Homomorphisms in abstract algebra
In this video we add some more definition to our toolbox before we go any further in our study into group theory and abstract algebra. The definition at hand is the homomorphism. A homomorphism is a function that maps the elements for one group to another whilst maintaining their structu
From playlist Abstract 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
How does mathematics describe the physical features of the world?
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From playlist Science Unplugged: Mathematics
Isomorphisms (Abstract Algebra)
An isomorphism is a homomorphism that is also a bijection. If there is an isomorphism between two groups G and H, then they are equivalent and we say they are "isomorphic." The groups may look different from each other, but their group properties will be the same. Be sure to subscribe s
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
Rupert Klein: Internal wave dynamics in the atmosphere - Lecture 2
Earth’s atmosphere hosts a rich spectrum of phenomena that involve interactions of a variety of processes across many length and time scales. A systematic approach to analyzing these scale dependent processes is a core task of theoretical meteorology and a prerequi- site to constructing re
From playlist Mathematical Physics
Divisibility, Prime Numbers, and Prime Factorization
Now that we understand division, we can talk about divisibility. A number is divisible by another if their quotient is a whole number. The smaller number is a factor of the larger one, but are there numbers with no factors at all? There's some pretty surprising stuff in this one! Watch th
From playlist Mathematics (All Of It)
What is a Group? | Abstract Algebra
Welcome to group theory! In today's lesson we'll be going over the definition of a group. We'll see the four group axioms in action with some examples, and some non-examples as well which violate the axioms and are thus not groups. In a fundamental way, groups are structures built from s
From playlist Abstract Algebra
Instability and stratifications of moduli problems in algebraic geometry - Daniel Halpern-Leistner
Daniel Halpern-Leistner Member, School of Mathematics September 23, 2014 More videos on http://video.ias.edu
From playlist Mathematics
Abstract Algebra: We define the notion of a subgroup and provide various examples. We also consider cyclic subgroups and subgroups generated by subsets in a given group G. Example include A4 and D8. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-
From playlist Abstract Algebra
Open questions in turbulent stratified mixing:Do we even know what we do not know? by C.P. Caulfield
ABSTRACT: Understanding how turbulence leads to the enhanced irreversible transport of heat and other scalars (such as salt and pollutants) in density-stratified fluids is a fundamental and central problem in geophysical and environmental fluid dynamics. There is a wide range of highly im
From playlist ICTS Colloquia
Beyond geometric invariant theory 1: Harder-Narasimhan theory by Daniel Halpern-Leistner
DISCUSSION MEETING: MODULI OF BUNDLES AND RELATED STRUCTURES ORGANIZERS : Rukmini Dey and Pranav Pandit DATE: 10 February 2020 to 14 February 2020 VENUE: Ramanujan Lecture Hall, ICTS, Bangalore Background: At its core, much of mathematics is concerned with the problem of classifying
From playlist Moduli Of Bundles And Related Structures 2020
Pierre Louis Lions - Tribute to Ennio De Giorgi - 19 September 2016
Lions , Pierre Louis "Interfaces, junctions and stratification: a viscosity solutions approach"
From playlist A Mathematical Tribute to Ennio De Giorgi
Number theory Full Course [A to Z]
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure #mathematics devoted primarily to the study of the integers and integer-valued functions. Number theorists study prime numbers as well as the properties of objects made out of integers (for example, ratio
From playlist Number Theory
Recursive combinatorial aspects of compactified moduli spaces – Lucia Caporaso – ICM2018
Algebraic and Complex Geometry Invited Lecture 4.3 Recursive combinatorial aspects of compactified moduli spaces Lucia Caporaso Abstract: In recent years an interesting connection has been established between some moduli spaces of algebro-geometric objects (e.g. algebraic stable curves)
From playlist Algebraic & Complex Geometry
Exit-path categories in geometry and topology - Peter James Haine
Short Talks by Postdoctoral Members Topic: Exit-path categories in geometry and topology Speaker: Peter James Haine Affiliation: Member, School of Mathematics Date: September 22, 2022
From playlist Mathematics
Analytic Geometric Langlands-correspondence: Relations to Conformal (Lecture 1) by Joerg Teschner
Program Quantum Fields, Geometry and Representation Theory 2021 (ONLINE) ORGANIZERS: Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pandi
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
Integer-valued Gromov-Witten type invariants - Guangbo Xu
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Topic: Integer-valued Gromov-Witten type invariants Speaker: Guangbo Xu Affiliation: Texas A&M University Date: June 03, 2022 Gromov-Witten invariants for a general target are rational-valued but not necessarily int
From playlist Mathematics
The structure of instability in moduli theory - Daniel Halpern-Leistner
Daniel Halpern-Leistner Member, School of Mathematics October 21, 2014 In many examples of moduli stacks which come equipped with a notion of stable points, one tests stability by considering "iso-trivial one parameter degenerations" of a point in the stack. To such a degeneration one can
From playlist Mathematics
Dimensions (1 of 3: The Traditional Definition - Directions)
More resources available at www.misterwootube.com
From playlist Exploring Mathematics: Fractals