Магистратура
2023/2024
Математический анализ
Статус:
Курс обязательный (Магистр по наукам о данных)
Направление:
01.04.02. Прикладная математика и информатика
Где читается:
Факультет компьютерных наук
Когда читается:
1-й курс, 2 модуль
Формат изучения:
с онлайн-курсом
Онлайн-часы:
52
Охват аудитории:
для своего кампуса
Преподаватели:
Лукьяненко Никита Сергеевич
Прогр. обучения:
Магистр по наукам о данных (о)
Язык:
английский
Кредиты:
3
Контактные часы:
10
Course Syllabus
Abstract
Our course aims to provide necessary background in Calculus sufficient for up-following Data Science courses.Course starts with basic introduction to concepts concerning functional mappings. Later students are assumed to study limits (in case of sequences, single- and multivariate functions), differentiability (once again starting from single variable up to multiple cases), integration, thus sequentially building up a base for the basic optimization. To provide an understanding of the practical skills set being taught, the course introduces the final programming project considering the usage of optimization routine in machine learning.Additional materials provided during the course include interactive plots in GeoGebra environment used during lectures, bonus reading materials with more general methods and more complicated basis for discussed themes.
Learning Objectives
- Students will develop understanding of variety of essential concepts of the single and multi-variable calculus and acquire a range of practical skills regarding aforementioned concepts.
- Amongst the skills and concepts, there should be stressed out the following: • derivatives of single and multi-variate functions • indefinite and definite integration • principle differences of functions of several variables
Expected Learning Outcomes
- Calculate discrete limit and the limit of sequences
- Learn asymptotic comparison of functions, Big- and little-o notations, famous important limits
- Calculate function's derivative
- Learn derivatives of single and multi-variate functions
- Learn indefinite and definite integration
- Learn principle differences of functions of several variables
Course Contents
- 1: Introduction: Numerical Sets, Functions, Limits
- 2: Limits and Multivariate Functions
- 3: Derivatives and Linear Approximations: Single variate Functions
- 4: Derivatives and Linear Approximations: Multivariate Functions
- 5: Integrals: Anti-derivative, Area under Curve
- 6: Optimization: Directional derivative, Extrema and Gradient Descent
Interim Assessment
- 2023/2024 2nd moduleThere are no blocking parts in the grading, but you have to get at least 40% to pass the course. The passing grade is 4/10. Please note that in order to get a grade of 9 or 10, students who have scored at least 7 points for the course will be invited to write a written test paper. Grading formula: IF (T*0.7+P*0.3 >=7; T*0.7+P*0.3+EX*0.2; T*0.7+P*0.3). T - tests P - project EX - exam (written test paper) Based on the results of all tasks the accumulated assessment is calculated: 0.7*tests + 0.3*project. The exam is counted with a weight of 0.2 only if the tests + project after graduation on the scale give at least 7. The connection between percents of completion and your grade will be found according to the following table: 1-10 1 2 3 4 5 6 7 8 min % 0 15 30 40 55 70 80 90
Bibliography
Recommended Core Bibliography
- Friedman, A. (2007). Advanced Calculus (Vol. Dover edition). Mineola, N.Y.: Dover Publications. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1153250
- James Stewart. (2016). Calculus, Early Transcendentals, International Metric Edition: Vol. Eighth edition, metric version. Cengage Learning.
- Jennifer F. Wood. (2015). Dowling, P. J., Festing, M., Engle Sr., A. D., International Human Resource Management (6th Edition), Cengage Learning EMEA, 2013. Management International Review, (4), 589. https://doi.org/10.1007/s11575-014-0236-1
Recommended Additional Bibliography
- William H. Press, Saul A. Teukolsky, William T. Vetterling, & Brian P. Flannery. (1992). Numerical Recipes in C: The Art of Scientific Computing. Second Edition. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.9CFCD6AE