Description:

Students will master the methods traditionally used in mathematics and related disciplines - informatics - from different periods of the development of mathematics, and will thus become acquainted with mathematical methods suitable for applications in contemporary computer science.

Contents:

1. Introduction. Problems and methods of the history of mathematics and informatics.

2. Mathematics in the oldest civilizations. Numeration. Numerical systems.

3. Encyclopedia of the Ancient times: Eukleid's Foundations. Mathematics in Hellenism.
4. The oldest computer aids. Archimedes and stomachion, Pick's theorem

5. Solving equations and their systems. Mathematics in the Renaissance.

6. Types of evidence: least descent method, mathematical induction. Fermat's discoveries.

7. Descarts' Debate on Method and Analytical Geometry. Mathematics at the beginning of Modern Times.
8. Beginnings of infinitesimal count. W. G. Leibniz and I. Newton. Problems with infinity.

9. Variation methods and optimization.Calculations of planes of planets and small bodies of the solar system and least square method.
10. The oldest mechanical calculators. Charles Babbage and Ada Lovelace

11. Development of combinatorics and discrete mathematics.

12. Gauss Number Theory and its further development

13. Approximation, convergence and computer speed. Alan Turing and Algorithm Concept

Seminar contents:

1 hour a week or 2 hours, once every 14 days - will be linked to the theme presented in the lecture. Specific tasks will be solved, students will prepare for independent work, work with sources.

Recommended literature:

1. Naumann, F.: Dějiny informatiky. Od abaku k internetu. Academia, Praha, 2009. (also in German).
2. Chabert, J.-L. et all: A History of Algorithms. From the Pebble to the Microchip, Springer, Berlin-Heidelberg-New York, 1999
3. Graham, R., Knuth, D., Patashnik, O.: ''Concrete Mathematics: A Foundation for Computer Science'', Addison-Wesley, Reading, Mass., 1989.
4. Lovász, L.: ''Combinatorial Problems and Exercises'', 2nd Ed., Akademiai Kiadó Budapest and North- Holland, Amsterdam, 1993.
5. Schroeder, R. M.: ''Number Theory in Science and Communication'', Springer, Berlin, 2006.
6. Křížek, M., Luca, F., Somer, L.: ''17 Lectures on Fermat Numbers: From Number Theory to Geometry'', Springer, New York, 2001.

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar