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Answering The Why With Applied Math · You've Got Options

• Clare: and welcome back to another episode. Today we are going over our applied math major, oftentimes referred to as APPM. If you're currently in the college, many of you may be familiar with or are currently taking APPM courses like Calc 1, Calc 2, but applied math is so much more than just calculus. So today we are going to be digging a little deeper. We have three special guests today to give us valuable perspectives, but before we dive in, let's cover some basics for the major. In applied math, to build your foundation, you can expect to take a lot of math, obviously, but you'll also learn computing, physics, and will take natural science courses like chemistry, biology, or further physics. But once you get further into the major, you will actually choose an area of application. These areas span many different subjects like aerospace, actuarial science, finance, computational biology, GIS, data science, chemical engineering, and many more. And taking the classes in these areas oftentimes helps you work towards a minor as well. So there is a lot of interdisciplinary work going on within this major. To give you an example, some of the research topics that are going on at CU are in areas like computational mathematics, statistics, geosciences. To give you a more real-world contextualized example, professors are working on things like the development of a multi-scale analytical and computational model that supports research in climate, atmosphere, and ocean science. Or they're working on things like bacterial community population dynamics, and they're also working in biomechanics and infectious diseases, And designing an artificial pancreas. So once again, this just highlights there is a lot of opportunity for interdisciplinary work within this major. As you can tell, graduates work in a wide range of fields depending on their interests. Many Sea Boulder graduates have been hired at companies like Deloitte, Goldman Sachs, Microsoft Oracle, Great West Life, and more. So these are just some of the basics of the major, But to understand a little bit more about what it actually means to be in Applied Math, We have two faculty members from Applied Math and a current student and engineering peer advisor to share what makes this major unique and meaningful to them. First, let's hear from our two faculty: Dr. Robert Benham, who is an associate teaching professor and faculty mentor for the Applied Math Department, and Dr. Ann Doggerty, who is a teaching professor for applied math. thank you both for coming on the podcast today. I appreciate giving your perspective about applied math. I think a lot of students do applied math, but they don't always know what it means. Before we get into the questions, I would just love to know how you both got into this field, what made you want to teach and mentor. I'm Bobby Benham. I'm a associate teaching professor in the Department of Applied Mathematics. I've been here for seven years now, in my seventh year. I knew pretty early on that I wanted to study mathematics. math always interested me. I liked that it made sense. and so it was just very natural. when I went to college at first. I was undeclared, but I very quickly became a math major because I ruled everything else out and it was like math is just what I want to do. and so I did that for undergrad, grad school, and then went into teaching in higher education. and I definitely have not regretted that. I've enjoyed getting to know students over the years, watching them grow, helping them on their journeys. Thanks for sharing. my name's Ann Dockerty, and I am a teaching professor in applied math. I've been here a long time. I started out as a chemistry math double major as an undergrad. And I didn't know if I wanted to do more of the experimental work, but I wanted the math to help me understand the equations that I was seeing. After I graduated, I still wasn't sure. And so I went to work in a lab And I was good at it, but I quickly realized I didn't really like it that much. And so I started going back to grad school. I did a masters in math. And then I went to the University of Wisconsin at Madison and did my PhD in applied probability. But it was more because I wanted to know why stuff worked. And I didn't quite get that in any of my non-math courses. They would give you a formula and say, Here's the formula, just use it. And I needed to know more than that. Well, that might lead in to the next question. Well, how would you describe this major to someone who knows nothing about it? Yeah, I think that is a good lead in. because it's about problem solving, it's about critical thinking, and it's about understanding the why. so it's not just about here's a formula, there you go. It's about why does that formula work? And I think it's also important to note to students that it's not just about finding the answers. it's also about asking the right questions. Because as soon as you get an answer, there's an important follow-up question that probably comes into play. and I think that's something that folks who graduate from our program pick up, the ability to ask that next question and to dig deeper. first of all, it's not an engineering field. Yes. the applied math degree is in the College of Engineering and Applied Science. We are part of the applied science part. so if you think about applied science, applied math, we are applying the mathematical ideas to other STEM areas. I agree with what Bobby said. Critical thinking skills are so important