• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site
For visually-impairedFor visually-impairedUser profile (HSE staff only)Search
Advanced search
Menu
HSE University
User profile (HSE staff only)Search
Advanced search

Course Syllabus

Master 2022/2023

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, 1 module
Mode of studies: distance learning
Online hours: 82
Open to: students of one campus
Instructors: Nikita Lukianenko
Master’s programme: Master of Data Science
Language: English
ECTS credits: 5
Contact hours: 8

Course Syllabus

Full 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

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

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

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

Assessment Elements

  • non-blocking Week Final Quizzes (weeks 1-5)
    Weekly Quizzes
  • non-blocking Practice Quizzes (week 6)
  • non-blocking SGA Open Question: Series
  • non-blocking First Week Extra Quiz
  • non-blocking SGA Open Question: Multivariate limit
  • non-blocking SGA Numerical Differentiation
  • non-blocking SGA Open Question: Extremum
  • non-blocking SGA Open Question: Chain Rule
  • non-blocking SGA Open Question: FTC
  • non-blocking SGA Numerical Integration
  • non-blocking Final Project
Interim Assessment

Interim Assessment

  • 2022/2023 1st module
    0.09 * SGA Numerical Integration + 0.09 * SGA Numerical Differentiation + 0.3 * Final Project + 0.04 * SGA Open Question: Chain Rule + 0.04 * SGA Open Question: Multivariate limit + 0.04 * SGA Open Question: FTC + 0.02 * First Week Extra Quiz + 0.04 * SGA Open Question: Series + 0.05 * Practice Quizzes (week 6) + 0.04 * SGA Open Question: Extremum + 0.25 * Week Final Quizzes (weeks 1-5)
Bibliography

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

Authors

  • PODOLSKIY VLADIMIR VLADIMIROVICH
  • Литвишкина Ален Витальевна
  • LUKYANENKO NIKITA SERGEEVICH