### New Mathematics Video Lectures

Hello everyone! This month I've new maths video lectures. They range from algebraic topology to basic trigonometry, and also include mathematical foundations, history of mathematics, hyperbolic geometry, linear algebra, discrete probability, simple algebra, proofs and pictures (visual thinking), how to turn a sphere inside out, and fractals in science, engineering and finance by Mandelbrot himself.

Rational Trigonometry, Linear Algebra, Algebraic Topology, History of Mathematics, Universal Hyperbolic Geometry, the Foundations of Mathematics and even an elementary introduction to K-6 mathematics.

Includes just 5 lectures for now. Discrete random variables, The Uniform Distribution, The Bernoulli Distribution, The Binomial Distribution, and problem sessions.

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODEs) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and eigenvectors; and Non-linear autonomous systems: critical point analysis and phase plane diagrams.

James Brown. Do you have to see it to believe it? James Robert Brown, Professor of Philosophy at the University of Toronto, will discuss the highly interesting but controversial topic of the legitimate role of visual thinking in mathematics and science. Examples of picture proofs and thought experiments will be given. An explanation of how they work will be sketched.

This video shows how a sphere can be turned inside out. Topology!

Roughness is ubiquitous and a major sensory input of Man. The first step to measure and simulate it was provided by fractal geometry. Illustrative examples will be drawn from the sciences, engineering (the internet) and (more extensively) the variation of financial prices. The beauty of fractals, an unanticipated "premium," helps in teaching and bridges some chasms between different aspects of knowing and feeling.

Have fun with these!

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**Lectures include:**Rational Trigonometry, Linear Algebra, Algebraic Topology, History of Mathematics, Universal Hyperbolic Geometry, the Foundations of Mathematics and even an elementary introduction to K-6 mathematics.

**Discrete Probability (Stanford's Open Classroom)****Course topics:**Includes just 5 lectures for now. Discrete random variables, The Uniform Distribution, The Bernoulli Distribution, The Binomial Distribution, and problem sessions.

**Algebra (Stanford's Open Classroom)****Course description:**Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODEs) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and eigenvectors; and Non-linear autonomous systems: critical point analysis and phase plane diagrams.

**Proofs and Pictures (Visual Thinking)****Abstract:**James Brown. Do you have to see it to believe it? James Robert Brown, Professor of Philosophy at the University of Toronto, will discuss the highly interesting but controversial topic of the legitimate role of visual thinking in mathematics and science. Examples of picture proofs and thought experiments will be given. An explanation of how they work will be sketched.

**How to turn a sphere inside out?****Video description:**This video shows how a sphere can be turned inside out. Topology!

**Fractals in Science, Engineering and Finance (Roughness and Beauty)**

**Lecture description:**Roughness is ubiquitous and a major sensory input of Man. The first step to measure and simulate it was provided by fractal geometry. Illustrative examples will be drawn from the sciences, engineering (the internet) and (more extensively) the variation of financial prices. The beauty of fractals, an unanticipated "premium," helps in teaching and bridges some chasms between different aspects of knowing and feeling.

Have fun with these!

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