Algebra II
Syllabus, Bachelor's level, 1MA006
- Code
- 1MA006
- 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
Algebra I
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 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.
Content
Number theory: Congruences, Euler's phi-function, Fermat's little theorem, linear congruences, the Chinese remainder theorem, 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. Examples of non-commutative rings.
Instruction
Lectures and problem solving sessions.
Assessment
Written and oral examination.. M
Reading list
- Reading list valid from Autumn 2023
- Reading list valid from Autumn 2022
- Reading list valid from Spring 2022
- Reading list valid from Spring 2020
- Reading list valid from Spring 2019
- Reading list valid from Autumn 2013, version 2
- Reading list valid from Autumn 2013, version 1
- Reading list valid from Spring 2013
- Reading list valid from Autumn 2009, version 2
- Reading list valid from Autumn 2009, version 1
- Reading list valid from Autumn 2007