Commutative algebra | Field (mathematics)
In abstract algebra, the field of fractions of an integral domain is the smallest field in which it can be embedded. The construction of the field of fractions is modeled on the relationship between the integral domain of integers and the field of rational numbers. Intuitively, it consists of ratios between integral domain elements. The field of fractions of is sometimes denoted by or , and the construction is sometimes also called the fraction field, field of quotients, or quotient field of . All four are in common usage, but are not to be confused with the quotient of a ring by an ideal, which is a quite different concept. For a commutative ring which is not an integral domain, the analogous construction is called the localization or ring of quotients. (Wikipedia).
This video is about polynomials with coefficients in a field.
From playlist Basics: Field Theory
What is a fraction? I use a number line to introduce what a fraction MEANS.
From playlist Fraction Concepts
Algebraic Fractions (1 of 2: Addition & Subtraction)
More resources available at www.misterwootube.com
From playlist Further Algebraic Techniques
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
Definition of a Field In this video, I define the concept of a field, which is basically any set where you can add, subtract, add, and divide things. Then I show some neat properties that have to be true in fields. Enjoy! What is an Ordered Field: https://youtu.be/6mc5E6x7FMQ Check out
From playlist Real Numbers
Field Theory: Integer Polynomials and Factorizations
This video is about integer polynomials.
From playlist Basics: Field Theory
Arithmetic with fractions | Arithmetic and Geometry Math Foundations 10 | N J Wildberger
We define addition and multiplication of fraction to parallel the operations for natural number quotients. A crucial step is to check that these operations are actually well-defined, that is that they respect the notion of equality built into the definition of a fraction. ****************
From playlist Math Foundations
The Structure of Fields: What is a field and a connection between groups and fields
This video is primarily meant to help develop some ideas around the structure of fields and a connection between groups and fields (which will allow me to create more abstract algebra videos in the future! 😀😅🤓) 00:00 Intro 01:04 What is a Field? Here we give the definition of a field in
From playlist The New CHALKboard
From playlist Abstract Algebra 2
Log Volume Computations - part 0.2 - Total Rings Of Fractions
This is the second part of the prerequisite videos for the log volume computations and is optional for continuing. In this video we explain how to take rings of fractions for reduced but not irreducible rings. We then show that the ring of fractions of a tensor product is the tensor prod
From playlist Log Volume Computations
MFEM Workshop 2022 | Stochastic Fractional PDEs: Random Field Generation & Topology Optimization
The LLNL-led MFEM (Modular Finite Element Methods) project provides high-order mathematical calculations for large-scale scientific simulations. The project’s second community workshop was held on October 25, 2022, with participants around the world. Learn more about MFEM at https://mfem.o
From playlist MFEM Community Workshop 2022
Mean field approximations to n-body projection Hamiltonians in FQHE by Sreejith G J
Indian Statistical Physics Community Meeting 2018 DATE:16 February 2018 to 18 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore This is an annual discussion meeting of the Indian statistical physics community which is attended by scientists, postdoctoral fellows, and graduate s
From playlist Indian Statistical Physics Community Meeting 2018
Tunneling between Landau levels in a quantum dot in the integer and by Marc Röösli
DISCUSSION MEETING : EDGE DYNAMICS IN TOPOLOGICAL PHASES ORGANIZERS : Subhro Bhattacharjee, Yuval Gefen, Ganpathy Murthy and Sumathi Rao DATE & TIME : 10 June 2019 to 14 June 2019 VENUE : Madhava Lecture Hall, ICTS Bangalore Topological phases of matter have been at the forefront of r
From playlist Edge dynamics in topological phases 2019
Correlated Electron Phenomena in Suspended Graphene - Amir Yacoby
DISCUSSION MEETING : ADVANCES IN GRAPHENE, MAJORANA FERMIONS, QUANTUM COMPUTATION DATES Wednesday 19 Dec, 2012 - Friday 21 Dec, 2012 VENUE Auditorium, New Physical Sciences Building, IISc Quantum computation is one of the most fundamental and important research topics today, from both th
From playlist Advances in Graphene, Majorana fermions, Quantum computation
Self-organized Dynamics of Freely-jointed Active Droplet Chains by Manoj Kumar
DISCUSSION MEETING APS SATELLITE MEETING AT ICTS ORGANIZERS Ranjini Bandyopadhyay (RRI, India), Subhro Bhattacharjee (ICTS-TIFR, India), Arindam Ghosh (IISc, India), Shobhana Narasimhan (JNCASR, India) and Sumantra Sarkar (IISc, India) DATE & TIME: 15 March 2022 to 18 March 2022 VENUE:
From playlist APS Satellite Meeting at ICTS-2022
Topological Phase Transitions in the Quantum Hall Effect by Prashant Kumar
COLLOQUIUM : TOPOLOGICAL PHASE TRANSITIONS IN THE QUANTUM HALL EFFECT SPEAKER : Prashant Kumar ( Princeton University) DATE : 21 February 2023, 11:30 VENUE : Emmy Noether Seminar Room & Online RESOURCES : ABSTRACT Phase transitions involving topological phases of matter are a rich set
From playlist ICTS Colloquia
Fractional quantum Hall states in bilayer graphene probed ... by Jurgen Smet
School on Current Frontiers in Condensed Matter Research URL: http://www.icts.res.in/program/cficmr16 DATES: Monday 20 Jun, 2016 - Wednesday 29 Jun, 2016 VENUE : Ramanujan Lecture Hall, ICTS Bangalore DESCRIPTION: Understanding strongly interacting quantum many body systems is one of
From playlist School on Current Frontiers in Condensed Matter Research
Abstract Algebra | The field of fractions of an integral domain.
We present the notion of the field of fractions of an arbitrary integral domain, give some examples, and prove that we indeed have constructed the smallest field containing the original integral domain. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Personal
From playlist Abstract Algebra