Charles Hoots

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Charles Hoots

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Curriculum Vitae

II. Teaching

Mathematics

2D Harmonic Functions

2D Wave Equation

3D Wave Equation

A Variant of the Heat Equation on the First Quadrant

Abel's Summability

Absolute Convergence of Double Series

Absolute Convergence Test and Properties

Abstract Simplicial Complexes

Accelerating Convergence for Iterative Methods

Additive Functions

Adjoint Operators and Matrices

Affine Spaces of Rn

Algebraic Topology

Alternating Tensor Algebra

Analytic Functions

Analytic Number Theory

Ancillary Statistic

Angular Momentum in Classical Mechanics

Applications of Fourier Series in a Mathematical Context

Approximations of the Riemann Integral in R

Arc-Length Integral in C

Argument Principle

Arithmetic of Cardinal Numbers

Arithmetic of Natural Numbers

Artin-Schreier Extensions

Arzelà–Ascoli Theorem

Asymptotic notation

Automorphism Group of a Covering Map

Automorphism Group of a Field Extension

Autonomous Differential Equations

Bases and Dimension

Basics to Algorithms

Bayesian Approach to Hypothesis Test

Bayesian Approach to Interval Estimation

Berlekamp's Factorisation Algorithm

Bernstein Polynomials

Bessel Functions

Beta Distribution

Binary Relations

Binomial Coefficients

Binomial Distribution

Bisection Method

Black-Scholes equation

Boolean Equations for Digital Circuits

Bounded Function Spaces

Bézout Domains

Cardinal Functions of Topological Spaces

Category Theory

Cauchy Principal Value in R

Cauchy's Integral Formula

Cauchy's Theorem Consequences

Cauchy's Theorem Local Version

Cauchy-Euler Differential Equation

Collectionwise Hausdorff spaces

Combinational Building Blocks for Digital Circuits

Commutator Subgroup

Compact Operators

Compact Sets in R

Compactly Generated

Compactly Supported de Rham Cohomology

Connected Sets in Rn

Context-Free Grammars and Parsing

Continuity on R

Continuous Actions of Groups

Continuous Distributions

Continuous Function Spaces

Convergence of Fourier Series

Convergence of Measurable Functions

Convergence of Nets

Convergence of Random Variables

Countable paracompactness

Covector Fields on Smooth Manifolds

Covering Space Actions

Cyclotomic Polynomials and Extensions

Damped Oscillations in Classical Mechanics

Darboux Sums in Rn

Dedekind Psi Function

Definitions for Classical Umbral Calculus

Determination of Equilibrium Output

Differentiabilty of vector valued functions of R

Differentiablity of Real valued functions of Rn

Differential Forms on Smooth Manifolds

Differential Geometry

Eigenvectors and Upper Triangular Matrices

Existence and Uniqueness of Solutions to Systems of Differential Equations

Existence of Maximums and Minimums of Functions on Metric Spaces

Existence of Solutions of First Order Differential Equations

Expected Value of Random Variables

Expected Value, and Covariance of Random Vectors

Exponential Distribution

Extension of Measures

Exterior Algebra of Multicovectors

Exterior Algebra of Vector Spaces

Extrema of a Differentiable Functions on Manifolds

Falling and Rising Factorials and Pochhamer Symbols

Feedforward Neural Networks

Fermat's Little Theorem

Fibre Bundles on Smooth Manifolds

Field Extensions

Filters and Ideals

Finite Abelian Groups

Finite and Countable Sets

First Order Differential Equations

First Order Linear Differential Equations

Fixed Point Iteration

Fundamental Group of the Circle

Fundamental Matrices for Linear System of Differential Equations

Fundamental Theorems in Functional Analysis

Gauss's Theorem and Divergence in R3

General Linear Group

