Caltech's math

Colleges and Universities A-Z California Institute of Technology
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<p>I've been accepted to Caltech as a transfer student and am interested in majoring in mathematics. There are a few questions I wanted to ask and I was wondering if someone could give some perspectives about the Caltech math program. </p>

<p>How difficult is it to get an A in a math course? Are the professors approachable? Are the TAs available and helpful? Furthermore, on working on a problem set (esp. in math), do the students at Caltech used to work together or do they mainly work alone? </p>

<p>One of my biggest considerations of moving to Caltech is its SURF program. But I don’t really have an idea how it works for a math student. Can students be involved in a math SURF even if they don’t have any research experience a priori?</p>

<p>I really appreciate it if someone could give me some opinions regarding these matters.</p>

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<p>Math classes tend to give out more 'A's than those in almost any other field, and the math major is pretty loose in requirements as compared to, say, physics or any engineering major. I have also heard that math majors have the highest average GPAs. On the other hand, the people who tend to major in math here tend to be really good at math, so it's very difficult to compare. Without knowing anything about your background, it's impossible to know if getting 'A's will be relatively easy for you, or if you'll struggle just to pass your classes. </p>

<p>What kind of experience do you have with proofs and what math classes have you already taken? If you've just taken the more practical "for scientists and engineers" math classes in calculus, linear algebra, multivariable calc, and differential equations at another university you're going to have a hard time when all of the other math majors have taken all of these courses in an analytic, purely proof-based context. If you're transferring from a community college, you may not have even had the option to, say, take calculus and linear algebra at the level of Apostol. It's worth noting that if you find that you like applied mathematics more than pure mathematics, we do offer a major in that.</p>

<p>I'm not sure what classes you'll be able to skip here -- you might be able to keep the credit for some of the courses you've taken elsewhere, and you might have to take exams to show that you know the material at the level it's taught at here. You'll probably be entering at the sophomore level, depending on how advanced the courses you've taken are. Also of note: How many science classes have you taken? You will have to complete Caltech's core science requirements if you haven't taken the equivalents somewhere else.</p>

<p>A typical sophomore math major schedule will look like:
Physics 2 or 12 (Waves, Quantum Mechanics, Statistical Mechanics)
Math 2 (Differential equations, Probability and Statistics)
Math 5 (Abstract Algebra)
An elective like Ma/CS 6 (Discrete Mathematics)
Some humanities and social science classes (one a term on average)</p>

<p>If you don't have a lot of experience with proofs, Ma 5 will be tough, but Ma 2 will probably be fine. The math option also requires graduate-level classes such as Ma 108 (classical analysis) and Ma 109 (geometry and topology), which you will probably find difficult regardless of background. On the plus side, the median grades in these classes tend to be 'A-'s, which is pretty generous. If you're interested in applying to top PhD programs in pure mathematics, you are going to need at least an A- average. If you're interested in applying to grad schools in other related fields (perhaps CS or biophysics), your GPA can be lower, particularly if you have research. If you're planning on getting a job right out of undergrad (which will obviously not be in pure mathematics), your GPA will be less important.</p>

<p>As for research, it's pretty easy to get a SURF in any field. You do not need to have any research experience to get one. If you are interested in more applied or computational mathematics, there are usually a ton of SURF announcements of opportunities in fields combining math and CS, geophysics, chemistry, astrophysics, etc. If you want to do research in pure mathematics, it might be better for you to just contact professors whose research looks interesting, even if you haven't taken a class with them. They'll help you come up with a research topic that is appropriate to your background. As long as you get started on finding a SURF mentor early, do all of the appropriate background readings, and don't procrastinate on writing your proposal, it will be very easy for you to get a SURF.</p>

<p>Most professors here seem to like undergrads, and plenty strongly encourage you to go to their office hours. I can't think of a class that I've taken where the professor didn't have office hours (in math or any other field), so that's always a good way to approach them. I've had good TAs and bad TAs, though I have to say that most were pretty good. If you have a bad TA, you can always switch sections to one you prefer. Every TA I've ever had tried to be helpful, though a few are just bad at teaching. Like at most major universities, some of the TAs here don't speak English as a first language, but I've never been taught by a TA who was less than fluent. If you're not used to certain accents, you can always just switch sections. Your non-core classes will generally be small enough that you will only be taught by the professor for the class.</p>

