Mathematics Majors?

[Lexxicos]

Hey guys. Some of you may have seen me around the forum from time to time. I've followed this board for quite a while, but I'm pretty quiet, and don't play any ITM instruments (Only GHB and Alto/Tenor Sax) - although I hope to remedy that in the next few years, hopefully living somewhere with an Uilleann Pipe Instructor nearby. Anyway, a quick introduction:

I am currently a senior in high school, and as of the beginning of second semester - I'm loving it. As for my plans next year, I am going to the University of Wisconsin-Madison, and living with my parents during at least a year or two at that time because of money issues, or the hope of not having money issues. Which, with that, brings me to my inquiry:

As of right now, my expected major is Mathematics going into Secondary Education, although lately I've been pondering doing a straight Math Major and tackling any education part on the side. I'm still unsure of how everything works. So, any of you who have taken upper echelon Math classes - Anything I should prepare myself for? Any subjects in particular or challenges you thought particularly, umm, challenging? And lastly, any advice? Honestly, I have no clue what to expect, and no clue what is going to jump out at me as hard to understand, seeing as I heard that Calc 2 was supposed to be incredibly abstract and esoteric, and being in it right now, I find it really no different in difficulty than, well, any math class.

So, any words anyone could take the time to say would be appreciated, even the "My God you're a masochist, aren't you?" ones.

Cheers -
Lexxicos

[Jack]

My academic advisor told me "Math majors always have a job, somewhere, waiting for them," and I believe she was serious.

[beowulf573]

Sadly my higher math skills have atrophied due to lack of use, however there was a day where solving differential equations was a fun way to spend the afternoon.

Go with what you enjoy. If Math is your thing go for it. I would suggest not sticking to just the degree plan but instead take advantage of your time at college to take other classes, even if this means going a big longer. I've actually used stuff that I learned in a linguistics class years later. If pure math seems a bit boring after a while, check out the Physics, Comp Sci, or Engineering programs, they can be math intensive too.

Don't feel you need to stay with the program you start with. Once you start a whole world of opportunities will open up. I never occurred to me in high school to major in Engineering, but I'm glad I switched to it.

[Lexxicos]

Yeah, that's what I plan to do. I enjoy Philosophy - alot, so I've resolved to take a lot of Philosophy classes as my humanities credits. I also enjoy Physics, probably because of the intensive math and philosophy behind it, and I intend to take the Physics AP test for some credit and take mostly that for Science credit. I can't stand chemistry. Trust me, I don't think I could stand straight math for however many years. Ugh... there's only so much you can take, as with any subject. Like Spanish, after this year - no more. Norwegian is where I'm headed.

[BigDavy]

Hi Lexxicos

You are a Masochist

Well you did say to call you one.

In my dim and distant Maths/Physics degree past, I liked Group Theory, Mathematical Logic, Non Euclidean Geometry and Computational Maths. Sample as many maths topics as you can, you will likely find some to your taste.

David

[MarcusR]

Hi Lexxicos!

The good thing with math is that it can be handy for a lot of things; you don’t really need to decide where you'll end up. I started out with two years of mathematics, passed through topology but realized half way through “theory of numbers" that I lacked the skills to become a mathematician. Switched to physics (a lot easier as approximations are valid enough and you don’t need to prove your assumptions ) and did astro physics for a semester before I ended up with a major in nuclear and radiation physics. Now I work in between the fields of physics, medicine and biomedical engineering.

Even if you end up with computers, economics, medicine, chemistry, biology... or even law. You will benefit from a year or two of math. Give it a try if you like it

Only advice I can give is to be prepared to spend a lot of time doing exercises on your own. In the math, the book is thin and the lectures are few, in the beginning it will feel like you have a lot of spare time, but you don’t. At least if you're not one of those with the gift

Good luck!

MarcusR

[fyffer]

Hi Lexxicos -
You're on the same path I was on -- about 22 years ago!
I actually did get my Bachelor's degree in Math, with a Secondary Ed certificate, with the intention of teaching HS math.

The end of the story: I don't teach HS math; I'm a computer programmer for a software company in the Northeast US. But don't let that discourage you. Seriously -- I loved all things math, and still do. I couldn't get enough. My suggestion though, is to throw some Computer Science in there, and get a double major if you can hack it. If you have any interest at all in programming, it could only help you land a job. And if you are *really* good at the whole math thing, only teach if it's really what you want to do and are passionate about, because honestly, if you want to make a million, you won't do it teaching. But also, don't do something *just* to make a million - make sure you love it, too.

