Affects of Double-Majoring in Undergrad if Student feels it is Highly Important

Graduate School
1

Hello everyone,
I will be studying Computer Science and/or Mathematics in UC Berkeley starting this fall. I want to pursue an academic career, so I will apply for PhD programs after these four years.

In this thread: http://talk.collegeconfidential.com/graduate-school/1770275-how-realistic-is-to-get-into-same-university-for-graduate-degree.html#latest @mathandcs (with a wonderful, and suitable nickname) suggested some things as it is a lot harder to get into a top grad school than to a top undergrad school. One of the related suggestions is “take hard classes.” And I believe that for me harder CS and math classes will compliment each other.

I researched a lot of double-majoring and understood that it does not give students any particular advantage. As it `may’ impact GPA and research opportunities negatively it can even be harmful for grad school applications. I bear this in my mind.

However, I can hardly see myself in the future without having a solid insight about mathematics or computer science, when I will be doing research in CS. I’m interested more in theorethical CS so topics such as discrete mathematics, type theory, computability theory, algorithmic complexity, lambda calculus etc… and I am at the moment considering to work in those field (I do know that this can change any moment during my four years).

For example https://csphd.sites.uchicago.edu/ here UChicago explains that they expect “more substantial mathematics background that includes advanced proof-based courses such as analysis, abstract algebra, probability and measure theory, logic, and topology.”

Another example: https://www.cs.princeton.edu/academics/ugradpgm/gsg#GREs Here Princeton says: “If you have a strong background in math it may be wise to take the Mathematics subject test, becuase graduate schools in CS love to see strength in math, particularly if you are interested in studying theory. Few, if any, CS graduate schools require this test, but if you happen to know the material, it’s worth a shot.”

But the most important thing for me as person is that I may regret, in the future, if I do not study mathematics or CS during my undergrad experience because I feel that they will compliment my intellectual experience. There is no CS minor in Berkeley (as far as I know) and I think being this much interested in math and its connections with CS, just a minor in Mathematics will not cut my passion towards it.

So my question: For an undergrad student interested in theorethical computer science that will apply for grad school, is double-majoring a good idea? Will I be somewhat disadvantaged because of this decision of mine?

2

Do your major in computer science and a math minor .
If you want to do two majors its going to take you longer than four years.
So can you afford that?
A math minor will qualify you to take the math subject test .
And for PhD programs you’ll have to choose which PhD program to apply to – computer science? Or math?

3

Check the catalog and see if a math minor includes all of the classes that Chicago suggests

4

Anyone can take the Math subject GRE, but a minor will give you pretty weak preparation, even if the 5th upper level class is chosen to be Topology. Half of the test is calculus/real analysis, and TAing calculus for a couple years will make success on that test much more attainable. Choosing to focus on CS and just doing a math minor will decrease your odds of doing well. You will be competing with students who have been living math for 3+ years on this exam – doing REUs, other research experience, taking every math class offered, half a dozen grad classes, TAing for 3 years, going to dozens of math talks, etc. That said, you could always take the Math GRE and if you don’t do well, just don’t report the score since it’s not required. Math grad school seems to be more competitive than CS, too, but I don’t have any numbers to back this up.

I would recommend starting out taking both Math and CS classes. By the time you get to classes like CS164/170 and Math104/113, it will become clear to you whether you like Math or CS better. At present, you probably know next to nothing about Math or CS. What you may know is some basic calculus and programming. If you can squeeze in a minor in the other subject, that’s great. If not, it’s not a big deal. It’s better to do one major and get a 3.8 than squeeze in two majors and get a 3.5.

You can always pick up a math book and read new stuff on your own. For example, I’ve bought several books on elliptic curves over the years. I’ve never taken a class on elliptic curves, algebraic geometry, or arithmetic geometry. The Math minor at UCB looks pretty good. What would you get out of a major but not the minor? Sure, you could take some interesting classes like algebraic topology or dynamical systems or something, but I find it highly unlikely a CS program wouldn’t admit you because you haven’t studied, say, measure theory or algebraic geometry. These are very difficult subjects that I’m sure have some applications to CS, but I find it hard to believe a computer scientist studying algorithms or FLAT would care about the existence of a non-measurable set. I suppose you might want to know some basic measure theory if you were using fourier analysis in your work, but that’s something you could learn once already in grad school.

I admire your ambition, but I’d recommend just figuring out which field you like more your first year or two, and focusing on that.

5

You also don’t have to specify a formal second major. You can major in CS and take as many classes in math as you want, without having to achieve a double major in it - so you can do more than a minor but less than a major, if that makes sense for your needs.

6

That’s a good point, although it looks like it’d only be an extra 3 classes for the major over the minor at UCB.

7

@menloparkmom

I don’t believe that’s the case. I already planned my schedule (I know that upper divs will vary, I just put MATH X, CS Y etc… for upper divs) And I can finish a double major in 4 years (with only 4 classes each semester, not even the upper limit), there is absolutely no reason to take a fifth year. And I can always enroll in summer session. Of course, these are provided that I don’t fail at some courses, but I’m not that stupid to continue a double major if I fail at some courses… If I see that I cannot manage a double major, I will just quit it.

@mathandcs and @juillet

Thank you for your long and elaborate response! As you said there is not much difference between a minor and a major, just a couple extra upper divs (and to be honest, there are some math upper divs I believe very crucial for CS, such as Cryptography, Metamathematics etc…) So if I complete a minor and take one or two upper divs that I want, what’s the point of not completing a major? Will it be harmful in my application that I have a double major? Does that alarm admission office that I may be an `intellectual dilettante’? Even if I explain myself correctly?

