Kathrine

Thank you for joining me today. To start, would you mind introducing yourself and what you study?

Jennifer

Yeah, hello, my name is Jennifer Tan. I currently study applied math and statistics as well as pursuing a minor in design at UC Berkeley. So I'm currently a sophomore and I'm very honored to be part of this interview.

Kathrine

So how would you explain applied mathematics to someone who has only experienced math through school classes?

Jennifer

Yeah, so I feel like as a degree it seems very daunting because it's like, oh, math at a more professional level. And I do think it is very different. Like it starts off being similar to high school math where it's more like calculations and kind of just like applying formulas.

Then you realize later on you're like second to third, fourth years that it's actually a lot more theory based. So I do think like applied math as a degree really dives into like more proofs, more, you know, kind of dissecting math at a deeper level. For example, like you learn algebra from like seventh to eighth grade, ninth grade for some people.

But in college you learn that, you know, algebra isn't just like adding numbers. You learn a lot more about things like groups and rings, which are basically just like categorizations of numbers. And then, I mean, I'm not going to go into that, but you learn a lot more about, I guess, like the art behind like math and, you know, how all the relationships work that you've just taken at face value before.

Kathrine

So what areas of applied math interest you right now?

Jennifer

So do you mean more like career paths or do you mean more like topics within math? I guess both. Wait, definitely.

I think in terms of math at school, some topics that I'm really interested in are just like number theory, which actually like isn't too much of like a required course in the curriculum, but it's something that, you know, I'm just interested in math in general. And I also really enjoy something called abstract algebra. You'll see that if you get more into the math degree later.

But those are two of my favorite topics within math itself. And in terms of like applying math to, you know, more like career path things, I would say like I'm pretty interested in like finance because there's like, I mean, finance in general, like there's a lot of like social studies, like backgrounds are involved in that too. But I think a lot of it is also like looking at past data for markets and then making predictions.

And then also like kind of estimating the probabilities about how everything's going to go up or down. So everything is like quantifiable. I think that's like very interesting and a great application of math.

I'm also interested in something called like computational biology, which is basically applying math to more like a biological context. So if you're interested in both topics, I think that's a great career path to go down. So I guess not Wall Street or something.

We actually did consider that at one point, but I do think like the work hours are very intense for Wall Street. I think like if you're interested in like more like math math, you might think of something called like quantitative finance, which has been very trendy lately or quant. So that one's more like, I mean, it is kind of like in the financial district of NYC as well.

You think like Jane Street, like Citadel. I don't know if you guys have like heard of those companies, but they're all big names in quantitative finance. And that's a very hard field to break into.

But if you really like math and problem solving, that's a very popular one. I think with Wall Street, it's usually a lot more like econ people that tend to go into Wall Street. But there are a lot of math people as well.

I think there's a lot of mathematical applications, but you also have to be someone who's very interested in finance and reading in general, too. So I do think it's a little bit less common than something that's a little bit more like hard math.

Kathrine

So thinking back, was there like a class, project, competition camp or other experience that first made you really interested in mathematics?

Jennifer

Yeah, I think it might be an interesting case because for me, I'm not like the craziest, like, oh, my God, like I love doing math, like math is my main thing. I feel like I'm studying math mainly just just because it's very, very like widely applicable to other fields. So for me, I'm using math, like, I think I'm studying math, not like just to study math.

I'm studying math as like a support for other fields like product management, and also like, like, once again, like finance and then data analysis. So I feel like for me, I might be just a more interesting case. But I guess like before college, what made me want to pursue math a little bit further was a like the flexibility you get and the fact that like the degree is pretty much applicable to anything.

So if you're just like not sure it's a great general degree to have, I think I just like that safety. And another thing was that I did like something called the AMC, which is like the American math competition. Back in high school, like I also started doing it since like middle school.

So I think like foundations for math, I think it's like very interesting because a lot of people start like more specialized topics like bio Olympiad in high school. But for math, like a lot of the kids have been starting since like third grade, fourth grade, with like math counts and like smaller like, like youth math competitions. So I feel like for me, like it was kind of my interest was kind of built from the start because my parents enrolled me in like, a bunch of like, I guess, like different math competitions since like fourth grade or like very early on.

And I feel like, like throughout the years, there's more and more opportunities to do that. So it was kind of just like something I've been doing my whole life. I also took like the AMI a couple times.

So I think that's one thing. And I also did like math team at my school. I think that was pretty cool, because you have to travel to other schools and then meet a lot of other people.

