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Discrete Mathematics, 6 credits

Diskret matematik, 6 hp

TATA65

Course starting semester

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Carl Johan Casselgren

Director of studies or equivalent

Jesper Thorén

Education components

Preliminary scheduled hours: 80 h
Recommended self-study hours: 80 h

Possible deviation from course syllabus/programme syllabus

ECV = Elective / Compulsory / Voluntary

Course offered for		Semester	Period	Timetable module	Language	Campus	ECV
6CDDD	Computer Science and Engineering, M Sc in Engineering	1 (Autumn 2017)	0, 1	-, 2	Swedish	Linköping, Valla	C
6CMJU	Computer Science and Software Engineering, M Sc in Engineering	1 (Autumn 2017)	0, 1	-, 2	Swedish	Linköping, Valla	C

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G1X

Course offered for

Computer Science and Engineering, M Sc in Engineering
Computer Science and Software Engineering, M Sc in Engineering

Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

Intended learning outcomes

The course provides the conceptual framework and the techniques in discrete mathematics used in software development, theoretical computer science, database theory and also in further studies in discrete mathematics. After the course students will be able to read and understand literature and articles of a theoretical nature in the computer sciences, and structure and present the content in these, which means that the student:

can assimilate and apply the language and operations of set theory and be familiar with the definitions and properties of relations and functions
will be able to prove statements by use of mathematical induction, as well as understand links between induction and recursion
can organize, formulate and solve combinatorial problems on permutations and combinations
has mastered the basics of integer arithmetics and congruence calculation and applications in cryptography
has a good knowledge of rules and structures of Boolean algebras and partial orders
knows graph theory terminology and applications such as tree and graph coloring and can use graph theory as a tool for modeling

Course content

Set theory with operations, Venn diagrams and counting. Relations. The
Binomial theorem. Permutations and Combinations. The Principle of
inclusion and exclusion. Induction and recursion. Graphs, trees, binary
trees. The coloring of graphs. Chromatic numbers and polynomials.
Number theory. Congruences. The Euclidean algorithm and Diophantine
equations. Partial orders and equivalence relations with partitions.
Lattice and Boolean functions.

Teaching and working methods

Lectures and lessons.

Examination

UPG1	Assignments	2 credits	U, G
TEN1	Written examination	4 credits	U, 3, 4, 5

Grades

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

Department

Matematiska institutionen

Director of Studies or equivalent

Jesper Thorén

Examiner

Carl Johan Casselgren

Course website and other links

http://www.mai.liu.se/und/kurser/index-amne-tm.html

Education components

Preliminary scheduled hours: 80 h
Recommended self-study hours: 80 h

Course literature

Fastställs senare

Code	Name	Scope	Grading scale
UPG1	Assignments	2 credits	U, G
TEN1	Written examination	4 credits	U, 3, 4, 5

Regulations (apply to LiU in its entirety)

The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.

LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva.

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

Course literature is preliminary.

Fastställs senare

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	Modules
1. DISCIPLINARY KNOWLEDGE AND REASONING
	1.1 Knowledge of underlying mathematics and science (G1X level)	X	X	TEN1
	1.2 Fundamental engineering knowledge (G1X level)	X
	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	TEN1 UPG1
	2.2 Experimentation, investigation, and knowledge discovery
	2.3 System thinking		X	TEN1 UPG1
	2.4 Attitudes, thought, and learning		X	TEN1
	2.5 Ethics, equity, and other responsibilities
3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
	3.1 Teamwork
	3.2 Communications		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
	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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