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Discrete Mathematics, 6 ECTS credits.
/Diskret matematik/
For:
D
U
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Prel. scheduled
hours: 80
Rec. self-study hours: 80
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Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
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Advancement level
(G1, G2, A): G1
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Aim:
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
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
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Organisation:
Lectures and lessons.
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Course contents:
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.
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Course literature:
Determined later
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Examination: |
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Written examination
Hand-in assignments
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4 ECTS
2 ECTS
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Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Jesper Thorén
Examiner: Carl Johan Casselgren
Link to the course homepage at the department
Course Syllabus in Swedish
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