Classical curves | Differential Geometry 1 | NJ Wildberger
The first lecture of a beginner's course on Differential Geometry! Given by Assoc Prof N J Wildberger of the School of Mathematics and Statistics at UNSW.
Insights into Mathematics
Differential geometry with finite fields | Differential Geometry 7 | NJ Wildberger
With an algebraic approach to differential geometry, the possibility of working over finite fields emerges. This is another key advantage to following Newton, ...
Insights into Mathematics
The Frenet Serret equations | Differential Geometry 18 | NJ Wildberger
The Frenet Serret equations describe what is happening to a unit speed space curve, twisting and rotating around in three dimensional space. This is done with ...
Insights into Mathematics
The Biggest Ideas in the Universe | 13. Geometry and Topology
The Biggest Ideas in the Universe is a series of videos where I talk informally about some of the fundamental concepts that help us understand our natural world.
Sean Carroll
The fundamental dream of algebra | Abstract Algebra Math Foundations 216 | NJ Wildberger
This video reveals the unfortunate truth about the "Fundamental Theorem of Algebra": namely that it is not actually correct. This is meant to be a core result in ...
Insights into Mathematics
Modern "Set Theory" - is it a religious belief system? | Set Theory Math Foundations 250
Modern pure mathematics suffers from a uniform disinterest in examining the foundations of the subject carefully and objectively. The current belief system that ...
Insights into Mathematics
Manifolds, classification of surfaces and Euler characteristic | Differential Geometry 25
Here we give an informal introduction to the modern idea of `manifold', putting aside all the many logical difficulties that are bound up in this definition: difficulties ...
Insights into Mathematics
Curvature, turning numbers and winding numbers | Differential Geometry 16 | NJ Wildberger
We discuss the curvature of planar curves and applications to turning numbers and winding numbers, also called the index. We use this opportunity to talk a little ...
Insights into Mathematics
Gauss's view of curvature and the Theorema Egregium | Differential Geometry 35 | NJ Wildberger
In this video we discuss Gauss's view of curvature in terms of the derivative of the Gauss-Rodrigues map (the image of a unit normal N) into the unit sphere, and ...
Insights into Mathematics
The Triple spread formula, circumcircles and curvature | Rational Geometry Math Foundations 146
This video looks at the projective Triple quad formula, also known as the Triple spread formula in Rational Trigonometry, and how it relates to curvature.
Insights into Mathematics
An introduction to algebraic curves | Arithmetic and Geometry Math Foundations 76 | N J Wildberger
This is a gentle introduction to curves and more specifically algebraic curves. We look at historical aspects of curves, going back to the ancient Greeks, then on ...
Insights into Mathematics
The basic framework for geometry (I) | Arithmetic and Geometry Math Foundations 23 | N J Wildberger
This video begins to lay out proper foundations for planar Euclidean geometry, based on arithmetic. We follow Descartes and Fermat in working in a coordinate ...
Insights into Mathematics
Projective view of conics and quadrics | Differential Geometry 9 | NJ Wildberger
In this video we introduce projective geometry into the study of conics and quadrics. Our point of view follows Mobius and Plucker: the projective plane is ...
Insights into Mathematics
Lines and parabolas I | Arithmetic and Geometry Math Foundations 73 | N J Wildberger
We study lines and parabolas using elementary calculus derived only from algebraic manipulations with polynomials, or polynumbers in our setting. We discuss ...
Insights into Mathematics
The decline of rigour in modern mathematics | Real numbers and limits Math Foundations 88
Rigour means logical validity or accuracy. In this lecture we look at this concept in some detail, describe the important role of Euclid's Elements, talk about proof, ...
Insights into Mathematics
Classification of 2-manifolds and Euler characteristic | Differential Geometry 26 | NJ Wildberger
We describe the important classification of compact, oriented 2-manifolds, and the relation with the topological invariant called the Euler characteristic. The idea ...
Insights into Mathematics
Mathematical space and a basic duality in geometry | Rational Geometry Math Foundations 122
In this video we introduce some basic orientation to the problem of how we represent, and think about, space in mathematics. One key idea is the fundamental ...
Insights into Mathematics
Euclid's Books VI--XIII | Arithmetic and Geometry Math Foundations 21 | N J Wildberger
A very brief outline of the contents of the later books in Euclid's Elements dealing with geometry. This includes the work on three dimensional, or solid, geometry, ...
Insights into Mathematics
Lecture 02, Differential Geometry. ( some more basics from elementary mathematics)
Some fundamentals which are useful in every field of mathematics are discussed in this video.
Rigorous Mathematics By Prof. Usman Ahmed Mansoor.
Duality, polarity and projective linear algebra (II) | Differential Geometry 11 | NJ Wildberger
We review the simple algebraic set-up for projective points and projective lines, expressed as row and column 3-vectors. Transformations via projective ...
Insights into Mathematics
Parallelograms and affine combinations | Arithmetic + Geometry Math Foundations 31 | N J Wildberger
We use vectors to introduce parallelograms, the parametric representation of a line, and affine combinations, such as midpoints. This video belongs to ...
