1. Name of the course
Mathematics
2. Department responsible for the course or equivalent
Institute of Computer Technologies and Information Security
Department of Higher Mathematics
3. Lecturer (name, academic title, e-mail)
Valeriy Mnukhin, PhD, vbmnuhin@sfedu.ru
4. Semester when the course unit is delivered
Semesters 1, 2, 3
5. Teaching hours per week
6 hours (3 lecture hours + 3 hours of tutorials)
6. Level of course unit
Bachelor’s level
7. ECTS credits
15 credits
8. Admission requirements
Knowledge, skills and abilities based on the previously obtained knowledge in general secondary education or secondary vocational education within the course «Mathematics».
9. Course objectives (aims)
The aims the course are to encourage and enable students to:
• develop an understanding of the principles and nature of mathematics
• communicate clearly and confidently in a variety of contexts
• develop logical, critical and creative thinking
• develop confidence, perseverance, and independence in mathematical thinking and problem-solving
• develop powers of generalization and abstraction
• appreciate the contribution of mathematics to other areas of knowledge
• develop the knowledge, skills and attitudes necessary to pursue further studies in mathematics
• develop the ability to reflect critically upon their own work and the work of others
10. Course contents
1. Analytic geometry and linear algebra
2. Differential and integral calculus of functions of one variable
3. Introduction to real analysis
4. Multivariable and vector calculus
5. Ordinary differential equations
6. Complex analysis
7. Fourier and Laplace transforms
8. Probability and statistics
11. Learning outcomes.
After studying this course, the student will receive the following knowledge skills and abilities:
Knowledge: bases of real and complex analysis, linear algebra, differential equations, probability and statistics
Skills: to solve systems of linear equations, use vectors, limits, derivatives, integrals and series, to solve differential equations, to solve various problems related with probability and statistics
Abilities: use of the basic tools of mathematics for solving applied problems
12. Planned learning activities and teaching methods
- Lecture-visualization using presentation material.
- Tutorials with a variety of examples of constructing mathematical models of problems and methods, solving practical problems in applied mathematics and computer science.
- Self-study.
- Use of reference books and Internet resources.
13. Assessment methods
During each of three semesters, the continuous assessment is based on two tests, each worth 25%, interviews worth totally 5%, and on tutorial attendance (5%), so that total continuous assessment is 60% per semester.
At the end of each semester, students have a summative final assessment (colloquium at the end of semester 1 and exams in semesters 2 and 3) based mostly on application of concepts taught during the semester. Each such assessment worth 40%. A minimum of 60% is required for an overall pass.
Students are expected to pass all three final assessments in order to complete the course.
14. Course literature
1. Bartle, R.G., Sherbert D.R. (2000). Introduction to Real Analysis. John Wiley & Sons, Inc. – 388 pp. ISBN: 0-471-32148-6.
2. Kreyszig, E. (2006). Advanced Engineering Mathematics. Wiley & Sons, Inc. – 1094 pp. ISBN: 0-471-72897-7.
3. Poole, D. (2006) Linear Algebra. A Modern Introduction. Thompson Brooks/Cole. – 712 pp. ISBN: 0-534-99845-3.
4. Brown, J.W., Churchill, R.V. (2009). Complex Variables with Applications. McGraw-Hill Higher Education. — 468 pp. ISBN: 0-07-305194-2.
5. Brannan, J.R., Boyse, W.E. (2007). Differential Equations. An Introduction with Modern Methods & Applications. John Wiley & Sons, Inc. – 682 pp. ISBN: 10 0-471-65141-9.
6. Mnukhin, V.B., Kupovykh G.V., Timoshenko, D.V. (2018). Linear Algebra. South Federal University. — 112 pp. ISBN: 978-5-9275-3088-5
7. Mnukhin, V.B., Kupovykh G.V., Timoshenko, D.V. (2018). Differential Calculus. South Federal University. — 115 pp. ISBN: 978-5-9275-3060-1
- Лектор курса: Мнухин Валерий Борисович