Should I Become a Mathematician?

In summary, to become a mathematician, you should read books by the greatest mathematicians, try to solve as many problems as possible, and understand how proofs are made and what ideas are used over and over.
  • #2,136


JasonRoxx, If I remember correctly you went to University somewhere in Ontario? I got accepted into the maths program at Waterloo and U of T - St.George campus, and I was wondering which one would you recommend for studying pure mathematics? Ignoring all other factors like location, money, etc.
 
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  • #2,137


JG89 said:
JasonRoxx, If I remember correctly you went to University somewhere in Ontario? I got accepted into the maths program at Waterloo and U of T - St.George campus, and I was wondering which one would you recommend for studying pure mathematics? Ignoring all other factors like location, money, etc.

Hey, I'm actually studying at Brock University.

I'm very happy with my choice. My supersivor made sure I had a good funding package so I don't have to work. I'm so thankful for that.

I have free time to learn what I need to learn. He knows so many people in his field that I don't need to worry about where I want to go for my PhD if I do a good Master's of course. The schools I want to go to are not top notch though. Sure Icould have gone to Waterloo and stuff, but I think I am way better here.
 
  • #2,138


Though I may be beating a dead horse here, which school is better for math, Waterloo or U of T?
 
  • #2,139


JG89 said:
Though I may be beating a dead horse here, which school is better for math, Waterloo or U of T?

Undergraduate or graduate?

Either way, I see no difference.
 
  • #2,140


Bourbaki1123 said:
How difficult would you(anyone who has completed some substantial part of the book) consider the problems in Atiyah MacDonald's Commutative Algebra? How long should it take to do say, one chapters worth of exercises?

It depends on your preparation. It took me about 3 months to do every exercise in the book just after having finished my 3 year bachelors. After all, the exercises are the beef of the book. The text itself is pretty trivial.

There are a few exercises which take more time to do, some required knowledge of Tor and Ext which I had to look up form Weibel...
 
  • #2,141


Can anyone recommend a book on topology that would be suitable for (casual?) self-study? Most of the topology books I have glanced at in the library are either too basic or too technical.

My background: Freshman, know a trivial amount of group theory, read all of Spivak and most of Baby Rudin, somewhat comfortable with linear algebra.
 
  • #2,142


Wretchosoft said:
Can anyone recommend a book on topology that would be suitable for (casual?) self-study? Most of the topology books I have glanced at in the library are either too basic or too technical.

My background: Freshman, know a trivial amount of group theory, read all of Spivak and most of Baby Rudin, somewhat comfortable with linear algebra.

Maybe Alexandroff's elementary concepts of topology. It's a dover book that goes for under 10$ written by one of the founders of topology.
 
  • #2,143


Wretchosoft said:
Can anyone recommend a book on topology that would be suitable for (casual?) self-study? Most of the topology books I have glanced at in the library are either too basic or too technical.

My background: Freshman, know a trivial amount of group theory, read all of Spivak and most of Baby Rudin, somewhat comfortable with linear algebra.

You're going to want to start with a basic topology book. No need to know any analysis or linear algebra.

Theral Mooral - Elementary Topology
James R. Munkres - Topology

Both of those are suitable for you. The first is cheaper, but won't cover as much. Although, I find the first to get the reader more involved.
 
  • #2,144


Wretchosoft said:
Can anyone recommend a book on topology that would be suitable for (casual?) self-study? Most of the topology books I have glanced at in the library are either too basic or too technical.

My background: Freshman, know a trivial amount of group theory, read all of Spivak and most of Baby Rudin, somewhat comfortable with linear algebra.

Munkres makes me sick. If you know that much math, there is nothing wrong with getting something like Bredon. Much more concise with general topology, and it goes into some smooth manifolds and algebraic topology.
 
  • #2,145


JasonRox said:
You're going to want to start with a basic topology book. No need to know any analysis or linear algebra.

Theral Mooral - Elementary Topology

I believe you mean Theral Moore.

He's a professor at my school who recently retired. While I never had him, I've only heard great stories about him. He was blind but still taught calculus courses for many years, and had all of the problems in the book memorized so that he could answer students' questions.
 
  • #2,146


Thanks for the replies.

Another question: What would you recommend studying first, real analysis or topology? I am currently working through a complex analysis book (Cartan) and will start on an algebra book after that, which I hope to be done with by, say, mid-summer, with school.
 
  • #2,147


I am a High school junior who plans to do partial differential equations via EPGY at Stanford. However, due to the economic situation I can't afford to take the prerequisites at EPGY and so I have to self study everything. I have finished single variable and most of multivariable calculus, however, I can't find any good resources for studying differential equations.

Are there any good online resources except for MIT OCW to learn differential and what are some good textbooks?
 
