Delivered at:: Department of Fundamental Mathematics (Faculty of Informatics, Mathematics, and Computer Science (HSE Nizhny Novgorod))

Course type:: Compulsory course

When:: 4 year, 1, 3 module

Instructor

Nozdrinova, Elena

Full Syllabus Ask Question

Abstract

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

Learning Objectives

Here we introduce basic concept the calculus course could not be imagine without: function. In order to properly do it, one should say that the function is a mapping from one set to another. Thus, we start with the ideas of numerical sets and mapping, then proceeding with functions itself. Since we are particularly interested in functions' graph, we spend a lot of time discussing simplest ways to produce a complex function graph from elementary case. In the second part of the week we start our calculus journey with a discrete limit, the limit of sequences, and master skills needed to calculate them.

Expected Learning Outcomes

Know the definition of the limit
Know the definition of function
Know about symptotic comparison of functions
Know about the slope of the functions

Course Contents

Introduction: Numerical Sets, Functions, Limits
Introduction: Numerical Sets, Functions, Limits
Derivatives and Linear Approximations: Singlevariate Functions
Limits and Multivariate Functions

Assessment Elements

Контрольная работа
Контрольная работа
Устный опрос

Interim Assessment

2024/2025 3rd module
0.3 * Контрольная работа + 0.4 * Контрольная работа + 0.3 * Устный опрос

Bibliography

Recommended Core Bibliography

Machine learning : a probabilistic perspective, Murphy, K. P., 2012
Machine learning, Mitchell, T. M., 1997

Recommended Additional Bibliography

Machine learning : beginner's guide to machine learning, data mining, big data, artificial intelligence and neural networks, Trinity, L., 2019

Authors

NOZDRINOVA ELENA Viacheslavovna

Bachelor’s Programme 'Pure and Applied Mathematics'

Computation and optimization for machine learning