What's It Like to Be a Math Major? Inside the College of Arts and Science Part 4

"Fun" probably isn't the first word that comes to mind when you think of math - unless you are, in fact, a "math person."  But is there such a thing as a "math person," anyway?  And can math be not just practical, but playful?

This week, Dr. Ross and student producer Ashley Worley continue their series highlighting inside stories and college prep practicalities from UT Tyler's Mathematics department. Mathematics professor Dr. Joseph Vandehey and graduate Mathematics major Millie Jeske join the discussion to share what's really happening in collegiate math classes. If you're choosing your degree, preparing for college life, or just curious about other experiences in higher ed, this series is for you. 

Have more questions about life inside a Math department? Email us at ADRquestions@gmail.com or leave a comment below. We'd love to hear from you!  

Want to learn more or connect with UT Tyler's Department of Mathematics? Click the link below! 

-Department webpage: https://www.uttyler.edu/academics/colleges-schools/arts-sciences/departments/mathematics/

Transcript

Why Arts And Sciences Matters

SPEAKER_01 0:02

So, as you all have probably figured out, one of the goals of this podcast is to educate folks about what goes on at universities. And the central college in most universities was the College of Arts and Sciences.

SPEAKER_03 0:16

For this series, we're going to be introducing each of our wonderful departments in the College of Arts and Sciences by bringing you a top professor in that department and one of the top students as well. We hope that this is very helpful to you as you're choosing your major or just wanting to learn more about what to expect from college life in general. Thank you for listening and we hope you enjoy.

Meet The Math Department Guests

SPEAKER_01 0:39

So this afternoon we're talking to some folks from the math department at UT Tyler. My first guest is Dr. Joseph Vande Hy. His research areas are number theory and ergodic theory, and he hopes one day to know how many sevens are in the decimal expansion of pi. We're trying to find out what are some of the things that are taught in the range of college math courses, and then tell us a little bit about what you teach.

What College Math Courses Cover

SPEAKER_00 1:03

So we kind of have several different levels of math courses that we typically teach. There tend to be the more, I might say, introductory sequences. These tend to be the courses that are required for other majors a lot more. So we have, you know, pre-calculus, calculus sequence, differential equations, linear algebra, all of these are different things where other parts of the university are like, oh, hey, we need our students to know that kind of math to do the science or to do the statistics that we're going to be doing. Then we have what might be kind of deemed more of like a pure math track. This is more of like studying the nuts and bolts of how does math actually work. One of the classes we have is real analysis. And real analysis is basically calculus all over again, but now it's calculus with proofs. So we're trying to understand why did all those things that we said in calculus actually work? Because we tend to sweep a lot under the rug. And then we also didn't have like just more advanced things where it's like, okay, maybe this is a course that only certain types of very specific engineers need to know this kind of math, but we'll offer that as like a maybe 3,000, 4,000 level math class as well.

SPEAKER_01 2:05

Aaron Ross Powell So what are some of the skills you expect students to have that take those classes? The lower level is sort of basic competency stuff. Is that what you're hoping for?

SPEAKER_00 2:14

Aaron Ross Powell I think that one's a little bit more of like the side of math, which is you have some problem that you need to find the answer to.

SPEAKER_01 2:20

Aaron Ross Powell So problem solving. What kind of skills then for the higher level of math?

SPEAKER_00 2:25

For the higher level math, there's actually a lot of needing to understand the logic of things

From Calculus To Proofs

SPEAKER_00 2:30

and needing to be able to express things in a certain way. So there's the class that we think of the intro to proofs class, and every university has their own version of the intro to proofs class. And this is usually the first class you take if you're going from being just a student who likes math to a student who wants to be a math major. And that class is where we teach you how to write a proof, how to organize your ideas in a logical fashion. And I always make the joke that when I teach it, I'm teaching it like I'm teaching an English class. Because it's so important that it's not just about finding the answer. It's not just about that number you get at the end of the problem. It's about being to express the whole sequence of steps to show anyone else who looks at your work that they also understand how they got from point A to point

Skills For Lower And Higher Math

SPEAKER_00 3:15

B.

