Planning for graduate school in mathematics

[DeadOriginal]

Its been a long ride. 4 years ago when I started college, I started as a finance major. I excelled in all of my classes but found the material to be a little boring so I changed to economics. I continued to get stellar grades and even now have nothing but A's in all of my economics courses. I have finished the core microeconomics Phd sequence at my university (think big ten) with A's. Simultaneously, I majored in mathematics, but my grades in my mathematics classes are less than stellar. I have a B+ average in my math classes (they are all honors classes). My cumulative GPA stands at approximately 3.5.

I have considered going to graduate school for economics but I really don't want to. I enjoy mathematics much more than I do economics. By Christmas time this year, I expect to have my honors thesis completed for mathematics. There is also a very high possibility of a publishable result. I can either graduate then or take one more year.

Is it still possible for me to go to graduate school in mathematics with my not so great mathematics grades? I am not aiming for a top ten or anything. I'd be happy going to a large state school. Say this is the route I want to take. What can I do to make my application stronger?

 

[Vanadium 50]

Did you take a comparable curriculum to math majors going on to grad school? This is substantially more rigorous than for math majors that don't.

 

[DeadOriginal]

My curriculum was heavy proofs from the very beginning.

My honors analysis class used Spivak. I also took a masters level analysis class that used baby Rudin. My abstract algebra class used Dummit and Foote. My other classes which include linear algebra, differential equations, number theory (Hardy and Wright), combinatorics, probability and differential geometry (Docarmo) used texts that were all considered classics and at a comparable level as the texts used in my analysis and algebra classes.

One of my professors who taught at UChicago said the honors curriculum at my school is based off of UChicago's honors math curriculum although admittedly, some of the classes are not as difficult as those taught at UChicago.

 

[micromass]

My curriculum was heavy proofs from the very beginning.

My honors analysis class used Spivak. I also took a masters level analysis class that used baby Rudin. My abstract algebra class used Dummit and Foote. My other classes which include linear algebra, differential equations, number theory (Hardy and Wright), combinatorics, probability and differential geometry (Docarmo) used texts that were all considered classics and at a comparable level as the texts used in my analysis and algebra classes.

One of my professors who taught at UChicago said the honors curriculum at my school is based off of UChicago's honors math curriculum although admittedly, some of the classes are not as difficult as those taught at UChicago.

Spivak for honors analysis and baby Rudin for masters analysis is not a very high level. Especially the Rudin choice, I don't see the point of doing stuff of baby Rudin for a grad class.

While you have done some significant amount of math classes, you also have some significant gaps. For example, you have nothing on advanced analysis like complex analysis, functional analysis, measure theory, topology. These are some serious gaps.

Dummit and Foote for abstract algebra is decent. But you probably didn't do the entire book. So you might have significant gap there too.

Do Carmo for differential geometry is excellent, but it's only curves and surfaces. Modern differential geometry requires the use of manifolds and hence of topology.

So I would say that you know the basics of pure math, but that you probably don't know any advanced (undergrad) mathematics. I don't know how this will reflect on your chances for grad school.

Of course, I will not be a member of the committee that judges your application, so I don't know how they will think. But I would advice you to take another year at your uni and to take some advanced math classes and maybe to improve your GPA.

 

[DeadOriginal]

Spivak for honors analysis and baby Rudin for masters analysis is not a very high level. Especially the Rudin choice, I don't see the point of doing stuff of baby Rudin for a grad class.

While you have done some significant amount of math classes, you also have some significant gaps. For example, you have nothing on advanced analysis like complex analysis, functional analysis, measure theory, topology. These are some serious gaps.

Dummit and Foote for abstract algebra is decent. But you probably didn't do the entire book. So you might have significant gap there too.

Do Carmo for differential geometry is excellent, but it's only curves and surfaces. Modern differential geometry requires the use of manifolds and hence of topology.

So I would say that you know the basics of pure math, but that you probably don't know any advanced (undergrad) mathematics. I don't know how this will reflect on your chances for grad school.

Of course, I will not be a member of the committee that judges your application, so I don't know how they will think. But I would advice you to take another year at your uni and to take some advanced math classes and maybe to improve your GPA.

Thank you for your input.

I totally forgot about complex analysis. I have also taken that class using Palka's Intro to Complex Function Theory. At my university, these are the "most advanced" undergraduate courses.

The algebra class was two-semesters long but as you have already noted, my class only made it through approximately two thirds of the text.

Surprisingly there is no undergraduate topology course. The next level would be PhD algebra and Phd analysis using Lang's Algebra and Folland's Real Analysis.

 

[micromass]

Thank you for your input.

I totally forgot about complex analysis. I have also taken that class using Palka's Intro to Complex Function Theory. At my university, these are the "most advanced" undergraduate courses.

The algebra class was two-semesters long but as you have already noted, my class only made it through approximately two thirds of the text.

Two thirds is actually quite reasonable. I would say you have a decent knowledge of abstract algebra then.

Surprisingly there is no undergraduate topology course. The next level would be PhD algebra and Phd analysis using Lang's Algebra and Folland's Real Analysis.

Hmm, I think that if you can take those classes and pass them with reasonable grades, then you would be better prepared for grad school.