Undegraduate Tips (thanks for reading)

[mathgeeko]

Hi,

I'm a raising college sophomore. I took Calc I through IV in high school and I'm on track to major in a completely different field (non-science) which I also love at a fine arts school which doesn't have a math dept.

After college, I want to get a PhD in Math. To gain admission and also because it would be very interesting, I would like to do some unpaid research for some professors at a nearby university but I'm not sure how to go about that. I've contacted one professor about research but he said he only worked for kids from his school. How could I increase my chances of getting such a position and what advice do you guys have on how to present myself in the best possible light given my background?

I can take one math class a semester as an elective for the next 3 years. What 6 classes should I select to get into a good math grad school? I'll take Linera Algebra in the Fall, but then is it better to take "core classes" like Intro to Modern Analysis and Algebra or is it better to self-study the material and register for more advanced classes which have these classes as pre-requisites?

Thanks a lot for your answers guys! I know this is super long and I appreciate your time.
MathGeeko

 

[Clever-Name]

Without an undergrad degree in math don't expect to get accepted to any graduate school. While this may be harsh you need to find a different school that offers a math program.

 

[streeters]

Without an undergrad degree in math don't expect to get accepted to any graduate school. While this may be harsh you need to find a different school that offers a math program.

I suspect this is the case, too.

 

[Null_]

I don't see how you can expect to get a PhD in math from a good school without taking many more (advanced) math classes than you will be taking. You may have to do an extra year of just math classes before applying to grad school. Why not go to a school with a math department, major in math, and minor or double major in the *completely different field*?

 

[micromass]

You can't get into math grad school without majoring in mathematics. In your plan, you will have taken about 6 math courses in total. To go to grad school you'll need about 20-30 math courses. They really aren't going to accept anybody with just 6 courses...

If you're ultimate dream is to do a math PhD, then major in math. Or at least do a double major!

 

[mathgeeko]

Thanks a lot for your replies guys, I appreciate it!

Actually I believe you need only 13-14 math courses (about 40 credits for a major at most schools, which is 13-14 classes worth 3 credits each).
Since I've taken 4 already, if I take 6 more, I'll be at 10 which is a little more (about 3 classes) than a minor. I was thinking of taking the 3 or 4 remaining classes during the summer at a university or as a visiting student for a semester.
I could also go to free grad school in my field, take 5-6 more math classes (total of 48 credits so far) as electives and then apply to math PhD? Does that make more sense?

How much does the Putnam fellowship, chess prizes and GRE scores count?

I choose my major because I hope I can do research which combines both. Few people have but there is interesting stuff to find there.

 

[micromass]

Thanks a lot for your replies guys, I appreciate it!

Actually I believe you need only 13-14 math courses (about 40 credits for a major at most schools, which is 13-14 classes worth 3 credits each).
Since I've taken 4 already, if I take 6 more, I'll be at 10 which is a little more (about 3 classes) than a minor. I was thinking of taking the 3 or 4 remaining classes during the summer at a university or as a visiting student for a semester.
I could also go to free grad school in my field, take 5-6 more math classes (total of 48 credits so far) as electives and then apply to math PhD? Does that make more sense?

How much does the Putnam fellowship, chess prizes and GRE scores count?

I choose my major because I hope I can do research which combines both. Few people have but there is interesting stuff to find there.

Here are all the courses I took as an undergraduate:

Discrete mathematics
Linear algebra
Affine and projective geometry
Differential geometry I
Differential geometry II
Algebraic geometry
Coding theory
Stochastic Processes
Analysis I
Analysis II
Functional Analysis
Topology
Complex Analysis
Measure theory
Probability theory
Mathematical statistics
Differential equations
Logic
Algebra I
Algebra II
Algebra III
Numerical mathematics I
Numerical mathematics II
Bachelor project

This amounts to 24 courses. I suppose that this is a typical undergraduate curriculum. In my country, they would not accept you at all with just 14 courses... But perhaps america is different.

Anyway, the grad committees will find it pretty strange that you want to do a PhD in mathematics, while you did a major in something else. Be prepared to explain this.

 

[mathgeeko]

Which of these classes did you consider
1. Most challenging
2. Most essential to your sucess in grad school
3. Most important to the long-term developpement of your math abilities ?

Thanks a lot

 

[micromass]

Which of these classes did you consider
1. Most challenging

That would be measure theory and probability theory. It was quite difficult, but very fulfilling.

