Math 101 Fall 2017 112917 Introduction to Compact Sets
Definition of an open cover. Definition of a compact set (in the real numbers). Examples and non-examples. Properties of compact sets: compact sets are bounded. Compact sets are closed. Closed subsets of compact sets are compact. Infinite subsets of compact sets have accumulation poi
From playlist Course 6: Introduction to Analysis (Fall 2017)
Now that we know what a quotient group is, let's take a look at an example to cement our understanding of the concepts involved.
From playlist Abstract algebra
What is a matrix? Free ebook http://tinyurl.com/EngMathYT
From playlist Intro to Matrices
Now that we have defined and understand quotient groups, we need to look at product groups. In this video I define the product of two groups as well as the group operation, proving that it is indeed a group.
From playlist Abstract algebra
This is a video I have been wanting to make for some time, in which I discuss what the quaternions are, as mathematical objects, and how we do calculations with them. In particular, we will see how the fundamental equation of the quaternions i^2=j^2=k^2=ijk=-1 easily generates the rule for
From playlist Quaternions
Linear Algebra for Computer Scientists. 12. Introducing the Matrix
This computer science video is one of a series of lessons about linear algebra for computer scientists. This video introduces the concept of a matrix. A matrix is a rectangular or square, two dimensional array of numbers, symbols, or expressions. A matrix is also classed a second order
From playlist Linear Algebra for Computer Scientists
Math 101 Introduction to Analysis 112515: Introduction to Compact Sets
Introduction to Compact Sets: open covers; examples of finite and infinite open covers; definition of compactness; example of a non-compact set; compact implies closed; closed subset of compact set is compact; continuous image of a compact set is compact
From playlist Course 6: Introduction to Analysis
This video is about compactness and some of its basic properties.
From playlist Basics: Topology
Theory of synchronization - CEB T2 2017 - Pikovsky - 3/3
Arkady Pikovsky (Univ. Potsdam) - 21/04/17 Theory of synchronization 1) Basics - oscillators, phase and amplitudes - isochrons and phase response curve - phase dynamics under small forcing - phase locking and frequency entrainment - beyond phase approximation - effects of noise -
From playlist 2017 - T2 - Stochastic Dynamics out of Equilibrium - CEB Trimester
Symmetric Groups (Abstract Algebra)
Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in
From playlist Abstract Algebra
Theory of synchronization - CEB T2 2017 - Pikovsky - 2/3
Arkady Pikovsky (Univ. Potsdam) - 18/04/17 Theory of synchronization 1) Basics - oscillators, phase and amplitudes - isochrons and phase response curve - phase dynamics under small forcing - phase locking and frequency entrainment - beyond phase approximation - effects of noise -
From playlist 2017 - T2 - Stochastic Dynamics out of Equilibrium - CEB Trimester
Theory of synchronization - CEB T2 2017 - Pikovsky - 1/3
Arkady Pikovsky (Univ. Potsdam) - 18/04/17 Theory of synchronization 1) Basics - oscillators, phase and amplitudes - isochrons and phase response curve - phase dynamics under small forcing - phase locking and frequency entrainment - beyond phase approximation - effects of noise -
From playlist 2017 - T2 - Stochastic Dynamics out of Equilibrium - CEB Trimester
Math 101 Introduction to Analysis 113015: Compact Sets, ct'd
Compact sets, continued. Recalling various facts about compact sets. Compact implies infinite subsets have limit points (accumulation points), that is, compactness implies limit point compactness; collections of compact sets with the finite intersection property have nonempty intersectio
From playlist Course 6: Introduction to Analysis