in this degree. I tell students I don't really care about this little toy problem or that little toy problem. I care about do you understand why the solution works? Do you know how to get it? And do you understand the bigger picture or the bigger context that that problem fits into? And so that's what I think we really focus on in our courses is the bigger picture. Even in our Calc I class and Calc II, students sometimes think it's really basic, but there's a lot of fundamental understanding and background during Calc One and Calc 2, we're laying the foundations for what's gonna come next. And There's a lot of theory and conceptual understanding that comes with those classes. What type of students would you say are drawn to this major if someone's undecided? How would they know that this is a good fit for them? certainly students who are interested in an interdisciplinary degree, I think are attracted to our degree program. and there's a couple of reasons for that. One, majors in our department, they have to have an area of application. and so that means that there's another area that they're gonna focus on with 25 credits. 24. 24 credits in that other area. and this area it's very flexible on what it can be. we have quite Quite a few outline in our curriculum guide, but truly, if somebody's interested in something that is a coherent area of application of mathematics, then that can be their area of application. lot of students get a minor or maybe even a double major out of this. So our major pairs nicely with the other interests that you may have. And I think a lot of students have been very creative in how they approach that. Yeah. Applied math plays well with others. but no I think the students who are going to be very attracted to this major are students who want to understand why things work. how does this equation work? What is this equation telling me? how can I make this algorithm do what I want it to do? And how do I interpret the results that it gives me? So students who are really interested in problem solving. And I do tell students, you don't have to be a genius in applied math to do well in our degree. You just have to be curious and be willing to work on understanding the material. And I would also like to talk about, because we get this question all the time, the difference between math and applied math. there is difference. And there's differences at multiple levels. There's differences in the coursework. we do focus quite a bit on courses that have applications. And there's also a difference in the focus of our research faculty. our research faculty tend to work on problems that have applications to them. and I tell students it's not math without theory. So there is quite a bit of theory in applied math, but it's not all theory. It's how do you use that theory and apply it to whatever problem you're interested in. kind of switching to the actual curriculum for the major, how flexible would you say it is? Obviously, there are these other kind of emphasis areas you can focus on. how easy it is it to integrate those other areas? Yeah, it's a very flexible degree program. and part of it is the area of application because there are many choices there. Some people do. Quantitative finance. Some people do different fields of engineering or anything in science, biology, or chemistry. Computer science. Computer science. We have some students who focus on education because they want to teach in secondary education. so it's very flexible there. but also within the coursework, after calculus, there's only a handful of courses. That every student has to take. And so, of course, you have to take a lot of applied math courses, but you get to kind of choose your path and focus on the things that interest you and that you will build on in your career. applied math is probably the most flexible degree in the College of Engineering and Applied Science. Because of that area of application, it's the easiest one to double major with or to major in applied math and get a minor in something else. how much hands-on learning or project-based work is there throughout the curriculum? Well, there's quite a bit. most of our classes at the upper division level, matrix methods, Fourier series, complex variables, they all have significant projects, in them. Some of our elective classes also have projects. There's also some exams and homework and sort of the standard makeup of a course. But there is quite a bit of hands-on work through the projects. And then our numerical analysis class has quite a bit of programming in it. Yeah, just tacking onto that. Programming is I think a pretty essential part of a modern applied math degree. Students get experience with a number of different programming languages, Python, R, maybe MATLAB. And is there kind of a point in this degree, whether that be a class, maybe an experience, that tends to be the most impactful for students, maybe where things start to click, they start to kind of understand what this degree is about. That clicking part is different for every student. For some students, it happens in differential equations, And they start to see the utility of the applied math. and they start realizing how different it is from high school. And then they say, this is more than I thought it would be, and then they want to do more. For other students, they might get that aha moment when they get to Fourier series and they start doing partial differential equations. they start to see the bigger picture and why applied math actually works. And so I think that aha moment comes at different places for different