2. Most essential to your sucess in grad school

All of these classes have helped me in one way or another, but the most important classes would include

Linear algebra
Affine and projective geometry
Differential geometry I
Differential geometry II
Algebraic geometry
Analysis I
Analysis II
Functional Analysis
Topology
Complex Analysis
Measure theory
Algebra I
Algebra II
Algebra III

3. Most important to the long-term developpement of your math abilities ?

All of them. Seriously. There isn't one class that I regret taking. Not all classes are useful to me know, but I'm very glad I know something about it anyway.

 

[mathgeeko]

Thanks a lot! So if I took:

Linear Algebra, Honors Complex Variables, Ordinary Differential Equations (S), Partial Differential Equations, Analytic Number Theory, Algebraic Number Theory, Probability (S), Logic (S), Knot Theory.

S stands for Summer Class and Modern Analysis and Algebra are self-studied. Would I have a shot?

 

[Clever-Name]

I highly doubt it.

There's still the problem of not having a degree in math. The graduate admissions committe is going to see you have a degree in "unrelated field" and strongly question your reasons for applying. They will definitely put someone with an actual degree in math infront of you.

 

[Poopsilon]

I really have to disagree with Clever-Name, streeters, and to a lesser extent micromass (since he lives in Belgium). Many, if not the majority, of graduate schools in the US do not have 'a bachelors degree in mathematics' as one of their requirements. Furthermore I am skeptical that they would automatically "put someone with an actual degree in math in front of you", considering what their primary motivations are for taking on and funding graduate students. You will however need to be competitive with those who do have math degrees, which will be difficult if you are majoring in something else.

 

[jbunniii]

You can't get into math grad school without majoring in mathematics.

I agree with the philosophy behind this remark and strongly echo the recommendation, but it's not literally true. I got into a top-20 math PhD program (in the US) with an EE undergraduate degree plus some extra coursework. Fine arts would be a different story, though!

 

[micromass]

I agree with the philosophy behind this remark and strongly echo the recommendation, but it's not literally true. I got into a top-20 math PhD program (in the US) with an EE undergraduate degree plus some extra coursework. Fine arts would be a different story, though!

OK, I was wrong with my comment But just for curiosity, how much extra coursework are we talking about??

 

[ArcanaNoir]

I would think it would be best to ask the grad school which you wish to go to! Find out what the entry requirements to the program are. Talk to an admissions counselor. That would seem to be the best way to know what you need to do.

 

[Pengwuino]

You can get into a math PHD program without a math degree. HOWEVER, there are no hard and fast rules to getting into phd programs other than the fact that you are competing with other people to get into the schools. They're almost all going to have degrees in math, more classes than you, probably better math GRE and GRE scores than you and their application will look better. So all that matters is how does your application look versus everyone elses. Also, no, chess stuff doesn't matter for graduate school. Your GRE is important but the subject GRE is the more important one. It's assumed you'll do nearly perfect if not perfect on the math portion of the GRE and at least decently on the rest of the GRE.

Getting into a fine arts PHD program, taking a bunch of math courses, and transferring seems highly suspect, although I'll leave this for people with more experience in the area. Also, self-studying is meaningless when it comes to looking like you know math on your application. If you say you studied X, Y, and Z courses, that's pretty much meaningless to them. They have to see transcripts with actual grades. Sure it helps you to actually know the material, but it doesn't make you look better on an application.

I have no idea why you're doing a fine arts BA. Why don't you transfer to a university with a math BS? If you do a math PHD, your fine arts degree is going to be just for show, I really don't understand this.

But whatever your reason is, just remember that at the end of the day, your application is going to get 15 minutes to prove to the admissions committee why they should allow you in compared to everyone else that applies. Any oddity or missing component to your application will only work against you.

 

[jbunniii]

OK, I was wrong with my comment But just for curiosity, how much extra coursework are we talking about??

During my undergraduate degree, the standard calculus 1,2,3, a couple of differential equations courses, linear algebra, real analysis (Baby Rudin), complex analysis, real analysis (Lebesgue/measure theory). Plus a bunch of probability and stochastic processes.

Some years later when I decided to apply to graduate programs, I took an honors-level abstract algebra sequence and a couple of other courses. I think I got in largely on the strength of letters of recommendation from the professors of those later courses. After I started the graduate program, I would say I was about middle of the pack or a bit higher in terms of preparation. I was fairly strong in algebra and analysis, very weak in topology, and of course missed out on stuff most of my peers had done, like REU's. I knew next to nothing about number theory. So it's possible with an unconventional background, but not the most efficient or recommended path!

