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The name of my art piece The Series Song. It is a parody of Dean Lewis's "Looks Like Me". My chosen math concept is the different convergence tests and my art piece illustrates it by going through the thinking of a typical student when they  are figuring out which conversion test to use for a series. It displays the struggle of choosing a test and the requirements of each of the different tests.

-Yasmine Morsy

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This story explains the concept of critical numbers, factoring, and quadratic equations. Through the use of a fictional superhero world, it depicts how zero is X's critical number. But, along his journey, X uses quadratics and factoring to overcome his archnemesis and emerge victorious.

I found this project very fun and enjoyable. It's rare that I'm able to engage in creative content like this in college, so creating a comic-book-like story to explain a mathematical concept was quite exhilarating. I initially struggled to incorporate an in-depth explanation of how quadratics work, but I think I ultimately did a pretty good job of explaining it and weaving it within the story well.

-Daniel Mendelson

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My art piece captures the mathematical concept of a two-sided limit using the character Gojo from the series Jujutsu Kaisen. In calculus, a two-sided limit is when a function approaches the same value from both the left and right-hand side but never actually reaches it. I decided to use Gojo to represent this concept because his ability works in a similar way. When an attacker tries to hit him, they get infinitely closer, but never actually hit/reach him, which perfectly mirrors how a limit behaves. I showed this by having Gojo stand the the middle, while two attackers, the left and right-sided limit approach/attack him, while his infinity prevents them from ever making contact.

Having to use my "creative" side to understand a math concept was a bit odd at first. I didn't understand the correlation between the two, but now, after looking at some math art pieces and having to create my own, I see how they are intertwined. So having to think of a math concept artistically was weird at first, but overall, sort of fun and rewarding in the end.

-Troy Ortega

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My art piece, Math at Disney, shows how math can be found in fun and creative places like theme parks and cartoons. The piece focuses on patterns, curves, and motion inspired by Disney rides and animations to represent concepts like geometry, angles, and functions. If this were shown in a cartoon or online class, the introduction to the method would explain math in a colorful and interactive way so students could connect formulas to real-life experiences instead of only seeing numbers on paper. The goal of the piece is to make math feel more exciting, visual, and easier to understand.

Working on this project pushed me to use my creative side in a way I normally do not when studying math. Usually, I think of math as solving problems step by step, but creating art around a math concept helped me look at it from a different perspective. It made the idea feel less intimidating and more connected to imagination and everyday life.

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"A Lens of Math" I photographed various objects, insects, and celestial bodies that I felt captured and specifically could be used in application with topics covered in this course, alongside fundamental topics such as the area under the curve and the infinitesimal width. The text overlayed on the images helps to see the physicality of the objects and helps represent where these ideas can be used or thought of in a different context.

-Angelo Volokh

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Math-Artist’s Statement

Title: Visual Exploration of Related Rates
Mathematical Topic: Related Rates (Calculus 1)
Prepared by: Alim Kham, Zeqian Mo

Key Ideas:
Our project focuses on Related Rates, a topic in Calculus that helps us understand how changing one quantity affects another over time when both are connected. Using derivatives, we can find the rate at which one variable changes based on the rate of change of another. This idea applies to many real-life scenarios where motion or growth happens at the same time across different quantities.

For this project, we created a short video showing three everyday examples that demonstrate Related Rates visually: pouring water into bottles, the growth of a shadow, and the motion of clock hands. Each scene shows how a change in one measurable value causes another to change at a related but different rate.

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The mathematical concept of divergence and convergence of a limit is presented here by the different colored waterfalls representing different functions. The different functions are growing in the water supply which continues to increase until it approaches a value; this shows convergence where a function will eventually approach a value.  The last waterfall flows infinitely in the void where its water supply is increasing and never approaches a value which shows divergence.

Initially, I found it difficult to tie a mathematical concept to my creative/artistic side because I usually don’t associate those two groups together. When I got the idea to use a video game to explain the mathematical concept I chose, I found it really fun to connect the two things and to just have fun playing a game I like. It challenged me to think of ways to explain convergence/divergence in limits which helped me understand this concept further.

