Topology | Spheres | Metric geometry
In mathematics, a ball is the solid figure bounded by a sphere; it is also called a solid sphere. It may be a closed ball (including the boundary points that constitute the sphere) or an open ball (excluding them). These concepts are defined not only in three-dimensional Euclidean space but also for lower and higher dimensions, and for metric spaces in general. A ball in n dimensions is called a hyperball or n-ball and is bounded by a hypersphere or (n−1)-sphere. Thus, for example, a ball in the Euclidean plane is the same thing as a disk, the area bounded by a circle. In Euclidean 3-space, a ball is taken to be the volume bounded by a 2-dimensional sphere. In a one-dimensional space, a ball is a line segment. In other contexts, such as in Euclidean geometry and informal use, sphere is sometimes used to mean ball. In the field of topology the closed -dimensional ball is often denoted as or while the open -dimensional ball is or . (Wikipedia).
Formal Definition of a Function using the Cartesian Product
Learning Objectives: In this video we give a formal definition of a function, one of the most foundation concepts in mathematics. We build this definition out of set theory. **************************************************** YOUR TURN! Learning math requires more than just watching vid
From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
This video explains what is taught in discrete mathematics.
From playlist Mathematical Statements (Discrete Math)
Calculus 1 Lecture 5.4 Part 6: Finding the Length of a Curve and The Surface Area of a Solid of Revolution.
From playlist Calculus 1 Playlist 2
The formal definition of a sequence.
We have an intuitive picture of sequences (infinite ordered lists). But there is a formal definition of sequences based out of the idea of a specific function between sets, specifically from the positive integers to the real numbers. ►Full DISCRETE MATH Course Playlist: https://www.youtu
From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
Maths for Programmers: Introduction (What Is Discrete Mathematics?)
Transcript: In this video, I will be explaining what Discrete Mathematics is, and why it's important for the field of Computer Science and Programming. Discrete Mathematics is a branch of mathematics that deals with discrete or finite sets of elements rather than continuous or infinite s
From playlist Maths for Programmers
Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https://twitter.com/worldscienceu
From playlist Science Unplugged: Mathematics
As part of the college algebra series, this Center of Math video will teach you the basics of functions, including how they're written and what they do.
From playlist Basics: College Algebra
4 Calculating some interesting limits
Now that we have got the ball rolling, let's do some examples.
From playlist Life Science Math: Limits in calculus
Counting and Probability Walkthrough
This video is a casual walkthough of a worksheet on a whole bunch of counting and probability problems. We have combinations and permutations, the additivity principle and the multiplication principle. ►FULL DISCRETE MATH PLAYLIST: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8f
From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
Steve Butler - Math and Juggling - CoM Oct 2020
Juggling can be described by the series of throws that you make. This is known as siteswap. We discuss a “string theory” approach to showing that the number of balls involved in a pattern is the average of these throws, and then look at how to take a collection of throws whose average is a
From playlist Celebration of Mind
Peter Winkler - Drawing from Urns - CoM Apr 2021
Many problems in probability and statistics can be modeled as follows: before you are two urns containing some colored balls. You know the contents of urn A, and the (different) contents of urn B, but you don't know which urn is A and which is B. You get two chances to draw a ball at rando
From playlist Celebration of Mind 2021
The mathematical soul of juggling
In this video the Mathologer captures the mathematical soul of juggling and has a lot of fun analysing the hell out of it. If you are really keen check out his book and articles on the math of juggling: http://tinyurl.com/glczdxl http://tinyurl.com/pryz6fw http://www.qedcat.com/books.htm
From playlist Recent videos
The Meaning of Energy? Core Physics Principle Explained by Parth G
Energy is an extremely important concept in all of physics. It is used everywhere to describe how different systems will behave. But what exactly is energy in the first place? What is the meaning of energy? This difficult-to-answer question can be thought of in terms of a few different ex
From playlist Thermodynamics by Parth G
Jürgen Jost (8/29/21): Geometry and Topology of Data
Data sets are often equipped with distances between data points, and thereby constitute a discrete metric space. We develop general notions of curvature that capture local and global properties of such spaces and relate them to topological concepts such as hyperconvexity. This also leads t
From playlist Beyond TDA - Persistent functions and its applications in data sciences, 2021
Galileo's investigation of uniformly accelerated motion due to gravity could, in many ways, be considered the birth of modern physics. Caltech's The Mechanical Universe episode on the law of falling bodies: https://youtu.be/livG1fp-q8s Feather & ball experiment: http://www.youtube.com/wat
From playlist Mechanics
How many ping-pong balls would it take to lift the Titanic?
Lifting the Titanic with ping pong balls was a real suggestion put forward in the 1970's that needless to say did not happen. Let's pretend it is possible and work out how many we would need using Archimedes Principle... This is the latest question from Tom Rocks Maths and I Love Mathemat
From playlist I Love Mathematics
Soccermatics: could a Premier League team one day be managed by a mathematician?
Oxford Mathematics Public Lectures: David Sumpter - Soccermatics: could a Premier League team one day be managed by a mathematician? What do you need to win the Premier League? Money? Sure. Good players? Yup. A great manager? It helps. Mathematics? Really? 100%. David Sumpter will expla
From playlist Oxford Mathematics Public Lectures
Jonglerie, automates et combinatoire - Florent Hivert - Mathématiques et mouvements - 13/03/18
Jonglerie, automate et combinatoire Résumé : Je me propose d'illustrer la démarche de modélisation en prenant comme problème les figures de jonglerie. En partant d'un "objet d'étude réel" -un jongleur-, une série de simplifications -la modélisation- fait apparaître naturellement un objet
From playlist Mathématiques et mouvements - 13/03/2018
Floating Balls and Lift - Numberphile
Tadashi discusses pressure and lift... with a toy of course! More links & stuff in full description below ↓↓↓ Lift and wings on Sixty Symbols: https://youtu.be/PF22LM8AbII Tadashi Playlist: http://bit.ly/tadashi_vids You can buy version of this toy on Amazon: https://amzn.to/2MLfpSC (af
From playlist Tadashi Tokieda on Numberphile
Geometry for Kids - Definitions
This is a series of videos on Geometry, with kids in mind (~ 9 or 10 years old). In this video we start with some basic definitions: point, plane, segment, line, ray, secant, parallel, circle, radius, and diameter. Click "show more" for links and more details. You can find our Algebra for
From playlist Geometry for Kids