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
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
Algebraic Expressions (Basics)
This video is about Algebraic Expressions
From playlist Algebraic Expressions and Properties
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
An introduction to abstract algebra | Abstract Algebra Math Foundations 213 | NJ Wildberger
How do we set up abstract algebra? In other words, how do we define basic algebraic objects such as groups, rings, fields, vector spaces, algebras, lattices, modules, Lie algebras, hypergroups etc etc?? This is a hugely important question, and not an easy one to answer. In this video we s
From playlist Math Foundations
What is a Tensor? Lesson 19: Algebraic Structures I
What is a Tensor? Lesson 19: Algebraic Structures Part One: Groupoids to Fields This is a redo or a recently posted lesson. Same content, a bit cleaner. Algebraic structures are frequently mentioned in the literature of general relativity, so it is good to understand the basic lexicon of
From playlist What is a Tensor?
Sets and other data structures | Data Structures in Mathematics Math Foundations 151
In mathematics we often want to organize objects. Sets are not the only way of doing this: there are other data types that are also useful and that can be considered together with set theory. In particular when we group objects together, there are two fundamental questions that naturally a
From playlist Math Foundations
Algebraic Expression Vocabulary (L2.2)
This video reviews the definition of term, coefficient, constant term, and factor. Video content created Jenifer Bohart, William Meacham, Judy Sutor, and Donna Guhse from SCC (CC-BY 4.0)
From playlist Algebraic Structures Module
Data Structures: List as abstract data type
See complete series of videos in data structures here: http://www.youtube.com/playlist?list=PL2_aWCzGMAwI3W_JlcBbtYTwiQSsOTa6P&feature=view_all In this lesson, we will introduce a dynamic list structure as an abstract data type and then see one possible implementation of dynamic list using
From playlist Data structures
Yanli Song: K-theory of the reduced C*-algebra of a real reductive Lie group
Talk by Yanli Song in Global Noncommutative Geometry Seminar (Americas) on January 28, 2022 in https://globalncgseminar.org/talks/tba-23/
From playlist Global Noncommutative Geometry Seminar (Americas)
Arnold Conjecture Over Integers - Shaoyun Bai
Topic: Arnold Conjecture Over Integers Speaker: Shaoyun Bai Affiliation: Stony Brook University Date: January 20, 2023 We show that for any closed symlectic manifold, the number of 1-periodic orbits of any non-degenerate Hamiltonian is bounded from below by a version of total Betti number
From playlist Mathematics
Bias vs Low Rank of Polynomials with...Algebraic Geometry - Abhishek Bhowmick
Let f be a polynomial of degree d in n variables over a finite field 𝔽. The polynomial is said to be unbiased if the distribution of f(x) for a uniform input x∈𝔽n is close to the uniform distribution over 𝔽, and is called biased otherwise. The polynomial is said to have low rank if it can
From playlist Mathematics
Noémie Combe - How many Frobenius manifolds are there?
In this talk an overview of my recent results is presented. In a joint work with Yu. Manin (2020) we discovered that an object central to information geometry: statistical manifolds (related to exponential families) have an F-manifold structure. This algebraic structure is a more general v
From playlist Research Spotlight
In this video I do a speed run of some of my math books. I go through math books covering algebra, trigonometry, calculus, advanced calculus, real analysis, abstract algebra, differential geometry, set theory, discrete math, finite math, graph theory, combinatorics, number theory, galois t
From playlist Book Reviews
José Carrión: "The abstract approach to classifying C*-algebras"
Actions of Tensor Categories on C*-algebras 2021 Mini Course: "The abstract approach to classifying C*-algebras" José Carrión - Texas Christian University Institute for Pure and Applied Mathematics, UCLA January 21, 2021 For more information: https://www.ipam.ucla.edu/atc2021
From playlist Actions of Tensor Categories on C*-algebras 2021
Geordie Williamson: Langlands and Bezrukavnikov II Lecture 9
SMRI Seminar Series: 'Langlands correspondence and Bezrukavnikov’s equivalence' Geordie Williamson (University of Sydney) Abstract: The second part of the course focuses on affine Hecke algebras and their categorifications. Last year I discussed the local Langlands correspondence in bro
From playlist Geordie Williamson: Langlands correspondence and Bezrukavnikov’s equivalence
Alon Nissan-Cohen: Towards an ∞-categorical version of real THH
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "Workshop: Hermitian K-theory and trace methods" Following Hesselholt and Madsen's development of the so-called "real" (i.e. Z/2-equivariant) version of algebraic K-theory, Dotto developed a th
From playlist HIM Lectures: Junior Trimester Program "Topology"
Learn Mathematics from START to FINISH (2nd Edition)
In this video I will show you how to learn mathematics from start to finish. I will give you three different ways to get started with mathematics. I hope this video helps someone. Here are the books Elementary Algebra https://amzn.to/3S7yG0Y Pre-Algebra https://amzn.to/3TpW8HK Discrete Ma
From playlist Book Reviews
Algebraic structure on the Euclidean projective line | Rational Geometry Math Foundations 137
In this video we look at some pleasant consequences of imposing a Euclidean structure on the projective line. We give a proof of the fundamental projective Triple quad formula, talk about the equal p-quadrances theorem, and see how the logistic map of chaos theory makes its appearance as t
From playlist Math Foundations
