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A course is the basic teaching unit, it's design as a medium for a student to acquire comprehensive knowledge and skills indispensable in the given field. A course guarantor is responsible for the factual content of the course.
For each course, there is a department responsible for the course organisation. A person responsible for timetabling for a given department sets a time schedule of teaching and for each class, s/he assigns an instructor and/or an examiner.
Expected time consumption of the course is expressed by a course attribute extent of teaching. For example, extent = 2 +2 indicates two teaching hours of lectures and two teaching hours of seminar (lab) per week.
At the end of each semester, the course instructor has to evaluate the extent to which a student has acquired the expected knowledge and skills. The type of this evaluation is indicated by the attribute completion. So, a course can be completed by just an assessment ('pouze zápočet'), by a graded assessment ('klasifikovaný zápočet'), or by just an examination ('pouze zkouška') or by an assessment and examination ('zápočet a zkouška') .
The difficulty of a given course is evaluated by the amount of ECTS credits.
The course is in session (cf. teaching is going on) during a semester. Each course is offered either in the winter ('zimní') or summer ('letní') semester of an academic year. Exceptionally, a course might be offered in both semesters.
The subject matter of a course is described in various texts.

NI-HMI2 History of Mathematics and Informatics Extent of teaching: 2P+1C
Instructor: Šolcová A. Completion: ZK
Department: 18105 Credits: 3 Semester: Z

Annotation:
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.

Lecture syllabus:
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.).

Seminar syllabus:
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.

Literature:
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.

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.

Informace o předmětu a výukové materiály naleznete na https://moodle-vyuka.cvut.cz/course/view.php?id=2237

The course is also part of the following Study plans:
Study Plan Study Branch/Specialization Role Recommended semester
NI-PB.2020 Computer Security V Není
NI-ZI.2020 Knowledge Engineering V Není
NI-SPOL.2020 Unspecified Branch/Specialisation of Study V Není
NI-TI.2020 Computer Science V Není
NI-TI.2023 Computer Science V Není
NI-NPVS.2020 Design and Programming of Embedded Systems V Není
NI-PSS.2020 Computer Systems and Networks V Není
NI-MI.2020 Managerial Informatics V Není
NI-SI.2020 Software Engineering (in Czech) V Není
NI-SP.2020 System Programming V Není
NI-WI.2020 Web Engineering V Není
NI-SP.2023 System Programming V Není


Page updated 29. 3. 2024, semester: L/2021-2, Z,L/2023-4, Z/2021-2, Z/2020-1, Z/2019-20, L/2020-1, Z,L/2022-3, L/2019-20, Send comments to the content presented here to Administrator of study plans Design and implementation: J. Novák, I. Halaška