How to Memorize Math Formulas
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- Опубликовано: 27 фев 2023
- 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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Thank you:)
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. 😎
It's hard for me to identify which formulas need to be applied. Do you have any tips for that?
@@supernovic99 That's a great question. The key for me is really understanding what the formula does, and what the values are that it contains. For example, in the formula for compounding interest: A = P(1+r/n)^nt you need to really understand that n=number of compounding periods per unit of time (often years), while t is how many units of time (years). You can then apply this formula backwards and forwards, even using logs, depending on your initial "givens." I guess what I'm really saying is practice and understanding are key. If the formula is just letters, and you're doing "plug and chug" then it will only work with cookie-cutter problems, all set up the same way, of the same type. And it's great to start there, until you really build understanding of what the formula does and the values it relates. I hope that helps. 🙂
@@FlatEarthMath Thanks a lot! I'm learning algebra and it's kind of hard to identify which equations to apply and where.
Excellent timing. There are so many formulas to memorize in Statistics.
Indeed!
omg.. thats literally why im here bcs im studying for ap stats 😭😭😭
@@angeIitealso me😭😭
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.
You got good grades in school?
@@newaryamen Rarely #1 in any class, but usually top 10%. not great, but not bad.
@@newaryamen grades don't imply intelligence. They reflect more so the system you are using to play the academic game. It's not the best way of measuring intelligence but it's something at least.
@@Alex-ns6hj Very true. You could have 20 IQ and still be 1# in the class just by having great memory alone
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
This is the way I taught it to my students when I taught math at community college and high school. I'd tell them to "count from 0 to 4".
However, I'd also explain to them where it came from. This helped the people who learn visually. If those people drew a 45-45-90 triangle and a 30-60-90 triangle, they could derive the values easily.
I have another reply about this where I developed the system I believe is the absolute easiest to learn though I don't have a method of uploading a sheet unfortunately. This is my other comment about this please let me know what y'all think:
"For the unit circle, I came up with my own system and it makes me feel bad that others don't know it because I learned it and will never forget it.
I found the unit circle has a pattern. I chunked the information and broke it down to make it easier. First I learned that all the values are divided by 2. Then I learned that all the values on the numerator are inside a square root. Yes this applies to square root of 1, which is just one. Then I learned that on quadrant one, these values on the x coordinate go from sqrt of 3, then sqrt of 2, then sqrt of 1. Pi/6 is sqrt(3), divided by two like every other value. Then pi/4 is sqrt(2)/2, then pi/6 is sqrt(1)/2, or 1/2. These are the same values all around the circle.
Now you just have to learn the radian angles (degree angles are very intuitive I wont explain here though it's too long). Starting in quadrant one, these angles I use as reference are pi/6 for the first line, pi/4 for the second line, and pi/3 for the last one before pi/2 which is just 90 degrees. I color coded all these. Every /6 is red, /4 blue, and /3 yellow. In quadrant one theyre just pi over their respective color. Second quadrant it's one less times pi than denominator (for example second quadrant for yellow which is 3, would be 2pi/3). 3rd quadrant would be one more than denominator (so for yellow, it's 4pi/3. Notice how the constant behind the pi is one more than the denominator). The last quadrant is 2x the denominator minus one (2x - 1 (where x is the denominator. So it is for yellow 3 so 3*2 = 6, 6-1 = 5, so 5pi/3).
I wish I could put up a picture. My way of learning these things is finding patterns because I like them. And making it as simple as possible.
Something that I am beginning to experiment with that I have NEVER seen anyone do is experiencing with mnemonics and memory palaces as well as creating my own fictional memory palaces and possibly a narrative within this palace in my mind alone through creativity. I want to see if it's effective to take this inspiration from memory athletes and create a vivid expression in my own mind to retain information and relate disparate ideas in my mind which will enhance as a byproduct my creativity, problem solving and critical thinking skills to innovate and apply. Someone let me know if they use something like this or something like the Major System or some other means to memorize math. Thanks!"
