University of Washington
Department of Mathematics Mini-Project

MATH 394: Probability I

Instructor: Arman Jahangiri

Overview

For this mini-project, you will create a short recorded presentation in which you teach a probabilistic concept not covered in our course. You should imagine that you are teaching the topic to a classmate in MATH 394 who has the background of this course.

Project Requirements

Please follow all of the requirements below:

1.

Length. Your video must be at least 10 minutes long.

2.

Individual work. This is an individual project.

3.

Slides are required. You should prepare slides and present by speaking over your slides.

4.

Presentation style. Your presentation should mainly consist of slides plus verbal explanation. You should not rely on writing extensively on the slides while presenting. Brief annotation, circling, underlining, or pointing for clarity is fine.

5.

Recording method. If you use macOS, I recommend recording with QuickTime Player. If you use another operating system, you may use any similar screen-recording app that allows you to record your screen and your voice. The recording should be of high quality and clear. Using cameras to externally record your screen is not accepted.

6.

Slides. There is no restriction on the number of slides.

7.

Content. Your presentation should include:

• a short introduction and motivation,
• a clear explanation of the main concept,
• at least one worked example, application, or illustrative scenario,
• a brief concluding summary.
• citations

8.

Sources. Your final slide should list the sources you used. Please use reliable sources and cite them clearly.

Topic Selection

You must choose a topic that is not covered in our course. A list of suggested topics appears below.

• Each student should choose one topic.
• Please submit your top five topic preferences (ranked from 1 to 5, where 1 is your most preferred topic and 5 is your least preferred) by completing this form no later than July 15, 10:00 PM. If no response is received by the deadline, it will be assumed that you do not wish to participate in this bonus project. After all responses are collected, you will receive your assigned topic. You can then choose to go with it, or in case it is not of your interest, you can choose a topic of your own not in the list.
• If you would like to present on a different topic, that is fine, but you must get approval first.

Suggested Topics

1.

Birthday Paradox

2.

The Banach Matchbox Problem

3.

Coupon Collector Problem

4.

Gambler’s Ruin

5.

Secretary Problem

6.

Buffon’s Needle

7.

Benford’s Law

8.

Simpson’s Paradox

9.

St. Petersburg Paradox

10.

Markov Chains

11.

Random Walks

12.

Poisson Processes

13.

Branching Processes

14.

Monte Carlo Methods

15.

Capture–Recapture Estimation

16.

Reservoir Sampling

17.

Bloom Filters

18.

PageRank

19.

Reliability of Systems and Networks

20.

Random Graphs (Erdős–Rényi Model)

Submission Instructions

Please submit the following on Canvas:

1.

a PDF of your slides, and

2.

either:

• an mp4 file, or
• a working video link.

3.

In the text prompt on Canvas, please answer Yes or No to the following two questions:
Question 1: Would you like your slides (not the video) to be used anonymously in the future on the instructor’s website?
Questions 2: Would you like your slides (not the video) to be shown anonymously as sample projects to the students taking this course in the future?

Your response should be one of the following: (Yes, Yes), (Yes, No), (No, Yes), (No, No).

Please make sure that:

• your video link works,
• your audio is clear,
• your slides are readable,
• your file names include your name.

Grading

• Mathematical correctness and understanding — 40%
• Clarity and organization of explanation — 30%
• Quality of example or application — 20%
• Professionalism and completion of instructions — 10%

A strong project is one that explains one idea clearly, correctly, and concisely.

Late Policy

Because final grades are due very shortly after the end of the quarter, late submissions cannot not be accepted.

Note

This project is meant to be a useful opportunity to practice learning by teaching. Choose a topic that you find interesting, explain it carefully, and aim to teach it in a way that would help one of your classmates understand it.

If you have any questions, please email me at armanjg@uw.edu or post it on Ed discussion.