Graphical concepts in set theory
A Randolph diagram (R-diagram) is a simple way to visualize logical expressions and combinations of sets. Randolph diagrams were created by mathematician John F. Randolph in 1965, while he was teaching at the University of Arkansas. (Wikipedia).
another Riemann-Zeta function identity.
We present an interesting identity involving the even values of the Riemann-Zeta function. Some more Riemann-zeta function identities: https://youtu.be/2W2Ghi9idxM https://youtu.be/bRdGQKwusiE https://youtu.be/JwxgwXUruRM Please Subscribe: https://www.youtube.com/michaelpennmath?sub_con
From playlist The Riemann Zeta Function
Representations of Finite Groups | A few more common examples.
We present a few more common examples of representations of finite groups. These include cyclic groups, dihedral groups, the quaternions, and the symmetric group. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Personal Website: http://www.michael-penn.net R
From playlist Representations of Finite Groups
Constructing interesting integrals
We give an example of an approach to construct interesting and surprising integrals. Playlist: https://youtube.com/playlist?list=PL22w63XsKjqzJpcuD6InKWZXep2L0z1H8 Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.com/stores/michael-pe
From playlist Interesting Integrals
A limit of a trigonometric integral.
Building on our last integral video, we prove a nice result involving the limit of a certain trigonometric integral. Last Time: https://youtu.be/nkaZEI_e2SU Playlist: https://youtube.com/playlist?list=PL22w63XsKjqzJpcuD6InKWZXep2L0z1H8 Please Subscribe: https://www.youtube.com/michaelpe
From playlist Interesting Limits
Maxwell's equations via differential forms.
We present a form of Maxwell's equations int he language of differential forms. These involve a relationship between the electromagnetic two form, the current one form, the Hodge operator, and the exterior derivative. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmat
From playlist Physics
Putnam Battle part 3!! @Michael Penn vs @ProfOmarMath
This is the third in a series of videos with @ProfOmarMath where we look at a total of four solutions to Question A6 from the 2018 William Lowell Putnam Mathematic Competition. Our strategy for this solution is to reinterpret the question as a linear algebra problem and use some nice pro
From playlist Putnam Exam Solutions
Introduction to Integer Partitions -- Number Theory 28
Suggest a problem: https://forms.gle/ea7Pw7HcKePGB4my5 Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math Personal Website: http://www.michael-penn.net Randolp
From playlist Number Theory v2
Quiz: Composition of Functions (Graph & Table)
Link: https://www.geogebra.org/m/QgN7nwCh
From playlist Algebra 1: Dynamic Interactives!
The Genesis of Vertex Algebras
We have a guest for this very special video. Richard Borcherds (Berkeley) has contributed a video regarding the history of vertex algebras. This video was also posted on his channel and is included here as well with permission and to increase its reach. Subscribe to his channel: https:/
From playlist Vertex Operator Algebras
We look at the precise definition of a function. Suggest a problem: https://forms.gle/ea7Pw7HcKePGB4my5 Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.com/stores/michael-penn-math Personal Website: http://www.michael-penn.net Randol
From playlist Proof Writing
Can you find the area of this triangle??
Suggest a problem: https://forms.gle/ea7Pw7HcKePGB4my5 Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math Personal Website: http://www.michael-penn.net Randolp
From playlist Geometry
Randolph, Rustin, & the Origins of the March on Washington: Crash Course Black American History #32
The March on Washington of 1963 is an enduring and widely-known event of the Civil Rights movement. But the March has its roots in an earlier planned March on Washington that didn't happen. In 1941, labor leader A. Philip Randolph began planning a gathering aimed at many of the same goals
From playlist Black American History
Lecture 12. Depression and Double V (continued)
American History: From Emancipation to the Present (AFAM 162) In this lecture, Professor Holloway continues discussing African American political possibilities in the second half of the 1930s by examining the new mentality at work in black America. He focuses on the National Negro Congres
From playlist American History: From Emancipation to the Present
A viewer suggested geometry problem.
We look at a nice geometry problem. Playlist: https://youtube.com/playlist?list=PL22w63XsKjqyZZAicSHbpVhJzLPfPMJf6 Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.com/stores/michael-penn-math Personal Website: http://www.michael-penn
From playlist Geometry
What is the radius of the large circle?
We solve a nice problem that originated as a classical Japanese temple geometry problem. Playlist: https://youtube.com/playlist?list=PL22w63XsKjqyZZAicSHbpVhJzLPfPMJf6 Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.com/stores/michae
From playlist Geometry
We look at a nice integral identity that allows us to evaluate an entire family of integrals. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.com/stores/michael-penn-math Personal Website: http://www.michael-penn.net Randolph College
From playlist Interesting Integrals
The trig functions you have never heard of!!
We present definitions of some historical trigonometric functions. Further investigation is made as to why they have fallen out of favor. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Personal Website: http://www.michael-penn.net Randolph College Math: http
From playlist Trigonometric Identities
An inscribed tower of squares.
We solve a nice traditional Japanese geometry. Playlist: https://youtube.com/playlist?list=PL22w63XsKjqyZZAicSHbpVhJzLPfPMJf6 Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.com/stores/michael-penn-math Personal Website: http://www.m
From playlist Geometry
We look at a nice problem involving calculating the area between a pair of parabolas and an inscribed regular hexagon. Playlist: https://youtube.com/playlist?list=PL22w63XsKjqyZZAicSHbpVhJzLPfPMJf6 Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: http
From playlist Geometry
All the world's a stage - Preparing our graduates for success - A/Prof Chinthaka Balasooriya
UNSW Scientia Education Academy Lecture Series All the world's a stage - Preparing our graduates for success on a global scale - A/Prof Chinthaka Balasooriya The world is changing. We know that the needs of the future could be radically different, but we don’t know how different they wil
From playlist UNSW Scientia Education Academy Lecture Series