1. SylabUZ
2. Faculty of Exact and Natural Sciences
3. winter term 2019/2020
4. computer science and econometrics - First-cycle studies leading to Bachelor's degree
5. Linear Algebra 1

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Linear Algebra 1 - course description

Aim of the course

The aim of the course is to acquaint the student with the basic of linear algebra.

Prerequisites

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Secondary school mathematics.

Scope

Lecture

1.  Complex numbers: the conjugate of a complex number, the modulus, the trigonometric form, the geometrical interpretation of operations, de Moivre's formula, the root of complex numbers. The fundamental theorem of algebra. (6 hours)
2. Matrices: operations on matrices, the determinant of a matrix and its properties, the inverse matrix, the rank of a matrix. (6 hours)
3. Solving systems of linear equations. The Kronecker-Cappelli theorem, the Cramer's theorem. The Gauss elimination method. (4 hours)
4. Analytical geometry in R3. The dot product and the cross product. The equation of a plane and a line. Quadric surfaces. (6 hours)
5. Relations and their properties. An equivalence relation and equivalence classes. A partial order relation, partially ordered sets. Lattices. (5 hours)
6. Algebraic structures: Boolean algebras, groups and fields. Examples. (3 hours)

Class

1. Complex numbers: the conjugate of a complex number, the modulus, the trigonometric form, the geometrical interpretation of operations, de Moivre's formula, the root of complex numbers. The fundamental theorem of algebra. (6 hours)
2. Matrices: operations on matrices, the determinant of a matrix and its properties, the inverse matrix, the rank of a matrix. (6 hours)
3. Solving systems of linear equations. The Kronecker-Cappelli theorem, the Cramer's theorem. The Gauss elimination method. (6 hours)
4. Analytical geometry in R³. The dot product and the cross product. The equation of a plane and a line. Quadric surfaces. (6 hours)
5. Relations and their properties. An equivalence relation and equivalence classes. A partial order relation, partially ordered sets. Lattices. (2 hours)

Teaching methods

Traditional lecturies and solving problems under the supervision of the instructor.

Learning outcomes and methods of theirs verification

Outcome description	Outcome symbols	Methods of verification	The class form

Assignment conditions

In order to be allowed to take the exam a student has to have a positive class grade and active participation in classes.

In order to pass the exam a student has to have a positive exam grade.

The final grade is an arithmetic average of the class grade  and the exam grade.

Recommended reading

1. Robert A. Beezer, A First Course in Linear Algebra.

2. Thomas W. Judson, Abstract Algebra:Theory and Applications.

3. Jim Hefferon, Linear Algebra.

Further reading

Notes

Modified by dr Alina Szelecka (last modification: 21-11-2020 06:10)