Powersets

Creating the set of all possible subsets, the powerset of a set with Scheme.

Pollards Algorithm

Pollards algorithm can be used to factor huge numbers.

Perfect Numbers

This demonstrates a mathematical concept of a perfect number in a computational abstraction utilizing scheme.

Python and CHOP Waveforms

How to generate waveforms with Python or CHOPs in Houdini.

Aligning LaTeX images

This bash script helps to align images, or define boundaries for external postscript files within a tex file that uses pstricks.

Unit Vectors PStricks

This generates the LaTeX code for creating vectors on a unit circle.

Generate LaTeX Matrices

This PHP script generates LaTeX code for a matrix.

LaTeX PStricks Stem Plots

This PHP script generates Stem Plots in LaTeX using PStricks.

BASH script for LaTeX generation

A simple BASH script for LaTeX rendering.

Math 55 Review

A comprehensive overview of the math 55 course.

Simple LaTeX

Some simple examples of generating files with LaTeX.

Structural Induction

Structural induction on ternary trees.

Expected Value

Expected value of a random variable in probability theory.

Distinguishable and Indistinguishable

Distinguishable and Indistinguishable boxes and objects. Combinations and permutations. Placing objects into boxes.

Infinite Series

Infinite Series in Calculus.

Linear Congruences

Rules for Linear Congruences.

Scheme mathematics

Using scheme to compute derivatives and integrals.

Discrete Fourier Transforms

A great video explaining Discrete Fourier Transforms.

Euclidean Algorithm

The Euclidean Algorithm is used to find the Greatest Common Divisor. Written in Scheme.

Base Expansion

How to compute a base b expansion of a number n.

Modular Exponentiation

Modular Exponentiation is an important algorithm in cryptography and computer science.

Graphing Guidelines

Graphing guidelines using first derivative test and concavity test (aka second derivative test).

Work

Basic work problems using integration techniques.

Area and Volume

Volume and area using integration techniques.

Series

Arithmetic and Geometric series.

Optimization

Applications of the derivative to optimize functions.

The Mean Value Theorem

Rolle's theorem and the Mean value theorem (MVT).

Related Rates

Related rate problems.

Vertical Tangent Lines

Finding vertical tangent lines of a function.

Derivative Problems

Some word problems involving rates and derivatives.

Finding Tangent Lines

Solving for equations of tangent lines involving specific points on a graph.

The Chain Rule

Solving derivatives using the chain rule.

Errors with Differentials

Determining maximum error, average and percentage error using differentials.

Increments and Differentials

Solving problems with the derivative and increments of x, involving linear approximation.

Techniques of Differentiation

Proofs for the product rule and quotient rule when finding the derivative.

Trigonometric derivatives

Proof of trigonometric derivatives using the Limit Definition of the Derivative.

Solving with the derivative

Some different problems using the derivative.

Division

Dividing floats with true division as opposed to floor division.

Factorial

Factorials using python.

Using derivative for velocity

Use the derivative to find the instantaneous velocity of a function.

Derivative

The Derivative, tangent lines, and rates of change.

Add Fractions

Adds two fractions, and reduces them using the modulus function.

Continuous Functions

Continuous functions!

Limits Discovering Asymptotes

Limits that lead to the discovery of a vertical asymptote.

Sandwich Theorem

Solving limits using the Sandwich Theorem, or Squeeze Theorem.

Intermediate Value Theorem

Explore continuous functions with the intermediate value theorem.

Limits Involving Infinity

Solving limits with unbounded values of infinity.

Scales

Musical scales.

Chords

Chords!

Intervals and inversions

This code will determine the musical relationship between different notes based on a tonic. Includes inversions.

Note Numbers

A keyboard with the note numbers for mathematical use.

Frequency

Mathematics, music theory, and programming to create a table of the 88 keys of a grand piano.

Implicit Differentiation

Techniques for finding the derivative using implicit differentiation.

Hyperbola

Hyperbolic functions to create hyperbolas.

Law of Cosines

Formulas for the law of cosines.

Proof of Limit

How to make a proof for a Limit of a function using delta and epsilon.

Definition of a Limit

The precise definition of the Limit of a function.

Cross Product

This demonstrates using the cross product in an expression in prepping normals for copy stamping.

Trigonometric Equations

Methods for solving trigonometric equations.

Sum and Difference Formulas

Formulas for the sum and difference of two angles within a trigonometric function.

Double and Half Angle Formulas

Formulas and identities for double and half angles.

Law of Sines

Formulas for the law of sines.

Inverses

Inverse trigonometric functions.

Interest and Investments

Formulas for compounding interest, and doubling investments.

Exponential Growth and Decay

Use of exponents and logorithms to solve problems involving half-life and population growth.

Transformations

Graph transformations.

Inequalities

Inequalities!

Greatest Integer Function

The greatest integer function.

Absolute Value Function

Absolute value function.

Square Root Function

The square root function!

Cube Root Function

The cube root function!

Rational Functions

Rational functions!

Exponential Functions

Rules of exponential functions and their graphs.

Identities

How the fundamental and Pythagorean identities were derived, along with a few identity problems.

Cosecant

Anatomy of the cosecant function.

Secant

Anatomy of the secant function.

Cotangent

Anatomy of the cotangent function.

Tangent

Anatomy of the tangent function.

Cosine

Anatomy of a cosine wave.

Helix

Use trigonometry to create a helix!

Quadratic

The quadratic formula.

Sine

Tbe trigonometric sine function.

Logarithm

Rules of logarithm functions and their graphs.

Unit Circle

The radians of the unit circle...a trigonometry must.

figure 8 Klien bottle

The Klein bottle is a closed nonorientable surface that has no inside or outside.

Iso Surface: Heart

A heart-shaped surface given by the sextic equation

Iso Surfaces: Barth Decic

Algebraic surfaces which can be represented implicitly by a polynomials of a degree of 10 in x, y, and z.

Oscillator

Copy stamping with oscillations using the math behind pitch.

Shading with Dot Product

A mathematical and visual look at the Dot Product in regards to shading.