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Studying Self-studying mathematics - Discussion

  1. Dec 27, 2016 #176
    If you're completely on your own and not in any classes relevant to pure mathematics, then send me a message. I might be able to help. This goes for everybody reading this.
  2. Jan 7, 2017 #177

    Stephen Tashi

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    Given the resources on the internet, it's possible to find the answers to most of the questions about math and physics that do have answers. The aspect of a mentor or study partner that is missing is the motivational aspect. There's a big difference between "I I'll study chapter 12 tonight" and "I'll study chapter 12 tonight, because I'm going to meet Ludwig tomorrow at lunch to talk about it."

    However, it is a statistically rare experience to have a mentor or a study partner. So if your education is dependent on motivation from a mentor or study partner, you'll probably have a tough time.

    We can learn things from interacting with people we don't respect or don't like. For example, the worst coder on the staff may be the best at getting the fax machine to work. A poorly written textbook may have some profound insights scattered in its pages. Such educational experiences are not an organized curriculum, but they are always available.
  3. Mar 3, 2017 #178


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    Hi all,

    I'm a physics graduate now working as a maths and physics teacher in a sixth form college. I loved my degree, though wish I'd had the work ethic I do now when I was studying full time. I took a theoretical physics course in my 4th year (syllabus here http://www-thphys.physics.ox.ac.uk/...012/Theoretical_Physics_Option_home_page.html), and passed the exam, but to be honest I feel like I learned processes without fully grasping their understanding. I felt this was especially true for the parts of the course in which i was most interested: looking at field theories. This was because at no point in my course up to that point had I ever done any group theory, and I didn't (at the time) have the motivation or though to teach myself some from scratch. I can't help but feel that with a good mathematical grounding I'd have been able to see the beauty in the course that I know is there, so I'd like to try to develop it now, but I'm wondering if anyone can give me some advice on where to start.

    Should I first learn about sets, rings, and (mathematical) fields? Or is there an introductory group theory text which would be sufficient to get me far enough that I could make another attempt at looking at field theories?

    Thanks in advance!
  4. Apr 20, 2017 #179
    I would like to share an observation that works for both mathematics and theoretical physics. If you're going to be extremely good at some subject , Let's say Quantum field theory or algebraic topology , the only way is to work out everything independently on your own. You know some basic tools & tricks and play with them in order to solve problems with varying levels of difficulties.You must invent your own problems as well. You don't really learn by reading a textbook. You learn by trying to rediscover these insights in the textbooks.
  5. Jun 11, 2017 #180
    Hello, I am a 12 year-old boy, and I am very interested in physics and maths. For maths, would you recommend me to keep learning by myself following the order of topics for example, in each year in KhanAcademy? Or should I learn it in a different order? For physics, for the moment, I don't want anything that requires too many math, I first prefer to have a good math base that can be used for physics, and then gradually go applying it to my physics learning. So in physics, what order should I follow of topics, Eg: should I follow a certain order in each field, quantum mechanics, motion, etc (If it includes some maths in does not matter, but I prefer it to explain the concepts more strongly)? If you know about any books about physics, that mainly and strongly explain concepts (if it includes some math it doesn't matter), could you please tell me? It would be very helpful.
    Currently, I am to self-studying about math, physics (mainly concepts), computer programming (before I was a bit confused and advancing little, as I was with many, now I am with just Python) and electronics. Do you think I should do them all at once, each one a smaller amount but at once, or 1 mainly at a time (and the rest but MUCH less time, so I keep thinking about them, and don`t forget), for a certain period of time, and then go changing which one I learn mainly and which one I revise in less time?
  6. Jun 11, 2017 #181
    Dear young friend. I did share your interest in physics and I was not bad at school. i think the way the Khan academy proceeds in physics is a good option and I would be you, I would follow their path. The same applies to mathematics. So far to the rational way to proceed.

    Emotionally physics was and is for me a fascinating science and dealing with it opens our sense for what our current science is finding out about it. Forget about quantum physics and relativity theories from your learning of physics. Look for good videos in youtube and find some that speak in a more general public kind about those fields of science. That puts you in touch with those topics and you can start to reflect about what you find interesting.

    With mathematics the way it is taught at school and which you will need to master your tests in mathematics at school the Kahn academy gives you solid information to learn. But as with physics, where there are topics that you need at school in which give you a starting point, mathematics offers at least equally fascinating topics that equal in opening your eyes for a whole new way to see the world around you. i f you allow me, I would to tell you a bit about what I mean!

    I did finish my studies at a technical university in 1979. That was then the last time I had to deal with mathematics in the way I did learn until then! So nearly 4 decades later the science about mathematics has also been developed very heavily. The mathematics as you learn to the end of high school really is not mathematics but is learning to apply formulas to solve equations. The top of this king of "mathematics" goes and includes calculus. Terms like differentiation and integration are ones that you can search via google and find information about it.

