Algebra I 360-MS1-2ALG1a
Ćwiczenia (CW) Rok akademicki 2024/25

During the course, the student has the following opportunities to get points:

1. Two tests. For each test, a student may receive a maximum of 50 points. There are two dates for each of the tests. The student may

take the test either on one date of his choice or on both dates. A student who takes the test for the second time may either fail to return

the solutions to the tasks and then the result achieved on the first date will be the most important, or the results obtained on the second

date will be the most important. In the case of excused absence from the test on both dates, the student will be able to take the test on an

additional date set by the teacher.

2. Homework. Tasks from the lists, not solved during the class, will be treated as homework. For each correct homework problem, the

student will receive a maximum of 2 points.

The basis for obtaining credit for the exercises is

1. class attendance. Two unexcused absences from classes are allowed. Each subsequent absence should be justified with an

appropriate certificate or made up for.

2. obtaining at least 15 points for each test.

3. obtaining a total of at least 51 points.

Assessment grading scale:

2 - insufficient - up to 50.9 points

3 - satisfactory - from 51 to 60.9 points

3,5 - sufficient plus - from 61 to 70.9 points

4 - good - from 71 to 80.9 points

4,5 - good plus - from 81 to 90.9 points

5 - very good - from 91 points.

A student who does not meet the above-mentioned conditions will be able to take the "last chance" test at the end of the semester

(covering material from the entire semester), provided that

1.the number of unexcused absences from classes will not exceed three. Any remaining absences will be excused or made up for.

2. the student obtained at least 15 points in at least one test.

Obtaining at least 51% of the points in the "last chance" test credits the exercises with a satisfactory grade.

Course content: Groups, examples of group (transformation groups including permutation groups, symmetry groups of plane figures,

matrix groups), subgroups, normal subgroup, quotient groups, direct products of groups, group homomorphisms, group isomorphism

theorem, Lagrange and Cayley theorems, relationships with number theory (Euler theorem, Fermat's little theorem), commutant and

group center, Abelian groups, cyclic groups, structure of finely generated Abelian groups. Rings, examples of rings (among others, the

ring of residue classes modulo n), subrings, ideals (principle, prime, maximum), quotient rings, ring homomorphisms, the ring

isomorphism theorem, polynomial rings, divisibility in integral domains, prime elements , irreducible elements, unique factorization

domains. Fields, finite fields, fields of fractions of integral domains, algebraic extensions of fields, algebraically closed fields, the

fundamental theorem of algebra.

Didactic methods: accounting exercises, consultations (conducted in real time in a stationary or remote system), work on literature, solving homework assignments, presentation of homework

solutions prepared at home in the forum of the group (conducted in real time in a stationary or remote system), discussions in groups, solving problems on the blackboard or virtual blackboard.