101. ^ Arhangel'Skii, A. (1996). General topology II: compactness, homologies of general spaces. Encyclopaedia of mathematical sciences. 50. Springer-Verlag. p. 59. ISBN 0-387-54695-2. Zbl 0830.00013. 
  102. ^ a b Arhangelʹskiĭ, A. V. (1969). "An approximation of the theory of dyadic bicompacta". Dokl. Akad. Nauk SSSR (in Russian). 184: 767–770. MR 243485. 
  103. ^ Tall, Franklin D. (1976). "The density topology". Pac. J. Math. 62: 275–284. Zbl 0305.54039. 
  104. ^ Šunić, Zoran (2014). "Cellular automata and groups, by Tullio Ceccherini-Silberstein and Michel Coornaert (book review)". Bulletin of the American Mathematical Society. 51 (2): 361–366. doi:10.1090/S0273-0979-2013-01425-3.