# Blake Weimer

### From www.norsemathology.org

## Contents |

## About Me

Hello! My name is Blake Weimer and I am currently studying Math, Stats, and Economics at NKU. I'm from Campbell County, so I have lived in Northern Kentucky pretty much my entire life. I really enjoy board games and outdoor activities such as camping, hiking, and backpacking. My favorite board game of all time is Settlers of Catan, and whenever I play I like to keep game statistics such as how many times a number gets rolled. Some of my favorite outdoor places to visit are the Red River Gorge in Kentucky and the Great Smoky Mountains in Tennessee. I have already been on one backpacking trip this year in Virginia with my friend Cornelius, and I have plans this summer to go to Nevada as well as a road trip to Rocky Mountain National Park, Arches National Park, and Zion National Park. One day I would like to thru or section hike the Pacific Crest Trial, Continental Divide, and the Appalachian trail. Alongside the outdoors, I really enjoy mathematics and statistics, hence why I'm studying them in college!

**Early Mathematical Life**

Growing up, I've always enjoyed school and learning. I went to a private grade school and during my time there my favorite subjects were either social studies or science, not math. It wasn't until about middle school when I really started to enjoy math, especially in 7th grade when I had a teacher named Mr. Sketch who taught geometry and pre-algebra. I remember there was a math contest and he had asked a few students if we wanted to participate and I was one of those he asked (I don't think I did so great). Unfortunately, the next year for algebra I didn't have Mr. Sketch and the teacher was not particularly the best. As a result, my foundational algebra was lacking. In high school, I switched to public school and we had to take a placement test for whether we could take geometry as a freshman instead of algebra. Well, like I said, my algebra skills were lacking so I did not qualify. So, throughout my high school career I always felt like I was "behind" in math in the sense that I knew I could be learning so much more but I was stuck a year behind. However, despite these setbacks, I found that I was really great at math and this is where my love for math truly began. My favorite math subject in high school was Algebra II which was taught by Mrs. Carrigan. She was an excellent teacher and she saw my potential. She was very encouraging and knew that I would go on to great mathematical things. My overall favorite subject, however, was economics which was taught by Mr. Goss. Though an econ teacher, Mr. Goss taught me to really work hard for the things that I want to achieve and he too has encouraged me and helped me, even throughout college. A lot of my favorite math problems were actually found in my econ courses. To me, it's cool to see how the math I am learning right now has been reduced to a simple level that I was learning it in my econ classes without even realizing it. Things like elasticity are simply just derivatives, finding the shutdown point for a firm is really just a minimization problem, the money multiplier is a converging series, just to name a few. As a result of AP Micro and AP Macro, I would go on to study economics in college. At the time, I didn't realize what an influence economics would have on my mathematical life, but it has brought me to where I am now.

## Recent Experiences - College Career

I started college as an economics major. Since the program is short I was able to double major, but I wasn't sure what I was going to do yet. Fall of freshman year I took STA 205. STA 205 was my first statistics course I have ever taken, and from my previous math experience I was nervous. Fortunately, I had Dr. Buckley as my professor and she was great (and I'm sure any other professor would have been too!). I remember visiting her during office hours and she convinced me to join the math and have mathematics be my second major. And thus began my college mathematical journey. Spring of my freshman year I took Calculus I and this time I was more confident in my abilities. Dr. Christensen was also a great professor. Looking back, I'm very glad that I took these classes in college because I don't think I would have made the same decisions I would have if I had taken them in AP. After taking calculus, I realized how much I had been missing out on knowing derivatives and integrals, and this knowledge would have made my intermediate economics courses a lot easier since calculus is currently not a requirement for econ majors at NKU (though I really think it should be!). As I continued throughout my college career, I realized that being a statistics major might complement my economics major better than a mathematics would. I had taken Econometrics I and II my sophomore year and I was sort of understanding the statistics behind regression but at the same time I really wasn't. I didn't really comprehend why we were doing what we were doing and this is in part because I was much further in my econ degree than I was with math and statistics. After meeting with Dr. Buckley in the spring of my sophomore year, she asked me "Why not do econ and math and stats?" and I thought about it and realized it was very doable. So since then I have been working towards a triple major in economics, mathematics, and statistics. And I'm almost done!