So I feel like getting involved in that community also, you know, encouraged me to continue doing it. I think another thing would just be, I just, I did like a summer camp, but it wasn't like math related. It was called like Simon's Summer Research Program.

That one was pretty fun. Yeah, that one was pretty interesting. I met a lot of really smart people.

But I do think that one like cultivated more of like an interest in data science, because I think I realized like, how applicable quantitative tools were outside of just like the theoretical context that you learn in classes. I think it's pretty cool, like getting to apply like, even if it's just basic math formulas into like tables, analyzing biological data, I feel like you learn a lot through, you know, hands-on applications. So I really recommend research as well.

Kathrine

Yeah, when you mentioned like the Simon's like summer camp, I immediately thought back to like someone else who also mentioned that they did that. And like, I think right now, they like have an MD and a PhD at the same time or something. So it seems like everyone who's done that has become very successful later on.

Jennifer

Wait, yeah, I feel like a lot of the people that I was like roommates with, and also just like my campmates as well, a lot of them have gone on like, it's only been like two or three years since then, but a lot of them have like gone on to do found like YC companies, and then go to like get crazy job placements as well. I feel like everyone's just so motivated. I think it's really cool to be part of that community.

It also like tells me like, damn, I gotta lock in a little bit more too.

Kathrine

Next, can you walk me through how your interest developed from high school and like those competitions into applied mathematics?

Jennifer

Yeah, I think, actually like I feel like it wasn't really like everything that I did that kind of led me to applied mathematics, like very, like, ironically, compared to what I just said, I think applied math, like, I think the main reason why I ended up just choosing it was just because like, I had no idea. I like did so many different like, like, for example, assignments, like my research was biology wasn't even math. It was like a marine biology too.

And then I also did like something called Science Olympiad back in high school. So that was like, for like, I don't know if you know the events, but there's like criminology sort of things. There's like cryptography, like a lot of different topics.

Like at that point, I was like, wow, like I lowkey like every single thing. And there's not too much like, I feel like a lot of like CS people, for example, like know their whole lives, like, damn, I love coding, like I'm gonna be a CS bro. But I think like, for me, I was like, God, like, I have no idea what major I want to be.

So I lowkey like chose a major off of just like, like, you know, which major would be the most flexible later on, like, I think math is one of the best ones for like indecisive people. And another thing is like, oh, damn, like, which one does my current like, resume stack fit the most? Because when you're applying to college, like, I feel like you also try to want to apply to a major that you know, your resume kind of tells a story for.

Because for example, like, if I'd never tried something physics related, why would I pick physics as my major? I feel like I wouldn't be able to convince people that I do well in physics. Definitely not true, like choose what you want.

But I also think like, from my personal strategic standpoint, I was like, oh, I'm gonna choose something that like, my resume, like my math club, like my math clubs, math camps and stuff, not math camp, sorry, math competitions, like a story that like, I can sell based on what I've done so far. So I think that's kind of why I chose math. And I kind of just stuck with it, because I was like, oh, it's pretty fun.

Kathrine

Oh, so like, at the beginning, like, um, like, is applied math something that you like, merely chose to, like, fit in with the rest of your resume, I guess?

Jennifer

Um, I wouldn't like kind of kind of I think, like, it's like a little bit of that. And also a little bit of just like, yeah, like, I've had previous math interest. And I like, definitely, like, can see myself continuing to do math.

So I think it was like, it's like partially that, but also like, I think it's mostly just like, like, yeah, I wanted to do it. But I wasn't too sure, like, out of all the things I liked, which one to choose the best.

Kathrine

Yeah. And you also mentioned that you chose applied math, because it was like, widely applicable to a lot of fields. But I feel like when most people think about applied math, they wouldn't necessarily think that it's like, this, like, very universal skill.

So like, where did you where and like, how did you learn that it could be applied across so many disciplines?

Jennifer

Yeah, I do think like, a lot of this was just, I guess, like, I didn't do too much research on it exactly, like before I applied, I think just like, in theory, like, applied math, like everything involves math. So someone who like has a really good mathematical thinking, mathematical thinking and logical reasoning skills should be good for like a lot of different roles. So that's kind of what I what I was thinking about.

And also, like, I was interested in computational biology. And that one was like a very unexpected application. So I was like, Oh, shoot, like, what are some other like, interesting, like, you know, math x something else crossovers.

And I realized, like, almost every single field had some sort of like mathematical variant to it. Like, for example, like math for finance, you have like quantitative finance, which is basically like mathematical finance, you have mathematical biology, I mean, physics is also basically just math. So pretty much everything, like obviously involves math, because everything involves optimization, right.

