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Probability Theory, Second Course, 6 credits
Sannolikhetslära, fortsättningskurs, 6 hp
TAMS46
Main field of study
Mathematics Applied MathematicsCourse level
Second cycleCourse type
Programme courseExaminer
Torkel ErhardssonDirector of studies or equivalent
Ingegerd SkoglundEducation components
Preliminary scheduled hours: 48 hRecommended self-study hours: 112 h
ECV = Elective / Compulsory / Voluntary
Main field of study
Mathematics, Applied MathematicsCourse level
Second cycleAdvancement level
A1XCourse offered for
- Mathematics, Master's Programme
- Mathematics
- Industrial Engineering and Management - International, M Sc in Engineering
- Industrial Engineering and Management, M Sc in Engineering
- Applied Physics and Electrical Engineering - International, M Sc in Engineering
- Applied Physics and Electrical Engineering, M Sc in Engineering
Specific information
The course is offered every second year. It will not be available during 2017
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.
Prerequisites
Linear algebra and multivariate analysis. Basic courses in probability and statistics.Intended learning outcomes
The course gives knowledge of probability theory at an advanced undergraduate level. After completing the course the student will be expected to be able to:
- describe advanced concepts and theorems of probability theory, e.g., different kinds of stochastic convergence and the Cramer-Slutsky theorem, and to prove some of the theorems.
- construct and analyse probabilistic models using advanced tools and methods, e.g., characteristic functions and conditioning.
- describe and prove some basic theorems of statistics.
- understand and assess probabilistic models and analyses occurring in other undergraduate courses, research reports, or the media.
- follow a graduate course in probability theory, and an advanced undergraduate course in statistics.
Course content
The transformation theorem. Conditioning. Probability generating function, moment generating function, characteristic function. Order statistics. The multivariate normal distribution, in particular orthogonal transformations and quadratic forms. Convergence concepts, e.g., convergence almost surely, in probability, in r-mean, and in distribution. The Borel-Cantelli lemma and the continuity theorem. The law of large numbers and the central limit theorem. The Cramer-Slutsky theorem.
Teaching and working methods
Teaching is performed in groups and consists of lessons dealing with theory and exercises.
Examination
| TEN1 | Written examination | 6 credits | U, 3, 4, 5 |
Grades
Four-grade scale, LiU, U, 3, 4, 5Department
Matematiska institutionenDirector of Studies or equivalent
Ingegerd SkoglundExaminer
Torkel ErhardssonCourse website and other links
http://courses.mai.liu.se/Lists/html/index-amne-matstat.htmlEducation components
Preliminary scheduled hours: 48 hRecommended self-study hours: 112 h
Course literature
Additional literature
Books
- Gut, A, (2009) An Intermediate Course in Probability 2nd ed
| Code | Name | Scope | Grading scale |
|---|---|---|---|
| TEN1 | Written examination | 6 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.
Additional literature
Books
Gut, A, (2009) An Intermediate Course in Probability 2nd ed
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 |
X
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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 |
X
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X
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X
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TEN1
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| 2.3 System thinking |
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| 2.4 Attitudes, thought, and learning |
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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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X
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TEN1
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| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
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X
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| 3.2 Communications |
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X
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TEN1
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| 3.3 Communication in foreign languages |
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X
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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 |
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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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