<p>Collaboration on problem sets is very strongly encouraged and very widespread here. I'm pretty sure I've never done a problem set in math or physics where I didn't at the very least discuss how to do a problem with someone. The problem sets tend to be difficult enough where, for most students, you need to collaborate, and I think this is a good thing. For most of my sets, I just work with a group of people until everyone is done. There will be some problems that everyone can solve on their own, and there will be some problems that will take hours and hours for even one person to get a good idea of how to do. Often, even if no one can figure out a problem individually, sharing ideas on approaches can cause a group of people to solve it together. </p>

<p>Even as a transfer student, you're going to have to go through Rotation like all of the freshmen and be put in an undergraduate House (regardless of whether you actually live there or off-campus.) This means that by the end of the first week of school, you'll have 60-120 instant friends, not including the other people in your classes or that you meet during rotation. Some of these will be math majors, and if you're taking core classes, many of them will be in those. This is the easiest way to find people to collaborate with. In your smaller classes, you'll probably know the other students in the class well enough where you'll work with them. This is a great way to get to know people from other Houses.</p>

<p>I'm a physics major, so while I'm in the same division as math and am pretty familiar with all of the major undergraduate math courses, I can't tell you too much in detail about the math research going on or the graduate-level classes. There are several math majors that read this forum that can add more or correct me.</p>

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<p>First of all, thank you so much! Your post is very helpful to me.</p>

<p>I am actually transferring from a 4 years U.S. institution. I have taken quite a few proof-based math-classes, like advanced linear algebra, intro. to number theory, intro. to graph theory, intro. to real analysis (where we used baby Rudin and Gaughan), probability and combinatorics. So, I’m pretty comfortable with the proof-based math. I just feel a bit intimidated, since many people told me that Caltech’s math is more suitable for grad students. </p>

<p>“On the plus side, the median grades in these classes tend to be 'A-'s, which is pretty generous.” </p>

<p>Does that mean that the average problem set grades, midterms, and finals are around 90% or do the grades get adjusted by a curve system? </p>

<p>As for the science classes, I have taken quite a few of physics courses (I was a physics major too (yay for physics!) before switching to math!). The physics I have covered are including:
Newtonian mechanics and Relativity (where we used Keppler & Kolenkow and Halliday, Resnick, & Krane)
Statistical Physics, Thermodynamics (we used Tippler for these two) & Waves (Halliday Resnick, & Krane)
Electromagnetism (Purcell & Halliday Resnick again)</p>

<p>I am also currently taking Quantum Mechanics where we follow Ohanian. </p>

<p>Do you know whom could I contact to ask if I can skip all these classes? One last thing, do you think the admission office can set me up with a math student at Caltech? </p>

<p>Again, thank you very much for your help and (very thorough) reply!</p>

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<p>It sounds like you are very well prepared for the math classes here. If you covered everything in Purcell, you wouldn't learn much in Ph 1. I'm not too sure what your waves, quantum, and statistical physics books cover compared to Ph 2 (French + Phillips + Kittel and Kroemer,) but if they're approximately the same (or your courses covered more) you'll be done with the minimum requirements for physics core. Assuming you took differential equations and multivariable calculus in addition to the math classes you mentioned, you wont have to take any math core classes (Ma 1 and Ma 2) either. You probably haven't taken any chemistry past the standard intro college chemistry, so you're going to have to take Ch 1 (two terms: fall and winter) and Bi 1 (one term: spring.) These aren't too painful, I swear, unless you haven't taken chemistry since high school. You'll also have to do the other core classes that they don't let people pass out of: Ch 3a (chemistry lab), menu class (astrophysics, geology, or information science), and frosh lab of your choice. I'm not sure how they deal with the humanities requirements for transfers. </p>

