Bibliography

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/

View Full Text

Details

  • File Type
    pdf
  • Upload Time
    -
  • Content Languages
    English
  • Upload User
    Anonymous/Not logged-in
  • File Pages
    15 Page
  • File Size
    -

Download

Channel Download Status
Express Download Enable

Copyright

We respect the copyrights and intellectual property rights of all users. All uploaded documents are either original works of the uploader or authorized works of the rightful owners.

  • Not to be reproduced or distributed without explicit permission.
  • Not used for commercial purposes outside of approved use cases.
  • Not used to infringe on the rights of the original creators.
  • If you believe any content infringes your copyright, please contact us immediately.

Support

For help with questions, suggestions, or problems, please contact us