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# Algebra and Pre-Calculus: Introductory Course (Low Level)

2021/2022
ENG
Instruction in English
3
ECTS credits
Course type:
Elective course
When:
1 year, 1, 2 module

### Course Syllabus

#### Abstract

The discipline «Algebra and analysis: introductory course (base level)» has a purpose to study the following sections: «Sets and functions», «Vectors », «Straight line on the plane and in space. The plane in space», «Complex numbers» and «Polynomials and rational fractions». This subject allows one to further master the educational disciplines, such as «Linear algebra», «Mathematical analysis-I», «Mathematical analysis-II», «Microeconomics», «Macroeconomics», «Econometrics». The course of "Algebra and Analysis: Introductory course (basic level)" will be approached in the theory and application of the disciplines of the economics cycle. The course materials can be used to construct and study mathematical models in various subject areas, primarily in economics.

#### Learning Objectives

• The goal of the course is study of the sections “Sets and functions”, “Vectors”, “Straight line on a plane and in a space. A plane in a space”, “Complex numbers” and “Polynomials and rational fractions” that allow to further understanding of the following courses: “Linear algebra”, “Mathematical analysis-I”, “Mathematical analysis-II”, “Microeconomics”, “Macroeconomics”, “Econometrics”

#### Expected Learning Outcomes

• Acquirement of competence to find a domain, set of values of a function, to investigate a function on monotonicity, even/odd, periodicity.
• Acquirement of the ability to apply basic operations over vectors to solve practical and geometric problems
• Acquirement of the ability to apply Bézout's and Descartes' theorems to specific polynomials, and to factor them into factors. Isolate an entire part from a rational fraction. Represent the correct rational fraction in the sum of the simplest fractions.
• Acquirement of the ability to work with complex numbers in an arbitrary form of writing, to solve algebraic equations with complex numbers, to perform arithmetic operations of elevation to degree and root extraction.
• The knowledge and understanding of basic elementary functions, the ability to construct graphs of elementary functions by means of basic transformations on a plane.
• The knowledge and understanding of the concept of the equation of a straight line in the plane, the ability to create the equation of a line, to construct a graph of a straight line, to apply conditions of mutual arrangement of lines in the plane in solving geometric and economic problems.
• The knowledge and understanding of the module, solving of equations and inequalities using the properties of the module

#### Course Contents

• Sets and functions
• Vectors in R^n
• Straight line on the plane and in space. The plane in space
• Complex numbers
• Polynomials and rational fractions

#### Assessment Elements

• Individual homework 1
Individual homework 1 consists of tasks on the topic "Sets and mappings". There are three days to complete the assignment.The completed homework 1 should be scanned and attached to SmartLMS. When students specify a task, the answers must be entered into the system. Upon the decision of the seminar professor, some individual homework may consist of auditorian work and extracurricular activities.
• Individual homework 2
Individual homework 2 consists of tasks on the topics "Complex numbers" and "Polynomials and rational fractions". There are three days to complete the assignment. Assignment options are provided on the SmartLMS platform. The completed homework 2 should be scanned and attached to SmartLMS. When students specify a task, the answers must be entered into the system. Upon the decision of the seminar professor, some individual homework may consist of auditorian work and extracurricular activities.
• Test
• Exam
• Quiz

#### Interim Assessment

• 2021/2022 2nd module
0.12 * Quiz + 0.1 * Individual homework 2 + 0.24 * Test + 0.1 * Individual homework 1 + 0.44 * Exam

#### Recommended Core Bibliography

• Ильин В.А., Садовничий В.А., Сендов Б.Х. - МАТЕМАТИЧЕСКИЙ АНАЛИЗ Ч. 1 4-е изд., пер. и доп. Учебник для бакалавров - М.:Издательство Юрайт - 2016 - 660с. - ISBN: 978-5-9916-2733-7 - Текст электронный // ЭБС ЮРАЙТ - URL: https://urait.ru/book/matematicheskiy-analiz-ch-1-389342
• Кудрявцев Л. Д. - КУРС МАТЕМАТИЧЕСКОГО АНАЛИЗА В 3 Т. ТОМ 1 6-е изд., пер. и доп. Учебник для бакалавров - М.:Издательство Юрайт - 2019 - 703с. - ISBN: 978-5-9916-3701-5 - Текст электронный // ЭБС ЮРАЙТ - URL: https://urait.ru/book/kurs-matematicheskogo-analiza-v-3-t-tom-1-425369