Should I Become a Mathematician?

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  • Thread starter mathwonk
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  • #1,826
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thanks everyone for advices, it's been helpful. well, i will try to do my best at this point, and working as hard as possible seems to be the way to go =).
 
  • #1,827
tgt
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Finally found that mathwonk got a gpa of 1.2 after first year. You were kicked out and worked as a meat slumber? How many years after did you get back into undergraduate again?
 
  • #1,828
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I havent studied any real analysis, except for basic stuff (open/connected sets, bolzano-weiestrass) but will do so soon.

I'm curious to know how it is different from advanced calculus?
 
  • #1,829
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ok here is my secret: I decided to quit pretending I was smarter than others and to try to see how good I really was: i.e. I decided to see how good I could be by aCTUALLY WORKING AS HARD AS POSSIBLE.

The result? I was nowhere near as good as I fantasized, but much better than I had been.

best wishes to you. you all know what you should be doing. my advice is merely that if you start doing those things, they will work for you.


Thanks for sharing all this mathwonk. It is encouraging.
 
  • #1,830
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Hi. I too am a second year student hoping to major in maths. I have a few questions, please bear with me.

How important is linear algebra to the mathematician? I have already taken a course in linear algebra, but I am thinking of studying it again over the break before 3rd year, since the course I took was not so good. Is it worth studying linear algebra properly, or should I focus on abstract algebra instead? Or both? I may not have time to revise both.

Should I study set theory and logic independently, or is it sufficient as it is given in the course of my undergrad years?

How good I have to be to get into grad school? Do I need 90% plus in my final year? Is that even acheivable?

Finally, should I do two majors or just maths? Would another major detract from my maths studies, or would two majors be a more 'rounded' degree?

Thanks.
 
  • #1,831
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Linear algebra is pretty important subject. The more you know from it, the better you'll be for it. If you feel your course in it was weak, then go study it independently. You'll find that many linear algebra concepts will be applicable to abstract algebra, so studying for linear algebra can help you study for abstract algebra.

I studied set theory a lot because it is rather important to what I study. However, it seems set theory and logic is something that you just kind of pick up as you go. At least, that's my experience.

Depends which graduate school you are applying for and if it is a masters or PhD.

You should do two majors if a second major interests you. I did mine major in mathematics and interior design. Don't ask why, but I did and I had fun, met my wife too, so it worked out pretty well. Sometimes it was hard to work through both majors but time management is key. If another field interest you, then go for it, if not, then you'll be pretty miserable.
 
  • #1,832
mathwonk
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i was out one year from undergrad. the bigger gap was from grad school. i went astray in 2nd or 3rd year, hung on until the fifth and took off for a 4 year job teaching.

then i went back and finished the phd in 3 more years, at 35. (does that sound old? it does sort of to me too for a grad student, but i wouldn't mind being 50 again now!)
 
  • #1,833
mathwonk
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oh and linear algebra is crucial. in that vein, i offer my free book on my website, notes for math 4050.
 
  • #1,834
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I studied set theory a lot because it is rather important to what I study. However, it seems set theory and logic is something that you just kind of pick up as you go. At least, that's my experience.

Formal logic is really nice when you aren't quite sure if you cheated during a proof. And you get a really good understanding of how variables play together in an equation.
 
  • #1,835
morphism
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How important is linear algebra to the mathematician? I have already taken a course in linear algebra, but I am thinking of studying it again over the break before 3rd year, since the course I took was not so good. Is it worth studying linear algebra properly, or should I focus on abstract algebra instead? Or both?
You can hit two birds with one stone. First review the basic topics, such as vector spaces, dimension, linear maps, etc. Then look at more 'abstract' topics, such as, say, canonical forms of matrices, spectral theory, etc.

There is a lot of overlap between the ideas you see in linear algebra and certain ideas you see in abstract algebra. An example is the classification of finitely generated abelian groups and modules over PIDs -- this is pretty much a generalization of the notion of canonical forms of matrices.

Also, a lot of the topics you would see in an advanced analysis course will stem from linear algebra. Some people like to refer to functional analysis as "infinite-dimensional linear algebra," and with good reason. So if you have any interest in doing any advanced coursework in analysis, then you would definitely want to have a solid grounding in linear algebra.
 
  • #1,836
tgt
520
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i was out one year from undergrad. the bigger gap was from grad school. i went astray in 2nd or 3rd year, hung on until the fifth and took off for a 4 year job teaching.

then i went back and finished the phd in 3 more years, at 35. (does that sound old? it does sort of to me too for a grad student, but i wouldn't mind being 50 again now!)

What was your gpa at the end of your undergrad studies, just out of interest? So you got into grad school but decided to get out early to teach high school? If so, why did you decide to do that?
 
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  • #1,837
840
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Thank-you everyone for answering my questions. Your answers have been very helpful to me!
 
  • #1,838
mathwonk
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qspeechc, you have learned a valuable lesson: namely, if you appreciate what you are given, you will receive more.


as my former teacher said: "attention will get you teachers".
 
  • #1,839
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lets start a list of good free books.

"Algebraic Curves" by Fulton available free on the author's web site.

http://www.math.lsa.umich.edu/~wfulton/" [Broken]
 
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  • #1,840
mathwonk
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outstanding reference! grab this great intro to alg geom! it has been almost totally unavailable for years, and is just superb.

this teaches basic commutative algebra from scratch and uses it to prove the three fundamental results of curve theory: 1) bezout's theorem on degree of intersections of plane curves; 2) resolution of singularities of plane curves; 3) riemann roch for plane curves.


while reading this, i will give you a small impression of the atmosphere of the 60's by recalling that bill fulton taught the entire contents of this book in one week at brandeis, in about 1968.
 
