Master 2023/2024

Calculus

Type: Compulsory course

Area of studies: Applied Mathematics and Informatics

Delivered by: Big Data and Information Retrieval School

Where: Faculty of Computer Science

When: 1 year, 2 module

Mode of studies: distance learning

Online hours: 52

Open to: students of one campus

Instructors: Nikita Lukianenko

Master’s programme: Магистр по наукам о данных (о)

Language: English

ECTS credits: 3

Contact hours: 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

Assessment Elements

• Quizzes
• Final Project
• Exam

Interim Assessment

• 2023/2024 2nd module
  There 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