Determine a Time Complexity of Code Using Big-O Notation: O(1), O(n), O(n^2)
This video explains how to determine the time complexity of given code. http://mathispower4u.com
From playlist Additional Topics: Generating Functions and Intro to Number Theory (Discrete Math)
Big O Notation: A Few Examples
This video is about Big O Notation: A Few Examples Time complexity is commonly estimated by counting the number of elementary operations (elementary operation = an operation that takes a fixed amount of time to preform) performed in the algorithm. Time complexity is classified by the nat
From playlist Computer Science and Software Engineering Theory with Briana
Ex: Limits Involving the Greatest Integer Function
This video provides four examples of how to determine limits of a greatest integer function. Site: http://mathispower4u.com
From playlist Limits
Determine Time Complexity Function and Time Complexity Using Big-O Notation: f(n)=(cn(n-1))/2
This video explains how to determine the time complexity of given code. http://mathispower4u.com
From playlist Additional Topics: Generating Functions and Intro to Number Theory (Discrete Math)
Compare Algorithm Complexity Given The Execution Time as a Function
This video explains how to use a limit at infinity to compare the complexity (growth rate) of two functions. http://mathispower4u.com
From playlist Additional Topics: Generating Functions and Intro to Number Theory (Discrete Math)
Upper Bounds in Integer Complexity-CTNT 2020
Define ||n|| to be the complexity of n, which is the smallest number of 1s needed to write n using an arbitrary combination of addition and multiplication. For example, 6=(1+1)(1+1+1) shows that ||6|| is at most 5. We discuss recent results concerning upper and lower bounds for ||n||
From playlist CTNT 2020 - Conference Videos
Greatest Integer Function With Limits & Graphs
This calculus video tutorial explains how to graph the greatest integer function and how to evaluate limits that contain it. This video contains plenty of examples and practice problems evaluating limits with the greatest integer function using the help of a number line. Examples include
From playlist New Calculus Video Playlist
Algorithms Explained: Computational Complexity
An overview of computational complexity including the basics of big O notation and common time complexities with examples of each. Understanding computational complexity is vital to understanding algorithms and why certain constructions or implementations are better than others. Even if y
From playlist Algorithms Explained
Determine a Time Complexity of Code Using Big-O Notation: O(n+m), O(n*m), O(log(n))
This video explains how to determine the time complexity of given code. http://mathispower4u.com
From playlist Additional Topics: Generating Functions and Intro to Number Theory (Discrete Math)
The (Coarse) Moduli Space of (Complex) Elliptic Curves | The Geometry of SL(2,Z), Section 1.3
We discuss complex elliptic curves, and describe their moduli space. Richard Borcherd's videos: Riemann-Roch Introduction: https://www.youtube.com/watch?v=uRfbnJ2a-Bs&ab_channel=RichardE.BORCHERDS Genus 1 Curves: https://www.youtube.com/watch?v=NDy4J_noKi8&ab_channel=RichardE.BORCHERDS
From playlist The Geometry of SL(2,Z)
A surprising application of complex numbers in combinatorics #SoME2
An adaptation of an excellent proof from the excellent "Proofs from THE BOOK" (Aigner & Ziegler) with a more intuitive and visual approach. Music: bensound.com Made with manim community edition. 0:00 - Intro 0:29 - Refresher 1:36 - The puzzle 2:25 - The h function 4:07 - The f function
From playlist Summer of Math Exposition 2 videos
"From Diophantus to Bitcoin: Why Are Elliptic Curves Everywhere?" by Alvaro Lozano-Robledo
This talk was organized by the Number Theory Unit of the Center for Advanced Mathematical Sciences at the American University of Beirut, on November 1st, 2022. Abstract: Elliptic curves are ubiquitous in number theory, algebraic geometry, complex analysis, cryptography, physics, and beyo
From playlist Math Talks
GLU Seminar: "The geometry of number theory, through Mobius transformations" by Katherine Stange
Speaker: Katherine Stange Title: The geometry of number theory, through Mobius transformations Abstract: Mobius transformations beautifully illustrate the geometry of complex numbers. My own interest arose when playing with some questions from number theory. I’ll show you some of the hid
From playlist My Math Talks
Happy Pi Day! A curious fact about Pi related to elliptic curves
This is an "extra" lecture on my grad course on elliptic curves about a curious fact about Pi that has an interesting explanation via the theory of elliptic curves.
From playlist An Introduction to the Arithmetic of Elliptic Curves
Counting points on the E8 lattice with modular forms (theta functions) | #SoME2
In this video, I show a use of modular forms to answer a question about the E8 lattice. This video is meant to serve as an introduction to theta functions of lattices and to modular forms for those with some knowledge of vector spaces and series. -------------- References: (Paper on MIT
From playlist Summer of Math Exposition 2 videos
Daniel Kral: Parametrized approach to block structured integer programs
Integer programming is one of the most fundamental problems in discrete optimization. While integer programming is computationally hard in general, there exist efficient algorithms for special instances. In particular, integer programming is fixed parameter tractable when parameterized by
From playlist Workshop: Parametrized complexity and discrete optimization
Introduction to number theory lecture 29. Rings in number theory
This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We show how to write several results in number theory, such as the Chines remainder theorem
From playlist Introduction to number theory (Berkeley Math 115)
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
Haotian Jiang: Minimizing Convex Functions with Integral Minimizers
Given a separation oracle SO for a convex function f that has an integral minimizer inside a box with radius R, we show how to find an exact minimizer of f using at most • O(n(n + log(R))) calls to SO and poly(n,log(R)) arithmetic operations, or • O(nlog(nR)) calls to SO and exp(O(n)) · po
From playlist Workshop: Continuous approaches to discrete optimization