History of Mathematics and Informatics
Code  Completion  Credits  Range  Language 

MIEHMI  Z,ZK  3  2P+1C  English 
 Garant předmětu:
 Lecturer:
 Tutor:
 Supervisor:
 Department of Applied Mathematics
 Synopsis:

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.
 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.
 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:

To know some important relations between mathematical methods and computer science through history. To get an overview of basic steps in the development of mathematical methods and computer science.
 Study materials:

1. Chabert, J.L. et all: A History of Algorithms. From the Pebble to the Microchip, Springer, BerlinHeidelbergNew York, 1999
2. Graham, R., Knuth, D., Patashnik, O.: 'Concrete Mathematics: A Foundation for Computer Science', AddisonWesley, 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.
And some internet sources, etc.
 Note:
 Further information:
 https://moodle.fit.cvut.cz/courses/MIEHMI/
 No timetable has been prepared for this course
 The course is a part of the following study plans: