Mohan Shankar

Mohan Shankar

Undergraduate in Chemistry, University of Virginia

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A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.

Pages

Posts

First Post

Published:

This page came default with this template. I’m not sure if I’ll do anything with it, but I’m leaving it up as an option right now. Currently, I think I’ll use it as a place for me to store “notes” from classes I’ve taken or content I’ve consumed. I think GitHhub Pages supports $\LaTeX$ syntax, so that could make my life easier if true.

portfolio

publications

Quantum Mechanical Effusion Rates out of a 2D Particle in a Box

Published in University of Virginia, 2024

The purpose of this study is to calculate rate constants for effusion of a particle described by quantum mechanics. The results from this study will hopefully be able to be used to compare different formulations of quantum transition state theories.

talks

String Theory: How do Musicians Know What Sounds Nice?

Published:

This talk was given for STEM Communication, a group of graduate students who made an exception and were willing to have an undergraduate sit in. My goal was quite lofty as I set out to explore a less rigorous topic in STEM to a group of theoretical physicists and chemists. I think there was a lot of ground to cover in more rigorous scientific fields related to the music including physics (wave mechanics), biology (interpretation of sounds and perhaps even consciousness), and math (measure theory). That said, I believe it went well, and it was a fun experience.

Linear Algebra v2: Regression and SVD?

Published:

Building off of my first talk, I will couple linear algebra and calculus to introduce the idea of the cost function along with the simple technique of linear regression. We’ll then revisit eigenvectors and values while briefly describing how to systematically find them. The Google Page Rank algorithm will also be shown again, this time with the numerical calculations of finding the eigenvector associated with $\lambda = 1$. From there, we’ll touch on the singular value decomposition (SVD), one of the most important linear algebraic tools given its utility for dimensionality reduction and look at image compression using the technique.

An Introduction to Group Theory and its Applications

Published:

Group theory is an incredibly elegant theory despite its somewhat dry mathematical definition: group theory is the study of algebraic structures known as groups. The main focus of the talk will be the of permutaion of three numbers denoted P(3) and the symmetry operations of an equilateral triangle, showing how these two are connected using group theory. Following this, a slight mention of group theory’s application in cryptography was made.

Distinguished Majors Symposium

Published:

This talk was given for the Distinguished Majors Program (DMP) symposium at the University of Virginia where undergraduates present their research. It consisted of a presentation followed Q&A where I presented on my quantum mechanics oriented undergraduate project that I also wrote my thesis on. In short, the goal is to develop a system describing quantum effusion to create a baseline model which quantum transition state (QTST) theories can be measured against, analagous to how classic TST used classical effusion as its model. Students in the DMP also had to create and present a poster at the regional ACS meeting.

teaching

Undergraduate Teaching Assistant (CHEM 2410)

Organic Chemistry, University of Virginia, Department of Chemistry, 2022

Organic Chemistry Lecture TA

  • Aided in real-time instruction by prompting discussion and guiding thinking
  • Graded portions of each exam and final (4 total) for a class size of $\sim 30$ students
  • Created and presented review materials outside of class to $\sim 30$ students before each exam

Undergraduate Teaching Assistant (CHEM 3410)

Quantum Chemistry, University of Virginia, Department of Chemistry, 2023

Quantum Chemistry Lecture TA

  • Facilitated content comprehension by holding office hours and writing code to visualize topics
  • Created review material to present content in alternative manners

Undergraduate Teaching Assistant (CHEM 3420)

Thermodynamics, University of Virginia, Department of Chemistry, 2024

Physical Chemistry II: Thermodynamics Lecture TA

  • Facilitated content comprehension by holding office hours and and review sessions
  • Created review material to present content in alternative manners