Tags
mini
An Electromagnetism Cycloid
Not an April Fool's joke! This is a mini article on an electromagnetism problem mentioned in one of our class's textbooks. The exact solution was said to be beyond the scope of the textbook, so, don't mind if I do!
A Combinatorial Totient Sum Identity
A very small article before winter break, featuring a clean double counting argument for a sum involving the Euler totient function.
physics
An Electromagnetism Cycloid
Not an April Fool's joke! This is a mini article on an electromagnetism problem mentioned in one of our class's textbooks. The exact solution was said to be beyond the scope of the textbook, so, don't mind if I do!
Drawing Equipotential Lines
Deriving an algorithm to draw equipotential lines for a vector field starting from a point with lots of fun math along the way.
linear-algebra
An Electromagnetism Cycloid
Not an April Fool's joke! This is a mini article on an electromagnetism problem mentioned in one of our class's textbooks. The exact solution was said to be beyond the scope of the textbook, so, don't mind if I do!
Music-Inspired Mathematics
An orchestra assignment special! In this article, I explore the connection between music and math concretely. In particular, we'll take a look at some signal processing and some even more out there connections to springboard into some fun pure math.
Convolution Canonicity: Dirichlet Convolutions!
The primer article in a series exploring convolution in group theory. The topic? Dirichlet convolutions! We'll generalize them over arbitrary fields and classify some certain cases.
A Remark on Commuting Matrices
Suppose matrices \( A \) and \( B \) commute. We explore the question of when one matrix can be expressed in terms of the other.
Codeforces: Problem 1916H1
A very mathy and beautiful 2700 rated Codeforces problem. This one had me really excited to solve.
Matrices Over Modular Arithmetic
Exploring properties of powers of matrices who have entries in the ring of integers modulo some integer.
Binomial Coefficient Matrices
Let's explore the properties of lower triangular matrices filled with binomial coefficients.
Perspective Projection
Developing a perspective projection for use in rendering 3D graphics. This particular derivation was used in my AP CSA final project :D
Drawing Equipotential Lines
Deriving an algorithm to draw equipotential lines for a vector field starting from a point with lots of fun math along the way.
Gradient Ascent Eigenvectors
Finding real eigenvectors of an arbitrary matrix using geometric intuition and gradient ascent.
differential-equations
An Electromagnetism Cycloid
Not an April Fool's joke! This is a mini article on an electromagnetism problem mentioned in one of our class's textbooks. The exact solution was said to be beyond the scope of the textbook, so, don't mind if I do!
complex-numbers
An Electromagnetism Cycloid
Not an April Fool's joke! This is a mini article on an electromagnetism problem mentioned in one of our class's textbooks. The exact solution was said to be beyond the scope of the textbook, so, don't mind if I do!
fourier-transform
Music-Inspired Mathematics
An orchestra assignment special! In this article, I explore the connection between music and math concretely. In particular, we'll take a look at some signal processing and some even more out there connections to springboard into some fun pure math.
signal-processing
Music-Inspired Mathematics
An orchestra assignment special! In this article, I explore the connection between music and math concretely. In particular, we'll take a look at some signal processing and some even more out there connections to springboard into some fun pure math.
analysis
Music-Inspired Mathematics
An orchestra assignment special! In this article, I explore the connection between music and math concretely. In particular, we'll take a look at some signal processing and some even more out there connections to springboard into some fun pure math.
Project Euler: Problem 779
Solving Project Euler Problem 779, a really beautiful number theory problem.
group-theory
Convolution Canonicity: Dirichlet Convolutions!
The primer article in a series exploring convolution in group theory. The topic? Dirichlet convolutions! We'll generalize them over arbitrary fields and classify some certain cases.
Project Euler: Problem 752
Solving Project Euler Problem 752, a nice problem on orders in fields with square roots.
Project Euler: Problem 421
Solving Project Euler Problem 421, a beautiful number theory puzzle on counting roots modulo primes with a cryptographic and probabilistic flavor.
Proving that the Euler Totient is Even
We prove that the Euler totient function is even using group theory.
Matrices Over Modular Arithmetic
Exploring properties of powers of matrices who have entries in the ring of integers modulo some integer.
abstract-algebra
Convolution Canonicity: Dirichlet Convolutions!
The primer article in a series exploring convolution in group theory. The topic? Dirichlet convolutions! We'll generalize them over arbitrary fields and classify some certain cases.
