DOCSLIB.ORG

Bibliography

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Bibliography Bibliography [A’C] Norbert A’Campo, A natural construction for the real numbers. arXiv:math.GN/0301015. [Apo67] Tom M. Apostol, Calculus. Vol. I: One-Variable Calculus, with an Introduction to Linear Algebra, 2nd ed., Blaisdell, Waltham, MA, 1967. [AH01] Jorg¨ Arndt and Christoph Haenel, Pi—Unleashed, 2nd ed., Springer-Verlag, Berlin, 2001. Translated from the 1998 German original by Catriona Lischka and David Lischka. [Art64] Emil Artin, The Gamma Function, Translated by Michael Butler. Athena Series: Selected Topics in Mathematics, Holt, Rinehart and Winston, New York, 1964. [Bar69] Margaret E. Baron, The Origins of the Infinitesimal Calculus, Pergamon Press, Oxford, 1969. [Bar96] Robert G. Bartle, Return to the Riemann integral, Amer. Math. Monthly 103 (1996), no. 8, 625–632. [Bea97] Alan F. Beardon, Limits: A New Approach to Real Analysis, Springer-Verlag, New York, 1997. [BBB04] Lennart Berggren, Jonathan Borwein, and Peter Borwein, Pi: A Source Book, 3rd ed., Springer-Verlag, New York, 2004. [BML] Garrett Birkhoff and Saunders Mac Lane, A Survey of Modern Algebra, 3rd ed., Macmillan, New York. [Blo00] Ethan D. Bloch, Proofs and Fundamentals: A First Course in Abstract Mathematics, Birkhauser,¨ Boston, 2000. [Blo10] , Proofs and Fundamentals: A First Course in Abstract Mathematics, 2nd ed., Springer-Verlag, New York, 2010. [Bol78] Vladimir G. Boltianski˘ı, Hilbert’s Third Problem, V. H. Winston & Sons, Wash- ington, DC, 1978. Translated from the Russian by Richard A. Silverman; With a foreword by Albert B. J. Novikoff; Scripta Series in Mathematics. [BD09] William Boyce and Richard DiPrima, Elementary Differential Equations and Boundary Value Problems, 9th ed., John Wiley & Sons, New York, 2009. E.D. Bloch, The Real Numbers and Real Analysis , DOI 10.1007/978-0-387-72177-4, 539 © Springer Science+Business Media, LLC 2011 540 Bibliography [Boy91] Carl Boyer, A History of Mathematics, 2nd ed., John Wiley & Sons, New York, 1991. [Boy49] Carl B. Boyer, The History of the Calculus and Its Conceptual Development, Dover, New York, 1949. [BC09] James W. Brown and Ruel V. Churchill, Complex Variables and Applications, 8th ed., McGraw-Hill, New York, 2009. [Bur67] Claude W. Burrill, Foundations of Real Numbers, McGraw-Hill, New York, 1967. [CK07] E. Ward Cheney and David R. Kincaid, Numerical Mathematics and Computing, 6th ed., Brooks/Cole, Belmont, CA, 2007. [Coo05] Roger Cooke, The History of Mathematics: A Brief Course, 2nd ed., Wiley- Interscience [John Wiley & Sons], Hoboken, NJ, 2005. [DSW94] Martin Davis, Ron Sigal, and Elaine Weyuker, Computability, Complexity, and Languages, 2nd ed., Academic Press, San Diego, 1994. [Dea66] Richard Dean, Elements of Abstract Algebra, John Wiley & Sons, New York, 1966. [Ded63] Richard Dedekind, Essays on the Theory of Numbers. I: Continuity and Irrational Numbers. II: The Nature and Meaning of Numbers, Authorized translation by Wooster Woodruff Beman, Dover, New York, 1963. [DKO+] James Douglas, Rony Kirollos, Ben Odgers, Ross Street, and Nguyen Hanh Vo, The Efficient Real Numbers, http://www.math.mq.edu.au/~street/EffR.pdf. [Edw79] C. H. Edwards Jr., The Historical Development of the Calculus, Springer-Verlag, New York, 1979. [End72] Herbert Enderton, A Mathematical Introduction to Logic, Academic Press, New York, 1972. [Est02] Donald Estep, Practical Analysis in One Variable, Springer-Verlag, New York, 2002. [EL04] Pierre Eymard and Jean-Pierre Lafon, The Number p, American Mathematical Society, Providence, RI, 2004. Translated from the 1999 French original by Stephen S. Wilson. [Fal03] Kenneth Falconer, Fractal Geometry: Mathematical Foundations and Applications, 2nd ed., John Wiley & Sons, Hoboken, NJ, 2003. [Fer08] Giovanni Ferraro, The Rise and