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
Logic: The Structure of Reason
As a tool for characterizing rational thought, logic cuts across many philosophical disciplines and lies at the core of mathematics and computer science. Drawing on Aristotle’s Organon, Russell’s Principia Mathematica, and other central works, this program tracks the evolution of logic, be
From playlist Logic & Philosophy of Mathematics
Abstract Algebra: The definition of a Ring
Learn the definition of a ring, one of the central objects in abstract algebra. We give several examples to illustrate this concept including matrices and polynomials. Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W ♦♦♦♦♦♦♦♦♦♦ We recommend th
From playlist Abstract Algebra
Now that we know what a quotient group is, let's take a look at an example to cement our understanding of the concepts involved.
From playlist Abstract algebra
The Weyl algebra and the Heisenberg Lie algebra
In this video we give a simple teaser into the world of operator algebras. In particular, we talk about the Weyl algebra and compute some expressions that fulfill the property which defines the Heisenberg Lie algebra http://math.uchicago.edu/~may/REU2012/REUPapers/Lingle.pdf https://en.w
From playlist Algebra
GT12. Aut(Z/n) and Fermat's Little Theorem
Abstract Algebra: We show that Aut(Z/n) is isomorphic to (Z/n)*, the group of units in Z/n. In turn, we show that the units consist of all m in Z/n with gcd(m,n)=1. Using (Z/n)*, we define the Euler totient function and state and prove Fermat's Little Theorem: if p is a prime, then, for
From playlist Abstract Algebra
Marc Levine: Refined enumerative geometry (Lecture 1)
The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields. Marc Levine: Refined enumerative geometry Abstract: Lecture 1: Milnor-Witt sheaves, motivic homotopy theory and Chow-Witt groups We review the Hoplins-Morel construction of the Miln
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
Algebra Absolute Value Equations b6p2
Algebra Absolute Value Equations b6p2 GoToMath.com
From playlist Algebra Gotomath
Marc Levine: Chow Witt groups, ramification and quadratic forms
The lecture was held within the framework of the Hausdorff Trimester Program: Periods in Number Theory, Algebraic Geometry and Physics. Abstract: Replacing the Chow groups with the Barge-Morel-Fasel Chow-Witt groups enables refining many classical constructions involving algebraic cycles
From playlist Workshop: "Periods and Regulators"
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
Units in a Ring (Abstract Algebra)
The units in a ring are those elements which have an inverse under multiplication. They form a group, and this “group of units” is very important in algebraic number theory. Using units you can also define the idea of an “associate” which lets you generalize the fundamental theorem of ar
From playlist Abstract Algebra
A. Shiho - On relative log de Rham-Witt complex
The notion of relative log de Rham-Witt complex, which is the log version of relative de Rham-Witt complex of Langer-Zink, is defined by Matsuue. In this talk, we give the comparison theorem between relative log de Rham-Witt cohomology and relative log crystalline cohomology for log smooth
From playlist Arithmetic and Algebraic Geometry: A conference in honor of Ofer Gabber on the occasion of his 60th birthday
Yonatan Harpaz - New perspectives in hermitian K-theory I
For questions and discussions of the lecture please go to our discussion forum: https://www.uni-muenster.de/TopologyQA/index.php?qa=k%26l-conference This lecture is part of the event "New perspectives on K- and L-theory", 21-25 September 2020, hosted by Mathematics Münster: https://go.wwu
From playlist New perspectives on K- and L-theory
Yonatan Harpaz - New perspectives in hermitian K-theory III
For questions and discussions of the lecture please go to our discussion forum: https://www.uni-muenster.de/TopologyQA/index.php?qa=k%26l-conference This lecture is part of the event "New perspectives on K- and L-theory", 21-25 September 2020, hosted by Mathematics Münster: https://go.wwu
From playlist New perspectives on K- and L-theory
Marc Levine: Atiyah-Bott localization for Witt sheaf cohomology, with applications
30 September 2021 Abstract: Atiyah-Bott localization for singular cohomology of a space with a torus action has proven to be an effective tool in many areas, including enumerative geometry. We give here a parallel for cohomology with Witt-sheaf coeffcients, which is useful for computing q
From playlist Representation theory's hidden motives (SMRI & Uni of Münster)
Laurent Fargues - Courbes et fibrés vectoriels en théorie de Hodge p-adique
Courbes et fibrés vectoriels en théorie de Hodge p-adique
From playlist 28ème Journées Arithmétiques 2013
Yonatan Harpaz - New perspectives in hermitian K-theory II
Warning: around 32:30 in the video, in the slide entitled "Karoubi's conjecture", a small mistake was made - in the third bulleted item the genuine quadratic structure appearing should be the genuine symmetric one (so both the green and red instances of the superscript gq should be gs), an
From playlist New perspectives on K- and L-theory
Lie groups: Poincare-Birkhoff-Witt theorem
This lecture is part of an online graduate course on Lie groups. We state the Poincare-Birkhoff Witt theorem, which shows that the universal enveloping algebra (UEA) of a Lie algebra is the same size as a polynomial algebra. We prove it for Lie algebras of Lie groups and sketch a proof of
From playlist Lie groups
Marc Levine: Refined enumerative geometry (Lecture 4)
The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields. Lecture 4: Characteristic classes in Witt-cohomology Classical enumerative geometry relies heavily on the theory of Chern classes of vector bundles and the splitting principle, which
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
Linear Algebra: Continuing with function properties of linear transformations, we recall the definition of an onto function and give a rule for onto linear transformations.
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics