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
Dying RELU Problem
Sigmoid Function
Logistic Function
Softmax
Step Function
Convolutional Neural Network
Deep Neural Network
Feedforward Neural Network
Layer Types
Convolutional Layer
Kernel
Dense Layer
Definition of a Layer of Dense Neurones
Definition of a Single Dense Neurone
Dropout Layer
Hidden Layer
Pre-Processing
Normalization
Min-Max Scaling
One Hot Encoding
Z-Score Normalization
Pitfalls
Overfitting
Underfitting
Training
Backpropagation
Backpropagation Example with One Neurone
Batching
Cost Function
Categorical Cross-Entropy Loss
Feature Set
Optimization
Gradient Descent
AdaGrad
Adam
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
Penalties
L1 Regularization
L2 Regularization
01 - Linear Algebra
Collinearity
Linear Combination
Linear Equation
Linear Independence
Linear Map
Injective Linear Map
Surjective Linear Map
Linear Span
Linear Subspace
Basis
Linear System
Elementary Row Operations
Gaussian Elimination
Homogeneous System
Parametric Vector Form
Solution Set
Trivial Solution
Lines in Three Dimensions
Matrix
Matrix Operations
Adjugate Matrix
Cofactor Matrix
Hadamard Product
Matrix Cofactor
Matrix Determinant
Laplace Expansion
Matrix Diagonal Operator
Matrix Inversion
Invertible Matrix Theorem
Matrix Minor
Matrix Product
Matrix Trace
Matrix Transposition
Matrix Subtypes
Column Vector
Identity Matrix
Row Vector
Square Matrix
Characteristic Polynomial
Eigenspace
Eigenvector
Plane
Point
Scalar
Vector
Vector Notation
Matrix Notation
Point Notation
Unit Vector Notation
Vector Operations
Cross Product
Right Hand Rule
Dot Product
Scalar Multiplication
Triple Product
Vector Addition
Vector Subtraction
Vector Properties
Vector Magnitude
Vector Orientation
02 - Calculus
Area Between Curves
Average Rate of Change
Continuous Function
Critical Point
Derivative
Concavity
Differentiable Function
Differentiation Rules
Chain Rule
Constant Multiples Rule
Constant Rule
Inverse Function Rule
Power Rule
Product Rule
Quotient Rule
Sum 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
Absolute Extrema
Absolute Maximum
Absolute Minimum
Local Extrema
Local Maximum
Local Minimum
Horizontal Asymptote
Inflection Point
Integral
Antiderivative Rules
Antiderivative Techniques
Integration by Partial Fractions
Integration by Parts
Integration by Substitution
Trigonometric Substitution
Antiderivative
Approximations
Riemann Sum
Examples
Simpson's Rule
Improper Integral
Comparison Test (Improper Integrals)
Limit Comparison Test (Improper Integrals)
Integral Properties
Intermediate Value Theorem
Interval
Closed Interval
Half-Open Interval
Interval Notation
Open Interval
Limit
Indeterminate Form
L'Hôpital's Rule
One-Sided Limits
Squeeze Theorem
Linearization
Mean Value Theorem
Mean Value Theorem for Derivatives
Normal Line
Rate of Change
Secant Line
Series
Geometric Series
Power Series
Taylor Series
Maclaurin Series
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
Ratio Test
The Integral Test
Signed Area
Solid of Revolution
Disc Integration
Shell Integration
Washer Integration
Tangent Line
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
Unit Tangent Vector
Osculating Circle
Osculating Plane
Parameterized Curve
Directional Derivative
Divergence Theorem
Divergence
Gradient Theorem
Green's Theorem
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
Stoke's Theorem
Surface Integral
Tangent Plane
Vector Field
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
Ammeter
Battery
Capacitance
Capacitor
Conductance
Current
Electrical Power
Kirchhoff's Current Law
Kirchhoff's Voltage Law
Ohm's Law
Parallel
Resistance
Resistor
Series (Electric Circuits)
Voltmeter
Electromagnetics
Electromagnetic Radiation
Light
Photon
Electrostatics
Charged Particle
Coulombs Constant
Coulombs Law
Electric Field
Uniform Electric Field
Electric Field Lines
Electric Potential Difference
Electric Potential Energy
Electric Potential
Elementary Charge
Parallel Plates
Geometrical Optics
Lenses
Focal Length
Image Point
Real Image
Thin Concave Lens
Thin Convex Lens
Virtual Image
Light Ray
Optical Medium
Refractive Index
Snell's Law
Vergence (Optics)
International System of Units
Electricity
Ampere
Coulomb
Farad
Volt
Energy
Joule
SI Base Units
Particle Physics
Electron
Elementary Particle
Fermion
Lepton
Proton
Physical Constants
Permeability of Free Space
Permittivity of Free Space
Planck's Constant
Speed of Light
Special Relativity
Event
Lorentz Transformation
Length Contraction
Lorentz Factor
Time Dilation
Simultaneity
Relativity of Simultaneity
05 - Algebra
Empty Product
Euclidean Division
Factorial
Function
Bijection
Even Function
Injection
Odd Function
Surjection
Integer
Natural Number
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)
Directed Graph
Edge
Directed Edge
Weighted Edge
Examples
Handshaking Theorem
Vertex (Discrete Math)
Weighted Graph
Minimum Spanning Tree
Spanning Tree
Tree (Discrete Mathematics)
Mathematical Proof
Mathematical Induction
Strong Mathematical Induction