-Eliana Yee

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The quest to retrieve the sacred Snickers lies along a mysterious path of a mathematical concept of integrals and series, whose convergence determines your fate. If the path converges, it leads to the sweet reward at a finite destination: the Snickers. But if it diverges, you're trapped in an endless journey down an infinite road, forever chasing, but never reaching that chocolatey salvation. This comic shows how series and integrals (the road) don't always converge to its destination, but can also diverge and approach an infinite number (road).

My experience in expressing my creativeness with mathematics and understanding it was  puzzling at first. I was stuck in thinking how I could express math through art, but then I thought about what mathematical concept stuck with me the most, which was whether or not an integral/series converges or diverges.  I later figured that this could be related to destinations and roads. This correlation gave me a bit more understanding with how convergence and divergence can work.

-Miguel Vasquez

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This art piece reflects the mathematical concept of determining a series' convergence or divergence by first deciding which series test should be used. Certain tests require specific conditions to be satisfied in order for them to be used while others are based on technique and strategy. This process is shown through my work as the plug represents the series given while the different outlets symbolize the various tests you can choose from to conclude convergence or divergence. Since the series given can be manipulated to satisfy the format needed to use the P-Series Test, the plug is shaped in a way that fits into that outlet.

By portraying the process of determining which series test to utilize artistically through my art piece, I'm able to visualize this operation mentally and, therefore, better understand how this concept works.

-Naila Surahmat

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I am inspired by M.C Escher drawings and this drawing inspired by his study for spirals.

Main concept is rotating around a curve and following along a curve. By following the main curve and rotating around it (main curve = red line) it is forming a tube around it.

Then I’m subdividing the tubes represented by the elipses. It helps me understand better how to find the areas with axis or curve rotations.

-Jasmine Aye Chan San

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This artwork uses Hooke’s Law and Work to represent motion and energy in the example of a pogo stick. The drawing shows a guy straining to compress the spring, then launching joyfully into the air. To tie in the math, I included the integral form of the work equation directly in the drawing's motion lines. This shows how work is calculated as the spring compresses which matches what’s happening visually. The farther the spring is compressed, the more work is done, which is also captured by the guy's facial expression and body motion.

Creating this helped me better understand why the work equation involves integration. It represents the total effort as the force changes. By drawing it, I realized that the spring gets harder to push the more it's compressed, which I always kind of knew, but now I fully get why.  By drawing it, I understood that the spring gets harder to push. The visual helped solidify how calculus explains real-world motion.

-Anthony Musnit

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In this children’s picture book, Defying Infinity, a young sea turtle asks his mom to explain the idea of infinity. The mother turtle, excited by her son’s curiosity, explains that in some instances, an infinite number of numbers can be added together but not reach infinity. She introduces her son to the concept of convergence via the Geometric Series Test (GST). As they count Star Fish in their home waters, the mother turtle demonstrates that when the absolute value of the common ratio, |r|, is less than 1, the infinite geometric series will converge to a finite value.

I sometimes find it challenging to conceptualize the essence of mathematical formulas and theorems. I often feel that I can “apply them” as needed, but at times, I lack a deep understanding of why the property works. In the process of creating this piece, I found that I was able to better grasp the mathematical concept by trying to make it simple enough for kids to understand. This forced me to unravel the theory of the Geometric Series Test into digestible pieces.

-Joshua Matz

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This artwork uses the washer method from calculus to represent the volume of a tornado. The swirling shape of the tornado naturally forms a 3D rotational figure, just like the solids you get when applying the washer method. In the piece, I sketched the tornado as a wide funnel narrowing down, and overlaid circular cross-sections to show how each washer adds to the total volume.

Making this tornado helped me understand the washer method a lot better. Before, I just plugged numbers into the formula. But by drawing it, I could see that each washer represents a small layer of volume and when those are all added up through integration, they build the whole tornado. It really helped me grasp how calculus can turn something complex and irregular into something measurable.

-Edwin Hernandez-Avina

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My artwork shows integration with U-sub by displaying substitution within basketball. In the art piece it shows players lining up for free throws with each players jersey number representing a part of the function that's being integrated. On the right end it shows one of the teams coaches performing the U-sub by substituting out one of his players for a player on the bench. The piece then shows the coach getting ready to sub in DU after the player that was subbed out for U gets differentiated.

Choosing this concept for the art piece has helped me with the process of U-sub. I found that showing the steps that need to be done in order, while also using basketball as a visual to understand the subbing process has cleared confusion when it comes to setting up an integration problem that uses U-sub.