    I like very much the current definition about the science of mathematics. Mathematics deals with finding "structures"! There is a course from the Standford University which can be taken for free here: "Introduction To Mathematical Thinking" This course has the purpose to help students to make the transition from the kind of mathematics they have been taught until then and to the kind of mathematics the students are required to learn and apply at the university. Do not let yourself be intimidated. Its even more! As you have not yet been spoiled to think the traditional way mathematics was done until about 200 years ago, you will probably have it easier to grasp this "Mathematical Way of Thinking! If you listen to the lecture of prof. Kevlin that you can see as videos, if you listen to the videos were he very detailed explains interesting topics as help for solving the challenges to think the mathematical way, you could have it easier than older ones to capture what is being taught.
  7. Jun 12, 2017 #182
    Thank you very much for this advice, I will take it into account, and definately check out the course on 'Mathematical Way of Thinking' :smile:. Currently, I am also in another Coursera course of Stanford University in 'Introduction to Logic'
  8. Jun 28, 2017 #183
    Study and practice
  9. Jun 29, 2017 #184
    When I was in your age, I liked Jay Orear's Physics and the Feynman lectures a lot. In general: You cannot learn physics without math. So if you want to learn physics, you must learn math first, namely vectors+matrices, analysis (differentiation and integration) and later vector calculus (the gradient, divergence and curl operations and the theorems of Gauss and Stokes). The Feynman lectures cover all this, Jay Orear expects you to know differentiation.
    Don't waste your time trying to learn physics without math or with as little math as possible. It doesn't work/will give you a pseudo-understanding.
    I'd recommend you start with differentiation (by the way, I don't think the explanation that Feynman gives is very good; I don't think I'd have understood it there if I hadn't known it before). I would simply start here (I learnt it first from the math formula reference book that we used at school, so not really a big difference): https://en.wikipedia.org/wiki/Derivative (sections 1.1, 1.4, 1.5, 1.6, 1.7, 1.8, 2.1, 2.2, 2.3, 3.1, 3.2, 3.3)
  10. Dec 25, 2017 #185
    What are the most reliable (preferably free) online courses for algebra 2, pre calc, and calc A, B, and C that give students a deep understanding of the topics? Would I be better off with textbooks or a paid online program?

    I would like to self-study the math necessary before I dive into physics, however, I would like to not break the bank in the process. I am currently enrolled in ALEKS MAT 130 and MAT 170 for algebra 2 and pre calc by ASU, but I’m not sure if they were intended for students who are getting exposed to the material for the first time. Furthermore, I’m not getting an understanding of the topics when I take algebra 2 from MAT 130. It is simply straight-up memorization. In this case, should I go for a paid online course or textbook? I don’t know about MAT 170, but if it’s anything like MAT 130, I don’t think it would be for me. I am also enrolled in Calculus 1A: Differentiation, Calculus 1B: Integration, and Calculus 1C: Coordinate systems and infinite series by MITx on Edx. I have yet to take anything from it, but it seems promising. If anybody has experience with it or suggestions for a source that provides a deeper understanding of calculus, please let me know.

    Last edited: Dec 25, 2017
  11. Dec 25, 2017 #186


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    ALEKS is useful for review, to check if students have any obvious holes in their knowledge, but it's not actually useful for learning anything well. If you want the best courses for students who love math and are good at it, check out Art of Problem Solving. My kid preferred the books to the online courses because he could go at his own pace.

    In any case, not free. Also not particularly expensive, especially the books. But really, really good.
  12. Dec 25, 2017 #187
    I've heard a lot of great stuff about AoPS! I will definitely check them out, and thanks for the quick response.
  13. Dec 25, 2017 #188
  14. Apr 13, 2018 #189
    I'm interested in learning math, partially for its own sake, but mostly because I am very interested in learning scientific computing (emphasis in environmental modeling, e.g. climate, groundwater). For that I'd like to be able to cover precalculus material (algebra, trig) and basic calculus (limits, differentiation, basics of integrals).

    Currently I'm going through Precalculus demystified and the Brilliant.org Algebra practice problems, which should take me through mid-May. I think two months should be a reasonable time to review algebra and trigonometry, I don't feel that it's terribly difficult (challenging, but not bang my head against the wall).

