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Courses Need advice on some math courses

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I will be a senior next year, graduating with a BS in Math. I want to go to graduate school. Unfortunately, my past few semesters were not the best. I wasn't the most motivated student.
Grades in math courses, in order, were:

Calc Sequence: A's

Diff Eq: A
Proofs (required): A

Linear Algebra: A
Combinatorics: B+

Abstract Algebra: C

Intro Analysis 1: C+
Complex Variables: B+

Intro Analysis 2: B+
Geometry:A

The C in Abstract Algebra and C+ in Analysis are really making my transcript look weak.

I have one year left, and I have narrowed down my options for the fall to the following:

Modern Analysis: undergrad and grad levels offered
Algebra 1: grad level
Topology: undergrad
Numerical Analysis: undergrad

What should I do to strengthen my application?

Option 1:
Modern Analysis: grad level
Toplogy
Numerical

Option 2:
Algebra 1: grad level
Modern Analysis: undergrad
Topology

Clearly, the second one would strengthen my application, but I run a greater risk of doing poorly, lowering my gpa, and forfeiting my chance of writing an honors research thesis with a professor, which in the end would just be embarrassing because I've already talked to my professor about it.

What would you do in this situation? I'm a better student now, and I'll be studying for the next two months. I'm thinking it might be worth the risk.

Any advice?
 

tmc

289
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I would go with option 2. With only 1 course in Algebra, and with a grade of C (which might as well be an F as far as grad schools are concerned), you should definitely learn more algebra, as well as prove to them that you're able to do algebra (unless, of course, you have no intention of going anywhere near algebra in grad school). That said, jumping from a single undergrad course in abstract algebra to grad level might be a bit harsh, depending on how the course is laid out, so you might have to start studying early for it. Undergrad analysis should be doable, and will also help show them that you're able to do analysis, such that they may forget about your earlier grades.
 
Hi. I got A's in my algebra courses for undergrad. We had multiple ones. But I took a C in the grad one. That and the C I got for grad topology are the only grades lower than a B on my transcript.

Here's my advice. Do an independent with an algebra type professor in algebra. Make it a part of your undergraduate thesis. That kills two birds with one stone and it shows you are big enought to face your weakness and do your best to stregthen them.

Don't toy with math grad classes unless you're ready. There is no shame in not being ready. There is shame in not trying to fix your weaknesses though.

I would take modern analysis too from your undergrad classes. Don't down play the difficulty in analysis. I assume it is going to be Measure theory or possibly Fourier Analysis. You need those. And if it's multi-dimensional analysis then you absolutely need that. All those will be assumed known when you get to grad school.
 
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You're going to need to do something spectacular to get into grad school. If you play it safe and get decent grads in the easy option, you won't get into grad school anyway. Might as well attempt to shoot the moon and ace all three courses in the difficult option.

If you can get an A in grad algebra or a great score on the GRE, it might look like you're gifted but lazy. Grad schools will take a chance on that. Otherwise, it just looks like you're an average student. They won't take a chance on that.
 
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I think it all depends on what type of school you want to go to.

I would say challenge yourself and don't shy away from it. Embrace it in fact. Because if you can't handle that workload, grad school is going to be even tougher. You have to remember in graduate school, at least for the first 2 years, you will be taking 3-4 homework intensive courses a semester. They want to see that you are able to handle the work. Get used to busting your ass or grad school really won't become a reality.
 

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