SPEAKER_01 3:15

Now, our other guest is Millie. And Millie is a senior here. She's from Tyler, homeschooled in our honors program. And the fellow over here who wants to know how many sevens are in the decimal expansion of pi is the reason that Millie became a math major. Is that right?

SPEAKER_02 3:34

It's kind of true, yeah. So as a freshman, I had to take honors cow one with him. And I was also taking a senior level Spanish class at the same time. So I jumped straight into that and I really enjoyed the class. It was really easy to understand. And I had taken calculus in high school. In high school, I didn't really understand it. It was really like difficult for me to understand. And I had my sister, she's an astrophysicist, and so she kind of stepped me through it, but it was still really hard to understand. But then when I took it freshman year, it all made sense and it was like really easy to understand and really fun. And I wasn't loving my Spanish class. A lot of it was repeat material from high school. And so I just liked the math class. And so I just switched based on that, which was kind of crazy.

SPEAKER_01 4:17

So how do you make math fun?

SPEAKER_00 4:20

I mean, the people listening to this can't see, but I have brought a number of items with me, including several of my massive collections of Rubik's Cubes.

SPEAKER_01 4:27

Is a Rubik's Cube a math problem?

SPEAKER_00 4:30

Oh, absolutely. But I'll do things where it's like I'll bring a different cube to class every day and just go, hey, did you know there's some like fun math behind this? I think there's over a quintillion different arrangements of the standard Rubik's Cube. And I'll just bring other crazy things and you know show them off to students. I'll tell stories about the history of mathematics, like the Pythagoreans. The Pythagoreans are real weird.

SPEAKER_01 4:52

Yeah. A lot of folks think, well, math is, you know, adding

A Student’s Pivot To Math

SPEAKER_01 4:55

and subtracting and multiplying and memorizing the multiplication tables. How do you explain to students that they ought to take calculus and that it's good for them?

SPEAKER_00 5:07

Aaron Powell Usually I don't have to do that explanation. Because usually most of my students in Cal 1 are there's a good chunk of engineers in that class, and they know they need to get the calculus done right because they already know that the engineering classes they're going to be taking require all of that calculus knowledge. Usually it's a bit more of a tougher sell for people who are taking the Cal 1 because it's a requirement, but maybe not as clear. So biologists who might need to take Cal 1, chemists who might need to take Cal 1, they're usually not as convinced for it. And especially nowadays where we have not just very powerful online calculators, we now have AI, which is trying to solve a lot of math problems. A lot of students are like, well, why do I need to know all this sort of stuff? I usually give the explanation of, sure, we have a calculator that can solve a lot of math problems, but that's a lot like saying, I have a dictionary here that goes from English to French. Is that good enough for me to go to France and be able to talk with the people there? Not so much, right? Because I'd need to constantly slowly be looking up every single word. This is not a way to hold a good conversation. And so if we don't have an intuitive way to be able to understand math on our own, the calculator isn't going to help us past a certain point. So there's two main kind of components to calculus, which

Making Math Playful With Puzzles

SPEAKER_00 6:20

we call the differential and integral parts of calculus. And the differential side of calculus is really just asking, I have some function that's changing over time, what is the rate of change? And that's all it's about. The flip side of this is integral calculus, and usually the best way to describe it is draw a picture with a weird curve on it, and ask yourself, what's the area beneath that? We know rectangles, we know triangles. But if you start doing parabolas, if you start doing other weird shapes, what's the area? And that's where calculus kind of comes into handy there.

SPEAKER_01 6:53

It's not so hard after all. Okay, all righty. So when did you decide you loved math?

SPEAKER_00 7:00

So I recognize that this as a podcast is supposed to be within a certain time limit, and I can't give you the entire story here because oh boy, it's a story. Probably the time where everyone realized, oh yeah, that's going to be a math kid. Seventh grade, I took my stepfather's calculus textbook off the shelf and I started taking it with me to school. So everyone else was out on recess, you know, playing on the swings, playing out in the football field, and I was sitting in a corner with this gigantic calculus textbook and slowly leafing through it. That's just what I did.

SPEAKER_01 7:30

Well, Millie, what about you? Was it this fellow's class or something else?

