Module also offered within study programmes:
General information:
Name:
Algebra
Course of study:
2017/2018
Code:
IES-1-106-s
Faculty of:
Computer Science, Electronics and Telecommunications
Study level:
First-cycle studies
Specialty:
-
Field of study:
Electronics and Telecommunications
Semester:
1
Profile of education:
Academic (A)
Lecture language:
English
Form and type of study:
Full-time studies
Course homepage:
 
Responsible teacher:
dr Mc Inerney Kinga (stolot@agh.edu.pl)
Academic teachers:
Module summary

Description of learning outcomes for module
MLO code Student after module completion has the knowledge/ knows how to/is able to Connections with FLO Method of learning outcomes verification (form of completion)
Social competence
M_K001 Knows how to explain mathematical phenomena in an understandable way ES1A_K06 Oral answer
Knowledge
M_W001 Has knowledge of calculus of complex numbers, knows how to solve polynomial equations in the complex domain ES1A_W01 Examination,
Test
M_W002 Has knowledge of vector spaces, dimension, change of base ES1A_W01 Examination,
Test
M_W003 Has knowledge of operation on matrices, how to find a Jordan form of a matrix, knows different methods of solving systems of linear equations ES1A_W01 Examination,
Test
M_W004 Has basic knowledge of analytic geometry, line, plane, distances between them ES1A_W01 Examination,
Test
FLO matrix in relation to forms of classes
MLO code Student after module completion has the knowledge/ knows how to/is able to Form of classes
Lecture
Audit. classes
Lab. classes
Project classes
Conv. seminar
Seminar classes
Pract. classes
Zaj. terenowe
Zaj. warsztatowe
Others
E-learning
Social competence
M_K001 Knows how to explain mathematical phenomena in an understandable way - + - - - - - - - - -
Knowledge
M_W001 Has knowledge of calculus of complex numbers, knows how to solve polynomial equations in the complex domain + + - - - - - - - - -
M_W002 Has knowledge of vector spaces, dimension, change of base + - - - - - - - - - -
M_W003 Has knowledge of operation on matrices, how to find a Jordan form of a matrix, knows different methods of solving systems of linear equations + + - - - - - - - - -
M_W004 Has basic knowledge of analytic geometry, line, plane, distances between them + + - - - - - - - - -
Module content
Lectures:

The course covers 28h of lectures and 28h of classes.

LECTURES

1. Complex numbers (4 h)
Explaining the need of extension of the set of real numbers. Algebraic, trigonometric and exponential form of
complex numbers. Adding, subtracting, multiplying and dividing complex numbers. Calculating roots, solving eqautions
involving complex numbers.
2. Vectors in R^n (4 h)
Operations on vectors in R^n, linear independence of vectors, the space generated by the set of vectors. Vector spaces, notion of the base and the dimension of the vector space. Change of base and expressing a vector in a new base.
3. Matrices (4 h)
Definition of a matrix, operations on matrices. Definition and different methods of calculating determinants of quadratic matrices. Trace and rank of a matrix. Finding the invers matrix (the Gauss algorithm). Echelon form of a matrix.
4. Systems of linear equations (4 h)
Methods of solving homogeneous and nonhomogeneous systems of linear equations. Matrix form of the equations.
5. Linear transformations (2 h)
Definition of a linear transformation, notion of a kernel and an image. The notion of monomorphism, epimorphism and endomorphism.
6. Matrix form of a linear transformation (4 h)
Transition matrix. Change of the matrix form of a transformation, while a base in the domain and the codomain is changed.
7. Jordan form of matrices (3 h)
Eigenvectors and eigenvalues and the Jordan decompositions of matrices.
8. Analytic geometry (2 h)
Norm of a vector. Scalar and cross product. Equations describing line and plane in R^3. Distances between lines, planes and points. Mutual positions of lines and planes in R^3.
9. Algebraic structures (1 h)
Definition of the group, ring and field with some examples presented.

Auditorium classes:

CLASSES:

1. Operations on complex numbers. Solving equations involving complex numbers. (3 h)
2. 1. Class Test (1 h)
3. Operations on matrices. (3 h)
4. Solving systems of linear equations. (3 h)
5. 2. Class Test (1 h)
6. Operations on vectors. Finding dimension and a base of a vector space. (5 h)
7. Linear transformations and their matrix form. (5 h)
8. Jordan decompositions. (3 h)
9. 3. Class Test (1 h)
10. Analytic geometry. (2 h)
11. 4. Final Class Test (1 h)

Student workload (ECTS credits balance)
Student activity form Student workload
Summary student workload 141 h
Module ECTS credits 5 ECTS
Participation in lectures 28 h
Participation in auditorium classes 28 h
Realization of independently performed tasks 55 h
Preparation of a report, presentation, written work, etc. 30 h
Additional information
Method of calculating the final grade:

1. The sufficient condition for being admitted to the exam is a positive mark from the classes.
The necessary condition for obtaining a positive final mark (OK) is positive mark both from classes and the exam.
2. After calculating SW = 0,49SOC+0,51SOE, where SOC is an arithmetic mean of all marks obtained from classes and SOE is an arithmetic mean of all marks obtained at the exams, the final mark (OK) is given on the basis of the algorithm:
if SW >4.75 then OK:=5.0 (bdb) else
if SW >4.25 then OK:=4.5 (db) else
if SW >3.75 then OK:=4.0 (db) else
if SW >3.25 then OK:=3.5 (dst) else OK:=3 (dst)

Prerequisites and additional requirements:

Mathematical knowledge at the secondary school level.

Recommended literature and teaching resources:

J. Bird, Higher Engineering Mathematics
T. K. Moon, W. C. Stirling, Mathematical methods and algorithms for signal processing

Scientific publications of module course instructors related to the topic of the module:

Additional scientific publications not specified

Additional information:

None