- systems of linear equations,
- matrix algebra (vectors, matrices, operations on matrices and vectors),
- the concepts of the base, the coordinates of the vector relative to the base,
- linear transformations of vector spaces.

**The total duration of the course is 12 weeks.**

### Detailed course structure

**Topic 1: Basic linear algebra**

- Linear systems (ie, systems of linear equations)
- Matrix algebra (matrices and operations with them)
- Rank of a matrix, solution set to the equation Ax=b
- Linear (in)dependence of vectors, bases of linear vector spaces
- Linear transformations and their representation via matrices

**Topic 2: Orthogonality Orthogonal vectors and subspaces**

- Pythagoras theorem
- Four subspaces theorem
- Projections and projectors; orthogonal vs oblique projection
- Least square solutions to linear systems and application in regression models
- Gram-Schmidt orthogonalization
- QR factorization via Gram-Schmidt
- Orthogonal and unitary transformations and their properties
- Householder reflections and Givens rotations; applications to QR factorization

**Topic 3: Eigenvalues and eigenvectors**

- Eigenvalues and eigenvectors and their characterization
- Diagonalisation of a square matrix under the change of basis
- Calculating A
^{n}for large n and solution of the related difference equations - Jordan canonical form
- Application to differential and difference equations

**Topic 4: Symmetric matrices and quadratic forms**

- Symmetric matrices and their properties
- Spectral decomposition of symmetric matrices
- Quadratic forms
- Principal component analysis

**Topic 5: Matrix Factorisation**

- Spectral decomposition
- Singular value decomposition (SVD) and its applications
- LU and Cholesky decomposition
- QR factorization etc.

**Topic 6: Iterative Methods**

- Jacobi, Gauss-Seidel, and SOR (successive over-relaxation) methods
- Conjugate gradient method
- Krylov subspaces method
- GMRES method

**Topic 7: Numerical Optimisation**

- Finding minima/maxima: First and second-order tests
- Gradient descent and Newton’s methods
- Convex analysis
- Saddle point approach

**Topic 8: Least Square Methods**

- Linear least square
- Non-linear least square
- Constrained least square

### Requirements for prior knowledge of course participants

Fundamentals of linear algebra:- systems of linear equations,
- matrix algebra (vectors, matrices, operations on matrices and vectors),
- concept of the base, coordinates of the vector relative to base,
- linear transforms of vector spaces.

### Learning format

The remote format provides follow-up activity for the course with available online services**Lectures**. Recorded in high-quality video lectures of the master’s course. Teaching and all course materials are in English. Lectures are opened every Monday.**Practical tasks**. Within the course, students complete practical tasks and a project. Teacher and assistants review each completed task and provide detailed explanations and feedback. The time for each practical lesson is one week.**Test tasks.**Each topic includes test questions for self-review and evaluation of the material learned.**Consultations.**Online consultations are held with the teacher through the service Zoom every week on Fridays. Consultation videos are also available for later viewing.**Communication**. Online communication occurs through service Slack.

### Schedule of modules

The course will begin on**October 15th, 2019.**

### Registration on the course

To make sure that the course format is suitable and convenient, we offer participants an access to the first two lectures of the course, which provides an overview of basic concepts of linear algebra. You can access by filling the registration form. After that, until**October 22nd**, you will have to pay the cost of participation in the course. Participants who will not pay before the specified date would be deducted from the course. On

**October 18th**, those who are currently enrolling in the course will have a briefing session with the course lecturer where participants will be able to ask their questions.

### Participation fee

The total fee for the “Linear algebra for data scientists” course is 14 000 UAH. 50% discount is available for the distant participants during the 2019’s fall. Accordingly, the price is 7 000 UAH on the condition of full payment. It is also possible to split the payment into three parts. In this case, the fee is 7,500 UAH and payment is made in equal parts of 2,500 UAH in October, November, and December. If the payment is not received on time, the participant will be blocked from access to the course.### Certificates

Upon completion of the course, participants who score at least 60 points out of 100 will receive a certificate of completion. This certificate can be used to earn credits for a similar course at UCU and at other universities (if it is allowed). The course is rated at 5 credits ECTS.### About the lecturer

**Rostyslav Hryniv, Ukrainian Catholic University**Dr. hab., Professor at the Ukrainian Catholic University, Head of the Department of Applied Math. He teaches “Linear Algebra” and “Probability Theory and Mathematical Statistics” for undergraduate and master’s degree programs in the Faculty of Applied Sciences. Honors:

- 2007: Grant DMS-0710477, National Science Foundation, U.S.A.
- 2005/07: Grant 436 UKR 113/84 (Co-Principal investigator in Ukraine) from Deutsche Forschungsgemeinschaft, Germany
- 2004/06: Alexander hom Humboldt Fellowship, the University of Bonn, Germany
- 2003: Prize of the President of Ukraine for Young Scientists
- 1998/99: PIMS Postdoctoral Fellowship and the University of Calgary, Canada
- 1994/95: Soros Graduate Student

- 2011/16 – Lecturer in Mathematics and Financial Mathematics at the Kyiv School of Economics
- 2009 – Lecturer in Financial Mathematics, Stochastic Analysis, Applied Statistics at the University of Rzeszów, Poland
- 2009 – Mini-course (6 lectures) “An introduction to the Black–Scholes model” at the Kyiv Mohyla Business School (KMBS), Kyiv, Ukraine
- 2007 – Mini-course (4 lectures) “Inverse spectral problems for singular Sturm–Liouville operators” at the University of Kentucky, Lexington, KY, U.S.A.
- 2000 – Lecturer in Mathematical and Applied Statistics and Financial Mathematics at the Lviv Franko National University, Ukraine
- 1998 – Lecturer in Analysis at the University of Calgary, Canada