SPEAKER_02 7:34

I think I enjoyed it in high school. I didn't obviously know that I wanted to do it then. I think in high school I wanted to be some sort of teacher, probably elementary. And then I really liked Spanish, and so I did Spanish and then ended up not liking

Why Learn Calculus In An AI World

SPEAKER_02 7:48

it and liking math. And that kind of started it off. But then after my sophomore year, I did a research experience here at UT Tyler, and that was when I really like loved it.

SPEAKER_01 7:58

So what did you research?

SPEAKER_02 8:00

There's a field called accommodatorics. So it's kind of like counting, but in special ways. But we were researching stuff about permutations, which you can just think of as like rearrangements of numbers, kind of restricting those rearrangements of numbers and figuring out what kind of patterns came from that.

SPEAKER_01 8:17

So looking for patterns. So I will honestly tell you that I only got up as far as algebra two and geometry in high school. And yet I had a really high math score on my SAT. But then I went to math in college and everybody thought I was gonna be pre-med because I was so high in the math level. I did great for about three months, and then somewhere along the line I got confused. And I never got unconfused. And people say, Well, you're just not a math person. Now, I don't like that idea. Because I think I kind of was a math person until something happened. Why do you think so many people are afraid of math and say they're just not a math person?

SPEAKER_00 9:01

I think part of it actually comes down to it's almost a cultural thing, where especially in America, we uh kind of think of math as like, oh, well, that's for the mathy people, and the rest of us don't need to really worry about it. So there's not like the emphasis, oh yeah, you should be good at math,

Rates, Areas, And The Heart Of Calculus

SPEAKER_00 9:17

or even you should enjoy math, or anything like that. Which is not necessarily true in other parts of the world. I know a lot of students in China, in Japan, where there's very much a different culture behind math classes, and so you have a lot more students who feel like they can accomplish it.

SPEAKER_01 9:33

You know, I was scheduled to go to China to give a lecture. I was going to speak about British literature, and when I started researching, they didn't have anything in the humanities area. They had nothing but STEM, math, computers, engineering. Their culture is all about the calculating, the mechanical engineering, the way things work, and the imaginative side wasn't there. Now, I bet you're gonna look at me and say, but math is imaginative.

SPEAKER_00 10:02

Partially, yes. I can go back a century to G. H. Hardy, who was a famous mathematician who lived at Cambridge. And he basically wrote what what's known as a mathematician's apology, apology in the old sense of the word. And he was talking about how he really felt that math was really kind of straddling the bounds between science and art. That you can do a lot of math that's related to science. It's the language by which science is expressed. But also there's lots of room to just explore math for its own sake, and in that sense, he thought it was art. It's also kind of funny because he almost took a note of pride in the idea that the math that he was studying did not have an actual application. Then we jump forward 90 years to the internet, and suddenly the sort of stuff he was doing is like one of the foundational ideas behind internet cryptography, without which we wouldn't have, you know, e-commerce.

Falling In Love With Math

SPEAKER_01 10:55

So math as an art, do you experience it that way?

SPEAKER_02 10:58

Aaron Powell I think a little bit. I think I more experienced it as I guess not necessarily art, but kind of as a puzzle. So like when I did my research and doing classes where we have to do proofs, it feels a lot like a puzzle that you're trying to figure out how to fit all the pieces together. But I mean like there's functions that create these beautiful pictures. And so I think in that way it's kind of related to art.

SPEAKER_01 11:20

I don't want to be afraid of math because I loved it when I was younger. Have you had to deal with students with math anxiety in the lower level classes?

SPEAKER_00 11:29

Oh, all the time. Kind of like I was uh talking about before, just like trying to bring a little bit of fun stuff to class and telling these silly stories of the history of mathematics can be just very good for just that initial anxiety barrier where students are like, oh, I have to be so uptight about all of this. And you can just knock down one of those barriers and just go, no, no, no. We're gonna have a bit of fun here, right? Come to class, you'll learn something that you never imagined was possible.

SPEAKER_01 11:54

Aaron Ross Powell One of the things we think about is what do we need to tell students out there? And one of them I think would be what should they prepare for to be able to do well in math.

