Syllabus for Algebra I

Algebra I

A revised version of the syllabus is available.

Syllabus

  • 5 credits
  • Course code: 1MA004
  • Education cycle: First cycle
  • Main field(s) of study and in-depth level: Mathematics G1F

    Explanation of codes

    The code indicates the education cycle and in-depth level of the course in relation to other courses within the same main field of study according to the requirements for general degrees:

    First cycle

    • G1N: has only upper-secondary level entry requirements
    • G1F: has less than 60 credits in first-cycle course/s as entry requirements
    • G1E: contains specially designed degree project for Higher Education Diploma
    • G2F: has at least 60 credits in first-cycle course/s as entry requirements
    • G2E: has at least 60 credits in first-cycle course/s as entry requirements, contains degree project for Bachelor of Arts/Bachelor of Science
    • GXX: in-depth level of the course cannot be classified

    Second cycle

    • A1N: has only first-cycle course/s as entry requirements
    • A1F: has second-cycle course/s as entry requirements
    • A1E: contains degree project for Master of Arts/Master of Science (60 credits)
    • A2E: contains degree project for Master of Arts/Master of Science (120 credits)
    • AXX: in-depth level of the course cannot be classified

  • Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
  • Established: 2007-03-19
  • Established by: The Faculty Board of Science and Technology
  • Applies from: Autumn 2007
  • Entry requirements: Basic Course in Mathematics
  • Responsible department: Department of 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 may be given during the course.

    Reading list

    Reading list

    Applies from: Spring 2009

    Some titles may be available electronically through the University library.

    • Vretblad, Anders; Ekstig, Kerstin Algebra och geometri

      2., [omarb. och utök.] uppl.: Malmö: Gleerup, 2006

      Find in the library

    Reading list revisions