San José State University
|
---|
applet-magic.com Thayer Watkins Silicon Valley & Tornado
Alley USA
|
- Mathematics possesses not only truth, but supreme beauty--
a beauty cold and austere, like that of sculpture, without appeal to any part of our
weaker nature… sublimely pure, and capable of a stern perfection such as only
the greatest art can show.
Bertand Russell
- The Asymptotic Limit of the Smallest Magnitude Root of a Polynomial Equation as the Constant Term Goes to Zero
- The Asymptotic Limits of the Roots of a Quadratic Equation as the Constant Term Goes to Zero
- The Relativistic Hamiltonian Function for a Particle in a Poteneial Field
- Quotients in Digit Sum Arithmetic
for Any Base and Any Divisor
- Relationships Involving the "Volume" of a Region, the "Area" of its Boundary Surface, and the
Average Distance from an Interior Point to that Boundary
- Quotients in Digit Sum Arithmetic
for Any Base
- Remainders and the Weighted Digit Sums of Numbers
- The Weighted Digit Sums of Multiples of Digits
- Simple, Elegant yet Neglected
Theorems Concerning Areas
and Volumes That Includes
Circles and Spheres as Limits
- A Function Relevant for Quantum Theoretic Analysis
- The Expected Value of Weighted Averages is the Expected Value of the Original Variable
- The Asymptotic Sine Integral of Functions
- Means and Variances of Probability Distributions, Quantum and Classical
- Fourier Transforms of the Time Independent Schroedinger Equation
- The Discovery by the Indian
Mathematician Brahmagupta
that the Product Two Negative
Numbers is a Positive Number
- Some Simple Theorems Concerning Monoids
- The Associativity of Function Composition
- The Transformation of the Time Dependent Schroedinger Equation
into Two Linked Equations Involving Only Real Dependent Variables
- The Computation of Functions of Square Matrices
- The Baker-Campbell-Hausdorff Formula for Exponential Matrices
- An Alternate Solution to the Generalized Helmholtz Equation of One Dimension
- A Solution to the Generalized Helmholtz Equation of One Dimension
- Noether's Theorem for Fields
- Noether's Theorem and Quantized Parameters
- Noether's Theorem: Its Explanation and Proof
- Digit Sum Arithmetic for Numbers with Nonintegral Bases
- Illustration of the Quotient Theorem of Digital Arithmetic
- Studies Concerning the Solution of the Generalized Helmholtz Equation
- A property of the Solution of a Generalized Helmholtz Equation of Any Dimension
- The Solution of a Generalized Helmholtz Equation of Two Dimensions
- The Nature and History of the Bayes Rule for Computing Inverse Probabilities
- Some Remarkable Properties of Polynomials
- An Exponential of a Purely Imaginary Matrix and the Trigonometric Identities
- The relative extrema of the solution to a generalized Helmholtz equation
- The Yoneda lemma in Category Theory
- The Concept of Functor in Category Theory
- Studies Concerning the Weighted Sums of the Coefficients of Polynomials
- Some Properties of the Sum of Digits Function
- The Nature and History of the Bayes Rule for Computing Inverse Probabilities
- Divisibility, Quotients and Remainders for Polynomials over a Commutative Ring
- Divisibility, Quotients and Remainders for Polynomials over a Field
- Quotients and Remainders in Digit Sum Arithmetic
- Weighted Summations of Polynomial Coefficients and Remainders
- The Scheme of Perturbation Analysis
- Divisibility and Remainders for Polynomials over a Field
- Six Lemmas on the Remainders for the Division of Polynomials
- The Net Sum of a Decimal Representation of a Number
Resulting From an Alternation of Addition and Subtraction
- Coefficient Sums for Infinite Polynomial Series
- Two General Theorems Concerning the Coefficient Sums of Polynomials over a Field
- Some general properties of polynomials over a field
- Some Interesting General Properties of Polynomials
- The Wong-Zakai Adjustment to a Stochastic Differential Equation
- The Introduction to Matrix Calculus:
The Extention of Calculus Operations
to Matrices
- The Solution to the Generalized Helmholtz Equation in Matrix Form
- A Transformation of a Generalized Helmholtz Equation
- The Functional Derivative: Its Natue and Use
- Cayley's Theorem and its Proof
- The Existence of Creator and Annihilator Operators in the
Canonical Quantization of a Field
- The Spatial Average of the Probability Density Function Derived from the Solution
to a Generalized Helmholtz Equation of One Dimension
- Lagrangian Field Theory
- The Solution to a Generalized Helmholtz Equation of One Dimension
- Decimal Numbers of Concatenated Blocks
Which are Fractional Numbers
- Decimal Numbers of Concatenated Blocks
Which are Reciprocals of Integers
- The Binomial Theorem: A Proof in One Step
- Finding the Unit Digits of Powers of Integers
- Benjamin's Theorem and the Power of Algebra
- The d'Alembert Solution to the Wave Equation with Initial Conditions
- Determinants and Area and Volumes of Parallelotopes (Parallelograms and Parallelopipeds)
- The Change of Variables Theorem for Integrals
- The Definition and Properties of a Mathematical Field
- A Lemma on the Associativity of the Composition of Functions
- The Helmholtz Equation and Its Solution
- The Similarity of a Square Matrix to a Jordan Canonical Form
- The Matrix Representation of Sets of Linear Combinations of Vectors
- The Generalized Eigenvectors of a Matrix and their Linear Indepence
- The Similarity of Square Matrices
- Decomposition of the Vector Space Associated with a Matrix in Terms of
the Null Spaces Associated with the Eigenvalues of that Matrix.