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
Taking breaks now and then after learning content could be worth investing your time into.
Taking breaks allows your body to 'recharge' and improve your ability to focus the next time you start another session.
If you're already taking breaks, having a cup of water next to you while you're study could help improve your concentration and short-term memory!
Hope that helped 😊
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
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!
I really needed this
Thanks a lot. Was learning trig identities when the notification came up. It's really helpful.
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.
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).
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.
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
Beyond what you've covered, I like rote memorization, especially using flashcards.
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.
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.
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.
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.
Relatable. Given enough draft paper, I can solve most problems I'm given that are expected of me to solve. Without them though, I struggle as I got terrible working memory.
I rely heavily on "vomiting" my thoughts onto paper and organizing them there rather than in my head.
Perfect timing as always
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.
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).
Great advice. It's the proper way of memorizing stuff like that integral--huge like for the video. Also, writing down formulas and stuff reinforces the memory a lot. Reviewing formulas and writing them down from memory also helps. For values of trig functions it is best to visualize their graphs and all values fall into place right away, like, sin 210 = - 0.5 The same graphs help see through trig angle reduction formulas instantly like sin (270 - x) = - cos x and dozens of formulas like that.
As to the derivative of the product, the direct derivation helps visualize it and instantly retrieve from memory too:
(u + Δu)(v + Δv) - uv = uΔv + vΔu + ΔuΔv. Now dividing by Δx we instantly get uv' + vu'. Like I said, that's basically a very rigorous math derivation but certain steps are kind of omitted/implied: not using limits symbols, discarding the last term automatically (as it approaches zero) and making the division in the head. So retrieving it from the memory goes like this:
(u + Δu)(v + Δv) - uv = uΔv + vΔu + ΔuΔv. Hence, uv' + vu'. Of course, I won't do any of such steps as basic formulas are way too ingrained in me. I don't need to derive them like that but some more rare formulas do require a process like that. Example is, like I said, visualizing sine and cosine to instantly get sin (270 - x) = - cos x and dozens of formulas like that including particular values, like, cos 240 = -0.5. This process I can't show here since I can't draw a sine graph in the comment but it is easy even for kids🙂 It can also be done on the unit circle (also not very difficult) but I find visualizing graphs more comfortable to retrieve formulas and values from memory.
Writing down formulas (to memorize them), repeating them verbally and visually--all this really helps to remember stuff absolutely on autopilot. *How else can you memorize state capitals and their spellings to retrieve from memory on autopilot?* Some things just need to be drilled through repetition. Writing down stuff does help as is repeating stuff verbally or in mind. *Around 50 trig formulas are so much easier to remember as you can visualize stuff. Capitals are way more difficult to remember by far as you can hardly fall back on logic trying to recall the capital!*
An excellent way to memorize the formula for cos (α - β) is its derivation too. Imagine a unit circle with two radius-vectors forming angles α and β (with the x-axis) in mind. The scalar product of these vectors is 1*1*cos (α - β) = cos (α - β). And through coordinates their product is x1x2 + y1y2. Since coordinates are definintions of trig formulas we see in mind instantly that cos (α - β) = cos α cos β + sin α sin β. Replacing -β with +β we get the formula for cos (α + β). And replacing (α - β) with (90 - (α + β)) = ((90 - α) - β) we get the formula for sine (α + β), but the latter is somewhat difficult to visualize in mind:
sin (α + β) = cos (90 - (α + β)) = cos ((90 - α) - β) = cos (90 - α) cos β + sin (90 - α) sin β = sin α cos β + cos α sin β. The difficulty is almost on par with multiplying two digit numbers in mind or something like that because you will probably have to derive the formula for cos (α - β) as the first step. Two steps make it a lot more difficult and time consuming. So my tip is to suck it up and rote-learn sin (α + β) but when cos (α - β) is needed, just imagine the product of two radius vectors on the unit circle and you'll see the formula in your head (no need to memorize it). And the formulas for sin (α - β) = sin (α + (-β)) and the same for cosine can be visualized instantly by replacing -β with +β or vice versa. No need to rote-learn them and confuse yourself. So, only one formula for sin (α + β) needs to be rote-learned. The rest can be visualized in mind instantly.
