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Course, academic year 2019/2020
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Introduction to Arithmetics and Algebra II - NMUM105
Title in English: Základy aritmetiky a algebry I
Guaranteed by: Department of Mathematics Education (32-KDM)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019
Semester: winter
E-Credits: 2
Hours per week, examination: winter s.:1/1 colloquium [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: not 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 > 1. 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 : NMTM105
Interchangeability : NMTM105
Is pre-requisite for: NMUM206
Annotation -
Last update: T_KDM (23.04.2012)
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.
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: Mgr. Zdeněk Halas, DiS., Ph.D. (14.06.2019)
  • 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.

 
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