Generalised Likelihood Ratio

Generation of Continuous Random Variables

Group Extensions

Gâteaux Derivative

Integration of Differential Forms on Smooth Manifolds

Isometries in Vector Spaces

Lie Group Actions

Limit Point Compactness

Limit Theorems of Probability

Limits and Continuity of Vector Valued Functions of R

limsup and liminf

Line Integral over a Vector Field

Line Integrals of Differential 1-forms

Mayer-Vietoris Theorem for Singular Homology

Mean Value Theorem for Fréchet Derivatives

Measurable Functions

Metacompactness

Normal and Galois Closure of a Field Extension

Normal Families of Functions in C

Normal Hausdorff Spaces

nth Order Linear Differential Equations

Null Space and Range

Open and Closed Sets in R

Operations and Structures

Product of Vector Spaces

Real Projective Space

Rectifiable Curves in Rn

Rectifiable Curves

Regular expressions

Regular Hausdorff spaces

Regular Open and Closed Sets

Riemann Integral in R

Riemann Integral in Rn

Riemann-Steiltjes Integral on R

Riemannian Metrics on Smooth Manifolds

Tests for Pseudo-random numbers

The Heat Equation on Euclidean space

The Heat Equation on the Real line

The Riemann Sphere

The Tensor Bundles

The Wave equation

The Zigzag Lemma

Time-Dependent Vector Fields and Flows

Physics

Angular Acceleration

Angular Displacement

Angular Frequency & Period

Angular Momentum

Angular Velocity

Center of Mass Acceleration

Center of Mass Displacement

Center of Mass Dynamics

Center of Mass Velocity & Momentum

Centrifugal Force

Centripetal Acceleration

Centripetal Force

Conservation of Momentum

External & Internal Forces

Frames of Reference

Gravitational Potential Energy

Impulse-Momentum Theorem

Kinetic Friction

Kinetic Potential Energy & Work-Energy Theorem

Linear Momentum

Moment of Inertia

Rolling Motion With No Slipping

Rotational Kinematics

Rotational Kinetic Energy & Work-Energy Theorem

Rotational Work

Static Friction

Uniform Circular Motion

Terminology

' P-primeS-prime '

' Period (wave) '

' PKIKP, (or P'', PKPDF) '

' PmKP (m=3,4,...) '

' Point Force '

' Point Source '

' Poisson Distribution '

' Poisson Solid '

' Random Vibration Theory '

' Rayleigh Waves '

' Rayleigh–Taylor instability '

' Recurrence Interval '

' Response Spectrum '

' S-diff (or Sc) '

' S-primeP-prime '

' safe shutdown earthquake '

' seismic discontinuity '

' seismic gap '

' seismic impedance '

' seismic moment '

' seismic moment tensor '

' seismic reflection or refraction line '

' seismic risk '

' seismic wave '

' seismic zonation '

' seismometer or seismograph '

' seismoscope '

' seismotectonic province '

' seismotectonics '

' shear stress '

' Snell's Law '

' spectral acceleration '

' spectral amplification '

' spectral ratio '

' spike test (tomography) '

' step function '

' Stonely waves '

' strain (elastic) '

' stress drop '

' strike of fault '

' strike-slip fault '

' strong ground-motion '

' surface reflections '

' SURFACE WAVES '

' surface waves (of earthquakes) '

' surface-wave magnitude '

' swarm (of earthquakes) '

' synthetic seismogram '

' takeoff angle '

' Taylor series '

' tectonic earthquakes '

' teleseismic distance '

' tensional (T) axis '

' tensor (mathematics) '

' tesseral harmonic '

' threshold (nuclear verification) '

' torodial mode '

' torsional mode '

' TPg (TSg, TRg) '

' transverse (seismogram) '

' travel-time curve '

' triggered earthquake '

' triggered slip '

' triple junction '

' tsunami earthquake '

' two-station method '

' UNIDENTIFIED ARRIVALS '

' variance (statistics) '

' velocity structure '

' viscoelastic material '

' volcanic earthquakes '

