What comes after Differential Equations?

[SuperDad]

My daughter just asked me this and I realized that I actually don't know. First she asked, "What comes after Algebra 2?" "Precalculus." "What comes after Precalculus?" "Calculus." "What comes after calculus?" "Well, you can do a lot of different things, like statistics and other things. And there are lots of different kinds of calculus too." "What comes after that?" "I think usually differential equations." "What about after that?" :confused: I really don't know. I don't mean about going "sideways", I mean in the standard linear progression.

I know that it's pretty much impossible to run out of math, but I always sort of stopped at Differential Equations and didn't think beyond that.

 

TIA.

[OLG]

Partial Differential Equations? Number Theory? Complex Analysis?

 

Mind you, I know nothing about these courses but have studied many a college curriculum page. My source for math descriptions has always been the EPGY course listing page if you want to check that out.

[cbollin]

good question...

 

ooh... now I'm all curious too. I'll have to ask my husband or find his college transcript. I remember he took AP Calc (BC level) in 11th grade. Then in 12th grade he had to ride his bike to the local university to take college sophomore level Differential Equations... and he did major in math as well as Chemistry... I can remember those stories. He took that class from the same prof who taught my stats class when I was a college sophomore. The prof use to talk about some geek kid from local high school who was taking his class in diff eq. oh well.... little did I know that one day.... :)

 

hmm.. what did he take as freshman in college and then. after. ? now you have me all curious and he's not here for me to ask... out buying new clothes for work or something... I don't think I have his undergrad transcript....

 

 

-crystal

[regentrude]

"Comes after" is not a suitable phrase, as it implies that there is a linear progression in math - it is only what the typical school/college math sequence suggests.

The closest it goes to a progression is Ordinary Differential Equations, then Partial Differential Equations, Nonlinear Differential Equations, Dynamical Systems (Chaos Theory), Complex Analysis, Field Theory.

 

It would also be possible to say that Topology comes after Geometry (OTOH, it is equally possible to say Topology is *before* geometry).

[Jane in NC]

Just a note that many students take a Linear Algebra course after finishing Differential Equations--not as a progression of the course material but as a general student of Mathematics. This could be followed by a basic Abstract Algebra course which leads to Group Theory, Ring Theory, etc.

 

I cannot tell you how many students seem to think that the Calculus sequence followed by Differential Equations is all there is to Math--as though nothing new has happened in the field in the last couple hundred years!

[AdventureMoms]

Well, in my school the progression depends on your major, lol.

 

For science majors it was:

Calc1 (differentiation), Calc2(integration), Calc3(multivariate), DiffEq, then Statistics, Probability, Linear Algebra and Advanced Calculus in any order

 

For Engineers it was:

Calc1, Calc2, DiffEq, Calc3, Statistics, Probability, Linear Algebra.

 

For business majors:

Statistics, Probability, then Calc

 

The reasoning behind the progressions is related to which math you need for your other classes. Engineers need Calc to understand Physics, business majors need Statistics to do their business classes. Engineers need DiffEq before Multivariate Calculus because of the engineering classes, scientists need Multivariate first because of the science classes.

 

In reality, once you''ve finished basic Calc (I & II) you can go in a lot of different directions. the DiffEq sequence (usually at least 2 courses), Statistics/Probability, Multivariable Calculus, Linear, etc.

[BarbaraL in OK]

It would also be possible to say that Topology comes after Geometry (OTOH, it is equally possible to say Topology is *before* geometry).

 

Hahaha! ... though I can't decide whether I think it's funny because I have studied too much math, or too little (and therefore don't know what I'm talking about) :blushing:

 

The last math class I took was complex analysis, during grad work in meteorology. A friend did the abstract algebra route, and that stuff was incredibly baffling to me. There's a LOT of mathematics.

[MyThreeSons]

and after DiffEQ, I took a course called something like Applied Engineering Math. That was the last required math class for my major, although I did take an Engineering Statistics class as an elective my last semester.

 

Before DiffEQ, I took two 4-unit semesters of Calculus.

[jennynd]

after ordinary DiffEQ, I took Partial differential equation than discrete math, . In graduate school, It was ODE, PDE, nonlinear algebra, numerical method.. engineering math.

 

I am Mechanical engineer

[Amy in TX]

I started out as a business major, and we took in our first 6 semesters:

 

Calc I

Calc II

Linear Algebra I

Linear Algebra II

Probability & Statistics I

Probability & Statistics II

[mumto2]

Integration--probably calculus part 2.

Edited May 27, 2012 by sawuk
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[Jane in NC]

Integration--probably calculus part 2.

 

While a couple of basic differential equations are introduced in a Calc I class, a full blown course of Differential Equations will follow Calc III for serious STEM types. Besides studying some classic DEs, students also learn about Fourier and Laplace Transforms, Bessel Functions, etc.. Integration Theory (Calc II) is a prerequisite for a Differential Equations course.

[kiana]

Mathematics has so many different areas, and many are accessible at different levels. For example, after the introductory calculus sequence, one could (at many universities) take linear algebra, discrete mathematics (a survey course), differential equations, statistics, or many other courses. Some of these courses do not require the machinery developed in the calculus courses, but rather a sufficient level of mathematical maturity, which is rarely seen in students who have not completed calculus.

 

There isn't a specific linear progression, as further courses will definitely depend on the student's major. As a matter of fact, at my undergraduate university it was possible to major in mathematics without ever taking differential equations, although most did -- some who were aiming at mathematics education or statistics did not. Furthermore, some students will take math courses without ever completing the calculus sequence -- for example, a student majoring in applied forms of computer science may take calc 1 and then discrete mathematics and then be done. A student majoring in nursing (at my university, anyway) will take college algebra, then introductory statistics, and then be done.

 

Here's an interesting survey of different areas of mathematics: http://www.math-atlas.org/welcome.html

 

There's a longer survey as well, this is the brief version.

[Jane in NC]

 

Here's an interesting survey of different areas of mathematics: http://www.math-atlas.org/welcome.html

 

There's a longer survey as well, this is the brief version.

 

Cool link! Thanks for posting this.