Algebra I

5 credits

Syllabus, Bachelor's level, 1MA004

A revised version of the syllabus is available.
Code
1MA004
Education cycle
First cycle
Main field(s) of study and in-depth level
Mathematics G1F
Grading system
Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by
The Faculty Board of Science and Technology, 24 April 2013
Responsible department
Department of Mathematics

Entry requirements

Basic Course in Mathematics.

Learning outcomes

In order to pass the course (grade 3) 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. Diophantine equations. Rational and irrational numbers. Denumerability. Polynomials over R and C: factorisation, Euclid's algorithm, multiple roots, rational roots of polynomials with integer coefficients.

Instruction

Lectures and problem solving sessions.

Assessment

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

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