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Discrete Mathematics, 6 credits
Diskret matematik, 6 hp
TADI31
Main field of study
Mathematics Applied MathematicsCourse level
First cycleCourse type
Programme courseExaminer
Daniel CarlssonDirector of studies or equivalent
Mikael LangerEducation components
Preliminary scheduled hours: 50 hRecommended self-study hours: 110 h
ECV = Elective / Compulsory / Voluntary
| Course offered for | Semester | Period | Timetable module | Language | Campus | ECV | |
|---|---|---|---|---|---|---|---|
| 6IDAT | Computer Engineering, Bachelor of Science in Engineering | 3 (Autumn 2025) | 2 | 1+2 | Swedish | Linköping, Valla | C |
Main field of study
Mathematics, Applied MathematicsCourse level
First cycleAdvancement level
G1FCourse offered for
- Bachelor of Science in Computer Engineering
Intended learning outcomes
The course will provide the conceptual framework and the techniques used within discrete mathematics for applications in program development, theoretical computer science, database theory, digital technology. After completing the course, the student will:
- be able to perform proofs by induction and be able to solve basic problems in integer arithmetic such as Diophantine equations,
- be able to apply the formula language and operations of set theory and be able to structure, formulate and solve combinatorial problems,
- be well acquainted with definitions and basic properties of graphs, and be able to use these for problem solving,
- be familiar with the language of set logic and logical operations and be able to evaluate the validity of logical conclusions and be able to present solutions and use the formulaic language of mathematics correctly.
Course content
1. Number theory; prime numbers, divisibility, Euclid's algorithm, Diophantine equations. Induction and recursion.
2. Sert theory with operations on sets, Venn diagrams and number counting. Combinatorics with permutations and combinations and the binomial theorem.
3. Graphs, trees, algorithms for least expensive networks, modeling and problem solving with graphs. Logic with connectives, truth value tables and methods for inference.
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 for examination modules are decided in accordance with the assessment criteria presented at the start of the course.
Grades
Four-grade scale, LiU, U, 3, 4, 5Other 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 such a way that there are equal opportunities with regard to sex, transgender identity or expression, ethnicity, religion or other belief, disability, sexual orientation and age.
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.
Department
Matematiska institutionenCourse 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 |
Grades for examination modules are decided in accordance with the assessment criteria presented at the start of the course.
Books
Asratian, A, Björn, A, Turesson, B O, (2020) Diskret matematik 1 Liber
ISBN: 978-91-47-13358-1
Note: The course matrix might contain more information in Swedish.
I = Introduce, U = Teach, A = Utilize
| I | U | A | Modules | Comment | ||
|---|---|---|---|---|---|---|
| 1. DISCIPLINARY KNOWLEDGE AND REASONING | ||||||
| 1.1 Knowledge of underlying mathematics and science (G1X level) |
X
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X
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X
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TEN1
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| 1.2 Fundamental engineering knowledge (G1X level) |
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| 1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level) |
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| 1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level) |
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| 1.5 Insight into current research and development work |
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| 2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES | ||||||
| 2.1 Analytical reasoning and problem solving |
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X
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X
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TEN1
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| 2.2 Experimentation, investigation, and knowledge discovery |
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X
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| 2.3 System thinking |
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X
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| 2.4 Attitudes, thought, and learning |
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X
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X
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TEN1
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| 2.5 Ethics, equity, and other responsibilities |
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| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
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| 3.2 Communications |
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X
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X
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UPG1
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| 3.3 Communication in foreign languages |
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| 4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT | ||||||
| 4.1 External, societal, and environmental context |
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| 4.2 Enterprise and business context |
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| 4.3 Conceiving, system engineering and management |
X
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| 4.4 Designing |
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| 4.5 Implementing |
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| 4.6 Operating |
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| 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 |
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| 5.2 Economic conditions for knowledge development |
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| 5.3 Identification of needs, structuring and planning of research or development projects |
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| 5.4 Execution of research or development projects |
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| 5.5 Presentation and evaluation of research or development projects |
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