Development of the Theory of Series up to the Early 1820s, Sources and Studies in the History of Mathematics and Physical Sciences, Springer, New York, 2008. [Gar87] Trudi Garland, Fascinating Fibonaccis, Dale Seymour, Palo Alto, 1987. [GO03] Bernard R. Gelbaum and John M. H. Olmsted, Counterexamples in Analysis, Dover, New York, 2003. Corrected reprint of the second (1965) edition. [Gil87] Leonard Gillman, Writing Mathematics Well, Mathematical Association of America, Washington, DC, 1987. [Gol98] Robert Goldblatt, Lectures on the Hyperreals: An Introduction to Nonstandard Analysis, Springer-Verlag, New York, 1998. [Gor02] Russell Gordon, Real Analysis: A First Course, 2nd ed., Addison-Wesley, Boston, 2002. Bibliography 541 [GKP94] Ronald Graham, Donald Knuth, and Oren Patashnik, Concrete Mathematics, 2nd ed., Addison-Wesley, Reading, MA, 1994. [Hav03] Julian Havil, Gamma: Exploring Euler’s Constant, Princeton University Press, Princeton, NJ, 2003. [HK03] James M. Henle and Eugene M. Kleinberg, Infinitesimal Calculus, Dover, New York, 2003. Reprint of the 1979 original [MIT Press, Cambridge, MA]. [Hig98] Nicholas J. Higham, Handbook of Writing for the Mathematical Sciences, 2nd ed., Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 1998. [HHP97] Peter Hilton, Derek Holton, and Jean Pedersen, Mathematical Reflections, Springer- Verlag, New York, 1997. [How66] Aughtum Howard, Classroom Notes: On the convergence of the binomial series, Amer. Math. Monthly 73 (1966), no. 7, 760–761. [HH99] John Hamal Hubbard and Barbara Burke Hubbard, Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach, Prentice Hall, Upper Saddle River, NJ, 1999. [Hun70] H. E. Huntley, The Divine Proportion, Dover, New York, 1970. [Jac85] Nathan Jacobson, Basic Algebra. I, 2nd ed., W. H. Freeman and Company, New York, 1985. [Jah03] Hans Niels Jahnke (ed.), A History of Analysis, History of Mathematics, vol. 24, American Mathematical Society, Providence, RI, 2003. Translated from the Ger- man. [Jef73] Harold Jeffreys, Scientific Inference, 3rd ed., Cambridge University Press, Cam- bridge, 1973. [Kas80] Toni Kasper, Integration in finite terms: the Liouville theory, Math. Mag. 53 (1980), no. 4, 195–201. [Kat98] Victor J. Katz, A History of Mathematics: An Introduction, 2nd ed., Addison- Wesley, Reading, MA, 1998. [Kei] Jerome Keisler, Elementary Calculus: An Approach Using Infinitesimals, http: //www.math.wisc.edu/~keisler/calc.html. [Knu73] Donald E. Knuth, The Art of Computer Programming, Volume 1: Fundamental Algorithms, 2nd ed., Addison-Wesley, Reading, MA, 1973. [KLR89] Donald Knuth, Tracy Larrabee, and Paul Roberts, Mathematical Writing, Mathe- matical Association of America, Washington, DC, 1989. [Lay01] Steven Lay, Analysis with an Introduction to Proof, Prentice Hall, Upper Saddle River, NJ, 2001. [MZ94] Elena Anne Marchisotto and Gholam-Ali Zakeri, An invitation to integration in finite terms, College Math. J. 25 (1994), no. 4, 295–308. [Mar61] Angelo Margaris, Successor axioms for the integers, Amer. Math. Monthly 68 (1961), 441–444. [McC53] John McCarthy, An everywhere continuous nowhere differentiable function, Amer. Math. Monthly 60 (1953), 709. 542 Bibliography [MM] Mechon Mamre, The Hebrew Bible According to the Jewish Publication Society 1917 Edition, http://www.mechon-mamre.org/p/pt/pt09a07.htm. [Men73] Elliott Mendelson, Number Systems and the Foundations of Analysis, Academic Press, New York, 1973. [Mor87] Ronald P. Morash, Bridge to Abstract Mathematics, Random House, New York, 1987. [Mul06] Jean-Michel Muller, Elementary Functions: Algorithms and Implementation, 2nd ed., Birkhauser,¨ Boston, 2006. [Mun00] J. R. Munkres, Topology, 2nd ed., Prentice Hall, Upper Saddle River, NJ, 2000. [New] Isaac Newton, Extracts from the Works of Isaac Newton, http://www.maths. tcd.ie/pub/HistMath/People/Newton/. [Niv47] Ivan