 

[chiro]

Hi,

I'm a raising college sophomore. I took Calc I through IV in high school and I'm on track to major in a completely different field (non-science) which I also love at a fine arts school which doesn't have a math dept.

After college, I want to get a PhD in Math. To gain admission and also because it would be very interesting, I would like to do some unpaid research for some professors at a nearby university but I'm not sure how to go about that. I've contacted one professor about research but he said he only worked for kids from his school. How could I increase my chances of getting such a position and what advice do you guys have on how to present myself in the best possible light given my background?

I can take one math class a semester as an elective for the next 3 years. What 6 classes should I select to get into a good math grad school? I'll take Linera Algebra in the Fall, but then is it better to take "core classes" like Intro to Modern Analysis and Algebra or is it better to self-study the material and register for more advanced classes which have these classes as pre-requisites?

Thanks a lot for your answers guys! I know this is super long and I appreciate your time.
MathGeeko

Hey mathgeeko and welcome to the forums.

I don't know about you, but in my experience you really have to be constantly doing and thinking about math to have any success in it.

I couldn't picture a PhD student having a half-hearted view of math. I don't know if the "all or nothing" principle is accurate of this, but in my short experience, I think this the case.

Micromasses class list is a good list and I want to emphasize that math is not just analysis, or statistics, or number theory, its the whole kit and kaboodle. Knowing a bit of everything adds to your toolkit of knowledge and seeing the sum of its parts in my opinion, really makes a difference between someone that just wants to know about math, to someone who wants to do and practice math.

I consider myself an average mathematician (I'm still studying), but from observations about other students (undergraduate or graduate), lecturers, or professors, it really is a full time endeavor and then some.

 

[physics girl phd]

I'll agree with Pengiuno that it's not impossible to gain acceptance... but rather that to gain admission to a program, you need to be in the top portion of the pool of applicants whose stack of applications sits in front of the admissions committee at that time. So conditions for acceptance can vary from year to year, although there are trends that admissions counselors (or the departments administrative assistants) may be able to provide to help you.

Generally, a degree in the field is helpful... but if you don't have a degree and nonetheless demonstrate aptitude in upper-level coursework you might be moved up in the stack. The degree, however, will help, because most departments will have qualifying exams, core coursework, and perhaps comprehensive exams over that core coursework before you can pursue research fully. The committee will want to know the you will be able to jump these hurdles successfully. They don't want to accept someone who can't... and the undergraduate degree is considered good preparation for these hurdles, but sometimes acceptance occurs with a degree in a related field and strong coursework in upper-level classes in the field.

Although I've served on graduate admissions committees, my field is physics (not math).. so I'm not sure how much the subject GRE matters for math (it generally matters quite a bit for physics). Getting a very high mathematics GRE score may also sufficiently demonstrate aptitude for some departments. Again, however, the mathematics major at universities is designed to help prepare a student for that... and your score will be compared with those of the other applicants who probably had that preparation for the test.

Doing some research will help (in my experience the committee definitely looked for this). It will show that you know what getting a Ph.D. is about, and are truly interested... not just thinking it sounds cool, or not just facing bleak post-undergraduate job prospects. Warning: Unfortunately, bleak job prospects is the case for many students now... and will increase the pool of applicants for graduate programs as graduating students try to increase their chances by applying to both jobs and graduate programs.

All that said... you ask this:

Hi,

I can take one math class a semester as an elective for the next 3 years. What 6 classes should I select to get into a good math grad school?

Do you have a list of generally offered coursework? Some may be slow to give advice without this (since your school doesn't have the degree program they may think offerings are scarce).

 

[mathgeeko]

Thanks again for your replies guys.

@physics girl phd: My school has an agreement with a nearby research university (an Ivy League school with a serious math dept) which enables me to register for the same classes as any college student. Sorry I wasn't clear about that. I can also register for graduate level classes and I am somewhat free to go around pre-requisites.
Given that I can take these classes, which ones do you think I should select? What skills and knowledge does an unpaid undergraduate research assistant usually needs to have and how hard is it usually to get such a position?

@chiro: Thank you for your welcoming words. I do think that math occupies a big place in my life, whether it is reading a lot about it, making up my own problems or trying to find patterns in series of number I randomly encounter. What more could you suggest for me to get a more "mathematician-like" way of thinking about math?

