Memorizing Formulas: Benefits of Note Cards for Long-Term Retention

[Miike012]

I've always preferred to read the book in order to understood the logic and theory behind the concepts in math and physics rather than just memorizing formulas. I believe the only thing one learns by memorizing formulas is how to plug in variables and one who tries to understand the logic and theory learns how to problem solve and develop their over all math and physics understanding. With that being said I think I've developed more skills than if I were to have just memorized formulas but as time passes I find myself forgetting the logic and theory in order to deduce the formulas.

My question is
is it beneficial to create note cards for long term memorization? And also do you use notecards in order to retain the material for longer periods of time?

However I still want to read the books because as I said I believe it's very important but I also want to make note cards with formulas and theory and proofs and whatever else I may thing is important so that hopefully I can retain the information in the long run.

Please post any thoughts and opinions. Thanks

 

[deekin]

I think notecards would be a big help. A math professor I had last semester gave me this other idea, something she used when she was a grad student. She said she had a wall where she would hang pieces of paper with formulas and theorems on them. Then every day, she would look at the wall and remind herself of the theorems, etc. This way, it is not something you have to carry around, it is very visible inside your room/study area. Kind of similar to notecards.

So far, the things I have remembered long term have been things that I used over and over again. Like think about integration or taking the derivative. You just remember the rules etc because you've done it so many times.

 

[Lavabug]

As someone who's reviewing for the PGRE, I'm finding the formulaies I made for myself throughout my undergrad very useful. Having all the main formulae and concepts for each course on a single A4 definitely saves a lot of time. Some were just written down for memorization purposes but I did like to write down at least cursory instructions on how to derive the more detailed ones (like the wave equation using just Newtonian mechanics or Bernoulli's straight from NS). Could never for the life of me remember the levels in a Hydrogen atom and deriving something like the thin lens equation in any practical situation is time consuming though.

I think it is "neat" -if not mandatory- to know how to derive all the basic formulas for core subjects for a physics major, at least anything that takes less than 4-5 lines (ie: not the velocity field for Poiseuille viscous flow, more like centripetal acceleration and the like, the Planck spectrum or the variance in a QHO, etc.).

 

[UltrafastPED]

The process of summarizing the explanations and the related formulas is itself a memory aid; the resulting note cards then jog your memory to recall the effort which has been put into that note card.

Thus if you were to simply copy another person's note cards it would not work so well!

 

[yungman]

I always derive all the formulas I studied, never just use it and plug in the numbers. You'll be surprised have many typos and wrong formulas textbooks have. Particular the post grad level books. Never trust the textbooks blindly. I have at least 4 different textbooks for each subject so I compare their formulas. If you see the same formula in different books, chances are they are correct. In fact my study in antenna theory stalled for almost a month because there was one formula I don't know how the book come up. In order to derive the formula, I have been reviewing Helmholtz, D'Alumbertian, Green's functions etc. before I go back. One formula cost me over one month if I can get it!

I am 60, and I am still studying. My memory is bad. Whenever I study, I write explanations into note books. I have note books for everything I studied. Books do not usually derive formulas in detail step by steps...lots of time, they don't even give the derivations. So when I worked out a derivation, I write it down in detail in my note book.

You can loose the Q cards or get them out of order, the best way is to spend the time to write it down. A tip for you, always write down the book and page number you use for the notes. So many time I found I don't quite understand what I wrote or don't quite agree with the notes, then I can go back to the book and read the original materials. There are time I actually mis-interpretated the book and I had to correct my notes. Also, if you can write it down to explain the material, you have a better chance to understand it.

Lastly, keep the note books after the course. I used my notes years after I studied them.

 

[Polluxy]

Yungman, that's really great advice. Now, I don't know how practical it would be to figure out how to derive every single result in, say, Jackson. Not because it's not worthwhile, but because in grad school, you just don't have the time. When confronted with a lengthy problem set that's due in a few days, just get it done whatever way you can. Afterwards, when you have a bit more time, you can go back and explore this or that series expansion or what approximations are made and why, and really try to understand every step.