Niven, A simple proof that p is irrational, Bull. Amer. Math. Soc. 53 (1947), 509. [OR] John O’Connor and Edmund Robertson, The MacTutor History of Mathematics archive, http://www-history.mcs.st-andrews.ac.uk/. [Olm62] John M. H. Olmsted, The Real Number System, Appleton-Century-Crofts, New York, 1962. [Pak] Igor Pak, Lectures on Discrete and Polyhedral Geometry, http://www.math. ucla.edu/~pak/book.htm. [Pow94] Malcolm Pownall, Real Analysis, Wm. C. Brown, Dubuque, 1994. [Rob86] Eric Roberts, Thinking Recursively, John Wiley & Sons, New York, 1986. [Rob84] Fred Roberts, Applied Combinatorics, Prentice Hall, Englewood Cliffs, NJ, 1984. [Ros05] Kenneth H. Rosen, Elementary Number Theory, 5th ed., Addison-Wesley, Reading, MA, 2005. [Ros68] Maxwell Rosenlicht, Introduction to Analysis, Dover, New York, 1968. [Ros72] , Integration in finite terms, Amer. Math. Monthly 79 (1972), 963–972. [Ros80] Kenneth A. Ross, Another approach to Riemann-Stieltjes integrals, Amer. Math. Monthly 87 (1980), no. 8, 660–662. [Ros10] Sheldon Ross, A First Course in Probability, 8th ed., Prentice Hall, Upper Saddle River, NJ, 2010. [Rud53] Walter Rudin, Principles of Mathematical Analysis, McGraw-Hill, New York, 1953. [Rud76] , Principles of Mathematical Analysis, 3rd ed., McGraw-Hill, New York, 1976. [Spi65] Michael Spivak, Calculus on Manifolds, Benjamin, New York, 1965. [Spi67] , Calculus, Benjamin, New York, 1967. [SHSD73] N. E. Steenrod, P. R. Halmos, M. M. Schiffer, and J. A. Dieudonne,´ How to Write Mathematics, American Mathematical Society, Providence, 1973. [Ste04] Ian Stewart, Galois Theory, 3rd ed., Chapman & Hall/CRC, Boca Raton, FL, 2004. [Sto01] Manfred Stoll, Introduction to Real Analysis, 2nd ed., Addison-Wesley, Boston, 2001. Bibliography 543 [Sto79] Robert R. Stoll, Set Theory and Logic, Dover, New York, 1979. Corrected reprint of the 1963 edition. [Str] Ross Street, Update on the Efficient Reals, http://www.math.mq.edu.au/
Load more

Recommended publications
  • A Diluted Al-Karaji in Abbacus Mathematics Actes Du 10^ Colloque Maghrebin Sur I’Histoire Des Mathematiques Arabes
    Actes du 10 Colloque Maghrebin sur THistoire des Mathematiques Arabes (Tunis, 29-30-31 mai 2010) Publications de 1’Association Tunisienne des Sciences Mathematiques Actes du 10^ colloque maghrebin sur I’histoire des mathematiques arabes A diluted al-Karajl in Abbacus Mathematics Jens H0yrup^ In several preceding Maghreb colloques I have argued, from varying perspectives, that the algebra of the Italian abbacus school was inspired neither from Latin algebraic writings (the translations of al-Khw5rizmT and the Liber abbaci) nor directly from authors like al-KhwarizmT, Abu Kamil and al-KarajT; instead, its root in the Arabic world is a level of algebra Actes du 10*“® Colloque Maghrebin (probably coupled to mu^Smalat mathematics) which until now has not been scrutinized systematically. sur THistoire des Mathematiques Going beyond this negative characterization I shall argue on the present Arabes occasion that abbacus algebra received indirect inspiration from al-KarajT. As it will turn out, however, this inspiration is consistently strongly diluted, (Tunis, 29-30-31 mai 2010) and certainly indirect. 1. Al-KhwSrizml, Abu Kamil and al-KarajI Let us briefly summarize the relevant aspects of what distinguishes al-KarajT from his algebraic predecessors. Firstly, there is the sequence of algebraic powers. Al-KhwarizmT [ed., trans. Rashed 2007], as is well known, deals with three powers only: census (to adopt the translation which will fit our coming discussion of abbacus algebra), roots, and simple numbers. So do ibn Turk [ed., trans. Say_l_ 1962] and Thabit ibn Qurrah [ed., trans. Luckey 1941] in their presentation of proofs for the basic mixed cases, which indeed involve only these same powers.
