How much math should I know to be fluent in math?

[Tuya]

I am a chem major in college and taking my first calc 1 course this semester-I am little late from my peers in learning math, I was bio major and did not have to take math that seriously before. So far I really like calculus and I don't have any trouble whatsoever in it. I am considering to take more advanced math courses after being done with all the calculus series, like Diff.Equation, linear algebra, statistics, etc.

I am wondering how much math one should know in science to be considered to have a strong background in math? One TA who does theoretical chem told me that more math I know, easier it will be in grad school chem, because most people's trouble tends to be a lack of math skills in science.

I am interested in having at least minor in physics, because I like quantum mech and want to do something like mixture of chem and physics. TAs and other people tell me that I need strong math skills and how much math is strong enough?

I saw there are abstract algebra and other courses like that, but do I really need that kind of abstract math? What other math courses or books, topics would you guys suggest to me beyond diff.eq and linear algebra?

I am done with all the humanities courses, so I have gaps in my schedule, which I plan to fill with extra math's. Then I need suggestions from people who know the facts of a real world.

Thank you.

 

[Jorriss]

If you want to have a solid foundation in math for the physical sciences, the absolute core are the following lower division courses:
1) Single and Multivariable calculus
2) Vector Calculus
3) Linear Algebra
4) Differential equations

That really is not a lot though and there is a lot more to know, other useful classes, in no particular order.
5) Complex Analysis
6) Probability Theory
7) Statistics
8) Partial Differential Equations
9) Mathematical Methods for physicists, chemist, engineers, whatever (Check Chemistry, physics, engineering and possibly math departments).
10) UD Linear Algebra

Classes to push your mathematical thinking but which are not directly useful to physical sciences (until deep in the game)
10) Real Analysis
11) Algebra
12) Topology

 

[thrill3rnit3]

group theory is particularly useful

 

[bpatrick]

I saw there are abstract algebra and other courses like that, but do I really need that kind of abstract math? What other math courses or books, topics would you guys suggest to me beyond diff.eq and linear algebra?

I'll chip in as well since I have a bit of a rounded science background. Most of it agrees very closely to the post by Jorriss ... so for a chemist, what I would consider a "solid math background" is:

calc 1-3
linear algebra**
differential equations
numerical analysis
prob/stats
mathematical methods*

*like Jorriss stated, math methods is typically offered by physics or engineering departments. Think of it as a cliff notes version of 5-6 upper level math courses containing only the applied bits you'll end up using in E&M + QM while leaving out all the theory you'd get during the actual math courses.

**If you really got into linear algebra and wanted to learn more, a good route is to next take an abstract algebra course that focuses on group theory, then start getting into graduate level topics in linear algebra.

Any more math than that and you're getting into the territory of being a mathematician since you'd have to start taking "pure math" in order to go much farther. Anything less than the bolded stuff in the above list and you probably wouldn't be that prepared for QM, upper level physical chemistry, nor grad level experimental stuff. The stuff that isn't bold is just what I'd recommend for building math/computer/statistics skills you might find useful in your career.

 

[Tuya]

Thank you.

So my plan looks like I will finish Calc 3, linear algebra, ordinary and partial diff.eq's. Those shouldn't be that much.
Plus, I plan to take Analysis 1, Statistics, and Complex Variables.

What is topology? Is it a fun class to take? Is it useful down the road in physics courses I plan to take? Topology sounds very interesting, I think I will like it, but still not sure.

Also, what is numerical analysis? It is even separate course. Do I need it?

Thank you all who reply.

 

[Robert1986]

There are also several applications of graph theory to chemistry, mostly modeling molecules as graphs.

 

[mathwonk]

well its a lot, so keep in mind that the basics are linear algebra and calculus.

 

[Tuya]

It is a lot, but I want to learn more math. Since I don't have any humanities courses to take, I want to improve myself on math ground. I changed my major into physics, because chem does not use much of math and I was not happy with that.

And I noticed I did not get perspective on topology course.

 

[Nano-Passion]

If you want to have a solid foundation in math for the physical sciences, the absolute core are the following lower division courses:
1) Single and Multivariable calculus
2) Vector Calculus
3) Linear Algebra
4) Differential equations

That really is not a lot though and there is a lot more to know, other useful classes, in no particular order.
5) Complex Analysis
6) Probability Theory
7) Statistics
8) Partial Differential Equations
9) Mathematical Methods for physicists, chemist, engineers, whatever (Check Chemistry, physics, engineering and possibly math departments).
10) UD Linear Algebra

Classes to push your mathematical thinking but which are not directly useful to physical sciences (until deep in the game)
10) Real Analysis
11) Algebra
12) Topology

What is UD linear algebra?

 

[Jorriss]

What is UD linear algebra?

Upper division.