Project Euler: Problem 752
Solving Project Euler Problem 752, a nice problem on orders in fields with square roots.
lie-theory
Convolution Canonicity: Dirichlet Convolutions!
The primer article in a series exploring convolution in group theory. The topic? Dirichlet convolutions! We'll generalize them over arbitrary fields and classify some certain cases.
number-theory
Convolution Canonicity: Dirichlet Convolutions!
The primer article in a series exploring convolution in group theory. The topic? Dirichlet convolutions! We'll generalize them over arbitrary fields and classify some certain cases.
A Combinatorial Totient Sum Identity
A very small article before winter break, featuring a clean double counting argument for a sum involving the Euler totient function.
Project Euler: Problem 752
Solving Project Euler Problem 752, a nice problem on orders in fields with square roots.
Project Euler: Problem 421
Solving Project Euler Problem 421, a beautiful number theory puzzle on counting roots modulo primes with a cryptographic and probabilistic flavor.
Proving that the Euler Totient is Even
We prove that the Euler totient function is even using group theory.
Codeforces: Problem 1916H1
A very mathy and beautiful 2700 rated Codeforces problem. This one had me really excited to solve.
Matrices Over Modular Arithmetic
Exploring properties of powers of matrices who have entries in the ring of integers modulo some integer.
Project Euler: Problem 779
Solving Project Euler Problem 779, a really beautiful number theory problem.
Project Euler: Problem 549
Solving Project Euler Problem 549, a nice number theory problem revolving around the factorization of factorials.
Codeforces: Problem 1909D
A nice little 1900 rated Codeforces problem on making all elements equal with operations.
Yukicoder: Problem 2664
Solving Yukicoder Problem 2664, a quick little graph and number theory problem, with the extra challenge of having to read the problem description in Japanese.
Codeforces: Problem 1902C
A quick little number theory Codeforces problem on minimizing costs.
Codeforces: Problem 1948E
A fun (slightly brute-force) constructive graph theory Codeforces problem, rated 2100.
Codeforces: Problem 1758D
A nice 1800 rated Codeforces problem on constructing an integer sequence. Multiple attempts, because an initial strategy doesn't always work but is nice to document.
matrices
Convolution Canonicity: Dirichlet Convolutions!
The primer article in a series exploring convolution in group theory. The topic? Dirichlet convolutions! We'll generalize them over arbitrary fields and classify some certain cases.
Project Euler: Problem 752
Solving Project Euler Problem 752, a nice problem on orders in fields with square roots.
A Remark on Commuting Matrices
Suppose matrices \( A \) and \( B \) commute. We explore the question of when one matrix can be expressed in terms of the other.
Codeforces: Problem 1916H1
A very mathy and beautiful 2700 rated Codeforces problem. This one had me really excited to solve.
Matrices Over Modular Arithmetic
Exploring properties of powers of matrices who have entries in the ring of integers modulo some integer.
Binomial Coefficient Matrices
Let's explore the properties of lower triangular matrices filled with binomial coefficients.
Project Euler: Problem 743
Solving Project Euler Problem 743, a really nice combo problem using a sliding window approach.
Gradient Ascent Eigenvectors
Finding real eigenvectors of an arbitrary matrix using geometric intuition and gradient ascent.
finite-fields
Convolution Canonicity: Dirichlet Convolutions!
The primer article in a series exploring convolution in group theory. The topic? Dirichlet convolutions! We'll generalize them over arbitrary fields and classify some certain cases.
combinatorics
A Combinatorial Totient Sum Identity
A very small article before winter break, featuring a clean double counting argument for a sum involving the Euler totient function.
Project Euler: Problem 421
Solving Project Euler Problem 421, a beautiful number theory puzzle on counting roots modulo primes with a cryptographic and probabilistic flavor.
Codeforces: Problem 1916H1
A very mathy and beautiful 2700 rated Codeforces problem. This one had me really excited to solve.
Matrices Over Modular Arithmetic
Exploring properties of powers of matrices who have entries in the ring of integers modulo some integer.
Codeforces: Problem 1763D
A 2200 rated Codeforces combinatorics problem with a whole lot of casework.
Binomial Coefficient Matrices
Let's explore the properties of lower triangular matrices filled with binomial coefficients.
Project Euler: Problem 743
Solving Project Euler Problem 743, a really nice combo problem using a sliding window approach.
project-euler
Project Euler: Problem 752
Solving Project Euler Problem 752, a nice problem on orders in fields with square roots.