Modular Arithmetic
Modulo
Numeral System
Binary Number
Bit
Floating Point Number
Two's Complement
Decimal Number
Hexadecimal Number
Numerical Digit
Radix
Sequence
Geometric Sequence
Summation
07 - Set Theory
Empty Set
Euler Diagram
Power Set
Set
Element
Operations
Complement
Intersection
Set Difference
Set Equality
Subset
Union
Set Builder Notation
Universal Set
08 - Chemistry
Atom
Chemical Formula
Ion
Ionic Bonding
Periodic Table
Periodic Trends
Structural Chemistry
Atomic Orbital
Electron Shell
Lewis Structure
Properties
Atomic Radius
Effective Nuclear Charge
Electron Affinity
Electronegativity
Ionization Energy
09 - Computer Science
Computer Systems
Asynchronous Operation
Byte Extension
Byte Truncation
Character Encoding
ASCII
Control Flow
Call Stack
Concurrent Control Flow
Asynchronous Condition Variable
Lock
Conditional (Computer Science)
Dynamic Control Flow
For Loop
Jump Table
Procedure
Data Structures
Array
Binary Heap
Disjoint Set (Data Structure)
Graph (Data Structure)
Traversals
Breadth-First Traversal
Depth-First Traversal
Graph Cycle
Hash Table
Open Addressing
Double Hashing
Linear Probing
Quadratic Probing
Separate Chaining
Instance Variables
Linked Lists
Doubly Linked List
Singly Linked List
Priority Queue
Queue
Set (Data Structure)
Stack
Structure
Tree (Data Structure)
B-Tree
Binary Tree
Balanced Binary Tree
AVL Tree
In-Order Binary Tree Traversal
Traversals
Breadth-First Tree Traversal
Depth-First Tree Traversal
Endianness
Memory
Dangling Pointers
Heap Memory
Memory Address
Address Alignment
Pointer
Memory Leak
Static Variable
Memory Management Systems
Reference Counting
Paradigms
Event-Driven Programming
Generic Programming
Object Oriented
Call Graph
Class Relationships
Abstract Class
Inheritance
Interface
Overloading
Protected Members
Super Keyword
Supertypes and Subtypes
Type Substitution
Class
Constructor
Data Abstraction
Data Abstraction Specifiers
Testing a Data Abstraction
Design Principles
Liskov Substitution Principle
Single Responsibility Principle
Cohesion
Coupling
Moderate Coupling
Semantic Coupling
Exceptions
Testing Exceptions
Method
Package Relationship Diagram
Package
Patterns
Composite Pattern
Iterator Pattern
Polymorphism
Robust Methods
Program Counter
thread
Cryptography
Hashing
Hash Function
Hardware
Common Circuits
Full Adder
Half Adder
I-O System
I-O Bus
I-O Controller
I-O Device
I-O Mapped Memory
Memory Bus
I-O Techniques
Direct Memory Access
Interrupt (Hardware)
Polling (Computer Science)
Programmed Input-Output
Logic Gate
AND Gate
NAND Gate
NOR Gate
NOT Gate
OR Gate
XNOR Gate
XOR Gate
Microcontroller
General Purpose Input and Output
Peripheral
Watchdog Timer
Persistence
Database
Database Instance
Relational Database
Database Attribute
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
Candidate Key
Primary Key
Super Key
Relation
Relational Algebra
Schema
Program Analysis
Algorithms
Graphs
Dijkstra's Algorithm
Kruskal's Algorithm
Prim's Algorithm
Sorting
Insertion Sort
Merge Sort
Selection Sort
Big-O Notation (Computer Science)
Loop Invariants
Programming Languages
C
Dynamic Array
Dynamic vs Static Arrays
Function Pointer
Static Array
Switch Statement
Java
Memory Management (Java)
Racket
Evaluation
Expression
Predicate (Racket)
Terminology
SM213 Assembly
Conditional (SM213)
For Loop (SM213)
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
Census
Sample Survey
Parameter
Population
Sample
Statistic
Variable (Statistics)
Descriptive Statistics
Bar Graph
Dot Plot
Frequency Table
Histogram
Measures of Centre
Mean
Median
Measures of Variability
Interquartile Range
Range
Standard Deviation
Variance
Pie Chart
Stem-and-Leaf Plots
Inferential Statistics
Analysis of Variance
Pooled Variance
Estimator
Hypothesis Testing
Errors
Type I Error
Type II Error
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
Linear Regression
Residual
Probability
Bayes' Theorem
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
Z-Score
11 - Formal Logic
Argument
Fallacy
Syllogism
Compound Statements
Contradiction
Creating a Statement from Truth Tables
Logical Equivalence
Logical Operator
Biconditional
Conditional
Conjunction
Disjunction
Exclusive Disjunction
Negation
Predicate
Truth Set
Quantifier
Existential Quantifier
Universal Quantifier
Universal Conditional Statements
Simplifying Statement Forms
Statement
Tautology
Truth Table
12 - Language
Languages
Spanish
Ser vs Estar
Tener vs Haber
Tenses
Present Tense
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
11-03-2026
12-03-2026
13-03-2026
17-03-2026
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
Brad Raffensperger
Donald Trump
Jim Runestad
John Eastman
Judges
Mark Howard Cohen
William M. Ray II
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
05 - Lab Trees
06 - Lab Dict
08 - Lab Hash
09 - Lab Heaps
10 - Lab Graphs
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
Web Work 2 (MATH 317)
Problem 1
For the given position vector
, compute the (tangent) velocity vector
for the given value of
(a). Let
, for