As to tan (α + β), it needs to be learned by rote too or you'll have to go through 2-3 confusing steps which might be too difficult to do in mind but it is easy on paper. You will remember it all for the rest of you life that way. Of course, some day, when you are 90 years old or much sooner (in a few years probably), the formulas for sin (α + β) and tan (α + β) will be forgotten but you can still retrieve them from memory by doing 2-3 steps based on the scalar product of two vectors even if you are 90 and forgot all the math! You will also forget the quadratic formula one day (ask your mom or dad if they remember it!) but it's important to remember the logic so that you can retrieve it fast (only 20 - 30 seconds to retrieve from memory without using a pen and paper when you have forgotten everything, say, you are 90 years old and didn't do math in eons):
x^2 + px + q = 0,
x^2 + 2*(p/2)x + (p/2)^2 - (p/2)^2 + q = 0,
(x + p/2)^2 = (p/2)^2 - q, and finally
x = - p/2 +/- √ ((p/2)^2 - q)
graphing proportion's relationships gives two frames to remember referenced duality beyond quantum flux static unknowing state
On the first example, I imagine if you remember the trick is to multiply by (secx + tanx) / (secx + tanx), it's not a big leap to just remember the integral formula itself.
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.
As being an autodidact, the only thing I "memorize" is definitions but, owing to being justified, I remember them with ease.
Can you explain more about mnemonic,and post more videos to memorize the math/maths formulas.
For that matter any other subjects like physics, chemistry.
Please.
Sometimes memory tricks are lengthy and confusing. For instance,to remember the signs of trig functions in different quadrants,we use All Students Take Calculus. Instead,i better remember it with ASCT thumb rule.
Similarly, remembering tri ratios with So(h),Ca(h),Toa.
I try to come up with some image or a turse explanation of what the formula represents. Especially stuff like the unit circle or physics formulas.
Hello Dr. Is it common for American students to do a PhD straight after an undergrad degree? I'm asking as in my country people have to do a masters degree before a Ph.D. But i saw in your other video you recommended doing a PhD instead of a masters, does this mean i ( as an international student ) can apply for PhD without a masters in america?
Keep up the great content!
When I took calculus II, the section on hyperbolic functions, I was horrified at the notion of learning all those hyperbolic function identities, having already made the trig functions memory items. Then I came across Osborn's Rule. The trig-to-hyperbolic conversion is easy but I still have a tough time remembering the name of the rule itself. I have tried tying it to the singer, Ozzy Osbourne, or his song, "Crazy Train." It hasn't really worked out so well.
I discovered it recently
But whenever I start doing question I try to recall all related formulae regarding that problem
Right now I was doing problems on Bayes theorem when you expand Bayes theorem in denominator you get theorem of total probability.
Mostly I use this trick in phyiscs which really saved me in yesterday final exam
For the unit circle, I came up with my own system and it makes me feel bad that others don't know it because I learned it and will never forget it.
I found the unit circle has a pattern. I chunked the information and broke it down to make it easier. First I learned that all the values are divided by 2. Then I learned that all the values on the numerator are inside a square root. Yes this applies to square root of 1, which is just one. Then I learned that on quadrant one, these values on the x coordinate go from sqrt of 3, then sqrt of 2, then sqrt of 1. Pi/6 is sqrt(3), divided by two like every other value. Then pi/4 is sqrt(2)/2, then pi/6 is sqrt(1)/2, or 1/2. These are the same values all around the circle.
