Combinatorics | Hypergraphs

Independence system

In combinatorial mathematics, an independence system is a pair , where is a finite set and is a collection of subsets of (called the independent sets or feasible sets) with the following properties: 1. * The empty set is independent, i.e., . (Alternatively, at least one subset of is independent, i.e., .) 2. * Every subset of an independent set is independent, i.e., for each , we have . This is sometimes called the hereditary property, or downward-closedness. Another term for an independence system is an abstract simplicial complex. (Wikipedia).

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A02 Independence of the solution set

The independence of a linear system. How to make sure that a set of solutions are not constant multiples of each other.

From playlist A Second Course in Differential Equations

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More Help with Independence

Further examination of independence

From playlist Unit 5 Probability A: Basic Probability

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More Help with Independence Part 2Indep FE pt 2

More insight into the probability concept of independence

From playlist Unit 5 Probability A: Basic Probability

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(PP 2.2) Independence

(0:00) Independence of two events (4:12) (Mutual) Independence of multiple events (9:30) Conditional Independence of two events A playlist of the Probability Primer series is available here: http://www.youtube.com/view_play_list?p=17567A1A3F5DB5E4

From playlist Probability Theory

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America the Story of Us: Declaration of Independence | History

The Declaration of Independence marks the first such document declaring the equality of men. Own America: The Story of Us on DVD or Blu-ray! http://www.shophistorystore.com/ HISTORY®, now reaching more than 98 million homes, is the leading destination for award-winning original series and

From playlist Presidential History

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Differential Equations: Linear Independence

Linear independence is a core idea from Linear Algebra. Surprisingly, it's also important in differential equations. This video is the second precursor to our discussion of homogeneous differential equations.

From playlist Differential Equations

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(PP 2.3) Independence (continued)

(0:00) (Mutual) Independence of an infinite sequence of events. (1:55) Conditional Independence of multiple events. (3:28) Relationship between independence and conditional probability. (7:23) Example illustrating the relationships between independence, pairwise independence, mutu

From playlist Probability Theory

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Linear Independence Problems - Using the Definition

In this video, I review the definition of linear independence and work through some practice problems using the definition. To learn more about linear independence, check out this lecture in my Linear Algebra Lectures video series: https://youtu.be/KE7xHcwfxzQ

From playlist Linear Algebra Lectures

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Microservices: A Retrospective

SOA has been around for decades, and its latest iteration - microservices - for a while now. Just five years ago microservices were hip, dominating the agenda at conferences; now we almost take them for granted. With microservice-focused conference talks losing steam, the time is ripe to c

From playlist Microservices

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W. Zheng - Compatible systems along the boundary

A theorem of Deligne says that compatible systems of l-adic sheaves on a smooth curve over a finite field are compatible along the boundary. I will present an extension of Deligne's theorem to schemes of finite type over the ring of integers of a local field, based on Gabber's theorem on c

From playlist Arithmetic and Algebraic Geometry: A conference in honor of Ofer Gabber on the occasion of his 60th birthday

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L03.9 Reliability

MIT RES.6-012 Introduction to Probability, Spring 2018 View the complete course: https://ocw.mit.edu/RES-6-012S18 Instructor: John Tsitsiklis License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses at https://ocw.mit.edu

From playlist MIT RES.6-012 Introduction to Probability, Spring 2018

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29 - Determining linear independence

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From playlist Algebra 1M

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(0.3.101) Exercise 0.3.101: Classifying Differential Equations

This video explains how to classify differential equations based upon their properties https://mathispower4u.com

From playlist Differential Equations: Complete Set of Course Videos

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Math 060 Linear Algebra 10 092914: Vector Space Bases

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From playlist Course 4: Linear Algebra

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Mod-01 Lec-7 Physical Properties of Crystals (Continued)

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From playlist NPTEL: Condensed Matter Physics - CosmoLearning.com Physics Course

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Controllability of a Linear System: The Controllability Matrix and the PBH Test

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From playlist Control Theory

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23 Algebraic system isomorphism

Isomorphic algebraic systems are systems in which there is a mapping from one to the other that is a one-to-one correspondence, with all relations and operations preserved in the correspondence.

From playlist Abstract algebra

Related pages

Abstract simplicial complex | Mathematics | Set (mathematics) | Combinatorics | Empty set | Hypergraph | Matroid | Subset