Terms for 2017
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Entertaining mathematics 2
The aim is to expand the courses Mathematics 1 and Mathematics 2 on the basics of some interesting areas of mathematics that compulsory courses doesn´t offered, but they also provide an interesting and often very entertaining view at the math. Additionally, students can find new effective tools to solve certain tasks or find a completely different way of viewing and displaying some issues. The course is intended primarily for students of second and third grade who have successfully completed courses Entertaining mathematics 1 and Entertaining mathematics 2.
What are you going to learn
Interesting numbers and various kinds of infinite - numbers based on prime numbers, perfect numbers, the Fibonacci sequence.
From geometry to topology - Combinatorial study of an area, seven bridges of Konigsberg, introduction to topology, homeomorphismus, dimension of surfaces, topological invariants.
Symmetry and chaos - The relationship of symmetry and mathematics, finding the structure in the chaos, the elements and operations of symmetry, discrete symmetry, theory of groups, spatial symmetry, Cantor set, fractals and their utilization.
Introduction to the theory of knots - Knots in math, comparison of knots, Reidemeister moves of knots, knots classification, crossing.
Something more about logics - Logics, reasoning, premises and conclusions, deductive validity, quantifiers, self-reference, inductive validity.
Calculus and Geometry - Region of the surface and integrals, order of differentials and its importance, double integral and its significance.
How the course is organized
Full time study
Course is organized in 12 lectures, each one 1.5 hours.
Part time study
The course is taught only in full time study form for part time students.
STAHL, S.: Geometry from Euclid to Knots, Dover Publications, 2012.
STAHL, S., STENSON, C.: Introduction to Topology and Geometry, Dover Publications, 2013.
EVEREST, G., WARD, T.: An introduction to number theory, Springer, 2006.
STEWART, I.: Symmetry: A very short Introduction. Oxford Univerzity Press, 2013.
FELDMAN, D. P.: Chaos and Fractals: An Elementary Introduction, Oxford Univerzity Press, 2012.