    From there I'm planning on taking couple computer science online courses through edx.org (Introduction to computer science and programming using Python and Simulation and Modeling for Engineering and Science), which don't require more than a reasonable aptitude for math, probabilty/statistics, and some programming (all of which I have). Once I'm completed with these I plan on going through Elementary Calculus (with supplemental problems, e.g. brilliant.org and Paul's online math notes).
  15. Apr 13, 2018 #190
    I know this is a bit of an old post, but I often find myself wanting to study more subjects than I should. How many hours per week do you partake in self-study?
  16. Apr 14, 2018 #191
    I am currently learning on math, physics (mostly conceptual), artificial intelligence using tensorflow in python, and sometimes I research and keep on learning on arduino, electrical engineering, space exploration and the geology of different planets or celestial bodies, with occasionally some other small topics. However, I sometimes feel I don't have enough time to do it all at the pace and depth that I would like. I usually try to organize myself weekly or bi-weekly, as a week may sometimes not be enough for me to cover or do what I want to do, learn, or keep researching. I also try to focus on math, as it will then let me learn even more on other topics such as physics and electrical engineering. If I try to do it the other way round, with math as something secondary, when I encounter something that isn't mainly conceptual, it is very difficult for me to understand it. In addition, I think that truly learning about physics, for example, is not about the formulas at all, but the concept itself, and why the formula is the way it is, and how it has been constructed through a series of experiments. Sometimes, previously, I didn't focus much on learning math, but physics concepts, or electrical engineering, but almost always complex math appeared when researching on something, which is why I turned it the opposite way round.

    With the number of hours each week, it really depends on which week I am on, or what I must do, even though I wouldn't really want to that thing, and rather just focus on what I truly like and interests me. To try to more or less balance what I do, with my primary focus on math, I may be 1 or 2 weeks just covering a reduced number of topics, to focus on a smaller number of topics at a time, and then I may switch some for another time period, maintaining some topics I consider very important to keep on learning further on other subjects.
  17. Jun 29, 2018 #192
    Please show me your ways, master.
  18. Jun 30, 2018 #193
    @PlanetGazer8350: I can very much identify myself with the kind of activities you are pursuing and why! I am now retired and to keep me busy and to have my days properly organized and to satisfy my curiosity I do exercise the muscle between my ears! I started to reactivate my hobby from my days at school, model building. As my financial situation is not anymore as it used to be i decided to switch from building planes to build a sale ship from scratch. Work with wood, lamination with epoxy, later building using aluminium the project of the sail ship model became more a path that brought me in touch with many technologies. As I used to work in the semiconductor industry and later in the telecommunication industry it became evident to me that using my own build electronics would open many new ways to realize projects related to the sailship. While over the years my workshop became more and more sophisticated, milling machine and lathe purchased based on the more mechanical aspects of my project, electronic has become my main technique. Investigating my own way to combine a stepper motor to control a pulley that controls the sheet that define how much a sail can open and wishing to do it the way it was done in early 20th century i run in conflict of this part of the project with naval modelers, experts in sailboats as they claimed this was impossible due to the friction of the sheets in the pulley and in their path through the body of the sailboat. Discussing it with the community of physics they said that friction was neglectable.. So I decided to model the system that was to control my sails. Doing a lot of research, Matlab and similar tools had no price for individuals and so where financially impossible to aquire, I decided to go with Mathematica from Wolfram and their tool "SystemModeler" that uses the language Modelica. I wanted further to compare the "quality" of my Modelica models by using the ability of the Wolfram software to collect data from physical experiments and to improve this way the quality of my models.
    Somewhere along the road of this activities I realized that mathematics are the language required for Physics, Electronics and Simulation. Suddenly I found a course MOOC, from Terence Tao that build the mathematics starting with the theory of numbers. The book used was available for free from Taos personal website. I fall in lough with mathematics! I even decided that it would be worthwhile to study mathematics at the "Technical University Munich". I wen to an introductory event and had the opportunity to talk with one of the mathematics professors. he told that since recent decades mathematics is viewed from the perspective of studying "structures". I had no clue of why it happen to be this way. Soon I found fascinating courses for physics, cosmology and mathematics that demonstrated the power of approaching mathematics by studying structures. Even a professor that gave a course available for free in the internet from the University of Erlangen went through the whole theoretical field of physics up to beginning master level using more and more sophisticated models of mathematical structures. Even there is a fantastic introductory course available for free as MOOC from the Stanford University named. "Introduction to Mathematical Thinking". A very worthwhile course to take. In his first lesson he defined mathematics as the science of structures!. I do not need to mention that also electronics is a science the uses mathematics. Also artificial intelligence uses statistical methods.
    I have taken the effort to present how I got into this trying to confirm your opinions and so be able to pass the message to you: science is advancing so fast in many fields that even me who is 24/7 available for this studies have come to the conclusion I need a method to combine the curiosity of the fields mentioned here with the chance to benefit from what I am learning, tools for the science disciplines that affect my project of a sail model ship build from scratch in my very own way.
    So I study mathematics in depth enough so that the software Mathematica takes the job to solve equations. To have my mathematics skills well enough advanced that I can capture the concepts I meet. This results in an iterative way to advance my mathematics studies.
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