University of Connecticut College of Liberal Arts and Sciences
Department of Mathematics
Tom Roby's Math 3160 Home Page (Spring 2015)

Questions or Comments?

Class Information

COORDINATES: Classes meet Tuesdays and Thursdays 9:30–10:45 in MSB 411. The registrar calls this Section 005.

PREREQUISITES: Math 2110Q or equivalent experience.

TEXT: Sheldon Ross: A First Course in Probability, 9th Edition.

WEBPAGE: The homepage for this course is There is also a Piazza Homepage, which has links to class notes, HW, and discussions forums. Please post your questions there rather than emailing them to me. That way the entire class can benefit from the discussion. Some others web resources are listed below.

SOFTWARE: While doing some computations by hand is generally essential for learning, having software that can do bigger computations or check one's work is very useful. I recommend the free open-source computer algebra system Sage, which has an extensively-developed collection of objects and algorithms implemented for many areas of mathematics, including combinatorics.

GRADING: Your grade will be based on one midterm exam, one final exam, weekly quizzes and homework.

The breakdown of points is:

HW Quizzes Midterm Final
10% 20% 35% 35%

MIDTERM EXAM: Will cover all the material up to that point in the term. It is currently scheduled for THURSDAY 5 MARCH 2015 during our usual class meeting. Please let me know immediately if you have a conflict with that date. There are no makeup exams.

QUIZZES: Quizzes will be given roughly once per week on THURSDAYS, covering the material from the previous week. The best way to prepare for them is to do more exercises than I've assigned. The first quiz will be 29 January. Both older and more recent educational research seems to indicate students do better at retaining information with regular quizzes than with the common approach of two midterms and a final. Those of you going onto careers as Actuaries will have an exam on approximately the material of this course early in your careers.

HOMEWORK: Homework will be assigned most weeks, and should be attempted by the following TUESDAY, when I will be happy to answer questions or provide hints. It will generally be handed in on Thursdays at the start of class, just before the quiz. Since I may discuss the homework problems in class the day they are due, late assignments will be accepted only under the most extreme circumstances. (Please let me know as soon as possible if you find yourself with a situation that might qualify.) The lowest written homework score will be dropped in any event.

The book has many exercises for each chapter, and I recommend you also attempt a number of those that are unassigned with answers in the back. If you get stuck on one, feel free to ask! The homework assignments will be posted on the Piazza page.

You may find some homework problems to be challenging, even frustrating, leading you to spend lots of time and effort working on them. This is a natural part of doing mathematics, faced by everyone from school children to top researchers. I encourage you to work with other people in person or electronically, and particularly to avail yourself of the discussion boards on Piazza. It's OK to get significant help from any resource, but in the end, please write your own solution in your own words. Copying someone else's work without credit is plagiarism and will be dealt with according to university policy. It also is a poor learning strategy.

ACADEMIC INTEGRITY: Please make sure you are familiar with and abide by The Student Code governing Academic Integrity in Undergraduate Education and Research. For quizzes and exams you may not discuss the material with anyone other than the instructor or offical proctor, and no calculators, phones, slide rules or other devices designed to aid communication or computation may be used.

ACKNOWLEDGEMENTS: Many people have influenced my approach to this material, particularly Scott Sheffield and James Propp.

CONTENT: Probability Theory is a fascinating topic in mathematics dealing with random phenomena. The modern theory is currently very actively researched by mathematicians in a variety of subfields, with deep connections to very challenging questions in analysis, geometry, and combinatorics. There are also numerous applications in science, engineering, business and games of chance, the latter being the original motivation. In fact, probability theory underlies the study of statistics, which provides useful insights in many fields of human endeavor, from medicine to politics.

Probability is also a fun topic, beyond its connection with games. There are certain paradoxes that come up, where the truth appears to be counterintuitive--at least until one develops better intuition about how random processes work. We'll explore some of these as we go along.

ACCESSIBILITY & DISABILITY ISSUES: Please contact me and UConn's Center for Students with Disabilities as soon as possible if you have any accessibility issues, have a (documented) disability and wish to discuss academic accommodations, or if you would need assistance in the event of an emergency.

LEARNING: The only way to learn mathematics is by doing it! Complete each assignment to the best of your ability, and get help when you are confused. Come to class prepared with questions. Don't hesitate to seek help from other students. Sometimes the point of view of someone who has just figured something out can be the most helpful.

Especially for learning this subject, it is important to do lots of problems—many more than I could reasonably assign you to hand in. Note that almost all problems are word problems, and careful attention to language is imperative.

CLASSTIME: In order to get through the essential material, lectures will be fast-paced. I will post slides on the Piazza page that summarize some of what we did, but will also work out many things on the board. There will not be time to "cover" all material in a lecture format so you will need to read and learn some topics on your own from the text, handouts, web sources, or otherwise. If you have to miss a class for some reason, please find out from a classmate what happened in class beyond what was in the slides for that day.

SCHEDULE: The following is the start of a tentative schedule that I will update throughout the semester. If you have a religious observance that conflicts with your participation in the course, please meet with me within the first two weeks of the term to discuss any appropriate accommodations.

Date Chapter Topics Etc.
1/20 T § 1.1–3 Intro to Prob., Basic Counting, permutations
1/22 R § 1.4 combinations, binomial coefficients & binomial theorem; Also: solving problems!
1/29 R § 1.5–6; 2.1–3 multinomial coefficients; sample spaces, axioms; Take home quiz due 2/3
2/3 T § 2.4–7 basic propositions, equally likely outcomes; HW #1 and take-home quiz #1 due;
2/5 R § n.j–k
2/10 T § n.j–k
2/12 R § n.j–k
2/17 T § n.j–k
2/19 R § n.j–k
2/24 T § 4.1
2/26 R § n.j–k
3/3 T § 1.1&ndash 3.5; Review Day

Web Resources


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Anonymous Feedback

Use this form to send me anonymous feedback or to answer the question: How can I improve your learning in this class?  I will respond to any constructive suggestions or comments in the space below the form. 

Feedback & Responses

  1. [1 Feb] I am finding this class to already be very difficult because the problems we are skimming the problems in class and not understanding the concrete reasoning and method to solve the problems and therefore I am struggling to solve them on my own. I think it would be beneficial to slightly stay away from the powerpoints and coordinate the lecture more with the book. In class we should be able to recognize certain types of problems and then be able to solve them on our own later in the homework, and other than a select few in the class many of us are struggling already to understand the content.

    Thanks for letting me know how things look from your point of view! I expected the homework problems could be a bit challenging, particularly if you haven't taken many 3000-level courses before. In calculus we typically do a lot more working of problems that are similar to the ones you will be expected to do; this holds much less for upper-division courses.

    As far as lectures go, I try to mostly use the slides (which are coordinated with the book) to help me keep the course organized on the important topics, and use the boards to give the in-depth explanations. You are always welcome to ask questions, slow me down, or ask to see something done in more detail. Don't be shy! Lectures need to cover the basic principles involved in solving problems, so there's not so much time for solving HW-like problems.

    Please use the Piazza page if you have HW questions! This will function as a kind of "recitation". Other 3160 instructors have reported good results with their classes, but it feels to me like it's underutilized in this section (or, less likely I think, most students have been finding the homework manageable without). I'm also happy to go over HW questions in class the Tuesday before they are due. And try the self-test problems, which should help you with the HW to be handed in.

  2. [Date] This is a test.

    This is only a test.

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