Quaternions as 4x4 Matrices - Connections to Linear Algebra
In math, it's usually possible to view an object or concept from many different (but equivalent) angles. In this video, we will see that the quaternions may be viewed as 4x4 real-valued matrices of a special form. What is interesting here is that if you know how to multiply matrices, you a
From playlist Quaternions
This is a video I have been wanting to make for some time, in which I discuss what the quaternions are, as mathematical objects, and how we do calculations with them. In particular, we will see how the fundamental equation of the quaternions i^2=j^2=k^2=ijk=-1 easily generates the rule for
From playlist Quaternions
Matrix Theory: For the quaternion alpha = 1 - i + j - k, find the norm N(alpha) and alpha^{-1}. Then write alpha as a product of a length and a direction.
From playlist Matrix Theory
https://github.com/timhutton/klein-quartic This is work in progress. The transition is linear at the moment, which causes a lot of self-intersection.
From playlist Geometry
The three types of eight-fold way path on the Klein Quartic
Source code and mesh files here: https://github.com/timhutton/klein-quartic
From playlist Geometry
Made from 24 heptagons. Source code and meshes here: https://github.com/timhutton/klein-quartic
From playlist Geometry
Artan Sheshmani : On the proof of S-duality modularity conjecture on quintic threefolds
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
Daniele Agostini - Curves and theta functions: algebra, geometry & physics
Riemann’s theta function is a central object throughout mathematics, from algebraic geometry to number theory, and from mathematical physics to statistics and cryptography. One of my long term projects is to develop a program to study and connect the various aspects - geometric, computatio
From playlist Research Spotlight
Alena Pirutka: Stable rationality - Lecture 2
Abstract: Let X be a smooth and projective complex algebraic variety. Several notions, describing how close X is to projective space, have been developed: X is rational if an open subset of X is isomorphic to an open of a projective space, X is stably rational if this property holds for a
From playlist Algebraic and Complex Geometry
Alena Pirutka: Stable rationality - Lecture 1
Abstract: Let X be a smooth and projective complex algebraic variety. Several notions, describing how close X is to projective space, have been developed: X is rational if an open subset of X is isomorphic to an open of a projective space, X is stably rational if this property holds for a
From playlist Algebraic and Complex Geometry
Alena Pirutka: Stable rationality - Lecture 3
Abstract: Let X be a smooth and projective complex algebraic variety. Several notions, describing how close X is to projective space, have been developed: X is rational if an open subset of X is isomorphic to an open of a projective space, X is stably rational if this property holds for a
From playlist Algebraic and Complex Geometry
In this video I show how to solve quartic polynomial equations by factoring. The concepts covered in this video involve factoring quartic polynomials, difference of two perfect squares, finding real and imaginary roots, zero product property, sum of two perfect squares, imaginary numbers.
From playlist Algebra 2
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys The Quaternion Group
From playlist Abstract Algebra
Alena Pirutka: On examples of varieties that are not stably rational
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
Tropical Geometry - Lecture 8 - Surfaces | Bernd Sturmfels
Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)
From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels
Counting rational points of cubic hypersurfaces - Salberger - Workshop 1 - CEB T2 2019
Per Salberger (Chalmers Univ. of Technology) / 23.05.2019 Counting rational points of cubic hypersurfaces Let N(X;B) be the number of rational points of height at most B on an integral cubic hypersurface X over Q. It is then a central problem in Diophantine geometry to study the asympto
From playlist 2019 - T2 - Reinventing rational points
Umberto Zannier - Unlikely Intersections and Pell's equations in polynomials
Unlikely Intersections and Pell's equations in polynomials
From playlist 28ème Journées Arithmétiques 2013
Set Theory (Part 14c): More on the Quaternions
No background in sets required for this video. In this video, we will learn how the quaternions can be thought of as pairings of complex numbers. We also will show how the quaternions can be written as a 2x2 complex matrix as opposed to a 4x4 real matrix and how the unit quaternions form t
From playlist Set Theory