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February 27th, 2015, 09:26 AM   #1
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How to become a mathematician?

I study Electric engineering and I have always loved Mathematics and now I want to study math and don't know where to start. I want to be like someone who graduated from a math department with no difference between us, so how should I study beside my current study? What plan should I follow and what books should I read for every topic?

Last edited by skipjack; March 3rd, 2015 at 11:12 PM.
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March 3rd, 2015, 10:41 AM   #2
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Hello. I am completely self-taught, so perhaps I can help you. First, what kind of mathematical background do you already have? Do you know pre-calculus from the high school level? I ask because many topics from that level never go away, such as trigonometry.

To clarify, I'm not a full fledged mathematician. However, I had the same thought as you did, wanting to study on my own time as a hobby because it was fascinating. I am still learning something new almost every day.
Thanks from jonah

Last edited by Compendium; March 3rd, 2015 at 10:58 AM.
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March 3rd, 2015, 03:13 PM   #3
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Compendium, I'm also same with you.
Can I know what kind of resources do you use to learn maths ? Books? Can you suggest some books or any resources to me ? Thanks
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March 4th, 2015, 02:23 AM   #4
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If you study electrical engineering, chances are you already have a good grounding in mathematics. I would get hold of a first-year undergraduate textbook for mathematics degree students and go from there. There are also plenty of resources online.
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March 4th, 2015, 11:47 AM   #5
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Originally Posted by jiasyuen View Post
Compendium, I'm also same with you.
Can I know what kind of resources do you use to learn maths ? Books? Can you suggest some books or any resources to me ? Thanks
I started learning calculus in high school using the calculus wiki book. At the time it was basic and incomplete. After high school I wanted a better teaching guide. I found a free PDF of calculus by Gilbert Strang, an instructor at MIT.

http://ocw.mit.edu/ans7870/resources...s/Calculus.pdf

I also watched some of MIT's open courseware on single- and multi-variable calculus, as well as ordinary differential equations.

I consulted mathworld.wolfram.com and wikipedia.org when I wanted some additional information on what I was learning about.

Dover mathematics books are relatively cheap. I bought Ordinary Differential Equations by Morris Tenenbaum and Harry Pollard. It is extremely thorough, but as I'm more interested in pure mathematics than physics, I didn't read everything. I also bought Advanced Calculus by David V. Widder (not a Dover book, but not expensive).

I just bought Elementary Real and Complex Analysis, another Dover book, and downloaded Real and Complex Analysis by Walter Rudin as a PDF, as that will be what I intend to learn next. I will also use Mathworld, Wikipedia, and probably this site for more information on what I learn.
Thanks from jiasyuen
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March 7th, 2015, 08:55 AM   #6
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Quote:
Originally Posted by Compendium View Post
Hello. I am completely self-taught, so perhaps I can help you. First, what kind of mathematical background do you already have? Do you know pre-calculus from the high school level? I ask because many topics from that level never go away, such as trigonometry.

To clarify, I'm not a full fledged mathematician. However, I had the same thought as you did, wanting to study on my own time as a hobby because it was fascinating. I am still learning something new almost every day.
It would be better to start from the begining, and please tell be a study plan and books for the topics, and for the topics I want to study all about math.
And thank you very much.
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March 7th, 2015, 10:03 AM   #7
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What can you tell us about your current level of mathematical understanding? Is there anything in particular you are interested in learning?
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March 7th, 2015, 05:24 PM   #8
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CRGreathouse. I'm interested in number theory. Is there anything I should learn about before starting number theory? Can you suggest some good books for number theory for a beginner ? Thanks a lot.
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March 7th, 2015, 05:40 PM   #9
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CRGreathouse. I'm interested in number theory. Is there anything I should learn about before starting number theory? Can you suggest some good books for number theory for a beginner ? Thanks a lot.
Number theory has no real prerequisites, as such, except for general mathematical maturity. I learned it from Ireland & Rosen, which is great, but not well-suited to self-study. Hardy & Wright is a classic, although you might only be able to get halfway through without a course in complex analysis. It's more enjoyable but less comprehensive than others (this isn't a bad thing). Silverman's A Friendly Introduction to Number Theory looks like it might be your best bet, though I haven't read it.
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March 8th, 2015, 10:23 AM   #10
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Number theory has no real prerequisites, as such, except for general mathematical maturity. I learned it from Ireland & Rosen, which is great, but not well-suited to self-study. Hardy & Wright is a classic, although you might only be able to get halfway through without a course in complex analysis. It's more enjoyable but less comprehensive than others (this isn't a bad thing). Silverman's A Friendly Introduction to Number Theory looks like it might be your best bet, though I haven't read it.
So I will start reading these books. For the Hardy&Wright, can I know which chapter that I cant study without a course in complex analysis? I'll get back to you when I've questions or anything. Thanks man!

Last edited by jiasyuen; March 8th, 2015 at 10:34 AM.
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