SPEAKER_00 12:03

I think of math a lot as a language. And like any language that you have learned, it builds upon itself constantly and constantly. Unless

Research In Combinatorics

SPEAKER_00 12:11

you know how to conjugate those simple verbs, you're never going to move on to more advanced bits of grammar. So in the same way with mathematics, if you're you know not getting that algebra down all the time, then you're really going to struggle moving on. In fact, I'd say when I see students who are struggling in calculus, students who fail Cal 1, for example, the biggest reason why tends to be that they don't have a good basis in algebra.

SPEAKER_01 12:34

So have a good solid background in the basics. I think the problem solving part is a big part of the pleasure of math.

SPEAKER_00 12:43

Like if I ever have to describe the process of math research, then I'm just like, imagine you're solving a Sudoku, but it's a Sudoku no one has ever solved before. Because it is just problem solving. It's figuring out, you know, what's the right steps of logic to get you from point A to point B.

SPEAKER_01 13:02

So tell me a little bit, Millie, about what is your sort of daily life like as a math major.

SPEAKER_02 13:08

I'm taking two math classes right now. As a senior mathematician, you have to take senior seminar one and senior seminar two. Senior Seminar One is in the fall and it kind of just teaches you how to research how to write a paper. And there's like a programming language you have to learn in order to format your paper. So you learn all of that. And then the second semester, you work with a professor and do it, doesn't always have to be original research. It can just be exploring a topic.

SPEAKER_01 13:32

Are you doing original research?

SPEAKER_02 13:34

We're not sure. We think it's original research, but we haven't

Math Anxiety And Cultural Attitudes

SPEAKER_02 13:38

looked because we don't want to disappoint ourselves if it's not. It's very similar to the research that I was explaining earlier. It it kind of has to do with permutations, which are rearrangements of numbers, and then looking at pictorial representations of them and kind of also looking at patterns. So I've done two summers of research.

SPEAKER_01 13:56

Wow, that sounds like a lot of fun.

SPEAKER_02 13:58

Yeah.

SPEAKER_01 13:59

So what are the other two math classes you're taking?

SPEAKER_02 14:01

The other two I'm taking one is combinatorics, which is the field that I've done research in, and then the other is geometric systems, which is the geometry class. And then for fun, I'm taking creative writing.

SPEAKER_01 14:13

Well, you know, I think math and literature oftentimes they're demonized by people. You know, someone taught them badly and they hate poetry now. Or math, the same thing, you know. But to me, the thing about math that I loved was that you could take something and apply it and solve and make bigger, interesting problems. When you think about what you're gonna do. Now you became a college professor of mathematics. You said you wanted to be a teacher, Millie. Are you gonna be a teacher of math or do you think there's something else you'll do with your math instead?

SPEAKER_02 14:46

I'm gonna get my master's, so I'm not all the way sure what I want to do. I think I might want to be like an honors coordinator, so work more with students than the teaching side of things. But I'm not sure because I do really love math research.

SPEAKER_01 14:59

Because that's always the big question people ask. Well, what are you gonna do with that degree? So here you go, Dr. Van De Hy. What are they gonna do with that degree besides be teachers?

SPEAKER_00 15:08

They could do just about whatever they want. One thing I try and tell, especially to parents, most jobs,

Math As Language And Foundation

SPEAKER_00 15:15

most companies especially, want to have people there that can do math. So if you have a math degree in addition to whatever else it is you're doing, that can be really beneficial. Also, University of Illinois at Ubana-Champaign, my alma mater, is working on this more of trying to get companies to say, well, let's just hire a mathematician. And maybe they're just a manufacturing firm and they hire a mathematician for an internship for a summer. And, you know, these firms were initially like, uh, you know, okay, we'll do this as a nice, you know, gift to the university. We'll just hire one of them, who knows what'll do. And then they come back at the end, they realize, oh, wait a minute, we had all these math problems sitting around that we didn't know what to do with because none of us are math people. Example that's a little bit more historical. There was a person named Ron Graham who worked for Bell Labs at ATT for years and years and years, and he was working on this problem of sorting numbers. Basically, you're given just a huge pile of numbers and you're told, fit this into like three boxes so that each box is as close to the same sum as the other ones. And he had devised a way to like get towards a better answer, like 5% faster or something like that. And you might be thinking, well, why why would he do that? Why would he care about that? Well, instead of numbers being sorted into boxes, imagine they are packages being arranged into shipping containers. And you have to try and, you know, even them all out so that it's easier to distribute them. By him working on that problem, he might have shaved off two percent from shipping costs all around the world,

Daily Life Of A Math Major

SPEAKER_00 16:45

which is an amazing thing to do.

