Eroxl's Notes

00 - Machine Learning

Learning Types

Supervised Learning

Features

Problem Types

Classification

Regression

Unsupervised Learning

Neural Networks

Activation Functions

Leaky ReLU Function

Parametric ReLU Function

Pitfalls

Exploding Gradient Problem

Vanishing Gradient Problem

Rectified Linear (ReLU) Function

Convolutional Neural Network

Deep Neural Network

Feedforward Neural Network

Definition of a Layer of Dense Neurones

Definition of a Single Dense Neurone

Pre-Processing

Z-Score Normalization

Pitfalls

Overfitting

Underfitting

Training

Backpropagation

Backpropagation Example with One Neurone

Batching

Cost Function

Categorical Cross-Entropy Loss

Batch Gradient Descent

Gradient Descent with Momentum

Learning Rate

Learning Rate Decay

Exponential Learning Rate Decay

Step Based Learning Rate Decay

Time Based Learning Rate Decay

Learning Rate Scheduling

Mini-Batch Gradient Descent

RMSProp

Stochastic Gradient Descent

01 - Linear Algebra

Surjective Linear Map

Elementary Row Operations

Gaussian Elimination

Homogeneous System

Parametric Vector Form

Solution Set

Trivial Solution

Lines in Three Dimensions

Matrix Diagonal Operator

Matrix Inversion

Invertible Matrix Theorem

Characteristic Polynomial

Scalar Multiplication

02 - Calculus

Average Rate of Change

Differentiable Function

Differentiation Rules

Chain Rule

Constant Multiples Rule

Constant Rule

Inverse Function Rule

First Derivative Test

Higher Order Derivatives

Notation

Lagrange's Notation

Leibniz's Notation

Optimization Using Derivatives

Second Derivative Test

Discontinuity

Essential Discontinuity

Jump Discontinuity

Removable Discontinuity

Extrema

Antiderivative Techniques

Integration by Partial Fractions

Integration by Parts

Integration by Substitution

Trigonometric Substitution

Approximations

Examples

Comparison Test (Improper Integrals)

Limit Comparison Test (Improper Integrals)

Integral Properties

Intermediate Value Theorem

Mean Value Theorem

Mean Value Theorem for Derivatives

Use Cases

Determining Higher Order Derivatives at a Point (Taylor Series)

Evaluating a Geometric Series with an Additional Reciprocal Term (Taylor Series)

Vergence Tests

Comparison Test

Divergence Test

Limit Comparison Test

The Fundamental Theorem of Calculus

03 - Differential Geometry

Averaging

Average Value of a Function

Weighted Average Value of a Function

Conservative Vector Field

Curl

Curves

Arc Length

Parameterization by Arc Length

Curvature

Frenet-Serret Formulas

Acceleration in Frenet-Serret Space

Binormal Vector

Principal Normal Vector

Directional Derivative

Limits in Multiple Dimensions

Line Integral

Multiple Integral

Techniques

Evaluating Double Integrals in Polar Coordinates

Evaluating Triple Integrals in Cylindrical Coordinates

Evaluating Triple Integrals in Spherical Coordinates

Multivariable Function

Optimization

Critical Points of Multivariable Functions

Saddle Point

Orientable

Partial Derivative

Chain Rule in Multiple Dimensions

Gradient

Hessian Matrix

Higher Order Partial Derivative

Implicit Differentiation in Multiple Dimensions

Jacobian Matrix

Second Partial Derivative Test

Polar Coordinates System

Vector-Valued Function

Visualizing 3D Surfaces

04 - Physics

Classical

Centre of Mass

Energy

Kinetic Energy

Galilean Transformation

Inertia

Inertial Frame of Reference

Momentum

Newton's Laws of Motion

Electric Circuits

Kirchhoff's Current Law

Kirchhoff's Voltage Law

Series (Electric Circuits)