    [Show full text]
  • In. ^Ifil Fiegree in PNILOSOPNY
    ISLAMIC PHILOSOPHY OF SCIENCE: A CRITICAL STUDY O F HOSSAIN NASR Dis««rtation Submitted TO THE Aiigarh Muslim University, Aligarh for the a^ar d of in. ^Ifil fiegree IN PNILOSOPNY BY SHBIKH ARJBD Abl Under the Kind Supervision of PROF. S. WAHEED AKHTAR Cbiimwa, D«ptt. ol PhiloMphy. DEPARTMENT OF PHILOSOPHY ALIGARH IWIUSLIIM UNIVERSITY ALIGARH 1993 nmiH DS2464 gg®g@eg^^@@@g@@€'@@@@gl| " 0 3 9 H ^ ? S f I O ( D .'^ ••• ¥4 H ,. f f 3« K &^: 3 * 9 m H m «< K t c * - ft .1 D i f m e Q > i j 8"' r E > H I > 5 C I- 115m Vi\ ?- 2 S? 1 i' C £ O H Tl < ACKNOWLEDGEMENT In the name of Allah« the Merciful and the Compassionate. It gives me great pleasure to thanks my kind hearted supervisor Prof. S. Waheed Akhtar, Chairman, Department of Philosophy, who guided me to complete this work. In spite of his multifarious intellectual activities, he gave me valuable time and encouraged me from time to time for this work. Not only he is a philosopher but also a man of literature and sugge'sted me such kind of topic. Without his careful guidance this work could not be completed in proper time. I am indebted to my parents, SK Samser All and Mrs. AJema Khatun and also thankful to my uncle Dr. Sheikh Amjad Ali for encouraging me in research. I am also thankful to my teachers in the department of Philosophy, Dr. M. Rafique, Dr. Tasaduque Hussain, Mr. Naushad, Mr. Muquim and Dr. Sayed.
    [Show full text]
  • Arithmetical Proofs in Arabic Algebra Jeffery A
    This article is published in: Ezzaim Laabid, ed., Actes du 12è Colloque Maghrébin sur l'Histoire des Mathématiques Arabes: Marrakech, 26-27-28 mai 2016. Marrakech: École Normale Supérieure 2018, pp 215-238. Arithmetical proofs in Arabic algebra Jeffery A. Oaks1 1. Introduction Much attention has been paid by historians of Arabic mathematics to the proofs by geometry of the rules for solving quadratic equations. The earliest Arabic books on algebra give geometric proofs, and many later algebraists introduced innovations and variations on them. The most cited authors in this story are al-Khwārizmī, Ibn Turk, Abū Kāmil, Thābit ibn Qurra, al-Karajī, al- Samawʾal, al-Khayyām, and Sharaf al-Dīn al-Ṭūsī.2 What we lack in the literature are discussions, or even an acknowledgement, of the shift in some authors beginning in the eleventh century to give these rules some kind of foundation in arithmetic. Al-Karajī is the earliest known algebraist to move away from geometric proof, and later we see arithmetical arguments justifying the rules for solving equations in Ibn al-Yāsamīn, Ibn al-Bannāʾ, Ibn al-Hāʾim, and al-Fārisī. In this article I review the arithmetical proofs of these five authors. There were certainly other algebraists who took a numerical approach to proving the rules of algebra, and hopefully this article will motivate others to add to the discussion. To remind readers, the powers of the unknown in Arabic algebra were given individual names. The first degree unknown, akin to our �, was called a shayʾ (thing) or jidhr (root), the second degree unknown (like our �") was called a māl (sum of money),3 and the third degree unknown (like our �#) was named a kaʿb (cube).