And don't forget to leave some time for the music. I actually started out as a music major (on Sax!), with the intent of getting into recording technology, but it was turning out to be a tech degree rather than being more math-oriented, so I lost interest (Oh yeah, and I partied a bit too much, too).

There's another girl on the board who is also a math dork -- I think her name is fluti31415 (get it? fluti-pi )

(.. Major Geek warning ..)
As for courses, I loved Discrete Math and Number Theory. I actually took a stab (though a feeble attempt) at solving one of the still unsolved conjectures in the math world. Ask me about it if you're really curious. I think I was on the right track, but I no longer have the skills to complete the task.

[chas]

I'm largely in the same boat as Marcus. Started college out deciding among physics, math, and chemistry as majors, leaning toward physics. One semester pretty much cinched the physics part, and, since I needed 8 courses in math for a physics major and 11 for a math major, I wound up doubling in physics and math. I did graduate school in physics; like Marcus, I'm doing something not exactly physics, but in my case it's kind of optical/mechanical engineering. I don't necessarily apply the specific subject matter on a daily basis, but I do use a lot of the techniques.

Only advice I can give is to be prepared to spend a lot of time doing exercises on your own. In the math, the book is thin and the lectures are few, in the beginning it will feel like you have a lot of spare time, but you don’t. At least if you're not one of those with the gift

That was a big difference between physics and math at my college -- in physics they encouraged collaboration on everything but exams. In math there wasn't nearly as much interaction among the students, although I shouldn't be one to judge. The Math department kind of hated the interlopers who were really physics students.

This was all years ago. I can give you a current example. One of my nephews is engaged to a young lady who majored in math and minored in economics. That's a VERY marketable combination. She's working for one of the big investment firms and doing very well. Other good secondary concentrations would be accounting, statistics (at UW/Madison probably available from at least two or three different schools), physics, chem, bio, etc.

One thing I'd like to say, and others have said it is, you're young. Don't lock yourself into anything. I always wanted to teach, and it wasn't till I was in my 30's that I came to the conclusion that I wasn't going to. And I'm REALLY glad I'm not teaching. Go to college to learn; learn what you want to learn. Madison is a great place, embrace the university, explore, enjoy, find your niche, don't worry about making yourself marketable.

[cowtime]

Although I'm math ignorant, my eldest daughter loves math. Started out at Va Tech with the idea of chemistry, then decided she really wanted to do math, but didn't want to teach. She talked to an advisor and said" I love math, what can I take in that field so I'll be able to get a good job when I graduate? She ended up with a degree in geophysics. The math she took for that has enabled her to sit for her engineering license because she took so much engineering math. So, it worked out well, since she's working as an engineer and really loves it.

[Lexxicos]

I hope I don't have to worry about learning anything just to make myself marketable. I actually pondered a Philosophy degree rather seriously before arriving at a somewhat more solid yet still tentative decision of Math. Philosophy still floats my boat, but I see it now as more of a side interest - like candy for the mind - than a possible mindset I could be in all hours of the day. Thinking about Kant and Spinoza for a couple of hours and discussing is fun, but writing papers and presenting arguments in whence your beliefs and self-esteem are wrapped up in a not-so-rigorous package where others are free to criticize and destroy your already somewhat faltering self-image sounds more masochistic than I want to be.

Longwinded run-on sentence rants aside - I am currently in the decision of math because:

1.) Ever since I took Calculus AB and got my first taste of "real" math, I realized that it involved all the Philosophy, juicy little mind-nuggets, wonder, and beauty I would ever need. It was then that I realized that me getting 97%-101% in every Math class I had ever taken may actually be of use, since now I may find real enjoyment to go along with a possible inkling of what-may-be some infinitesimal bit of talent. I was very careful not to overstate that.

2.) I hate writing reports. I love history, I love the humanities in general, but I could never seriously pursue it for a degree. The amount and type of work required would disagree with the amount and type of work I wish to do for humanities. Again, more like a hobby than a discipline.

3.) I hate experiments/labs. I can't explain it, but sitting down in front of a contraption, row of test tubes, or microscope and writing down observations and decimal approximations if phenomena to later infer possible statistical correlation just never sat well with me. It isn't "for sure". It isn't the purity that I want.

