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Course, academic year 2018/2019
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Introduction to the history of early modern mathematics - NMAG168
Title in English: Úvod do dějin novověké matematiky
Guaranteed by: Department of Algebra (32-KA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018 to 2018
Semester: summer
E-Credits: 3
Hours per week, examination: summer s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: prof. RNDr. Ladislav Kvasz, DSc., Dr.
Annotation -
Last update: JUDr. Dana Macharová (21.12.2015)
The goal of the course is on the example of three disciplines -- geometry, algera and mathematical analysis -- to illustrate the changes in the understanding of the fundamental notions of mathematics during the 16th, 17th and 18the centuries. That enables us to understand the motives of the creation of modern abstract mathematics based on the abstract notions of space, group and continuity.
Course completion requirements - Czech
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (11.06.2019)

Předmět je zakončen napsáním eseje.

Literature -
Last update: JUDr. Dana Macharová (21.12.2015)

Courant, R a Robbins, H. (1942): What is mathematics?

Struik, D. J. (1963): Dějiny matematiky.

Kline, M. (1972): Mathematical thought from ancient to modern time.

Edwards, C. H. (1979): The historical development of the calculus

Gray, J. (1979): Ideas of space, Euclidean, non-Euclidean and

relativistic

van der Waerden, B. L. (1985): A history of algebra

Fauvel, J. a Gray, J. (1987): The history of mathematics: A reader

Jahnke, H. N. (ed. 1999): Historie analýzy. Český překlad 2011.

Různé díly edice Dějiny matematiky, vydávané na MFF UK

Requirements to the exam - Czech
Last update: doc. Mgr. et Mgr. Jan Žemlička, Ph.D. (11.06.2019)

Předmět je zakončen napsáním eseje na vybrané téma z historie matematiky.

Syllabus -
Last update: JUDr. Dana Macharová (21.12.2015)

1. The origin of the concept of space in Renaissance painting and its

transfer into projective geometry

2. Origins and some interesting results of non-Euclidean geometry

3. The origin of the concept a model, Beltrami-Klein's model and Klein's

classification geometries

4. The birth of algebra and the lengthy journey to standardized

algebraic

symbolism

5. Solving algebraic equations of the 3rd and 4th degree by Cardano, and

the notion of a resolvent

6. Origins of complex numbers and the fundamental theorem of algebra

7. The proof of insolvability of the problem of trisecting an angle,

duplicating the cube and constructing of a regular heptagon

8. The birth of the concept of a group and the proof insolvability of

the

general equation of the fifth degree.

9. The emergence of the concept of integral and the discovery of its

relation to differentiation.

10. Infinite series as approximations tools and as means to define new

functions

11. Euler and infinite series in the complex domain

12. The concept of fractals and the notion of a fractional dimension

 
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