How to Memorize Math Formulas

In this video I talk about how to memorize math formulas. There are different ways of doing this and in this video I will discuss some of those ways. I give some very specific examples involving Calculus and Trigonometry. Do you have any advice for people? If so, please leave a comment below.

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[FlatEarthMath]

As a high school math teacher, I always give the advice your teacher gave you at 7:58... Always recopy a formula each time you use it. Every problem. No exceptions. It's a great discipline, and you'll memorize the formula without effort. 😎

[byronwilliams]

Excellent timing. There are so many formulas to memorize in Statistics.

[fudgenuggets]

I'm a big believer in the idea of writing down the formula for every problem you work on. Back when I was in college I took it to another level and the day before a big exam I would take the most important formulas and write them down sometimes up to one hundred times until I had them down cold. I can still recall some of them with my eyes closed 30 years later.

[jonko]

Nice video. Here is another way to memorize those common trig values for sine and cosine. It is always the square root of a number divided by two, you start with sin(0) and 0 and then increase the number under the square root by one for each successive increase in angle:
sin(0) = sqrt(0)/2 = 0
sin(pi/6) = sqrt(1)/2 = 1/2
sin(pi/4) = sqrt(2)/2
sin(pi/3) = sqrt(3)/2
sin(pi/2) = sqrt(4)/2 = 2/2 = 1

And for cosine it is the opposite order to sine where you start with the largest angle, cos(pi/2) and then decrease the angle:

cos(pi/2) = sqrt(0)/2 = 0
cos(pi/3) = sqrt(1)/2 = 1/2
cos(pi/4) = sqrt(2)/2
cos(pi/6) = sqrt(3)/2
cos(0) = sqrt(4)/2 = 2/2 = 1

[bluedreamtv]

I started to practice recalling my daily actions and words as much as I can of the whole day at midday and at night and I found my ability to memorize equations drastically increased

[daniellejdevlin]

What I do to memorize formulas is writing them over and over and at a slow pace. I find taking my time with math I actually learn more. Thanks for the cool trig tricks!

[Hconinja]

Thank you, i'm glad i found your video talking about how it's okay to have your own way of memorising methods.

For me in particular, I had a different way of memorising methods compared to my colleagues. When i told my colleagues my methods when they asked, they would think it's silly and put me down for it.

Eventually, the feeling of being different caught up to me and i was slowly doing less.

After seeing this video and reading the comments, I feel more comfortable knowing that's it's not just me who uses different memorising methods.

This might be a silly story, but I really needed this motivating push.
Thank you

[mrmitchell]

One of my favorite channels by far. Getting a new grip on math at 37. I want to learn as many languages of math as possible. One step at a time. Your channel is great. Thanks

[budgarner]

That's my college text you've got there. Took 10 hrs to review the first half of the first semesters. Starting to slow down in the differentials section. Thanks for the memory techniques for memorizing them. I had to learn them by discovery and tried to teach my students the same. Writing the formula first, how powerful.

[DavesMathVideos]

As you said it's important to have an idea of how things work. It's hard to memorize everything, but if you have a somewhat deeper understanding of how things work, you can often reconstruct formulas that you've forgotten (just as long as time is of no concern).

[byronwilliams]

I also used the technique where you write the formula being used for that type of problem from memory. I found that using that approach in conjunction with a large number of problems really helped hammer home the formula. I also would derive the formula. For whatever reason, I could never remember formulas so I would always ask for extra paper, where I would derive every formula or value I would need.

Hope this helps.

[God-ldll]

I heard about using "creativity" to bring about an analog memetic story. Though i find the "story" is already there in the sense of finding out, loosely say, the utility(s) of such concepts or etymology for ex.

Ideally it should be an experience like seeing an awe landscape or good story. You (likely) never forget such a show.

[xbrtyld]

For the quadratic formula, there are at least 3 tunes that fit. In Canada we use Frere Jacques (Are you sleeping, brother John). Repeat each part twice (x = negative b, x = negative b...) Also, the Pop goes the Weasel song. Lastly there is the Michigan football song. Putting a formula to music is very effective, when possible.

[erthx]

Wizard you should put together an ebook on your mathematical ideas. You are mentor and coach.
I believe that the meaning that math has in our lives in any given time is paramount to our individual experience.
Going back your original discussion, how does one memorize these relations? We need to focus on the passion for identifying the patterns and symmetries. Rigor + Life experience.
If mathematics is truly the queen of sciences, then all that love and adore her, no matter what rank they serve, must never give up.

[mannydossantos]

I forget these type of memory tricks. As an alternative, I use a photographic memory trick as I visualize pages in a textbook. However, it got me into trouble in some exams, when facts need to be regurgitated, as it seemed like cheating to some teachers.

[nubeebee]

Beyond what you've covered, I like rote memorization, especially using flashcards.

[AlbinoJedi]

The big thing for me that helps is exactly what you said at 2:23. Whether in math or anything else, it's easier to remember something if I understand where it came from and why it is. This provides more back context to connect the memory to.

[xylh]

As far as memorizing formulas, it really depends on your field of study. I see formulas that involve elementary algebra as some sort of statement composed of parts that all balance together. I brute force the memorization through flash cards and I try to apply them in repetition to get a baseline association. Then, I reinforce my knowledge by trying to find a proof of the formula if I can. When you know the logic behind why a substitution or formula works, it seems to stick better. When the proof is too complex, I let the brute force memorization and application suffice.

[kushagrachadha]

Thanks a lot. Was learning trig identities when the notification came up. It's really helpful.

[hrenhrenov]

Well, in my humble personal experience, pronouncing the formula in addition to writing it down somewhat helps. And yes, when you have a bunch of related formulas, it helps to remember how you can derive each formula from others (not only in the sequence they were derived in your textbook). Sometimes it is easier to remember the whole lot of related formulas than to remember only one of them (that is, if you see how they are related).