John Nuestro

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Contents

Early Life

I was born in Manila, Philippines, and moved to the U.S when I was around six years old. I have now lived in Northern Kentucky for the past 15 years. I went to Hinsdale and White's Tower for elementary school, Woodland for middle school. I never really knew what I wanted to do throughout my life as my hobbies were building Legos and playing video games, and at the time those weren't the best life choices. All I knew was that I was good at Math. However, math wasn't my first choice in my career. My first choice was computer engineering and it wasn't until my sophomore year of college that I realized that I wanted to do Mathematics.

Early Experience with Math, Stats, and STEM

The earliest experience of "real" math during high school would have to be Pre-Calculus and Calculus. I never took any statistics class during high school mainly because only one of them was offered and it never fit my schedule considering my college, AP classes, and band classes.

The earliest record of STEM, math, or stats experience I can recall is an introduction to an engineering class that I took sophomore year. In this class, we were assigned and collaborated in random groups to do different projects. These projects consisted of a small motor car, an egg container that prevents the egg from breaking, etc. After our build times, the groups would be set to compete to see which group was the most successful. We would then have to accurately sketch out the project we made to the centimeter.

Through High School

I went to Scott High School in Taylor Mill which is a few minutes from campus. During high school, I took math classes starting with Algebra to AP Calculus BC.

Influences

My influence in my decision to go with a mathematics major was my Calculus teacher, Mrs. Meyer. She was the one who convinced me to take AP Calculus BC. As a student who was lazy and didn't feel like doing much during high school, this was a feat in itself. I had decided to make my senior year not challenging and generally "easy," so for me to decide to do that was surprising to me. I had Mrs. Meyer as a sort of "homeroom" teacher for all four years of my high school as well as being my Pre-Calculus teacher and Calculus teacher for the last two years. Throughout the years she helped me learn how to study and was also there for me during tough times in my life. I also spent a good amount of time aiding her in grading and teaching. I also helped with after-school tutoring for her Calculus students for a few years.

To this day, Mrs. Meyer is ultimately one of the few reasons why I decided to become a math major and I cannot thank her enough.

As for past references, I didn't have any historical influences, not even now. I tend to look more on the side of the present for influences. There was no particular historical math figure that made me want to go into math. I thought they were great people to read about and what they discovered and figured out was life-changing, but none of them were ever really the reason I made the decisions that I have made.

Favorite Subjects

My favorite subject through high school was all of the math subjects. Only because I found it interesting and fun to learn about different problems and how to solve them. My favorite subject during high school was AP Calculus BC. It helped with my transition to college and helped develop my critical thinking skills that early high school classes didn't.

As for my favorite subject now, my favorite subject that I have taken was Linear Programming. Linear Programming was using linear equations and their behaviors to optimize problems. It felt like the love child between math and programming. It was quite an interesting subject, and I would like to dip my toe in it a little more.

Favorite Problems

My favorite problems come from AP Calculus BC and they were integrating problems. Integrating problems had so many methods to do it and my favorite one, in particular, was u-substitution. U-substitution was interesting to me because it seemed like a cheap, but smart way to solve a difficult problem. It made problems that were a bother to solve so much easier and simple.

As for my favorite problems right now, it goes hand in hand with my favorite subject right in which my favorite problems are Linear programming problems for the same reason why the class is my favorite subject.

Recent Experiences

I started my college career at University of Cincinnati as a Computer Engineering Major and it wasn't until my Sophomore year that I transitioned to a Math major and then the semester after was when I transferred to NKU. However, I have not been able to experience the NKU culture because I transferred during the COVID Era. I have also spent some time tutoring and aiding for my old high school.

Career Thoughts

For a future career I would like to get into something math and computer science related. In doing some research I would probably like to get involved in cryptography if I could and hopefully take the Cryptology class at NKU next Spring semester so I could dip my toe in the water. However, there are numerous possibilities with a math major and computer science is a field that I would definitely be interested in trying out.

Reflections on my Studies

My studies have been confusing with my change in majors and my change in school. Math is enjoyable to me because of all the patterns that I can see in all the different math classes I have taken. Being able to find patterns and figure them out fills with me a sense of enjoyment. In addition, the critical thinking needed to solve mathematical and logical problems allows the gears in my head to turn like no other subject can.

Throughout my courses, I have taken a various amount of classes that were math, engineering, and computer science-based but in the end, my favorite subject to learn about was linear programming and linear algebra. The idea that linear equations can do so much while being such a simple concept with definite properties made it more interesting. In high school, I thought Calculus was the doorway I needed to get through to go into any STEM field, but linear programming and linear algebra have helped me see that something as "simple" as linear equations.

