Nadharia ya namba

Nadharia ya namba (kwa Kiingereza Theory of numbers; awali: arithmetic^[1]^[2]) ni tawi la hisabati linalochunguza hasa nambakamili.

Mwanahisabati Mjerumani Carl Friedrich Gauss (1777–1855) alisema, "Hisabati ndiyo malkia wa sayansi zote, na nadharia ya namba ndiyo malkia wa hisabati zote."

Tanbihi

↑ Already in 1921, T. L. Heath had to explain: "By arithmetic, Plato meant, not arithmetic in our sense, but the science which considers numbers in themselves, in other words, what we mean by the Theory of Numbers." (Heath 1921, p. 13)
↑ Take, for example, Serre 1973. In 1952, Davenport still had to specify that he meant The Higher Arithmetic. Hardy and Wright wrote in the introduction to An Introduction to the Theory of Numbers (1938): "We proposed at one time to change [the title] to An introduction to arithmetic, a more novel and in some ways a more appropriate title; but it was pointed out that this might lead to misunderstandings about the content of the book."

Vyanzo

Apostol, Tom M. (1976). Introduction to analytic number theory. Undergraduate Texts in Mathematics. Springer. ISBN 978-0-387-90163-3. Iliwekwa mnamo 2016-02-28. {{cite book}}: Invalid |ref=harv (help)
Apostol, Tom M. (n.d.). "An Introduction to the Theory of Numbers". (Review of Hardy & Wright.) Mathematical Reviews (MathSciNet) MR 0568909. American Mathematical Society. Iliwekwa mnamo 2016-02-28. {{cite journal}}: Cite journal requires |journal= (help); External link in |series= (help); Invalid |ref=harv (help) (Subscription needed)
Becker, Oskar (1936). "Die Lehre von Geraden und Ungeraden im neunten Buch der euklidischen Elemente". Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik. Abteilung B:Studien (kwa German). 3: 533–53. {{cite journal}}: Invalid |ref=harv (help)CS1 maint: unrecognized language (link)
Boyer, Carl Benjamin; Merzbach, Uta C. (1991) [1968]. A History of Mathematics (tol. la 2nd). New York: Wiley. ISBN 978-0-471-54397-8. {{cite book}}: Invalid |ref=harv (help) 1968 edition at archive.org
Clark, Walter Eugene (trans.) (1930). The Āryabhaṭīya of Āryabhaṭa: An ancient Indian work on Mathematics and Astronomy. University of Chicago Press. Iliwekwa mnamo 2016-02-28. {{cite book}}: Invalid |ref=harv (help)
Colebrooke, Henry Thomas (1817). Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmegupta and Bháscara. London: J. Murray. Iliwekwa mnamo 2016-02-28. {{cite book}}: Invalid |ref=harv (help)
Davenport, Harold; Montgomery, Hugh L. (2000). Multiplicative Number Theory. Graduate texts in mathematics. Juz. la 74 (tol. la revised 3rd). Springer. ISBN 978-0-387-95097-6. {{cite book}}: Invalid |ref=harv (help)
Edwards, Harold M. (Novemba 1983). "Euler and Quadratic Reciprocity". Mathematics Magazine. 56 (5): 285–91. doi:10.2307/2690368. JSTOR 2690368. {{cite journal}}: Invalid |ref=harv (help)CS1 maint: date auto-translated (link)
Edwards, Harold M. (2000) [1977]. Fermat's Last Theorem: a Genetic Introduction to Algebraic Number Theory. Graduate Texts in Mathematics. Juz. la 50 (tol. la reprint of 1977). Springer Verlag. ISBN 978-0-387-95002-0. {{cite book}}: Invalid |ref=harv (help)
Fermat, Pierre de (1679). Varia Opera Mathematica (kwa French na Latin). Toulouse: Joannis Pech. Iliwekwa mnamo 2016-02-28. {{cite book}}: Invalid |ref=harv (help)CS1 maint: unrecognized language (link)
Friberg, Jöran (Agosti 1981). "Methods and Traditions of Babylonian Mathematics: Plimpton 322, Pythagorean Triples and the Babylonian Triangle Parameter Equations". Historia Mathematica. 8 (3): 277–318. doi:10.1016/0315-0860(81)90069-0. {{cite journal}}: Invalid |ref=harv (help)CS1 maint: date auto-translated (link)
von Fritz, Kurt (2004). "The Discovery of Incommensurability by Hippasus of Metapontum". Katika Christianidis, J. (mhr.). Classics in the History of Greek Mathematics. Berlin: Kluwer (Springer). ISBN 978-1-4020-0081-2. {{cite book}}: Invalid |ref=harv (help)
Gauss, Carl Friedrich; Waterhouse, William C. (trans.) (1966) [1801]. Disquisitiones Arithmeticae. Springer. ISBN 978-0-387-96254-2.
Goldfeld, Dorian M. (2003). "Elementary Proof of the Prime Number Theorem: a Historical Perspective" (PDF). Iliwekwa mnamo 2016-02-28. {{cite web}}: Invalid |ref=harv (help)