I honestly don’t think my problem is a simple “I like both math and CS”, as I explained myself, I am more interested in the intersection of these disciplines, and I won’t be satisfied with studying just only one of these. Don’t you think I can explain this well enough in my application essays, motivation letters that admission committee can get me?

Another thing is, yes I know that my interests, and motivations may, and will change. I know pretty much nothing about Math or CS (as you said only calculus and programming experience). But don’t you think that it doesn’t necessarily mean I cannot figure out what I like’ and what Idon’t like’ at the moment? If I end up hating math I can simply just not declare a double major (I’ll declare major in my sophomore year, everyone in Berkeley L&S are undeclared). I know all these “humans-are-not-static” arguments. But what if I don’t? What if I end up having same interests at today? I’m trying to plan for that so I won’t regret the classes I took in my senior year…

So about my first semester, Both CS and Math lower div prereqs are same (except Math has extra multivariable calculus). So, whether I will double-major, minor, or not won’t matter that much in my freshman and sophomore years. I’ll see what I like, don’t like in my sophomore year and declare according to them.

8

I honestly don’t see why you think a double major will hurt you. The double major won’t hurt you unless it means that you are so overextended in your classes that you don’t do well (as in, get a high GPA). But as long as your grades are good, double majors can have a neutral to positive effect in applying to graduate school. In your case - since your interests lie at the intersection of math and CS, and you’re interested in theoretical CS - I think it can actually be a positive, especially if you need to use advanced math in your scholarship.

So

Yes, I do think that you can quite easily explain this, and back it up by doing some work in undergrad that shows your interest in the two - like an independent study.

And of course, yes, you should plan ahead and follow your interests. We can’t predict the future, so honestly you have to do what you think is a good idea now and what you think will be the best combination. But that’s what @mathandcs is saying - take a few classes in each subject to begin with and see what shakes out.

9

I agree that courses like cryptography are interesting and lie at the intersection of math and CS. I myself took that class during college (as a math major) and it was one of my favorites. That class is very self-contained. All the number theory and algebra you need will be taught in that class. But most of the math classes, like real analysis, abstract algebra, and topology, will be useless to pretty much anyone doing CS. There’s just no chance a grad committee will be upset because you don’t know how to use the Sylow theorems to show that every group of order p^2q (p, q prime) is not simple, or how to prove the Dominated Convergence Theorem. If you need some area of math for your CS research, you will be able to pick up a book and learn whatever you need to know at that time.

For example, in calculus, you learn the extreme value theorem: a continuous function defined on a closed interval [a, b] attains a max and min (thus you check the endpoints and find the critical points for the interior of the domain). In multi-dimensional calculus, you learn the extreme value theorem also holds for domains like [a1, b1] x a2, b2. If you study real analysis or topology, you will learn that the EVT holds for a continuous function on any compact domain. You will also learn the Heine-Borel theorem: compact if and only if closed and bounded (which holds for certain classes of metric spaces, including R^n). Every mathematician knows this theorem, but no teacher will ever mention that the EVT is really a statement about continuous functions defined on compact subsets of R^n to CS students, or to anyone else taking a basic calculus sequence. All they will mention is what’s known as the “closed interval method.”

I realize some schools may be impressed by a strong Math Subject GRE score (I myself took the Math GRE for my CS applications, and I’m interested in theory, but I also had already majored in Math and had been to grad school for Math so the test was pretty basic for me with essentially no dedicated preparation for the exam), and you’ll need to know this stuff to do well on that test. But some of those schools’ pages are out of date (one of the ones you linked to also mentions the CS GRE, which was discontinued 2 years ago). More importantly, your time can be better spent focusing on research or programming projects.

Nobody on adcoms will have a problem with you doing a 2nd major, unless it brings your GPA down, or gets in the way of your research (which is a real possibility). But doing a Ph.D. is about focus, not about being a jack of all trades (and master of none).

Like I said, it’s great to have all these ideas about your future, but just go to UCB and start taking Math 1A/1B/53 (depending on how much Calculus you have from high school), Math55, and CS61A/B/C, make some friends, and have some fun in college. After your first year or two, it’ll be clear what you want to major in. Then focus on that. When I was in college, I met tons of freshmen every year who came in thinking they’d be some Math+CS+Physics triple major. Hearing this over and over again got old quickly. Pretty much every single one of them just majored in one subject.

Based on personal observation, most people who take Math and CS classes do well in one and really struggle in the other. Most math students will struggle in classes like Computer Organization and Operating Systems because they’re so low-level and almost like engineering classes (but they’ll do well in classes like algorithms). Most CS students will struggle in algebra, analysis, and topology because they really don’t appreciate pure math (but they’ll do well in classes like crypto, dynamical systems, probability, etc.). When I took complex analysis, there were tons of engineers who could do the calculus computations, but got stuck on things as simple as combining de Moivre’s formula with the binomial theorem. Heck, tons of CS students struggle mightily with calculus and can’t even get an A in Calculus II.

That said, my algorithms professor did have a bunch of algebraic topology books in his office, so there are some people who really like both areas. If you end up loving the calculus sequence and you go on to take algebra and analysis, and you do well in them and enjoy them, then that’s great. But just take your life one step at a time.

10

There is a CS minor:

http://www.eecs.berkeley.edu/csugrad/minor.shtml

It is also possible to double major without adding an additional semester or year. My son is completing a double major in CS and Statistics in 4 years. (But, I don’t know if a math major requires more classes than statistics.)

11

@juillet and @mathandcs
These are awesome replies that clarified a lot of questions on my head! Now, I feel better about my future and my future schedule. All I have to do is to take classes and see what I struggle at, like and dislike. So I can decide which one should I pursue later, possibly in sophomore year.

Thank you a lot, it is not really enough to only say you have been helpful!