**Courses I've Enjoyed**

So far, I've enjoyed all the math and stat courses that I've taken. Some more than others, but my favorite courses have been the SAS statistical computing course (STA 360), linear algebra (MAT 234), statistics with simulation and resampling (STA 394 topics), statistics II (STA 341), and regression (STA 316). I really like these courses in particular because they're very applied courses, but they also have enough theory to them to balance them out. The SAS course was great not only because I got certified in SAS but also because the challenge of coding is something I had never really experienced yet and it was a course that made me think of many different ways to get the same results. Linear algebra was also one of my favorites because I liked how interconnected the topics were and we also had some applied linear algebra topics (Dr. Waters always mentioned there should be 2 linear algebra courses - one theory and one applied - and I agree!). Statistics with simulation and resampling has been a great course too because we were introduced to null and bootstrap distributions and the application of those is amazing. Plus, learning R has been a bonus. Statistics II has really solidified my statistical foundation and really it's the core to my understanding behind all the other statistics courses that I've taken thus far. Regression has been great because I took econometrics and this course has helped me better understand what I've learned so far. It's also shown me that I've really only hit the tip of the iceberg with understanding regression and I'm excited to continue to learn new techniques.

**Tutoring and Internships**

Another aspect to my college experience has been tutoring as well as working at the Burkardt Consulting Center (BCC) and the Center for Economic Analysis and Development (CEAD). In high school, I really enjoyed helping my classmates understand economics. As a senior in AP Macro, I would stay after school and help tutor AP Micro students and I loved it. Freshman year, I became a PLUS tutor for principles of micro and macro as well as for STA 205 and I really enjoyed it. Unfortunately, I had to stop since I got good student job offer working at CEAD. Now, I still work at CEAD, but I also work in the Math/Stat Lab as a tutor as well as in the BCC. This semester I was also offered a TA position for the intermediate microeconomics course. I think the favorite out them still has to be tutoring and I get my fair share of that through the Math/Stat Lab as well as the TA position. That's not to say that I haven't enjoyed BCC or CEAD. Both have been really great for me to apply my stats and econ knowledge to real world examples and I'm really excited to work at both over the summer.

**Things I Would Have Done Differently**

If there was anything that I would do different is that I would have liked to start taking my math and stat courses sooner. I only took calculus I the fall of my freshman year and I slowly trickled more and more math and stat courses in until I fully decided for math and stats to be my majors. Another thing that I think would have been helpful would to have been able to go into econometrics with STA 316 and STA 341 under my belt. I think that those two classes would have made me better understand econometrics. At the same time, the I retained the knowledge I learned from econometrics and it still has helped be throughout my current statistics courses.

**Where to Next?**

As I'm nearing the end of my college career (senior in standing), I'm not really sure where I'm headed next. Tutoring has really shown me that I enjoy teaching others and has made me consider teaching as a profession. At the same time, CEAD and the BCC have made me want to possibly work in the industry as some sort of consultant. Either way, I believe grad school is going to be a next step but I'm not entirely sure what I want to pursue yet. A masters in either applied economics or statistics have piqued my interest recently, perhaps maybe even a PhD, though I'm still not sure yet and I'm going to spend the next month or so deciding.

## Spotlight on Mathematics

**Game Theory, Cicadas, and Primes**

One thing that I love about mathematics and economics is that they're everywhere in the world, and one of my favorite topics shared between the two is game theory!

So what is game theory? In basic terms, it is a framework for portraying a social situation among competing "players". It is essentially the science of strategy and internally, its how people make decisions. A game is a model of an interactive situation between two (basic) or more rational players and the goal is for each player to maximize their payoffs based off the other players decisions. There are strategies and equilibrium, one such being the Nash equilibrium named after John Nash (mathematician and economist) where players end in an outcome where neither play can increase their payoff by changing decisions.

