Introduction to Arithmetics and Algebra II - NMUM206
Title: Základy aritmetiky a algebry II
Guaranteed by: Department of Mathematics Education (32-KDM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
Semester: summer
E-Credits: 2
Hours per week, examination: summer s.:1/1, colloquium [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: cancelled
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 : NMTM206, NMUM809
Pre-requisite : NMUM105
Interchangeability : NMTM206, NMUM809, NUMP019
Is incompatible with: NUMZ011, NMTM206, NUMP019
Is interchangeable with: NMTM206, NUMP019, NUMZ011, NMUE033
Opinion survey results   Examination dates   Schedule   Noticeboard   
Annotation -
Introductory course devoted to the elements of arithmetics and algebra, especially to basic results on number systems, operations, sequences, and elementary functions.
Last update: T_KDM (15.09.2013)
Course completion requirements -

The condition for obtaining credit is successful completion of two written tests.

The final exam verifies practical and theoretical knowledge and skills,

i.e. understanding of concepts (definitions), understanding of knowledge (theorems),

understanding mathematical argumentation (proofs), mastering numerical procedures (examples).

Final exam consists of:

  • written test (120 minutes), it is possible to use a separate calculator (not on mobile).

It is necessary to demonstrate understanding of all topics discussed during the semester.

  • portfolio evaluation.

Last update: Halas Zdeněk, Mgr., DiS., Ph.D. (29.10.2019)
Literature -

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

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

Last update: T_KDM (15.09.2013)