Category: Math and Other Fields

Career Path Interview (Spring 2018, Part I)

Interviewee: H.L.
Major: Mathematics
Year: Senior

1) Why did you choose maths as your major?
H.L.: I have always been interested in numbers, patterns and how things operate. However, upon entering college, I was introduced to political science, economics, philosophy, anthropology and other subjects, which caught so much of my attention that I considered majoring in one of those fields. Nevertheless, the attention was only momentary. Mathematics remained my favorite, and was hence chosen as my major. As I advanced, mathematics grew on me, and became my ultimate intellectual pursuit.

2) What are the areas of math that you have studied?
H.L.: Like most undergraduate math students, I took courses in calculus, linear algebra, real/complex analysis, abstract algebra, topology, ordinary/partial differential equations, discrete structures, set theory, etc. In terms of more advanced materials, I studied elements of measure theory, distribution theory and probability, functional analysis, Fourier analysis, approximation theory, analysis on PDE, matrix theory, computational group theory, ring, module, field, Galois theory, elements of representation theory, categorical language, algebraic topology, homological algebra, etc. I am also introduced to other branches of mathematics including mathematical logic and differential geometry.

3) Do you have any comment on these areas?
H.L.: Given my current maturity, I may not be qualified to give any deep comment about these subjects. However, the impression I have is that many topics in analysis and abstract algebra often resort to the study of linear algebra. Just to name a few, the concept of duality is one of the principal elements in the study of module theory, which is itself a generalized study of vector space over a field. In functional analysis, which is roughly speaking the study of infinite-dimensional vector spaces equipped with topological or metric structure, whose fundamental elements also include the Riesz representation theorems and dual of Hilbert and Banach spaces. In PDE, the solvability of second-order elliptic equations is firstly established by the existence of weak solutions, which turned out to be a consequence of what is known as the Fredholm alternative given the condition of a compact linear operator involved in the partial equation. There are also other topics in algebraic analysis where application of matrix theory is ubiquitous.

4) Which area is your favourite?
H.L.: Thus far, I am mostly interested in measure theory, functional analysis, and PDE.

5) What’s you plan after college?
H.L.: I recently applied to several Ph.D. programs. I wish to pursue graduate study primarily in the area of mathematical analysis.

6) Have you ever considered working as opposed to grad school?
H.L.: I have wanted to pursue an academic career since I was in high school. However, if things do not turn out well, I am open to opportunities in math-related industries.

7) Did your math research experience affect your perspective? If so, in what way?
H.L.: My participation in summer 2017 REU at Cornell University, and in directed reading courses at Berkeley definitely helped form my perspective on mathematical research. Prior to these experiences, I did not know what a life of a researcher would entail. It was not just about learning and being exposed to a vast amount of materials relevant to the research project, but also about honing my communication skills. By frequently discussing problems and concepts that I struggled to understand with other group members, I learned how to organize and present mathematical ideas in such a way that not only my partners, but also participants working on other projects, can understand. As a result, I received intuitive feedback, which helped me form fresh insights into difficult problems. Additionally, I find it very helpful and motivating to attend graduate seminars organized by faculty members as well as graduate students at Berkeley, even though my comprehension of the presented materials may not be adequate and may even be, a lot of times, absent. However, these seminars provide intuitions in terms of how materials I learned in graduate courses are used and developed. Thereby, they portrait a clearer picture of what the disciplines look like at the forefront and how important it is to communicate with other mathematicians about new ideas on unsolved problems.

8) Do you mind sharing with us your long-term career goal?
H.L.: Upon obtaining a Ph.D degree, I hope to get a postdoctoral and then a faculty position at some research university to fulfil my dream of teaching and conducting original research in mathematics.

Experiences and Advice about Double/Triple Majoring

 

Hey everyone! It’s Fahad again with the peer advising blog! This week, I wanted to talk about my experiences being a Math, Computer Science, and Statistics triple major, and my recommendations for anyone who’s considering doing more than one major! If you’re wondering about my experiences, head to the next paragraph. If you’re wondering about my advice, check out the third paragraph!

I’ll start with my experiences and some of the myths I learned really weren’t true. The first thing I want to talk about, and probably the most important, is the course load and time commitments.  I will warn you, more than one major definitely takes up a significant amount of time; just fitting in the classes itself is a pain. But as a triple major, I was able to plan out a 4 year schedule in which I got to take a couple of classes for fun and stay at 4 courses per semester, and it only required me to take all technical classes two semesters and a couple of summer classes! This might seem like a lot for some people; which is why the option of taking a 5th or 6th semester exists, but at no point should you have to take 20+ grueling units for multiple semester (unless you want to!). It’s about planning correctly. Overall I’ve had a positive experience doing a triple major, and it’s because, as I’ll touch on in the next semester, I was truly interested in everything I’m studying.

So, on for some practical advice. The biggest, most important piece of advice I can give is to actually be interested in what you’re majoring in. You’re not cooler because you’re a double or triple majoring and almost no employers will bat an eye if you aren’t truly enthusiastic about everything you’re studying. Your coursework will come easier as well as either your majors will be similar and you’ll have one specific topic you’re focusing on, or your majors are very different and you’re truly passionate about everything you’re studying, making class less of a necessity and more of a fun task. For reference, when I was thinking about triple majoring, it was because I had already taken some core classes and I went through all of the department courses and listed all the classes I was interested in taking. After looking at this list, the triple major just came naturally. This is something I would definitely recommend, as you get to know whether you have enough classes you’re actually interested in. It makes the experience worth it, and much easier. College is amazing because you are not forced to take any classes, you study what you want! Take advantage of this to the fullest extent; don’t major in something just because it will look good. Do it because you like it. My second piece of advice is to use your advisors! Whether it be your peer advisors, your major advisors, or your L&S advisor, they’re a great resources in helping you plan out your schedule! They know the courses with the most workload and the relative success of previous people who might have been in your shoes before, so they know exactly how you feel and how to help you get to where you wanna be! My

Thanks for reading! Feel free to comment or email me if you want to learn more, or come to my peer advising office hours! For general questions, other peer advisors also hold weekly office hours found here: https://math.berkeley.edu/programs/undergraduate/advising.