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Discrete Mathematics, 8 ECTS credits.
/Diskret matematik/
For:
Mat
Y
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Prel. scheduled
hours: 76
Rec. self-study hours: 137
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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:
To give the basic knowledge of discrete mathematics that is needed for
further courses in mathematics, natural science and computer science.
After this course the student should be able to:
- understand and use the terminology and laws of set theory
- formulate and solve combinatorial problems on permutations and
combinations
- use the principle of mathematical induction to prove theorems and
formulas
- perform calculations in modular arithmetic with applications in
RSA-cryptography
- use the Euclidean algorithm to solve Diophantine equations
- identify equivalence relations and partial orders
- determine the disjunctive and conjunctive normal forms for Boolean
functions
- master the foundation of graph theory and use graphs as a tool to
model real-life problems
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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:
Teaching is done through lectures and problem classes.
The course runs over the entire autumn semester.
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Course contents:
Set operations, the laws of set theory and Venn diagrams. Mathematical
induction and recursion. Combinatorics with permutations and
combinations. Number theory with some applications in cryptography.
Relations and functions, especially partial orders, equivalence
relations and Boolean functions. Graphs: planarity, coloring, chromatic
polynom, Euler tours and some applications.
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Course literature:
Asratian, Björn och Turesson: Diskret matematik. 8:e ed. Produced at the Department of Mathematics.
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Examination: |
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Written examination
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8 ECTS
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Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Jesper Thorén
Examiner: Armen Asratian
Link to the course homepage at the department
Course Syllabus in Swedish
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