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Introduction to Arithmetics and Algebra II - NMUM105

Title:	Základy aritmetiky a algebry I
Guaranteed by:	Department of Mathematics Education (32-KDM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2012 to 2015
Semester:	winter
E-Credits:	2
Hours per week, examination:	winter s.:1/1, colloquium [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
Teaching methods:	full-time

Guarantor:	doc. RNDr. Jindřich Bečvář, CSc. RNDr. Eliška Pecinová, 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

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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.

Literature -

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

Hruša, K. Elementární aritmetika. Přírodovědecké nakladatelství, Praha, 1953.

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

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

Hruša, K., Kraemer, E., Sedláček, J., Vyšín, J., Zelinka, R.: Přehled elementární matematiky. SNTL, Praha, 1964.

Aritmetika pro první, …, čtvrtou třídu středních škol. Státní nakladatelství, Praha, 1950.

Algebra pro devátý až jedenáctý postupný ročník. SPN, Praha, 1954.

Katriňák, T. Algebra a teoretická aritmetika (1). Alfa, SNTL, 1985.

Šalát, T. Algebra a teoretická aritmetika (2). Alfa, SNTL, 1986.

Kořínek, V. Základy algebry. ČSAV, Praha, 1953 (2. vydání, 1956).

Klein, F. Elementary Mathematics from an Advanced Standpoint. Arithmetic, Algebra, Analysis. Cosimo Classics, 2009.

Courant, R., Robbins, H., Stewart, I. What Is Mathematics? An Elementary Approach to Ideas and Methods. Oxford University Press, 1996.

Schwarz, Š. Základy náuky o riešení rovníc. SAV, Bratislava, 1967 (2. vydání, 1968).

Hruša, K. a kol. Přehled elementární matematiky. 4., nezměněné vyd., SNTL, Praha, 1964.

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.