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Course, academic year 2019/2020
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Introduction to Arithmetics and Algebra II - NMUM206
Title in English: Základy aritmetiky a algebry II
Guaranteed by: Department of Mathematics Education (32-KDM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2018
Semester: summer
E-Credits: 2
Hours per week, examination: summer s.:1/1 colloquium [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Additional information: http://www.karlin.mff.cuni.cz/~becvar/
Guarantor: Mgr. Zdeněk Halas, DiS., Ph.D.
Class: M Bc. MZV
M Bc. MZV > Povinné
M Bc. MZV > 2. ročník
Classification: Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Incompatibility : NMUM809
Pre-requisite : NMUM105
Interchangeability : NMUM809, NUMP019
Annotation -
Last update: T_KDM (15.09.2013)
Introductory course devoted to the elements of arithmetics and algebra, especially to basic results on number systems, operations, sequences, and elementary functions.
Course completion requirements - Czech
Last update: Mgr. Zdeněk Halas, DiS., Ph.D. (07.06.2019)

Kolokvium prověřuje praktické i teoretické znalosti a dovednosti, tj. porozumění pojmům (definice), porozumění poznatkům (věty),

porozumění matematickému odvozování a zdůvodňování (důkazy), ovládnutí početních postupů (příklady),

formulační dovednosti (vyjadřování slovem a písmem s využitím matematické symboliky).

Kolokvium je písemné (120 minut), je možno užívat samostatnou kalkulačku (ne v mobilu).

Je třeba prokázat porozumění všem tématům probíraným v průběhu semestru.

Literature -
Last update: doc. RNDr. Jindřich Bečvář, CSc. (07.10.2017)

V. Dlab, J. Bečvář: Od aritmetiky k abstraktní algebře, Serifa, Praha, 2016.

Syllabus -
Last update: T_KDM (15.09.2013)
  • Various types of algebraic equations.
  • Algebraic aspects of number systems. Binary operations and their properties. Structures and substructures.
  • Quaternions, octonions.
  • Sequences and series. Boundedness, convergence, divergence.
  • Arithmetic and geometric sequences, geometric series. Harmonic series.
  • Reals numbers as limits of sequences.
  • Elementary functions.
  • Cardinalities of number systems.

 
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