Goldstein, Catherine; Schappacher, Norbert (2007). "A book in search of a discipline". Katika Goldstein, C.; Schappacher, N.; Schwermer, Joachim (whr.). The Shaping of Arithmetic after C.F. Gauss's "Disquisitiones Arithmeticae". Berlin & Heidelberg: Springer. ku. 3–66. ISBN 978-3-540-20441-1. Iliwekwa mnamo 2016-02-28. {{cite book}}: Invalid |ref=harv (help)
Granville, Andrew (2008). "Analytic number theory". Katika Gowers, Timothy; Barrow-Green, June; Leader, Imre (whr.). The Princeton Companion to Mathematics. Princeton University Press. ISBN 978-0-691-11880-2. Iliwekwa mnamo 2016-02-28. {{cite book}}: Invalid |ref=harv (help)
Porphyry; Guthrie, K.S. (trans.) (1920). Life of Pythagoras. Alpine, New Jersey: Platonist Press.
Guthrie, Kenneth Sylvan (1987). The Pythagorean Sourcebook and Library. Grand Rapids, Michigan: Phanes Press. ISBN 978-0-933999-51-0. {{cite book}}: Invalid |ref=harv (help)
Hardy, Godfrey Harold; Wright, E.M. (2008) [1938]. An Introduction to the Theory of Numbers (tol. la Sixth). Oxford University Press. ISBN 978-0-19-921986-5. MR 2445243. {{cite book}}: Invalid |ref=harv (help)
Heath, Thomas L. (1921). A History of Greek Mathematics, Volume 1: From Thales to Euclid. Oxford: Clarendon Press. Iliwekwa mnamo 2016-02-28. {{cite book}}: Invalid |ref=harv (help)
Hopkins, J.F.P. (1990). "Geographical and Navigational Literature". Katika Young, M.J.L.; Latham, J.D.; Serjeant, R.B. (whr.). Religion, Learning and Science in the 'Abbasid Period. The Cambridge history of Arabic literature. Cambridge University Press. ISBN 978-0-521-32763-3. {{cite book}}: Invalid |ref=harv (help)
Huffman, Carl A. (8 Agosti 2011). Zalta, Edward N. (mhr.). "Pythagoras". Stanford Encyclopaedia of Philosophy (tol. la Fall 2011). Iliwekwa mnamo 7 Februari 2012. {{cite web}}: Invalid |ref=harv (help)CS1 maint: date auto-translated (link)
Iwaniec, Henryk; Kowalski, Emmanuel (2004). Analytic Number Theory. American Mathematical Society Colloquium Publications. Juz. la 53. Providence, RI: American Mathematical Society. ISBN 978-0-8218-3633-0. {{cite book}}: Invalid |ref=harv (help)
Plato; Jowett, Benjamin (trans.) (1871). Theaetetus. Ilihifadhiwa kwenye nyaraka kutoka chanzo mnamo 2011-07-09. Iliwekwa mnamo 2019-08-04. {{cite book}}: Unknown parameter |dead-url= ignored (|url-status= suggested) (help)
Lam, Lay Yong; Ang, Tian Se (2004). Fleeting Footsteps: Tracing the Conception of Arithmetic and Algebra in Ancient China (tol. la revised). Singapore: World Scientific. ISBN 978-981-238-696-0. Iliwekwa mnamo 2016-02-28. {{cite book}}: Invalid |ref=harv (help)
Long, Calvin T. (1972). Elementary Introduction to Number Theory (tol. la 2nd). Lexington, VA: D.C. Heath and Company. LCCN 77171950. {{cite book}}: Invalid |ref=harv (help)
Mahoney, M.S. (1994). The Mathematical Career of Pierre de Fermat, 1601–1665 (tol. la Reprint, 2nd). Princeton University Press. ISBN 978-0-691-03666-3. Iliwekwa mnamo 2016-02-28. {{cite book}}: Invalid |ref=harv (help)
Milne, J.S. (2014). "Algebraic Number Theory". Available at www.jmilne.org/math. {{cite web}}: Missing or empty |url= (help)CS1 maint: ref duplicates default (link)
Montgomery, Hugh L.; Vaughan, Robert C. (2007). Multiplicative Number Theory: I, Classical Theory. Cambridge University Press. ISBN 978-0-521-84903-6. Iliwekwa mnamo 2016-02-28. {{cite book}}: Invalid |ref=harv (help)
Morrow, Glenn Raymond (trans., ed.); Proclus (1992). A Commentary on Book 1 of Euclid's Elements. Princeton University Press. ISBN 978-0-691-02090-7.{{cite book}}: CS1 maint: multiple names: authors list (link)
Mumford, David (Machi 2010). "Mathematics in India: reviewed by David Mumford" (PDF). Notices of the American Mathematical Society. 57 (3): 387. ISSN 1088-9477. {{cite journal}}: Invalid |ref=harv (help)CS1 maint: date auto-translated (link)
Neugebauer, Otto E. (1969). The Exact Sciences in Antiquity (tol. la corrected reprint of the 1957). New York: Dover Publications. ISBN 978-0-486-22332-2. Iliwekwa mnamo 2016-03-02. {{cite book}}: Invalid |ref=harv (help)
