Item card
General Algebra and Number Theory
Some basic information about the module
Cycle of education:
2019/2020
The name of the faculty organization unit:
The faculty Mathematics and Applied Physics
The name of the field of study:
Mathematics
The area of study:
sciences
The profile of studing:
The level of study:
first degree study
Type of study:
full time
discipline specialities :
Applications of Mathematics in Economics
The degree after graduating from university:
bachelor's degree
The name of the module department :
Departament of Topology and Algebra
The code of the module:
1046
The module status:
mandatory for teaching programme Applications of Mathematics in Economics
The position in the studies teaching programme:
sem: 3 / W30 C30 / 6 ECTS / E
The language of the lecture:
Polish
The name of the coordinator:
Prof. Dov Bronisław Wajnryb, DSc, PhD
office hours of the coordinator:
wtorek 10:30 - 12
czwartek 10:30 - 12
The aim of studying and bibliography
The main aim of study:
To teach students the basic notions and theorems from Number Theory, Group Theory, Rings and Fields.
The general information about the module:
Regular studies, semester III, lectures 30 hours, exercises 30 hours, ends with an exam.
Bibliography required to complete the module
| 1 | A. Białynicki-Birula | Algebra | PWN, Warszawa,. | 1980 |
| 2 | J. Browkin, | Wybrane Zagadnienia Algebry | PWN, Warszawa. | 1968 |
| 3 | . B. Gleichgewicht | Algebra | Oficyna Wydawnicz G i S Wrocław. | 2002 |
Basic requirements in category knowledge/skills/social competences
Formal requirements:
The student satisfies the formal requirements set out in the study regulations
Basic requirements in category knowledge:
Knowledge of linear algebra and basic notions of set theory.
Basic requirements in category skills:
performs operations on matrices, computes determinants
Basic requirements in category social competences:
Has the ability to define priorities needed for the realization of a particular task, determined by himself/herself or by others.
Module outcomes
| MEK | The student who completed the module | Types of classes / teaching methods leading to achieving a given outcome of teaching | Methods of verifying every mentioned outcome of teaching | Relationships with KEK | Relationships with PRK |
|---|---|---|---|---|---|
| MEK01 | uses the Algorithm of Euclid to solve diophantine equations. | lectures, exercises | written exam and written tests |
K-W01+ K-W02+ K-W03+ K-U01+ K-K01+ |
P6S-KK P6S-UK P6S-WG P6S-WK |
| MEK02 | knows examples of groups, rings and fields. | lectures and exercises | written exam and written tests |
K-W05+ K-U05+ K-K01+ |
P6S-KK P6S-UK P6S-UW P6S-WG |
| MEK03 | checks properties of groups and rings | lectures and exercises | written exam and written tests |
K-W04+ K-U17+ K-K01+ |
P6S-KK P6S-UW P6S-WG P6S-WK |
| MEK04 | knows the notion of an algebraic number and a transcendental number | lectures and exercises | written exam and written tests |
K-U01+ K-K01+ |
P6S-KK P6S-UK |
The syllabus of the module
| Sem. | TK | The content | realized in | MEK |
|---|---|---|---|---|
| 3 | TK01 | W01 - W03, C01-C03 | MEK01 | |
| 3 | TK02 | W04 - W09, C04 - C09 | MEK02 MEK03 | |
| 3 | TK03 | W10 - W 12,C10 - C12 | MEK02 MEK03 | |
| 3 | TK04 | W13 - W15 ,C13 - C15 | MEK04 |
The student's effort
| The type of classes | The work before classes | The participation in classes | The work after classes |
|---|---|---|---|
| Lecture (sem. 3) | The preparation for a test:
10.00 hours/sem. |
contact hours:
30.00 hours/sem. |
complementing/reading through notes:
15.00 hours/sem. Studying the recommended bibliography: 5.00 hours/sem. |
| Class (sem. 3) | The preparation for a Class:
10.00 hours/sem. The preparation for a test: 8.00 hours/sem. Others: 8.00 hours/sem. |
contact hours:
30.00 hours/sem. |
Finishing/Studying tasks:
7.00 hours/sem. |
| Advice (sem. 3) | The preparation for Advice:
3.00 hours/sem. |
The participation in Advice:
3.00 hours/sem. |
|
| Exam (sem. 3) | The preparation for an Exam:
20.00 hours/sem. |
The written exam:
2.00 hours/sem. |
The way of giving the component module grades and the final grade
| The type of classes | The way of giving the final grade |
|---|---|
| Lecture | No grade for participation in the lecture. |
| Class | Passing grade from exercises based on grades from two tests. In the border case the activity during the execises may tip the scale. |
| The final grade |
Sample problems
Required during the exam/when receiving the credit
egzamAlgebra2010.pdf
Realized during classes/laboratories/projects
(-)
Others
(-)
Can a student use any teaching aids during the exam/when receiving the credit : no
The contents of the module are associated with the research profile yes
| 1 | D. Wajnryb | The braid group and its presentation | 2021 |