Algebraic Structures: Groups, Rings, and Fields
This video covers the definitions for some basic algebraic structures, including groups and rings. I give examples of each and discuss how to verify the properties for each type of structure.
From playlist Abstract Algebra
Algebraic Expressions (Basics)
This video is about Algebraic Expressions
From playlist Algebraic Expressions and Properties
AlgTopReview: An informal introduction to abstract algebra
This is a review lecture on some aspects of abstract algebra useful for algebraic topology. It provides some background on fields, rings and vector spaces for those of you who have not studied these objects before, and perhaps gives an overview for those of you who have. Our treatment is
From playlist Algebraic Topology
What are the Types of Numbers? Real vs. Imaginary, Rational vs. Irrational
We've mentioned in passing some different ways to classify numbers, like rational, irrational, real, imaginary, integers, fractions, and more. If this is confusing, then take a look at this handy-dandy guide to the taxonomy of numbers! It turns out we can use a hierarchical scheme just lik
From playlist Algebra 1 & 2
An interesting homotopy (in fact, an ambient isotopy) of two surfaces.
From playlist Algebraic Topology
Ralph KAUFMANN - Categorical Interactions in Algebra, Geometry and Physics
Categorical Interactions in Algebra, Geometry and Physics: Cubical Structures and Truncations There are several interactions between algebra and geometry coming from polytopic complexes as for instance demonstrated by several versions of Deligne's conjecture. These are related through bl
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
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 the 17th century work of Descartes. We point out some of the difficulties with Jordan's notion of curve, and move to the polynu
From playlist Math Foundations
algebraic geometry 23 Categories
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It gives a quick review of category theory as background for the definition of morphisms of algebraic varieties.
From playlist Algebraic geometry I: Varieties
Group equation examples Lesson 26
In this video we solve algebraic expressions using the properties of groups. It is always good to work through a few examples. You must get familiar with solving equations where the variables are group elements and not placeholders for numbers only.
From playlist Abstract algebra
Transcendental numbers powered by Cantor's infinities
In today's video the Mathologer sets out to give an introduction to the notoriously hard topic of transcendental numbers that is both in depth and accessible to anybody with a bit of common sense. Find out how Georg Cantor's infinities can be used in a very simple and off the beaten track
From playlist Recent videos
Tangents to Parametric Curves (New) | Algebraic Calculus One | Wild Egg
Tangents are an essential part of the differential calculus. Here we introduce these important lines which approximate curves at points in an algebraic fashion -- finessing the need for infinite processes to support takings of limits. We begin by a discussion of tangents historically, espe
From playlist Algebraic Calculus One
Tangents to Parametric Curves | Algebraic Calculus One | Wild Egg
Tangents are an essential part of the differential calculus. Here we introduce these important lines which approximate curves at points in an algebraic fashion -- finessing the need for infinite processes to support takings of limits. We begin by a discussion of tangents historically, espe
From playlist Algebraic Calculus One from Wild Egg
The Three/Four bridge and Apollonius duality for conics | Six: A course in pure maths 5 | Wild Egg
The Three / Four bridge plays an important role in understanding the remarkable duality discover by Apollonius between points and lines in the plane once a conic is specified. This is a purely projective construction that works for ellipses, and their special case of a circle, for parabola
From playlist Six: An elementary course in Pure Mathematics
The Three / Four bridge in Triangle Geometry: Incentres and Orthocentres | Six 6 | Wild Egg
We look at how to cross the Three / Four bridge geometrically: in both directions. This connects with some classical triangle geometry, involving triangle centres going back to ancient Greek geometry. We will touch base with the algebraic orientation to angle bisection, modifying a little
From playlist Six: An elementary course in Pure Mathematics
Representations of Galois algebras – Vyacheslav Futorny – ICM2018
Lie Theory and Generalizations Invited Lecture 7.3 Representations of Galois algebras Vyacheslav Futorny Abstract: Galois algebras allow an effective study of their representations based on the invariant skew group structure. We will survey their theory including recent results on Gelfan
From playlist Lie Theory and Generalizations
IGA: Singularities of Hermitian Yang Mills Connections
After introducing some background about stable bundles and HYM connections, I will explain both the analytic and algebraic sides when studying singularities of HYM connections. It turns out that local algebraic invariants can be extracted to characterize the analytic side. In particular, t
From playlist Informal Geometric Analysis Seminar
L. Boyle: Non-commutative geometry, non-associative geometry, and the std. model of particle physics
Connes' notion of non-commutative geometry (NCG) generalizes Riemannian geometry and yields a striking reinterepretation of the standard model of particle physics, coupled to Einstein gravity. We suggest a simple reformulation with two key mathematical advantages: (i) it unifies many of t
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Euclid's construction problems I | Famous Math Problems 12 | NJ Wildberger
Euclid's treatise the Elements is easily the greatest mathematical text of all time. Book I lays out basics of planar geometry, with an alternation between theory and practice, where practice means solving explicit construction problems with straight-edge and compass. In this lecture we lo
From playlist Famous Math Problems
Curves from Antiquity | Algebraic Calculus One | Wild Egg
We begin a discussion of curves, which are central objects in calculus. There are different kinds of curves, coming from geometric constructions as well as physical or mechanical motions. In this video we look at classical curves that go back to antiquity, such as prominently the conic sec
From playlist Algebraic Calculus One from Wild Egg