History of Mathematics and Informatics

Garant předmětu:

Alena Šolcová

Přednášející:

Alena Šolcová

Cvičící:

Alena Šolcová

Předmět zajišťuje:

katedra aplikované matematiky

Anotace:

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.

Požadavky:

Osnova přednášek:

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. Descartes' 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

Osnova cvičení:

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.

Cíle studia:

Mathematics as a language for description of the world is a key discipline for an informatics engineer. The aim of this module is introduce students to the relevant parts of history of mathematics that form the theoretical background of many informatics disciplines, and to find wth students suitable mathematical methods applicable in computer science.

Studijní materiály:

1. Naumann, F.: Dějiny informatiky. Od abaku k internetu. Academia, Praha, 2009.

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

Poznámka:

Information about the course and courseware are available at https://moodle-vyuka.cvut.cz/course/search.php?search=BI-HMI

Další informace:

https://moodle-vyuka.cvut.cz/course/search.php?search=BI-HMI

Rozvrh na zimní semestr 2024/2025:

Rozvrh není připraven

Rozvrh na letní semestr 2024/2025:

Rozvrh není připraven

Předmět je součástí následujících studijních plánů:

• Bachelor branch Security and Information Technology, in English, 2015-2020 (povinně volitelný humanitní předmět)
• Bachelor branch Web and Software Engineering, spec. Software Engineering, in English, 2015-2020 (povinně volitelný humanitní předmět)
• Bachelor branch Computer Science, in English, 2015-2020 (povinně volitelný humanitní předmět)
• Bachelor branch Computer Science, in English, 2015-2020 original version (povinně volitelný humanitní předmět)