' volcanic tremor '

' Young's modulus (E) '

' Z-transform '

'Acoustic Phases'

'Aseismic Front'

'Aseismic Region'

'Auxiliary Fault Plane'

'Band Pass Filter'

'Body Wave Magnitude'

'Capable Fault'

'Caustic (Waves)'

'Characteristic Earthquake'

'Checkerboard Test (tomography)'

'Coefficient of Friction'

'Compressional (P) Axis'

'Conrad Discontinuity'

'Core (of Earth)'

'Correlation (mathematics)'

'Covariant Matrix (modeling)'

'Critical Facilities'

'CRUSTAL PHASES'

'Deconvolution'

'Delta Function'

'Deterministic Hazard Assessment'

'Deterministic Methods'

'Dilatancy (of rocks)'

'Dilation (waves)'

'Dip-Slip Fault'

'Earthquake Occurence (Recurrence) Interval'

'Earthquake Segment'

'Eigenfunction'

'Elastic Dislocation Theory'

'Fault Propagation Fold'

'Fault-Bend Fold'

'Floating Earthquake'

'Focal Depth (of earthquakes)'

'Forward Modeling Problem (for seismology)'

'Free Oscillation'

'Fundamental Mode (frequencies)'

'Gaussian Filter'

'Gaussian Noise Spectrum'

'Gutenberg-Richter recurrence relationship'

'High Pass Filter'

'Higher Modes (overtones)'

'Impulse Response Function'

'Instrument Response'

'Inverse Modeling Problem (for seismology)'

'J-B Table (Jeffreys-Bullen)'

'Kernel (excitation)'

'Least-Squares Fit'

'Least-Squares Inverse'

'Linear Filter System'

'Near-Field Term (displacements)'

'Orthogonal Function'

III. Reading

Have Read

A Little Larger Than the Entire Universe

A Musical Offering

A People's History of the United States

A Short Account of the Destruction of the Indies

Admiring Silence

Against Interpretation and Other Essays

Barracoon: The Story of the Last "Black Cargo"

Between the World and Me

General System Theory

Group Psychology and the Analysis of the Ego

Gödel, Escher, Bach: An Eternal Golden Braid

Homage to Catalonia

House of Leaves

How Religion Evolved: And Why It Endures

Man's Search for Meaning

Manto: Selected Stories

Meditations: The Annotated Edition

Narrow Road to the Interior: And Other Writings

On the Origin of Species

Pale Blue Dot: A Vision of the Human Future in Space

Permanent Record

Project Hail Mary by Andy Weir

Spinoza's Ethics

SPQR: A History of Ancient Rome

The Anarchy: The East India Company, Corporate Violence, and the Pillage of an Empire

The Book of Disquiet: The Complete Edition

The Conference of the Birds

The Craft of Dying

The Denial of Death

The Fundamental Wisdom of the Middle Way: Nāgārjuna's Mūlamadhyamakakārikā

The God Delusion

The Hero With a Thousand Faces

The Lord of the Rings

The Ministry of Truth: The Biography of George Orwell's 1984

The Noble Eightfold Path: Way to the End of Suffering

The Poetry of Zen

The Power of Myth

The Remains of the Day

The Riddler: Year One

The Setting Sun

The Society of the Spectacle

The Souls of Black Folk

The Structure of Scientific Revolutions

The Three-Body Problem

The Water Dancer

Thought is Your Enemy

Tractatus Logico-Philosophicus

Treat It Gentle

Tristes Tropiques

Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy

What Is Real?: The Unfinished Quest for the Meaning of Quantum Physics

What is the Fourth Dimension?