Aside from math classes, my favorite subjects were any coding course that I have taken. While I would like to give a specific course, I have taken numerous classes involving different languages. Each of them taught me numerous coding practices and a better understanding of the coding process. While coding is frustrating it has felt like it had been the most satisfying and rewarding subjects if you get it right.

However, my college career has not all been rainbows and happiness. I have taken numerous classes that I ended up losing interest in or just ended up not enjoying. One example was digital design, a class I took while I was attending the University of Cincinnati. Digital design was the teaching of how computer chips worked as well as the different gates and systems that were invented to make the computers that we use today possible. Learning the subject was interesting, and the lab that came with it was certainly educational, but in the end, I realized it wasn't for me.

Besides classes that lost my interest, I would say that my college career could've been better if I didn't have to deal with the COVID Era. The COVID Era made me less motivated in all of my classes and learning. I'm hoping that the next semester will be better for me in terms of my ability to learn and focus. I could've also made more connections at the University of Cincinnati, and I wish I had more time to make connections here at NKU considering that I only have about a year left.

Related Experiences

I have worked on some small coding projects on the side outside of work and have contributed to small amounts of work to my friends Discord bot. However, none of these small projects were anything significant. I have also tutored Calculus at my old high school and aided for the same teacher as well.

What's Next?

I am unsure of what's after my college career. I am not planning on going into graduate studies, and I originally planned on being a computer engineer but I ended up switching majors so anything could happen. I didn't particularly enjoy tutoring nor did I have the knack for it. Because of that, I don't see myself going into a teaching profession. I am considering applying for an internship to see where my interests take me and see what I enjoy and what I would like to pursue. While it might have been better to do that earlier in my college career, a math major has opened to many different possibilities that my possibilities and choices are essentially endless.

Mathematical Spotlight

The Fibonacci Sequence

Throughout this course, I have had an obsession with one piece of math and that piece is the Fibonacci sequence.

For those that don't know about this amazing sequence, the Fibonacci sequence is a sequence of numbers that is progressed by adding the previous two terms before it. Here is the equation:

Image:fibEq.jpg

The reason for my obsession with this sequence that provides almost no usefulness in the daily life of a human being in the 21st century began with a YouTube video my junior year of high school. A video series that I will link at the bottom of the page for anyone curious about it. In the video, the creator begins with a talk of spirals and all the different kinds of spirals you can make and then wonders to herself how you could achieve a "perfect" spiral. She then introduces the Fibonacci sequence and shows how the sequence itself is shown all over nature. She first shows how different pinecones (and a pineapple) all contain a Fibonacci number within their spirals. To further prove her argument, she begins to count the spirals on flowers which then showcases a Fibonacci number of spirals. Here it is on a sunflower:

Image:sunflower.jpg

and Vihart, the creator of the video I mentioned, has said that sunflowers have been known to have spirals as big 144. The "founder" of the Fibonacci sequence is Leonardo Pisano (Fibonacci). It is said that the reason he even discovered it was that he found that rabbits multiplied in the same progression as Fibonacci numbers i.e. 1, 2, 3, 5, 8, etc. His work is in his book, Liber Abaci. Setting Pisano's work aside, the reason why I put founder in quotes above is that the Fibonacci sequence was also apparent in Indian mathematics, but the Fibonacci sequence made its first appearance outside of India in Pisano's book.

Doodling in Math: Spirals, Fibonacci, and Being a Plant: Part 1

The Golden Ratio

The golden ratio, otherwise known as Phi, can be obtained from the Fibonacci sequence, but it is not a direct consequence. The reason is that the Lucas numbers can also be used to obtain the golden ratio and can closely compare to the Fibonacci sequence. However, this spotlight is on the Fibonacci sequence, so we set that aside for now. Who am I as an undergraduate mathematics major to say that the golden ratio is a consequence of one set of numbers but not the other? For all I know, it's probably not a direct consequence of either, and it is a direct consequence of nature.

The golden ratio is 1.61803398875 and so on. For those that don't know, the golden ratio can come from the Fibonacci sequence by dividing each pair of adjacent numbers; as the numbers you are dividing increase, the quotient ends up slowly getting closer and closer to the golden ratio:

3 / 2 = 1.5

5 / 3 = 1.666

8 / 5 = 1.6

13 / 8 = 1.625

21 / 13 = 1.615

34 / 21 = 1.619

etc...

Much like the Fibonacci sequence, the golden ratio is seen throughout nature as well. It is apparent in how plants grow their leaves to maximize their exposure to sunlight. If you measure the angle between the leaves, then the angle you get is the golden ratio.

Fun fact: The conversion rate between miles to KM is 1.61 which is close enough to the golden ratio. So if you ever need to convert between miles to km then just remember the golden ratio and multiply! If that doesn't sell you on the Fibonacci sequence and the golden ratio, then I don't know what will.

Doodling in Math: Spirals, Fibonacci, and Being a Plant: Part 2

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