students. what seems to on the opposite end challenge students the most as they go through this degree? I think for a lot of students there comes a point, in the middle of a semester sometime where there's just a lot going on. You've got a lot on your plate. And so there might be a moment where, a little bit of, my gosh, I've got so much going on. Yes. and you know, to those students, we try to tell them, okay, slow things down, organize yourself, think about what you have to do. If we catch them before that, we kind of try to remind them don't procrastinate, stay on top of everything. because you're definitely gonna be challenged in this degree program. But I think if you're organized and careful, you can thrive. I think a lot of students have that moment when they're coming from high school to college and they're taking their first university level applied math class. And they start to realize, I never had to study in high school and now I have to study. And so they have to make that transition. And we will help them if they come to office hours. We have the Calc Help Center. We have lots and lots of resources for them, but they do have to make that transition. Yeah. So for the listeners, regardless of if you major in our courses, when you're in our lower division classes, use the exam archive to help prepare for the exams. All the students I've talked to who have been successful in our courses, without an exception, say, I did a lot of exams in the exam archive. Yes, absolutely. There are so many applied math resources. So I totally agree. You just have to use them. You have to seek them out. And not every student needs every resource. Right. but there is something for everyone. Exactly. And kind of going back to these areas of application, do you have any advice for students on trying to figure out what they might wanna apply in, what they might want to add on? that's a tough one. I was having a conversation with a student about this earlier because he was interested in two very different things. And I don't know if he liked my answer because I was telling him you gotta think about what you're interested in, what you see yourself doing, and make this area of application further your long term goals. and that's not something that we can do for a student. Students gotta come up with that on their own. So when I have students who have a couple different areas that they're interested in, I try and get them to try both for a little while. Maybe they take one or two courses in each of those areas so that they can explore them a little bit more, give themselves another semester or two to think through what they might be interested in doing. we do want students to intentionally plan their degree with us. I don't want them to do one semester planning at a time. I like them to think through what would it look like next year. The next year, the year after that, when you graduate, I want them to intentionally plan out their entire program to the best of their ability, with the understanding that we'll switch it up if their interests change. it's good advice yeah for your entire life. Not just not just for the next four years of your Academic career. Right, right. are there any opportunities specifically within the department that you think students should be more aware of or take advantage early on? there's a variety of opportunities. later on, maybe not early on, but later on students can seek out research opportunities with different faculty. Our faculty are very excited to work with students who are well engaged and prepared. we have lots of opportunities to meet folks in industry. There's different people coming on campus all the time, hosting events, career fairs. And I try to tell students that even if you're not on the job market right now, if you're not trying to get an internship right now, it's good to start talking to these folks. you can start building up a social network maybe, but more importantly, you can figure out what they're looking for, and that can help you figure out what you're looking for. and another opportunity is. we end up hiring a lot of our undergraduate students to do different jobs in our department. a lot of folks start out as learning assistants, but also tutors, course assistants, and a few other things as well. That's great. Now we're gonna move on to our rapid fire round. I'll ask a question and just kind of the first thing that comes to your mind, what is the biggest misconception people have about applied math? The courses are too hard. I think that's the biggest misconception amongst our non-majors. they're challenging for sure. But I don't think they're beyond what a student can do. we want to make sure that we cover the theory, the applications, both, and that the students understand how they can use those mathematical concepts in whatever area they want to pursue. So whether they're truly an engineering major and they want to be a better engineer because they understand more of the mathematics, or they want to be an applied math major and use the applied math for its own sake. Either way, it's just very, very important that students understand that we teach challenging courses because Because we know what the students need to know and we are trying our best to help them get there. And in going through these challenging courses, they do grow a lot, which is what they're here for. And I think most of the students come away appreciating that. what habits or mindsets can help set students up for success? I think we talked about this a little bit earlier, but you know, don't procrastinate. don't wait to last