Operations on structures | Geometric topology | Differential topology | Knot theory
In mathematics, specifically in topology, the operation of connected sum is a geometric modification on manifolds. Its effect is to join two given manifolds together near a chosen point on each. This construction plays a key role in the classification of closed surfaces. More generally, one can also join manifolds together along identical submanifolds; this generalization is often called the fiber sum. There is also a closely related notion of a connected sum on knots, called the knot sum or composition of knots. (Wikipedia).
How to determine if ratios are equivalent or not
👉 Learn all about multiplying and dividing fractions. In this playlist we will explore how to multiply and divide fractions when they are represented as mixed numbers or improper fractions. We will also explore how to simplify our fractions before and after the operation. 👏SUBSCRIBE to
From playlist How to Multiply Fractions
This video introduces similarity and explains how to determine if two figures are similar or not. http://mathispower4u.com
From playlist Number Sense - Decimals, Percents, and Ratios
👉 Learn how to understand the concept of fractions using parts of a whole. Fractions are parts of a whole and this concept can be illustrated using bars and circles. This concept can also be extended to understand equivalent fractions. When a whole bar is divided into, say, two equal parts
From playlist Learn About Fractions
How to find equivalent fractions and understanding what they are
👉 Learn how to understand the concept of fractions using parts of a whole. Fractions are parts of a whole and this concept can be illustrated using bars and circles. This concept can also be extended to understand equivalent fractions. When a whole bar is divided into, say, two equal parts
From playlist Learn About Fractions
Fraction concept with circlular wholes - help me with math - free online tutoring
👉 Learn how to understand the concept of fractions using parts of a whole. Fractions are parts of a whole and this concept can be illustrated using bars and circles. This concept can also be extended to understand equivalent fractions. When a whole bar is divided into, say, two equal parts
From playlist Learn About Fractions
How to determine if two ratios are equivalent
👉 Learn all about multiplying and dividing fractions. In this playlist we will explore how to multiply and divide fractions when they are represented as mixed numbers or improper fractions. We will also explore how to simplify our fractions before and after the operation. 👏SUBSCRIBE to
From playlist How to Multiply Fractions
How to determine equivalent ratios
👉 Learn all about multiplying and dividing fractions. In this playlist we will explore how to multiply and divide fractions when they are represented as mixed numbers or improper fractions. We will also explore how to simplify our fractions before and after the operation. 👏SUBSCRIBE to
From playlist How to Multiply Fractions
Overview of fractions - free math help - online tutor
👉 Learn how to understand the concept of fractions using parts of a whole. Fractions are parts of a whole and this concept can be illustrated using bars and circles. This concept can also be extended to understand equivalent fractions. When a whole bar is divided into, say, two equal parts
From playlist Learn About Fractions
Learn what fractions are - learn math online
👉 Learn how to understand the concept of fractions using parts of a whole. Fractions are parts of a whole and this concept can be illustrated using bars and circles. This concept can also be extended to understand equivalent fractions. When a whole bar is divided into, say, two equal parts
From playlist Learn About Fractions
Geometry of Surfaces - Topological Surfaces Lecture 4 : Oxford Mathematics 3rd Year Student Lecture
This is the fourth of four lectures from Dominic Joyce's 3rd Year Geometry of Surfaces course. The four lectures cover topological surfaces and conclude with a big result, namely the classification of surfaces. This lecture covers connected sums, orientations, and finally the classificatio
From playlist Oxford Mathematics Student Lectures - Geometry of Surfaces
Do KNOT watch this video! #SoME1
This video is an entry to the 3Blue1Brown, The Summer of Math Exposition, about proving the existence of prime knots and the interesting steps towards the result. Some images produced with SeifertView, Jarke J. van Wijk, Technische Universiteit Eindhoven. Download SeifertView at the link
From playlist Summer of Math Exposition Youtube Videos
Hugo Duminil-Copin: Lecture #2
Second lecture on "Marginal triviality of the scaling limits of critical 4D Ising and ϕ^4_4 models" by Professor Hugo Duminil-Copin. For more materials and slides visit: https://sites.google.com/view/oneworld-pderandom/home
From playlist Summer School on PDE & Randomness
Simple Message Passing on Graphs
Join my FREE course Basics of Graph Neural Networks (https://www.graphneuralnets.com/p/basics-of-gnns/?src=yt)! This video discusses the adjacency matrix and how it can be used to implement basic message passing on graphs. A simple example is given using Python. Code: https://github.co
From playlist Graph Neural Networks
Hugo Duminil-Copin - 3/4 Triviality of the 4D Ising Model
We prove that the scaling limits of spin fluctuations in four-dimensional Ising-type models with nearest-neighbor ferromagnetic interaction at or near the critical point are Gaussian. A similar statement is proven for the λφ4 fields over R^4 with a lattice ultraviolet cutoff, in the limit
From playlist Hugo Duminil-Copin - Triviality of the 4D Ising Model
Jamie Scott (9/23/21): Applications of Surgery to a Generalized Rudyak Conjecture
Rudyak’s conjecture states that cat (M) is at least cat (N) given a degree one map f between the closed manifolds M and N. In the recent paper "Surgery Approach to Rudyak's Conjecture", the following theorem was proven: Theorem. Let f from M to N be a normal map of degree one between clos
From playlist Topological Complexity Seminar
Samantha Moore (6/1/2022): The Generalized Persistence Diagram Encodes the Bigraded Betti Numbers
We show that the generalized persistence diagram (introduced by Kim and Mémoli) encodes the bigraded Betti numbers of finite 2-parameter persistence modules. More interestingly, we show that the bigraded Betti numbers can be visually read off from the generalized persistence diagram in a m
From playlist AATRN 2022
Solving a proportion using the cross product ex 7, 8/5 = (4/3x)
👉 Learn how to solve proportions. Two ratios are said to be proportional when the two ratios are equal. Thus, proportion problems are problems involving the equality of two ratios. When given a proportion problem with an unknown, we usually cross-multiply the two ratios and then solve for
From playlist How to Solve a Proportion
Hugo Duminil-Copin: Lecture #4
The final lecture on "Marginal triviality of the scaling limits of critical 4D Ising and ϕ^4_4 models" by Professor Hugo Duminil-Copin. For more materials and slides visit: https://sites.google.com/view/oneworld-pderandom/home
From playlist Summer School on PDE & Randomness