Sitemap
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
Future Blog Post
Published:
This post will show up by default. To disable scheduling of future posts, edit config.yml and set future: false.
Blog Post number 4
Published:
This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.
Blog Post number 3
Published:
This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.
Blog Post number 2
Published:
This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.
Blog Post number 1
Published:
This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.
coursework
Euler Circle
Euler Circle is a program that teaches advanced college-level math to motivated high school students.
Online Learning
The main platforms I have used to take courses online are MITx, HarvardX, and Stanford ULO.
University of California San Diego (UCSD)
I have taken advanced math classes at UCSD.
expository
An Introduction to Topological Combinatorics
Published in Euler Circle, 2021
This is an expository paper I wrote at the end of the Combinatorics (Summer session 1, 2021) class at Euler Circle.
Recommended citation: Madhukara, N. (2021). "An Introduction to Topological Combinatorics." Euler Circle.
Download Paper | Download Slides
Hyperbolic 3-Manifolds and Their Constructions
Published in Euler Circle, 2022
This is an expository paper I wrote at the end of the Independent Research and Paper Writing (Summer Session 1, 2022) class at Euler Circle.
Recommended citation: Madhukara, N. (2022). "Hyperbolic 3-Manifolds and Their Constructions." Euler Circle.
Download Paper | Download Slides
Elliptic Curve Cryptography
Published in A Math Summer Program for High School Students, 2022
This is an expository paper I wrote at the end of "A Math Summer Program for High School Students" in 2022. This was a reading program where I read A Friendly Introduction to Number Theory by Joseph Silverman with a UCSD graduate student. One of the last topics we covered was elliptic curves, so I wrote this paper after doing some research on how elliptic curves are related to cryptography.
Recommended citation: Madhukara, N. (2022). "Elliptic Curve Cryptography." A Math Summer Program for High School Students.
Download Paper
Linear Error-Correcting Codes
Published in Euler Circle, 2023
This is an expository paper I wrote at the end of the Gems of Linear Algebra (Winter 2023) class at Euler Circle.
Recommended citation: Madhukara, N. (2023). "Linear Error-Correcting Codes." Euler Circle.
Download Paper
An Introduction to De Rham Cohomology
Published in Euler Circle, 2023
This is an expository paper I wrote at the end of the Differential Topology (Spring 2023) class at Euler Circle.
Recommended citation: Madhukara, N. (2023). "An Introduction to De Rham Cohomology." Euler Circle.
Download Paper | Download Slides
An Introduction to the Geometry of Numbers
Published in Euler Circle, 2023
This is an expository paper I wrote at the end of the Number Theory (Fall 2023) class at Euler Circle.
Recommended citation: Madhukara, N. (2023). "An Introduction to the Geometry of Numbers." Euler Circle.
Download Paper
The Wigner-Eckart Theorem
Published in MITx, 2025
This is an expository paper I wrote at the end of my MITx 8.06x Applications of Quantum Mechanics class in 2025.
Recommended citation: Madhukara, N. (2025). "The Wigner-Eckart Theorem." MITx.
Download Paper
portfolio
No Cloning Theorem
Published:
Maxwell’s Demon and Entropy
Published:
Buffon’s Needle Problem
Published:
Bell’s Theorem
Published:
Quantum Field Theory
Published:
portfolio2
publications
Analyzing the Effects of Fifth and Seventh Order Terms in a Generalized Hénon-Heiles Potential
Published in Applications and Applied Mathematics: An International Journal, 2024
Preprint on arXiv: https://doi.org/10.48550/arXiv.2309.03449
Recommended citation: Madhukara, Nandana (2024). (R2078) Analyzing the Effects of Fifth and Seventh Order Terms in a Generalized Henon-Heiles Potential, Applications and Applied Mathematics: An International Journal (AAM), Vol. 19, Iss. 2, Article 3.
Download Paper
talks
Talk 1 on Relevant Topic in Your Field
Published:
This is a description of your talk, which is a markdown files that can be all markdown-ified like any other post. Yay markdown!
Conference Proceeding talk 3 on Relevant Topic in Your Field
Published:
This is a description of your conference proceedings talk, note the different field in type. You can put anything in this field.
teaching
Fun With Fiziks
Summer Camp
Fun With Fiziks is a program that I founded to introduce physics to younger students through interactive experiments and demonstrations. I noticed there are not a lot of programs to get young students excited about physics, so I wanted to create this program to fill this gap. I ran this program, with some help from my school’s physics club, in 2022 and 2023. In 2024, I was able to expand Fun With Fiziks to an impoverished school in India named Channamgere Middle School. (Photos)
San Diego Math Circle (SDMC)
Lectures
SDMC is a program at UCSD which aims to teach advanced math not typically taught at school to motivated students.