Main field(s) of study and in-depth level:
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:
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.
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.
Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
The Faculty Board of Science and Technology
On completion of the course, the student should be able to:
give an account of important concepts and definitions in the theory of rings and fields;
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;
use the theory, methods and techniques of the course to solve simple number theoretic problems and problems about rings and fields;
present mathematical arguments to others.
Number theory: Congruences, Euler's phi-function, Fermat's little theorem, linear congruences, , the RSA algorithm. An introduction to ring and field theory: Properties of addition and multiplication in Z, Q, R, Z[x] and C[x]. The ring and field concepts. Invertible elements and prime elements. Unique factorisation in Z and in K[x]. The Euclidean ring notion, unique factorisation and the ring Z[i] of Gaussian integers. Isomorphism, homomorphism, ideal, quotient field. The ring Z_n of integers modulo n. Chinese remainder Theorem as a ring isomorphism. Examples of non-commutative rings.
Lectures and problem solving sessions.
Written (4 Credit Points) and oral (1 Credit points) examination.
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.