Advice for a potential career in Pure mathematics

  • #1
I use to hate math during highschool. However some eight years after graduating and being in the military help with my attitude towards math. I am reviewing a GRE math review book and I haven't been able to put it down. I just learned quadriatic equations and am pursuing into intermediate and advance algebra. I just never realized how much I actually enjoyed math till last year. I am teaching myself all this and I'm getting it more easy then I would ever imagine. So i jumped into the world of mathematics, discovering the field of Pure Mathematics. So my goal is to get a BA in Mathematics from SNHU and a Phd in Pure Mathematics from UCONN. Any advice/tips?
 

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  • #2
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Research what are good books. Patience and tenacity is key. Read the book constantly with paper and pencil. Most of my books (older math books), tend to have larger margins. I write in the books, rewrite sentences and explain the proofs in the examples on the margins. Try to think about the why. Look at the proof. Practice it, and follow each line asking why it is true. Then after practicing alot, attempt the proof. If you get stuck after a while(not five mins then looking st the derivation), Re read it. And go again. Once you have it down practice for an hour without looking. Make sure you understand and not just memorizing. After proceeding a bit further in the book. Stop, grab a blank sheet of paper and summarize what you have learned. Then think of the proofs you practiced and re produce them on that blank paper without looking.
 
  • #3
Research what are good books. Patience and tenacity is key. Read the book constantly with paper and pencil. Most of my books (older math books), tend to have larger margins. I write in the books, rewrite sentences and explain the proofs in the examples on the margins. Try to think about the why. Look at the proof. Practice it, and follow each line asking why it is true. Then after practicing alot, attempt the proof. If you get stuck after a while(not five mins then looking st the derivation), Re read it. And go again. Once you have it down practice for an hour without looking. Make sure you understand and not just memorizing. After proceeding a bit further in the book. Stop, grab a blank sheet of paper and summarize what you have learned. Then think of the proofs you practiced and re produce them on that blank paper without looking.
Thank you! What areas should I be focusing on the most in pursuit of this? For my BA it's Calc, statistics, those things but I want to specialize in Algebra/Abstract Algebra
 
  • #4
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Depends what level ypu are at mathematically and proceed from there. I am still in the process of school. I have just completed linear algebra. How far have you gone in mathematics?
 
  • #5
Depends what level ypu are at mathematically and proceed from there. I am still in the process of school. I have just completed linear algebra. How far have you gone in mathematics?
I am just starting to learn linear algebra. I can add, subtract and multiply. I am learning how to division.
 
  • #6
mathwonk
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There is a thread here in the academic guidance section that was called something like "who wants to be a mathematician?", and now called perhaps "should i be a mathematician?" that was started for people like you. It is now very long but the first few pages are still relevant I suspect. There are lots of lists of good books and advice on taking courses in college. I started it about 9 years ago. I am a retired math professor with a PhD in algebraic geometry, that I obtained after taking a break in my schooling, being a meat lugger, and college teacher for a while, then starting a family and going back to grad school.
 
  • #7
There is a thread here in the academic guidance section that was called something like "who wants to be a mathematician?", and now called perhaps "should i be a mathematician?" that was started for people like you. It is now very long but the first few pages are still relevant I suspect. There are lots of lists of good books and advice on taking courses in college. I started it about 9 years ago. I am a retired math professor with a PhD in algebraic geometry, that I obtained after taking a break in my schooling, being a meat lugger, and college teacher for a while, then starting a family and going back to grad school.
Thank you sir. I'll dig through and find the thread. So how hard was it to balance your family and school life?
 
  • #8
mathwonk
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very hard, the hardest thing i ever did; but if that is your goal, what choice do you have?
 
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  • #9
very hard, the hardest thing i ever did; but if that is your goal, what choice do you have?
I apologize for the long delay in replying but I agree and I'm lucky that my wife is supportative of it.
 
  • #10
mathwonk
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me too!
 

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