Injective, Surjective and Bijective Functions (continued)
This video is the second part of an introduction to the basic concepts of functions. It looks at the different ways of representing injective, surjective and bijective functions. Along the way I describe a neat way to arrive at the graphical representation of a function.
From playlist Foundational Math
This video explains what a mathematical function is and how it defines a relationship between two sets, the domain and the range. It also introduces three important categories of function: injective, surjective and bijective.
From playlist Foundational Math
Determine if a Relation is a Function
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From playlist Intro to Functions
How to determine if a set of points is a function, onto, one to one, domain, range
👉 Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r
From playlist What is the Domain and Range of the Function
Definition of a Surjective Function and a Function that is NOT Surjective
We define what it means for a function to be surjective and explain the intuition behind the definition. We then do an example where we show a function is not surjective. Surjective functions are also called onto functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear ht
From playlist Injective, Surjective, and Bijective Functions
How to determine if an ordered pair is a function or not
👉 Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r
From playlist What is the Domain and Range of the Function
Using the vertical line test to determine if a graph is a function or not
👉 Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r
From playlist What is the Domain and Range of the Function
Deeparnab Chakrabarty: Polynomial Lower Bounds for Parallel Submodular Function Minimization
HIM Workshop: Continuous approaches to discrete optimization
From playlist Workshop: Continuous approaches to discrete optimization
Seffi Naor: Recent Results on Maximizing Submodular Functions
I will survey recent progress on submodular maximization, both constrained and unconstrained, and for both monotone and non-monotone submodular functions. The lecture was held within the framework of the Hausdorff Trimester Program: Combinatorial Optimization.
From playlist HIM Lectures 2015
Pre-Calculus - Vocabulary of functions
This video describes some of the vocabulary used with functions. Specifically it covers what a function is as well as the basic idea behind its domain and range. For more videos visit http://www.mysecretmathtutor.com
From playlist Pre-Calculus - Functions
Kazuo Murota: Extensions and Ramifications of Discrete Convexity Concepts
Submodular functions are widely recognized as a discrete analogue of convex functions. This convexity view of submodularity was established in the early 1980's by the fundamental works of A. Frank, S. Fujishige and L. Lovasz. Discrete convex analysis extends this view to broader classes of
From playlist HIM Lectures 2015
Niv Buchbinder: Deterministic Algorithms for Submodular Maximization Problems
Randomization is a fundamental tool used in many theoretical and practical areas of computer science. We study here the role of randomization in the area of submodular function maximization. In this area most algorithms are randomized, and in almost all cases the approximation ratios obtai
From playlist HIM Lectures 2015
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
Bill Jackson: Generic Rigidity of Point Line Frameworks
A point-line framework is a collection of points and lines in the plane which are linked by pairwise constraints that fix some angles between pairs of lines and also some point-line and point-point distances. It is rigid if every continuous motion of the points and lines which preserves th
From playlist HIM Lectures 2015
Michael Joswig: Generalized permutahedra and optimal auctions
We study a family of convex polytopes, called SIM-bodies, which were introduced by Giannakopoulos and Koutsoupias (2018) to analyze so-called Straight-Jacket Auctions. First, we show that the SIM-bodies belong to the class of generalized permutahedra. Second, we prove an optimality result
From playlist Workshop: Tropical geometry and the geometry of linear programming
Optimisation algorithms for computer vision and machine learning
Bio Pankaj is a second year PhD student in the Engineering Science department at University of Oxford and an enrichment year student at The Alan Turing Institute. His research interests lie in optimisation and machine learning. At Oxford, he is a member of the OVAL group under Prof. Pawan
From playlist Short Talks
Definition of an Injective Function and Sample Proof
We define what it means for a function to be injective and do a simple proof where we show a specific function is injective. Injective functions are also called one-to-one functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear https://amzn.to/3BFvcxp (these are my affil
From playlist Injective, Surjective, and Bijective Functions
M. Zadimoghaddam: Randomized Composable Core-sets for Submodular Maximization
Morteza Zadimoghaddam: Randomized Composable Core-sets for Distributed Submodular and Diversity Maximization An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a represen
From playlist HIM Lectures 2015
Pre-Calculus - Subtraction of two functions f(x) = 2x -5 , g(x) = 2-x
👉 Learn how to add or subtract two functions. Given two functions, say f(x) and g(x), to add (f+g)(x) or f(x) + g(x) or to subtract (f - g)(x) or f(x) - g(x) the two functions we use the method of adding/subtracting algebraic expressions together. To add or subtract two linear functions, w
From playlist Add Subtract Multiply Divide Functions
Standa Zivny: The Power of Sherali Adams Relaxations for General Valued CSPs
In this talk, we survey recent results on the power of LP relaxations (the basic LP relaxation and Sherali-Adams relaxations) in the context of valued constraint satisfaction problems (VCSP). We give precise characterisations of constraint languages for which these relaxations are exact, a
From playlist HIM Lectures 2015