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.
NIE-HMI History of Mathematics and Informatics Extent of teaching: 2P+1C Instructor: Šolcová A. Completion: Z,ZK Department: 18105 Credits: 3 Semester: Z Annotation:
The course focuses on selected topics from calculus, general algebra, number theory, numerical mathematics and logic - useful for today computer science The topics are selected for finding some relations between computer science and mathematical methods. Some examples of applications of mathematics to computer sciences will be showed.
Lecture syllabus:
Mathematics in the celestial mechanics. From J. Keplera and P. Laplace to A. Seydler.
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. Combinatorics in "kabbala". The applications in the number theory.
3. Descartes' "Discourse de la Méthode". Algorithms of arithmetic operations, Leibniz and Pelikán binary arithmetics. 4. The oldest mechanical calculators. Schickard, Pascal, Leibniz. (Cramer Rule, Gauss Elimination Method, Least Square Method, Jacobi and Seidel Method, Cauchy and unlinear epilogue).
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. Development of the number systems and its applications: Complex numbers, Hamilton's quaternions.
8. Number Theory (Gauss congruence, factorization algorithms, Pépin's test). Change of dimension - Abbot's Flatland, 100 years of hypercube, Hermann Minkowski.
9. General algebra - Symmetries and searching for Lie groups. E. Galois. Eliptic curves from Adam. The development of the typography. (A. Duerer, D. Knuth, etc.).
10. From mathematical linguistic (kvantitative, algebraic, computer linguistic). From logic of the 20th Century: A. Whitehead, B. Russel - Principia mathematica, K. Gödel, S. C. Kleene - recursive functions.
11. The 19th Century in Computer Science - Analytical Engine, Charles Babbage, Ada Byron. History of the Czech Technical University in Prague.
12. Mathematics, informatics and the development of computer science. Computers in the 20th Century. A. Svoboda and V. Vand, its ideas and applications.
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:
And some internet sources, etc.
1. Chabert, J.-L. et all: A History of Algorithms. From the Pebble to the Microchip, Springer, Berlin-Heidelberg-New York, 1999 2. Graham, R., Knuth, D., Patashnik, O.: 'Concrete Mathematics: A Foundation for Computer Science', Addison-Wesley, Reading, Mass., 1989. 3. Lovász, L.: 'Combinatorial Problems and Exercises', 2nd Ed., Akademiai Kiadó Budapest and North- Holland, Amsterdam, 1993. 4. Schroeder, R. M.: ''Number Theory in Science and Communication'', Springer, Berlin, 2006. 5. Křížek, M., Luca, F., Somer, L.: ''17 Lectures on Fermat Numbers: From Number Theory to Geometry'', Springer, New York, 2001 6. Bentley, P. J.: The Book of Numbers, Octopus Publishing Group, 2008. 7. Pickover, C. A. Mathematical Book. 2009 8. Crilly, T.: Mathematics 50 Mathematical Ideas You Really to Know, Quercus, 2007. Requirements:
Knowledge of high school mathematics and of basic courses at the faculty and an ability to solve concrete basic tasks from mathematics and informatics.
Information about the course and courseware are available at https://moodle.fit.cvut.cz/courses/MIE-HMI/ The course is also part of the following Study plans:
Study Plan Study Branch/Specialization Role Recommended semester NIE-SI.21 Software Engineering 2021 V Není NIE-TI.21 Computer Science 2021 V Není NIE-DBE.2023 Digital Business Engineering V Není NIE-NPVS.21 Design and Programming of Embedded Systems 2021 V Není NIE-PSS.21 Computer Systems and Networks 2021 V Není NIE-PB.21 Computer Security 2021 V Není
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