- The Linear Independence of the Eigenspaces of a Matrix
- The Cardinality of the Algebraic Numbers
- The Irrationality of the Square Root of 2
- The Theorem of George Green and its Proof
- The Components of Mandelbrot Sets Associated with Limit 2-Cycles
- The Powers of a Jordan Canonical Form Matrix
- The Square of a Jordan Canonical Form Matrix
- The Theorem on the Canonical Form of Matrices by Camille Jordan
- The Theorem that the Sum of the Eigenvalues of a Matrix is Equal to its Trace
- The Symmetries of the General Structures of Mandelbrot Sets
- A Beautiful Theorem Concerning Determinants
- The Relationship Between Group Representations and Their Generators
-
The General Structures of the Fully General Mandelbrot Sets
- The Barest Introduction to Category Theory
- The Amazing, Incredible
Life of the Mathematician, Alexander Grothendieck
- SU(2), the Special Unitary Group
of Order 2
- The Representation of
Rational Numbers as Decimal Numbers
- The Sets of
Repeating Decimals
- The Properties of
Integers and Their Extension to Integral Domains
- Some Applications
of the Notion of an Infinitesimal in Geometry
- Infinitesimals and the
Extention of the Real Number System
- The Uncertainty
Principle for Energy and Time
- The Derivation of the
Uncertainty Principle
- Quantum Theory and the
Interactions of Electrons in Multi-Electron Atoms
- The Discrete
Approximations of the 2nd Derivatives of a Function of Two Variables
- The Digit Sum
Arithmetic of Exponentiation
- The Digit Sum of a
Number to Base 10 is Equivalent to Its Remainder Upon Division by 9
- The Real Numbers Are Not
Enough: The Need for More Numbers (the Hyperreals) to Label Ordered Sets
- The DigitSum of a Number
and Its Remainder for Division by Nine
- Remainders and
Representations: Simple Applications of Number Theory
- Fermat's Little
Theorem
- The Interesting Properties of
1001, Scheherezade's Number
- The Cayley-Hamilton Theorem:
Its Nature and Its Proof
- An Euler-type
Theorem for Exponentially Weighted Homogeneous Functions
- Polyhedra with Three
Types of Faces and One Type of Vertex
- The Regularities of the
Platonic and Archimedean Polyhedra
- The Algebraic
Determination of the Structures of Polyhedra
- On the Algebraic
Determination of the Structure of Polyhedra
- The Analogues
of the Dual Theorem of Euler's Twelve Pentagon Theorem
- Euler-type
Theorems Concerning the Number of Polygons of Polyhedra
- The Euler-Poincare
Characteristic of Conjoined Polyhedra
- Proof That There
Are Only Five Platonic Polyhedra
- The Theorem Dual to
Euler's Twelve Pentagon Theorem
- Euler's Theorem Concerning
Polyhedra Composed of Pentagons and Hexagons: There Must Be Exactly 12
Pentagons
- The Virial Theorem and the
Matter of the Origin of the Position Vectors of the Particles
- The Relative Variance
of a Binary Function of Random Variables Compared to that of the
Corresponding Unary Function
- Élie Cartan's
Generalization of the Frenet-Serret Formulas
- The Virial Theorem: Its
Explanation, Proof, Application and Limitations
- Real Numbers as Dedekind
Cuts
- The Area of an
(n-1)-Dimensional Subsphere in Terms of the Arc Distance in the
n-Dimensional Sphere
- Real Numbers as Partitions
of the Ordered Field of Rational Numbers (Dedekind Cuts)
- The Characteristic Function
of Algebraic Combinations of Random Variables and cumulative Sums of Random
Disturbances
- Simple, Yet Amazing Theorems
Concerning the Cumulative Curvature of a Curve Between Two Points
- The Estimation of the
Parameters of the Characteristic Function of a Levy-Stable Probability
Distribution
- The Euler-Poincare
Characteristic of Strip and Straps: Open, Closed and Mobius
- The Evaluation of the
integral ∫r∞(exp(-z)/z²)dz
- Noether's Theorem and its
Proof
- Self-Similar
Mathematical Structures
- Srinivasa Ramanujan: A
Mathematician Brilliant Beyond Comparison
- The Euler Poincaré
Characteristic for Different Dimensions of Geometric Figures
- The Euler Poincaré
Characteristic of Polyhedral Solids
- The Euler
Characteristic of Polyhedra
- An Introduction to Tensor
Analysis
- The Spectra of Various
Transformations of White Noise
