Jan 4, 2010

MathPages: Algebra



Multiple Linear Regression
Periods of Fibonacci Sequences mod m
Kummer's Objection
Irreducibility Criteria
Proving Algebraic Inequalities
Bit-String Orbits Under Rotate-XOR
Piano Keys
The Crystallographic Restriction
Polynomials For Sums of Square Roots
Leaning Ladders
On Ptolmey's Theorem
Machin's Merit
The Twelve-Step Cycle of 4/sin(x)
Finite Subgroups of the Mobius Group
The Fundamental Theorem of Algebra
String Algebra
Apollonius' Tangency Problem
Asymptotic Approach to 2D Arrays
Iterated Logarithmic Functions
Eigenvalue Problems and Matrix Invariants
Iterated Means
Fibonacci, 1/89, And All That
Square Roots by Pencil and Paper
A Quasi-Periodic Sequence
Sums of Powers in Terms of Symmetric Functions
Self-Similar Reverse-Sum Sequences
Generalized Mediant
Tangents, Exponentials, and PI
Recurrences For Harmonic Sums
Bernoulli Numbers and Harmonic Series
Laminar Transformations
Ancient Square Roots
Pythagoras On Dot and Cross Products
Infinite Products and a Tangent Fan
Exponential Partitions
Geometric Dot Products and Digit Reversals
Radical Expression For cos(2pi/7)
On f(x^2+y^2) = f(x)^2 + f(y)^2
Series Solution of Non-Linear Equation
Compressor Stalls and Mobius Transformations
Convoluting Arrays
Harmonic Sums of Integers with k Binary 1's
Interleaving Fibonacci Numbers
Gauss' Lemma Without Divisibility Arguments
Mnemonic Coins and Pattern Avoidance
The Shortest Path To Trigonometric Identities
Polynomials From Pascal's Triangle
Bras, Kets, and Matrices
Decimal Representations as Power Series
Sudoku Symmetries
Resistor Grids
Rounding Up to PI
Reflecting on the Geometric Mean
Sums of Powers
Forests and Trees on a Complex Plain
Inverse Square Weighted Interpolation
The Fundamental Theorem For Palindromic Polynomials
Reducing Quartics to Cubics
Annuities With Inflation
On Eulerian Numbers
Intersections of Polynomials
Angular Angst
Quarky Vector Triple-Product
From the Geometric Series to Stirling Numbers
Orthomagic Square of Squares
Automedian Triangles and Eigen Vectors
Continued Fractions and Characteristic Recurrences
On the Solution of the Cubic
Phased Summations
Arranging the Solutions of f(x+y+z)=xyz
Tangent To PI
Cross-Linear Interpolation
The Super-Symmetric Mean
Rational Sines of Rational Multiples of PI
Cyclic Redundancy Checks
Permutation Loops
Simplex Volumes and the Cayley-Menger Determinant
Loxodromic Aliasing
Determining the Galois Group of a Polynomial
Formal-Numeric Series
Discrete Fourier Transforms
Napoleonic Vectors
Continuous From Discrete Transfer Functions
Expulsion Sets
Bi-Rational Substitutions Giving Squares
Cyclic Divisibility
The Tetratorus and Other Multi-Layered Polyhedra
Maxwell and Second-Degree Commutation
Inverse-Square Forces and Orthogonal Polynomials
Harmonia Mensurarum
Iterative Isoscelizing
Galois Groups
Hermitian Matrices
An Algebraic Duality
Linear Fractional Transformations
The Resultant and Bezout's Theorem
Isospectral Point Sets in Higher Dimensions
Rotation Matrices
Iterative Solutions of Homogeneous Linear Systems
Binary Reverse-Sum Automata
The Cayley-Hamilton Theorem

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