<p>Your number theory and graph theory classes will be useful in terms of doing well in your classes at Caltech, but I don't think they'll allow you to pass out of anything. Ma 5 is required for a lot of the graduate level classes you'll need to take to graduate. The book used for it (all three terms) is Dummit & Foote, so that might be worth buying since you'll either have to take Ma 5 next year or know all of the material from it to pass out. </p>

<p>For freshmen, the only way to pass out of classes is to take placement exams. AP/IB exams and college classes are worthless unless you can prove you've learned enough in them. For transfers, it's a little different. I do know that they'll let you out of some classes based off of material you've covered at your previous school. I'm not exactly sure how they determine what you should pass out of. Caltech will probably send you information on how to pass out of classes to you during the summer, especially since it's relevant to all transfer students. If for whatever reason they do not, you can always contact the Registrar, since she's the one who determines if you graduate. The worst hoop they might make you jump through is taking some placement exams or contacting a professor for a class that you want to skip out of.</p>

<p>How long are you thinking you want to take to graduate? If you just pass out of Ph 1, Ph 2, Ma 1, and Ma 2, you'll be just a little ahead most sophomore math majors and significantly behind most junior math majors. Since the math option doesn't have many requirements, you could probably manage to graduate in two years. On the other hand, you'll probably be able to do better in your classes and take more that interest you if you take 3 years and lighten up your course load a little. It depends on what you're planning on doing after graduation, how much Caltech is costing you, etc. Just warning you, since I think most transfers take 3 years to graduate, even if they've taken 2 or more years at another school.
*
Does that mean that the average problem set grades, midterms, and finals are around 90% or do the grades get adjusted by a curve system?*</p>

<p>Not necessarily either. It is pretty safe to say that you will not encounter very many exams at Caltech where the average is around a 90%. However, a 90% average on problem sets can be very reasonable, depending on the class. On the other hand, almost all of the classes you'll be taking will be small enough that fitting a curve to the grades would be ridiculous. A lot of professors determine what letter grades go to what score based on their experience and what level of work they deem to be "passing", "good", "excellent", etc. It may seem arbitrary, but they do this in such a way that it can only help you. I doubt you're ever going to take a class where a 90% is less than a B+. On the other hand, you might take classes where a 40% is an A. Sometimes professors give exams that they don't expect anyone to be able to do most of. In the more advanced math classes, I know they sometimes like to sneak unsolved problems into exams to see if they can trick you into solving them. :D Graduate level classes tend to be very grade-inflated, regardless of university, so as long as you can hold your own against the graduate students in your classes, you'll be getting pretty good grades. It's not as scary as it sounds. The average graduate student probably isn't going to be any smarter than you and will only have a couple years experience over you.</p>

<p>*One last thing, do you think the admission office can set me up with a math student at Caltech? *</p>

<p>If you just have a few questions, I know there are at least two math majors who frequent this forum. The admissions office employs a lot of undergrads, so they probably have at least one math major who can talk to you, particularly if you're still trying to decide whether or not to attend Caltech. You should probably stop worrying so much though, since you seem very well prepared for math here.</p>