SPEAKER_01 16:47

So there are all sorts of practical applications of these adventures with numbers, if you will. Now, Dr. Vanden Hey came in with a bag. And in his bag are some toys. And I wanted you to tell us a little bit about what you brought here. Because this is really pretty fun. I don't think I've ever had anybody come with a bunch of toys. Maybe I can try and do some very brief ASMR and just playing with one of his Rubik's cubes and he's about to change it over and oh my goodness, has he solved it already?

SPEAKER_00 17:18

I'm not solving it. No, I'm just scrambling it right now. I also brought a pair of citrimen dice. So these are standard six-sided die, or because yes, I am that nerd and I play Dungeons and Dragons, a D6. Except that these have very different numbers on them. So for example, you might notice that there's an eight on that one. And this one has two copies of the number three on it, which is not what you expect standard dice to do. It turns out these are dice that if I roll them, and of course I drop it all the way onto the floor. But if you roll them and you add up the result, the probabilities are exactly the same as if you rolled two standard six-sided dice. So normally you can get anywhere from two to twelve in certain probabilities.

Careers Beyond Teaching

SPEAKER_00 18:02

These two, when you roll them, will go from two to twelve in the exact same probabilities, even though they are differently numbered. I brought books, and of course I can't show off all the books, but one of the books I brought was a geometry of music. Basically, this author, Dmitry Tomozko, was trying to talk about so there's a lot of kind of geometry that you can use to visualize things that are happening in music. Like anyone who's done some music before knows that there's the octave, and the octave is a key thing. You go from middle C to the C above it. And in between, you have C, C sharp, D, D sharp, E, F, F sharp, G, G sharp, A, A sharp, B, C. So you can envision that C to C, because we kind of think of the C's as being the same note, even if they're on different octaves, as the same thing. And so then that takes that line from C, C sharp all the way up to C again, and it bends around and forms a circle. And then it's like, okay, well, that's if you look at one note at a time. What if you do two notes at a time? Right? You can have lots of different ways that those notes bend together. And how does that

Toys, Dice, And Hidden Probability

SPEAKER_00 19:02

kind of form a shape? Turns out it forms a Mobius band.

SPEAKER_01 19:06

Oh my goodness. That's kind of mind-blowing.

SPEAKER_00 19:09

I'll save the best one for last. I brought a book called The Geometry of Voting, which is what's the mathematic behind different styles of voting. So this book is basically trying to say, okay, well, can we visualize the different styles of voting and different ways in which people vote as a geometry problem? And then can we like use geometry to help us understand like the flaws or the benefits of different styles of voting? We normally think of the standard way in which we vote, one person, one vote, whoever gets the most votes win, as being a very reasonable system. But if I just make a small tweak to it, it becomes what you would think of as an absolutely unreasonable system. And that is each person gets one vote. Whoever gets the least number of votes wins. So basically instead of voting for people, you're voting against people. And if we tried to put that into our modern American electoral system, this would cause immediate and absolute chaos. Because, sure, probably most of the Democrats would vote against Republicans, and most of the Republicans would vote against Democrats. So who's going to win? Some not third party, but like fifth-party, you know, platform that no one's ever heard of because no one knows about them well enough to vote against them. There's questions of mathematics

Geometry Of Music And Voting

SPEAKER_00 20:15

that are being used today. There's a specific mathematician, Moon Dutchon, who has worked a lot on this. She's, I think, talked before the U.S. Supreme Court, specifically with relation to things like gerrymandering. How do we arrange the voting districts, basically?

