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How to Study Mathematics (2017)

math.uh.edu

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Re: How to Study Mathematics (2017)

#41

Post by rfrey »

ectopod wrote: post #36
baby wrote: post #26

Earlier quoted context omitted.

When you spend most of your time in class, when do you have the time to do the assigned work? That’s what I struggled with.

How much class did you have? My first year at university had three hours of tutorials and ten hours of optional lectures per week. Subsequent years had less. There was plenty of time.

My engineering degree had six classes per term at 3 hours of class time per course. Two of those would be labs with a 3h lab each week. So 24 hours of in person time per week, with an expectation of 2-3 hours or outside work for every in class hour.

Re: How to Study Mathematics (2017)

#42

Post by kinghtown »

ACosmicDust wrote: post #17
ZephyrBlu wrote: post #14

Although the title is "How to Study Mathematics", I think a more accurate title would be "How to Study Mathematics as a Mathematician ". I am studying some maths right now with the goal of understanding some statistical methods. Having a rock solid understanding of all the underlying maths is counter-productive to my end goal though (Applying the statistical methods), because it would be extremely time consuming. If…

I am sort of facing the same problem. On one hand I like math, abstract algebra, calculus etc but on the other hand I know I am not great with it. I am slow, I am not creative. So, when trying to learn something for programming like differential geometry, when I go deeper than I need to, I feel like I am wasting my time. And sometimes it is particularly hard to read a book written for mathematicians because my knowle…

Well, a mathematics degree is one of the highest income earners for a reason so its usefulness is beyond dispute. I personally have life and artistic goals which take priority of my time over math but I’m willing to allow mathematics (together with high-level scientific understanding) a place in my life as a tertiary goal or drive. We are all a little too hard on ourselves to get everything done before we turn 30 or 40 as though it were some kind of deadline and then why bother, right?

If you find pure math interesting then give yourself the slack to learn it long term. Think of it like a rock garden which you tend to over the years.

Re: How to Study Mathematics (2017)

#43

Post by the_only_law »

kinghtown wrote: post #42
ACosmicDust wrote: post #17

Earlier quoted context omitted.

I am sort of facing the same problem. On one hand I like math, abstract algebra, calculus etc but on the other hand I know I am not great with it. I am slow, I am not creative. So, when trying to learn something for programming like differential geometry, when I go deeper than I need to, I feel like I am wasting my time. And sometimes it is particularly hard to read a book written for mathematicians because my knowle…

Well, a mathematics degree is one of the highest income earners for a reason so its usefulness is beyond dispute. I personally have life and artistic goals which take priority of my time over math but I’m willing to allow mathematics (together with high-level scientific understanding) a place in my life as a tertiary goal or drive. We are all a little too hard on ourselves to get everything done before we turn 30 or…

I want to go back to school, and if I do, it will probably end up doing CS because it’s about the only “useful” degree accessible to working professionals, but if I had a choice, I’d probably pick a mathematics degree given how widely applicable the learned concepts can be.

Re: How to Study Mathematics (2017)

#44

Post by kodachrome64 »

rfrey wrote: post #41
ectopod wrote: post #36

Earlier quoted context omitted.

How much class did you have? My first year at university had three hours of tutorials and ten hours of optional lectures per week. Subsequent years had less. There was plenty of time.

My engineering degree had six classes per term at 3 hours of class time per course. Two of those would be labs with a 3h lab each week. So 24 hours of in person time per week, with an expectation of 2-3 hours or outside work for every in class hour.

This was probably my biggest gripe with my mech eng degree. Every minute you spent grinding through a difficult topic until you understood it, was a minute that you needed to be studying for another exam or working on a project. In the end I came out with a pretty decent GPA, but a serious case of impostor syndrome as I never really felt like I had absorbed most of the material. Of course engineering is a demanding field, but I've often wondered if students would benefit from having five classes per term.

Re: How to Study Mathematics (2017)

#46

Post by stevegalla »

baby wrote: post #26
alisonkisk wrote: post #24

Earlier quoted context omitted.

Doing the assigned work is good way to learn the material. Most teachers know better than most students what is need to do to succeed in the class.

When you spend most of your time in class, when do you have the time to do the assigned work? That’s what I struggled with.

