Course aims:

• The overall objective of this discipline is the consolidation of the concepts of linear algebra studied in high school, including at the same time, elements of superior algebra and analytical geometry necessary for other educational objects.
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Course Entry Requirements:

Knowledge of high school algebra

Course contents:

1. Introduction. Algebraic structures 2. Matrix operations 3. Vector spaces. Euclidean spaces 4. Linear transformations 5. Eigenvectors and eigenvalues 6. Multiline algebra and tensor product. Bilinear applications, quadratic forms 7. Vectors 8. Lines and planes in space 9. Transformations 10. Conics 11. Quadrics 12. Differential geometry 13. Surfaces

Teaching methods:

Lecture, conversation, exemplification.

Learning outcomes:

After completing this course students should: • Understand the definitions and various properties of algebraic and geometrical structures. • Be proficient at writing proofs and understand any proof presented throughout the course. • Be able to classify specific properties for the studied notions. • Be able to solve specific problems from this field.

Learning outcomes verification and assessment criteria:

Written paper – 70%; continuous assessment – 30%.

Recommended reading:

Steve Leon, Linear algebra with application, Pearson, -, 2019, -.
William McCrea, Analytical Geometry of Three Dimensions, Dover Publ., -, 2006, -.
Taha Sochi, Introduction to Differential Geometry of Space Curves and Surfaces, Independently Publ., -, 2009, -.
D. Lay, Linear algebra and its applications, Addison-Wesley Publishing, -, 2003, -.