minute on everything. Be organized, plan ahead. planning ahead for an exam that you have a week away from now, and planning out your degree plan. So that's kind of an overall theme. but also we do want to emphasize that it's important to do the work for yourself, Modern technology makes it so that maybe you can get away without doing some of the work yourself. But then you're not challenging yourself. You're not giving yourself that room to grow. and you want to give yourself that room. What makes this discipline meaningful to you? The most important thing for me is that it helps explain how the world works. that's the bottom line. Applied math helps you understand how the world works, whether that's weather modeling, climate forecasting, financial engineering, you name it. if you wanna understand how the world works, you have to understand the underlying mathematics. And it's foundational to a lot of the big things going on right now. Quantum, AI, space is big. All of that has a mathematical foundation. and students from our degree program, they can go and get jobs in those fields and meaningfully contribute. I'll just add on one more thing. we do have three or four classes in AI. it's not how to use AI, it's why does AI work? What's the underlying mathematics there? We have courses in the mathematics of quantum computing, that course actually is coming online in this coming spring semester. So we do have lots of courses that students can take after they have covered the foundational work. That's good to know. Yeah, all of these emerging fields, there's always gonna be a place for knowing the basics and knowing the foundations. All right, last question. What is one takeaway you hope the listeners remember? I think applied math is fun. I really do. I think you get a lot of personal satisfaction just from taking a hard problem, studying it, figuring it out, and sort of being able to pat yourself on the back after you've solved it. And then as you get further and further into the degree program, you realize you can do that with bigger and bigger problems. Yeah, I agree with that. it's satisfying and empowering to understand how things work. Well, thank you both so much. Yeah, thank you. We did it. I am joined today by one of our engineering peer advisors, Kristen, and she is gonna talk all about her experience in the applied math major. Welcome, Kristen, to the podcast. Excited to have you on today. Kristen is one of our engineering peer advisors, and I will just let you introduce yourself. I think you can do it better than I can. I'm Kristen Fitzcharles. I'm a junior in applied math and I'm studying actuarial science with minors in economics and statistics. Well, thanks again, Kristen, for coming on. So, where are you from? What made you choose C U Boulder as your school? So I'm originally from Birdsboro, a small town in southeast Pennsylvania, I wanted to go to a school that was kind of like Pennsylvania. still gave me all four seasons, I wanted to be out of state and go to a really big school. and I originally wanted to go to Clemson but I was like I miss CU Boulder after having a visit here. I miss the mountains. I like the lack of humidity and I love the Wagyu burgers 'cause I'm a foodie. that's very specific. So if you want a good burger, go to the sink. Okay. Pro tip. well we're glad you did choose C U Boulder because here you are. so tell me a little bit about your major journey, how did you decide on your current major? Were you considering others? If so, what made you land on applied math? So I knew in school that math was my thing. but I just wanted to be a pure mathematician at first and then my grandmother told me about a friend that she had and she said that actuarial science was a really good mix of a really large challenge a little bit of business but But it still had the math that I wanted. and so from there I just went to college fairs looking for actuarial science. and I was only looking at schools that had mathematical sciences or applied math. I didn't really want to go into just math. And what have you found the most rewarding part of your major? If I were to look back at myself, I would have thought I was a genius if I looked at myself today as a senior in high school. your tolerance for math goes up. And it's really rewarding to see how much I've been able to do. And I thought, I'm just like an average student. and then I come here and I'm like, Wow, I'm average but I'm really doing great things. I love that. And flip side, what's challenged you the most or been the most challenging as you've gone through this major? So I have to take exams for actual science. So the hardest thing was taking those professional certificates and exams at the same time as trying to take my classes. and then also trying to balance having relationships with people and having time to go out and have fun. that's the most challenging part. And hopefully I have it this year. But you've got it down. Well yes, we're gonna get into that later for sure. so when you started in this major was there anything that surprised you it really surprised me the difference between applied math and math. I just thought they were the same and I thought they were the same major. Mm-hmm. and then the more classes I took in applied math I realized this isn't like high school math and math is the math department is a lot like high school where you just get to know the formulas, the theorems and just have to apply those. Where when you're in applied math it's real life examples and you have to think outside the box. we talk a lot about the difference between applied