So, I don't know what I'm trying to say or who I'm trying to convince (in all likelyhood it's myself), but I have learned in this, my last year, that I would much rather, and tend to be more motivated, if you ask me to prove this:

infinity
_____
..\
...\ ..(-1)^(n-1)
.../ __________ = The Integral Of[x^x] From[0] To[Infinity]
../ .......n^n
-------
n=0

Assuming 0^0 is taken as equal to 1, rather than undefined.

(Forgive my horrible attempt at notation)

Rather than ask me to write a paper investigating how the ideas of John Locke have influenced American Government.

Oh, and as a last bit, I realize my decision will most likely change, but right now I just felt the need to admit all this.

So, this was a longwinded post, as it was more for my benefit that anyone else's boredom, but I apologize if I come off as

a) A jackass
b) A hopeless nerd
c) Someone with a negative self-image
d) A closed-minded jackass
e) All of the above

But hey, at least I'm not that guy.

[Flyingcursor]

You forgot

f) None of the above.

I was a CS major with a math minor. My favorite math classes were statistics, math/logic class. I learned enough Calc to get a decent grade and promptly forgot it. I had had very little high school math so I ended up having to start of at the lowest rung of the math ladder which extended my studenthood by a year.

One mistake I made was taking my one required electrical engineering class before taking the math/logic class. The latter would have helped immensly.

[mrosenlof]

I was a math major, but my wife is more of a mathematician than I am. She has a PhD in Atmospheric Science (basically mathematics applied to fluid physics). I do embedded software. I've known a few very good software engineers who were math majors.

There are a ton of things you can do with good mathematical ability. A lot of them are interesting, and most pay reasonably well. Others in this thread have listed several.

You say you don't like writing reports... There is a lot of value in being able to write well. If you follow a research path, you will be writing papers, they will define your academic standing in many ways. In the commercial world, you will still be asked to be a writer on occasion sometimes a lot. Even if you have great ideas, you need to express them well for others to understand them.

[Lexxicos]

Oh, I'm fine with reports for communications and ideas purposes, but the Thesis, support, support, support, conclusion model is, well, it steals a bit of my zest for life with every word I write. I can write one well, I just don'tlike doing them much.

[Caj]

So, any of you who have taken upper echelon Math classes - Anything I should prepare myself for?

Yes. Expect the numbers to vanish sometime around your junior year.

There's the mathematics everyone else knows about, the stuff that engineers use: calc and diffEQ and linear algebra. Then there is our own private stash of subjects you only get by majoring in mathematics, and that stuff is really abstract and profound. Once you reach that level you spend less time working with actual numbers and more time studying abstract truths about abstract things. As you say, it's like philosophy (except with more Greek letters.)

Keep that in mind if you're seeking advice from non-math-majors: the subjects you study within the major are completely different from the subjects offered as service courses to other majors. Engineers will not see what's so profound about studying mathematics by itself, because what they know of mathematics is all the concrete stuff useful for problem-solving. It's a bit like someone guessing what an English major does by extrapolating from all the English classes they had to take.

Anyways, if you like it, go for it. Be a mathematician, it's awesome in all but a finite number of instances. I offer one piece of advice: I started with a double major in mathematics and CS and then went to graduate school in mathematics, because I felt there was a lot I still needed to learn. I noticed that having that degree in CS was very useful because I never spent a minute worrying about future employment, and was completely free to take classes in anything I wanted regardless of applicability. And pure mathematics is all about disdain for applicability. The discovery of modern cryptography was a bit of a spiritual crisis when we realized that number theory could be ... used for something.

I eventually left mathematics, but those years were some of the best times of my life, the most fun I had in school, and I learned a lot that I use as an EE professor almost every day.

Caj

[Innocent Bystander]

I did Architecture. I wish I had done Maths. My Brother-in-Law did Maths - he works for a telecomms company and earns at least twice what I do. But it's not the money I envy him: it's the Maths.

Once, as a programmer, I was helping one of my clients (the acting IT Manager in a Housing Association) who was having trouble doing her day-release course: a Diploma in Maths. "I just can't see the point of it," she complained.

What I said to her, in an attempt to convince her of its worth, bears repetition.
"There is NO human activity that mathematics cannot advance and improve."