Combinations & Binomial Coefficients
Notes on combinations, binomial coefficients, and their variants.
Posts by Tag
- math 16
- analysis 8
- philosophy 5
- set-theory 5
- computer-science 4
- artificial-intelligence 3
- logic 3
- projects 2
- differential-equations 2
- combinatorics 2
- physics 1
- linear-algebra 1
- algorithms 1
- probability-theory 1
math
The Inclusion-Exclusion Principle
Generalizing a key theorem of set theory and probability theory to measure theory.
Permutations
Notes on the definition, notation, and variants of the permutation.
Autonomous Differential Equations
An overview of the class of differential equations that are invariant over time.
Separable Differential Equations
An overview of separable differential equations
Relations
Defining relations and key terminology related to them.
Cartesian Product
A rigorous look at the definitions and properties of the Cartesian product.
Iverson Bracket
A rigorous treatment of the Iverson bracket along with an overview of its properties and uses.
Expressing Boolean Logic with Matrices
How to express and compute boolean logic in terms of matrix algebra.
When $\pi$ doesn’t equal 3.14…
An exploration of the circle constant and how it changes with different notions of distance.
$n$-Tuples
A rigorous look at the definition and properties of $n$-tuples.
Superfactorial and Hyperfactorial
A brief introduction to two interesting variations of the factorial function: the superfactorial and hyperfactorial.
The Dottie Number
An overview of an interesting, but oft-overlooked, real constant: the Dottie Number.
Fractional Derivatives
A derivation and explanation of fractional derivatives of polynomials.
Applications of Euler’s Formula
An exploration of the uses of Euler’s formula in complex arithmetic.
Understanding Euler’s Formula
A accessible derivation and explanation of Euler’s famous formula requiring only a basic knowledge of calculus.
analysis
Autonomous Differential Equations
An overview of the class of differential equations that are invariant over time.
Separable Differential Equations
An overview of separable differential equations
When $\pi$ doesn’t equal 3.14…
An exploration of the circle constant and how it changes with different notions of distance.
Superfactorial and Hyperfactorial
A brief introduction to two interesting variations of the factorial function: the superfactorial and hyperfactorial.
The Dottie Number
An overview of an interesting, but oft-overlooked, real constant: the Dottie Number.
Fractional Derivatives
A derivation and explanation of fractional derivatives of polynomials.
Applications of Euler’s Formula
An exploration of the uses of Euler’s formula in complex arithmetic.
Understanding Euler’s Formula
A accessible derivation and explanation of Euler’s famous formula requiring only a basic knowledge of calculus.
philosophy
On Turing’s “Computing Machinery and Intelligence”
My thoughts and comments on Alan Turing’s seminal 1950 paper.
On the Chinese Room Argument
My take and objections to John Searle’s popular Chinese room argument for the non-“consciousness” of computers.
On Singer’s “All Animals are Equal”
My responses, mostly objections, to Peter Singer’s “All Animals are Equal”.
Arguments
Defining and classifying the non-formal arguments present in philosophy.
On the Grounding of Ideas
My attempt at showing that abstract concepts like “love”, or “cat”, or any other idea can be considered as real, and physically grounded.
set-theory
The Inclusion-Exclusion Principle
Generalizing a key theorem of set theory and probability theory to measure theory.
Relations
Defining relations and key terminology related to them.
Cartesian Product
A rigorous look at the definitions and properties of the Cartesian product.
Iverson Bracket
A rigorous treatment of the Iverson bracket along with an overview of its properties and uses.
$n$-Tuples
A rigorous look at the definition and properties of $n$-tuples.
computer-science
Sequential Search
Defining and analyzing the sequential search algorithm.
Compression, Images, and FileToPNG
A writeup of the interesting observations I’ve made playing around with my FileToPNG project.
Breast Cancer Classification
A tutorial and explanation of my breast cancer neural network.
Binary Prefixes
An explanation of the difference between the decimal and binary prefix systems.
artificial-intelligence
On Turing’s “Computing Machinery and Intelligence”
My thoughts and comments on Alan Turing’s seminal 1950 paper.
On the Chinese Room Argument
My take and objections to John Searle’s popular Chinese room argument for the non-“consciousness” of computers.
Breast Cancer Classification
A tutorial and explanation of my breast cancer neural network.
logic
Arguments
Defining and classifying the non-formal arguments present in philosophy.
Iverson Bracket
A rigorous treatment of the Iverson bracket along with an overview of its properties and uses.
Expressing Boolean Logic with Matrices
How to express and compute boolean logic in terms of matrix algebra.
projects
Compression, Images, and FileToPNG
A writeup of the interesting observations I’ve made playing around with my FileToPNG project.
Breast Cancer Classification
A tutorial and explanation of my breast cancer neural network.
differential-equations
Autonomous Differential Equations
An overview of the class of differential equations that are invariant over time.
Separable Differential Equations
An overview of separable differential equations
combinatorics
Combinations & Binomial Coefficients
Notes on combinations, binomial coefficients, and their variants.
Permutations
Notes on the definition, notation, and variants of the permutation.
physics
Kinematics
On the kinematic equations of classical mechanics.
linear-algebra
Expressing Boolean Logic with Matrices
How to express and compute boolean logic in terms of matrix algebra.
algorithms
Sequential Search
Defining and analyzing the sequential search algorithm.
probability-theory
The Inclusion-Exclusion Principle
Generalizing a key theorem of set theory and probability theory to measure theory.