History of Mathematics and Informatics

Course guarantor:

Alena Šolcová

Lecturer:

Alena Šolcová

Tutor:

Alena Šolcová

Supervisor:

Department of Applied Mathematics

Synopsis:

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.

Requirements:

Syllabus of lectures:

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

Syllabus of tutorials:

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.

Study Objective:

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.

Study materials:

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.

Note:

Further information:

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

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Bachelor branch Security and Information Technology, in English, 2015-2020 (compulsory elective humanities course)
• Bachelor branch Web and Software Engineering, spec. Software Engineering, in English, 2015-2020 (compulsory elective humanities course)
• Bachelor branch Computer Science, in English, 2015-2020 (compulsory elective humanities course)
• Bachelor branch Computer Science, in English, 2015-2020 original version (compulsory elective humanities course)