-Trevor Grosso

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The aim of my not-so-artistic piece was to define my understanding of the shell method and finding volume, specifically using Russian nesting dolls. Each doll, though poorly drawn, is meant to represent a hollow cylindrical “shell” (as named in the concept). Stacking these dolls within one another shows how these shells add up to a total volume when rotated around a specific axis, connecting to how in calculus, we would find an area being rotated around said axis. I included an outline of a cylinder as well to link back to the concept of the shells from the nesting dolls.

Drawing the nesting dolls just helped me remember the concept of shells better, as I think out of all the things we’ve learned I have already understood this most. However, seeing my own understanding of the shell method actually drawn out in front of me just reminded me about where exactly the radius, height, and thickness from the original integral/formula came from, helping me picture all the original shells not as just formulas, but actual layers (thanks to the dolls). It helped the whole thing feel more like an actual thinking process rather than just mindless integration.

-Aerin Ganatra

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The p-series test of convergence tells us whether a given series in the form 1/(n^P) will converge. When p is greater than 1, we know the original series will converge to a number eventually, where as when p is equal to or less than 1, we know the series will diverge to infinity. This can be displayed as a staircase to heaven.

For me, the p-series test stood out as a good & present example to use. With learning so many series tests, it definitely helped stick the p-series test into my brain. Additionally, I think it overall was great to represent convergence and divergence in a new way that helps my brain process something so abstract into a concrete or semi-practical environment.

-Jazz Beecham

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My art piece is a visual representation of the squeeze theorem, which is used to determine the limit of a function by comparing it to two other functions with known limits. The picture shown is a water balloon being compressed. Even when it is squeezed very hard, the water balloon casing confines the water within it.

I think doing this project helped bring out my creative side within math. Being able to visualize mathematical concepts is very important for me because it helps me connect the dots between different concepts and overall better my understanding of Calculus. Coming up with this concept for my art project was not too difficult because the "squeeze" theorem already presents a visual way to understand it.

-Annie Chiappe

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Our video exemplifies the classic joke of an infinite series of mathematicians walking into a bar. Similar to and infinite series converging to a finite sum, an endless line of mathematicians can still end up ordering a perfectly reasonable number of beers. My peers and I collaborated to play as the individuals making up the infinite number of mathematicians in a silent movie. Enjoy! We hope it made you laugh :)

"Choosing and creating this visual representation helped me better understand a geometric series by understanding that an infinite amount of terms, in this case, beer orders, may only reach one number :)" -Anaka Bamba

"While working on this piece, I gained a deeper understanding of how a series can be represented, both physically and conceptually. I also learned that math can be a little more enjoyable over a couple of beers with some friends." - Tony Hernandez

"Filming and being part of this video has definitely helped me understand what a converging geometric series looks like. After attempting many times to all come to an agreement of how we would portray this on film, it definitely solidified my understanding of an infinite sum of numbers converging to a finite number."-Cherise Lopez

"reating this piece helped me understand how an infinite number of terms can still result in a finite number which was something that felt abstract at first. By turning it into something visual and relatable, like people ordering drinks, the math became more real." - Heidi Pico

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The mathematical idea I choose was the sine^2(x) + cos^2(x)=1.  I choose this because that equation really tells us how important and how well it works together to equal 1, where we see this is on the unit circle and we get to see how everything well equal 1.

-Lester Vega

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I wanted to capture the counter-intuitiveness of the outcome when indeterminate limits get resolved after L'Hospital's rule gets applied. I find that when looking at at the function itself, without having the visualization of a graph, it's easy for me to have a degree of separation and not realize what's really going on, so the whole thing can feel magical.

-Conor Ney

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After watching the original Dragon Ball over the holiday, I noticed something pretty cool about Goku's Afterimage Technique that connects perfectly with calculus. When he moves so fast that he leaves those copies of himself behind, he's actually giving us a perfect visual for understanding rate of change. Those afterimages are basically his "clones" frozen in different spots are like snapshots of his position as he zips around. Looking at the spaces between these images, we can figure out his speed, just like when we calculate velocity in calculus. And when those images start blurring together, getting closer and closer? That's exactly what we're looking at when we study derivatives and instantaneous velocity.

