Course content

• Matrices: Basic matrix arithmetic - Equation systems and Gaussian elimination - Least squares method - Transformations in 2 dimensions.
• Logics: Statements, arguments, basic proof theory. Mathematical induction.
• Set theory and discrete functions. Relations.
• Number theory: Divisibility and congruence, Euclid's algorithm, RSA as application.
• Graph theory: Important types of graphs, graph isomorphy, trees. Graph theoretical algorithms, such as Prim's and Dijkstra's algorithms.
• Combinatorics: Counting results related to quantities, functions, relations and graphs. Four standard formulas.

Learning outcome

The course will give students knowledge of how mathematics is used in solving problems in computer science. It will also provide a foundation for further specialisation in mathematics and computer science. The course emphasises applications.

Knowledge: The candidate should demonstrate knowledge of the following

• matrices, basic matrix operations and linear systems
• transformations in two dimensions.
• the concepts of series and convergence in general and geometric series in particular.
• Taylor series of important function types.
• functions of several variable and partial derivation.
• concepts in logic of statements.
• common forms of mathematical proofs, including mathematical induction.
• basic set theory.
• relations and discrete functions.
• concepts and algorithms related to graphs, including trees and graphisomorphism.
• concepts, methods and results in number theory, modular calculus and cryptography.

Skills: The candidate can

• do calculations with complex numbers in normal and polar forms and can apply Euler's formula.
• apply characteristic polynomials in finding eigenvalues ​​and eigenvectors of a square matrix.
• use matrix multiplication to combine transformations in the plane
• apply eigenvalues ​​in practical applications
• use power series in approximations, knows Taylor's formula with residual term and can use the residual term to estimate the error in calculations
• derive partial derivatives and total differential and use them to linearize functions and to find stationary points of functions of two variables
• apply basic concepts, results and methods from the theory of statements and arguments, for example determine whether an argument is valid or invalid and determine whether two statements are equivalent
• construct simple mathematical proofs, including inductive proofs
• apply basic concepts and results related to set theory, discrete functions and can represent these in different ways
• apply basic concepts and results related to relations and graphs, including equivalence relations, paths in graphs and graphisomorphism
• apply algorithms to smaller examples,
• apply basic concepts and methods from number theory related to divisibility, including Euclid's method
• apply congruences calculations and perform RSA encryption and decryption  

General competence: The candidate

• The candidate can use computational and analytical tools to visualize and solve mathematical problems.
• can use mathematics to model and solve theoretical and practical problems in situations relevant to their own field, in academic and professional contexts.

Learning methods and activities

Lectures and exercises. Exercises will be based on assignments in a digital assessment system.  Exercises and learning videos for self-study will be available as a supplement to the lectures.

Compulsory work: at least 75% of the exercises must be approved for admission to the exam. The number of obligatory assignments and weighting will be announced at the start of the semester.

Compulsory assignments

• Obligatorisk arbeidskrav- 4 godkjente innleveringer

Specific conditions

Recommended previous knowledge

Mathematics from secondary education

Course materials

Discrete Mathematics With Applications, (International Edition) Susanna S. Epp

Eventual notes will be released on the Blackboard page.

Credit reductions