Euler Circle
Euler Circle is a program that teaches advanced college-level math to motivated high school students.
Posts by Collection
coursework
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.
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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.
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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.
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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.
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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.
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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.
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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.
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portfolio
No Cloning Theorem
Published:
Maxwell’s Demon and Entropy
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Buffon’s Needle Problem
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Bell’s Theorem
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Quantum Field Theory
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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.
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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.