-Daniel Knight

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I have taken photos for a long time and I tend to enjoy lots of linearity through various shapes. I wanted to see if the "math is all around us" concept applies to my photos. All but the last one shot on 35mm film.

I think it gives a focal line to the photos and highlights what is being centered. Its a cool way to see various shapes from certain angles and be able to pin point a specific function.

-Khalil Toubba

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This art piece combines the mathematical concept of limits with societal beauty standards. In calculus, a limit is about the process of approaching something without necessarily reaching it. Similarly beauty is not about meeting ever-changing ideals but about embracing the journey of authenticity and self-discovery.

-Heidi Pico

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I chose the mathematical property of functions, I chose it because I was originally thinking of a set, and then I wanted to try something that we learned a bit more recently. This drawing is a bijective function, where A is time and B is the rose. Every input of time has a different rose.

-Brenna Stewart

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Here is a partition of the rainbow of colors into small cute little handcrafted origami paper stars in a tall glass vase. The little stars each represent elements in this set of colors. I did change this from my original idea of subdivisions of triangles but I think little stars are more beautiful.

I think this let me understand a slight bit of the mathematical rigor used in creating various complex proofs or even complex sets. This project took hours of making these little stars out of paper by hand this semester. I know many difficult proofs can take years. The only solved Millennium prize problem (Poincare conjecture) took 7 years to solve by one man who had over 200iq and essentially locked himself in a room for those seven years for pure dedication and focus just to solve the problem. This project is nothing compared to that, but sometimes just making one set or getting the details right on one little aspect of the problem where it's all about making sure the rigor is perfect felt a little similar to my work on this art piece.

I think it gave me a deeper appreciation and way to look at sets. Before I made this art piece, I just saw sets the same way someone sees numbers as just abstractions to be used in everyday life. I now see sets in a deeper light with how they can be made. I think it is fascinating how mathematicians can do crazy stuff with numbers like making dark numbers and transcendental numbers that non-mathematicians don't often know about since they aren't used in everyday life. It let me see something beyond sets as pure tools; it let me see the potential for beauty behind them.

-Andrew Wason

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Eloquent Precision of Linguistics & Math Notation

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Eloquent Precision of Linguistics & Math Notation

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I decided to demonstrate the way that math is a subset of extremely intelligent conversation by utilizing several proof techniques. We all know how this class has blended English and Mathematics, and how our homework looks more like paragraphs than equations. Witness what we have really been learning how to say, and enjoy!

This was so fun and so intense. Took me about 3 or 4 hours to get all these synonyms and form simple statement like "if then" into coherent sentences. I really had to dig deep into exactly what the proof techniques were saying, direct proof in

Figure 1, contrapositive and induction proofs in

Figure 2, and proof by contradiction in

Figure 3. The most difficult things to understand well enough to incorporate were proof by induction, which I had a lot of trouble with before, and proof by contradiction, which goes deeper than P, Q, ~P and ~Q.

This was incredible fun, and mostly based off something an English teacher said to me in junior high or high school that stuck, "A good writer does not repeat words if possible". If you can imagine entire essays written this way, you better believe I've done it. As with mathematics however, simpler can be better.

-Dylan Guzlow

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This set of drawings is my artistic interpretation of the logical concepts in math, based on Chapter 2 of our textbook. It took me 2 hours to finish, and I used acrylic markers because I like their brightness and contrast of colors.

The first drawing is based on the idea that theoretically, a statement is either true or false. I try to illustrate how a statement can't be both true and false with two opposing people, one representing "true" and the other "false", whose colors would never blend.

The second one is a girl looking at her own reflection in the air, portraying the concept of negation. The girl and her shadow are the same but in opposite positions, as the negation of a mathematical statement have the same components but the opposite truth value.

The third concept is "biconditional" statement. I drew two people hugging to illustrate how I feel about two statements being both sufficient and necessary conditions for each other. It feels like they are inseparable and they only need each other.

The fourth one is abstract because I want to capture the concept of tautology, the compound statement that always result in truth regardless of the truth value of its components. In the drawing, the figure representing truth will look exactly the same before, during and after going through a maze that means the truth tables.

The fifth one means logical equivalence, as the two figures create equivalence despite looking different.

The last drawing is a girl finding a like-minded soul in the crowd to illustrate that like the existential quantified statement, there exists at least one among all that fits your standards, and they are ready to be found.

