Choose Wisely: Deciding Math Courses for a Math Major

[PhysicsHigh]

I see for math majors that there are A Lot of classes to choose from! How do you know what you want to take or should take? I guess it depends on what you are preparing for. Just how do you decide what math courses you are going to take because you can only take so much at school. Thanks, sorry for the bad question.

 

[Msh1]

I know there are usually lots of math courses but no matter what you like or which area of math you like to do research on, the following list of math courses will serve as a basis for all advanced work and I think any math major should take them.

1-two semesters in Single Variable Calculus
2-two semesters in Multivariable Calculus & Calculus on Manifolds
3-two semester in Linear Algebra
4-one semester in Ordinary Differential Equations
5-one semester in Topology (basic point-set topology, compactness, connectedness, metric spaces ... although most of these concepts should already be covered in you multivariable calculus course)
6-one or two semester in Abstract Algebra(Rings, Fields and Galois theory)
7-one semester in Partial Differential Equations
8-one semester in Real Analysis (This should not just be an advanced version of Calculus)
9-one semester in Complex Analysis

Now if you are sure you are really interested in mathematics and perhaps want to do research then you should not care what you like, take the courses I listed, you have nothing to lose and they are absolutely essential in all areas of math. If take them all then you will have a pretty good idea what other math courses you like and you can easily pick from the large pool of courses offered in you school.

 

[qspeechc]

Usually the department makes it clear to you which courses you need and usually when to take them by, so you should consult your mathematics department first. A slightly different list from Msh1's, in approximate order, is:

Three semester of calculus.
One semester of linear algebra.
Two semesters of real analysis.
Two semesters of algebra.
One semester of complex analysis.
One semester of general topology.
One semester of measure theory.
One semester of differential geometry.

As you see it may vary slightly from university to university, but the above would be roughly the minimum, I think, that every math undergrad is expected to know.

 

[Chaostamer]

As far as my school goes, there's Pure Math and Applied Math. There are also Computational Math, Mathematical Economics, and Mathematical Physics, but those are just Applied Math majors with classes thrown in from Computer Science, Economics, and Physics/Engineering, respectively.

Pure Math
Three semesters of Calculus (two single-variable, one multivariable/vector)
Two semesters of Linear Algebra (one applied, one proof-based)
One semester of ODEs
One semester of PDEs
One semester of Combinatorics or Graph Theory
One semester of Complex Variables (an applied Complex Analysis class)
Two semesters of Analysis
One semester of Abstract Algebra
One semester of Topology

Admittedly, my school doesn't have the most rigorous program around, despite our predominantly great professors. I plan to take Abstract Algebra II (which isn't required), a graduate Complex Analysis class (instead of Complex Variables), and a handful of other grad classes to better prepare myself for grad school. Seeing how much rigorous math other schools require, I want to be as prepared as possible.

Applied Math

Three semesters of Calculus (two single-variable, one multivariable/vector)
Two semesters of Linear Algebra (one applied, one proof-based)
One semester of ODEs
Two semester of PDEs
One semester of Vector Analysis
One semester of Complex Variables (an applied Complex Analysis class)
One semesters of Analysis
One semester of Numerical Methods
One semester of Mathematical Modeling

Our Applied program is such that our department doesn't recommend it unless one doesn't plan on math grad school. It seems that the only Applied majors who get into good grad schools are those who have taken several advanced grad applied classes and have some experience to their name as an undergrad.

 

[PhysicsHigh]

Wow thanks a lot. Do you get to take math courses that your interested in for fun? Math majors have a lot of courses to complete.

 

[Chaostamer]

Wow thanks a lot. Do you get to take math courses that your interested in for fun? Math majors have a lot of courses to complete.

Indeed, and I don't know about most programs, but the programs I know of also require two semesters of Physics and two of Computer Science--on top of other classes. As for fun math classes, I personally have room in each semester for a math elective (last semester I took a class in Theory of Computation and next semester, I'll be taking Graph Theory), but I also came in with all of my gen-eds complete from AP and I plan to stay an extra year. I guess it all depends on what you want to put into it.

