History of mathematics II 1000-00HM2-OG
Berkeley and Maclaurin. Euler, d'Alembert and Lagrange.
The role of mechanics -- Laplace; determinism and randomness.
Gauss. Abel and Galois. Grassmann and Hamilton. Cayley and Sylvester.
The works Kummer and Kronecker. Dirichlet. Abstract algebra takes shape. Dedekind. Klein and Lie - group theory. Boole.
The perspective. Monge and Poncelet. The German school.
The problem of noneuclidean geometries. Saccheri. Gauss, Bolyai, Lobachevski. Beltrami and Klein.
Differential geometry. Euler and Gauss. Riemann. The Italian school. Darboux.
Introducing rigour into analysis. Cauchy. Weierstrass. Kovalevska; the problem of women in science.
Cantor's set theory. Distribution of transcendental numbers. Formalisation of real numbers.
Klein's programme. Poincar'e. The conceptual crisis and specialisation. Congresses.
Hilbert' problems.
Logic. Methodological schools: logicism, formalism, intuitionism, constructivism and the Bourbakist idea.
Polish School of Mathematics.
Course coordinators
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Type of course
Bibliography
Extended lecture notes:
M. Kordos, Wykłady z historii matematyki, WSiP 1994, Script 2005
In Polish:
D.J. Struik, Krótki zarys historii matematyki do końca XIX wieku, PWN 1963
Historia matematyki, pod red.A.P. Juszkiewicza, PWN 1978-1985
N. Bourbaki, Elementy historii matematyki, PWN 1980
S. Kulczycki, Z dziejów matematyki greckiej, PWN 1973
J. Mioduszewski, Ciągłość. Szkice z historii matematyki, WSiP 1996
Filozofia matematyki: antologia tekstów klasycznych, wyb. i opr. R. Murawski, Wyd. Naukowe UAM 1986
R. Murawski, Filozofia matematyki, PWN 1995
In other languages:
M. Kline, Mathematical Thought from Ancient to Modern Times, Oxford UP 1972
M. Kline, Mathematics, The Loss of Certainty, Oxford UP 1980
M. Kline, Mathematics in Western Culture, Oxford UP, 1958
A. Dahan-Dalmedico, J. Peiffer, Routes et dedales, Etudes Vivantes 1982 (French)
F. Klein, Vorlesungen uber die Entwicklung der Mathematik im 19.Jahrhundert, Springer 1926 (German)
(a series) Matematika XX wieka, red. A.N. Kolmogorov, A.P. Yushlevich, Nauka, 1978-1990 (Russian)
S.G. Gindikin, Rasskazy o fizikah i matematikah, Nauka 1981 (Russian)
(a selection of texts) Ob osnovanyah geometrii, Nauka 1988 (Russian)