<p>I just finished my sophomore year at Columbia. </p>
<p>I got a B in calculus 4, and a B+ in linear algebra. Prior to this I had a 4.0 GPA, overall.</p>
<p>Are my chances at being admitted to a top institution for a PhD in mathematics (such as UChicago, NYU, Berkeley, etc) are lower/nonexistant because of these poor grades?</p>
<p>No, especially if you do better later in more advanced math classes.</p>
<p>This will not be a deal breaker at all assuming you’ll get good grades in upper level classes, especially at a school like columbia. </p>
<p>But I must say you might be slightly behind on your coursework for ‘top’ math phd programs if you took calculus 4 and linear algebra your sophomore year.</p>
<p>depends on the level of linear algebra I guess. There’s certainly a higher level linear algebra class useful for things like functional analysis.</p>
<p>I am slightly behind, because I changed my major. I was originally molecular biology and pre-med. I didn’t think it would be an issue, however…Is there something I can do (ie double up or take certain courses) to make up or attempt to make up for this?</p>
<p>Pocket, what do you mean by level of linear algebra? I took the basic, 2000-level class.</p>
<p>Some colleges offer two or three versions of linear algebra: the basic matrix arithmetic one for freshmen and sophomores, an abstract proof-based one for math majors, and maybe a computational/algorithmic one for students interested in scientific computing.</p>
<p>well. For instance, the study of infinitely dimensional matrices is considered higher level I think. Besides, linear algebra is not really just matrix algebra. Linear Algebra and its application to math and other fields in itself is quite a substantial subject. You can literally spend 2 years studying it.</p>
<p>If you changed your major then it is understandable. </p>
<p>If you want to catch up you should take real analysis, algebra, geometry/topology, etc, as soon as possible and apply of REU for next summer. And you’ll want to take at least a few grad classes your senior year. This is almost standard for top math phd programs.</p>
<p>You might honestly be better off doing a masters first and then doing a phd afterward.</p>
<p>Ah, alright. I took the course for math majors. It used a matrix-approach, but it was also proof-based.</p>
<p>I’m doing an REU this summer and took my first grad class this past semester (Graph Theory).
I’m taking analysis, combinatorics, and mathematical logic (graduate) in the fall. I plan to finish the analysis and algebra sequence while adding on a few more graduate courses every semester.</p>
<p>When you say masters, hfkjds, do you mean like a terminal masters? I have heard students who get masters are usually coming from non-US institutions; but, unless anyone can think of a reason why I should not pursue that track, it sounds like a good strategy, hfkjds. Thanks!</p>
<p>I looked at Columbia’s website and you didn’t tell whether or not you took the honors version of linear algebra or not? The standard one seems to be the course where you mainly compute with matrices. The honors version at least seemed to cover stuff like generalized eigenvectors, spectral theorems and canonical forms.</p>
<p>The only really important undergraduate classes are real/complex analysis, abstract algebra and topology. You need to understand these perfectly and I wouldn’t waste much time on classes like combinatorics unless you want to do research in that field. These are topics that you can self-study (which is really something you should do). Usually the top graduate programs want you to have seen some advanced mathematics in these core fields. Thus depending on what you want to focus on, I would suggest that you make a plan, so that you can take one of the core graduate sequences at Columbia. Aim to complete at least one of these and choose your courses with respect to the prerequisites of the sequence you want to take. In other words, try to take one of these:</p>
<p>Analysis I/II (MATH4151/4152)
Modern Geometry I/II (MATH4402/4403)
Algebraic Topology I/II (MATH4307/4308)
Algebraic Geometry and Number Theory (MATH4261 followed by 4262 or 4657)</p>
<p>If you take one of these, you will have seen the material of at least one of the core courses in your future grad program and if it is the field you are interested in, it will help it sink in much better. If you really ace these courses, then you can also place out of the corresponding sequence at your Ph.D. program.</p>
<p>These courses are hard (I know some people at Columbia), so you’re going to have to work like crazy. For figuring out the required prerequisites look at the following page:</p>
<p>[What</a> Graduate Students Are Assumed to Know](<a href=“http://www.math.columbia.edu/programs/main/graduate/gradknowledge.html]What”>http://www.math.columbia.edu/programs/main/graduate/gradknowledge.html)</p>
<p>If you know all that stuff, then you’re free to take the courses listed above.</p>
<p>EDIT: I don’t recommend going for a terminal masters. They are expensive and won’t help getting into a top program. People at top schools practically never have masters degrees which proves this point. You have plenty of time to show your potential and that is what matters in grad school admissions, not just whether or not you had math as a hobby since you were 5.</p>
<p>if you take analysis, combinatorics and mathematical logic(although I’d agree with eof that analysis/algebra/topology should be first) at the graduate level next semester and are doing an REU this summer then you are on track to go straight for a phd, your not as behind as I thought you were. </p>
<p>If you do finish the algebra/analysis sequence and take a few grad classes with a good gpa(3.9+), then I don’t see any reason a top tier school wouldn’t take you.</p>