Voltmeter

Electromagnetics

Electromagnetic Radiation

Electrostatics

Uniform Electric Field

Electric Field Lines

Electric Potential Difference

Electric Potential Energy

International System of Units

Electricity

Energy

Particle Physics

Physical Constants

Permeability of Free Space

Permittivity of Free Space

Lorentz Transformation

Relativity of Simultaneity

05 - Algebra

Partial Fraction Decomposition

Polynomial

Completing the Square

Monomial

Polynomial Degree

Proper Fraction

06 - Discrete Mathematics

Big-O Notation (Discrete Math)

Formal Language

Graph Theory

Graph (Discrete Mathematics)

Connectivity (Discrete Mathematics)

Examples

Vertex (Discrete Math)

Weighted Graph

Minimum Spanning Tree

Spanning Tree

Tree (Discrete Mathematics)

Mathematical Proof

Mathematical Induction

Strong Mathematical Induction

Floating Point Number

07 - Set Theory

Operations

08 - Chemistry

Structural Chemistry

Properties

Effective Nuclear Charge

Electron Affinity

Electronegativity

Ionization Energy

09 - Computer Science

Computer Systems

Asynchronous Operation

Character Encoding

Control Flow

Concurrent Control Flow

Asynchronous Condition Variable

Lock

Conditional (Computer Science)

Data Structures

Disjoint Set (Data Structure)

Graph (Data Structure)

Traversals

Breadth-First Traversal

Depth-First Traversal

Linked Lists

Tree (Data Structure)

In-Order Binary Tree Traversal

Traversals

Breadth-First Tree Traversal

Depth-First Tree Traversal

Memory Management Systems

Reference Counting

Paradigms

Event-Driven Programming

Object Oriented

Class Relationships

Supertypes and Subtypes

Type Substitution

Class

Constructor

Data Abstraction

Data Abstraction Specifiers

Testing a Data Abstraction

Design Principles

Liskov Substitution Principle

Single Responsibility Principle

Package Relationship Diagram

Patterns

Cryptography

Hashing

Hash Function

Hardware

Common Circuits

I-O System

I-O Techniques

Polling (Computer Science)

Programmed Input-Output

Microcontroller

General Purpose Input and Output

Persistence

Relational Database

Database Normalization

Normal Form

Boyce-Codd Normal Form

First Normal Form

Second Normal Form

Third Normal Form

Relationship Decomposition

Database Tuple

Entity-Relationship Diagram

Aggregation

Examples

Generalization

Specialization

Translating an Entity-Relationship Diagram to Relations

Weak Entity

Functional Dependence

Program Analysis

Algorithms

Graphs

Sorting

Big-O Notation (Computer Science)

Loop Invariants

Programming Languages

Dynamic Array

Dynamic vs Static Arrays

Function Pointer

Static Array

Switch Statement

Java

Memory Management (Java)

Racket

SM213 Assembly

Instruction Set (SM213)

Structured Query Language

Data Definition Language

Data Manipulation Language

Aggregate Functions (DML)

DELETE Statement (DML)

INSERT Statement (DML)

JOIN Clause (DML)

SELECT Statement (DML)

Set Operations (DML)

UPDATE Statement (DML)

10 - Statistics

Concepts

Data Collection

Variable (Statistics)

