
#1
Sep813, 11:46 AM

P: 111

Hi, the title is selfexplanatory. I am wondering if there is something I can do to be able to read mathematics like I am reading a newspaper or book. Regardless of what the single letters are describing in natural language, I can understand but maybe not conceptually grasp what is being conveyed.
However, in maths, when I see simple things like F = m.a, yes I know what they mean because I have been told, however, I want to reach a level that I can identify and characterize, say, systems by just "reading" their relevant mathematics. One example is EM fields. The operations of multiplication, division, add/subtract has no "meaning" to me in a, say, 4D differential equation. I study electromagnetics at a grad level. I don't need to be more "skilled" or "adept" at "solving" problems. Pleas help! Thank you very much. 



#2
Sep813, 04:55 PM

Mentor
P: 10,840





#3
Sep813, 07:46 PM

Sci Advisor
Thanks
P: 2,960





#4
Sep913, 10:21 AM

Sci Advisor
P: 3,175

Read Mathematics like a newspaper?
I once took a course in mathematical economics taught by a professor who mentioned that he had taken the "Evelyn Wood" speed reading course with the goal to being able to read mathematical articles quickly. He found he couldn't. When he complained to the company, they told him he couldn't expect to read technical material as quickly as ordinary text and they refunded the money he paid for the course.
I think the only way to go over mathematical articles quickly amounts to skipping parts of them. For example, if you are reading a textbook and it begins to explain the properties of a vector space or something you already know then you can skip those parts. There is a slight risk in doing this since you may miss something important and not obvious. 



#5
Sep913, 01:46 PM

HW Helper
P: 1,373

My advice is to always ask the question, "what does it mean?". So you read something, you understand what it is saying, but then ask, what does it mean. For example, I see the chain rule in differentiation: D(f(g(x))) = f'(x) D(g(x)), so I ask, what does it mean? And the answer I get is, it means the same thing as this: D(f(x)) = f(x) dx  here g(x) = x. So it is a generalization of the standard rule of differentiating a function. And now when I see ##{\partial f \over \partial x} dx##, I see an analog of the above, the result of f being differentiated in the x direction, so this is the directional xderivative. And directional derivatives are now more easy for me to understand.
Try to make these connections, you could call it conceptual economy, try to have as few concepts as possible that do the widest possible work. 



#6
Sep913, 11:08 PM

P: 4,570

verty makes some very good points.
When you read mathematics, you are not reading the symbols: you are interpreting what they mean and the context that they are in. Within language, its not about the letters but what the meaning that is conveyed: this is also true of mathematics (as it is for any language). When you look at integral or a derivative, you are looking at accumulations or changes. An integral looks at summing changes whether those changes are areas, volumes, projections or something else. If you are trying to understand symbols alone, then you will be missing all the meaning that was originally intended to be conveyed. 



#7
Sep1013, 09:32 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,895

I wouldn't want to "read mathematics like a newspaper". You should always read mathematics with pencil and paper near by and do the mathematics while reading it.



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