And also, like all businesses want like profitability, and all those are just like a numbers game. So in the end, like you realize a lot of them just want like people who are really, I mean, people who like know a lot of people who obviously like are more tailored to that field, too, but also people who can do math. So I do think, you know, since every company needs someone who, you know, someone who can do math in some sort of way, and applied math degree definitely is a valuable asset for most of those positions.

Kathrine

Next, can you describe one memorable project, research experience, or math problem that you've worked on or are currently working on?

Jennifer

Yeah, so I think actually, for me, like, I'm not working too many on like the traditional math problems that you'd be thinking about, like the like math research groups that do like directed readings and stuff like that. I think those ones, like I'm not doing too much of like pure math research. But I think like a lot of the projects I've been working on are more like applications of math and data.

So for example, like, I'm in like a consulting club, and then we do things like, you know, help give recommendations to businesses that are clients. So some of the projects that we've been working on are like designing a designing a game, for example, I can't go too much into it, because of like an NDA. But a lot of it is also like, for example, like user research, and then, you know, doing analysis on the data that we get to recommend, like, oh, like, how much can we improve this company by?

How much do we charge for this product? And a lot of those are all just like many optimizations that we think about, for us to like, you know, how much the company should price the product and stuff. So obviously, they're gonna have their own people that are probably better than us for doing those numbers.

But just to give the recommendations, like you want to give them like something to work off of. That's the thing. And other things that like I'm in a finance club, I'm on like the quantitative side.

So we do some projects here and there about like, like obviously, like making models to trade on. So some things that I've been working on are just like, you know, researching different strategies, for example, something we've worked on is like a theta and Vega neutral butterfly spread strategy. Like, I don't know if you know about that.

But like, something that we're doing is basically just like researching what it what it is, obviously, like how how the strategy works, and then trying to implement our own version of it using pandas, which is like a Python package. So that's kind of just another thing that we've been working on a lot of just like random like math x data, math x finance, different like applications of math.

Kathrine

Awesome. So next, what has been your favorite applied math related class in college? And what do you guys actually do in that class?

Jennifer

Yeah, so I think, actually, like the math classes are like contrary to like, people's belief that like applied math should be very, very applied. The applied math curriculum is actually like not too much different from the pure math curriculum. So it's mostly like, like just like math theory.

So I would say like within the math theory classes I've taken, I really enjoyed abstract algebra. So like I mentioned that earlier, I feel like it really like changed my perspective on everything I knew about algebra and numbers in general. I feel like it was very recommend for anyone who wants to study math.

But in terms of like more application based classes, I do take a lot of classes in other departments, which are not part of my degree, but just for like personal interest. So I've taken a lot of like data classes and also statistics classes. So I do think like for statistics classes, I liked a probability class I took.

It's just called concepts of probability. But I think it was really interesting because you learn a lot about different distributions and also like ways to like, you know, calculate probabilities manually. So I think that's that one's very useful, I would say, in like industry.

So I totally recommend that class.

Kathrine

So earlier, you were talking about how you're consulting for companies. And I was wondering, like, which classes gave you the skills or like gave you most of the skills that you needed for that kind of work?

Jennifer

So like, if I'm gonna be completely honest, like you don't need any skills for that. I feel like a lot of it is like, I feel like consulting is one of the easiest things you can like, kind of like learn. I would say a lot of it is just like getting data, and then just doing research.

And then, you know, like, chatting solutions, or like, searching up common solutions, I feel like there's only certain recommendations you can give as high school students. And it's always like the same couple of frameworks. So I do think like consulting is like, okay, I don't want to say consulting is easy, because I don't know too much about it.

But just like, I feel like from at least like a junior, or like aspiring consultant standpoint is not hard to learn at all. Like, it's not hard to be a consultant, it might be hard to be a good consultant though. But yeah, I would say like some useful classes that other people have taken are probably like the business classes, but I haven't taken any of them.

So I probably can't speak on them.

Kathrine

So I guess like your consulting work wasn't necessarily related to your major.

Jennifer

Yeah, it wasn't related. But um, it's like you can twist it to be related to your major.

Kathrine

Yeah. Um, next, what do people often misunderstand about applied mathematics?

Jennifer

Yeah, I think I think the thing that people commonly misunderstand is that the curriculum is very similar. Sorry, sorry, the curriculum is very different from pure math. Because like, oh, pure math, and then applied math, like pure math is so jobless, applied math has so much money.

Like, it's not like the degree is any different. It's basically one or two classes difference. At least at Berkeley, it is.

