Introduction to Algebra

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

The course covers introductory topics of linear algebra and analytic geometry in space. They include matrices, matrix operations, inversion of matrices, vector spaces, bases and dimension and their applications to solving systems of linear equations. Free vectors, dot product and cross product of free vectors and applications to investigating lines and planes in 3-space. Polynomials.

Requirements:

The requirement for receiving the credit is an active participation in the tutorials.

Syllabus of lectures:

1. Matrices, operations with matrices

2. Determinants

3. Inverse matrices

4. Arithmetic vectors, linear independence, linear dependence

5. Basis, dimension, coordinates of vectors

6. Linear mappings

7. Systems of linear equations

8. Polynomials, roots of polynomials

9. Rational functions and partial fractions

10. Free vectors, dot product, cross product

11. Lines and planes in three-dimensional Euclidean space

12. Quadratics in three-dimensional Euclidean space

13. Abstract linear spaces

14. Back-up class

Syllabus of tutorials:

1. Matrices, operations with matrices

2. Determinants

3. Inverse matrices

4. Arithmetic vectors, linear independence, linear dependence

5. Basis, dimension, coordinates of vectors

6. Linear mappings

7. Systems of linear equations

8. Polynomials, roots of polynomials

9. Rational functions and partial fractions

10. Free vectors, dot product, cross product

11. Lines and planes in three-dimensional Euclidean space

12. Quadratics in three-dimensional Euclidean space

13. Abstract linear spaces

14. Back-up class

Study Objective:

Study materials:

1. P. Pták: Introduction to Linear Algebra. ČVUT, Praha 1997.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Common plan- structured studies (compulsory course)
• Computer Technology- structured studies (compulsory course)
• Electronics and Communication Technology - structured studies (compulsory course)
• Cybernetics and Measurements- structured studies (compulsory course)
• Heavy-current Engineering- structured studies (compulsory course)