math and math. So I appreciate that perspective. so other than obviously building a lot of your math skills, what are some of the biggest skills that you've developed in the majors so far? So this can be like ability to utilize a certain software, soft skills like communication, really anything. I mean, I could say like all the coding I've learned and all the things like theoretically. but I think in engineering as itself or just applied math you learn resilience. everything's gonna be hard in this major and in any engineering field, but you're going to come out on the other end, if you just put time and effort in. so resilience is the biggest skill I've learned, Well, kind of along those same lines of resiliency, what has helped you succeed academically? So I just found out this year that I have anxiety and I might have ADHD. Mm-hmm. And so I didn't know these two things my first two years of college and so this semester I focused on structure. I stay on campus from 7 AM to 5 PM every day to get my homework done so that I can go home and I don't have to do anything or I don't have to do a lot. and I feel focused while I'm at school. but at the same time, I also have been doing time blocking. So I'm putting in those breaks and those times that I can just do whatever I want to. I can go on my Xbox. I can go on the internet and everything and just watch shows. so just having that structure has helped. I have heard the tip before of like treat school like a full time job. Cause it is really nice to go home and just not have to worry about those things. what's been one of your favorite classes so far or project so far? So I have two classes, I couldn't choose one. one was differential equations and linear algebra. it felt like I was able to take the math skills that I've learned from Calc one through three and use them. in real life examples, I feel like in calculus I didn't have that where I understood why I was using it or how it could be used later. 'Cause they're really foundational topics that don't strictly play a like part. but differential equations definitely kind of realize how much I love math again. so we did a few projects, and one was on a bridge and I had to make a bridge and I based it around making a new bridge for Farsi Bridge over in the other end of campus. It's apparently one of the oldest bridges in Boulder. and then I'm actually taking it already started good, but wow I'm starting to take Stat 2600 this semester. It's intro to data science, and the professor teaching. it really well and he keeps everybody engaged you learn so many skills in that class, even in the first week. So I was liking that. It also kinda opened up maybe on changing my emphasis. so it gave me a little bit of a different perspective on a job I want to do. great. you have tips for students trying to choose an emphasis? I would say write down all your values on a piece of paper and then add in what you value in your like spare time. So one of my biggest values is when I have kids, I wanna be able to spend time with family. I do not wanna be at work hours and hours. but also I'm a first gen student. So, I just wanna give other people the motivation to do better than I did. so those are my values. but anything, even just graduating was my reward. Yeah, that was that was your goal that you were getting to. yeah. Good. Are there any clubs or organizations you recommend to getting involved with? for this major or just in general on campus? I'm just gonna promote my club first. So I started the C U Actuarial Club. I think it was my freshman year of college. and it was just supposed to be a bridge between all of the different majors that are interested in actuarial science, 'cause there's a lot of different majors. but also I was really involved my first year. So I went to the Mahjong Club, I went to databuffs and women in finance. and out of all the clubs I've been in, the Mahjong Club was the best club I was in. They always felt welcoming That's awesome. And also can you describe actuarial science for anyone that doesn't know what that is? Yeah, so actuarial science is what I describe as you use calculus and statistics. I know it but you use those to make insurance premiums. you can also work in health consulting, but it's usually used in government jobs such as pensions or insurance. so it's more of like a probability of you getting in a car crash at this certain age for like auto insurance and then some other things for like health insurance. So very applicable to everyday life. Yeah. And have you done any industry work like internships, research, et cetera? Yeah, so I did one coming out of my freshman year. While it wasn't in the emphasis that I wanted, I was able to get an internship back home from Penske Truck Rental. I was a consumer reservation specialist, which just means I was working in customer service and sales. So I learned a lot of sales information they pushed me to do my best every day and they wanted us to have more sales and more sales but it didn't feel like it was a company thing. It was a we wanna see you grow. it was a great job. That's great. And do you have tips for trying to get internships or research or getting involved? Anything that worked for you? Nowadays it's the people you know. Make every connection you can and if someone knows LinkedIn around you, find them and tell them that they need to help you. because I try to make my LinkedIn the best that I possibly can. and that's that's helped me a lot. but I always say for resumes, put more on your LinkedIn than you do on your resume so it doesn't get flagged as AI. Wow, good