Fat Chance: Counting & Probability mooc

Course: Fat Chance: Probability from the Ground Up
Length: 7 weeks, 3-5 hrs/wk (self paced; this session open until October 2018)
School/platform: Harvard/edX
Instructor: Benedict Gross, Joseph Harris, Emily Riehl
Quote:

Increase your quantitative reasoning skills through a deeper understanding of probability and statistics.
Created specifically for those who are new to the study of probability, or for those who are seeking an approachable review of core concepts prior to enrolling in a college-level statistics course, Fat Chance prioritizes the development of a mathematical mode of thought over rote memorization of terms and formulae. Through highly visual lessons and guided practice, this course explores the quantitative reasoning behind probability and the cumulative nature of mathematics by tracing probability and statistics back to a foundation in the principles of counting.

My experience with math moocs (I’ve taken about a dozen) has been: it all depends on where you’re starting from, and what kind of instruction/exercises work best for you. This course was perfect for me: it went over some basics I needed to review, and went just a little beyond my comfort zone. Both the “how it works” and the “how to do it” were covered clearly. There was enough repetition to build a kind of security, in both explanation and exercises. An occasional hint of goofiness made it fun. I got lost a couple of times, but plenty of signposts helped me find my way back. Perfect.

The seven units that comprised the course were released two at a time. I see now that each unit was expected to take two weeks (I really MUST start paying attention to introductory material and instructions) but I had no problem completing it all in four weeks. Each lesson, usually three or four per unit, featured a lecture video that gave the basics of the concepts to be covered, showed how important formulas were derived, and ran through an example or two. Each of these lessons was followed by a short set of 2 to 4 practice exercises, complete with an “office hours” step-by-step video, usually showing a slightly different way of working the problem than was presented in the lecture (I could have used a couple more of these in some units, but it was sufficient as is). Each unit ended with an evaluation problem set covering all the lessons of the week. The instructors were all personable and relatable; diagrams helped concretize abstract ideas, and little drawings brought in a little fun.

The practice exercises made up 20% of the grade – and, since they were mostly multiple choice and allowed unlimited attempts, were more or less “gimme” points. The weekly evaluations, also multiple choice but allowing 2 attempts, counted for 80%.

The first two units covered counting. Now, when I was in school back in the Dark Ages, counting meant… well, counting. 1, 2, 3, etc. You were done with it by 2nd grade. But it means more than that now (it probably always did, but way back in the days of yore, nobody thought it mattered). It’s all about permutations and combinations (in this class, referred to as sequences and collections, which is more familiar to programmers) with or without replacement, binomial and multinomial coefficients, x choose y. But it’s all put in very understandable terms: pulling marbles of different colors out of a bag, making anagrams, assigning dorm rooms of different sizes to a group of students.

The third unit covered the basics of probability, which boils down to: success over possibility, with slightly different twists depending on whether you’re dealing with coins, dice, or cards. Then we got into expected value in the fourth unit – why slot machines are a losing game – a topic I’ve seen several times in various contexts. Conditional probability in unit 5 – the Monty Hall problem, election probability – got a little scary but made sense. The sixth unit on Bernoulli Trials was one place I got lost – it was where I completely dropped the ball in a prior class – but eventually I caught on. Normal distribution, likewise, was tricky, but thanks to the Office Hours videos, I was able to work my way through it.

I found this course extremely helpful in my continuing struggle to learn math, any math. I’m still concerned, because my grasp of all this is very context-dependent. For instance, I don’t really see the connection between Bernoulli trials, random walks, and distributions as covered in earlier classes, and as covered here. Maybe that means I just need to get a wider view.

And in that vein, the best part is: there’s more! In July, yet another HarvardX course, Intro to Probability, will begin, and the teaser video looks like a lot of fun (I’m a sucker for any math course that includes good animation). It doesn’t look like it was intended to be a Part II to this course, so I’m not sure how much is overlap and how much is new material, but I’m betting it’s going to be worth it either way. [Addendum: The “Look! Animations!” teaser was bait-and-switch; this was seriously mathy stuff, theorems and proofs and now go figure out what to do with them. I got through the first two weeks just fine, but really, seriously crashed and burned on week 3; week 4 only got worse, so I went looking for a different sequel, and found Purdue’s course; it’s archived, so there’s no support, but it’s working out a little better]