SPEAKER_01 20:29

So I think what I'm hearing here is that math is incredibly useful, of course. We knew that. And it's not necessarily the scary thing that a lot of people think of. It's a playful thing. It's something that can actually impose some meaning and some clarity on a world that is sometimes incredibly confusing. I'm fascinated. I'm a little intimidated, but I'm also delighted that you all have shared these things with us. When you think about what you'd like young people coming to the university to know about math, Billy, what was something you want to be sure that they hear you say?

SPEAKER_02 21:08

I mean, I think what you were saying is that it's not as scary as it seems. And the faculty at UT Tyler are so wonderful and really good at working with each student and like talking them through problems and having office hours. And then I've experienced the students around me have been super helpful. We work on homework

Community, Support, And Success

SPEAKER_02 21:26

together. And so I think that it's not as scary as it seems. And if you really plug yourself in and go to office hours and interact with your professors, interact with your peers, then it's a lot easier of an experience than if you try to do it by yourself and don't use those tools that are accessible to you.

SPEAKER_01 21:43

So I was going to ask you the same question, Dr. Vande Hy. What do you want to say to the high school kids that think, oh, I don't know about college math?

SPEAKER_00 21:51

I think one of the most important things that you can do going into college math, besides the you know, the preparation, is find friends. Because like what Millie was talking about, having these connections between different students makes it so much easier to get through that material. And I think there's even been studies that say, you know, students who work with other students succeed so much more.

SPEAKER_01 22:13

Ashley, do you have any comments that you want to add to this conversation, but

Why We Love Math

SPEAKER_01 22:18

sure.

SPEAKER_03 22:18

I mean, first of all, I'm a mass communications student and I'm the person who had to take algebra twice and who fought tooth and nail to survive through algebra too. So from that perspective, I would love to hear what it is that both of you love about math. So much that you made it where you wanted to become a professor of it and you wanted to study it in college and are thinking about maybe being a professor of it.

SPEAKER_02 22:44

I don't know. I think it was when I did research, just the figuring out it's very logical. And I didn't know that I was such a logical person, but I love that most math, you can like start with definitions and all you have to do is kind of fit the pieces together and see how they work. And so I think it's really fun and exciting, especially like the research that I've done, getting to find these new formulas or getting to find these new connections. And then I've been able to present them at conferences, and I've been able to present them at conferences where it's all different

Open Questions And The Wonder Of Pi

SPEAKER_02 23:14

disciplines. That's made math really fun for me because I've been able to share it with other people that don't know math, and they'll get a little glimpse of it and be really excited about it. And so I think probably my favorite part is like sharing it, and then also just the community at UT Teller with student-wise is a lot of fun. We have a lot of fun doing homework together, and as Dr. Vanderheiß said, doing board game nights and things like that. And so I think those are my favorite parts.

SPEAKER_00 23:39

So the thing that I think really pulled me in, besides the, you know, hey, I was just kind of that kid who just loved learning things and you know would just happily pick up a calculus book. I think it's actually related to, you know, you mentioned that bit of stuff from my bio about the digits of pi. And I heard this story, I think when I was in high school. People have been studying the digits of pi for centuries at this point. When the ENIAC was built, one of the first things they did is a bunch of mathematicians like, we have to test how many digits of pi we can calculate now. And there's a very simple question you can ask, which is just, you know, look at all the digits from zero to nine. Do they appear in the same frequency? Because you'd expect that it would, because there shouldn't be any reasonable pattern to the digits of pi for any reason. But it's a question that has not been answered. It's been, you know, two millennia since we've really been focusing in on, you know, deep questions

Closing And Listener Questions

SPEAKER_00 24:30

of math, and we're no closer, really, it feels to solving that than we were when we started. And how could that be? It's pi. I love that. I love that there's these sometimes very simple questions that we just don't have answers to. And sometimes we have these very simple answers to incredibly complex questions.

SPEAKER_01 24:46

Well, listen, I think the math department is really lucky to have both of you. And we are so thrilled that you came to talk to us and brought us your toys. And we hope that if anybody has some questions about math, that they will send them in. Ashley gets all the questions and then we take them and we try to get folks like you all to answer them. We just talk to historians. And you know what historians and you do? You tell stories. And guess what English professors do? We tell stories. And I think finally that's what this podcast is about is telling y'all a story. And I'm glad you shared a little bit of it with us.