  • #1,841
morphism
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I think that's going to be the text for the algebraic curves course I'm doing in the Winter. I'm glad to hear it's a good one!
 
  • #1,842
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What do you guys think about this linear algebra book:

ftp://joshua.smcvt.edu/pub/hefferon/book/book.pdf[/URL]
 
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  • #1,843
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Thanks for the link! I was actually going to post here asking for a good introductory text for getting into algebraic geometry. I've just started my postgrad to find out it's not being offered as a course this year. This is particularly annoying for me since one of the main reasons I chose to go elsewhere for my postgraduate studies was that algebraic geometry was offered (last year anyway!).
 
  • #1,844
thrill3rnit3
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mathwonk (or anyone)

Have you read this book called Geometry by Kiselev (Russian)? There's actually two books. My math teacher recommended them to me. Have you read that book, and if so, what do you think of it?

here's the link to the english translation version

http://www.sumizdat.org/
 
  • #1,845
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Hey everyone. I've got a bit of a question.

I think it would be accurate to call myself a jack of all trades. My quantitative skills are verbal skills are quite similar when compared on an intelligence test; however, in comparison to most other students at my college, my verbal skills far exceed most others, simply because it seems like they have had a serious lack of education in that area. So far, at my liberal arts school, where study in all fields is necessary, I have been able to receive A's across the board.

I am currently debating whether or not I would like to pursue a mathematics or physics major. My passion lies in these two fields, and I also love to write. Unfortunately, I question whether or not I am talented enough to pursue a science or math major and still perform well. I thought Calc I and II were jokes last year. My intro physics class this year is quite intuitive for me. I am also enrolled in Calc III and a discrete mathematics course this year. The later is a joke while the former is definitely challenging for me, as is it for the rest of the class. This is quite discouraging for me; I'm used to quickly grasping concepts. If my limit for quick understanding lies at such a basic level of math, I question whether or not I am fit to continue.


Granted, my school has this fun thing called grad deflation, the opposite of what most schools have. As a result, homework problems and tests are absurdly difficult. While this is good for me in the long run, it sure makes things tough now. hmm... might also be important to note that multivariable calculus used to be taught in two semesters and is now squeezed into one, resulting in quite a challenging class. Perhaps my ability's appear dampened to me simply because of the rigor of the course.

Next semester I am definitely taking linear algebra; however, in order to continue to take future math classes, I would need to take a course called principles of analysis, which is typically infamous for being the toughest course required of a math major. The kids who breeze through Calc III find it very difficulty. I question how I will fair.

While someone can always say I will just need to work a bit harder, I don't think this is too possible as this point. I have been blessed and cursed with a learning disability. Things take me a long time; however, I can complete many tasks others do not have the aptitude to complete. I already devote 30 hours or more to Calc III and week and see my professor multiple times as well. Because the college of the holy cross is a small school, we lack many of the resources of larger schools, meaning that tutors are scarce.

What do you guys think my options are? I love math. Should I sacrifice my perfectionist mentality and concede that I might not receive an A, or should I simply peruse something I enjoy slightly less - but still love - and perform well?
 
  • #1,847
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http://tutorial.math.lamar.edu/Classes/CalcIII/CalcIII.aspx

Is this the same information you're going over in your Calc III class? If it is, use it Paul's Online Notes is a great resource. You also might want to try studying a different way, if your current method seems inefficient.

Hah, funny you should post that. I discovered that site just the other week and absolutely loved the guys teaching style. It really helped with the quadratic surfaces; it was assumed I understood these from high school, but since I was placed in all low level classes there, I had never seen any of them before. It made identifying 3-d surfaces quite difficult to say the least.

I am using Stewart's Calc III book and, quite unfortunately, despite the teacher of that website's incredible skill for explain complex concepts, it in no way covers the depth or breadth of my book and class. If someone was brilliant and could solve any problem simply through the application of concepts, that site would be great for him. It's a bit more difficult for the rest of us.

Thank you for the site, though. I am sure I am going to use it more in the future.

By the way, concerning the previous post... I think I should mention that I really don't intend to actually use what I am majoring in. I simply enjoy learning. I will likely do something with personal development in my future, self-employing myself. I will probably make a website.
 
  • #1,848
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In math at some point everyone - I don't care who you are - hits a wall where your intuition/talent fails and you have to work hard.

If you are the sort of person who can look on this as a challenge and enjoy the fun of slowly figuring out the puzzle, then I would recommend math or physics for you.

On the other hand, if that sort of thing is not fun for you, then a lot of math and physics is just going to be a ton of pain so why put yourself through it?
 
  • #1,849
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I do love the puzzles. I really do. I can spend hours and hours on one problem. I enjoy it. I'm just not sure if there will be enough time in the day for me to learn it all. I have had to work hard at school since a very young age, partly because I like to master material and partly because work simply takes me longer because of my learning difficulties. I've been doing 80 hour weeks of homework and classes combined since I've been at school, and it's only supposed to get harder. That's what I'm worried about. I don't want to get in over my head and then learn that I can't graduate on time, which would distinct possibility if I were to drop a class now or in the future.

My parents actually said that they would be okay if it took my longer to graduate. They know I work as hard as I possibly can. I simply don't know if I would feel okay making them pay 90k for the extra year, though. Plus, all my friends would be leaving. it would be tough.

serious ethical dilemma and case of over thinking here.....
 
  • #1,850
659
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edit: nevermind you already answered my question
 
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