This article is part of the series “Common Beginner Questions“.
This article will answer the question, “I meet the prerequisites, but I can’t understand your course. Why?”
The short answer:
You think you meet the prerequisites, but in reality, you do not.
Questions you should ask yourself:
- Do I have any incentive to lie to you about the prerequisites? Why would I want to have a bunch of frustrated students who won’t go on to buy more courses in the future?
- Does it make sense for the student to decide whether or not they meet the prerequisites, or the instructor?
- If you think “the student decides the prerequisites!”: That’s like saying a student of a driving school can decide whether or not they are ready to drive, which is clearly nonsense. The driving instructor decides whether or not you are ready! Obviously, driving would be very unsafe if we just let everyone decide for themselves when they are allowed to drive…
The long answer:
Not everyone is an A+ student
Let’s get this out of the way. Not everyone is an A+ student.
If you got a B or a C (or worse), there were many things you didn’t understand.
You passed the course, but it still means you didn’t understand 20% or more of the material.
That’s fine if you just need the course to progress in your degree.
That’s not fine if you need to apply the concepts in later courses.
If you got a D or an F, forget it. It doesn’t count at all.
So when I say “calculus is a prerequisite”, I don’t mean “you took a calculus class”, I mean you actually understand everything you learned and you’re able to apply it now.
If you got a B/C/D/F/whatever, act like a mature, responsible adult and just be proactive. Learn the skills you need to learn to get where you want to go, and stop blaming others for your insufficiencies.
To be very clear: this is not me being elitist.
I’m telling you to build these skills before taking this course, because you need these skills during the course. It’s a good thing!
Telling you how to be prepared so that you achieve the optimal result isn’t bad, it’s good! Why do people get offended by it?
Isn’t this just common sense?
“I did calculus 20 years ago and forgot everything, does that count?”
It should go without saying: no, it does not count.
You need to apply these concepts.
If you don’t know the concepts, you can’t apply them.
Many of the “older” generation like the idea of credentials.
“If I just get a piece of paper saying I know this subject, I’m good!”
No, you’re not good.
When I say calculus is a prerequisite, I don’t mean you need to show me a certificate saying you’ve learned calculus. (C’mon guys).
You need the skills to back it up.
The reason should be obvious.
Additionally, one thing less-mature / naive students don’t understand is that your goal isn’t to be a calculus master and have all the facts memorized and ready to go at all times. That would be ridiculous. You don’t need calculus for most things in your life, like cooking, playing sports, debugging code, etc.
The whole point of having been exposed to calculus in the past is that it becomes easier to refresh in the future when it’s needed.
Compare that to someone who’s never learned calculus at all – they have no chance.
By saying you need to have calculus prerequisites, it’s not saying that you can solve every problem in a college textbook and get 100% on an exam today – think rationally. It simply means you must be skilled enough to learn or review the necessary tools, on an on demand basis.
“You shouldn’t assume students know <X>”
This one always gets me.
I always laugh when I see this and think, “yup, another person who can’t wrap their head around the concept of following instructions”.
Guys, the instructions are there.
They’re called the prerequisites.
Udemy students are notorious for not following instructions, which is why I’ve listed them twice in the course description.
On top of that, I mention it again in the lecture “How to succeed in this course”, which usually follows the introduction and outline lecture.
I mention them again in the FAQ, in the lectures “Is this course for beginners or experts?” and “How to succeed in this course (long version)”.
Yes, I really mention it that many times, because some students are that resistant to following them.
Really, it’s just an excuse for me to say: “I mentioned the prerequisites five times, and you still didn’t follow them?” 😉
There’s a difference between:
- Assuming you know something and not giving you any warning
- Assuming you know something because I instructed you to know it and reminded you several times
I hope that the difference is obvious.
Prerequisites are not obstacles, they are stepping stones
Let’s be clear: the question “I meet the prerequisites, so why can’t I understand your course?” is not even a good question to ask.
When students ask this question, it really exposes a low level of maturity and learning ability.
You (incorrectly) believe you meet all the prerequisites, and thus you expect that the course will be a breeze – you deserve it for all your hard work in meeting the prerequisites. You are in fact entitled to it! This is completely the wrong perspective.