 

[PhysicsHigh]

What is your guys gpa? Or is it difficult to keep a high gpa upon graduation?

 

[General_Sax]

Or is it difficult to keep a high gpa upon graduation?

ya think? ;p

 

[Msh1]

Wow thanks a lot. Do you get to take math courses that your interested in for fun? Math majors have a lot of courses to complete.

In my school we had room to choose a lot of math electives in the program, around 8 - 10 in the pure mathematics program. But I know that number can be even higher in some schools. As for fun math classes there are a lot of them and they are really interesting and tend to be easier than the courses required for the math majors. Some common "fun" math classes are Chaos Theory, Fractals & Dynamics, Logic, Theory of Computation(this is more in computer science), Graph Theory, Number Theory (The elementary number theory version).

What is your guys gpa? Or is it difficult to keep a high gpa upon graduation?

It differs but I would say the average GPA for math majors might be a little lower than other programs, but to me it was easier to do well in math courses simply because there is no projects, no team work and most importantly no LABS!. But seriously think about your decision about choosing math as a major. Don't listen to all the people saying "If you like it you should do it". money matters! So do it if you know you can do well enough to make a living for yourself.

 

[PhysicsHigh]

Oh cool thanks. Sounds like fun

 

[PhysicsHigh]

ya think? ;p

No I don't :(?

 

[chiro]

Wow thanks a lot. Do you get to take math courses that your interested in for fun? Math majors have a lot of courses to complete.

Math is one of those things where there are so many connections between the different perspectives and branches that its a good idea to dabble in a bit of everything.

I've heard that in universities in the states that you have to take 'breadth' subjects like say humanities subjects in a technical major. In australia we can take four math classes in undergrad years if we want per semester (standard full time load is 4 courses for most degrees here).

Not sure about the requirements over there but for my uni we have to take at least one class in every area (stats, applied, discrete/finite) along with the standard pure stream (calc I,II,III,IV, lin algebra, complex analysis) and then major or double major in a branch of math.

Getting exposure to what's all that's out there can't hurt and if you want to do math as a career I'd strongly recommend it.

 

[discrete*]

It's really interesting to see such a wide variety of program requirements. At my university to earn a BA in mathematics you need:

- Four semesters of Calculus (2 single variable, and 2 multivariable)
- One semester of Mathematical Thinking (this is -- for all intents and purposes -- a course on logic, set theory and proofs, with a bit of number theory thrown in)
- One semester of Linear Algebra
- Two semesters of Advanced Calculus (this is calculus from a proof-based perspective)
- One semester of Ordinary Differential Equations
- Two semesters of Theory of Functions of a Complex Variable
- Senior seminar
- Two semesters of Physics
- Two semesters of Computer Science (I don't know what these are as I transferred in with my CS credits, and needn't worry about them.)

For a BS I think two semesters of Real Analysis, and one semester of PDEs are required on top of the others that I listed.

As for the OPs original question.. Typically an undergrad math degree is designed to give everyone a stable base with which to build upon. I'm in a combined program, so the only time I get any freedom in choosing classes is when I'm registering for grad courses -- and even than, I'm restricted because the second year of my grad studies has to contain two semesters of Complex Analysis. The others, I can choose whatever I want.

 

[PhysicsHigh]

When learning so much math at the same time do you ever get mixed up with your classes and everything becomes one big blur?

 

[Chaostamer]

When learning so much math at the same time do you ever get mixed up with your classes and everything becomes one big blur?

It's never happened to me. I took four math classes this semester and I had no trouble keeping track of each one. In fact, when the subjects are similar, the overlapping material might make everything a bit easier and more interesting.

 

[discrete*]

When learning so much math at the same time do you ever get mixed up with your classes and everything becomes one big blur?

It's actually never happened to me, either. I will admit that it was a concern of mine before I started taking heavy course loads, but it never came to fruition. I think so many areas of mathematics are so diverse, not only in the material that they cover, but in concept, so in some cases there's a very real separation between courses. Other times, like if you take ODEs and Calc III at the same time, they often overlap nicely and it ends up being beneficial rather than detrimental.