**Classic Example - The Prisoners' Dilemma**

A classic example of game theory and a zero-sum game is the prisoners' dilemma. The story goes like this:

Two accomplices, A and B, are accused of a crime and are sat down for interrogation separately, so they cannot cooperate with each other. Each prisoner is given the choice to confess or to remain silent. If one confess and their partner remains silent, the confessor will be let go and the while their partner will face 20 years in prison. If both confess, they each receive 5 years. If they both stay silent, they each receive 1 year. So, what's the outcome?

To see the outcome, consider prisoner A. From prisoner A's perspective, his choice is dependent on prisoner B's choice. If B chooses to confess, A should confess since A would receive 5 years for confessing instead of 20 years if staying silent. If B chooses to stay silent, A should choose to confess since he would receive 0 years for confessing instead of 1 year for remaining silent. So no matter what, A should always confess! This is A's dominant strategy: to always confess!

The same outcome is true for prisoner B. Given A's choices, prisoner B should always confess! So B's dominant strategy is to also confess! Therefore we have reached an equilibrium where both prisoners confess and each receive 5 years in jail. This is also a Nash equilibrium since neither play can be better off by changing their decision given the other player's decision.

There are of course other scenarios of the prisoners' dilemma such as one where the prisoners are allowed to cooperate or scenarios of repetitive games. The outcomes might be different, but the way of reaching those outcomes remain the same! Given the choice of your opponent, what is your best choice?

This can be extended to all sorts of subjects such as psychology, economics, mathematics, ecology, and much more!

**Cicadas and Primes**
As many people might know, 2021 is a special year for our region. It's the year the Brood X Cicadas emerge after spending the last 17 years in the ground. The last time they emerged was in 2004 and they won't emerge again until 2038. What's interesting is that cicadas have brooding periods of either 13 or 17 and that these numbers are prime numbers. They're only divisible by themself and 1. So how did this come to be?

**Predation Cycles**

In nature, predator and prey cycles often line up with each other. They're synchronized. Now, suppose cicadas had a 12 year brooding cycle instead of the 13 or 17 year cycle. Well, 12 is an easily divisible number, so any predator with a 2, 3, 4, or 6 year cycle will coincide with the 12 year cicada cycle and the predators could adapt to depend on the cicada feast. By having prime number cycles, cicadas minimize their risk of being taken out by predators. For example, suppose that there's a brood that emerges every 17 years and a predator with a 5-year life cycle. The cicadas will only face a peak predator population once every 85 years (5*17)! Another interesting component to these cycles is that they're used to protect one brood of cicadas from another brood. Broods are typically geographically separated. 13-year and 17-year broods do want to swap their genes because this would mess with their respective brooding cycles. As such, since 13 and 17 are both relatively prime, this minimizes their chance to emerge at the same time. In fact, in 2015 brood IV (17-year) and brood XXII (13-year) emerged at the same time! And this won't happen again for another 221 years (13*17) until 2236!

**Application to Game Theory**

So how does game theory apply to cicadas? In paleontologist Stephen J. Gould's essay of "Of Bamboo, Cicadas, and the Economy of Adam Smith", he compares these cicadas to the boom and bust cycles of the economy. The boom-and-bust population cycles can be devastating to creatures with a long developmental phase such as cicadas. Most predators have a 2-to-10 year population cycle, so a 12-year cicada brood would be a feast to a large variety of predators! So by this logical reasoning and evolutionary conditions, any cicada with an easily divisible cycle is vulnerable. Gould goes on to describe how Adam Smith's invisible hand is at work. Each individual cicadas is working in their own self-interest. But collectively, they can work together to create a highly organized and mathematically precise behavior that benefits the group as a whole. This is the essence of game theory. Given the population cycles of predators, what is the best population cycle for a cicada? It's one that is prime!

## Citations

[[1]] Mathematicians explore cicada's mysterious link with primes

[[2]] Periodical cicadas

[[3]] 50 Mathematical Ideas You Really Need to Know

[[4]] 50 Economic Ideas You Really Need to Know

[[5]] Game Theory - Investopedia