I really enjoyed using art to understand math, as I do love art and I think math always has a romantic and poetic side to it. Making this art piece helps me see these concepts of logic as more than just symbols and words, but with realistic meanings and even stories.

-Diandian Shi

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This is the fibonacci spiral garden. The lengths of the curves are representative of each number in the Fibonacci sequence, a sequence starting with two 1's wherein each consecutive number is the sum of the previous two numbers. Flowers are dotted at each point that is representative of a number in the sequence, with blue flowers representing even numbers and red flowers representing odd numbers. You'll notice that there are two red flowers then one blue flower, which is a consistent trend throughout the sequence.

Essentially, the spiral is generated by drawing squares next to each other that each have a side length equal to a number in the fibonacci sequence. When you connect the farthest corners of each square, you'll generate a sort of diagonal spiral that, when "circle-fied" and drawn as curves instead of straight lines, gives you this beautiful spiral.

I've added flowers, either pink (for odd numbers) or blue (for even numbers) on the sides of each square of each number in the sequence. I thought this was a nice touch since we talked about the parity of numbers in the sequence in the class before.

Finally, the sequence itself represents a bonus question from exam 2 that asked us to prove that the limit of ratios of consecutive fibonacci numbers gears towards the golden ratio. As the spiral expands, the rectangle bounding the rectangle gets closer and closer to the rectangle the golden ratio was actually derived from. This took maybe 30 minutes to an hour to throw together on Canva, but it took much longer to explore the actual math behind it. It was a really interesting exercise to hand draw the spiral, something I encourage each of you all to do as well.

Some surprising things: first, the sequence gets big, fast. I thought I was going to have space for more, but I really didn't, which was quite shocking.

Secondly: seemingly, proofs involving recursive sequences have very little to do with the numbers themselves and much more to do with the actual recursive formula. Quite similarly to how we proved that 9.99999999 - .9999999 was equal to 9 via expression as fractions, you may do the same with recursion only using consecutive elements instead of multiplying by ten to observe some similiarity. I'm one hundred percent sure that explanation makes no sense to a reader, but it definitely made sense in my head and was a connection I wouldn't have drawn before exploring the concept.

-Roy Lee

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For this piece, I use set theory to explain the consonance of piano chords that lie on the same scale. (In music, consonance simply means that two chords work well together.) I will play the chords C major, F major, and G major, all of which lie on the scale of C major, in hopes of demonstrating that two piano chords are consonant either when they share one or more notes with each other, or when both share one or more notes with a third chord.

In terms of set theory, a musical scale is a set containing seven elements—in this case, those elements are musical notes. Chords are subsets of a given scale—most often comprising three noncontiguous elements. (I find it fascinating that any three noncontiguous elements of a scale make a chord on that scale.) For two chords to be consonant with one another, either they must have a nonempty intersection with each other or they both must have a nonempty intersection with a shared, third chord. In mathematical form, I would write this as:

Let A, B and C be unique chords which are all subsets of the same scale. A and B are consonant if and only if A and B not disjoint OR there exists some C such that A & B are not disjoint with C.

Approaching scales and chords in terms of set theory helps me better understand the relationships among chords. Previously, I struggled to determine consonance without repeatedly playing the chords and hearing them for myself. In turn, this limited my ability to improvise or create new music. As I demonstrate in this extemporaneous piece, I need only consider which chords share notes with each other or which share a third, consonant chord.

In creating this piece, I learned that set theory has an incredibly wide scope of applications, ranging far beyond those we covered in class. I am looking forward to applying it in other real-world situations.

-Arieh Black

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The drawing I made displayed the Fibonacci sequence in nature, such as ferns, whales, snails, shells, and tree branches. It is not only a fascinating mathematical concept but also widely observable in nature.

Creating this artwork is a lot harder than I thought. Mainly because I am not good at drawing so it's hard to put the image in my mind into a real art piece. But I really enjoyed drawing the spirals and the branching patterns and was fascinated by the beauty of math concepts in nature.

I think looking at real-life examples like ferns, snails, whales, etc. is like discovering the hidden patterns of nature. It helped me better understand the Fibonacci sequence because I was able to see that it actually exists, not just a blurry concept in the textbook anymore.