 

[Chaostamer]

Linear Algebra also goes well with Calc III and ODEs, and from what I've been hearing, Analysis and Topology complement each other nicely. Another good combination is Combinatorics and Probability.

 

[PhysicsHigh]

I was looking at schools and at one they have only a math major and one of the specializations is computational math. It showed what you have to take and then it said you have to choose from this group and it was there was an introduction to chaos and a lab for it. Why would you take that? That is it on chaos so would it be for graduate school? There was also a couple classes for bio so I guess it would prepare you for mathematical biology so why the intro to chaos?

 

[discrete*]

I was looking at schools and at one they have only a math major and one of the specializations is computational math. It showed what you have to take and then it said you have to choose from this group and it was there was an introduction to chaos and a lab for it. Why would you take that? That is it on chaos so would it be for graduate school? There was also a couple classes for bio so I guess it would prepare you for mathematical biology so why the intro to chaos?

Possibly to prepare you for other applied fields like quantitative finance. I'm sure chaos theory has applications in the biomedical sciences as well, though I must admit it's just a hunch.

 

[eumyang]

For another perspective, here are the courses required for a math major at my undergrad school:

2 "Basic" Courses (200-level):
- Calculus I & II

4 "Intermediate" Courses (300-level):
- Calculus III
- Linear Algebra
- Discrete Methods
- Principles of Statistics

8 "Advanced" Courses (400-level):
- Analysis I (all math majors, regardless of concentration, have to take this)
- the rest depend on concentration

Cognates:
- 2 semesters of intro computer science
- General Biology I OR General Chemistry I OR General Physics I

I selected the "Pure Mathematics" concentration, and the requirements for the "advanced" courses were as follows:
- Analysis I & II
- Algebraic Structures I & II
- four other 400-level courses
Among the remaining four 400-level courses, I chose:
- Complex Varaibles
- ODE
- Numerical Analysis
- Number Theory

Notice that Topology is not on the list. My school didn't offer it, to my dismay. I would have loved to have taken it.

 

[Chaostamer]

As far as my school goes, there's Pure Math and Applied Math. There are also Computational Math, Mathematical Economics, and Mathematical Physics, but those are just Applied Math majors with classes thrown in from Computer Science, Economics, and Physics/Engineering, respectively.

Pure Math
Three semesters of Calculus (two single-variable, one multivariable/vector)
Two semesters of Linear Algebra (one applied, one proof-based)
One semester of ODEs
One semester of PDEs
One semester of Combinatorics or Graph Theory
One semester of Complex Variables (an applied Complex Analysis class)
Two semesters of Analysis
One semester of Abstract Algebra
One semester of Topology

Admittedly, my school doesn't have the most rigorous program around, despite our predominantly great professors. I plan to take Abstract Algebra II (which isn't required), a graduate Complex Analysis class (instead of Complex Variables), and a handful of other grad classes to better prepare myself for grad school. Seeing how much rigorous math other schools require, I want to be as prepared as possible.

Applied Math

Three semesters of Calculus (two single-variable, one multivariable/vector)
Two semesters of Linear Algebra (one applied, one proof-based)
One semester of ODEs
Two semester of PDEs
One semester of Vector Analysis
One semester of Complex Variables (an applied Complex Analysis class)
One semesters of Analysis
One semester of Numerical Methods
One semester of Mathematical Modeling

Our Applied program is such that our department doesn't recommend it unless one doesn't plan on math grad school. It seems that the only Applied majors who get into good grad schools are those who have taken several advanced grad applied classes and have some experience to their name as an undergrad.

Oops, I forgot to mention a couple other classes.

All tracks require two semesters of Statistical Theory (mostly probability theory with some mathematical statistics).

All tracks require a science elective (like Physics III, Chem II, or some higher-level Physics course).

All tracks require either one semester of Logic and Proof or one semester of Discrete Mathematics. Both of them serve as an introduction to higher-level, proof-based math and thus are prerequisites for all of the "big" classes.