  • #2,148


tyrant91101 said:
I am a High school junior who plans to do partial differential equations via EPGY at Stanford. However, due to the economic situation I can't afford to take the prerequisites at EPGY and so I have to self study everything. I have finished single variable and most of multivariable calculus, however, I can't find any good resources for studying differential equations.

Are there any good online resources except for MIT OCW to learn differential and what are some good textbooks?

Do you know much linear algebra? For ODE I really like Arnold's book, but I have trouble remembering what the prerequisites are. The one by Devaney is a good one too.

I don't know any undergrad PDE textbooks. Maybe Strauss.
 
  • #2,149


Unknot said:
Do you know much linear algebra? For ODE I really like Arnold's book, but I have trouble remembering what the prerequisites are. The one by Devaney is a good one too.

I don't know any undergrad PDE textbooks. Maybe Strauss.

I don't know much about it but I have a good textbook for reference if needed
 
  • #2,150


tyrant91101 said:
I don't know much about it but I have a good textbook for reference if needed

You should really learn linear algebra first. You have plenty of time to learn math, no need to learn your interests now.
 
  • #2,151


tyrant91101 said:
I don't know much about it but I have a good textbook for reference if needed

I don't think I would recommend Arnold's ODE text for you, for your first time encountering differential equations. You'd probably want a book along the lines of Boyce and Diprima (but cheaper probably)
 
  • #2,152


axeae said:
I don't think I would recommend Arnold's ODE text for you, for your first time encountering differential equations. You'd probably want a book along the lines of Boyce and Diprima (but cheaper probably)

Yes, you are right. Now Tenenbaum comes to mind. Widely used text and also cheap.
 
  • #2,153


Well, real analysis is a gentle introduction to point set topology but learning topology first will probably make real analysis pretty trivial (at least for the early parts). My friend did topology first and he thinks of real analysis as just a special case.
 
  • #2,154


axeae said:
I don't think I would recommend Arnold's ODE text for you, for your first time encountering differential equations. You'd probably want a book along the lines of Boyce and Diprima (but cheaper probably)

Thank you very much for the advice. I took a look at the Boyce & DiPrima textbook in my library and I think I will get it. It is a good textbook
 
  • #2,155


Does one have to be a genius to choose math as his career path?
 
  • #2,156


thrill3rnit3 said:
Does one have to be a genius to choose math as his career path?

I hope not, as I am far from genius and it's the career path I have chosen.
 
  • #2,157


How is it going so far?
 
  • #2,158


mathwonk said:
as to those planning a career in math, here is a relevant joke i got from a site provided by astronuc:

Q: What is the difference between a Ph.D. in mathematics and a large pizza?
A: A large pizza can feed a family of four...

ANother joke:
Q: Why do mathematicians wear glasses when they go to sleep?
A: So that they can figure out their dreams.
 
  • #2,159


Man, I hate throwing in the towel on a book, but Henri Cartan's Elementary Theory of Analytic blah just isn't working for self-study. It's torturous, and my retention is poor.

/whine
 
  • #2,160


Wretchosoft said:
Man, I hate throwing in the towel on a book, but Henri Cartan's Elementary Theory of Analytic blah just isn't working for self-study. It's torturous, and my retention is poor.

/whine

Sorry to hear that but it is perhaps the most rigorous treatment of complex analysis. I cannot think of a more thorough or rigorous book on complex analysis.
 
  • #2,161


It's more rigorous than Ahlfors? =O

Anyway, which (book but also in terms of approach) is more suited for further study in multivariable complex analysis (for algebraic geometry).
 
  • #2,162


What are the best resources for self studying Galois Theory?
 
  • #2,163


I would definitely recommend dummit and foote partnered with Michael Artin's Algebra
 
  • #2,164


Thank you for the recommendation. Do you know if Michael Artin's father's book on Galois Theory is worth taking a look at?
 
  • #2,165


It's going to be far more difficult to get through, but yes, Emil Artin was a master of algebra so I'm sure the material would be worthwhile. I'm not sure how much knowledge is assumed in his book, and the style is probably pretty different.
 
  • #2,168
Tobias Funke said:
Never looked at it, but it's online for free, thanks to MIT.

http://ocw.mit.edu/ans7870/resources/Strang/strangtext.htm

I know. That's why I'm asking opinions about it :smile:
 
  • #2,169


From what I've seen of his linear algebra lectures, I like Strang. I don't think the book is as rigorous as Apostol, but depending on your preferences that may be a good thing. Anyway, you can't go wrong with a free book by a respected mathematician.
 
  • #2,170


I like Strang as a lecturer and a professor. As a book author, not as much.

I mean, I haven't read his calculus book but his linear algebra book isn't as good as his lectures, let's just say it like that.
 

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