Please help...

[winterHLepsilon]

I have a friend here who is in high school, who is crazy about math and who wants to major in mathematics in college. She has already learned some of the college subjects but she wonders whether she has learned the right ones.

Would anybody who knows sometihng about college math curriculum kindly help her? She needs a detailed math curriculum (courses you must take if you are a math major in college) in time order. Many thanks to those who'd like to help. Thank you.
_________________
*HL--^H^e^L^en *
=A girl from Guangzhou, China, Asia=

Ask, and it shall be given you;
Seek, and ye shall find;
Knock, and it shall be opened unto you.

[Logain]

Not sure exactly what there is someone would need to know about the curriculum. I'm a Chem. Engr. but I was pretty familiar with a math major's schedule because I considered minoring in it...I never finished since I couldn't fit the the last two math electives in my course schedule since they had to be 4 credit courses rather than the 3 credits I always had room for.

Basically you have to take Calculus 1-4 as the main requirements the first two years, then the rest is up in the air because (also depending on the school) you basically pick and choose the math electives based on what you want to specialize in. Usually the required couses for Juniors and Seniors are some type of Geometry, and Modern/Linear Algebra courses. Except for Calc I-III, I don't think any order is really required...except upper level courses that are I and II also. Calc III and IV sometimes go by different names (ie, calc 4 = differential equations), and technically they don't require each other. I managed to take III and IV in the same semester.

[Mercuria]

it also depends on what schools you're talking about. i know virginia tech has two different math majors: calculatory and discrete (algebraic? i'm not sure which one's on the title), though that doesn't make too much of a difference in starting out...

what kind of math is she interested in?

[jadesmar]

There's a decent webpage here:
http://www.math.uwaterloo.ca/navigation/programsLists/UGPrograms.shtml

It's one of the few schools offering a B.Math as opposed to B.Sci in Mathematics.

[Lepton]

Waterloo is also the home of MAPLE, which is 100 times better than Mathematica.

At my school, a math major takes the following required courses (plus some math electives to fulfill academic calender requirements):

[winterHLepsilon]

Thanks for your info.
_________________
*HL--^H^e^L^en *
=A girl from Guangzhou, China, Asia=

Ask, and it shall be given you;
Seek, and ye shall find;
Knock, and it shall be opened unto you.

[kevinatilusa]

Here's what the situation is like at UCSD (descriptions of the courses are at http://www.math.ucsd.edu/resources/course_descriptions/undergraduate_courses.html :

In your first two years, students take a sequence covering everything from one variable calculus through multivariable, differential equations, and linear algebra (20A-20F). The same course is taken by physicists and other science majors, and students can place out of it if they've taken Calculus before and do well on a placement exam.

Towards the end of their second year, students take 'Mathematical Reasoning' (109), a course giving an introduction to the basics of writing proofs and making arguments rigorous.

Their third and fourth year, students take upper division math classes (About 2 per term). The students have a fairly flexible selection (any courses above 100), but their courseload must include

1 year of an "Algebra" course (100ABC or 102/103). Not much relation to High School Algebra I and II, the course consists of studying what happens when we have operations which share some, but not all of the properties of addition or multiplication. For example, what if we have a function which is associative (a+(b+c)=(a+b)+c), has an identity(0+a=a), and is invertible (a+(-a)=0), but may not be commutative (a+b may not equal b+a)?

1 year of an "Analysis" course. Depending on the course chosen, this can be anything from just a MUCH more rigorous look at calculus (142 AB) to a study on how concepts like a distance function and continuity can be adapted to more general systems than the real numbers (140ABC).

Around the third and fourth year students do start to spread out a bit more depending on what their future plans are (people going on to graduate school tend to take the more abstract courses when they have a choice, people going into industry often do the reverse).

If your friend thinks she may have had some of the stuff before (especially above calculus) she probably would want to take to the Professor of whichever course she thinks she's had before skipping it. I've had a couple instances where I knew 80% of the content of a course before taking it, but if I tried skipping the course the other 20% would cause huge problems in the next math class I tried to take.

[Antrax]

Bloody hell. If I'm understanding these links correctly, the stuff I'm studying as part of my CS degree here is second year material for math majors in the US. Have I mentioned how I hate the Technion lately?
Antrax
_________________
After years of disappointment with get rich quick schemes, I know I'm gonna get rich with this scheme. And quick!

[The Ragin' South Asian]

http://www.washington.edu/students/gencat/academic/mathematics.html

[kevinatilusa]

If it makes you feel any better, I had to take a few CS courses along the way to my math degree too (%$#% logic class). I think we were the exception rather than the rule though.

[extro...]

[Antrax]

Yeah, the duality exists here regarding those courses, as well as a few others (for example, the dreaded combinatorics, where in the CS version of the course there's more focus on graph theory and especially trees). My problem is with stuff like advanced calc 2 (I took it this semester) which is basically multiple-variable functions, vectors, surface integrals and other crap like that, which has absolutely no bearing on anything I will ever do, and yet is compulsory.
Antrax
_________________
After years of disappointment with get rich quick schemes, I know I'm gonna get rich with this scheme. And quick!

[Guest]

Combinatorics and graph theory - how could I forget those? I actually liked them quite a bit. Theorems about graphs, algorithms that work on graphs, proofs that they work, and their complexity - fun stuff. Traditional math courses would deal more with the just the graphs and less with algorithms that opearte on them.

[kevinatilusa]

In this case the logic course was rather heavily focused on the "mathematical" type of logic (first-order stuff, computability, turing machines, etc.).

[extropalopakettle]

So it was (what once was) a math course taught by the CS department. (I used to teach that course)

[Beartalon]

For my B.Sc in Math, the logic courses were taught in the Philosophy department. They were the two non-elective courses taught solely by a different department than math or computer studies.

[Mercuria]

antrax: don't blame it on technion. i was done with all the courses specified in lepton's post, minus the linear II and diff eq. II, by the end of my first year. required. in fact, i'd finished other courses, too.

most degrees will require many credits that you will never use in the future, and most tech-related degrees require lots of advanced math (which, of course, means you have to take the lesser maths as well)

school is a bureaucracy. annoying, but true.