Neugebauer, Otto E.; Sachs, Abraham Joseph; Götze, Albrecht (1945). Mathematical Cuneiform Texts. American Oriental Series. Juz. la 29. American Oriental Society etc.
O'Grady, Patricia (Septemba 2004). "Thales of Miletus". The Internet Encyclopaedia of Philosophy. Iliwekwa mnamo 7 Februari 2012. {{cite web}}: Invalid |ref=harv (help)CS1 maint: date auto-translated (link)
Pingree, David; Ya'qub, ibn Tariq (1968). "The Fragments of the Works of Ya'qub ibn Tariq". Journal of Near Eastern Studies. 26.
Pingree, D.; al-Fazari (1970). "The Fragments of the Works of al-Fazari". Journal of Near Eastern Studies. 28.
Plofker, Kim (2008). Mathematics in India. Princeton University Press. ISBN 978-0-691-12067-6. {{cite book}}: Invalid |ref=harv (help)
Qian, Baocong, mhr. (1963). Suanjing shi shu (Ten Mathematical Classics) (kwa Chinese). Beijing: Zhonghua shuju. Iliwekwa mnamo 2016-02-28. {{cite book}}: Invalid |ref=harv (help)CS1 maint: unrecognized language (link)
Rashed, Roshdi (1980). "Ibn al-Haytham et le théorème de Wilson". Archive for History of Exact Sciences. 22 (4): 305–21. doi:10.1007/BF00717654. {{cite journal}}: Invalid |ref=harv (help)
Robson, Eleanor (2001). "Neither Sherlock Holmes nor Babylon: a Reassessment of Plimpton 322" (PDF). Historia Mathematica. 28 (3): 167–206. doi:10.1006/hmat.2001.2317. Ilihifadhiwa kwenye nyaraka kutoka chanzo (PDF) mnamo 2014-10-21. {{cite journal}}: Invalid |ref=harv (help)
Sachau, Eduard; Bīrūni, ̄Muḥammad ibn Aḥmad (1888). Alberuni's India: An Account of the Religion, Philosophy, Literature, Geography, Chronology, Astronomy and Astrology of India, Vol. 1. London: Kegan, Paul, Trench, Trübner & Co. Iliwekwa mnamo 2016-02-28. {{cite book}}: Invalid |ref=harv (help)
Serre, Jean-Pierre (1996) [1973]. A Course in Arithmetic. Graduate texts in mathematics. Juz. la 7. Springer. ISBN 978-0-387-90040-7. {{cite book}}: Invalid |ref=harv (help)
Smith, D.E. (1958). History of Mathematics, Vol I. New York: Dover Publications. {{cite book}}: Invalid |ref=harv (help)
Tannery, Paul; Henry, Charles (eds.); Fermat, Pierre de (1891). Oeuvres de Fermat. (4 Vols.) (kwa French na Latin). Paris: Imprimerie Gauthier-Villars et Fils. {{cite book}}: |first2= has generic name (help)CS1 maint: unrecognized language (link) Volume 1 Volume 2 Volume 3 Volume 4 (1912)
Iamblichus; Taylor, Thomas (trans.) (1818). Life of Pythagoras or, Pythagoric Life. London: J.M. Watkins. Ilihifadhiwa kwenye nyaraka kutoka chanzo mnamo 2011-07-21. {{cite book}}: Unknown parameter |deadurl= ignored (|url-status= suggested) (help) For other editions, see Iamblichus#List of editions and translations
Truesdell, C.A. (1984). "Leonard Euler, Supreme Geometer". Katika Hewlett, John (trans.) (mhr.). Leonard Euler, Elements of Algebra (tol. la reprint of 1840 5th). New York: Springer-Verlag. ISBN 978-0-387-96014-2. {{cite book}}: Invalid |ref=harv (help) This Google books preview of Elements of algebra lacks Truesdell's intro, which is reprinted (slightly abridged) in the following book:
Truesdell, C.A. (2007). "Leonard Euler, Supreme Geometer". Katika Dunham, William (mhr.). The Genius of Euler: reflections on his life and work. Volume 2 of MAA tercentenary Euler celebration. New York: Mathematical Association of America. ISBN 978-0-88385-558-4. Iliwekwa mnamo 2016-02-28. {{cite book}}: Invalid |ref=harv (help)
Varadarajan, V.S. (2006). Euler Through Time: A New Look at Old Themes. American Mathematical Society. ISBN 978-0-8218-3580-7. Iliwekwa mnamo 2016-02-28. {{cite book}}: Invalid |ref=harv (help)
Vardi, Ilan (Aprili 1998). "Archimedes' Cattle Problem" (PDF). American Mathematical Monthly. 105 (4): 305–19. CiteSeerX 10.1.1.383.545. doi:10.2307/2589706. JSTOR 2589706. {{cite journal}}: Invalid |ref=harv (help)CS1 maint: date auto-translated (link)
van der Waerden, Bartel L.; Dresden, Arnold (trans) (1961). Science Awakening. Juz. la Vol. 1 or Vol 2. New York: Oxford University Press. {{cite book}}: |volume= has extra text (help)
Weil, André (1984). Number Theory: an Approach Through History – from Hammurapi to Legendre. Boston: Birkhäuser. ISBN 978-0-8176-3141-3. Iliwekwa mnamo 2016-02-28. {{cite book}}: Invalid |ref=harv (help)