Now you just have to learn the radian angles (degree angles are very intuitive I wont explain here though it's too long). Starting in quadrant one, these angles I use as reference are pi/6 for the first line, pi/4 for the second line, and pi/3 for the last one before pi/2 which is just 90 degrees. I color coded all these. Every /6 is red, /4 blue, and /3 yellow. In quadrant one theyre just pi over their respective color. Second quadrant it's one less times pi than denominator (for example second quadrant for yellow which is 3, would be 2pi/3). 3rd quadrant would be one more than denominator (so for yellow, it's 4pi/3. Notice how the constant behind the pi is one more than the denominator). The last quadrant is 2x the denominator minus one (2x - 1 (where x is the denominator. So it is for yellow 3 so 3*2 = 6, 6-1 = 5, so 5pi/3).
I wish I could put up a picture. My way of learning these things is finding patterns because I like them. And making it as simple as possible.
Something that I am beginning to experiment with that I have NEVER seen anyone do is experiencing with mnemonics and memory palaces as well as creating my own fictional memory palaces and possibly a narrative within this palace in my mind alone through creativity. I want to see if it's effective to take this inspiration from memory athletes and create a vivid expression in my own mind to retain information and relate disparate ideas in my mind which will enhance as a byproduct my creativity, problem solving and critical thinking skills to innovate and apply. Someone let me know if they use something like this or something like the Major System or some other means to memorize math. Thanks!
I don't have any mnemonic stunts to suggest but I would like to know where to get an indexed collection, in book form, of all the formulas and tables a student of calculus needs to know.
In the video, where you talked about the intelligent investor, you said that you know about finance. Do you have any idea if the models in mathematical finance work?
Can you make a video on notation?
Very few people explain this at all.
which paper sheet you are used to solve maths?
Which is better, horizontal or vertical, since we tend to list things vertically. How could you memorize formulas (and examples) horizontally?
How can one memorize process techniques for solving systems of linear algebra equations and concepts?
Well, in general I would say that if you have to rely on your memory too much, you are doing it wrong.
As you say, understanding is really the key here. Then you won't have to see memorization as a separate process at all.
If you just want to use some long and complicated formula at work or in your later studies, you simply look it up.
Memorization takes up unessecary mental resources you could have used for understanding instead.
But some kind of mental map of mathematics becomes necessary on higher levels.
I find it helpful to draw mind/concept maps using A3 papers and a lot of colors to draw connections between mathematical concepts and results. It should be simple. If you need too much detail to explain, you probably have missed the main basic ideas.
Mental recollection of concepts and their connections and consequences is also a good idea.
There are easy ways to memorize every formula you want, within minutes, absolutely accurately and without forgetting it again. Memorizing hundreds of formulas in a few days is no problem at all with classical memory techniques.
Sure, understanding can be a useful memory device, too, but there are surely better ways than just writing it down so many times ...
Classical memory techniques, applied to math formulas, can be a very powerful tool that I teach to my students in my memory courses. Using these techniques saves time and energy and makes it also much more probable to recall the information when it counts.
I'd be interested in what these classical memory techniques are. Do you have a reference I could consult?
sir how can i be better in calc and 20 days are left for my entrance exam jee mains and 70 days for jee adv and calc of adv is very tough
What about lambda expressions and lambda calculus? What books on them are out there?
How do you find more of theses memorization tricks
Circumference of a circle = the derivative of its area.
Surface area of a sphere = derivative of the volume of a sphere.
In my opinion
best way to memorize formulae is
just do a lot of questions related to that formula
i think just solve some 3 to 6 good/basic questions then any formula can be easily memorized
Sir pls tell us about jee advance mathematics
Do you have any tips or advices to understand math formulae or notations? Usually in math books they will explain the concept like x is equal to bla bla, where k is 1,2,3 something and I REALLY have trouble making sense of that.
Once there was a meme post where someone says that scary math symbol (summation, capital sigma) is just 'for loop' (like in coding) and I was like aaahh
Talking to someone about it or writing it down on a random part of the day. Along with remembering or reviewing it in your mind before bed. The more you see it the more it sticks.
I drill. Even the "boring" stuff. At the same time I gamify, particularly in setting challenges for myself.
Try Anki. If anyone says you can not memorize stuff very good. Try anki for 3 days.
