Syllabus for Algebra I

Algebra I

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:
  • Revised: 2021-10-18
  • Revised by: The Faculty Board of Science and Technology
  • Applies from: week 27, 2022
  • Entry requirements: Participation in Basic Course in Mathematics or Introduction to Studies in Mathematics, which also may be taken in parallel with this course.
  • Responsible department: Department of Mathematics

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. The Chinese remainder Theorem. 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. 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.

Reading list

Reading list

Applies from: week 27, 2022

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