In all seriousness, I stopped going to lectures* and studied at my own pace. My learning isn’t linear, so there will be some topics that are easy that you can move quickly on. Other topics take more time. Sometimes you can take a detour and dive deeper kn interesting topics.

Going to lecture, sitting in lecture, waiting around, etc. provided very little information per unit time for me. I can’t learn math or anything quantitative from watching someone do it. By using lecture time as study time I was able to double the time spent learning the material.

When you get stuck, go to office hours. Or look for notes from similar courses for a different perspective.

At the start of the course look at the book and see what the prerequisite material is. Review that material during the first week when there is time.

* exceptions being courses that have a participation grade.

I tried my best to have profs that followed a textbook.

Re: How to Study Mathematics (2017)

#47

Post by dorchadas »

tunesmith wrote: post #35

Are there any resources for taking a self-assessment to know what to learn next as a self-studier?

In math? You could follow a standard undergraduate curriculum, such as the one used at MIT (with their OCW stuff). Or you can just pursue what topics interest you, and trace back their prereqs to make sure you've covered everything you need to know.

Re: How to Study Mathematics (2017)

#48

Post by fizixer »

As an experienced programmer, I have spent enough time trying to understand and make sense of some aspects of pure/higher math, specifically logic, that I feel qualified to say this:

- Experienced programmers are better trained at formality and precision than mathematicians, in some respects, and are able to ask questions that make experienced mathematicians go "why are you asking this question?" or "just get used to the idea (because that's what everyone does)"

- Much of higher math study advice (such as the one posted here) is aimed at laymen. And experienced programmers are no laymen.

- Mathematicians are laymen in many aspects compared to experienced programmers. An experienced programmer will have an easier time learning and using a proof assistant. Mathematicians (most of them) run away as fast as they can the moment they hear the phrase 'proof assistant.'

Re: How to Study Mathematics (2017)

#49

Post by hansvm »

baby wrote: post #26
alisonkisk wrote: post #24

Earlier quoted context omitted.

Doing the assigned work is good way to learn the material. Most teachers know better than most students what is need to do to succeed in the class.

When you spend most of your time in class, when do you have the time to do the assigned work? That’s what I struggled with.

If you have other significant demands on your time then school is going to be hard no matter what strategy you choose and might just take a lot of years to finish (please vote for UBI to help change that status quo). Assuming you can commit to school full-time though, it's less of an issue:

- You can finish a typical bachelor's degree in 5y by devoting 48h/week to school (12h for classes, 36h for assigned work). That's more time than most teachers expect, and except for a few unlucky points in time where multiple large projects coexist you'll rarely have to actually spend that long studying.

- It's hard to express just how much of a difference it makes to start with a little easier content to ensure you have the requisite background; don't let your pride hold you back. E.g., if the university places you in math class X, start at class X-1. You'll spend less total time learning throughout your education, be far less stressed, get better grades, and understand the material better.

- If you just want the degree, a lot of the first 1-2yrs of college courses can be replaced with CLEP/AP/... tests. Anyone can take them (not just in high school), and it'll take a lot fewer hours and dollars to get a passing score on one of those than it will to get a good grade in an equivalent college course (at most universities such tests won't affect your GPA, so even a score of 40% on some of them still gets you a passing grade).

- It's quite a bit more efficient to take more courses at once, especially if they're closely related (e.g., topology, abstract algebra, real analysis, ...). If you have closer to 70-100h/w to spend in class and studying then consider finishing your degree in 2-3y instead of 4-5y. You'll still have plenty of time to do fun things over the summer and winter holidays, and I know I personally found it more motivating to have an end date in the near future.

Re: How to Study Mathematics (2017)

#50

Post by hansvm »

stevegalla wrote: post #46
baby wrote: post #26

Earlier quoted context omitted.

When you spend most of your time in class, when do you have the time to do the assigned work? That’s what I struggled with.

In all seriousness, I stopped going to lectures* and studied at my own pace. My learning isn’t linear, so there will be some topics that are easy that you can move quickly on. Other topics take more time. Sometimes you can take a detour and dive deeper kn interesting topics. Going to lecture, sitting in lecture, waiting around, etc. provided very little information per unit time for me. I can’t learn math or anything…

You'll win a lot more social points with your profs if you show up to the lectures and work on your own problems in your notebook. As an added benefit, if the lecture offers something special beyond what you can gain from the book then you'll be there in person to receive it.
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