History of mathematics *

2022/2023
Programme:
Mathematics Education
Year:
4 ali 5 year
Semester:
first
Kind:
mandatory
ECTS:
5
Language:
slovenian
Hours per week – 1. semester:
Lectures
2
Seminar
0
Tutorial
2
Lab
0
Content (Syllabus outline)

Mathematics in antient Egypt and Mesopotamia. Pythagorean mathematics. Mathematics of Euclid's Elements. Archimedes and Apollonius. Hellenistic mathematics in the Roman Empire. Mathematics in antient India and China. Mathematics in the Arab Empire. Middle ages and the renaissance of European mathematics. Fermat, Descartes and Pascal. Newton and Leibniz. Euler, Lagrange and Laplace. Gauss and Legendre. Algebra, analysis and geometry in the nineteenth century. Set theory and foundations of mathematics. Modern mathematics and its applications.

Readings

B. Cipra: What's Happening in the Mathematical Sciences, AMS, Providence, 2002.
R. Cooke: The History of Mathematics, A Brief Course, John Wiley and Sons, New York, 1997.
V. J. Katz: A History of Mathematics, An Introduction, Addison Wesley, Boston, New York, 1998.
W. S. Anglin: Mathematics : A Concise History and Philosophy, Springer, New York, 1996.
F. Križanič: Križem po matematiki, Mladinska knjiga, Ljubljana 1960.
D. J. Struik: Kratka zgodovina matematike, DMFA, Ljubljana, 1986.
http://www-history.mcs.st-and.ac.uk/history/

Objectives and competences

Students learn about the development of mathematical ideas as they evolved historically.

Intended learning outcomes

Knowledge and understanding of the historical development of mathematical ideas and its use in teaching.

Learning and teaching methods

lectures, exercise sessions, consultations

Assessment

Homeworks, project work
Written and oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

Gregor Cigler:
CIGLER, Gregor, JERMAN, Marjan. On separation of eigenvalues by certain matrix subgroups. Linear Algebra and its Applications. [Print ed.]. 2014, vol. 440, str. 213-217. ISSN 0024-3795. [COBISS-SI-ID 16862297]
CIGLER, Gregor, DRNOVŠEK, Roman. On semigroups of matrices with nonnegative diagonals. Linear Algebra and its Applications. [Print ed.]. 2013, vol. 438, iss. 1, str. 626-633. ISSN 0024-3795. [COBISS-SI-ID 16528473]
CIGLER, Gregor, DRNOVŠEK, Roman. From local to global similarity of matrix groups. Linear Algebra and its Applications. [Print ed.]. 2011, vol. 435, iss. 6, str. 1285-1295. ISSN 0024-3795. [COBISS-SI-ID 15929433]

Aleš Vavpetič:
VAVPETIČ, Aleš, ŽAGAR, Emil. A general framework for the optimal approximation of circular arcs by parametric polynomial curves. Journal of Computational and Applied Mathematics. 2019, let. 345, str. 146-158. [COBISS-SI-ID 18388057]
KANDIĆ, Marko, VAVPETIČ, Aleš. Topological aspects of order in C(X). Positivity. 2019, let. 23, št. 3, str. 617-635. [COBISS-SI-ID 18551897]
VAVPETIČ, Aleš. Commutators of cycles in permutation groups.
Ars mathematica contemporanea. 2016, let. 10, št. 1, str. 67-77. [COBISS-SI-ID 17731929]