# Author Archives: Brandon Coya

## My Experience Teaching Differential Equations

This summer I taught lower division differential equations. The purpose of this post is to share my experiences and recommendations for teaching mathematicsÂ with differential equations as an example. In summary I emulated the things that I’ve seen John Baez do … Continue reading

## Category Theory for the Working non-Mathematician 2

Last time I talked about the very basics of Category Theory, objects and morphisms and what exactly a Category consisted of. If nothing else sticks just remember that categories consist things (objects) and ways to go between things (morphisms) where … Continue reading

## Category Theory for the Working non-Mathematician 1

After another long break from writing about math in order to write about other math, I am back to write about math. Eventually I should talk about my own research so in order to get to that point I am … Continue reading

## Is Math the same on other planets?

I went to an amazing wedding this pi day for my cousin Jonathan and his now wife Kd where the following question was posed on the dance floor by Kd’s friend Jade, “Would math be the same on Jupiter?” I … Continue reading

## Calculus: The Derivative

Since I am finally TAing for a calculus class it seemed like a good time to write about this topic. Unfortunately I still can’t make nice pictures and a good visualization is extremely useful in intuitively understanding calculus. Before taking … Continue reading

## Algebra Qual Study Problems: 7

Qual 2011 #1 (Hungerford 4.5.9a): Let I be a two-sided ideal in a ring R and let IM be the abelian subgroup of an R-module M generated by all elements of the form . (i) Show that IM is a … Continue reading

## Algebra Qual Study Problems: 6

Theorem: The following are equivalent on an R-module P- (i) is split exact. (ii) P is a direct summand of a free module (iii) P is projective. Proof- Assume that P is projective and let be a short exact sequence. … Continue reading