# Amanda T

- Research Program Mentor

## MS candidate at Tufts University

Expertise

combinatorics, graph theory, algebra, math but make it girlypop, girlypop but make it math, co-opting math content from one area and using it in wildly incompatible (but not really) areas

### Bio

I’m a graph theorist and combinatorialist disguised as a very disgruntled algebraist! I study graphs in algebraic systems and classify the various funky geometries that exist in that space using linear algebra, graph theory, polynomial algebra, and ProCreate’s animation feature. I believe everyone’s got an inner mathematician, and sometimes that mathematician just wants to make friendship bracelets, and that, my friends, is called Knot Theory! Personally, I’m a huge crafter. I knit, crochet, draw, animate, dance (I’m a popper!), make beaded bracelets, make knotted bracelets, procure various paracord creations, sometimes I’ll yassify my friends in doodles, all sorts of fun things like that! Sometimes, if I’m feeling fancy, I even do all of this…but outside…perhaps even while hiking around the woods!### Project ideas

#### “The Prime Project” (ft Games You Played In 3rd Grade)

Imagine a number system that had some “prime amount” of numbers. How would that behave? What could it do? How would its polynomials behave? How do the numbers relate to one another? Could we visualize this? What do its polygons look like? Are the graphs planar? How do we color it? COULD WE even color it? Are we sure this is even math?! These are EXACTLY the questions that I ask myself when I do my research in combinatorics and graph theory (with an algebra flavor), and the questions I teach my students to ask as well! Not only will we learn “pure math” through literature review (whatever that means), we’ll synthesize new and exciting ideas using our absolute FAVORITE theorems ever…in unexpected places. You like (discrete) graphs but also really like the Mean Value Property in analysis? We can make that happen. You want to see how the Four Color Theorem applies to homogeneous graphs? We can do that too! By the end of our project, you’ll have a neat little math research project, all your own, to publish in journals (or submit to JMM or other conferences, fancy!)

#### “This is why we only work with prime numbers”

Like in the Prime Project, the premise is similar…but somehow…marginally more horrifying… Imagine a number system that had some “COMPOSITE amount” of numbers. How would that behave? What could it do? How would its polynomials behave? How do the numbers relate to one another? Could we visualize this? What do its polygons look like? Are the graphs planar? How do we color it? COULD WE even color it? Are we sure this is even math?! AND this isn’t to mention that in a composite system…the kernel of functions aren’t trivial…there are a LOT of things that get sent to 0… how does that affect the geometry? These are EXACTLY the questions that I ask myself when I do my research in combinatorics and graph theory (with an algebra flavor), and the questions I teach my students to ask as well! Not only will we learn “pure math” through literature review (whatever that means), we’ll synthesize new and exciting ideas using our absolute FAVORITE theorems ever…in unexpected places. You like (discrete) graphs but also really like the Mean Value Property in analysis? We can make that happen. You want to see how the Four Color Theorem applies to homogeneous graphs? We can do that too! By the end of our project, you’ll have a neat little math research project, all your own, to publish in journals (or submit to JMM or other conferences, fancy!)