MathDoctorBob

FIT1.1. Number Fields

BM10.1. The Euclidean Algorithm for the Integers

Example of Spectral Theorem (3x3 Symmetric Matrix)

Example of Chain Rule 3 - Trig Functions

Definition of Tangent Line

Example of Geometric Sum

BCA2.1. Linear Equations in Two Variables

Example of Linear Combination

Example of Group Automorphism 1 (Requires Linear Algebra)

Inverse of 4x4 Matrix Using Adjugate Formula

Positive Semi-Definite Matrix 2: Spectral Theorem

Positive Semi-Definite Matrix 1: Square Root

Positive Semi-Definite Matrix 3: Factorization of Invertible Matrices

Consistency of a System of Linear Equations

Multiplying Complex Numbers

Example of Skew-Symmetric Matrix

Power Rule for Rational Exponents

Limits 1f - Trigonometric Functions

Example of De Moivres Theorem

FIT4.3.2. Example of Galois Group over Finite Field

Using Synthetic Division to Evaluate a Polynomial

Absolute Convergence Test

Example of Sampling Distribution of the Mean

Complex Numbers for ODEs (4 of 4)

GT4. Normal Subgroups and Quotient Groups

FIT4.3.1. Galois Group of Order 8

Spectral Theorem for Real Matrices: General nxn Case

Orthogonal Transformations 2: 3x3 Case

GT22. The Fundamental Theorem of Finite Abelian Groups

FIT4.3. Galois Correspondence 1 - Examples

Angle Between Two Planes

Overview of Summation Formulas

Domain of a Vector-Valued Function

FIT4.1. Galois Group of a Polynomial

RNT2.3. Euclidean Domains

Fast Factorization of Polynomial

Inverse of a Matrix Using the Cayley-Hamilton Theorem

Planes: Parallel, Equal, or Intersecting?

Limit and Derivative of Vector Function

Implicit Differentiation with e^x

Cayley-Hamilton Theorem for 2x2 Matrices

Cayley-Hamilton Theorem: General Case

Cayley-Hamilton Theorem Example 2

RT7.1: Finite Abelian Groups: Character Orthogonality

Fourier Series: Example of Orthonormal Set of Functions

Improper Integrals 1 - Infinite Limits of Integration

Unit Tangent and Normal Vectors for a Helix

FIT3.2.1. Cyclotomic Polynomials

Directional Derivative of f(x,y,z) = xy + yz

BCA4.3. Polynomials: Division

Example of Proof by Induction 4 - Hard Inequality