The prerequisites are not obstacles in the sense that, once you feel like you’ve conquered those obstacles, it will be smooth sailing from there on out.
The correct approach is to see that the prerequisites are stepping stones – they are guides.
If you don’t understand something in the course, say, matrix inversion, then you can look at the prerequisites, figure out which topic “matrix inversion” belongs to, and then refresh your knowledge.
Compare this to if the prerequisites were not listed at all.
With no prerequisites listed, you might encounter “matrix inversion”, have no idea what that means, and be completely stuck on how to learn more about it.
As such, the role of the prerequisites is to tell you where to refresh your knowledge, if need be.
A corollary of the above is that, even if you ignored my instructions to meet the prerequisites, you can still succeed in the course!
(But please note that, ignoring my instructions is not recommended, so fix that promptly.)
Too many students just throw their hands in the air and say, “I give up!” because they decide that the prerequisite instructions are simply too much to bear.
Obviously, this is being unnecessarily weak. Just learn what you have to learn, improve your mind, improve your skills, and catch up to your peers by using the prerequisites as your guide. It really is that easy.
Prerequisites are Tools
To add to the above, knowing the prerequisites does not automatically imply that you’re well on your way to an easy ride through the course. Otherwise, what would be the point of the course? You could just read Wikipedia and viola, you know everything.
In reality, the prerequisites are tools.
That’s why they are prerequisites.
If you don’t have them, then you won’t have the tools to build what you need to build in the course.
If you do have them, this doesn’t imply everything will just automatically build itself.
You still have to apply those tools and build new skills.
Hence, your ability to build the new skills in the new course is dependent on your proficiency with the existing tools.
Just because you think you can use a hammer, a saw, a screwdriver, etc. does not imply that the chair you build will look nice.
Example of How to Apply Prerequisites
The simplest way to discuss this is by way of example. Let’s take my Linear Regression course.
It depends on 3 undergraduate / college-level math topics:
- Matrix arithmetic (I hesitate to say “linear algebra” because it doesn’t depend on most of the college-level topics of linear algebra, just high school-level matrix manipulation)
The matrix and vector arithmetic part should have already been covered in your high school math courses, and you should have applied those concepts already in Calculus 3, which typically covers vector calculus and some differential equations.
Example 1: Matrix Calculus
Let’s give some examples of students who think they meet the prerequisites, but really don’t.
A good example is matrix calculus, used a few times in my Linear Regression course (in a very basic way).
It’s meant to be an introductory course in machine learning and paves the way for all the other more advanced courses I teach (25+ so far).
- Matrix calculus is not a prerequisite of this course
- Matrix calculus doesn’t need to be a prerequisite to this course
- There is no “class” on matrix calculus that you can take (proof: check any CS/eng undergrad curriculum)
Some beginner students see the Matrix Cookbook and freak out. Why?
It’s not because I’ve failed to teach them “matrix calculus”.
In fact, there is no such course called “matrix calculus”. I can’t make it a prerequisite, because it’s not as if you can sign up for a course and learn it. There is no course for it! What is the real issue?
It’s because they are not good at regular calculus! (And to be clear – that’s your fault).
Remember, after you’ve passed your calculus 1/2/3 classes, it’s all about applying what you learned in later courses.
Matrix calculus is essentially partial differentiation applied to the matrix and vector arithmetic you already learned in high school.
Some beginner students have asked me to show them the relevant rule in the matrix cookbook, or assume that there’s some “trick” to learning how to use this book.
It’s a book. You’re supposed to have the skills to read a book.
Given a book, you should be able to look up relevant information.
These are basic life skills, man!
Example 2: Multivariate Normal Distribution and Probability
Probability is a tricky subject, because it’s taught at all levels (high school, college, and graduate school).
For machine learning, the most relevant level is college level. You can watch this video for more details: https://youtu.be/5Iq7tcrTnWA
It should be obvious in any case:
- Obviously, I don’t mean high school probability, since machine learning is a 3rd-4th year subject
- Obviously, I don’t mean graduate level probability, because grad school would come after a typical ML course (undergrad)
If your level of probability is: p(Heads) = Heads / (Heads + Tails), that’s just not enough.
