Nadharia ya namba
(Elekezwa kutoka Arithmetic)
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[hariri | hariri chanzo]
- ↑ 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[hariri | hariri chanzo]
- 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.
- Apostol, Tom M. (n.d.). "An Introduction to the Theory of Numbers". (Review of Hardy & Wright.) Mathematical Reviews (MathSciNet) Kigezo:MR. American Mathematical Society. Iliwekwa mnamo 2016-02-28. (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.
- Boyer, Carl Benjamin; Merzbach, Uta C. (1991) [1968]. A History of Mathematics (toleo la 2nd). New York: Wiley. ISBN 978-0-471-54397-8. 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.
- Colebrooke, Henry Thomas (1817). Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmegupta and Bháscara. London: J. Murray. Iliwekwa mnamo 2016-02-28.
- Davenport, Harold; Montgomery, Hugh L. (2000). Multiplicative Number Theory. Graduate texts in mathematics 74 (toleo la revised 3rd). Springer. ISBN 978-0-387-95097-6.
- Edwards, Harold M. (November 1983). "Euler and Quadratic Reciprocity". Mathematics Magazine 56 (5): 285–91. JSTOR 2690368. doi:10.2307/2690368. Check date values in:
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(help) - Edwards, Harold M. (2000) [1977]. Fermat's Last Theorem: a Genetic Introduction to Algebraic Number Theory. Graduate Texts in Mathematics 50 (toleo la reprint of 1977). Springer Verlag. ISBN 978-0-387-95002-0.
- Fermat, Pierre de (1679). Varia Opera Mathematica (kwa French, Latin). Toulouse: Joannis Pech. Iliwekwa mnamo 2016-02-28.
- Friberg, Jöran (August 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. Check date values in:
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(help) - von Fritz, Kurt (2004). "The Discovery of Incommensurability by Hippasus of Metapontum". Katika Christianidis, J. Classics in the History of Greek Mathematics. Berlin: Kluwer (Springer). ISBN 978-1-4020-0081-2.
- 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". Iliwekwa mnamo 2016-02-28.
- Goldstein, Catherine; Schappacher, Norbert (2007). "A book in search of a discipline". Katika Goldstein, C.; Schappacher, N.; Schwermer, Joachim. 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.
- Granville, Andrew (2008). "Analytic number theory". Katika Gowers, Timothy; Barrow-Green, June; Leader, Imre. The Princeton Companion to Mathematics. Princeton University Press. ISBN 978-0-691-11880-2. Iliwekwa mnamo 2016-02-28.
- 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.
- Hardy, Godfrey Harold; Wright, E.M. (2008) [1938]. An Introduction to the Theory of Numbers (toleo la Sixth). Oxford University Press. ISBN 978-0-19-921986-5. MR 2445243.
- Heath, Thomas L. (1921). A History of Greek Mathematics, Volume 1: From Thales to Euclid. Oxford: Clarendon Press. Iliwekwa mnamo 2016-02-28.
- Hopkins, J.F.P. (1990). "Geographical and Navigational Literature". Katika Young, M.J.L.; Latham, J.D.; Serjeant, R.B. Religion, Learning and Science in the 'Abbasid Period. The Cambridge history of Arabic literature. Cambridge University Press. ISBN 978-0-521-32763-3.
- Huffman, Carl A. (8 August 2011). Zalta, Edward N., mhariri. "Pythagoras". Stanford Encyclopaedia of Philosophy (toleo la Fall 2011). Iliwekwa mnamo 7 February 2012. Check date values in:
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(help) - Iwaniec, Henryk; Kowalski, Emmanuel (2004). Analytic Number Theory. American Mathematical Society Colloquium Publications 53. Providence, RI: American Mathematical Society. ISBN 978-0-8218-3633-0.
- Plato; Jowett, Benjamin (trans.) (1871). Theaetetus. Ilihifadhi kwenye nyaraka kutoka chanzo mnamo 2011-07-09. Iliwekwa mnamo 2019-08-04.
- Lam, Lay Yong; Ang, Tian Se (2004). Fleeting Footsteps: Tracing the Conception of Arithmetic and Algebra in Ancient China (toleo la revised). Singapore: World Scientific. ISBN 978-981-238-696-0. Iliwekwa mnamo 2016-02-28.