    [Show full text]
  • The History of Arabic Sciences: a Selected Bibliography
    THE HISTORY OF ARABIC SCIENCES: A SELECTED BIBLIOGRAPHY Mohamed ABATTOUY Fez University Max Planck Institut für Wissenschaftsgeschichte, Berlin A first version of this bibliography was presented to the Group Frühe Neuzeit (Max Planck Institute for History of Science, Berlin) in April 1996. I revised and expanded it during a stay of research in MPIWG during the summer 1996 and in Fez (november 1996). During the Workshop Experience and Knowledge Structures in Arabic and Latin Sciences, held in the Max Planck Institute for the History of Science in Berlin on December 16-17, 1996, a limited number of copies of the present Bibliography was already distributed. Finally, I express my gratitude to Paul Weinig (Berlin) for valuable advice and for proofreading. PREFACE The principal sources for the history of Arabic and Islamic sciences are of course original works written mainly in Arabic between the VIIIth and the XVIth centuries, for the most part. A great part of this scientific material is still in original manuscripts, but many texts had been edited since the XIXth century, and in many cases translated to European languages. In the case of sciences as astronomy and mechanics, instruments and mechanical devices still extant and preserved in museums throughout the world bring important informations. A total of several thousands of mathematical, astronomical, physical, alchemical, biologico-medical manuscripts survived. They are written mainly in Arabic, but some are in Persian and Turkish. The main libraries in which they are preserved are those in the Arabic World: Cairo, Damascus, Tunis, Algiers, Rabat ... as well as in private collections. Beside this material in the Arabic countries, the Deutsche Staatsbibliothek in Berlin, the Biblioteca del Escorial near Madrid, the British Museum and the Bodleian Library in England, the Bibliothèque Nationale in Paris, the Süleymaniye and Topkapi Libraries in Istanbul, the National Libraries in Iran, India, Pakistan..
    [Show full text]
  • Islamic Mathematics
    Islamic mathematics Bibliography of Mathematics in Medieval Islamic Civilization Version 13 January 1999. This bibliography is a revised, enlarged and updated version of the bibliography on Islamic mathematics by Richard Lorch on pp. 65-86 of Joseph W. Dauben's The History of Mathematics from Antiquity to the Present: A Selective Bibliography, New York and London: Garland, 1985. This bibliography of Islamic mathematics will appear as a chapter in the updated (1999?) version of Dauben's book which will be made available as a CD-Rom. Reactions and suggestions are very welcome, and can be sent to [email protected]. In this preliminary form, no attention has been paid to diacritical marks in Arabic names. The items in the bibliography have been numbered *1, *2, ... *122, *122a, *122b, *123 etc. and many cross-references have been provided. General Introduction Introductory Works Bibliographies and Handbooks Illustrated Works Texts and Commentaries (Specific Authors in Chronological Order) Studies on Specific Subjects Transmission of Mathematics Mathematics in Specific Areas in the Islamic World Arithmetic Irrational Magnitudes Algebra Number Theory, Indeterminate Equations and Magic Squares Geometry Trigonometry Timekeeping Interpolation, Tables, Analysis of Tables Cultural Context: Islamic Aspects Mathematical Astronomy and Astrology Instruments Mathematics, Art and Architecture Optics Geography Reprinted Works and Collections of Articles General Introduction file:///P|/Igitur%20archief_repository/PR&beleid%20Ig...bsites/HOGENDIJK/hogendijk_00_islamic_mathematics.htm (1 van 33)12-2-2007 14:36:27 Islamic mathematics Islamic mathematics and Arabic mathematics are modern historical terms for the mathematical sciences in Islamic civilization from the beginning of Islam (A.D. 622) until the 17th century.
