Dr. Trefor Bazett

Bayesian Truth Serum // Using MATH to catch liars

Bayes Theorem Example: Surprising False Positives

The Bernoulli Equation // Substitutions in Differential Equations

Chain Rule: the Derivative of a Composition

Intro to Conditional Probability

A beautiful combinatorical proof of the Brouwer Fixed Point Theorem - Via Sperners Lemma

COMPLEX Eigenvalues, Eigenvectors & Diagonalization **full example**

Two Conditional Probability Examples (whats the difference???)

The Polar Form of COMPLEX NUMBERS // Finding the nth roots of -1

The Multi-Variable Chain Rule: Derivatives of Compositions

Properties in Graph Theory: Complete, Connected, Subgraph, Induced Subgraph

Making a Math Concept Map | Ex: Linear Independence

Estimating the Remainder of a Series Approximation via the Integral Test

Undetermined Coefficients: Solving non-homogeneous ODEs

Line Integrals in 3D // Formula & Three Applications

Proof by Contrapositive | Method & First Example

Algebraic operations on Matrices - scalar multiplication, matrix addition, and transposition

Plotting Parametric Curves

Angle between vectors leads to defining the Dot Product | Multivariable Calculus

Derivative Rules: Power Rule, Additivity, and Scalar Multiplication

How to Find the Equation of a Tangent Line

Whats the big idea of Linear Algebra? **Course Intro**

The Definite Integral Part I: Approximating Areas with rectangles

Geometric Series | Convergence, Derivation, and Example

Integers & Rationals are both infinite but is it the SAME infinity?

Fundamental Theorem of Calculus II

Applying LHopitals Rule to Exponential Indeterminate Forms

Areas in Polar Coordinates

The Laplace Transform of Derivatives and Integrals

Ex: Optimizing the Volume of a Box With Fixed Surface Area

Higher Order Constant Coefficient Differential Equations: y+y=0 and y-3y+3y-y=0

The union of two sets

Using determinants to compute eigenvalues & eigenvectors

The Chain Rule using Leibniz notation

My Favorite Theorem: The Borsuk-Ulam Theorem

Intro to Mathematical Induction

Logarithmic Differentiation | Example: x^sinx

Using Elementary Row Operations to Solve Systems of Linear Equations

Coordinate Systems From Non-Standard Bases | Definitions + Visualization

Line Integrals: Full Example

Induction Proofs Involving Inequalities.

Invertible Matrices correspond with Invertible Transformations **proof**

Infinite Limit vs Limits at Infinity of a Composite Function

The Theory of Higher Order Differential Equations

Logical Equivalence of Two Statements

Linear Differential Equations & the Method of Integrating Factors

The Method of Integrating Factors for Linear 1st Order ODEs **full example**

Limits of Sequences, Limit laws & Function Representations

Finding the scalar potential function for a conservative vector field // Vector Calculus

Triple Integrals in Cartesian Coordinates | Volume between Surfaces

Biconditional Statements | if and only if