# Algebra I

5 credits

Syllabus, Bachelor's level, 1MA004

Code
1MA004
Education cycle
First cycle
Main field(s) of study and in-depth level
Mathematics G1F
Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by
The Faculty Board of Science and Technology, 9 February 2023
Responsible department
Department of Mathematics

## Entry requirements

Participation in Basic Course in Mathematics, Introduction to Studies in Mathematics or Geometry and Analysis I, which also may be taken in parallel with this course.

## Learning outcomes

On completion of the course, the student should be able to:

• give an account of important concepts and definitions in the area of the course;
• exemplify and interpret important concepts in specific cases;
• formulate important results and theorems covered by the course;
• describe the main features of the proofs of important theorems;
• express problems from relevant areas of applications in a mathematical form suitable for further analysis;
• use the theory, methods and techniques of the course to solve mathematical problems;
• present mathematical arguments to others.

## Content

Elementary logic and set theory. Functions and relations. Equivalence relations. Natural numbers and integers: induction, divisibility, primes, Euclid's algorithm, congruences, representation of numbers in different bases. Linear congruences, the Chinese remainder Theorem, Euler's phi-function, Euler's Theorem, Fermat's little theorem. Diophantine equations. Rational and irrational numbers. Denumerability and cardinality. Rational, real and complex polynomials: factorisation, irreducible polynomials, Euclid's algorithm, multiple roots, rational roots of polynomials with integer coefficients.

## Instruction

Lectures and problem solving sessions. Problem solving with Python.

## Assessment

Written examination at the end of the course. Moreover, compulsory assignments during the course.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.