    [Show full text]
  • Islamic Mathematics
    Islamic Mathematics Elizabeth Rogers MATH 390: Islamic Mathematics Supervised by Professor George Francis University of Illinois at Urbana-Champaign August 2008 1 0.1 Abstract This project will provide a summary of the transmission of Greek mathe- matics through the Islamic world, the resulting development of algebra by Muhammad ibn Musa al-Khwarizmi, and the applications of Islamic algebra in modern mathematics through the formulation of the Fundamental Theo- rem of Algebra. In addition to this, I will attempt to address several cultural issues surrounding the development of algebra by Persian mathematicians and the transmission of Greek mathematics through Islamic mathematicians. These cultural issues include the following questions: Why was the geometry of Euclid transmitted verbatim while algebra was created and innovated by Muslim mathematicians? Why didn't the Persian mathematicians expand or invent new theorems or proofs, though they preserved the definition-theorem-proof model for ge- ometry? In addition, why did the definition-theorem-proof model not carry over from Greek mathematics (such as geometry) to algebra? Why were most of the leading mathematicians, in this time period, Mus- lim? In addition, why were there no Jewish mathematicians until recently? Why were there no Orthodox or Arab Christian mathematicians? 0.2 Arabic Names and Transliteration Arabic names are probably unfamiliar to many readers, so a note on how to read Arabic names may be helpful. A child of a Muslim family usually receives a first name ('ism), followed by the phrase \son of ··· "(ibn ··· ). For example, Th¯abitibn Qurra is Th¯abit,son of Qurra. Genealogies can be combined; for example, Ibr¯ah¯ımibn Sin¯anibn Th¯abitibn Qurra means that Ibr¯ah¯ımis the son of Sin¯an,grandson of Th¯abit,and great-grandson of Qurra.
    [Show full text]
  • Mathematics 153–001, Spring 2010, Examination 2 Answer
    NAME: Mathematics 153{001, Spring 2010, Examination 2 Answer Key 1 1. [15 points] If L is the secant line to the parabola y = x2 which goes through the points (1; 1) and (4; 16), find the point (c; c2) on the parabola at which the tangent line is parallel to L. | Recall that two lines are parallel if their slopes are equal. SOLUTION The slope of the secant line is just 16 − 1 15 = = 5 4 − 1 3 while the slope of the tangent line at (c; c2) is 2c. The latter will be parallel to the secant line if and only if 2c = 5, or equivalently if and only if c = 5=2. 2 2. [20 points] Suppose we are given two closed regions A and B in the first quadrant of the coordinate plane such that B is the result of moving A vertically upwards by k units. Suppose that the centroid of A has coordinates (x; y). Let S and T be the solids of revolution obtained by rotating A and B (respectively) about the x-axis. Using the Pappus Centroid Theorem, find the ratio Volume(T )=Volume(S). [Hint: What are the coordinates for the centroid of B?] SOLUTION The centroid of B is (x; y + k). Therefore by the Pappus Centroid Theorem we have Volume(S) = Area(A) · 2πy ; Volume(T ) = Area(B) · 2π(y + k) : Since B is obtained from A by vertical translation, the areas of B and A are equal. If we substitute this into the formula for the volume of T and take ratios, this implies that Volume(T ) Area(A) · 2π(y + k) y + k = = : Volume(S) Area(A) · 2πy y 3 3.
    [Show full text]
  • Arapski Temeljiˇskolske Matematike
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by University of Zagreb Repository SVEUCILIˇ STEˇ U ZAGREBU PRIRODOSLOVNO–MATEMATICKIˇ FAKULTET MATEMATICKIˇ ODSJEK Sebastijan Kocijan ARAPSKI TEMELJI SKOLSKEˇ MATEMATIKE Diplomski rad Voditelj rada: doc. dr. sc. Franka Miriam Brueckler Zagreb, 2016. Ovaj diplomski rad obranjen je dana pred ispitnim povjerenstvom u sastavu: 1. , predsjednik 2. , clanˇ 3. , clanˇ Povjerenstvo je rad ocijenilo ocjenom . Potpisi clanovaˇ povjerenstva: 1. 2. 3. Hvala od srca mojoj obitelji na podrˇscii ˇstosu mi omogu´cilida strudiram ono ˇstovolim, te hvala mojoj djevojci na potpori. Zahvale mentorici zbog ukazanog razumijevanja i pomo´ci. Sadrzajˇ Sadrzajˇ iv Uvod 2 1 Arapske brojke 3 2 Arapski matematicariˇ 6 2.1 Al-Khwarizmi . 6 2.2 Thabit ibn Qurra . 14 2.3 Al-Battani . 17 2.4 Abu‘l-Wafa . 20 2.5 Al-Karaji . 25 2.6 Al-Haytham . 26 2.7 Al-Biruni . 29 2.8 Omar Khayyam . 32 2.9 Al-Tusi . 36 2.10 Al-Kashi . 39 2.11 Ostali znacajniˇ arapski matematicariˇ . 42 3 Usporedba arapskih matematickihˇ doprinosa i skolskihˇ programa matema- tike 48 Bibliografija 52 iv Uvod Opce´ je poznato da je Europa vecinu´ starogrckihˇ matematickihˇ otkrica´ saznala upravo preko Arapa. Starogrckaˇ matematika je u Europu stigla zaobilaznim putem preko Spanjolskeˇ koja je bila u sastavu arapskog kalifata. Takoder, mnoga starogrckaˇ djela sacuvanaˇ su samo u arapskom prijevodu. No, iako mnogi smatraju da su doprinosi arapskog podrucjaˇ mate- matici samo prevodenje i prijenos podataka koje su ranije otkrili stari Grci ili Indijci, to nije tocno.ˇ Dapace,ˇ danasnjaˇ matematika je mnogo slicnijaˇ arapskoj nego starogrckoj.ˇ Nakon stoˇ je 622.
