Probability and Statistics are fundamentally important, but also subtle and very misunderstood. This combination provides a market for a lot of material online. There are YouTube videos, which admittedly can be way more slick than your millennial, GenX or boomer professor can do in class.

I watch Number Blocks with my toddler, and I know how useful these can be. Past students have told me about 3blue1brown, Zach Star (though this is more for EE 345), Khan Academy and I am sure there are many other resources. It is hard to give an overview of all resources since there are so many of them. But I did watch all the 3blue1brown and Khan Academy videos on probability so I could tell you how to best use these resources.

The short (and unfortunately unkind) answer is that these (3blue1brown or Khan Academy) are videos you must see before you start the material in class. They are at high school, not an undergraduate level. High school level is where you think you understand, but your teacher (or the person making these videos) also knows you have been gently lulled into thinking so. You aren’t really expected to generalize, but redo what you have been shown (maybe by changing a few numbers, etc). It has its utility, because at that stage of development, giving you the confidence you can do something is often more important than the content.

The answer is also unkind because high school instruction is very variable. It is not your fault if you haven’t seen this before in high school. It is not on you. But if you haven’t, as suggested in various modules, please try to watch the videos at least before we take up the content in class. You don’t have to understand everything, but you should watch it. And then ask questions in class (reference the video you watched, we will watch it together and I can comment).

There are also lecture notes and video recordings of undergrad or graduate classes online. Obviously the previous comment (about being high school level) does not apply to them. But the best use I can think of for all these resources: watch these videos and use the content to challenge me in class.

At the undergraduate level, you see the same topics all over again in some of the more fundamental subjects. But this time you are more capable, and so you can and should be challenged more. Instead of rote learning and drill problems, the goal is to get you to think in these formalisms. Some will tell you that you can pass an undergraduate course with high school knowledge. They would be right, and honestly, there is rampant grade inflation (though not for the reasons you would think—the reason for grade inflation is often the hope that it will encourage you to learn some day if not today). But then you are not getting out of this course what you can.

These fundamental topics are now presented in more powerful and deeper ways, more in line with how “grown ups” do things. As a consequence, the undergraduate level should reshape your world. You are still protected from the true extent of how far we have gone in these topics are (see the experiences in each module), but not as much as in high school.

Each time you relearn these topics, it is neither comfortable nor is it meant to be. But it will be wonderful if you have the attitude that you have to figure these things out. If you do that, by the undergraduate/beginning graduate level, you would have rewired your thinking to include these topics.