Engineers often have to deal with uncertainty. When we design a bus schedule, we don't know how many people will be waiting at the stop. When we set up a computer network, we don't know which servers will experience a power failure. Probability is the mathematics that allows us to model and make decisions about scenarios that involve uncertainty. In this course we will learn about probabilistic models and how to solve them.
| date | topic | readings | lecture | |
|---|---|---|---|---|
| 1 | Jan 7 Jan 9 Jan 14* |
Combinatorial analysis | §1.1-1.4, 1.6 | ppt py |
| 2 | Jan 16 Jan 21* |
Axioms of probability I | §2.1-2.5 | ppt py |
| 3 | Jan 23 Jan 28* |
Axioms of probability II | §2.5 | ppt py |
| Jan 30 Feb 4 |
No class, spring festival | |||
| 4 | Feb 6 Feb 11* |
Conditional probability | §3.1-3.3 | ppt |
| Feb 13 | Midterm exam 1 | |||
| 5 | Feb 18 Feb 20 Feb 25* |
Conditional probability and independence | §3.4 | ppt |
| 6 | Feb 27 Mar 4* |
Random variables I | §4.1-4.4 | ppt |
| 7 | Mar 6 Mar 11* |
Random variables II | §4.5-4.7, 4.9 | ppt py |
| 8 | Mar 13 Mar 18* |
Continuous random variables | §5.1-5.3, 5.5 |
ppt |
| Mar 20 | Midterm exam 2 | |||
| 9 | Mar 25 Mar 27 Apr 1* |
Jointly distributed random variables | §6.1-6.3 | ppt py |
| 10 | Apr 3 Apr 8* |
Properties of expectation | §7.1-7.2, 7.4, (7.5) | ppt |
| 11 | Apr 10 Apr 15* |
Limit theorems | §8.1-8.3 | ppt py |
| 12 | Apr 17 | The probabilistic method | ppt | |
| May 13 |
Final exam |
* Reserved for presentation and discussion of homework solutions
Homeworks will be issued on Friday every week and will be discussed in tutorials on the following Monday. Feel free to ask any questions about the homeworks there.
You will not turn in your homework solutions for grading. However some of you will be called upon to present solutions in class on Tuesday. Your solution will then be discussed among your classmates.
This presentation will count towards your grade. Students will be selected to present randomly with repetition. This means you may be called to present at any time, and more than once. It is important that you show up in class every week and that you are prepared to present solutions to (most of) the problems for that week. If you cannot make it to class on any particular week, let us know in advance.
You can use the ENGG 2040C discussion board on the CU e-learning system to ask questions and participate in online discussions related to the course.