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My eyes are destroyed. I have been unable to learn math beyond decimal division in school due to laziness and unhelpful teachers. I am now trying to mitigate this mistake by learning math from the beginning. I do not have any teachers or any kind of specialized tools. I am only using a computer and screen reading software that reads texts and equations. I am trying to learn all the math required for understanding calculus. I wish to learn calculus to be able to learn analysis of algorithms in computer science.

Through the help of many online lectures and videos, I have been able to learn a lot of basic algebra on my own (E.G. exponents, functions and some basic polynomial manipulations). However, areas with graphs, lines and trigonometry completely destroyed me. Online lectures and videos do not help because they usually do not describe the graphs, or lines they've drawn. So I am left with imagining what they might look like.

I believe I got a few things right. For example, In a graph, x axis means left to right. Y-axis means upwards to downwards. Negative numbers are left and downwards while positive numbers are upwards and right. For example, if I were to graph (3,5) I would move three points to the right and go upwards 5 points. I believe I managed to understand what slope means. But beyond that I am totally lost.

I understand this is an extremely unusual way to learn, but since I am learning on my own I may have no choice.

My questions are:

  • Is it possible to learn critical elements of algebra while completely ignoring graphs?
  • I've read a lot about graphing a function. Is it so important to graph a function?
  • Is it possible to understand trigonometric functions without knowing what they mean visually? I have no interest in trigonometry, I will just studdy them to help me with calculus.

In general, is it possible to learn math required for analysis of algorithms while only using equations and totally avoiding visual things like graphs, slopes and lines? If no, is it possible, however small, to learn and use graphs without seeing them?

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  • $\begingroup$ The word is "axis", not "access". Graphs are an important part of understanding functions...why would one want to disregard them? The algebraic part of working with functions is very important too, but don't forget that most functions are too difficult to work with algebraically. It's nice to have other tools to use. $\endgroup$ – lulu Aug 25 '18 at 19:39
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    $\begingroup$ Have courage: Euler is arguably the greatest mathematician of all time and he worked for many years blind. Perhaps Mathematica will help, especially if you can type: Speak[x^2 + y^2 == 1] speaks the equation aloud. $\endgroup$ – David G. Stork Aug 25 '18 at 19:42
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    $\begingroup$ @morbidCode: Hmmm... of course you can use Mathematica to graph functions (in innumerable ways), but I'm not sure how to represent visual information in the proper way for the visually impaired. Given a function (e.g., a Gaussian times a sine wave), what would be your ideal output to help you learn and understand? $\endgroup$ – David G. Stork Aug 25 '18 at 19:51
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    $\begingroup$ This does not answer the question, but I want to mention that Pontryagin lost his vision at the age of 14 and managed to become one of the greatest mathematican in the century! He made some celebrated contributions to geometry (much more than a graph). It might be tough, but I guess there should be a way to understand graph. $\endgroup$ – Cave Johnson Aug 25 '18 at 20:11
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    $\begingroup$ Another interesting example: In Karl R. Stromberg's An Introduction to Classical Real Analysis, the section About the Author ends with “The absence of figures and the few typographical imperfections in the present book should be attributed to the fact that for his whole professional life the author was virtually (and, indeed, legally) blind”. $\endgroup$ – Hans Lundmark Aug 26 '18 at 7:17
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Nemeth Code is Braile for Mathematics. If you are visually impaired you should find out about it and get yourself Mathematics books for the visually impaired.

https://nfb.org/images/nfb/publications/fr/fr28/fr280119.htm

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  • $\begingroup$ Unfortunately I am unable to get these at the moment. Probably in the future. $\endgroup$ – morbidCode Aug 25 '18 at 20:11
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I read a doctoral thesis on teaching geometry to non-seeing pupils. The most important thing for these children was to touch and compare objects.

As for graphs - you can learn without them, however math are much more beautiful and easier with graphs, courbes, figures etc.

You are not excluded from the possibility to use them! It is possible to buy plastic templates (stencils) which allow to dress a parabola, circle, ellipse, hyperbola ... other serve for sinusoid, tangential courbe ... They are similar to rulers. I cannot enclose a link to a supplier, it would be a prohibited ad; however you could easily find a stock. These small tools will help you make progress faster.

Another option, though more expensive, is a 3D printer.

A 3D unit helix can be found in a toy shop. It is a color "spiral" - it helps tu understand the relation between sine/cosine function and a unit circle.

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