-Maggie Chuang

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This art project depicts the mathematical property of induction which relies on establishing a truth for a base case, and then proving that if any case (n) is true, the next case (n+1) must also be true.

I drew this on a program called Krita after looking up many drawings of Ouroboros which is a symbol depicting a serpent or dragon eating its own tail.  I'm pretty bad at drawing so that's why I needed so many references so the end product looked half decent so I could show what I was meaning to relay. I chose two different elements. For the snake itself, I chose to draw ouroboros because it relates to the principle of mathematical induction and how the next case (next segment of the snakes body) is true (eaten). For the way the body looks I chose this because induction was really confusing when I first learned it so I decided to draw the snake's body in a confusing manner which is why it twists and turns a lot.

The head of the ouroboros, where it begins to consume itself, can symbolize the base case in induction. Then as the ouroboros continues to eat, it progresses along its body, similar to moving from the hypothesis that a statement is true for n to proving it true for n+1. This is as simple as induction can be explained, and this drawing helps illustrate this principle of math.

-Jay Chong

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For this project, I chose to write a poem about proof by contradiction. Initially, I just wanted to write a short piece that shows the steps of a proof by contradiction. But as I wrote I decided to write on a theme. I wrote the poem in the context of a traveler walking through a building to find a truth.

It was difficult to find so many words that could rhyme and flow through my poem, but from the feedback given in my drafts by my peers, I decided to focus on the content and the flow of the poem instead of the rhymes. Writing this poem has expressed an artistic side of me that I rarely see. I did not know that I had it in me to write an artistic poem about a mathematical concept. The process was exciting and frustrating at times, but the final product really made it all worth it.

It made me think of writing proofs in a different way. My initial understanding of the basis of a proof by contradiction was very simple, if a statement cannot be false, then it is true. But after writing about proof by contradiction in a different context, I could visualize the flow of writing a good proof.

-Audrey Goenanto

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For my project I wrote drums in 4/4 time signature. As you know, music is a gateway to understand math. Rhythm is a mixture of beats that are coming together into one. The way I approached my project was to see my song in a universal set. Within it, it contained my song, which is its own set, and within that set "S" contains the drums. The set "S" contains elements that are themselves sets containing different notes that pertain to a different drum or percussion. If you notice on the sheet, each line has a particular note that pertains to a specific part of the drum. And all of these parts are organized in such a way to make a song. Every four measures two grooves are being repeated and ending with a small fill at the end of it. Repeated three times.

It was confusing using the software musescore to make the sheet but after I got the hang of it I was able to work it out the way that I wanted. By choosing this art piece piece, the idea of sets is in our everday life. Everything belongs to some set, and that set to another. Seeing the world in that way, obviously with wisdom, you can work things out on how things relate to another much easier. I often find myself relating one things to another because they both belong to a larger set.

The title is supposed to be a joke FYI.

-Andres Diaz

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This piece used permutations in order to compose a piece of music that is guaranteed to have no notes emphasized any more than any others, thus providing a way to escape traditional tonality. An initial permutation of the twelve notes in an octave was chosen, then that was used to create 11 other permutations for a total of twelve. They were chosen in a manner that if you put them in the order they were created in a grid, you will also get permutations as you go down the grid instead of across, each one unique, thus giving a total of 24 permutations to choose from. The song doesn't sound that good to the ear, but that goes for most 12-tone music written by anyone ever.

In general, proof writing requires more creativity than some other math problems, so my creative side was useful during this class in most of the proofs we did.

I don't believe that this art piece helped me understand the concept better necessarily - it was quite different from the way we used permutations, but still interesting nonetheless.

-Nathan Mann

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I decided to capture the idea of injection, surjection, and bijection in a function. My art piece is more literal but it is an interactive posterboard that allows the user to understand what mapping a function

f: A->B can look like when it is injective, surjective, or bijective while also defining all of the important concepts.

I really wanted to help the user understand visually mapping a function that is either injective, surjective, or bijective because that helped me a lot to understand it. So I wanted to really implement that in my art piece. My creative/artistic side mostly came from the organization and building process sides whereas my final product is a bit more literal.

I was having a hard time understanding injectivity, surjectivity, and bijectivity until I understood it as literally mapping, so while making this diagram, I was able to make the poster as space efficient and informational as possible which came with understanding the subjects as a whole.

-Tyler MacClelland