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<p>I'm a senior math major at Caltech, so I can probably answer most questions you have about the math department, advanced classes, etc.
As Antiquark said, the grades in (post-core) math classes tend to be centered around an A-, although this varies greatly according to instructor preferences.
The grade distribution does NOT at all depend on the difficulty of the course. I have taken easy classes where 90% is an A- and conceptually very difficult courses with an unofficial policy of "register-get an A+". A lot of the graduate courses have no HW/no exams so every who registers and comes to class even half the time will get an A/A+; these are generally classes on relatively recent research on which books and problem sets have not been written and the profs don't want to waste time to prepare them. And as Antiquark said, if you don't have at least an A- (prefferably better) GPA in math classes you are unlikely get into the top dozen or so math Ph.D programs, but from what I've observed people from here have about as much trouble getting into them as people of comparable ability at peer schools like Harvad/MIT/Princeton/UChicago.
Most Professors are approachable and nice people- even if some of them can't/don't want to teach particularly well. Because of this last factor, some classes have a <25% attendance rate. The availability (and even existence) of TA's differs from class to class.
Getting a SURF in pure math is not hard- just make sure to start asking faculty you're interested in working with early- like in December/early January, since many of the profs may make alternate plans for the summer. And no, you definitely don't need previous research experience to get a SURF.
The requirements for a math major here are:
1. Ma 5abc, Ma 108abc, Ma 109abc, Ma 10.
2. Ma/CS 6a or Ma 121a.
3. Ma/CS 6c or Ma 116a or Ma/CS 117a.
4. 45 additional units in Ma or ACM. Courses in other options with high mathematical content may be used to fulfill this requirement with the approval of the executive officer for mathematics.
5. Math majors must take two quarters (18 units) of a single course, chosen from the mathematics course listings with numbers between 110 and 190, inclusive. (In years where one of these courses is given as a one-term course only, it cannot be used to satisfy this requirement.) These two quarters may be used to meet requirements 2, 3, or 4.
6. Passing grades must be earned in a total of 483 units, including the courses listed above.</p>

<p>108ab is real analysis, 108c is complex analysis, 5c is abstract algebra,
109a is (baby) algebraic topology, 109b is basic differential geometry/geometric group theory, 109c is geometric topology, (6a or 121a) is combinatorics, (6c or 116a or 117a) is logic, and classes numbered 110+ are graduate classes.</p>

<p>Considering you've taken real analysis using baby Rudin, I imagine you know most of the material from Ma 108ab- you probably won't get actual credit for it, but you can ask the math department to waive the requirement and allow you to take Math 110 (graduate analysis) instead. To meet the discrete math requirement here we have the choice of taking the undergraduate or graduate versions of a combinatorics course, and I don't think the math department would let use your combinatorics class at your old school to get out of the requirement completely, but you can always ask. Other than that, the classes you said you've taken appear to be almost disjoint from the requirements here.</p>

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<p>Thank you so much for all of your replies. They are all really helpful. </p>

<p>*How long are you thinking you want to take to graduate? *</p>

<p>I am planning to graduate in 3 years at Caltech. Even if I stay here at my current school, I also plan to graduate in 3 years. I do not think I want to rush it all in 2 years >.<</p>

<p>You probably haven't taken any chemistry past the standard intro college chemistry</p>

<p>I actually took two quarters of Chemistry my first year. </p>

<p>The first one is:
General Analytic Chemistry (including lab): Qualitative and quantitative measurements to develop laboratory technique and demonstrate the basic concepts of stoichiometry, chemical bonding, gas laws, chemical equilibrium and acid-base chemistry. </p>

<p>And the second one is:
General Physical Chemistry: Thermodynamics, electrochemistry, chemical kinetics, atomic and molecular structure, and chemical bonding.</p>

<p>I think one of the most crucial factor that would determine my decision is the number of non-math classes that I need to retake. I do not mind at all repeating the 108ab series or if I have to take more combinatorial classes, since I think it would be a good review as well as an opportunity for me to learn new things. I am interested to know if I can skip physics 2, since I am really interested in taking Math 108abc next year. I emailed the admission officer yesterday, if they could do a 'Transfer Credit Evaluation' before June 1st, so I am still waiting for an answer. </p>

<p>And can I ask, how many people from Caltech's math go to the top PhD program in math?</p>

<p>Once again, thank you!</p>

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<p>In the last three years the Caltech math majors who went to grad school in math went to (number in parentheses):
MIT(2)
UChicago(3)
Berkeley(3)
Stanford(1)
Harvard Stats (1)
Princeton PACM (1)
Michigan(1)
Courant(1)
Columbia(1)
UCLA(3)
UCSD(2)
U. Washington (1)
UCSB(1)
UTAustin (1)
Stony Brook(1)
U. North Carolina (1)
(I may be missing some, but as far as I know the list is comprehensive).
There are also quite a few math majors with requisite backgrounds who get into grad school at top programs in economics, computer science, and physics.</p>