History of Mathematics. Specialized Topics

• Cryptography:

• Decrypted Secrets
F. C. Bauer. History and some technical description. $28
• Algebraic aspects of Cryptography, Chapter 1
Neal Koblitz. $60.
• Elementary Cryptanalysis
Helen Fouché Gaines $6:50.

• Indian Mathematics:

• B. Datta and A. N. Singh, Hindu Mathematics
Available from Firestone Library, Princeton
I have a xerox copy
• Colebrooke, Hindu Algebra and Mensuration
Available from Firestone Library, Princeton
I have extensive extracts

• The notion of Proof

• General views

• Imre Lakatos, Proofs and Refutations
See the biography of Lakatos (with references) at the St. Andrews site.

• Euclid, and the Parallel Postulate

• Hilbert, Foundations of Geometry
• Proclos, Saccheri, Bolyai, Lobachevski, Non-Euclidean geometry

• Logic

• Nagel and Newman, Godel's Proof

• Proofs of impossibility

• Classic Greek problems
Quadrature of the circle, trisection of the angle, duplication of the cube

• Proof by computer

• Peter L. Renz, Mathematical Proof: what it is and what it ought to be, Two-Year Coll. Math. J. 12 (1981), 83-103
• Doron Zeilberger

• Medieval European Mathematics

Some suggestions by Teresa Kuo
• A website with links and references focussed on this topic.
A mixed bag
• Books by Suppes/Moravcsik/Mendell, Pearl Kibre, and Marshall Clagett
(Iris search).

• Descartes

Selections from the St. Andrews site reference list
Books
• Descartes: Philosophy, Mathematics, and Physics
S. Gaukroger, editor
• The Scientific Work of René Descartes
J. F. Scott (1987)
Articles
• Descartes and the philosophy of mathematics
A. LoBello, Math. Intelligencer 13 (1991), 35-39
• Descartes and the geometrization of algebra
C. Boyer, Amer. Math. Monthly 66 (1959), 390-393
• Fermat and Descartes
C. Boyer, Scripta Mathematica 18 (1952), 189-217.
• Descartes and the birth of analytic geometry
E. Forbes, Historia Mathematica 4 (1977), 141-151
• Descartes' "Geometry" and the classical tradition
E. Grosholz, in Revolution and Continuity 183-196 (1991).
• Mathematics, Descartes, and the rise of modernity
R. Harris, Philos. Math. 3 (1988), 1-20
• Descartes and the geometrization of thought: the methodological background of Descartes' "Geometrie"
T. Lenoir, Historia Mathematica 6 (1979).
• Shifting the foundations: Descartes' transformation of ancient geometry
A. Molland, Historia Mathematica 3 (1976), 21-49
• The influence of mathematics on the philosophy of Descartes
R. Moorman, Nat. Math. Magazine 17 (1943)

• Operations Research

Two links
• Military OR History
• OR Notes by J. E. Beasley

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File date: Spring 2002