[HN Gopher] How to Study Mathematics (2017)
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How to Study Mathematics (2017)
Author : qnsi
Score : 80 points
Date : 2021-03-20 18:13 UTC (4 hours ago)
(HTM) web link (www.math.uh.edu)
(TXT) w3m dump (www.math.uh.edu)
| erichahn wrote:
| Bad rules. My suggestions ask yourself the following all the time
| 1) Do I ~really~ understand what the definition / theorem is
| supposed to tell me. 2) A proof is just a reason why something is
| true in maths. Do you understand ~why~ a statement is true? 3)
| Exercise all the time. You won't learn math by memorizing
| definitions, theorems and proofs.
| qsort wrote:
| How is this disagreeing with the OP? It specifically says that
| memorizing e.g. theorems is bad.
| ZephyrBlu wrote:
| 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 you want to learn maths for the sake of understanding maths,
| then this could be the right approach. But it's definitely not a
| pragmatic approach.
| hyperpallium2 wrote:
| > How to make sense of a proof
|
| > When you finish you should know why each step follows from what
| came before. You may not see how anyone could have thought to do
| the proof that way, but you should be able to see that it is
| correct.
|
| Knowing _that_ something is true is not the same as knowing _why_
| it is true.
|
| I don't know what the problem is with understanding, but here's
| three thoughts:
|
| 1. You need a deeper level understanding - you can't understand a
| problem at the same level you encountered it. Perhaps,
| understanding different but related areas, so you see the same
| problem from a different perspective. Perhaps understanding the
| formal system that is used to define terms used in the problem
| description.
|
| 2. You need familiarity, which creates the feeling of
| "intuition". If you know how it behaves in all situations, you
| will feel you understand it, even if you don't. So, just lots of
| practice/exercises.
|
| 3. You need to fully understand the components from which the
| problem is formed. For example, the natural numbers and addition,
| and build up from there.
| bollu wrote:
| Also, use computers! I use SAGE extensively to get a feeling for
| lots of mathematical objects!
|
| 1. Grobner bases: http://bollu.github.io/computing-equivalent-
| gate-sets-using-... 2. Localization:
| https://github.com/bollu/bollu.github.io/blob/8cd335687ff3ef...
| 3. More broadly, an answer on math.stackexchange on how to debug
| math: https://math.stackexchange.com/questions/1769475/how-to-
| debu... 4. (WIP) continued fractions to compute pi:
| https://bollu.github.io/fractions/index.html
|
| And so forth. I find the computational aspects of most theories
| to be very rich, and it's really gratifying to code something up
| and "read off" the results.
| yoaviram wrote:
| Slight tangent - any suggestions on none conventional ways to
| teach children math?
| jdlyga wrote:
| I would love to get back and really learn math. I was really
| interested back in High School with Geometry and Algebra. But my
| interested totally burned out with poorly taught and punishing
| Calculus classes in College.
| ipnon wrote:
| It's a long journey with many paths. The best you can do is set
| aside time everyday. I do an hour and it adds up quickly.
| no_wizard wrote:
| What would anyone recommend to someone who really only had high
| school math[0] to get up to speed on enough math to handle more
| advanced computer science concepts?
|
| I'm really interested but all the material I can find is either
| for kids (which just isn't sufficiently stimulating for an
| adult) or aimed at college kids with a decent background in
| math that is fresh
|
| [0]: not even calculus just what they called technical math
| which is like all practical example based curriculum. One of my
| life regrets here to be honest
| flir wrote:
| I'm working my way through this: https://pimbook.org/
|
| I'm not very far in so I can't exactly recommend it, but I am
| enjoying it. In places where I'm rusty, I'm falling back on
| Khan Academy.
| dvfjsdhgfv wrote:
| In theory, any introduction to discrete mathematics would do.
| In practice, there are many differences in depth and breath
| of the material. You probably will do well if you choose
| Rosen, but there are several great alternatives, such as
| Levin[0] that you can start right away with.
|
| http://discrete.openmathbooks.org/dmoi3.html
| ivan_ah wrote:
| I have two books that might be a good fit for you since they
| are specially written for adult learners in mind.
| (disclaimer: I wrote these books and I have a financial
| interest in promoting them)
|
| The _No Bullshit Guide to Math & Physics_ [1] is a condensed
| review of high school math, followed by mechanics (PHYS 101)
| and calculus (CALC I and II). It's not as rigorous as other
| more proof-oriented textbooks, but it still covers all the
| material.
|
| The _No Bullshit Guide to Linear Algebra_ [2] is all about
| linear algebra and also includes three chapters on
| applications, so you 'll learn the fundamental ideas but also
| what they are used for IRL.
|
| Both books come with exercises and problem sets with answers,
| which is essential for learning. In fact one could say all
| math learning happens when you try to solve problems on your
| own, not just reading.
|
| [1] https://minireference.com/static/excerpts/noBSmathphys_v5
| _pr... [2] https://minireference.com/static/excerpts/noBSLA_v
| 2_preview....
|
| See the reviews on amazon for what people say.
| [deleted]
| dvfjsdhgfv wrote:
| That's a shame, Calculus is a fascinating subject and a basis
| for many interesting applications. Basically, there are two
| ways to approach it: to pass your exams (and there are just a
| couple of rules to learn, it's not that complicated), and to
| really understand what it's about. If you choose the second
| approach, you don't even need to memorize any formulas, because
| you will be able to reconstruct all of them as you need them.
| Moreover, you won't be conceptually limited to the geometric
| interpretation (which is invaluavle in giving some intuition in
| the early phases but might get in your way later).
| SkyMarshal wrote:
| "Calculus Made Easy" might help you get back into it. Lots of
| discussion over the years on it:
|
| https://hn.algolia.com/?q=calculus+made+easy
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