 

[chiro]

Thanks again for your replies guys.
@chiro: Thank you for your welcoming words. I do think that math occupies a big place in my life, whether it is reading a lot about it, making up my own problems or trying to find patterns in series of number I randomly encounter. What more could you suggest for me to get a more "mathematician-like" way of thinking about math?

Just a disclaimer: I'm still a student studying, so with that in mind here are my suggestions:

There is as you probably well know, different types of math. I think it would be wrong to say that these are disjoint from one another, but none the less they have a different focus in mind from the other kinds.

With any kind of math you can focus on the mechanics of what you are doing, the philosophy of what you are doing, and how the assumptions of your methods help explain these in the context of your field.

With probability and statistics you are typically trying to make sense of data and use techniques to come up with an inference that will aid you in making a decision based on the data.

Now a lot of the introductory stuff is based on is using a variety of techniques to get make an inference based on specific likelihood calculations in which you use that to help make a decision.

But on the other side like every area of math you have the assumptions and the whole machinery behind the techniques that helps analyze things in the context of those assumptions.

With the standard techniques, the main idea is based on each sampling distribution working on the basis of a large number of samples, which is what the central limit theorem uses.

A scientist that doesn't understand this may end up using the tools with wrong assumptions (like a small number of samples) and make an inference that is completely out of whack.

It's the same sort of situation for other math.

I guess what I am trying to say is that you need to figure out a specific area and then figure out the perspective you want to "hone" into. But to do this you need to have a good basic groundwork of "essential math" (Calculus sequence, differential equations, linear algebra, some analysis, applied math, and intro statistics) and then go deep into some area.

When you go deep into an area you will soon learn not only the current mathematical machinery and "why it works" (as opposed to how), but also have an idea of the area you want to go into. If for example you wanted to work in an applied setting, your perspective would be very different than if you wanted to work in a more theoretical based perspective.

The other thing is to be aware of the environment you are working in and who you are working "for". If you're for example an applied statistician you will probably be working for people that don't have the same command of mathematics that you do and the expectations will be different than if you were a researcher working in some obscure form of abstract pure math. The difference in audience means that part of your job as a statistician will mean that your communication skills will be different and something like that becomes a crucial skill.

There may be crossover, especially when people in an applied field update their knowledge to stay on top of their game, (and if they are working in a profession, it might be required both to keeping their accreditation and for legal purposes). In this case the blur between theory and applied can become blurry.

So the bottom line of this point is to get some kind of solid understanding about the whole of what is involved with a particular area. It's not just about math: it involves a whole host of issues that need to be considered and made aware of to help you make an informed choice.

Regardless of what area you choose to go into, being a mathematician is no different than other career: you choose an area and get your hands dirty. With that requirement considered and other things being equal, I wouldn't consider a researcher in an abstract field be more or less of a mathematician than a statistician that actively applies mathematics in the same manner in the context of a proper career. They both think about maths, and most importantly they both do maths. If you think about something without doing it at all, you are just a philosopher. Also note that I find a lot of great philosophers in a particular field, are people with a detailed history in that field (example, Kurt Godel for Logic).

One piece of advice for you in terms of "mathematical thinking": always question the assumptions and understand what they mean. This is universal for every form of mathematics and is pretty much the basis for understanding and reasoning in science. If you understand assumptions, you will know what it describes (and subsequently what its limitations are), and also what it does not describe. As a result you will be able to understand what situations it works in, and more importantly ones in which it does not. One thing never fits all, and in mathematics this is more profound than you realize.

 

[Anonymous217]

The name of your degree does not make a difference. It's simply the courses you took. A math major is recommended because you should basically be taking all the classes a typical math major takes anyways: 2 semesters Linear Algebra, 1 semester Diff Eq., 1 semester Multivar. Calculus, 1 semester Real Analysis, 1 semester Complex, 1 semester Abstract Algebra, and at least 5 more upper division courses, preferably related to your concentration but by no means required to.

So you see, this general outline is basically what you should accomplish, and you just get the "math" major for having completed these.

 

[Clever-Name]

The reason I keep saying you should get a degree specifically in math is because (well at least from my experience and from events that have happened to friends of mine) the graduate committee has to decide if you're suitable for the program. If math is an afterthought for you and you devote most of your time to this other program, and as such not put as much effort into your math courses and don't take as many math courses, then that would in my eyes be a sign of weakness. If I saw an application like yours I would be strongly questioning your decision to apply to the graduate program and also be strongly questioning your ability to succeed in graduate level mathematics.