Marejeo mengine

G.H. Hardy; E.M. Wright (2008) [1938]. An introduction to the theory of numbers (tol. la rev. by D.R. Heath-Brown and J.H. Silverman, 6th). Oxford University Press. ISBN 978-0-19-921986-5. Iliwekwa mnamo 2016-03-02. {{cite book}}: Invalid |ref=harv (help)
Vinogradov, I.M. (2003) [1954]. Elements of Number Theory (tol. la reprint of the 1954). Mineola, NY: Dover Publications. {{cite book}}: Invalid |ref=harv (help)
Ivan M. Niven; Herbert S. Zuckerman; Hugh L. Montgomery (2008) [1960]. An introduction to the theory of numbers (tol. la reprint of the 5th edition 1991). John Wiley & Sons. ISBN 978-81-265-1811-1. Iliwekwa mnamo 2016-02-28.
Kenneth H. Rosen (2010). Elementary Number Theory (tol. la 6th). Pearson Education. ISBN 978-0-321-71775-7. Iliwekwa mnamo 2016-02-28.
Borevich, A. I.; Shafarevich, Igor R. (1966). Number theory. Pure and Applied Mathematics. Juz. la 20. Boston, MA: Academic Press. ISBN 978-0-12-117850-5. MR 0195803.
Serre, Jean-Pierre (1996) [1973]. A course in arithmetic. Graduate texts in mathematics. Juz. la 7. Springer. ISBN 978-0-387-90040-7. {{cite book}}: Invalid |ref=harv (help)

Viungo vya nje

Number Theory Web

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[1] Already in 1921, T. L. Heath had to explain: "By arithmetic, Plato meant, not arithmetic in our sense, but the science which considers numbers in themselves, in other words, what we mean by the Theory of Numbers." (Heath 1921, p. 13)

[2] Take, for example, Serre 1973. In 1952, Davenport still had to specify that he meant The Higher Arithmetic. Hardy and Wright wrote in the introduction to An Introduction to the Theory of Numbers (1938): "We proposed at one time to change [the title] to An introduction to arithmetic, a more novel and in some ways a more appropriate title; but it was pointed out that this might lead to misunderstandings about the content of the book."

[1]

[2]