Algebra for Beginners | Basics of Algebra
#Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. Table of Conten
From playlist Linear Algebra
Group Definition (expanded) - Abstract Algebra
The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to contin
From playlist Abstract Algebra
Algebra for beginners || Basics of Algebra
In this course you will learn about algebra which is ideal for absolute beginners. #Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions. It involves variables like x, y, z, and mathematical operations like
From playlist Algebra
Abstract Algebra - 11.1 Fundamental Theorem of Finite Abelian Groups
We complete our study of Abstract Algebra in the topic of groups by studying the Fundamental Theorem of Finite Abelian Groups. This tells us that every finite abelian group is a direct product of cyclic groups of prime-power order. Video Chapters: Intro 0:00 Before the Fundamental Theorem
From playlist Abstract Algebra - Entire Course
Simple Groups - Abstract Algebra
Simple groups are the building blocks of finite groups. After decades of hard work, mathematicians have finally classified all finite simple groups. Today we talk about why simple groups are so important, and then cover the four main classes of simple groups: cyclic groups of prime order
From playlist Abstract Algebra
Field Definition (expanded) - Abstract Algebra
The field is one of the key objects you will learn about in abstract algebra. Fields generalize the real numbers and complex numbers. They are sets with two operations that come with all the features you could wish for: commutativity, inverses, identities, associativity, and more. They
From playlist Abstract Algebra
What is Abstract Algebra? (Modern Algebra)
Abstract Algebra is very different than the algebra most people study in high school. This math subject focuses on abstract structures with names like groups, rings, fields and modules. These structures have applications in many areas of mathematics, and are being used more and more in t
From playlist Abstract Algebra
Linear Algebra Full Course for Beginners to Experts
Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis may be basically viewed as the application of l
From playlist Linear Algebra
Groups in abstract algebra examples
In this tutorial I discuss two more examples of groups. The first contains four elements and they are the four fourth roots of 1. The second contains only three elements and they are the three cube roots of 1. Under the binary operation of multiplication, these sets are in fact groups.
From playlist Abstract algebra
Permutation Orbifolds of Vertex Operator Algebras
This is a recording of a talk I gave at the Illinois State University Algebra Seminar. Suggest a problem: https://forms.gle/ea7Pw7HcKePGB4my5 Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.com/stores/michael-penn-math Personal Websi
From playlist Research Talks
Moduli of Representations and Pseudorepresentations - Carl Wang Erickson
Carl Wang Erickson Harvard University May 2, 2013 A continuous representation of a profinite group induces a continuous pseudorepresentation, where a pseudorepresentation is the data of the characteristic polynomial coefficients. We discuss the geometry of the resulting map from the moduli
From playlist Mathematics
Generalized Kepler Problems - Guowu Meng
Generalized Kepler Problems Guowu Meng Hong Kong University of Science & Technology; Joint Member, School of Mathematics & Natural Sciences February 4, 2011 ANALYSIS/MATHEMATICAL PHYSICS SEMINAR For many elegant mathematical examples, one can 1) find theories behind them, 2) understand wh
From playlist Mathematics
Emmy Noether: breathtaking mathematics - Georgia Benkart
Celebrating Emmy Noether Topic: Emmy Noether: breathtaking mathematics Speaker: Georgia Benkart Affiliation: University of Wisconsin-Madison Date: Friday, May 6 By the mid 1920s, Emmy Noether had made fundamental contributions to commutative algebra and to the theory of invariants.
From playlist Celebrating Emmy Noether
Algebraic groups and all in characteristic p - Ivan Loseu
Quantum Groups Seminar Topic: Algebraic groups and all in characteristic p Speaker: Ivan Loseu Affiliation: Member, School of Mathematics Date: March 18, 2021 For more video please visit http://video.ias.edu
From playlist Quantum Groups Seminar
Ben Webster - Representation theory of symplectic singularities
Research lecture at the Worldwide Center of Mathematics
From playlist Center of Math Research: the Worldwide Lecture Seminar Series
8ECM Invited Lecture: Stuart White
From playlist 8ECM Invited Lectures
Center of quantum group - Arun Kannan
Quantum Groups Seminar Topic: Center of quantum group Speaker: Arun Kannan Affiliation: Massachusetts Institute of Technology Date: February 04, 2021 For more video please visit http://video.ias.edu
From playlist Quantum Groups Seminar
A Hecke action on the principal block of a semisimple algebraic group - Simon Riche
Workshop on Representation Theory and Geometry Topic: A Hecke action on the principal block of a semisimple algebraic group Speaker: Simon Riche Affiliation: Université Paris 6; Member, School of Mathematics Date: April 01, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Ana Balibanu: The partial compactification of the universal centralizer
Abstract: Let G be a semisimple algebraic group of adjoint type. The universal centralizer is the family of centralizers in G of regular elements in Lie(G), parametrized by their conjugacy classes. It has a natural symplectic structure, obtained by Hamiltonian reduction from the cotangent
From playlist Algebra
RNT1.4. Ideals and Quotient Rings
Ring Theory: We define ideals in rings as an analogue of normal subgroups in group theory. We give a correspondence between (two-sided) ideals and kernels of homomorphisms using quotient rings. We also state the First Isomorphism Theorem for Rings and give examples.
From playlist Abstract Algebra