Seeing a multivariate normal PDF shouldn’t scare you.
If it does, then the correct course of action is not: “Hey, you haven’t explained this! Bad teacher! You need to bring the course down to my level!”
The correct course of action is: “Hmm, I wonder why I haven’t seen this before? Let me look it up and double check whether or not I meet the prerequisites. I’ll research this by myself so I can catch up to my fellow students”.
It’s your responsibility to look up the correct level of probability of this course (after I’ve made it clear), and it’s your responsibility to catch up on topics you don’t know.
It’s not my responsibility to teach you everything from scratch (a whole new course or multiple courses for free, in your dreams!)
Basic topics you should know (covered in any college-level probability course):
- PDFs, PMFs, CDFs
- Common distributions: Bernoulli, Binomial, Poisson, Exponential, Normal, Multivariate Normal
- Conditional distributions, Bayes’ rule
- Expected values and functions of random variables
You do not need exposure to statistics concepts like maximum likelihood estimation or MAP estimation.
You should be good enough with probability to learn MLE and MAP as you take this course.
If you cannot, that means your skills in probability are not sufficient and you do not meet the prerequisites.
I know the topics you listed, but I still can’t understand
Many people will see these “lists” (like: PDFs, PMFs, and CDFs) and say, “yes, I know these topics”.
Is that good enough?
People often confuse:
- Being exposed to a concept
- Being able to solve problems using the concept
When I say “know PDFs”, I don’t just mean “know what a PDF is”, I mean, actually be able to do useful computations involving PDFs.
In other words:
Reading a Wikipedia page or watching a YouTube / Khan Academy video is not enough.
You must be able to solve problems and do math.
Example 3: Relationship between Squared Error, MLE, Regularization, and MAP
In my linear Regression course, we show the equivalence of squared error minimization and MLE, and the equivalence of regularized regression and MAP.
This only requires exponentiating the loss function to recognize that the “form” or “shape” of the loss is proportional to the likelihood (or posterior in the MAP case).
Some beginner students have trouble “seeing” the equivalence, even when the equations are presented in front of their very eyes.
If you can’t see this equivalence, again, it’s because your skills in probability are not sufficient.
It means you need to improve your math knowledge.
The big mistake students make is thinking that they are perfect – they don’t need to improve.
They believe others should be bending over backwards to make things easier for them.
This is a self-centered approach which only hurts them in the end.
By not recognizing that they lack skills (in many cases, insisting that it cannot be true!), they will never gain new skills.
So, I suppose they reap what they sow in the end.
What is the solution?
The solution is obvious, and I’ve alluded to it earlier in this article.
No, it’s not just “meet the prerequisites”. If all students could precisely interpret what that meant, there would be no need for this article. But hopefully this article helped to clear up any incorrect notions you had.
See, you really have 2 options:
- Blame other people for your insufficient prerequisite knowledge.
- Blame yourself for your insufficient prerequisite knowledge. Proactively and enthusiastically improve your knowledge to meet the prerequisites sufficiently.
Obviously, only one of these will actually make you a better, more knowledgeable person.
The type 1 people often say things like: “You should have explained X, Y, Z, etc.” presuming that their knowledge of the prerequisites is perfect.
They presumed that it must be my prerequisite knowledge was wrong, because I didn’t know what they knew.
Of course I don’t know what you know.
I don’t know you. I can’t know what you know or don’t know.
I can’t tailor the course to meet your incorrect notions of what “calculus” entails or what “probability” entails. The course will not be customized exactly for your background. Since I don’t know you, obviously that would be impossible.
Instead, it is customized to the most correct and most universally accepted standards of the listed prerequisites.
What happens when you are in the real world?
Do you go to your college professor and say, “Hey man! You made this course too hard! I demand that you help me review the prerequisites!”?
No, no you don’t do that.
It’s called “catching up”.
You work hard and “catch up” to your peers, so that you can pass the class.
You don’t ask for the rest of the class to wait for you.
I suppose that since the bar for getting into college is much higher than signing up for a random online course, the maturity level there is also higher. However, realize that eventually, you’re going to be competing with those people for jobs.
If your approach is not to bring yourself up to their level, but instead to ask everyone to make things easier for you – you will simply not be competitive.