TMA4162 - Computational Algebra


Examination arrangement

Examination arrangement: School exam
Grade: Letter grades

Evaluation Weighting Duration Grade deviation Examination aids
School exam 100/100 4 hours A

Course content

An introduction to computational methods in modern algebra, primarily motivated by cryptographic problems. The course will contain an overview of the number field sieve for factoring, techniques for solving lattice problems and Gröbner basis methods for commutative rings. In order to present this material, there will also be an introduction to general algebraic number theory, including relevant computational algorithms. There will also be an introduction to basic lattice theory, the ideas of reduced lattice bases, and the relation of classical lattice theory to modern cryptography. There will also be an introduction to Gröbner basis theory, including its motivating problems in cryptography and general mathematics.

Learning outcome

1. Knowledge

The student has sufficient knowledge about algebraic number theory, lattices and Gröbner basis theory to be able to understand the relevant algorithms and their analysis, as well as their application in cryptography and general mathematics.

2. Skills

The student is able to use computational algorithms in algebraic number theory, lattices and Gröbner basis theory in order to solve important cryptographic and computational mathematical problems.

3. General competence

The course will allow students to participate in research and scientific discussions on an international level and be able to learn new topics in computational algebra.

Learning methods and activities

Lectures and mandatory exercises, including a programming project.

Compulsory assignments

  • Exercises

Further on evaluation

The final grade is based on the written exam. The re-sit examination may be given as an oral examination.

Required previous knowledge

Knowledge about programming is necessary for the exercises and the project.

Course materials

The course material will be announced at semester start.

More on the course

Version: 1
Credits:  7.5 SP
Study level: Second degree level


Term no.: 1
Teaching semester:  SPRING 2024

Language of instruction: -

Location: Trondheim

Subject area(s)
  • Algebra
  • Mathematics
Contact information
Course coordinator:

Department with academic responsibility
Department of Mathematical Sciences


Examination arrangement: School exam

Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
Spring ORD School exam 100/100 A 2024-05-21 15:00 INSPERA
Room Building Number of candidates
SL311 orange sone Sluppenvegen 14 11
SL520 Sluppenvegen 14 1
Summer UTS School exam 100/100 A INSPERA
Room Building Number of candidates
  • * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.

For more information regarding registration for examination and examination procedures, see "Innsida - Exams"

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