Descriptive Statistics

Measures of Centre

Measures of Variability

Inferential Statistics

Errors

Test Statistics

Multiple Sample

F-Statistic

Two Sample t-Statistic

One Sample

Chi-Squared Statistic

Z-Statistic

t-Statistic

Two-Sample Hypothesis Testing

Interval Estimator

Point Estimator

Regression Analysis

Closed Form Solutions

Ordinary Least Squares

Estimation Methods

Least Squares

Sum of Squared Residuals

Models

Central Limit Theorem

Conditional Probability

Covariance

Density Functions

Cumulative Distribution Function

Probability Density Function

Expected Value

Extrema of Independent Random Variables

Independent Events

Random Variable

Bernoulli Random Variable

Specific Distributions

Bernoulli Distribution

Binomial Distribution

Binomial Coefficient

Ten Percent Condition

Exponential Distribution

Geometric Distribution

Normal Distribution

Poisson Distribution

Poisson Process

Standard Normal Distribution

Standardization

11 - Formal Logic

Creating a Statement from Truth Tables

Exclusive Disjunction

Existential Quantifier

Universal Quantifier

Universal Conditional Statements

Simplifying Statement Forms

Statement

Tautology

Truth Table

12 - Language

Languages

Tenses

Verb Conjugations

Conjugating Regular Verbs

Regular -ar Conjugation Table

Regular -er Conjugation Table

Regular -ir Conjugation Table

Stem Changing Verbs

e > i Stem Changing Verbs

e > ie Stem Changing Verbs

o > ue Stem Changing Verbs

13 - Politics

Background

United States

State Bills

Michigan

Senate Bill 757

Nevada

Emergency Election Procedures Bill

Pennsylvania

Act 77

Pennsylvania Election Code - Omnibus Amendments

United States Electoral System

Certificate of Ascertainment

Organizations

Democratic Party

Republican Party

President of the Senate

Daily News

Events

2020 Election Interference

2020 Georgian Election Audit

False Electors Plot

Eastman Memos

Claims Made in Memorandum Two of the Eastman Memos

January 4th Oval Office Meeting - Eastman's First Pitch to Pence

January 5th West Wing Meeting - Eastman's Legal Argument to Pence's Advisors

Lawsuits

Georgia Democratic Party v. Raffensperger

Trump v. Kemp

Trumps Publicized Meeting with Governors Hutchinson and Kelly

Trump–Raffensperger Phone Call

2020-2021 U.S

2020-2021 U.S. Troop Withdrawal from Afghanistan

Agreement for Bringing Peace to Afghanistan

2026 Midterm Redistricting

2025 Texas Redistricting

Texas Democrats Leave State to Stop Redistricting Vote

Greg Abbott Requests an Emergency Petition for Writ of Quo Warranto

John Cornyn Issues Request to the FBI to Help Locate or Arrest Texas Democrats who Left State to Stop Redistricting Vote

Kash Patel Approves John Cornyn's Request for FBI Assistance

Texas Attorney General Ken Paxton's Response to Greg Abbott's Petition

Texas House Issues Civil Arrest Warrants for Democrats who Fled State to Avoid Redistricting Vote

Texas Enacts 2025 Gerrymandered Congressional Maps

Trump Comments on Texas Redistricting Proposals - 05.08.2025 CNBC Trump Interview

Trump-Abbott Phone Call on Texas Redistricting

Trump Federalizes D.C. Police and Deploys National Guard to D.C

3 States Deploy National Guard Troops to D.C.

D.C. Attorney General Sues to Stop Federal Government Takeover of Metropolitan Police Department

Pam Bondi Initiates Temporary Takeover of D.C. Metropolitan Police Department

Trump Federalizes D.C. Police and Deploys National Guard to D.C.

People

Judges

Research

Effects of Cows Milk on Muscle Growth

Literature

Capital - A Critique of Political Economy

99 - Classes

Computer Science

CPSC 213

Assignment 1 - Numbers and Memory

Assignment 2 - CPU & Static Variables

Assignment 3 - Dynamic Arrays & C Pointers

Assignment 4 - Structs & Dynamic Allocation

Assignment 6 - Static Control Flow

Assignment 9 - IO and Asynchrony

Practice

01 - Numbers and Memory (CPSC 213 Practice)

02 - CPU & Static Variables (CPSC 213 Practice)

03 - Dynamic Arrays and C Pointers (CPSC 213 Practice)

04 - Structs and Dynamic Allocation (CPSC 213 Practice)

05 - Memory Management and Reference Counting (CPSC 213 Practice)

06 - Static Control Flow (CPSC 213 Practice)

07 - Procedure Calls and the Stack (CPSC 213 Practice)

08 - Dynamic Control Flow (CPSC 213 Practice)

09 - I-O, Asynchrony and Threads (CPSC 213 Practice)

10 - Synchronization (CPSC 213 Practice)

CPSC 221

CPSC 221 Examlets

Examlet Week 10 (CPSC 221)

Examlet Week 4 (CPSC 221)

Examlet Week 7 (CPSC 221)

Examlet Week 8 (CPSC 221)

Examlet Week 9 (CPSC 221)