Insights into Mathematics
Duality, polarity and projective linear algebra | Differential Geometry 10 | NJ Wildberger
Projective geometry is a fundamental subject in mathematics, which remarkably is little studied by undergraduates these days. But this situation is about to ...
Insights into Mathematics
Spacetime Foundations of General Relativity and Differential Geometry Lecture Notes in Physics Monog
Sharon Walsh
Why angles don't really work (II) | Arithmetic and Geometry Math Foundations 39 | N J Wildberger
This video continues to discuss difficulties with angles. It takes a historical approach, and emphasizes that with angles, imprecision is unavoidable for most ...
Insights into Mathematics
Metrical structure and curvature of a parabola | Differential Geometry 12 | NJ Wildberger
In this lecture we introduce a general approach to metrical structure, via a symmetric bilinear form in either an affine or projective setting, and then begin studying ...
Insights into Mathematics
Programa de Mestrado: Geometria Diferencial - Aula 01
Programa de Mestrado 2014: Geometria Diferencial Professor: Luis Adrián Florit Aula 01 - 11-03-2014 Página: ...
Instituto de Matemática Pura e Aplicada
Logical weakness in modern pure mathematics | Real numbers and limits Math Foundations 87
We begin PART II of this video course: "Mathematics on trial - why modern pure mathematics doesn't work". This video outlines the case for the prosecution: that ...
Insights into Mathematics
A celebration of 200 videos of MathFoundations | Data Structures Math Foundations 201
We have just arrived at the 200 video mark in the MathFoundations series, which aims to promote critical thinking about the foundations of mathematics and ...
Insights into Mathematics
Visualizing the folium surface with GeoGebra | Differential Geometry 6 | NJ Wildberger
In this tutorial we explore the surface z=x^3+y^3+3xy using GeoGebra. The aim is to develop our skills using this dynamic geometry package, at the same time ...
Insights into Mathematics
Meusnier, Monge and Dupin II | Differential Geometry 32 | NJ Wildberger
Here we continue our study of the works of three important French differential geometers. Today we discuss G. Monge, who is sometimes called the father of the ...
Insights into Mathematics
Parametrized curves and algebraic curves | Differential Geometry 3 | NJ Wildberger
This lecture discusses parametrization of curves. We start with the case of conics, going back to the ancient Greeks, and then move to more general algebraic ...
Insights into Mathematics
Paraboloids and associated quadratic forms | Differential Geometry 23 | NJ Wildberger
Paraboloids are going to play a special role in our understanding of curvature. The idea is that we are going to locally approximate a surface S near a point by a ...
Insights into Mathematics
Affine one-dimensional geometry and the Triple Quad Formula | Rational Geometry Math Foundations 123
In this video we introduce the second most important theorem in all of mathematics (excluding the laws of arithmetic)! It is certainly remarkable that the ...
Insights into Mathematics
Computational Differential Geometry, Optimization Algorithms by Mark Transtrum
26 December 2016 to 07 January 2017 VENUE: Madhava Lecture Hall, ICTS Bangalore Information theory and computational complexity have emerged as ...
International Centre for Theoretical Sciences
General Relativity Lecture 3
(October 8, 2012) Leonard Susskind continues his discussion of Riemannian geometry and uses it as a foundation for general relativity. This series is the fourth ...
Stanford
The projective Quadruple quad formula | Rational Geometry Math Foundations 148 | NJ Wildberger
In this video we introduce the projective version of the Quadruple quad formula, which not only controls the relationship between four projective points, but has a ...
Insights into Mathematics
Meusnier, Monge and Dupin I | Differential Geometry 31 | NJ Wildberger
This is the first of three videos that discuss the mathematical lives and works of three influential French differential geometers. We begin with J. Meusnier, who ...
Insights into Mathematics
Discrete Differential Geometry - Helping Machines (and People) Think Clearly about Shape
For more information, see: http://keenan.is/here) The world around us is full of shapes: airplane wings and cell phones, brain tumors and rising loaves of bread, ...
Keenan Crane
Understand Calculus in 10 Minutes
TabletClass Math http://www.tabletclass.com learn the basics of calculus quickly. This video is designed to introduce calculus concepts for all math students and ...
TabletClass Math
The Essence of Calculus, Chapter 1
What might it feel like to invent calculus? Brought to you by you: http://3b1b.co/eoc1-thanks Home page: https://www.3blue1brown.com/ In this first video of the ...
3Blue1Brown
The Foundations of Mathematics
Topic 3 of "Brief Introduction to the Foundations of Mathematics" lecture. ----------------------------------- In this video we will talk very briefly about the evolution of The ...
MathVideoLectures.com
Computational Information Geometry (CIG) in Statistics: foundations (1)
Computational Information Geometry (CIG) in Statistics: foundations (1) by Frank Critchley, Karim Anaya-Izquierdo, Paul Marriott, Paul Vos.
GSI2013
