Right now I am in Calc 3 and I find it difficult to memorize theorems and formulae. I’ve successfully been able to encode some things like quadric surfaces, but the repeated reference of such things as absolute values, trig functions, and exponents for theorems makes it quite hard to differentiate between them.
Does anyone have a proven framework for encoding these sorts of things while keeping them each novel and well differentiated?
As a successful math major myself, I can guarantee you that success in Mathematics is not from memorization, but from having an accurate visual mental representation of the area of Mathematics, so I could fluidly think of the abstract ideas.
Areas where I had this (probability, real analysis, …) I found relatively easy and most of the formulas seemed “obvious” after a little thinking.
Areas where I couldn’t make a good representation (complex analysis, spectral analysis, special relativity, …) were almost impossible to me and felt like I’d need to memorize endless stuff that I didn’t know how to use. If I knew then what exactly I was missing, I would have worked to develop it.
Some of my studies required us to memorize long proofs of theorems (sometimes more than 1 side of A4 handwritten in my fairly compact writing!) Students who understood the topic well had to memorize relatively little in order to write out a valid proof. Students who didn’t understand the topic would have to memorize almost every detail—considerably more work!
So my first advice would be to try to understand the material: how could you represent / draw / animate the ideas? How do different topics relate to each other? Why is this formula important to people (except for your exam lol)?
This will minimize your need for using mnemonics, and will scale much better.
If you want a more direct approach using mnemonics, Anthony Metivier describes his approach here (memorizing math and equations) and he’s sometimes active on these forums (@metivier).
I would recommend reading Measurement by Paul Lockhart, as a way of learning to visualise maths in a way you can approach it. It doesn’t so much as teach you maths as teach you a new way of embracing it and the further into the book you go the more intuitive mathematics becomes. I found I could remember more mathematical functions and formulae after reading it because I no longer saw them as empty statements
I just researched it on Amazon and sounds like a great concept for a book! Maybe it wouldn’t treat the specific topics that OP needs, but nice recommendation regardless.
I get the struggle with memorizing those formulas and theorems. It’s not just about remembering them, it’s about keeping them distinct.
One thing that might help is focusing on the stories behind the formulas. Try visualizing what they represent geometrically, or think about the steps involved in deriving them. That can make them stick better than just rote memorization.
Also, maybe try breaking them down into smaller, more manageable chunks. Instead of trying to memorize the whole theorem at once, focus on the key components and how they relate. And don’t forget to practice applying them! The more you use them, the more they’ll become second nature.
For the absolute value, trig, and exponent stuff, maybe create visual cues or mnemonics that are unique to each formula. You could even use color coding for different types of functions. Good luck!
To memorize formulas I use NPI (reverse Polish notation) to avoid the use of parenthesis, as this tends to be repeated a lot, but here is the way I use, it can be NPI or Infix expression:
You need a way to memorize the symbols and here is my way of doing it, which I learned from the author M.A. KOHAIN and his book “Mnemotechnics: The Art and Science of Memory Techniques”, well here are some examples:
Use the name of the equation as the peg for the equation to memorize, it can be using substitute word or you can break the name into single letters and create places for example A - airplane, E - ear, C - carpet, etc…, this is relatively simple and you can store the equations in the letters that define it, remember that after having everything you must make it unique, for example in one the plane falls in flames, an ear with an eye inside, etc., well here everything is left to your inner criterion of how that image would be, remember it is an image what you create with movement, seeing it in 3d is very strong, in 2d too, so play with it.
Symbol - Images, actions or affections.
Addition - Acts of creativity or improvement.
Subtraction - Acts of destruction or disfigurement.
Multiplication - Substances of creation.
Division - Substances of destruction.
Derivative - Quality of creation.
Integral - Quality of destruction.
Exponent - Acts from above.
Root - Acts from below.
Parenthesis - Substances of containment or delimiting images.
Equality - Juxtaposed images that do not interact causally.
Delta - Triangular forms.
Decimal - Acts of emergence.
Consecutivity - Some Elongated Connection.
For Latin letters that often appear in mathematical formulas:
Adapted - Numerical value - Character.
Α α - alpha - 1 - Alan Ritchson.
Β β - beta - 2 - Ben Hardy
Γ ɣ - gamma - 3 - Gabriel Howell
Δ δ - delta - 4 - Dexter (Michael C. Hall)
Ε ε - epsilon - 5 - Ephraim Sykes
Ζ ζ - dseta - 7 - Dzidra Ritenberga
Η η - eta - 8 - Etan Cohen
Θ θ - zeta - 9 - Zeta Makrypoulia
Ι ι - iota - 10 - Ione Skye
Κ κ - kappa (tb. cappa) - 20 - Kayla Wallace
Λ λ - lambda - 30 - Lacey Chabert
Μ μ - mi - 40 - Michelle Randolph
Ν ν - ni - 50 - Nico Parker
Ξ ξ - xi - 60 - Xi Qi
Ο ο - omicron - 70 - Omiros Poulakis
Π π - pi - 80 - Pip Torrens
Ρ ρ - ro - 100 - Rosa Salazar
Σ σ ς - sigma - 200 - Stephanie Sigman
Τ τ - tau - 300 - Tau Wan Yue
Υ υ - ípsilon - 400 - Ipsita Paul
Φ φ - fi - 500 - Fiona Gubelmann
Χ χ - ji - 600 - Jill Wagner
Ψ ψ - psi - 700 - Phillipa Soo
Ω ω - omega - 800 - Omar Epps
Now remember that there are several letters that usually appear in the formulas, but we won’t worry about this, just put any character, shape or thing that comes to mind that begins with this or that letter or preferably create a predefined list of character, action and object in the manner of giordano bruno, you will only need to use the following categories to make the images different from each other for example substance, quantity, quality, place, time, state/condition, action and affection…, so that apart from changing one of these from the previous form or substance you can make something new and distinctive.
My last advice is to practice solving mathematical problems using AI, that is, solve exercises and ask for the results and analyze where you make the mistake and keep a record of the areas in which you falter and usually make mistakes, but when you solve a doubt, write it down so you can review it, which rules you usually ignore when solving equations, so you will have a deep knowledge of the subject, memorizing concepts is relatively simple since you can use characters and make them reflect the concept since there can be several events from one character, also memorizing equations is not complex at all based on my experience.