History of Mathematics and Informatics

Course guarantor:

Alena Šolcová

Lecturer:

Alena Šolcová

Tutor:

Alena Šolcová

Supervisor:

Department of Applied Mathematics

Synopsis:

This course is presented in Czech. Selected topics {Infinitesimal calculus, probability, number theory, general algebra, different examples of algorithms, transformations, recursive functions, eliptic curves, etc.) note on possibilities of applications of some mathematical methods in informatics and its development.

Requirements:

The course is completed by exam consisting from 2 parts.

1. The written part: 10 questions from topics of lectures and excercises.

2. The oral part: Discussion on seminary work - essay (4-5 prepared pages of text and presentation

We recommend completing course Bi HMIin the bachelor study programm, but it is not necessary.

Syllabus of lectures:

1. Mathematics in the 17th Century. First steps of Calculus - Newton, Leibniz. Sources in Greek mathematics - introduction to the programme of course.

2. The role of Pierre Fermat in the probability theory.

Mathematics in the celestial mechanics. From J. Keplera and P. Laplace to A. Seydler.

3. Descartes' „Discourse de la Méthode“. Algorithms of arithmetic operations, Leibniz and Pelikán binary arithmetics.

4. The oldest mechanical calculators. Schickard, Pascal, Leibniz.

Combinatorics in „kabbala“. The applications in the number theory.

5. The Pell equation and the development of algebra. Lagrange's results and its applications.

6. Mathematics of the 18th Century: Approximations of functions - L. Euler, Ch. Fourier, FFT (Fast Fourier Transform).

7. Solution of the system of the linear equations.

(Cramer Rule, Gauss Elimination Method, Least Square Method, Jacobi and Seidel Method, Cauchy and unlinear epilogue).

8. Number Theory (Gauss congruence, factorization algorithms, Pépin's test).

Development of the number systems and its applications: Complex numbers, Hamilton's quaternions.

9. General algebra - Symmetries and searching for Lie groups. E. Galois. Eliptic curves from Adam.

Change of dimension - Abbot's Flatland, 100 years of hypercube, Hermann Minkowski.

10. From mathematical linguistic (kvantitative, algebraic, computer linguistic).

The development of the typography. (A. Duerer, D. Knuth, etc.).

11. The 19th Century in Computer Science - Analytical Engine, Charles Babbage, Ada Byron.

From logic of the 20th Century: A. Whitehead, B. Russel - Principia mathematica, K. Gödel, S. C. Kleene - recursive functions.

12. Mathematics, informatics and the development of computer science. Computers in the 20th Century. A. Svoboda and V. Vand, its ideas and applications.

History of the Czech Technical University in Prague.

13. On the character of matematical thinking - H. Poincaré. Hilbert's problems for the 20th Century and opem problems for the 21st Century (Kepler hypothesis, etc.).

Syllabus of tutorials:

1. Methodological introduction and work with historical sources in exact sciences.

2. Interesting calculus, joy of solving, discussion on individual essays.

3. Descartes questions and problems. An introduction to the Leibniz binary system of numbers. „Arithmeticus perfectus“ of Václav Josef Pelikán (1713).

4..Mathematical Topography of Prague. First computers in Prague. (A lecture in the streets.)

5. Bernoulli numbers, their properties and Ada Lovelace. Approximations of functions.

6. Boolean algebra and Boole's Mathematical Analysis of Logic. Brief development of symbols and description of algorithms. A presentation of student's individual works.

Study Objective:

Mathematics as language for description of cosmos is for engineers of informatics the key discipline. The goal of this course is to introduce students with significant relevant parts of history of mathematics, which create base of a serie of informatic disciplines and discover together with students suitable mathematical methods for use in informatics. By solving tasks we want to stimulate and expand the imagination and ability of abstraction, which is necessary for independent creative work.

Study materials:

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

7. Bentley, P. J.: Kniha o číslech, REBO Productions, 2013 (Z anglického originálu The Book of Numbers, Octopus Publishing Group, 2008, přeložil M. Chvátal).

8. Pickover, C. A. Mathematická kniha. Od Pýthagora po 57. dimenzi: 250 milníků v dějinách matematiky, Argo/Dokořán, 2012

(Z anglického originálu a roku 2009, přeložil Petr Holčák)

9. Crilly, T.: Matematika: 50 myšlenek, které musíte znát, Slovart, Praha 2010 (Z anglického originálu 50 Mathematical Ideas You Really to Know, Quercus, 2007, přeložil Jozef Koval.)

a další dle doporučení přednášející.

Note:

Further information:

https://moodle-vyuka.cvut.cz/course/view.php?id=2237

Time-table for winter semester 2024/2025:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
Wed	roomTH:A-1247 Šolcová A. 11:00–12:30 (lecture parallel1) Thákurova 7 (budova FSv) roomTH:A-1242 Šolcová A. 16:15–17:45 ODD WEEK (lecture parallel1 parallel nr.101) Thákurova 7 (budova FSv)
Thu
Fri

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Master specialization Computer Security, in Czech, 2020 (elective course)
• Master specialization Design and Programming of Embedded Systems, in Czech, 2020 (elective course)
• Master specialization Computer Systems and Networks, in Czech, 202 (elective course)
• Master specialization Management Informatics, in Czech, 2020 (elective course)
• Master specialization Software Engineering, in Czech, 2020 (elective course)
• Master specialization System Programming, in Czech, version from 2020 (elective course)
• Master specialization Web Engineering, in Czech, 2020 (elective course)
• Master specialization Knowledge Engineering, in Czech, 2020 (elective course)
• Master specialization Computer Science, in Czech, 2020 (elective course)
• Mgr. programme, for the phase of study without specialisation, ver. for 2020 and higher (elective course)
• Study plan for Ukrainian refugees (elective course)
• Master specialization System Programming, in Czech, version from 2023 (elective course)
• Master specialization Computer Science, in Czech, 2023 (elective course)