Bachelor
2021/2022

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

Type:
Elective course (Economics)

Area of studies:
Economics

Delivered by:
Department of Mathematics

When:
1 year, 1, 2 module

Mode of studies:
offline

Open to:
students of one campus

Instructors:
Alexandra Grinikh

Language:
English

ECTS credits:
3

Contact hours:
30

### 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 1Individual 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 2Individual 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.
- TestUpon the decision of the seminar professor, control work may consist of auditorian work and extracurricular activities, according to the agreement of seminar professors and lecturer control work is carried out for the whole student flow on the platform of Smart LMS. The control work is conducted remotely in writing. The control work must be completed in 80 minutes and students have 10 minutes for loading the tasks. Work is conducted on the SmartLMS platform with additional use of Zoom or MS Teams. The control work session must be started 15 minutes before the start, upon the teacher’s signal to start solving tasks in SmartLMS. The student’s computer must meet the following requirements: presence of a working camera and microphone, high-speed Internet, support Zoom/MS Teams. The answers to the task must be written on white paper sheets A4, with a black pen, the sheets must be numbered, and when it is specified in the task, the answers must be additionally entered in the answer window. After finishing the control work,students must take a photo/scan his decision and upload it to SmartLMS. The photos should be vertical so that the text is not blurred and read unambiguously. The answers and the task numbers should be selected. The camera and microphone must be switched on during the whole work. The camera must be positioned side-by-side or frontally from itself in such a way that it is aimed at the working field - the sheet on which the work is performed - on the student and the space around the student (the room must be well lit). It is permitted to use the login to Zoom / MS Teams from a mobile phone with its camera. At the professor’s request, the student is obliged to switch to the transmission of his screen: turn on the back camera of the mobile phone or turn the phone to the computer screen within 5 seconds, or start a display of the screen. You cannot leave the room during inspection work. On the table you can have only writing accessories, no pencils, blank sheets of paper and water. The presence of any media around the workplace of the student, as well as other people, is considered as a violation and ends with the removal of the student from work and with a score of «0». Students are not allowed to turn off the camera and microphone during the test: until the end of the control work, the video and sound must remain active, including time to scan the completed work and send it for inspection. A short-term interruption of communication during control work is considered to be less than 5 minutes and not more than once. Long-term disruption of communication during control work is considered to be a 5-minute or more disruption. In case of a long-term disruption of communication, the student may continue to participate in the writing of the work at the professor’s discretion.
- ExamThe exam is conducted remotely on the platform of Smart LMS in writing. The examk must be completed in 90 minutes and students have 15 minutes for loading the tasks. The exam is conducted on the SmartLMS platform with additional use of Zoom or MS Teams. The exam session must be started 15 minutes before the start, upon the teacher’s signal to start solving tasks in SmartLMS. The student’s computer must meet the following requirements: presence of a working camera and microphone, high-speed Internet, support Zoom/MS Teams. The answers to the task are written on white paper sheets A4, with a black pen, the sheets must be numbered, and when it is specified in the task, the answers must be additionally entered in the answer window. After finishing the exam,students must take a photo/scan his decision and upload it to SmartLMS. The photos should be vertical so that the text is not blurred and read unambiguously. The answers and the task numbers should be selected. The camera and microphone shall be switched on during the whole exam. The camera must be positioned side-by-side or frontally from itself in such a way that it is aimed at the working field - the sheet on which the work is performed - on the student and the space around the student (the room must be well lit). It is permitted to use the login to Zoom / MS Teams from a mobile phone with its camera. At the professor’s request, the student is obliged to switch to the transmission of his screen: turn on the back camera of the mobile phone or turn the phone to the computer screen within 5 seconds, or start a display of the screen. Students cannot leave the room during the inspection exam. On the table students can have only writing accessories, no pencils, blank sheets of paper and water. The presence of any media around the workplace of the student, as well as other people, is considered as a violation and ends with the removal of the student from the exam and with a score of «0». Students are not allowed to turn off the camera and microphone during the exam: until the end of the exam, the video and sound must remain active, including time to scan the completed work and send it for inspection. A short-term interruption of communication during control work is considered to be less than 5 minutes and not more than once. Long-term disruption of communication during exam is considered to be a 5-minute or more disruption. In case of a long-term disruption of communication, the student may continue to participate in the writing of the exam at the professor’s discretion.
- Quiz

#### Interim Assessment

- 2021/2022 2nd module0.12 * Quiz + 0.1 * Individual homework 2 + 0.24 * Test + 0.1 * Individual homework 1 + 0.44 * Exam

#### Bibliography

#### 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

#### Recommended Additional Bibliography

- Путко Б.А., Тришин И.М., Кремер Н.Ш. - под ред. - МАТЕМАТИЧЕСКИЙ АНАЛИЗ В 2 Т. Учебник и практикум для академического бакалавриата - М.:Издательство Юрайт - 2016 - 634с. - ISBN: 978-5-9916-6238-3 - Текст электронный // ЭБС ЮРАЙТ - URL: https://urait.ru/book/matematicheskiy-analiz-v-2-t-388079