You're basically taking the bare minimum required to have the equivalent of a math major. The bare minimum usually isn't enough to either succeed in a grad program or to even get accepted to it.

You will be compared to others who have devoted their undergrad life to studying math, who have taken additional difficult courses to gain more knowledge, and who definitely have the capacity to succeed. Seeing your application with majority fine arts courses will put you lower on the stack when compared to the other applicants.

And even if you do get accepted you still have a huge challenge ahead of you; you'll need to change your mindset from fine-arts with a hint of math to pure hardcore math, and that may be difficult.

 

[n1person]

Discrete mathematics
Linear algebra
Affine and projective geometry
Differential geometry I
Differential geometry II
Algebraic geometry
Coding theory
Stochastic Processes
Analysis I
Analysis II
Functional Analysis
Topology
Complex Analysis
Measure theory
Probability theory
Mathematical statistics
Differential equations
Logic
Algebra I
Algebra II
Algebra III
Numerical mathematics I
Numerical mathematics II
Bachelor project

This amounts to 24 courses. I suppose that this is a typical undergraduate curriculum. In my country, they would not accept you at all with just 14 courses... But perhaps america is different.

American universities are VERY different :P, at my university a sort of average major would be: (http://math.yale.edu/undergrad/mathematics-major)

Multivariable Calculus
Linear Algebra
Intro to Analysis
Real Analysis
Abstract Algebra I
Abstract Algebra II
Algebraic Topology
Differential Geometry
Number Theory
Complex Analysis I
Complex Analysis II
Senior Seminar

Probably those that want to go onto grad school might also take 1-3 graduate school classes, making about 12-15 classes.

 

[Anonymous217]

^ Slightly off-topic, but what's the difference between Intro to Analysis and Real Analysis in Yale courses? In Berkeley, we often interchange the two terms to mean the same thing.

 

[eumyang]

^ Slightly off-topic, but what's the difference between Intro to Analysis and Real Analysis in Yale courses? In Berkeley, we often interchange the two terms to mean the same thing.

Well, if you look at Yale's http://students.yale.edu/oci/ycps/y...ATH&dept=Mathematics&term=201103&term=201201":

MATH 301a , Introduction to Analysis .
Permission of instructor required
Foundations of real analysis, including metric spaces and point set topology, infinite series, and function spaces.
After MATH 230, 231 or equivalent.

MATH 305b , Real Analysis .
The Lebesgue integral, Fourier series, applications to differential equations.
After MATH 301 or with permission of instructor.


I'm guessing that Yale's Math 305b corresponds to Berkeley's Math 105, "Second Course in Analysis."

 

[n1person]

Lol, yeah. Pretty much all math majors take 301 (or its Spring equivalent, 300), as well as lots of engineering and science people. Significantly less people take 305, and even less 310 and 315, Measure Theory and Functional Analysis, the next 2 in the "analysis" series.

We really don't have two semester math courses (except 230 to 231). Even what I listed as "abstract algebra II" is really "Galios Theory", but i decided not to confuse those who aren't familiar with subfields of abstract algebra. Graduate classes sometimes have two semester courses (Modern Algebra I,II; Algebraic Topology I,II).

 

[Anonymous217]

Well, if you look at Yale's http://students.yale.edu/oci/ycps/y...ATH&dept=Mathematics&term=201103&term=201201":
...
I'm guessing that Yale's Math 305b corresponds to Berkeley's Math 105, "Second Course in Analysis."

Ah, I see. I figured that would be the case. Thanks for the link to the catalog. I was partially lazy to search for it on Google.

Lol, yeah. Pretty much all math majors take 301 (or its Spring equivalent, 300), as well as lots of engineering and science people.
...
Graduate classes sometimes have two semester courses (Modern Algebra I,II; Algebraic Topology I,II).

That seems similar to Berkeley. The first semester in Real Analysis and Abstract Algebra are necessary, but a second semester in either is not. And the second semester in Abs. Alg. is also Galois Theory while the second in Real covers Lebesgue integ., etc. However, some people skip the second semester of Real Analysis and cover a faster-paced grad course, which covers Lebesgue, measure theory, topology, and functional analysis.

Oh, and sorry for the digression.