বিষয় চলচ্চিত্র‌

Notes and Highlights

Notes from A History of Reading by Alberto Manguel

Notes from A Little Larger Than the Entire Universe

A Musical Offering

Notes from A People's History of the United States by Howard Zinn

Notes from A Short Account of the Destruction of the Indies by Bartolome Las Casas

Notes from Admiring Silence by Gurnah Abdulrazak

Notes from Against Interpretation and Other Essays by Susan Sontag

Notes from Animal Farm by George Orwell

Notes from Annihilation of Caste by B.R. Ambedkar

Notes from Barabbas by Par Lagerkvist

Notes from Barracoon

Notes from Being and Time by Martin Heidegger

Notes from Between the World and Me by Ta-Nehisi Coates

General System Theory: Foundations, Development, Applications

Notes from Group Psychology and The Analysis of The Ego

Gödel, Escher, Bach: An Eternal Golden Braid

Notes from Homage to Catalonia

House Of Leaves

Notes from How Religion Evolved by Robin Dunbar

Notes from In the World

Notes from Man’s Search For Meaning by Viktor E Frankl

Notes from Meditations: The Annotated Edition by Marcus Aurelius, Robin Waterfield (editor)

Midnight's Children

Notes from My Name Is Red

Notes from Narrow Road to the Interior and Other Writings by Matsuo Bashō

Notes and Highlights

Notes from Cosmos by Carl Sagan

Thought is Your Enemy

On the origin of species_ by means of natural selection

Notes from Pale Blue Dot

Notes from Permanent Record

Silence by Shūsaku Endō

Notes from Spinoza's Ethics by George Elliot

SPQR: A History of Ancient Rome

Notes from The Anarchy

Notes from The Book of Disquiet by Fernando Pessoa

Notes from The Conference of the Birds

Notes from The Craft of Dying, 40th Anniversary Edition

Notes from The Denial of Death

Notes from The Fundamental Wisdom of the Middle Way

Notes from The God Delusion

Notes from The Hero With a Thousand Faces

The Lord of the Rings

Notes from The Ministry of Truth, The Biography of George Orwell's 1984

Notes from The Noble Eightfold Path by Bhikkhu Bodhi

Notes from The Poetry of Zen by Sam Hamill, J.P. Seaton

Notes from The Power of Myth

Notes from The Sea by John Banville

The Setting Sun

Notes from The Society of the Spectacle by Guy Debord

Souls of Black Folk by W. E. B. Du Bois

Notes from The Structure of Scientific Revolutions by Thomas S. Kuhn

The Three-Body Problem

Notes from Tractatus Logico-Philosophicus by Ludwig Wittgenstein

Notes from Treat it Gentle by Sidney Bechet

Notes from Tristes Tropiques by Claude Lévi-Strauss

V for Vendetta: Mentioned Works

Notes from Walking by Thomas Bernhard

Notes from Weapons of Math Destruction

Notes from What I Believe

Notes from What is Real by Adam Becker

Notes from What is the Fourth Dimension by Charles Howard Hinton

Notes from Why Men Fight

Reading Note Convention

IV. Journal

Living in the PNW

Geologist in the PNW

Living in the PNW

Moving from Hawaii

Teaching in the PNW

A Mountain Willow

About Programming

How AI-generated Contents May Affect Marketing?

Belief, Religion, and the Illusion of Knowledge

Cogito, ergo sum

On AI Note-taking

The Importance of Dying Sincerely

V. Research

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Group Theory

Overview

Topics

Groups
Subgroups
- Normal Subgroups and Quotient Groups
  - Commutator Subgroup
Group Homomorphisms and Isomorphisms
- Automorphism Group
Direct Product of Groups
Group Actions
- Group Equivariant Maps
- Cauchy and Sylow Theorems
  - Semidirect Product of Groups
    - Wreath Product of Groups
  - Classification of Groups of order p^2q
Simple Groups
Solvable Groups
- Nilpotent Groups
Free Product of Groups
- Free Groups
  - Free Abelian Groups
- Group Presentations
Topological Groups
- Continuous Actions of Groups
  - Homogeneous Spaces
- Lie Groups

Connected Pages

Depth