Project Euler: Problem 421
Solving Project Euler Problem 421, a beautiful number theory puzzle on counting roots modulo primes with a cryptographic and probabilistic flavor.
Project Euler: Problem 743
Solving Project Euler Problem 743, a really nice combo problem using a sliding window approach.
Project Euler: Problem 779
Solving Project Euler Problem 779, a really beautiful number theory problem.
Project Euler: Problem 549
Solving Project Euler Problem 549, a nice number theory problem revolving around the factorization of factorials.
Project Euler: Problem 323
Solving Project Euler Problem 323, a fun problem involving bitwise OR and expected values.
notes
PUMAC Power Round 2024: The Hausdorff Measure
Notes on and a review of what our team managed to solve in PUMAC Power Round 2024! Featuring measure theory, topology, and fractals.
contest
PUMAC Power Round 2024: The Hausdorff Measure
Notes on and a review of what our team managed to solve in PUMAC Power Round 2024! Featuring measure theory, topology, and fractals.
topology
PUMAC Power Round 2024: The Hausdorff Measure
Notes on and a review of what our team managed to solve in PUMAC Power Round 2024! Featuring measure theory, topology, and fractals.
measure-theory
PUMAC Power Round 2024: The Hausdorff Measure
Notes on and a review of what our team managed to solve in PUMAC Power Round 2024! Featuring measure theory, topology, and fractals.
probability
Project Euler: Problem 421
Solving Project Euler Problem 421, a beautiful number theory puzzle on counting roots modulo primes with a cryptographic and probabilistic flavor.
Project Euler: Problem 323
Solving Project Euler Problem 323, a fun problem involving bitwise OR and expected values.
cryptography
Project Euler: Problem 421
Solving Project Euler Problem 421, a beautiful number theory puzzle on counting roots modulo primes with a cryptographic and probabilistic flavor.
codeforces
Codeforces: Problem 1916H1
A very mathy and beautiful 2700 rated Codeforces problem. This one had me really excited to solve.
Codeforces: Problem 1763D
A 2200 rated Codeforces combinatorics problem with a whole lot of casework.
Codeforces: Problem 1909D
A nice little 1900 rated Codeforces problem on making all elements equal with operations.
Codeforces: Problem 1902C
A quick little number theory Codeforces problem on minimizing costs.
Codeforces: Problem 1948E
A fun (slightly brute-force) constructive graph theory Codeforces problem, rated 2100.
Codeforces: Problem 1758D
A nice 1800 rated Codeforces problem on constructing an integer sequence. Multiple attempts, because an initial strategy doesn't always work but is nice to document.
permutations
Codeforces: Problem 1763D
A 2200 rated Codeforces combinatorics problem with a whole lot of casework.
Codeforces: Problem 1948E
A fun (slightly brute-force) constructive graph theory Codeforces problem, rated 2100.
binomial-coefficient
Binomial Coefficient Matrices
Let's explore the properties of lower triangular matrices filled with binomial coefficients.
primes
Project Euler: Problem 779
Solving Project Euler Problem 779, a really beautiful number theory problem.
graphics
Perspective Projection
Developing a perspective projection for use in rendering 3D graphics. This particular derivation was used in my AP CSA final project :D
multivariable-calculus
Drawing Equipotential Lines
Deriving an algorithm to draw equipotential lines for a vector field starting from a point with lots of fun math along the way.
gradient-descent
Gradient Ascent Eigenvectors
Finding real eigenvectors of an arbitrary matrix using geometric intuition and gradient ascent.
optimization
Codeforces: Problem 1909D
A nice little 1900 rated Codeforces problem on making all elements equal with operations.
Codeforces: Problem 1902C
A quick little number theory Codeforces problem on minimizing costs.
yukicoder
Yukicoder: Problem 2664
Solving Yukicoder Problem 2664, a quick little graph and number theory problem, with the extra challenge of having to read the problem description in Japanese.
graph-theory
Yukicoder: Problem 2664
Solving Yukicoder Problem 2664, a quick little graph and number theory problem, with the extra challenge of having to read the problem description in Japanese.
Codeforces: Problem 1948E
A fun (slightly brute-force) constructive graph theory Codeforces problem, rated 2100.
dfs
Yukicoder: Problem 2664
Solving Yukicoder Problem 2664, a quick little graph and number theory problem, with the extra challenge of having to read the problem description in Japanese.
bitmasks
Project Euler: Problem 323
Solving Project Euler Problem 323, a fun problem involving bitwise OR and expected values.