Course syllabus adopted 2026-02-26 by Head of Programme (or corresponding).
Overview
- Swedish nameDiskret matematik med tillämpningar
- CodeMVE795
- Credits7.5 Credits
- OwnerTKTEM
- Education cycleFirst-cycle
- Main field of studyGlobal systems, Mathematics
- DepartmentMATHEMATICAL SCIENCES
- GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Course round 1
- Teaching language Swedish
- Application code 59135
- Open for exchange studentsNo
- Only students with the course round in the programme overview.
Credit distribution
Module | Sp1 | Sp2 | Sp3 | Sp4 | Summer | Not Sp | Examination dates |
|---|---|---|---|---|---|---|---|
| 0126 Examination 7.5 c Grading: TH | 7.5 c |
In programmes
Examiner
- Peter Hegarty
- Professor, Algebra and Geometry, Mathematical Sciences
Eligibility
General entry requirements for bachelor's level (first cycle)Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements
Specific entry requirements
The same as for the programme that owns the courseApplicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements
Course specific prerequisites
One-variable calculus, linear algebraAim
The course aims to provide basic knowledge of discrete structures and their applications in mathematics, as well as, for example, in computer science and optimization theory. As part of this, an introduction to numerical methods for solving equations in one variable is included.Learning outcomes (after completion of the course the student should be able to)
- To understand and be able to apply basic principles of enumerative combinatorics (counting principles), based on the addition and multiplication principles, as well as understand the probabilistic interpretations of these.
- To understand and be able to onself formulate recursive and inductive arguments. To be able to apply algebraic methods to solve recursive equations, in particular generating functions. To apply iterative methods to the numerical solution of algebraic and ordinary differential equations.
- To master basic number theory, and appreciate the underlying algebraic structures. To learn how basic number theory is applied in modern cryptography.
- To learn basic concepts from graph theory, and become acquainted with classical historical applications which motivate these concepts. To also become acquainted with some more modern applications of graph theory, e.g. in modelling social networks and AI.
Content
- Basic enumerative combinatorics: addition and multiplication principles, permutations and combinations, balls and bins, pigeonhole principle.
- Induction and recursion. Algebraic methods for solving recursion formulas. Iterative methods for the solution of algebraic equations and ordinary differential equations.
- Basic number theory, algebraic perspective and applications to cryptography.
- Graph theory with a focus on concrete applications of basic concepts. Also some examples of more modern fields of application.
Organisation
Lectures and exercise sessions.Literature
There is no required textbook, as the teacher will prepare complete lecture notes.The following two books (in Swedish), which can be purchased as a single package, are recommended as reference literature for discrete mathematics. Lists of recommended exercises from these books will be published in Canvas:
K. Eriksson, H. Gavel: Diskret matematik och diskreta modeller, Studentlitteratur, upplaga 2, 2013 och
K. Eriksson, H. Gavel: Diskret matematik, fördjupning, Studentlitteratur, upplaga 1, 2003
Examination including compulsory elements
Written exam. Voluntary homework exercises which give bonus points.The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers about disability study support.