Maths

Online maths video
Symbols used
Methods/heuristics/principles (under construction)
Sequences
Golden ratio and Fibonacci sequence $0,1,1,2,3,5,8,13\dots$
the Thue-Morse sequence $0,1,1,0,1,0,0,1,1,0,0,1,0,1,1,0\dots$
Farey sequence – under construction
root sequence – under construction

Triangles, geometry, trigonometry
sin, cos, tan etc – under construction

Polynomials
Ruffini’s rule/synthetic division/Horner’s form/Horner’s method etc
Lill’s method of finding roots graphically
Quadratic equations etc (under construction)
Finding 2 numbers from their product and sum
the quadratic formula
The discriminant and the roots of a quadratic equation
symmetric functions

Series
Sums of powers of integers, finding sums
Jakob Bernoulli’s power sum problem and Bernoulli numbers – see also method of undetermined coefficients
Calculus vs Finite calculus, and falling powers
table of differences and sums
some applications of finite calculus
telescoping series (under construction)
geometric series
some simple series illustrated
the harmonic series
p-series
Riemann zeta function
tests for series convergence/divergence (under construction)
Power series
power series, transcendental functions, interpolation etc – historical (under construction)
Maclaurin and Taylor series, series for e, sin etc
Kummer’s method
power series convergence/divergence (under construction)
series acceleration
– linear transformations
Euler transformation
what wikipedia calls ‘van Wijngaarden transformation’ (which isn’t)
– non-linear transformations
Padé approximants
Aitken’s $\Delta^2$ process
Shanks transformation
Wynn’s $\epsilon$ method
Levin transformations

Generating functions
User-unfriendly guide to Generating functions
Some basic sequences, generating functions, closed forms

Products
$n!$
telescoping products (under construction)
Stirling’s approximation of n! (under construction)

Continued fractions etc
Euclid’s algorithm = continued fractions = squares in a rectangle
The magic table method of finding convergents (under construction)
Combinatorial interpretation of CFs
How to calculate the continued fraction of $\sqrt{13}$ (unfinished)
Gallery of continued fractions
sums and continued fractions – for $\pi/4$
Finding a CF for a given sequence of approximants
Formulas for CFs
common functions as CFs
Series and CFs
CF equivalence transformations
Fractions constructible with $n$ different-sized squares (under construction 🙂 )
3D Euclidean jigsaw method (under construction)
some applications of CFs (under construction)
3D CFs
Pics of CFs

Calculus
A picture of differentiation
Differentiation rules and standard derivatives
integration by parts
series and definite integral

Number theory etc
modular arithmetic
Modular arithmetic & residues – Pictures of possible values of $x^2+y^2$
The binomial theorem
the arithmetic, geometric and harmonic mean and the AMGM inequality
the exponential inequality
Fermat’s (little) theorem
a picture of Fermat’s last theorem
pictures of Primes and prime factors
Euclid, perfect numbers and Mersenne primes
Euler’s phi (totient) function
The Fermat-Euler Theorem
Wilson’s theorem
Euler’s number e
Euler’s number $\gamma$

Dynamical systems, fractals, chaos
Mandelbrot set

to add: – lectures/courses/talks – Prisoner’s dilemma, game theory – RBMs, neural nets – knots – chords, codes – prime formulae – origami – squared rectangles/squares, circuits, graphs – curves, fractals, interpolation – analytic & harmonic complex functions
Bernoulli numbers, Catalan numbers, Lucas numbers, Stern-Brocot tree, Calkin-Wilf tree, squaring rectangles/squares = electric circuit theory, cellular automata

my stuff
Squaring the plane II
Squaring the plane
phinary
chess board equations – board designs (Is this maths or art?! Game design? All 3 I guess.)
$?$ and $\circ$ operators – $?\to+\to\times\to\circ$

my areas of interest (under construction)

Some exercises from Godemont’s Algebra (1968):

adamponting.com

Maths

Leave a Reply Cancel reply