115videosMichael Penn
356K subscribers on YouTube
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Playlists · 60
All 60 playlists
- Proof Writing · 27 videos
- Putnam Exam Solutions: A1/B1 · 24 videos
- The Floor is Lava · 20 videos
- Differential Forms · 22 videos
- Primitive Roots Modulo n · 21 videos
- Multivariable Calculus: Multivariable functions. · 21 videos
- Interesting Limits · 19 videos
- Putnam Exam Solutions: A2/B2 · 18 videos
- Viewer suggestions. · 17 videos
- Multivariable Calculus | Line Integrals · 17 videos
- The Laplace Transform · 16 videos
- Abstract Algebra: The basics of rings. · 16 videos
- Multivariable Calculus | Surface Integrals · 16 videos
- Abstract Algebra | Preliminaries · 13 videos
- Series Solutions for Differential Equations · 13 videos
- Mathematics named after Leonhard Euler · 12 videos
- Interesting Sums · 11 videos
- Systems of Differential Equations · 12 videos
- Quadratic Residues, the Legendre Symbol, and Quadratic Reciprocity · 10 videos
- Identities involving Fibonacci numbers · 10 videos
- Calculus of vector valued functions · 10 videos
- Abstract Algebra | Integral Domains · 10 videos
- Vectors for Multivariable Calculus · 10 videos
- Vertex Operator Algebras · 10 videos
- Modular Arithmetic and Linear Congruences · 9 videos
- Linear Differential Equations · 9 videos
- Rogers-Ramanujan Identities · 8 videos
- International Mathematics Olympiad Problems · 8 videos
- Exact Differential Equations · 7 videos
- Trigonometric Identities · 7 videos
- Overkill | Solving simple problems with overpowered math. · 7 videos
- Abstract Algebra | Polynomial Rings · 7 videos
- Sums of Squares · 7 videos
- Divisibility and the Euclidean Algorithm · 6 videos
- Putnam Exam Solutions: A3/B3 · 6 videos
- Chinese Remainder Theorem · 6 videos
- Putnam Exam Solutions A4/B4 · 5 videos
- Problem Solving Techniques · 5 videos
- Abstract Algebra | Cyclic Groups · 5 videos
- Abstract Algebra: Examples of Groups · 5 videos
- Cauchy-Euler Differential Equations · 5 videos
- Numerical Methods for Differential Equations · 4 videos
- Interesting Products · 4 videos
- Primes of the Form... · 4 videos
- Lines and Planes in Three Dimensions · 4 videos
- Differential Equations -- Separation of Variables · 4 videos
- The Dilogarithm · 3 videos
- First Order Linear Differential Equations · 3 videos
22:14a positive number smaller than every fraction
37.4K viewsBuilds a positive number smaller than every fraction, introducing non-Archimedean ordered fields.
23:16any rational power of e is irrational!
15.4K viewsProves that e raised to any non-zero rational power is irrational.
48:08every number system where 1+1=0 (that actually works)
11.4K viewsA tour of the number systems of characteristic 2, where 1+1=0, and what algebra still works in them.
43:18how to understand all of lie algebras with one picture
71.4K viewsAn overview of how Lie algebras are classified, organised around Dynkin-diagram style pictures.
24:34the famous goat problem
113K viewsSolves the famous goat-grazing problem and explains why it has no closed form.
32:57the first proof of the irrationality of pi!
22.6K viewsWalks through Lambert's original proof that pi is irrational.
37:11the number system where 1+2+4+8+⋯ really is −1
10.6K viewsIntroduces the 2-adic numbers, where 1+2+4+8+... converges to -1, and why that is consistent.
1:02:45why some number systems can’t divide
20.6K viewsWhy some number systems have zero divisors and so cannot divide, with rings like Z/nZ and beyond.
24:56why you can't order 43 nuggets.
19.6K viewsThe Frobenius coin problem: why 43 McNuggets can't be bought from boxes of 6, 9 and 20.
14:29"almost" a generating function...
A 14-minute video from Michael Penn's catalogue; the title names its topic.
27:37"infinite" arithmetic is strange
A 28-minute video from Michael Penn's catalogue; the title names its topic.
20:12"measuring" infinite dimensions
A 20-minute video from Michael Penn's catalogue; the title names its topic.
11:48"onederful" numbers
A 12-minute video from Michael Penn's catalogue; the title names its topic.
17:31"proving" a result Erdős said was "hopeless"
A 18-minute video from Michael Penn's catalogue; the title names its topic.
11:58"tricky" derivatives with the limit definition.
A 12-minute video from Michael Penn's catalogue; the title names its topic.
13:16"tuning" a recursive sequence
A 13-minute video from Michael Penn's catalogue; the title names its topic.
10:27"tweaking" the Fermat last theorem equation
A 10-minute video from Michael Penn's catalogue; the title names its topic.
24:56(co) balancing numbers
A 25-minute video from Michael Penn's catalogue; the title names its topic.
16:20(mathematical) applications of the tensor product.
A 16-minute video from Michael Penn's catalogue; the title names its topic.
17:011674 is not a perfect cube.
A 17-minute video from Michael Penn's catalogue; the title names its topic.
20:111886 Cambridge University Exam Integral
A 20-minute video from Michael Penn's catalogue; the title names its topic.
12:482 viewer suggested recursive sequences.
A 13-minute video from Michael Penn's catalogue; the title names its topic.
8:232012 European Mathematics Cup
A 8-minute video from Michael Penn's catalogue; the title names its topic.
20:552014 Argentina Mathematical Olympiad
A 21-minute video from Michael Penn's catalogue; the title names its topic.
19:432022 Putnam Problem B2
A 20-minute video from Michael Penn's catalogue; the title names its topic.
8:542025 Putnam Exam -- Problem B1
A 9-minute video from Michael Penn's catalogue; the title names its topic.
12:175 facts for Prime day!
A 12-minute video from Michael Penn's catalogue; the title names its topic.
6:46@blackpenredpen told me it was too late for integrals on YouTube....
A 7-minute video from Michael Penn's catalogue; the title names its topic.
10:05A "cruel" limit for a beginning calculus class
A 10-minute video from Michael Penn's catalogue; the title names its topic.
10:03A "non-elementary" differential equation.
A 10-minute video from Michael Penn's catalogue; the title names its topic.
7:38A "symmetric" system of equations.
A 8-minute video from Michael Penn's catalogue; the title names its topic.
4:43A Canadian number puzzle.
A 5-minute video from Michael Penn's catalogue; the title names its topic.
12:20A Central American inequality.
A 12-minute video from Michael Penn's catalogue; the title names its topic.
11:58A Complete Explanation of Hausdorff Spaces | Live Example
A 12-minute video from Michael Penn's catalogue; the title names its topic.
9:54A Fermat quotient square.
A 10-minute video from Michael Penn's catalogue; the title names its topic.
15:21A Fibonacci bounded partial sum of the Harmonic series.
A 15-minute video from Michael Penn's catalogue; the title names its topic.
Books that go with these videos
- An Introduction to the Theory of Numbers, Hardy & WrightHardy & Wright, the classic number theory text
- The Joy of x, Steven StrogatzSteven Strogatz's friendly tour of maths' big ideas
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