Formal languages | Trace theory | Combinatorics | Free algebraic structures | Semigroup theory
In computer science, a trace is a set of strings, wherein certain letters in the string are allowed to commute, but others are not. It generalizes the concept of a string, by not forcing the letters to always be in a fixed order, but allowing certain reshufflings to take place. Traces were introduced by Pierre Cartier and Dominique Foata in 1969 to give a combinatorial proof of MacMahon's master theorem. Traces are used in theories of concurrent computation, where commuting letters stand for portions of a job that can execute independently of one another, while non-commuting letters stand for locks, synchronization points or thread joins. The trace monoid or free partially commutative monoid is a monoid of traces. In a nutshell, it is constructed as follows: sets of commuting letters are given by an independency relation. These induce an equivalence relation of equivalent strings; the elements of the equivalence classes are the traces. The equivalence relation then partitions up the free monoid (the set of all strings of finite length) into a set of equivalence classes; the result is still a monoid; it is a quotient monoid and is called the trace monoid. The trace monoid is universal, in that all dependency-homomorphic (see below) monoids are in fact isomorphic. Trace monoids are commonly used to model concurrent computation, forming the foundation for process calculi. They are the object of study in trace theory. The utility of trace monoids comes from the fact that they are isomorphic to the monoid of dependency graphs; thus allowing algebraic techniques to be applied to graphs, and vice versa. They are also isomorphic to history monoids, which model the history of computation of individual processes in the context of all scheduled processes on one or more computers. (Wikipedia).
Math 031 031017 Monotone Sequence Theorem
The rational numbers have holes: square root of 2 is irrational. Bounded sequences; bounded above, bounded below. Q. Does bounded imply convergent? (No.) Q. Does convergent imply bounded? (Yes.) Proof that convergent implies bounded. Statement of Monotone Sequence Theorem. Definition
From playlist Course 3: Calculus II (Spring 2017)
Geometry of Frobenioids - part 2 - (Set) Monoids
This is an introduction to the basic properties of Monoids. This video intended to be a starting place for log-schemes, Mochizuki's IUT or other absolute geometric constructions using monoids.
From playlist Geometry of Frobenioids
Monotonic Sequences and Bounded Sequences - Calculus 2
This calculus 2 video tutorial provides a basic introduction into monotonic sequences and bounded sequences. A monotonic sequence is a sequence that is always increasing or decreasing. You can prove that a sequence is always increasing by showing that the next term is greater than the p
From playlist New Calculus Video Playlist
Categories 6 Monoidal categories
This lecture is part of an online course on categories. We define strict monoidal categories, and then show how to relax the definition by introducing coherence conditions to define (non-strict) monoidal categories. We finish by defining symmetric monoidal categories and showing how super
From playlist Categories for the idle mathematician
How to Determine if a Sequence is Monotonic and Bounded: Example with n/(n^2 + 1)
In this video we look at a sequence and determine if it is bounded and monotonic. We use the definition of what it means for a sequence to be bounded to show that it is bounded, and we use the derivative to show it is monotonic. I hope this helps. If you enjoyed this video please consider
From playlist Sequences in Calculus
Monotone Subsequence Theorem (Every Sequence has Monotone Subsequence) | Real Analysis
How nice of a subsequence does any given sequence has? We've seen that not every sequence converges, and some don't even have convergent subsequences. But today we'll prove what is sometimes called the Monotone Subsequence theorem, telling us that every sequence has a monotone subsequence.
From playlist Real Analysis
What is the definition of a monomial and polynomials with examples
👉 Learn how to classify polynomials based on the number of terms as well as the leading coefficient and the degree. When we are classifying polynomials by the number of terms we will focus on monomials, binomials, and trinomials, whereas classifying polynomials by the degree will focus on
From playlist Classify Polynomials
Nadia Larsen: Equilibrium states for C*-algebras of right LCM monoids.
Talk by Nadia Larsen in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on October 13, 2020.
From playlist Global Noncommutative Geometry Seminar (Europe)
Learn how to distribute a negative x to a trinomial
http://www.freemathvideos.com In this video playlist I will show you the basics for polynomial functions. We will start with factoring polynomial equations to determine the zeros of a polynomial. We will then learn how to write the polynomial given a set of zeros. Multiplying, adding and
From playlist How to Multiply a Trinomial by a Monomial
Inna Zakharevich, Characteristic polynomials and traces
Global Noncommutative Geometry Seminar (Americas) on 10/22/21 https://globalncgseminar.org/talks/3584/
From playlist Global Noncommutative Geometry Seminar (Americas)
Representation Theory & Categorification II - Catharina Stroppel
2021 Women and Mathematics - Uhlenbeck Course Lecture Topic: Representation Theory & Categorification II Speaker: Catharina Stroppel Affiliation: University of Bonn Date: May 25, 2021 In modern representation theory we often study the category of modules over an algebra, in particular i
From playlist Mathematics
Alon Nissan-Cohen: Towards an ∞-categorical version of real THH
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "Workshop: Hermitian K-theory and trace methods" Following Hesselholt and Madsen's development of the so-called "real" (i.e. Z/2-equivariant) version of algebraic K-theory, Dotto developed a th
From playlist HIM Lectures: Junior Trimester Program "Topology"
Gabriele Vezzosi - Applications of non-commutative algebraic geometry to arithmetic geometry
Abstract: We will briefly recall the general philosophy of non-commutative (and derived) algebraic geometry in order to establish a precise link between dg-derived category of singularities of Landau-Ginzburg models and vanishing cohomology, over an arbitrary henselian trait. We will then
From playlist Algebraic Analysis in honor of Masaki Kashiwara's 70th birthday
Bounded and Monotonic Sequences
We define bounded sequences and monotone sequences, then look at the Monotone Sequence Theorem. This video is part of a Calculus II course taught at the University of Cincinnati.
From playlist Older Calculus II (New Playlist For Spring 2019)
Flag manifolds over semifields I - Huanchen Bao
Workshop on Representation Theory and Geometry Topic: Flag manifolds over semifields I Speaker: Huanchen Bao Affiliation: National University of Singapore; Member, School of Mathematics Date: March 30, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Bâo Chảu Ngô - Vinberg's monoid and automorphic L-functions
Séminaire de Géométrie Arithmétique Paris-Pékin-Tokyo avec Bâo Chảu Ngô (University of Chicago, VIASM) - Vinberg's monoid and automorphic L-functions.
From playlist Conférences Paris Pékin Tokyo
Duality In Higher Categories IV by Pranav Pandit
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
José Manuel GarcÃa-Calcines (6/24/21): Topological complexity using arbitrary covers
Title: Topological complexity using arbitrary covers
From playlist Topological Complexity Seminar
Learn to divide a binomial by a monomial
👉 Learn how to divide polynomials by a monomial using the long division algorithm. A monomial is an algebraic expression with one term while a polynomial is an algebraic expression with more than one term. To divide a polynomial by a monomial using the long division algorithm, we divide ea
From playlist Divide Polynomials using Long Division with monomial divisor
The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: Workshop "Hermitian K-theory and trace methods"
From playlist HIM Lectures: Junior Trimester Program "Topology"