In the theory of formal languages, the interchange lemma states a necessary condition for a language to be context-free, just like the pumping lemma for context-free languages. It states that for every context-free language there is a such that for all for any collection of length words there is a with , and decompositions such that each of , , is independent of , moreover, , and the words are in for every and . The first application of the interchange lemma was to show that the set of repetitive strings (i.e., strings of the form with ) over an alphabet of three or more characters is not context-free. (Wikipedia).
Integration by substitution -- Calculus I
This lecture is on Calculus I. It follows Part I of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.
From playlist Calculus I
Integration 8 The Substitution Rule in Integration Part 2 Example 1
Working through an example of substitution in integration.
From playlist Integration
Integration 8 The Substitution Rule in Integration Part 2 Example 6
Working through an example using substitution in integration.
From playlist Integration
Integration 8 The Substitution Rule in Integration Part 2 Example 7
Working through an example using substitution in integration.
From playlist Integration
Integration 8 The Substitution Rule in Integration Part 2 Example 5
Working through an example using the substitution rule in integration.
From playlist Integration
Integration 8 The Substitution Rule in Integration Part 2 Example 9
Working through an example using substitution in integration.
From playlist Integration
B22 Introduction to Substitutions
An overview of the three type of substitutions as a new method of solving linear, exact, and "almost" separable differential equations.
From playlist Differential Equations
Integration 8 The Substitution Rule in Integration Part 2 Example 8
Working through an example using substitution in integration.
From playlist Integration
Topics in Combinatorics lecture 11.1 --- Subadditivity of entropy and Shearer's lemma
A useful rule that is satisfied by entropy is that if X_1,...,X_n are random variables, then H[X_1,...,X_n] is at most H[X_1]+...+H[X_n]. Shearer's lemma is a generalization of this, where one compares H[X_1,...,X_n] by a suitable weighted average of joint entropies of the form H[X_i : i i
From playlist Topics in Combinatorics (Cambridge Part III course)
Maths Problem: Complete Noughts and Crosses (Burnside's Lemma)
How many ways are there to complete a noughts and crosses board - an excuse to show you a little bit of Group Theory. Rotations, reflections and orbits - oh my! Burnside's Lemma http://en.wikipedia.org/wiki/Burnside_lemma Complete sequence https://oeis.org/A082963
From playlist My Maths Videos
The Green - Tao Theorem (Lecture 2) by D. S. Ramana
Program Workshop on Additive Combinatorics ORGANIZERS: S. D. Adhikari and D. S. Ramana DATE: 24 February 2020 to 06 March 2020 VENUE: Madhava Lecture Hall, ICTS Bangalore Additive combinatorics is an active branch of mathematics that interfaces with combinatorics, number theory, ergod
From playlist Workshop on Additive Combinatorics 2020
Integration 12_5_3 Trigonometric Integration.mov
Another example of trigonometric substitution.
From playlist Integration
The Large Sieve (Lecture 3) by Satadal Ganguly
Program Workshop on Additive Combinatorics ORGANIZERS: S. D. Adhikari and D. S. Ramana DATE: 24 February 2020 to 06 March 2020 VENUE: Madhava Lecture Hall, ICTS Bangalore Additive combinatorics is an active branch of mathematics that interfaces with combinatorics, number theory, ergod
From playlist Workshop on Additive Combinatorics 2020
Billy Price and Will Troiani present a series of seminars on foundations of mathematics. In this seminar Billy completes the proof that any consistent, complete and saturated system (in natural deduction) is satisfiable. You can join this seminar from anywhere, on any device, at https://
From playlist Foundations seminar
Determinants and Row Reduction
Effects of row reduction on determinant In this video, we analyze the effects of row-reduction on the determinant. For example, what happens to the determinant of a matrix when you interchange two rows? When you multiply a row by a constant? When you add a row to another? Check out my De
From playlist Determinants
Unterschied Theorem, Lemma und Korollar? Was sind Axiome? | Die Matrix der Mathematik
Wir setzten die Begriffe Definition, Axiom, Satz, und Beweis in einen gemeinsamen Kontext. Außerdem klären wir die Unterschiede zwischen Theorem, Lemma und Korollar. In diesem Video sehen wir uns Mathematik aus der Metaperspektive an. Du wirst sehen: Die Basis mathematischen Arbeitens ist
From playlist Summer of Math Exposition Youtube Videos
Kyle Broder -- Recent Developments Concerning the Schwarz Lemma
A lecture I gave at the Beijing International Center for Mathematical Research geometric analysis seminar. The title being Recent Developments Concerning the Schwarz Lemma with applications to the Wu--Yau Theorem. This contains some recent results concerning the Bochner technique for the G
From playlist Research Lectures
Equivalences and Partitions, Axiomatic Set Theory 2 2
Defining equivalences and partitions of sets, and proving some theorems about their relations to each other. My Twitter: https://twitter.com/KristapsBalodi3 Equivalence Relations:(0:00) Partitions:(9:22) Connecting Equivalence and Partitions:(14:09) Representatives:(27:04)
From playlist Axiomatic Set Theory
Integration 12_5_4 Trigonometric Integration.mov
Another example of trigonometric substitution.
From playlist Integration
Number Theory: Primitive Roots - Oxford Mathematics 2nd Year Student Lecture
Like many Universities around the world, Oxford has gone online for lockdown. So how do our student lectures look? In this, the second online lecture we are making widely available, world-renowned mathematician Ben Green introduces and delivers a short lecture on Primitive Roots, part of t
From playlist Oxford Mathematics 2nd Year Student Lectures