    [Show full text]
  • Islamic Civilization: Astronomers, Mathematicians, Geographers
    Selected Astronomers, Mathematicians, Geographers, and Cartographers in Islamic Civilization A website list of astronomers, mathematicians, geographers and cartographers within Islamic civilization is compiled below, whose cultures came from the Middle East, Central Asia, Spain and North Africa during and after the classical age of Islam, with Muslim, Christian, Jewish, or Sabean faith backgrounds. The SALAM Library also has resource books with encyclopedic articles or essays about the topic. A more comprehensive glossary of scientists including the names below appears in Jim Al- Khalili’s The House of Wisdom: How Arabic Science Saved Ancient Knowledge and Gave Us the Renaissance. New York: Penguin, 2011. Astronomers: Al- Battani - https://www.famousscientists.org/al-battani/ Al- Biruni - https://www.britannica.com/biography/al-Biruni Al- Fadl ibn Nawbakht - https://en.wikipedia.org/wiki/Al-Fadl_ibn_Naubakht Al- Farghani - http://www.muslimheritage.com/scholars/al-farghani Al- Fazari - http://www.muslimheritage.com/scholars/ibrahim-al-fazari Ibn al- Haythem - https://www.britannica.com/biography/Ibn-al-Haytham Masha’Allah (Manasseh) - http://enacademic.com/dic.nsf/enwiki/843096 Ibn al- Shatir- http://www.oxfordreference.com/view/10.1093/oi/authority.20110803095955504 http://islamsci.mcgill.ca/RASI/BEA/Ibn_al-Shatir_BEA.htm Al-Shirazi -https://en.wikipedia.org/wiki/Qutb_al-Din_al-Shirazi Ibn Sina - https://www.britannica.com/biography/Avicenna Nasr al-Din al-Tusi- https://www.britannica.com/biography/Nasir-al-Din-al-Tusi al –Urdi- http://www.muslimheritage.com/scholars/al-urdi
    [Show full text]
  • Bc1500-Ad1500
    BC1600-AD1500 Irrational number BC 4000-2500 Hindu India BC 2000 Judaism BC1680-1620 Ahmes Egypt Rhind Papyrus 1650 BC BC 800-740 Baudhayana India 800 BC Sulbasutra book, Vedic, quadratic equation, pi number, square root two BC 750-690 Manava India Manava Sulbasutra, pi BC 624-546 Thales Asia minor first natural philosopher, teacher of Anaximander, Geometer, Thales theorem BC 611-545 Anaximander Greek BC 600-540 Apastamba India Apastamba's Sulbasutra, pi number in series, BC 580-520 Pythagoras Samos first pure mathematician, BC 535 in Egypt, Geometry BC 563-483 Buddha India BC 551-479 Confucius China BC 540-480 Heracleitus Greek fire forms the basic material principle of an orderly universe BC 520-460 Panini Pakistan Sanskrit grammarian, Astaka, under 4000 sutras BC 499-428 Anaxagoras Turkey infinite number of elements, or basic building blocks BC 492-432 Empedocles Italy four element hypothesis, finite velocity of light BC 490-430 Zeno of Elea Italy Zeno's paradoxes, infinitesimals, warm and cold, dry and wet world BC 490-420 Oenopides Greek period of the Great Year, lunar month of 29.53013 days, fire and air basic elements BC 480-420 Leucippus Asia minor The Great World System and On the Mind, an area by approximating of a sequence of polygons. BC 480-411 Antiphon Greek Squaring the circle BC 470-410 Hippocrates Greek Elements of Geometry, square the areas of lunes BC 499-399 Socrates Greek critical reasoning, sentenced, drank poison BC 465-398 Theodorus Libya tutor of Plato, Proof of irrational number 2, BC 460-400 Hippias Greek geometry
    [Show full text]
  • Aristotle's Journey to Europe: a Synthetic History of the Role Played