tip. And then what kind of career paths are you considering in parentheses? It's okay if you don't know. Yeah. so originally I wanted to be an actuary. at first I didn't know if I wanted to go into the casualty route, which is like auto and home, or if I wanted to go into health and life. so I kind of finally decided last year I was like, I'm gonna go into the casualty route. And then this year I took a class and now I'm interested in data science and I didn't realize how much I liked coding. so I think right now I'm going on the track of the data science route. But if you need any help with the actual route, I'm still good with that. I know that subject inside and out. I'm a little scared about the data science 'cause I don't know anything about it. Yeah, yeah. What are your plans for like exploring that side? Do you have any ideas of how you're gonna get a better sense other than taking classes of course? I'm actually looking for an internship currently. Okay for the summer of twenty twenty seven. and I'm talking to one of the I would say best professors in the statistics department. he's a super approachable guy. So it does help. Okay. I think we covered most of the main questions and now we have rapid fire. So first thing that comes to your mind, let's go. What is the biggest misconception people have about AP PM? A P PM's hard and professors don't care about you. they do care about you if you're trying. Yeah. If you don't try, they don't want to put the effort in because you're not putting the effort in. Right. and yeah, APPM is hard and you're an engineer. You you gotta work through it. Mm-hmm. Yep. And then how do you balance academics with life outside of school? First of all, I eat. make sure that you make time for eating. I know a lot of people are like, I forgot to eat all day. I'm like Why didn't you put a break for that? and also pack snacks. if you're in your sophomore year, I know you have a meal plan, you have options. Right. But if you don't, at least have a granola bar in your backpack. and kinda on the time blocking thing, make time for the people and things you love. I am a bowler and I haven't done that for the first two years. so I'm gonna start back up again. I love that. So make time for the things you love or your mental health will go down. And then knowing what you know now, what advice would you give your first year self? Read the textbook and also go to office hours. everybody says go to office hours, but I usually plan out when I'm gonna go. It's a lot easier to tell when people are available and then I don't miss them. but for reading the textbook Sometimes it'll be physically reading it and sometimes it will be just solving example problems and solving your own. you understand the topic then before you go into class and it doesn't feel like the professor's just writing things on the board and you have to code them afterwards. Yeah, yeah. Good advice. And then lastly, what makes this major meaningful to you? Specifically for me, I moved fifteen hundred miles to study one of the hardest subjects out there. and I'll make it through and I'm proud of that, especially as a first gen student. because of this, I give my future kids the option to go even farther than I did. And then I will have you talk about one last thing. So you're an engineering peer advisor. do you wanna explain to the listeners what engineering peer advisors do, how you're here to help? Yes. we are current students that work with your academic advisors to help with advising needs, such as course registration, schedules, or even if you just wanna talk. I like to talk. I don't know about my coworkers, but I love to talk. but we are available every day of the week on Buff Word Advising. just make sure it says engineering peer advisor. if not, you might be going to career services or a coach or your academic advisor. So just be sure to read the name of it. Yeah. so I just wanted to mention that we are actually looking for new peer advisors mostly every semester. try to say after your first two semesters of being on campus. if you are interested in that, look on the newsletters. Sometimes it can be called CU Engineering today, and sometimes it could be called Engineering Connections. It just depends if you're a first year or not. Great. And I'll make a couple of plugs. They have drop ins during the week. They also have an email. It's just engineering.advising at Colorado.edu. Most likely if you reach out to that email, one of our peer advisors will be answering back. So they're available for all kinds of questions. They are fully trained on the scope of basic registration questions. How do I add a class? How do I drop a class? Is this gonna be too big of a workload? A lot of the times they know. Better than the professional advisors. I have never taken Calc 1, Calc 2. I've never taken physics one. So sometimes I don't have the knowledge that you want of is this gonna be too hard of a course load? How does this structure of my schedule look? They're great for questions like those that really need that student perspective. But that's it. Do you have anything else you want to say? Leave us with? I hope someone chooses applied math. We have a really small major. but all of us have our own specific route that we're taking. Awesome. Well, thank you so much for coming on the podcast and giving your perspective. thank you, Kristen. Woo! We did it. And that wraps up our episode on applied math. I hope you found this interesting, useful, valuable. Hope you learned a little something. And as always, keep your ears and eyes open for another episode. Bye y'all.