Calculus and Optimization for Machine Learning

Hi! Our online course aims to provide necessary background in Calculus sufficient for up-following Data Science courses

  • The course is related to the online specialization ''Mathematics for Data Science"
  • Flexible Terms
  • 6 weeks (2 credits)
  • Time to completion: 33 hours
  • Online
  • Certificate
Apply for the specialization

About the Course

Course starts with a 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 optimisation. To provide an understanding of the practical skills set being taught, the course introduces the final programming project considering the usage of optimisation 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


Course Objectives


Calculate various limits of sequences by several different techniques


Understand and interpret the definition of sequence's limit


Apply basic graph transformations to existing plot to produce a more sophisticated one

Learning Outcomes

1. Illustrate the multivariate functions with surface or level plots

2. Distinguish between differetiable and non-differentiable cases

3. Use linear approximations to produce close estimation of the true value of the function

4. Provide a full extrema analysis for the function by its derivative

Course Syllabus

Week 1. Introduction: Numerical Sets, Functions, Limits

Week 2. Limits and Multivariate Functions

Week 3. Derivatives and Linear Approximations: Singlevariate Functions

Week 4. Derivatives and Linear Approximations: Multivariate Functions

Week. 5 Integrals: Anti-derivative, Area under Curve

Week 6. Optimization: Directional derivative, Extrema and Gradient Descent

Anton Savostianov

Lecturer: Faculty of Computer Science


All the themes demand only mathematical background amongst the ordinary school program and initial Python programming skills

Graduation Document

Earn a Certificate upon completion



Learning Activities



Low-Stakes Assignments


High-Stakes Assignments

Final project

Cost and Conditions

17 000 ₽

Full access to the learning materials + Graduation document

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