Other Should I Become a Mathematician?

[Tac-Tics]

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.

 

[morphism]

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.

 

[tgt]

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?

 

[qspeechc]

Thank-you everyone for answering my questions. Your answers have been very helpful to me!

 

[mathwonk]

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".

 

[CoCoA]

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/"

 

[mathwonk]

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. 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.

 

[morphism]

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!

 

[JG89]

What do you guys think about this linear algebra book:

ftp://joshua.smcvt.edu/pub/hefferon/book/book.pdf[/URL]

 

[Tom86]

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!).

 

[thrill3rnit3]

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/

 

[zoner7]

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?

 

[Feldoh]

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.

 

[zoner7]

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.

 

[maze]

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?

 

[zoner7]

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...

 

[maze]

edit: nevermind you already answered my question

 

[merjalaginven]

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?

Do what makes you happy- you only get older and life gets shorter-
I am a new mom with no time at all on my hands yet I manage.
If your parents money is the issue then apply for a student loan-
i am in debt bc of mine yet my world is still in equilibrium and everything is ok!
Linear algebra was fun when you think about it and not just memorize.
Calc 4 is the same way- and then you enter what you are talking about- advanced calc analysis in one or several variables- topology- abstract abgebra (my fav!)
These classes are MEANT to be challenging. Sometimes I would spend ten hours (while entertaining the little one lol) trying to figure out the puzzle of the proof- how to prove a sequence converges monotonically to----- lol whatever else-
and I too- have limited resources- our campus tutors are not qualified and I do not have a sitter to attend any extra study sessions- but-
I love it- so I pursue it-
Please do the same- do not be discouraged!
'Perfectionist mentality' - do you know what great minds in the past were farrrrr from perfect- they were DIFFERENT and PASSIONATE!
You will find words only get you so far- do what CHALLENGES your mind not what comes easy to it- good luck!

 

[merjalaginven]

i would say this definition is only a small step in a long chain of work going back to the greeks who showed the area of a circle was a number that could be neither less than nor greater than pi R^2 essentially by showing that is was a limit of quantities that differed from pi R^2 by less than any given amount (any epsilon).

so many many people for hundreds and thousands of years gave arguments essentially equivalent to what we have as the epsilon delta definition of limit. i.e. limits were well understood by the masters for a long time before they were stated in the form we have now, and their use of them is roughly equivalent to ours.

i would say the discovery of the method limits by the greeks stand far above the much later precise statement of that method. the statement came from analyzing the method, not the other way round.

Yes I concur :)
I hate the outlined epsilon - N notation- genius, yes- still I am amazed at things like the rhind papyrus (obviously not applying to limits)- so old, so simple (now--maybe :) )- yet so important- see even then they thought math was all the 'mysteries' and 'secrets' of life... ;)

 

[thrill3rnit3]

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/

nobody has read Kiselev's Geometry in here??

 

[mathwonk]

you can be first!

 

[thrill3rnit3]

yeah...I guess

i ordered both books from Amazon. The book also had pretty good reviews. I guess I'll give them a shot.

 

[matqkks]

There are various definitions for mathematics and mathematicians. For example:
Paul Erdos said mathematics is a machine which converts coffee into theorems and proofs.
Lord Kelvin talking to his engineering students at Cambridge asked the question 'whom do you call a mathematician'. Like most lectures he goes on to answer, 'A mathematician is a person who finds
int(exp(-x²))dx between the limits +infinity and -infinity is equal to square_root(pi)
as obvious as you find 2x2=4'.
Another definition for mathematics is 'science of patterns' and a mathematicians is someone who is a pattern searcher.
Remember Plato had written on one of his archways 'Let no man ignorant of geometry enter here'.
I am sure many of you have your own definitions.

 

[qspeechc]

I found this site with some free e-books.

http://www.math.uiuc.edu/~r-ash/

 

[Tom86]

Thanks for that. Looks like some good stuff there...I'm going to have a read through the Pari tutorial later.

This has probably been posted before but those more algebraicly inclined may find this link useful:
http://www.jmilne.org/math/index.html

 

[elfboy]

if you want to become proficient at math prepare to spend atleast two hours a day deriving stuff and exepect to become frustrated. It also helps to have mathematica but don't rely on it as a crutch.

 

[CoCoA]

I finished most of Fulton's book Algebraic curves and did about half of the exercises, except I did quite get his presentation of resolution of singularities. Any suggestions on materials for that?

 

[arshavin]

I am curious if other people have same issues, on desire to do maths. In my case, motivation to study fluctuates alot, on some days I have intense interest and can work for hours. Then there are times where i can't be bothered to do anything, even when i know the stuff is supposed to be interesting. I'm in undergrad, so this means my coursework is very inconsistent

 

[mathwonk]

coca you might try walker's book for resolution of singularities. or i could send some notes, or put them on my website.

 

[mathwonk]

the basic idea for resolving singularities, is to look at a curve that resembles the union of the x and y axes, hence has a "singularity" at the origin, because there are two "branches" passing through one point, and separate those two branches so they no longer intersect there.

Riemann just reached into the plane and lifted the two branches out and replaced the origin by two points, getting an abstract curve that did not cross itself.

more later