Arithmetic and algebra I - NMTM105
Title: Aritmetika a algebra I
Guaranteed by: Department of Mathematics Education (32-KDM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2021
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/1, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: Mgr. Zdeněk Halas, DiS., Ph.D.
doc. RNDr. Jindřich Bečvář, CSc.
Teacher(s): Mgr. Zdeněk Halas, DiS., Ph.D.
Incompatibility : NMUM105
Interchangeability : NMUM105
Is incompatible with: NMUM105
Is interchangeable with: NMUM105
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Annotation -
An introductory course and seminar whose aim is to provide a firm foundation for arithmetic and algebra. It focuses especially on number sets, operations, ordering, and linear and quadratic equations.
Last update: Staněk Jakub, RNDr., Ph.D. (14.06.2019)
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 -

Basic literature:

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

Supplementary literature:

Stanovský D.: Základy algebry. Matfyzpress, Praha, 2010.

Blažek J. a kol.: Algebra a teoretická aritmetika I. SPN, Praha, 1983.

Blažek J. a kol.: Algebra a teoretická aritmetika II. SPN, Praha, 1985.

Katriňák T. a kol.: Algebra a teoretická aritmetika I. Alfa, Bratislava, 1985.

Šalát T. a kol.: Algebra a teoretická aritmetika II. Alfa, Bratislava, 1986.

Last update: Halas Zdeněk, Mgr., DiS., Ph.D. (14.06.2019)
Syllabus -
  • Natural numbers. The path from natural numbers to integers. Operations and their properties. Ordering and its properties. Divisibility. The basic theorem of arithmetic.
  • The path from integers to rational numbers. Operations and their properties. Ordering and its properties. Decimal expansions.
  • Incommensurability, irrationality. The path to real numbers. Decimal expansions. Ordering. Real axis.
  • Arithmetic, geometric and harmonic mean.
  • Calculating with letters. Algebraic expressions and their transformations. Algebraic formulas and their geometric interpretation.
  • Linear equations and their geometric meaning. Quadratic equations and their solvability. Vièta's formulas.
  • Complex numbers as pairs of real numbers, their algebraic and geometric form. Derivation of trigonometric formulas. Gaussian numbers. Dual numbers.

Last update: Halas Zdeněk, Mgr., DiS., Ph.D. (14.06.2019)