Pre-Calculus - Boundedness theorem for polynomials
This video covers the boundedness theorem for polynomials. This tells us if the zero we tested while using synthetic division is an upper or lower bound for the zeros. Watch carefully on the criteria that must be satisfied to use this theorem. For more videos please visit http://www.mys
From playlist Pre-Calculus
Math 131 Spring 2022 041122 Uniform Convergence and Continuity
Exercise: the limit of uniformly convergent continuous functions is continuous. Theorem: generalization. Theorem: pointwise convergence on a compact set + extra conditions guarantees uniform convergence. Digression: supremum norm metric on bounded continuous functions. Definitions.
From playlist Math 131 Spring 2022 Principles of Mathematical Analysis (Rudin)
Math 131 111416 Sequences of Functions: Pointwise and Uniform Convergence
Definition of pointwise convergence. Examples, nonexamples. Pointwise convergence does not preserve continuity, differentiability, or integrability, or commute with differentiation or integration. Uniform convergence. Cauchy criterion for uniform convergence. Weierstrass M-test to imp
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
Math 131 092816 Continuity; Continuity and Compactness
Review definition of limit. Definition of continuity at a point; remark about isolated points; connection with limits. Composition of continuous functions. Alternate characterization of continuous functions (topological definition). Continuity and compactness: continuous image of a com
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
Joseph Silverman, Moduli problems and moduli spaces in algebraic dynamics
VaNTAGe seminar on June 23, 2020. License: CC-BY-NC-SA. Closed captions provided by Max Weinreich
From playlist Arithmetic dynamics
Determine Infinite Limits of a Rational Function Using a Table and Graph (Squared Denominator)
This video explains how to determine a limits and one-sided limits. The results are verified using a table and a graph.
From playlist Infinite Limits
Recovering elliptic curves from their p-torsion - Benjamin Bakker
Benjamin Bakker New York University May 2, 2014 Given an elliptic curve EE over a field kk, its p-torsion EpEp gives a 2-dimensional representation of the Galois group GkGk over đť”˝pFp. The Frey-Mazur conjecture asserts that for k=â„šk=Q and p13p13, EE is in fact determined up to isogeny by th
From playlist Mathematics
Wei Ho, Integral points on elliptic curves
VaNTAGe seminar, on Oct 13, 2020 License: CC-BY-NC-SA. Closed captions provided by Rachana Madhukara.
From playlist Rational points on elliptic curves
VaNTAGe seminar, on Sep 15, 2020 License: CC-BY-NC-SA.
From playlist Rational points on elliptic curves
Zarhin's trick and geometric boundedness results for K3 surfaces - François Charles
François Charles Université Paris-Sud November 11, 2014 Tate's conjecture for divisors on algebraic varieties can be rephrased as a finiteness statement for certain families of polarized varieties with unbounded degrees. In the case of abelian varieties, the geometric part of these finite
From playlist Mathematics
Math 131 112816 Uniform Convergence and Differentiation, Nowhere differentiable continuous function
When can one commute limit and differentiation? (continued from previous lecture). Construction of a continuous, nowhere-differentiable function. Question: what is "sequential compactness" for a set of functions? Definitions: pointwise bounded set of functions, uniformly bounded set of
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
Incidence Theory and Uniform Distribution in Higher Dimensions - Alex Iosevich
Special Year Research Seminar Topic: Incidence Theory and Uniform Distribution in Higher Dimensions Speaker: Alex Iosevich Affiliation: University of Rochester Date: February 14, 2023 2:00pm Simonyi Hall 101 Incidence bound for points and spheres in higher dimensions generally becomes tr
From playlist Mathematics
Math 131 Fall 2018 111918 Uniform Convergence, continued
Exercise: if a sequence of continuous functions converges uniformly, the limit is also continuous. Alternate view of uniform continuity: supremum norm on the set of bounded continuous functions. Related metric. Completeness of this metric space. Crash course in Riemann integrable funct
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)
Pablo Shmerkin: Additive combinatorics methods in fractal geometry - lecture 1
In the last few years ideas from additive combinatorics were applied to problems in fractal geometry and led to progress on some classical problems, particularly on the smoothness of Bernoulli convolutions and other self-similar measures. We will introduce some of these tools from additive
From playlist Combinatorics
Mazur's program B. - Zureick-Brown - Workshop 2 - CEB T2 2019
David Zureick-Brown (Emory University, Atlanta USA) / 25.06.2019 Mazur's program B. I’ll discuss recent progress on Mazur’s “Program B” – the problem of classifying all possibilities for the “image of Galois” for an elliptic curve over Q (equivalently, classification of all rational poi
From playlist 2019 - T2 - Reinventing rational points
Bianca Viray, The Brauer group and the Brauer-Manin obstruction on K3 surfaces
VaNTAGe seminar, February 23, 2021
From playlist Arithmetic of K3 Surfaces
From metric spaces to topological spaces -- Proofs
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
Math 131 Fall 2018 111618 Uniform convergence, continued
Review of uniform convergence: definition and Cauchy criterion. Rephrasal of uniform convergence. Weierstrass M-test for uniform convergence of a series. Uniform convergence and continuous functions. Pointwise convergence of a decreasing sequence of continuous functions on a compact se
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)
Fields Medal Lecture: Classification of algebraic varieties — Caucher Birkar — ICM2018
Classification of algebraic varieties Caucher Birkar Abstract: The aim of this talk is to describe the classification problem of algebraic varieties in the framework of modern birational geometry. This problem which lies at the heart of algebraic geometry has seen tremendous advances in t
From playlist Special / Prizes Lectures
The Difference Between Pointwise Convergence and Uniform Convergence
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys The Difference Between Pointwise Convergence and Uniform Convergence
From playlist Advanced Calculus