Topological groups | Continuum theory | P-adic numbers | Number theory | Ring theory | Algebraic topology
In mathematics, a solenoid is a compact connected topological space (i.e. a continuum) that may be obtained as the inverse limit of an inverse system of topological groups and continuous homomorphisms where each is a circle and fi is the map that uniformly wraps the circle for times around the circle . This construction can be carried out geometrically in the three-dimensional Euclidean space R3. A solenoid is a one-dimensional homogeneous indecomposable continuum that has the structure of a compact topological group. Solenoids were first introduced by Vietoris for the case, and by van Dantzig the case, where is fixed. Such a solenoid arises as a one-dimensional expanding attractor, or Smale–Williams attractor, and forms an important example in the theory of hyperbolic dynamical systems. (Wikipedia).
An introduction to the Tropical calculus | Data Structures in Mathematics Math Foundations 158
We give a short informal introduction to the Tropical calculus, which for us is a novel way of working with the algebra of sets and multisets. This involves defining rather unusual notions of addition and multiplication-- coming from union and addition respectively. **********************
From playlist Math Foundations
What is a number? | Arithmetic and Geometry Math Foundations 1 | N J Wildberger
The first of a series that will discuss foundations of mathematics. Contains a general introduction to the series, and then the beginnings of arithmetic with natural numbers. This series will methodically develop a lot of basic mathematics, starting with arithmetic, then geometry, then alg
From playlist Math Foundations
Visualizing decimal numbers and their arithmetic 67 | Arithmetic and Geometry Math Foundations
This video gives a precise definition of a decimal number as a special kind of rational number; one for which there is an expression a/b where a and b are integers, with b a power of ten. For such a number we can extend the Hindu-Arabic notation for integers by introducing the decimal form
From playlist Math Foundations
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
What is a Module? (Abstract Algebra)
A module is a generalization of a vector space. You can think of it as a group of vectors with scalars from a ring instead of a field. In this lesson, we introduce the module, give a variety of examples, and talk about the ways in which modules and vector spaces are different from one an
From playlist Abstract Algebra
The problem with `functions' | Arithmetic and Geometry Math Foundations 42a
[First of two parts] Here we address a core logical problem with modern mathematics--the usual definition of a `function' does not contain precise enough bounds on the nature of the rules or procedures (or computer programs) allowed. Here we discuss the difficulty in the context of funct
From playlist Math Foundations
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
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
Evaluating a rational expression and order of operations
👉 Learn how to evaluate mathematics expressions. A mathematics expression is a finite combination of numbers and symbols formed following a set of operations or rules. To evaluate a mathematics expression means to obtain the solution to the expression given the value(s) of the variable(s)
From playlist Simplify Expressions Using Order of Operations
We DON'T Understand Magnetism (According to Quantum Mechanics) - Aharonov-Bohm Effect by Parth G
The first 1000 people to use the link will get a free trial of Skillshare Premium Membership: https://skl.sh/parthg06211 Scientists have often thought that magnetic (and electric) fields are fundamental quantities that relate to real, physical, observable things in the universe. And they
From playlist Quantum Physics by Parth G
mod-15 lec-15 Proportional Solenoid Pilot Operated Two Stage Pressure Relief Valve
Fundamentals of Industrial Oil Hydraulics and Pneumatics by Prof. R.N. Maiti,Department of Mechanical Engineering,IIT Kharagpur.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Kharagpur: Fundamentals of Industrial Oil Hydraulics and Pneumatics (CosmoLearning Mechanical Engineering)
Biot-Savart and Ampere's Laws - Review for AP Physics C: Electricity and Magnetism
AP Physics C: Electricity and Magnetism review of magnetic fields including: the basics of magnetic dipoles, ferromagnetic and paramagnetic materials, the Earth’s B field, magnetic permeability, the magnetic force on a moving charge, the right-hand rule for direction, 7 examples of right-h
From playlist AP Physics C: Electricity & Magnetism Review
Mod-03 Lec-25 Magnetic Vector Potential
Electromagnetic Theory by Prof. D.K. Ghosh,Department of Physics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Bombay: Electromagnetic Theory
My textbook on vector calculus is available here: https://github.com/Kylebroder/VectorCalculusBook/raw/main/VC_Notes.pdf Vector Calculus and Differential Equations Playlist -- https://www.youtube.com/watch?v=UhuxxkOocdY&list=PL912tg7wFUfXIwSKeTyxU5LTqdRZ8Urza&index=1 More videos on geome
From playlist MATH2305 -- Semester 1 2022
Lecture 8 | Modern Physics: Special Relativity (Stanford)
Lecture 8 of Leonard Susskind's Modern Physics course concentrating on Special Relativity. Recorded June 9, 2008 at Stanford University. This Stanford Continuing Studies course is the first of a six-quarter sequence of classes exploring the essential theoretical foundations of modern ph
From playlist Lecture Collection | Modern Physics: Special Relativity
Physics - Electromagnetism: Lenz's Law
This is the 5th lesson in the series, "Electromagnetism." It investigates the relationship between the induced emf and the induced current and shows how to calculate the magnitude of the induced current using Faraday's Law. It also shows how to predict the direction of the induced current
From playlist Physics - Electromagnetism
For more information about Professor Shankar's book based on the lectures from this course, Fundamentals of Physics: Mechanics, Relativity, and Thermodynamics, visit http://bit.ly/1jFIqNu. Fundamentals of Physics, II (PHYS 201) Ampere's Law is used to find the magnetic field generated by
From playlist Fundamentals of Physics II with Ramamurti Shankar
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
Davide Fermi - Domenico Monaco - Badreddine Benhellal - Léo Morin
* Magnetic perturbations of Aharonov-Bohm and 2-body anyonic Hamiltonians - Davide Fermi * (De)localized Wannier functions for quantum Hall systems - Domenico Monaco * Quantum Con inement induced by Dirac operators with anomalous magnetic - Badreddine Benhellal * Spectral Asymptotics for
From playlist Mathematics of Condensed Matter and Beyond (February 22-25, 2021)