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HU Credits:
3
Degree/Cycle:
1st degree (Bachelor)
Responsible Department:
statistics
Semester:
2nd Semester
Teaching Languages:
Hebrew
Campus:
Mt. Scopus
Course/Module Coordinator:
Dr. Lily Tamir
Coordinator Office Hours:
By mail
Teaching Staff:
Dr. Lily Agranat
Course/Module description:
The course presents central themes from Measure Theory - the mathematical basis of Probability Theory. For that goal the course describes relevant branches of mathematics that are relevant for understanding the mathematical derivations.
Course/Module aims:
The main goal of the course is the preparation of the student towards the course in probability and stochastic processes that is required in the masters degree. A large part of the probabilistic subjects from that course are presented in a slower pace with an attempt to understand the background and the motivations.
Learning outcomes - On successful completion of this module, students should be able to:
1. To quote and apply the definitions that were presented in the course.
2. To restore independently the proofs of the claims that were stated in the course.
3. To describe at least 1 example in the context of any claim.
4. To prove independently simple variants of claims that were stated in class.
Attendance requirements(%):
No attendance requirement
Teaching arrangement and method of instruction:
lectures and tutorials
Course/Module Content:
1. Cantor's set theory.
2. Introduction to measure theory.
3. The construction of a measure.
4. Measurable functions.
5. Measurability of the limit of a sequence.
6. Integration (part a).
7. Integration (part b).
8. Integral convergence theorems.
9. The computation of integrals.
10. Independence and product measures.
11. The strong law of large numbers.
12. Approximations of functions.
13. The central limit theorem.
Required Reading:
None
Additional Reading Material:
Dorrett, R: Probability, theory and examples
Abbott, S: Understanding Analysis
Course/Module evaluation:
End of year written/oral examination 70 %
Presentation 0 %
Participation in Tutorials 0 %
Project work 0 %
Assignments 15 %
Reports 0 %
Research project 0 %
Quizzes 15 %
Other 0 %
Additional information:
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