But when I self-study I always keep notebooks and I always try to convince myself of a book's results. Which reminds me of my E&M professor's favorite saying: "Convince yourself this is true." In other words, he didn't feel like explaining the derivation. ;) And OP, if you're at the undergrad level and you're studying for the GRE or something like that, YES, notecards are probably the single best thing you can do --- it forces you to have all the information on "instant recall," you can spit it back out whenever you're asked. I'd flip through them a few times each day and make note of the ones you have difficulty recalling so you can work on those a bit more.

 

[yungman]

Yungman, that's really great advice. Now, I don't know how practical it would be to figure out how to derive every single result in, say, Jackson. Not because it's not worthwhile, but because in grad school, you just don't have the time. When confronted with a lengthy problem set that's due in a few days, just get it done whatever way you can. Afterwards, when you have a bit more time, you can go back and explore this or that series expansion or what approximations are made and why, and really try to understand every step.

But when I self-study I always keep notebooks and I always try to convince myself of a book's results. Which reminds me of my E&M professor's favorite saying: "Convince yourself this is true." In other words, he didn't feel like explaining the derivation. ;) And OP, if you're at the undergrad level and you're studying for the GRE or something like that, YES, notecards are probably the single best thing you can do --- it forces you to have all the information on "instant recall," you can spit it back out whenever you're asked. I'd flip through them a few times each day and make note of the ones you have difficulty recalling so you can work on those a bit more.

Ha ha! Time is not my issue, I am retired, I have all the time in the world. I really don't think most people can understand EM by just taking the class once. It all depends on whether you need to use it later or not. I think if you need to use it, you need to review it and then do the derivation and write notes. I am going to study Jackson in the future, but my field is electronics, we concentrate more on wave propagation, phasor, transmission lines, antennas etc. Jackson does not fit very well on this. But I know Jackson is hard, I have the book. That will be like climbing Mt Everest for me in the future after all the stuffs I want to study. That will be my next cross word puzzle!

 

[UltrafastPED]

Engineers don't need Jackson's Electrodynamics ... unless they are accelerator engineers! Accelerator work was the motivation for his original text. The additional material added over the years is mostly aimed at physics graduate students ... they say its good for the soul. :-)

PS: I've had four courses in electromagnetic field theory - its worth studying for its own sake.

 

[yungman]

Engineers don't need Jackson's Electrodynamics ... unless they are accelerator engineers! Accelerator work was the motivation for his original text. The additional material added over the years is mostly aimed at physics graduate students ... they say its good for the soul. :-)

PS: I've had four courses in electromagnetic field theory - its worth studying for its own sake.

Yes, that's why I put it on my wish list. Yes, I think it's good for the soul...and good for the eagle! I am retired, so it's not important whether it's useful for me, I still plan to get to it...Like you said, it's good for the soul!

I studied field theory using Field and Wave Electromagnetics by David K Cheng. Then I studied a few RF and microwave books that is mainly fields and phasors. I am studying antenna theory by Balanis which takes a lot of field theory to derive the formulas. Those are like extension to Cheng's book. Any other books you can suggest?

Thanks

 

[UltrafastPED]

For undergraduate I like Griffiths' "Introduction to Electrodynamics"; widely used for undergraduate physics, junior/senior level. I was reviewing introductory field theory texts for engineering for a teaching assignment at the University of Liberia this fall, but then the it was switched to introductory circuits. However, I wound up in Germany, helping to look after my granddaughter.

Anyway - I don't have access to my library, but I can recommend Purcell's "Electricity and Magnetism", volume 2 of the Berkeley Physics Course; it is more introductory, but excellent.

 

[yungman]

Thanks, I already finished Griffiths and Chengs. Cheng is the same level as Griffiths in field and waves. Griffiths doesn't have much on field and waves and none in transmission lines. Griffiths use retard potential in chapter 10 and 11 that is not useful for RF and antennas. The antenna theory use some of the EM field theory that are in the advanced electromagnetics by Balanis. So I really need more the advanced level book.

Thanks

 

[UltrafastPED]

Try "Classical Electromagnetic Radiation" by Heald & Marion - I sometimes use it as a reference - it certainly covers radiation thoroughly.

But you may do better with engineering texts; physics texts are more about principles than applications.

 

[yungman]

Try "Classical Electromagnetic Radiation" by Heald & Marion - I sometimes use it as a reference - it certainly covers radiation thoroughly.

But you may do better with engineering texts; physics texts are more about principles than applications.

Thanks

 

[yungman]

I just bought it on Amazon.