1. I just thought I would ask this question because I wasn't quite sure what exactly are the classes that a student might progress though if they took every math class there is. This is from my perspective from an American student at my math level.

1) Elementry Math: numbers, adding, subtracting, multiplying, dividing, square roots, exponents.

2) Algebra 1: formulating Elementry math into equations, using equations to problem solve.

3) Geometry: learning how to graph equations on a 2 dimensional grid, learning of areas, volumes, surface areas, the pythagorean theorm, pi.

4) Algebra 2: further development of equations, quadratic equations

5) Trigonometry: Trig functions, Trig identities, further study of triangles and circles and the pythagorean theom.

6) Math Analysis: (I actually don't remember much of this class except that it was very tedious.)

7) Calculus 1: functions, limits, differentiation

8 ) Calculus 2: Integration

9) Multivariable Calculus: umm.. calculus with more than one independent variable?

10) ?  2.

3. There are a ton of classes associated with math analysis. Also some others I could think of: statistics and probability, linear algebra, differential equations. . . . .  4. The "math analysis" course that comes before calculus is often called precalculus. In my high school, this course basically made sure you understood the ins and outs of functions--namely: algebraic functions, trig functions, exponentials and logs, graphing functions, composing functions, that sort of thing.

After multivariable calculus, most people who continue in math move on to differential equations. Some schools even call this calculus 4. Most schools also offer some basic statistics and discrete mathematics courses at this level, but these are not typically required. The next class is linear algebra, although I think some people reverse the order of linear algebra and differential equations, as the former is useful in the latter. After that, things start to split off depending on what you're interested in.

If you're going an applied route, you might take numerical analysis for engineering, linear programming for operations research, discrete math for computer science, to name a few. If you're going into theoretical physics or probability, you're probably interested in taking some analysis courses (and, unlike high school analysis, which is precalculus, analysis here is postcalculus, or really, is the theory underlining calculus).

If you're going into pure math, you want algebra, real and complex analysis, and topology under your belt. Then things really start to become disjointed depending on what field of math you want to go into: algebra, analysis, topology, geometry, logic and set theory, number theory, discrete math, to name the real big areas. And each of these areas splits up into myriad subdisciplines, and they also commingle with each other: for example, algebra manifests itself in different disciplines as algebraic topology, algebraic geometry, and algebraic number theory.

Really, your list basically ends where math starts becoming nonlinear.  5. I once took a class in tensor analysis in college. I passed, but I'm still not sure what a tensor is.  6. Ahhh geez. Off the top of my head:

Before college:
Arithmetic
Pre-algebra
Algebra I
Geometry
Algebra II
Calculus (AP calc in HS)

College courses:
Calculus II
Calculus III
Bridge to higher mathematics (basically an intro to proofs and mathematical language)
Discrete mathematics
Combinatorics
Number Theory
Graph Theory
Intro to linear algebra
Linear Algebra
Game theory
Geometry and Spatial sense
Analysis I
Analysis II
Modern Algebra I
Modern Algebra II
Mathematical Statistics I
Mathematical Statistics II
Cryptography

I think I took a few more, but I can't remember.  7. I wish there was a game theory class I could have taken, but oh well. A couple class I didn't see mentioned so far are: complex analysis, abstract algebra and ... Err, there was something else I was going to mention, but it's slipped my mind now. :P  Bookmarks
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