Ask HN: How do you keep your mathematical knowledge sharp over time?

3 pointsby sharmivor 11 Jahren3 comments

I am working on machine learning from the basics. I want to do it the right way and I am learning probability and statistics. At school and college, mathematics was my favorite subject and I loved treating every problem as a new challenge leading to a fresh perspective. Then life intervened. Now, after a few years, I realize, much to my chagrin, that most of the higher level math I had learned, has evaporated. So there is much I have to relearn. Also, unfortunately, unlike college, it is not possible for me to sit x hours everyday to learn. Currently, I am learning in bursts, sometimes followed by long passive time. So I often have to revise and reorient myself when I sit to study again. I would like to avoid this. Has anyone faced this? How do you tackle it?

One solution seems to be using Spaced Repetition cards, like Anki. But it to seems to have it's limitations. http://lesswrong.com/lw/juq/a_vote_against_spaced_repetition/

Obviously, whatever I learn in math, I try to apply it to a lots of problems. But inevitably, there is some fading of knowledge as time passes, and I might not be able to keep redoing the problems.

Please share your experiences. Thank you.

3 comments

nitin_flankervor 11 Jahren

I have not been into the same problem as you are having but yeah I have been into a similar one. I also used to get forgotten what I studied few days back in Maths,while studying Physics and doing a derivation. So, I used to go back to the same chapter and used to skim through it.

Later I made a rule that I will be revisiting whatever I have read after one week and then after 10 days and the like.

I used to go to my college by bus that used to take 1.15 hrs. So I utilized that time to revisit the lessons that I studied few days back.

Now I dont know how you travel but if you use public transport and gets a seat to sit then, you can also apply this method. This will keep the concept fresh in your mind and you won't be spending any extra time to do that.

Nowadays, I use to read Quora while traveling to the office.

sharmivor 11 Jahren

Thanks for the input Nitin. My main issue is I'm out of college. So, unfortunately, education cannot be my highest priority anymore and predictability in my study time has become a luxury. It is managing my lessons and remembering them in my erratic schedule that bothers me.

bit2maskvor 11 Jahren

I have been trying to answer this question for myself, and one measure I've taken towards this goal is to record all of my mathematical reading, work, and random thoughts in a journal. I highly recommend the practice as it has been very illuminating to me since I started a few months ago. Reviewing my previous readings allows me to ascertain how much math I actually end up retaining from my study sessions, and keeping all of my work in one place (as opposed to throwaway scrap paper) allows me to spot any particularly common mistakes.

So far, I've found that my memory is far more tenuous than I had previously assumed. I'd look at last month's entries and realize that I'd only retained 20% of what I had learned; fine details being especially prone to slippage. Yet from analyzing my mistakes, I've also found that those very details are much more crucial than I had thought.

The result of all of this is that I've started to shift my focus from "learning new math rapidly" to "winning the uphill battle against memory loss." From this new perspective, the old adage: "the only way to learn mathematics is through doing" begins to make a lot more sense. While active learning is far from any cure to forgetfulness, given my own mnemonic capabilities I have come to see that it would probably be a better long-term investment to spend a month on fully working and understanding a chapter, than to spend the same time blazing through several chapters but skipping the exercises (having done both.)

I emphasize again that this is my own conclusion based on my own characteristics, and that is precisely why I recommend everyone to find their own answer to this question by keeping their own math notebook.

Ayietim1vor 11 Jahren