Amateur tip: get the sin(π/3) or cos(π/3) with a little "1-2-√3" triangle and Pythagoras
"You will be mistaken as a pilot"
*adds to cart*
LOL
Its obviously the orb of power that allows him to memorize everything
spatial visual reasoning
and use visual proof
Unit circle is your friend
I'll just stare at the formula until it gets etched in my memory like an afterimage and then I'll recall 🤷🤷
I feel that the role of memorizing in math and physics is downplayed by some of us. Being able to derive/prove promotes conceptual understanding and memorization ensures speed and relearning. It’s a feedback loop that ensures long term understanding by continuously refilling the gaps.
I used to make 2 copies of my flash cards
1 copy would be fornulas taped to the inside of my medicine cabinet. I'd read it *aloud* every time I washed my hands.
*"After that, the hard part was not remembering the formulas,"* I exclaimed, *"but mouthing the words silently during a test."*
You should glue a miniature math book in the sorcerer's hand or, maybe, a protractor, calculator, pencil, etc.
Haha
I had a language teacher who told us when introducing new material: "it's just what you think it to be." "You already know this." So, that may be an anti-anxiety trick. Students don't approach new material as if it just appeared out of nowhere.
I bet if i gave most smart people a test with math questions about percentages or fractions they have a hard remembering the formulas for those cuz they focused only on algebraband above
Also, i group ideas and re-sort and re-group. Connect with something I know.
I used to write on a piece of paper then chew on them. I also write on paper and create anime into a monster - works for me. I also tried taking pictures blinking my eyes. Last but not least I prayed. All works most like due to extensive efforts.
Want to memorize a formula? Deduce it, learn the logic behind it. Then, even if you forget it, you’ll know how to bring it up again. It’s kind of like learning a jazz standard, you wanna learn it? Transcribe it by ear instead of relying on the chart, then you’ll have the melody and harmony in your ear.
I keep a pocket book with me 😁
I don't want to memorize but derive them
Forget memorizing math formulas how can we memorize proofs 😭 I have systematic memorization where I memorize small parts that can all be mentally linked together in an order to solve problems so for applied concepts I never had trouble memorizing however with proofs my mind just stops working
Math is very interesting to dream at night while sleeping
Simple answer write them down. For every single problem you practice. if possible make a song. Carry a tiny pocket book with all the formulas you use
I have a techniques of integration exam tomorrow. Wish me luck
Greetings from Turkey. My method: Read proof-based mathematics textbooks and understand what you are reading, and do the exercises.
Do you have a favorite science?
One big factor to crystallizing information is SLEEP!
Consider inclined bed therapy, which is fairly cheap to try.
I'm not an advocate for memorisation. 'Tis far better to know how the formulæ are derived and to do a lot of problems until they stick. Mathematics is not a memorisation subject unlike history or biology where regurgitation of facts earns you an "A". Mathematics is like a music instrument grade examination, say piano or violin: fail to practise and it shows on the day of the exam. Just do enough problems and the formulæ stick. There really isn't a shortcut to getting an "A" grade in maths except for sheer practice. Maths like physics and computer science does not reward pulling an all-nighter. It rewards constant and consistent practice.
Bruh.
😆😆😆😆😆😆🤣😆😆😆😆😆😆😆🤣
why did you pick a pencil instead of a pen? Is it an american thing?
Hmm I don't think so, but most people do use pencil for math:)
Even before listening to what you have to say I know it's not going to work for me. Yes, I'm that bad at memorizing math.
I guess I shouldn't have been that pessimistic. The last trick seemed helpful.
yeah you can do it:)
I have andislexianin math formulas.. i can remember like cross multiply a fraction and add neg intagers even if prob is subtract ..i can memorize square roots. But when it puts it all in proboem woth square roots answers are half page long square root and A 2 or neg -8 under the sqayer rooted drawn out andwer like ?? I been getting one off so i add one to my answers and end up right answers. Its QUADRATDIC FORMULAS..