- The Effect of Averaging
Variables Which are the Cumulative Sum of Random Disturbances
- Digit Sum
Arithmetic
- The Real Numbers Are Not Enough: The Need for More Numbers (the Hyperreals) to Label Ordered Sets
- Remainders and Representations: Simple Applications of Number Theory
- Fermat's Little Theorem
- The Cayley-Hamilton Theorem: Its Nature and Its Proof
- The Interesting Properties of 1001, Scheherezade's Number
- Theorems Concerning the Existence of Solutions to Systems of Ordinary Differential Equations
- Polyhedra with Three Types of Faces and One Type of Vertex
- The Polyhedral Structure of Nuclear Shells
- The Regularities of the Platonic and Archimedean Polyhedra
- The Algebraic Determination of the Structures of Polyhedra
- On the Algebraic Determination of the Structure of Polyhedra
- The Analogues of the Dual Theorem of Euler's Twelve Pentagon Theorem
- Euler-type Theorems Concerning the Number of Polygons of Polyhedra
- The Euler-Poincare Characteristic of Conjoined Polyhedra
- Proof That There Are Only Five Platonic Polyhedra
- The Theorem Dual to Euler's Twelve Pentagon Theorem
- Euler's Theorem Concerning Polyhedra Composed of Pentagons
and Hexagons: There Must Be Exactly 12 Pentagons
- Élie Cartan's Generalization of the Frenet-Serret Formulas
- Real Numbers as Partitions of the Ordered Field of Rational Numbers (Dedekind Cuts)
- An Introduction to Tensor Analysis
- Spherical Geometry and Trigonometry
- Bezout's Theorem
- The Envelope Theorem
- The Central Limit Theorem
- Area-Volume Formulas
- Pontryagin's Maximum Principle
- Second Order Conditions for Extremes
- Mandelbrot's Variation of Certain Speculative
Prices
- Foundations of Algebraic Topology
- Georg Cantor and Cantor's Theorem
- Characteristic
Functions
- Inversion of a
Characteristic Function
- Complex
Numbers
- Convex Sets
- Differential Forms
- Differential Geometry from
a Differential Forms
Point of View
- Principal
Component Analysis
- Quadratic Equation
Solver
- The Nature of the
Real Numbers
- Stable
Distributions
- Stochastic
Processes
- The Generalized Stokes Theorem
- Perturbation
Theory
- Infinitely
Divisible Random Variables
- Infinitesimal
Random Variables
- Fuzzy Sets
- Georg Cantor and Cantor's Theorem
- The Arithmetic
of Cardinal Numbers
- The Arithmetic of
Ordinal Numbers
- Fixed Point Theorems
- The Lambda Calculus
- Conditional Expectations and Random Walks of Security
Prices
- Foundations of Point Set Topology
- Kuratowski's Closure Operation in Topology
- An Introduction to Cohomology in Topology
- The Hausdorff Separation Axiom and Other Separation
Axioms in Topology
- The Euler-Poincaré Formula in Topology
- The Factor Group of a Group With Respect to a
Normal Subgroup
- Axial Vectors in Rotating Coordinate Systems
- Euler's Theorem and Its Generalization
- Basic Theory of Groups
- The Converse of Euler's Theorem
- Fundamentals of Lie Algebras
- The Structure of the Set of Lie Algebras
- The Gauss-Bonnet Theorem and Its Generalization
- The Gauss-Bonnet Formula for Curves
- Mikusinki's Operational Calculus
- Spherical Geometry and Trigonometry
- The Nature of Spinors
- Levi-Civita's Concept of the Parallel
Transport
of Vectors on a Surface
- The Implicit Function Theorem
- The Second Order Conditions for Extremes:
Constrained and
Unconstrained
- The Gamma Function: Euler's Generalization
of the Factorial
Function
- Extensions of the Central Limit Theorem
- Filters and Ultrafilters
- The Calculus of Infinitesimals
- An Introduction to Elementary Algebra
- Traveling Wave Solutions to the Regularized Long Wave Equation (RLWE)
- Traveling Wave Solutions to the Korteweg de Vries Equation (KdV)
- The Hyperbolic Secant Solution a·sech²(bz).
- Secondary Solitary Waves in the Collision of Solutions to the
Regularized Long Wave Equation
- The Summation of Series Using the Anti-Differencing Operation
- The Nature of Differential Forms
- Kakutani's Fixed Point Theorem
- Real Numbers as Equivalence Classes of Cauchy Sequences of
Rational Numbers
- The Structures of the Mandelbrot Sets
- The Elastic Collision of Spheres
- Digit Sum Arithmetic
- The Lagrange Theorem for Groups