- Long, Calvin T. (1972). Elementary Introduction to Number Theory (toleo la 2nd). Lexington, VA: D.C. Heath and Company. LCCN 77171950.
- Mahoney, M.S. (1994). The Mathematical Career of Pierre de Fermat, 1601–1665 (toleo la Reprint, 2nd). Princeton University Press. ISBN 978-0-691-03666-3. Iliwekwa mnamo 2016-02-28.
- Milne, J.S. (2014). "Algebraic Number Theory". Available at www.jmilne.org/math.
- 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.
- 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.
- Mumford, David (March 2010). "Mathematics in India: reviewed by David Mumford". Notices of the American Mathematical Society 57 (3): 387. ISSN 1088-9477. Check date values in:
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(help) - Neugebauer, Otto E. (1969). The Exact Sciences in Antiquity (toleo la corrected reprint of the 1957). New York: Dover Publications. ISBN 978-0-486-22332-2. Iliwekwa mnamo 2016-03-02.
- Neugebauer, Otto E.; Sachs, Abraham Joseph; Götze, Albrecht (1945). Mathematical Cuneiform Texts. American Oriental Series 29. American Oriental Society etc.
- O'Grady, Patricia (September 2004). "Thales of Miletus". The Internet Encyclopaedia of Philosophy. Iliwekwa mnamo 7 February 2012. Check date values in:
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(help) - 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.
- Qian, Baocong, mhariri (1963). Suanjing shi shu (Ten Mathematical Classics) (kwa Chinese). Beijing: Zhonghua shuju. Iliwekwa mnamo 2016-02-28.
- 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.
- Robson, Eleanor (2001). "Neither Sherlock Holmes nor Babylon: a Reassessment of Plimpton 322". Historia Mathematica 28 (3): 167–206. doi:10.1006/hmat.2001.2317. Ilihifadhi kwenye nyaraka kutoka chanzo mnamo 2014-10-21.
- 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.
- Serre, Jean-Pierre (1996) [1973]. A Course in Arithmetic. Graduate texts in mathematics 7. Springer. ISBN 978-0-387-90040-7.
- Smith, D.E. (1958). History of Mathematics, Vol I. New York: Dover Publications.
- Tannery, Paul; Henry, Charles (eds.); Fermat, Pierre de (1891). Oeuvres de Fermat. (4 Vols.) (kwa French, Latin). Paris: Imprimerie Gauthier-Villars et Fils. Volume 1 Volume 2 Volume 3 Volume 4 (1912)
- Iamblichus; Taylor, Thomas (trans.) (1818). Life of Pythagoras or, Pythagoric Life. London: J.M. Watkins. Ilihifadhi kwenye nyaraka kutoka chanzo mnamo 2011-07-21. For other editions, see Iamblichus#List of editions and translations
- Truesdell, C.A. (1984). "Leonard Euler, Supreme Geometer". Katika Hewlett, John (trans.). Leonard Euler, Elements of Algebra (toleo la reprint of 1840 5th). New York: Springer-Verlag. ISBN 978-0-387-96014-2. 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. 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.
- 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.
- Vardi, Ilan (April 1998). "Archimedes' Cattle Problem". American Mathematical Monthly 105 (4): 305–19. JSTOR 2589706. doi:10.2307/2589706. Unknown parameter
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ignored (help); Check date values in:|date=
(help) - van der Waerden, Bartel L.; Dresden, Arnold (trans) (1961). Science Awakening. Vol. 1 or Vol 2. New York: Oxford University Press.
- 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.
Marejeo mengine[hariri | hariri chanzo]
- G.H. Hardy; E.M. Wright (2008) [1938]. An introduction to the theory of numbers (toleo 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.
- Vinogradov, I.M. (2003) [1954]. Elements of Number Theory (toleo la reprint of the 1954). Mineola, NY: Dover Publications.
- Ivan M. Niven; Herbert S. Zuckerman; Hugh L. Montgomery (2008) [1960]. An introduction to the theory of numbers (toleo 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 (toleo 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 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 7. Springer. ISBN 978-0-387-90040-7.
Viungo vya nje[hariri | hariri chanzo]
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