CPSC 221 Labs

02 - Lab Debugging

03 - Lab Linked Lists

Practice

Practice 12 (CPSC 221)

CPSC 304

Assignments

Normalization 2 (CPSC 304)

Relational Model 1 (CPSC 304)

Practice

Midterm 1

Midterm 1 - CPSC 304 (2023T1)

Midterm 1 - CPSC 304 (2024T1)

Midterm 1 - CPSC 304 (2024T2)

Midterm 1 - CPSC 304 (2025T1)

Relational Algebra

Relational Algebra (Practice Questions)

Project

Milestone 1 (CPSC 304)

Mathematics

MATH 200

Homework

Web Work 10 (MATH 200)

Web Work 6 (MATH 200)

Web Work 7 (MATH 200)

Web Work 9 (MATH 200)

Practice

Chain Rule in Multiple Dimensions (Practice)

Double Integrals (Practice)

Double Integrals in Polar Coordinates (Practice)

Equations of Lines in 3D (Practice)

Equations of Planes in 3D (Practice)

Final Exam

MATH 200 Final Exam - 2015w1

MATH 200 Final Exam - 2016w1

Limits in Multiple Dimensions (Practice)

Maximum and Minimum Values (Practice)

Midterm 2

MATH 200 Midterm Test 2

Points (Practice)

Triple Integrals in Spherical Coordinates (Practice)

Vectors (Practice)

MATH 221

Practice

Diagonalization and Similar Matrices

Eigenvalues and Eigenvectors

Linear Transformations (Practice)

Midterm 1

Midterm 1 - MATH 221 (2007T2)

Midterm 1 - MATH 221 (2017T2)

Midterm 1 - MATH 221 (2018T1)

Midterm 2

Midterm 2 - MATH 221 (2007T2)

Midterm 2 - MATH 221 (2017T2)

Midterm 2 - MATH 221 (2018T2)

Star Problems

Practice Problems 1 (MATH 221)

Practice Problems 10 (MATH 221)

Practice Problems 2 (MATH 221)

Practice Problems 3 (MATH 221)

Practice Problems 8 (MATH 221)

Practice Problems 9 (MATH 221)

Web Works

Web Work 1 (MATH 221)

Web Work 10 (MATH 221)

Web Work 2 (MATH 221)

Web Work 3 (MATH 221)

Web Work 8 (MATH 221)

Web Work 9 (MATH 221)

MATH 317

Homework

Web Work 1 (MATH 317)

Web Work 2 (MATH 317)

Web Work 3 (MATH 317)

Web Work 4 (MATH 317)

Web Work 7 (MATH 317)

Web Work 8 (MATH 317)

Web Work 9 (MATH 317)

Practice

Gradients, Divergence and Curl (Practice)

Green's Theorem (Practice)

Line Integrals (Practice)

Midterm 1

Midterm 1 - MATH 317 (2011T2)

Midterm 1 - MATH 317 (2014T2)

Midterm 1 - MATH 317 (2016T2)

Midterm 1 - MATH 317 (2017T1)

Midterm 1 - MATH 317 (2017T2)

Midterm 2

Midterm 2 - MATH 227 (2010T2)

Midterm 2 - MATH 227 (2015T2)

Midterm 2 - MATH 317 (2011T2)

Midterm 2 - MATH 317 (2015T2)

Midterm 2 - MATH 317 (2017T2)

Surface Integrals (Practice)

Statistics

STAT 251

Homework

Web Work 1 (STAT 251)

Web Work 5 (STAT 251)

Web Work 7 (STAT 251)

Web Work 8 (STAT 251)

Written Assignment 1 (STAT 254)

Written Assignment 2 (STAT 251)

Practice

Final Exam

STAT 251 Final Practice Problems - 1

Midterm

STAT 251 Midterm Practice Problems - 1

STAT 251 Midterm Practice Problems - 2

STAT 251 Midterm Practice Problems - 3

STAT 251 Practice - Probability

Predicate (Racket)

Predicates are functions that return a boolean value based on the input arguments.

Examples

>
<=
=
string=?