Discrete Mathematics, 6 credits

Diskret matematik, 6 hp

TADI31

Course starting semester

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Daniel Carlsson

Director of studies or equivalent

Jesper Thorén

Education components

Preliminary scheduled hours: 50 h
Recommended self-study hours: 110 h

Possible deviation from course syllabus/programme syllabus

ECV = Elective / Compulsory / Voluntary

Course offered for		Semester	Period	Timetable module	Language	Campus	ECV
6IDAT	Computer Engineering, Bachelor of Science in Engineering	3 (Autumn 2023)	2	1+3	Swedish	Linköping, Valla	C

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G1X

Course offered for

Bachelor of Science in Computer Engineering

Intended learning outcomes

To give the basic knowledge of discrete mathematics that is needed for further courses in mathematics, natural and computer science. After completing the course the student should be able to

use the Euclidean algorithm to solve Diophantine equations
use the principle of mathematical induction to solve recursive problems
understand and use the terminology and laws of set theory
formulate and solve combinatorial problems on combinations and permutations
master the foundations of graph theory and use graphs as a tool to model real-life problems
use the language of propositional logic, be familiar to logic operations and be able to evaluate the validity of logical conclusions.

Course content

Number theory; prime numbers, divisibility, Euclidean algorithm, Diophantine equations,
Mathematical induction and recursion.
Set theory, the laws of set theory and Venn diagrams.
Combinatorics with permutations and combinations.
Graphs: Euler paths, Hamilton cycles, trees and some applications in computer science
Logic; propositional logic, logic operations, truth tables and conclusions.

Teaching and working methods

Teaching is done through lectures and problem sessions

Examination

UPG1	Hand-in-assignment	2 credits	U, G
TEN1	A written examination	4 credits	U, 3, 4, 5

Grades

Four-grade scale, LiU, U, 3, 4, 5

Other information

Supplementary courses

The course complements courses in Switching Theory, Programming, Data Structures and Algorithms.

About teaching and examination language

The teaching language is presented in the Overview tab for each course. The examination language relates to the teaching language as follows:

If teaching language is “Swedish”, the course as a whole could be given in Swedish, or partly in English. Examination language is Swedish, but parts of the examination can be in English.
If teaching language is “English”, the course as a whole is taught in English. Examination language is English.
If teaching language is “Swedish/English”, the course as a whole will be taught in English if students without prior knowledge of the Swedish language participate. Examination language is Swedish or English depending on teaching language.

Other

The course is conducted in a manner where both men's and women's experience and knowledge are made visible and developed.

The planning and implementation of a course should correspond to the course syllabus. The course evaluation should therefore be conducted with the course syllabus as a starting point.

The course is campus-based at the location specified for the course, unless otherwise stated under “Teaching and working methods”. Please note, in a campus-based course occasional remote sessions could be included.

If special circumstances prevail, the vice-chancellor may in a special decision specify the preconditions for temporary deviations from this course syllabus, and delegate the right to take such decisions.

Department

Matematiska institutionen

Course literature

Books

Asratian, A, Björn, A, Turesson, B O, (2020) Diskret matematik 1 Liber
ISBN: 978-91-47-13358-1

Code	Name	Scope	Grading scale
UPG1	Hand-in-assignment	2 credits	U, G
TEN1	A written examination	4 credits	U, 3, 4, 5

Student rights and obligations (login required)
Linköping University common rules and regulations (in Swedish)

Books

Asratian, A, Björn, A, Turesson, B O, (2020) Diskret matematik 1 Liber

ISBN: 978-91-47-13358-1

Download

Download course literature list as PDF

Note: The course matrix might contain more information in Swedish.

I = Introduce, U = Teach, A = Utilize

		I	U	A	Modules
1. DISCIPLINARY KNOWLEDGE AND REASONING
	1.1 Knowledge of underlying mathematics and science (G1X level)	X	X	X	TEN1
	1.2 Fundamental engineering knowledge (G1X level)
	1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level)
	1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level)
	1.5 Insight into current research and development work
2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES
	2.1 Analytical reasoning and problem solving		X	X	TEN1
	2.2 Experimentation, investigation, and knowledge discovery			X
	2.3 System thinking		X
	2.4 Attitudes, thought, and learning		X	X	TEN1
	2.5 Ethics, equity, and other responsibilities
3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
	3.1 Teamwork
	3.2 Communications		X	X	UPG1
	3.3 Communication in foreign languages
4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT
	4.1 External, societal, and environmental context
	4.2 Enterprise and business context
	4.3 Conceiving, system engineering and management	X
	4.4 Designing
	4.5 Implementing
	4.6 Operating
5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS
	5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development
	5.2 Economic conditions for knowledge development
	5.3 Identification of needs, structuring and planning of research or development projects
	5.4 Execution of research or development projects
	5.5 Presentation and evaluation of research or development projects

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