    Aristotle’s Journey to Europe: A Synthetic History of the Role Played by the Islamic Empire in the Transmission of Western Educational Philosophy Sources from the Fall of Rome through the Medieval Period By Randall R. Cloud B.A., Point Loma Nazarene University, 1977 M.A., Point Loma University, 1979 M. Div., Nazarene Theological Seminary, 1982 Submitted to the: School of Education Department of Educational Leadership and Policy Studies Program: Educational Policy and Leadership Concentration: Foundations of Education and the Faculty of the Graduate School of the University of Kansas in partial fulfillment of the requirements for the degree of Doctor of Philosophy Dissertation Committee: _______________________________________ Suzanne Rice, Chairperson _______________________________________ Ray Hiner _______________________________________ Jim Hillesheim _______________________________________ Marc Mahlios _______________________________________ Sally Roberts Dissertation Defended: November 6, 2007 The Dissertation Committee for Randall R. Cloud certifies that this is the approved version of the following dissertation: Aristotle’s Journey to Europe: A Synthetic History of the Role Played by the Islamic Empire in the Transmission of Western Educational Philosophy Sources from the Fall of Rome through the Medieval Period Dissertation Committee: _______________________________________ Suzanne Rice, Chairperson _______________________________________ Ray Hiner _______________________________________ Jim Hillesheim _______________________________________
    [Show full text]
  • THEORY and PRACTICE of GEOMETRY in MEDIEVAL ARCHITECTURE in the MIDDLE EAST (10Th-14Th CENTURIES)
    THEORY AND PRACTICE OF GEOMETRY IN MEDIEVAL ARCHITECTURE IN THE MIDDLE EAST (10th-14th CENTURIES) A THESIS SUBMITTED TO THE GRADUATE SCHOOL OF SOCIAL SCIENCES OF MIDDLE EAST TECHNICAL UNIVERSITY BY DENİZ ÖZDEN IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS IN HISTORY OF ARCHITECTURE FEBRUARY 2015 Approval of the Graduate School of Social Sciences Prof. Dr. Meliha Altunışık Director I certify that this thesis satisfies all the requirements as a thesis for the degree of Master of Science/Arts / Doctor of Philosophy. Prof. Dr. T. Elvan Altan Head of Department This is to certify that we have read this thesis and that in our opinion it is fully adequate, in scope and quality, as a thesis for the degree of Master of Arts. Prof. Dr. Ali Uzay Peker Supervisor Examining Committee Members Prof. Dr. Ömür Bakırer (METU, REST) Prof. Dr. Ali Uzay Peker (METU, AH) Assoc. Prof. Dr. Namık Günay Erkal (METU, AH) ii I hereby declare that all information in this document has been obtained and presented in accordance with academic rules and ethical conduct. I also declare that, as required by these rules and conduct, I have fully cited and referenced all material and results that are not original to this work. Name, Last name: Deniz Özden Signature: iii ABSTRACT THEORY AND PRACTICE OF GEOMETRY IN MEDIEVAL ARCHITECTURE IN THE MIDDLE EAST (10th-14th CENTURIES) Özden, Deniz M.A. Department of Architectural History Supervisor: Prof. Dr. Ali Uzay PEKER March 2015, 94 pages The aim of this research is to investigate the use of geometry in architecture of the Medieval Middle East considering the place of geometry in the classification of sciences in records of medieval Islamic philosophers and the practical application of geometry in the area of architecture through documents on geometric ornaments and geometric analysis of North Dome of Friday Mosque of Isfahan.
    [Show full text]