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I am currently a third year undergraduate student in university. A year ago I decided to study pure math because I liked its rigorousness. As time moves on, frustration accumulates because I don't know what I can do with all the things I've learnt. Maybe it's partly because I haven't learnt enough, but you know what I mean. Since I am already in the third year and it's impossible for me to change my major in my undergraduate study, I am hoping to change to another major when applying for the graduate school. Not that I don't like math anymore, but I want to be able to do something with it.

The following fields are of my consideration:

  • applied math
  • computer science
  • electronic engineering
  • artificial intelligence, machine learning, image processing
  • physics

These are the difficulties I believe am facing:

  • My GPA is okay, but not great. If converted to US standards, I have a GPA of 3.5+, ranking approximately 20%~30%. My university is world top 50 (maybe even top 20, but different ranking systems do differ a lot).

  • Lack of research experience. Honestly, there's just not much research to do for an undergraduate pure math students. We spend most of our time studying existing theories, and there's not much experiment to do for pure math.

  • Most courses I have taken are centered at pure math. I may lack sufficient knowledge of the fields mentioned above. For example, a CS major student studies data structure in his/her undergraduate years, but I don't. This certainly weakens my competitiveness if our applications appear together on the desk of the admission office.

On the other hand, based on what I've heard and my understanding of my own capabilities, I do think there are some advantages.

  • A professor who taught a CS course actually said to us that other departments (engineering, CS, etc.) are actually very fond of math students and that we are very welcome to join them.

  • Ever since I've gotten used to pure math and have built a solid foundation, I find it considerably easier to read literatures from other fields. Sometimes my friends would ask me (nontrivial) questions in their own majors (physics, chemistry, economics, etc.) and after a little research, I would be able to provide answers.

  • I have taken some graduate courses. And I am studying a graduate-level (maybe even research-level) topic under the guidance of a professor.

That's basically my situation. And I would like to know:

  1. How possible is it for me to change my major when applying for graduate school? What kind of school can I hope to get into (preferably in North America or Europe)?

  2. Is it true that other departments welcome pure math students, as is said by the professor mentioned above? Would an admission officer focus more on my advantages or disadvantages?

  3. What other fields can you suggest?

p.s. It would be helpful if in your answer, you can tell me whether you have experience being on an admission committee.

  • How strong are your programming skills? – cag51 Dec 4 '19 at 4:34
  • @cag51 C++ (the most familar one to me, I have been using it since high school and have taken two courses in university), matlab and python (learned these in univesity). I've learnt algorithms like dynamic programming, etc. But not as good as a CS major student. – rsch Dec 4 '19 at 4:54
  • @cag51 I'd say my knowledge of these languages and algorithms is enough. Data structure might be my weakness though. I only know the simplie ones like queue and stack. – rsch Dec 4 '19 at 5:01
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How possible is it for me to change my major when applying for graduate school? What kind of school can I hope to get into (preferably in North America or Europe)?

This isn't all that uncommon. In the CS Msc programme at my university (Leiden) for example, we get a lot of people coming in from Statistics. The emerging field of Data Science has caused Statistics and CS to become much more closely related fields.

Exact requirements will probably vary by university, but at least in the EU the system is set up to make it possible for people to combine pieces of education from multiple universities. A BSc in mathematics together with some catch-up CS classes will probably get you in the door in a CS master.

That's not the of the story though. Individual courses often have their own requirements; a masters' course on advanced data mining might require prior basic data mining knowledge. But that doesn't mean you have to have taken the data mining class offered at that university. Our CS master attracts a lot of students from other universities. The requirement just means that if you don't know anything about data mining yet, you're going to get thrown into the deep end.

Since these requirements are mostly "you should already have a foundation in", not "you must strictly have this particular class", you could also fill in those blanks with online courses or reading relevant handbooks.

Is it true that other departments welcome pure math students, as is said by the professor mentioned above? Would an admission officer focus more on my advantages or disadvantages?

What the admissions officer focuses on will differ from institution to institution. However, you should not be too discouraged by lists for formal requirements. People move from all kinds of places to all kinds of places, so partial matches are extremely common. Often you should be able to come to an agreement along the lines of "You already match ABC, but you need to pick up XYZ as well before you can enter".

Me for example, I wanted to switch from History to CS. For CS I needed a particular flavor of high school math as an entry requirement, but the remedial course they usually used was already fully booked. I found a remedial course at a different university and proposed that one, and they accepted that.

So approach the advantage/disadvantage discussion as a discussion where you look for a mutually acceptable solution. Be imaginative and constructive.

Right now, about halfway in the current academic year, is actually a good time to do this. If you can come to an agreement with regards to requirements, there is still a whole semester to take some remedial courses in a university or an online course that the admissions officer considers acceptable.

What other fields can you suggest?

As a CS student I'm a bit biased of course, but if you want to apply math, I'd definitely consider a CS Master. Machine learning and data science tends to be a significant part of that, and a strong math background is quite useful there.

Apart from the hip neural network side of things (which is much more about matrices than you'd expect), I would also recommend optimization/decision support as an area of study. This has a big mathematical component to it, which "native" CS students aren't always as strong in. In the field of natural computing in particular, there are a lot of people doing projects based on interesting proof of concepts, but lacking theoretical/mathematical analyis. That's something that a math background could help you with.

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I don't think it should be too much of a problem if you want to go into AI, Applied Math, or CS — even the top schools in the U.S. are willing to take pure math majors in these fields if they've taken a relevant introductory course or two in their desired field of study (and you have enough time to do that before you apply to grad schools). I don't know what EE will think of this situation. Physics would be harder because physics departments expect incoming graduate students to have a much deeper background.

You should email Applied Math/CS/EE/Physics graduate admissions at some of the places you're interested in, and ask them about your situation, and how much background they require. Graduate admissions departments usually try to help potential applicants and will answer questions like this.

I suppose if you're at some school where they won't let you take courses outside your field of study, or where they don't have computer science courses (say), you could be in a much more difficult situation. Are you?

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  • Actually there are plenty of courses to choose from, including all the fields that I am interested in. The problem is, to be able to graduate, I have to finish a certain collection of courses. And those courses take a lot of time and energy. Math classes aren't easy, as you can imagine. If I choose another course in another field, say a CS course, I am not sure I can handle the workload and guarantee a good grade. – rsch Dec 8 '19 at 16:10

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