Complex Image Mapping
Published:
In this blog post I will be talking about a piece of software I made for my final project in my Senior year highschool art class.
Posts by Tags
Algebra
Dirichlet Convolutions
Published:
An introduction to Dirichlet convolution, written the summer after my junior year of high school. I knew the Möbius function existed but deliberately didn’t look up its definition, so I could try to reconstruct it from what it had to do: invert the constant-one function under convolution. The write-up builds up from that.
Fields
Published:
This is part 3 of a three-part series, written in my junior year of high school, that works up to proving that (Z/pZ)× is cyclic: the multiplicative group of integers mod a prime has a generator. I was teaching myself group theory at the time and worked out the route on my own, so the proofs are mine rather than the textbook’s.
Factoring Polynomials in Arbitrary Fields
Published:
This is part 2 of a three-part series, written in my junior year of high school, that works up to proving that (Z/pZ)× is cyclic: the multiplicative group of integers mod a prime has a generator. I was teaching myself group theory at the time and worked out the route on my own, so the proofs are mine rather than the textbook’s.
Some Results with Kernels
Published:
This is part 1 of a three-part series, written in my junior year of high school, that works up to proving that (Z/pZ)× is cyclic: the multiplicative group of integers mod a prime has a generator. I was teaching myself group theory at the time and worked out the route on my own, so the proofs are mine rather than the textbook’s.
Complex Numbers
Complex Image Mapping
Published:
In this blog post I will be talking about a piece of software I made for my final project in my Senior year highschool art class.
Computer Science
Complex Image Mapping
Published:
In this blog post I will be talking about a piece of software I made for my final project in my Senior year highschool art class.
Field Theory
Fields
Published:
This is part 3 of a three-part series, written in my junior year of high school, that works up to proving that (Z/pZ)× is cyclic: the multiplicative group of integers mod a prime has a generator. I was teaching myself group theory at the time and worked out the route on my own, so the proofs are mine rather than the textbook’s.
Group Theory
Fields
Published:
This is part 3 of a three-part series, written in my junior year of high school, that works up to proving that (Z/pZ)× is cyclic: the multiplicative group of integers mod a prime has a generator. I was teaching myself group theory at the time and worked out the route on my own, so the proofs are mine rather than the textbook’s.
Factoring Polynomials in Arbitrary Fields
Published:
This is part 2 of a three-part series, written in my junior year of high school, that works up to proving that (Z/pZ)× is cyclic: the multiplicative group of integers mod a prime has a generator. I was teaching myself group theory at the time and worked out the route on my own, so the proofs are mine rather than the textbook’s.
Some Results with Kernels
Published:
This is part 1 of a three-part series, written in my junior year of high school, that works up to proving that (Z/pZ)× is cyclic: the multiplicative group of integers mod a prime has a generator. I was teaching myself group theory at the time and worked out the route on my own, so the proofs are mine rather than the textbook’s.
Math
Complex Image Mapping
Published:
In this blog post I will be talking about a piece of software I made for my final project in my Senior year highschool art class.
Dirichlet Convolutions
Published:
An introduction to Dirichlet convolution, written the summer after my junior year of high school. I knew the Möbius function existed but deliberately didn’t look up its definition, so I could try to reconstruct it from what it had to do: invert the constant-one function under convolution. The write-up builds up from that.
Fields
Published:
This is part 3 of a three-part series, written in my junior year of high school, that works up to proving that (Z/pZ)× is cyclic: the multiplicative group of integers mod a prime has a generator. I was teaching myself group theory at the time and worked out the route on my own, so the proofs are mine rather than the textbook’s.
Factoring Polynomials in Arbitrary Fields
Published:
This is part 2 of a three-part series, written in my junior year of high school, that works up to proving that (Z/pZ)× is cyclic: the multiplicative group of integers mod a prime has a generator. I was teaching myself group theory at the time and worked out the route on my own, so the proofs are mine rather than the textbook’s.
Some Results with Kernels
Published:
This is part 1 of a three-part series, written in my junior year of high school, that works up to proving that (Z/pZ)× is cyclic: the multiplicative group of integers mod a prime has a generator. I was teaching myself group theory at the time and worked out the route on my own, so the proofs are mine rather than the textbook’s.
Number Theory
Dirichlet Convolutions
Published:
An introduction to Dirichlet convolution, written the summer after my junior year of high school. I knew the Möbius function existed but deliberately didn’t look up its definition, so I could try to reconstruct it from what it had to do: invert the constant-one function under convolution. The write-up builds up from that.