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How to take notes in self studying Maths?

  1. Apr 26, 2015 #1
    Hi there,

    Thank you for stopping by this thread. I'm an engineering student rekindling an interest in Maths. I just love studying Maths in my free time (and sometimes it trespasses into my non free time). I have plenty of fantastic books on my iPad and it's really helping me.

    However, I have been reading a lot of different books of late and it's getting a little jumbled in my head. I'm getting the impression that I'm getting a lot of superficial knowledge and then forgetting it very quickly. So, I decided that I have to start taking notes. I think that maybe if I take notes and then revise them I will be able to review them often and will get more out of my learning experience.

    I have downloaded the Microsoft OneNote app. It's a neat app and allows you to maintain multiple notebooks. I plan on maintaining a notebook for every book I read. I just love electronic notebooks. You save so much paper, write faster, easier to maintain and so much moe neater ! :)

    So, now my question is how do I maintain notes ?
    I'm a bit confused regarding what I should write. So, if anybody could offer any guidance, it would be excellent !

    Also, please tell me how to maintain notes for different kinds of books. For example, books on Maths History like "Journey Through Genius" and "Crest of a Peacock" will require different kinds of notes than a technical books like "Visual complex analysis". And, in all my recently acquired enthusiasm, I want to maintain notes for all of them !

    Any help will be much appreciated !
    Thanks and may God bless you !
  2. jcsd
  3. Apr 26, 2015 #2


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    Maths is a subject that needs time to digest. Unless it's very simple material, you'll probably need to go over it more than once. You also need to give your brain time to organise what you've learned.

    You'll also have to do problems using the material you've learned. It's important to "exercise" your brain in this way - this should help you really understand what you've learned.

    What maths are you learning?
  4. Apr 26, 2015 #3
    Right now, I'm reading a couple of history books on Maths because I find them easier to follow. Journey Through Genius is one I'm reading right now.

    I'm also working on improving my problem solving skills by doing books on proble, solving by Aurthur Engel and Larson. However, I'm finding them quite difficult even though only elementary concepts are involved. I'm not able to find the solution to the problems in the exercise on my own without referring to the solutions. Do you have any suggestions ?
  5. Apr 26, 2015 #4


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    What level are you at? What would you say is the most advanced maths you can do?
  6. Apr 26, 2015 #5
    I'm pretty good at Maths. I can solve differential equations and know Laplace Transforms.

    I'm working on these problem solving books because that kind of skill is not taught in schools. They require an advanced degree of skill rather than just greater knowledge.
  7. Apr 26, 2015 #6
    Taking notes will not help you if you are not going to use the mathematics that you are learning. You could do this forever............ What is your motivation for studying the mathematics you are studying ? It is very important to have an aim in mathematics............. your aim may be a bit childish or vague but it is very important, for instance my aim maybe to be able to fully appreciate Chen's Theorem so I start studying Sieve Theory, or maybe I want to learn QM so I start studying Linear Algebra. Such motivation will last throughout and will actually help you if you are discouraged.
    Such books are simply meant for entertainment and inspiration, you are being rather over enthusiastic and you fill find that that will not last more than a couple of days.........
    [Source: Personal experience, Cheers :)]
  8. Apr 26, 2015 #7
    Well to be frank, I don't know what my motivation is. Maybe it started out as a desire to be better than anybody else in my class in Maths. But, I'm not a very competitive person and that isn't the real reason.

    I don't think there's an underlying reason. I just have this insatiable desire to know as much Maths as possible.

    I know those books are for fun. I read them when I am not able to read some of the more serious books.
  9. Apr 26, 2015 #8


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    Once your at this level, there's no set programme. And, as certainly says, it depends on what you want to do. Also, whether you want to learn a bit about a range of topics or study one in detail. Something like differential equations, for example, is open-ended: you could spend a lifetime studying that and nothing else.
  10. Apr 26, 2015 #9
    That's what my point is............ you must have an aim. Let's face it, we don't live in the 1600's anymore where mathematics is a set of disconnected ancient books by the Greeks mixed with some new stuff, that people like Fermat can pursue just as a hobby and still be called great.
    That is great but direct this desire towards knowing as much mathematics as possible that is relevant to your field. You will find that this itself is not at all easy (otherwise we'd all be Edward Wittens.) and that is because mathematics is all very connected now. And those connections are still increasing. You never know which branch of mathematics may have applications in others, but I just can't go around studying chaos theory to expand my knowledge of mathematics if I what I really want to be is a number theorist.
  11. Apr 26, 2015 #10
    Hmm ... So how can I choose a field of maths to specialise in ?
  12. Apr 26, 2015 #11
    you know differential equations and laplace transforms. You must have had a little exposure to just about everything by now..............
    (except maybe, number theory). What do you like most ?
    But you're an engineering student, right?
    I don't know much about engineering myself, but I think engineering must require a good deal of stuff like PDE's and ODE's....................
    [EDIT:- this thread might be useful...............]
  13. Apr 26, 2015 #12
    I'm in my second semester of computer science engineering. I want to do something with my mathematical skill like publish a research paper or find some elegant results ... Something.

    That's why I started doing a wide amount of reading in Maths.
  14. Apr 26, 2015 #13
    Hi, i like just signed up here.
    I started trig/calc in 6th grade, and what i did was i carried around a composition notebook and first wrote down the fundamentals. i let the ideas and how stuff worked flow around my head all the time, and eventually all the ideas will come together and make sense. <3
  15. Apr 26, 2015 #14
    Hi there !

    Welcome to the website.

    But, I didn't understand the last part of what you said. Can you explain ?
  16. Apr 26, 2015 #15
    Sorry can't help you there.........
    you have to find for yourself what you really like....... ;)
  17. Apr 26, 2015 #16

    Stephen Tashi

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    Maths Absorber,
    It sounds like you are experiencing the first "rush" of an addiction to mathematics. During that phase, you will study a lot of particular topics and not see how they fit together or exist as special cases of more general ideas. Notes you take in this phase aren't likely to be useful in the future. However, the act of writing notes can be useful, even if the notes are not used afterward.

    Much of the value in taking notes is work of composing the notes - i.e. getting things straight in your mind and writing them down clearly. (After the notes are written, I find them relatively useless!)

    Writing notes as you read can be a way of keeping your mind from wandering. Notes taken that way tend to be excerpts taken from the pages of the book. They are likely to be less useful in the future than the book itself.

    If you anticipate teaching subject, you could write notes as if they were an outline for a textbook. To do that, you'd have to write down things that your students need to learn even if these are things you are not likely to forget yourself.

    If you are concerned with rote memory, you should use the tried-and-true devices. Make up jingles, write down the important facts over and over again, dictate important facts to a digital voice recorder, transfer them to you computer and listen to them while you do routine household chores.
    Last edited: Apr 26, 2015
  18. Apr 26, 2015 #17
    I used to take extensive notes from the mathematics textbook but I realized that such task is not necessary since everything I was just copying the information directly out from a book. Now I usually take notes within the textbooks by using their margins and also the post-it notes, writing down my thoughts on theorems and proofs, counter-examples, additional piece of helpful information from other books, etc; I found this very helpful and reduced the time. Some people argue that it is very important to keep a separate notebook for each textbook, but I do not think this is necessary.
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