The incredibly useful field of mathematics comes at the price of being notoriously difficult for many. Even for those with a great deal of experience, there are times when a problem can escape the best. Whether you’re using postgraduate study to get into mathematics or are a seasoned veteran, here are some tips we’re sure you’ve heard before that you may like reminding of!
Our brains are incredible in that they can process issues that occupied our waking attention. By simply going to sleep at a reasonable time rather than staying up trying to decipher a problem, we can perform the remarkably efficient combination of sleeping and problem solving simultaneously. When you wake, you may find the answer’s yours. This ties into a broader issue that students of mathematics suffer from: unwillingness to sleep! As much as we may long for a future in which sleep can be synthesised or our organic components are replaceable with superior aluminum alloy parts that merely require a light spritz of fusion power to keep us going, we’re not there yet. Sleeping is the best available way to recharge and rethink problems.
Sleeping’s good, but during the day it’s important to continually work at sticky problems on a regular basis. In a similar manner to sleeping, you want to make thinking about that problem an almost subconscious process. Working on similar problems can help to this end. Mathematics, as you should well know by now, is not something you can simply read about to get all the answers, even if your memory is sharp. Problem solving is the secret sauce that makes mathematical ability ripen.
As stated above, you’re not learning much in mathematics if you’re not problem solving. This doesn’t make lectures entirely useless, however. Simply use them as a guide to where you ought to next direct your attention. After all, the people running the things are often the same people running the course; they know what the assessed material’s going to be! So, take the lecture slides home, or your notes on the lectures, and try to rustle up some problems to do that utilise that knowledge if you haven’t been provided any already. Preferably, you’ll be doing those problems right after the lecture ends instead of later one when you may have forgotten a lot of what’s been said. While you’re in there however, see if you can talk to the prof after class to clarify any material. Whatever he says can be added to your notes to further supplement your individual learning later.
Hopefully, these small reminders have given you renewed motivation! Mathematics can be difficult when stressing over singular problems on many-a sleepless night, so doing simple things like getting some sleep and engaging in the material as often as possible can make life so much easier. Wherever you end up with your qualification, we wish you all the best.
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