It's been awhile since I wrote a blog post, and with this one I am going to diverge from the topic of programming to talk about something else I have been diving into recently — math.
I am writing this post at a rather interesting time in history. I am not sure what it will be called in textbooks, but currently the world is at the mercy of the coronavirus. And now is also an interesting time for individuals who may be at home, unemployed and scared, wondering what to do next. My advice would be to focus on learning. It begs the question what to learn. That is a subjective question, though here I am going to recommend math. More importantly, however, I am going to recommend math to those who hate math, who feel they could never be "good" at it. Of course, I am sure it is of no surprise that I once considered myself one of those individuals, someone who felt completely inept with numbers. But now I don't. I went from getting a D in elementary algebra to getting As in precalculus through calculus 2. Alright, so I am no mathemetician, but I know what proved effective for me in combatting my fear of numbers, and hope my strategy may be helpful to others.
Practice for the GRE
Regardless of whether or not you plan on applying to graduate school, practicing for the quantitative section of the GRE (https://www.ets.org/gre/) is an excellent way to start learning math. Here is why:
- It gets you up to speed relatively quickly on a lot of topics that you probably don't remember or never learned, but that are essential to success in more advanced math.
- The learning resources are relatively cheap.
- Teaches you tricks for quicker mental math, which is an invaluable skill during timed exams.
That last point is particularly important, as it will ensure you don't use your cognitive resources unecessarily. Math exams are tiring and your brain only has so much fuel — quick mental math will make that fuel last, I promise.
Study materials
When studying for the quant GRE section, it's important to know that not all resources are made equal. Some GRE study products are overpriced, do not teach effective test taking strategies, and have questions not reflective of those you'd face on the actual GRE. Why is that important if you don't plan on taking the exam? Well, what if one day you do want to take the GRE? And it's also a matter of integrity — why support companies that sell misleading products?
Here is a great write-up of GRE resources:
https://magoosh.com/gre/2020/best-gre-books/
Buy a whiteboard
It's easier to visualize a problem when it is written largely and clearly on a whiteboard, even more so when each step is in a different color. As you progress in math and the equations become more complex, finding where in the process you made a mistake that leads to an incorrect result becomes increasingly important.
Another benefit of a whiteboard is it removes the context clues your brain are used to when working on math. In other words, always using a pencil and paper is not giving your brain the sort of muscle confusion it needs to really get this stuff down. Also, if people see you have a whiteboard with math problems on it, they'll think you're super smart.
A little bit every day
Going to cram for that calc test the weekend before your test? Yea, that's a bad idea. That's analagous to running a lot the day before a marathon, hoping it will make up for all those months sitting around eating Elio's pizza.
You need to create those math pathways in your brain through daily repitition. By doing 30 minutes or so of math daily, you are quite literally creating a math mind.
Go on walks and think about math
You know those brain pathways we talked about earlier? To get them even stronger, think about math when you're not in front of your notes or homework or anything related to math class.
As an exercise, go walking in the woods and look at a tree through a lens of math. For example, if you knew a tree was 50 feet tall, how would you compute the distance between the top of the tree and where you are standing? If you know the circumference of a tree, what else do you know about it? What would you have to divide the circumference by to get the radius? Now that you have the radius and assuming the same circumference throughout the tree, can you compute the volume of the 50ft tree?
Pretend you're teaching a math class
When attempting a problem on a white board, say out loud each step you are taking to solve it as though you were explaining it to a group of students, your grandma, whoever. Explain the process.
Sit with being uncomfortable
Alright, so you're getting all misanthropic genius, looking quizzically at trees and explaining rules of exponents to an imaginary audience, but the true battle comes when you feel completely hopeless at math. That's the feeling you want! It's completely normal! There is an illusion that the people we see do well in math don't get overwhelmed, but that's not true. Feeling inept, hopeless, like you will never get it right is all a sign of progress. Like most things that are difficult to learn, you have to feel dumb before you can feel smart.
Pomodoro Technique
To lessen the stress of studying math, use the Pomodoro Technique — a time management skill that is awesome for studying things that make you anxious.
The basic idea behind the technique is to schedule your studying in 25 minute increments, followed by a short break. This helps in alleviating anxiety because the time you are studying is finite and relatively short — you can see the light at the end of the tunnel, knowing once it's over you did your job of studying for 25 minutes, no more, no less...and no guilt!
Here is the site I use for the pomodoro:
It's not your fault
If you ever seen the movie Good Will Hunting, there is a scene where Will's therapist tells him "it's not your fault." The same can be said about learning math later in life. It's not your fault you didn't succeed in math in HS or your first round of college. We see people do well in math, but what you don't see are the parents who are employed as engineers, the quality home life, the expensive tutors — all of these things and more make it much easier to learn math on the prescribed timeline, so don't feel bad that you didn't have those, it's not your fault. Be patient and kind to yourself during this process, because it is hard, you will feel like a fool, but that's part of progress — embrace it.
Conclusion
I hope this proves helpful. If you were to tell me a few years ago that I could get an A in calc 2, I would not have believed you. I was convinced some people got it and others don't. Through necessity though, I had to learn math. Now if someone asks if I am good with numbers, I can say "yes," and for some reason that feels really, really good.