Math403
Math Refresher for Masters
Faculty
Serhii Denysov
Senior algorithms R&D at drawer.ai, Programming and math university teacher.
Course length
Duration
Total hours
Credits
Language
Course type
Fee for single course
Fee for degree students
Skills you’ll learn
Overview
Understanding Machine Learning requires fundamental knowledge in mathematical areas such as linear algebra, calculus, optimization, probability and statistics. The Math Refresher course focuses, through practical examples and assignments, on revising the necessary topics that will allow students to join future Machine Learning courses and gain thorough knowledge about modern Artificial Intelligence.
Learning highlights
- Helping students acquire a solid foundation for key mathematical concepts
- Possibility to understand Machine Learning algorithms.
Course outline
15 classes
Session 1. Higher math refresher.
Course overview and initial knowledge test.
Higher mathematics notation. Mathematical reasoning and proofs.
Session 2. Linear Algebra.
Linear algebra basics.
Vectors. Scalar product. Norms, length and distances. Angles and Orthogonality.
Vector spaces and Euclidean spaces.
Session 3. Linear Algebra
Linear combinations and basis.
Change of basis.
Matrices as Linear transforms.
Geometric interpretation of linear transforms. Matrix algebra.
Session 4. Linear Algebra.
Matrices.
Determinant. Trace. Rank. Matrix norm.
Systems of linear equations.
Gaussian elimination. Number of solutions. Linear regression.
Session 5. Linear Algebra.
Matrix decomposition.
Eigenvalues and eigenvectors. Principal Component Analysis.
Singular value decomposition (reduced SVD).
Session 6. Calculus.
Linear algebra test.
Handling infinity
Limits. O and o notation.
Univariate functions.
Monotonicity. Limit of a function. Continuous functions.
Session 7.Calculus.
Integration.
Intuition and formalization. Definite integral. Indefinite integral. Improper integral. Integral as a limit.
Numerical integration algorithms.
Session 8. Calculus/algorithms.
Extreme of a function.
First and second derivatives. Chain rule. Extreme conditions. Convexity.
Basics of iterative algorithms.
Iterative algorithms. Convergence and stability. Iterative root finding.
Session 9. Optimization.
Optimization.
Iterative minimization in 1D.
Matrix calculus.
Multivariate optimization. Gradient. Hessian.
Session 10. Optimization.
Optimization.
Constrained Optimization and Lagrange Multipliers. Convex optimization. Numerical optimization. Gradient Descent.
Session 11. Scientific computing.
Approximation.
The problem. Approaches. Interpolation. L1 and L2 approximation. Least squares.
Regularization
Machine learning as an approximation problem. L2 regularization. Other regularizations.
Session 12. Probability theory.
Calculus / sci. comp. test
- Basic set theory and combinatorics.
Number of permutations, combinations and partitions.
Discrete Random variables.
Common discrete distributions.
Basic Probability.
(Conditional) probability and Independence. Bayes’ theorem.
Session 13. Probability theory.
Random variables properties.
Expectation, variance, covariance and correlation.
Continuous Random variables.
Density. Common continuous distributions and their properties.
Session 14. Statistics.
Statistics basics.
- Parameter estimation. Method of maximum likelihood.
Bonus topic and final test preparation session.
Most likely: random walk, PageRank.
Session 15.
Final test and open discussion.
Prerequisites
Basic knowledge of Mathematics and Programming paradigms (e.g. Python basics)is required. Previous courses on Linear Algebra, Calculus, Optimization, Combinatorics or Probability and Statistics are appreciated.
Methodology
The course will consist of three-hour sessions and self-study practical assignments. The sessions will contain both theoretical and practical parts, with the ratio depending on the covered topics.
Grading
Serhii has worked in the software engineering industry in different positions for many years. Roles included software developer, system architect, IT consultant, project manager and CTO. He is also an experienced educator and is always glad to help students learn how to start having fun with programming and math and become top-level software developers or R&D engineers.
He has taken part in a long row of business automation projects for different businesses, with many small and several big projects, such as one of the biggest outdoor advertising agency in Ukraine and a country-wide software cash registers company, processing millions of transactions per day. Now he is a senior algorithms R&D in a highly dynamic startup drawer.ai.
See full profileApply for this course
Math Refresher for Masters
by Serhii Denysov
Total hours
45 Hours
Dates
Oct 20 - Nov 07, 2025
Fee for single course
€1500
Fee for degree students
€750
How to secure your spot
Complete the form below to kickstart your application
Schedule your Harbour.Space interview
If successful, get ready to join us on campus
FAQ
Will I receive a certificate after completion?
Yes. Upon completion of the course, you will receive a certificate signed by the director of the program your course belonged to.
Do I need a visa?
This depends on your case. Please check with the Spanish or Thai consulate in your country of residence about visa requirements. We will do our part to provide you with the necessary documents, such as the Certificate of Enrollment.
Can I get a discount?
Yes. The easiest way to enroll in a course at a discounted price is to register for multiple courses. Registering for multiple courses will reduce the cost per individual course. Please ask the Admissions Office for more information about the other kinds of discounts we offer and what you can do to receive one.