It's mostly just like the people that you know, choose to do each of them. I would say there's a big like cultural difference between the two majors. I think I've noticed that like a lot of pure math majors, for example, like really are just like in it for the love of the game.

Like they love math. And they just like they're fine with being jobless for the rest of their lives as long as they get to study math. I feel like that's like the general pure math culture I see, which is pretty interesting.

But for applied math, you feel like I feel like there's like a big, a big mix between there. Like there's not too many like diehard like I love math. Those are all pure math people.

I think applied math is more so like people who you know, really want to apply math to like finance or something else. I think applied math is definitely like, it's not like the chiller and easier version of pure math. I think it's just like the types of people that choose to go into each of them.

Kathrine

That's kind of funny.

Jennifer

Yeah.

Kathrine

Is there anything you really love about studying your major and anything that you perhaps don't like?

Jennifer

Well, yeah, I think I can only really like, like, it's like talk about my experience at Berkeley and not any other school. But I think like something I really like about my major is that I thought there'd be like a lot of pretentious people there because it's like, oh, it's a STEM major. It's probably gonna be like a lot of dudes that are like, oh my God, like, how are you not getting such good, like the same answer that I am?

Like you're so stupid. Like I thought it would be like that. Cause that's like the high school experience of like learning STEM as a girl.

But like in college, I realized that like people are genuinely like really collaborative, really friendly. Like people are actually really real within the department. They're like, God, like I got cooked by that exam.

Like I'm probably getting like a 10%. Like I feel like everyone's so raw about that. And we're all like low key in it together.

So I feel like the applied math culture is pretty cute here, which I like a lot. I also think like something else I really like about the major is that there's something called like, like a cluster, which is like take three extra courses for your credits. And then you can choose like any other department to like technically like apply your math in.

So for me, like I'm choosing a probability theory cluster. So I'm taking like some other like statistics classes and also like this kind of like measure theory class. So those are all like, this is like a cluster that like, it's like, oh, this is my specialization and how I'm like applying my math, which is pretty cool.

And then I think some things that I don't like about the major. Let me think. I think one thing is that like, it's like a little too theoretical, I would say.

For like an applied math major, I do think that like they don't need all the required courses to be like different, like very like unapplicable theoretical courses. I do think they're like great courses in general, but I do think like everyone agrees that like you're literally never going to use half of this stuff later on your life. So I think, I do think that like they should keep a lot of those to pure math and then, you know, enforce a lot more like, or give us a lot more like, like actual like applied math classes.

Because technically they can just be like, oh, just take statistics classes, which they're already doing with the cluster thing. But I do think like mandating us taking like five really difficult, like pure theory courses for upper division requirements is quite like difficult for a lot of people. And also like not really why a lot of people chose the major.

So I think just the major requirements is like not a really good thing.

Kathrine

Yeah, I guess it's a little bit of a misleading name.

Jennifer

Oh yeah.

Kathrine

So next, what advice would you give to a student who is good at math, but isn't sure if they want to study applied mathematics?

Jennifer

Well, yeah, no, definitely. I think like if you're genuinely interested in math, you're going to do great. I feel like for me, I was like, oh, like I should be calm because I did math like for a lot of my life.

And I'm also like, I'm probably like ahead of a lot of people. Because I remember like the first day I was talking to, I was like doing like this other like me applied math freshman event. And then a lot of them were like, oh God, like I haven't even taken like Calc BC yet.

Or like, like I lowkey like don't know what I'm doing that much. But I just thought like, I think I'm pretty interested in that. And like a lot of those people, like they were like, they started off a little bit more behind, but they've been doing like better than me in some of my classes for math.

Just because like, I mean, first of all, like theoretical math is very different from what you're used to. So for me, I was like, I'm so used to like competition math, where it's like you involve a lot of tricks and stuff. And I think like theoretical math, like there is like a high correlation between like people who've done well there and then people who've done well in like more theoretical math as well, because it is also still like puzzle pieces.

But I do think it's like been a little bit harder for me to wrap my head around immediately, because I wasn't super used to it. And it feels very brand new. And I also feel like a lot of kids who have like, like a lot of those kids who were like, who started off behind, like they just took a lot of classes or freshman year, and I felt it was completely fine.

They were able to pick up on time. And then they're, they're absolutely like thriving in their upper div classes. Like, even if it takes you like a little bit more effort, I feel like a lot of people like started from like, like, obviously, like below average for the major and then you know, just work their way up to through like pure hard work.

So I do think like, like not everyone starts off being like super cracked in math or applied math. Like a lot of people are just like literally like the only thing they have to their name for math is like just an interest. I think they're still doing great.

So definitely like do it if you have passion.

Kathrine

Okay, so um, if you could go back, what would you tell your ninth grade self?

Jennifer

Dude, lowkey like a lot of things. I feel like the main thing you just feel like, I feel like in college, like the reason why I feel like my lifestyle nowadays is more like chill and more like, damn, like I lowkey just want to have a good time. I think it's just because in high school, I really regretted not having like, a better time and then like, you know, hanging out with my friends more.

I do think like in high school, I was very like locked in in the sense that like, I'd be like pretty upset if I got like anything below like an A in a class or like, I lowkey be like, like for like club like leadership positions and stuff. I lowkey be like, damn, like I gotta get it. Like I was like super serious about it for like no reason at all.

Like I'm looking back and I'm like, damn, like I was so not chill. How did I have friends? So I think like lowkey, like, like, yeah, like I think I was pretty locked in in high school, which is like what got me here.

But I do think like, was it like worth it? Like not too much. I think like, if you can like accomplish a lot while also having fun, I think that's like the best way to do it.

Like, obviously, it's great to have discipline, but never like, never like take it too seriously. Like never get upset at people never get upset at yourself just because of like, small things like, oh my god, like this grade didn't work out or like, I didn't get this like summer program or something like that. It's like never that deep.

Kathrine

So is there like any subject that you wish you had started exploring earlier?

Jennifer

Actually, like not really. I do feel like even now I'm like, not super sure. Like I'm still exploring.

I think in like high school, most people like don't know what they're doing. And even like coming into college, no one has any idea what they're doing. So I do think like high school is like just the time where you're supposed to explore anything.

And then like, yeah, you'll wish that you found the thing that you eventually found yourself liking the most. Like, you really hope that you found it earlier. But in the end, I think it's like also like the timeline of things.

Like maybe I found this one topic that I'm really interested in at a time where I was like getting better at that subject versus like if I found it earlier, I might have been like, God, I hate this so much. You know what I mean? I think like the timing is like meant to be, you know what I mean?

Like always just like explore and never be afraid to try new things.

Kathrine

And next, what is one step a student could take this month to explore applied mathematics?

Jennifer

I think like, oh, do you mean like the degree or like the topic in general? And then like to like a high school or to like a college student?

Kathrine

To the topic in general and a high school student.

Jennifer

Yeah, I think with math, there's like not too much theoretical math you really need in high school. I think like, I think just like having a good problem solving, like understanding of like how to problem solve and how to how to have like a problem solving mindset is the most important thing that will carry you and then do you well in college. I think that's like the main thing, like just get used to like being able to solve, you know, like problems and not give up at them.

I think it's always good to have like a mindset where you're like or like a workflow where you're like analytically breaking down a problem, like any problem, even if it's like calculus or like algebra or like something as simple as like a pre-algebra. You can like, I think you look, you just like got to be able to look at a problem and like be able to like dissect it in your head without like immediately relying on GPT or like someone else to help you out. They can like really be able to sit there and think through a problem is very important to, you know, being good at math.

Kathrine

So do you have like any recommendations for books, videos, courses, like websites that people could look at?

Jennifer

Wait, definitely. I think like with getting into math competitions, there's this one AOPS book. I think it's just called like the volume one or something.

It's like, I think it's just like intro to problem solving. I totally forgot the name, but I really recommend that to like all of my friends who've like been wanting to start and get better at like math probability, especially and like geometry as well. I think it's like a book of like, it's a very good like potpourri of like basic problems that also teaches you like enough foundations about every subject too.

So I feel like it's a really good starter book. Volume two gets like, I feel like it gets like exponentially harder, but I also would recommend volume two if you like, you know, really want some more challenging problems or if you're like pretty cracked. And also like, like the competition itself too, like that's like under more of like a timed environment, but if you want to challenge yourself there, always pretty cool.

And then like snag the awards and stuff like that too. But I do think like with exploring math, I feel like it's always very like topics based, like everything I've explored is like its own textbook. Like I can't really recommend like something that will teach you all of it together besides that one, like problem solving book.

So I do think like, like, yeah, like, especially in high school, like you don't need to be diving into like advanced like number theory or anything. So I think like just that book is great for high schoolers.

Kathrine

Okay. So that's all my questions. Thank you so much for taking the time to share your experiences and I really appreciate it.

Jennifer

Well, thank you so much for having me. These are really good questions.

Kathrine

Thank you.