44:31
Lie algebras visualized: why are they defined like that? Why Jacobi identity?
22:44
Matrix trace isn't just summing the diagonal | Lie groups, algebras, brackets #5
30:09
Can we exponentiate d/dx? Vector (fields)? What is exp? | Lie groups, algebras, brackets #4
21:57
What is Lie theory? Here is the big picture. | Lie groups, algebras, brackets #3
13:23
How to rotate in higher dimensions? Complex dimensions? | Lie groups, algebras, brackets #2
04:26
Why study Lie theory? | Lie groups, algebras, brackets #1
14:02
How many terms do we need in the exp series?
25:25
Queuing theory and Poisson process
40:13
Theorema Egregium: why all maps are wrong
34:06
The biggest misconception about spin 1/2
20:33
I use PowerPoint to edit all* videos (and hit 100k subs!)
25:41
The deeper meaning of matrix transpose
54:32
How hard was my Cambridge interview? (ft. @TomRocksMaths)
18:22
Random walks in 2D and 3D are fundamentally different (Markov chains approach)
21:44
The weirdest paradox in statistics (and machine learning)
45:24
Why you can't solve quintic equations (Galois theory approach) #SoME2
19:13
The simplest reason why π/4 = 1 - 1/3 + 1/5 -...
22:02
The geometric interpretation of sin x = x - x³/3! + x⁵/5! -...
40:45
Complex integration, Cauchy and residue theorems | Essence of Complex Analysis #6
25:27
What if we define 1/0 = ∞? | Möbius transformations visualized
28:33
What do complex functions look like? | Essence of complex analysis #4
14:32
The 5 ways to visualize complex functions | Essence of complex analysis #3
32:11
What are complex numbers? | Essence of complex analysis #2
03:55
Why care about complex analysis? | Essence of complex analysis #1
22:52
Green's functions: the genius way to solve DEs
12:58
From miller to entering Cambridge at age 40 - George Green
15:13
Solved simply: the impossible integral
27:14
What is Jacobian? | The right way of thinking derivatives and integrals
11:05
The numerical simulation is NOT as easy as you think! - Average distance #2
26:05
Dream cheating scandal - explaining ALL the math simply
08:55
What is the average distance of two points in a disc? (PART 1)
12:28
Icosahedral symmetry - conjugacy classes and simplicity
04:39
Without integration, why is the volume of a paraboloid half of its inscribing cylinder? (DIw/oI #8)
11:47
Problem of Apollonius - what does it teach us about problem solving?
10:00
Burnside's Lemma (Part 2) - combining math, science and music
13:45
Burnside's Lemma (Part 1) - combining group theory and combinatorics
09:27
Limitations of mathematical models; historical context of BGW process [PART III]
10:11
How likely is coronavirus (COVID-19) eradicated? [PART II]
12:00
Alternative to SIR: Modelling coronavirus (COVID-19) with stochastic process [PART I]
11:27
Summary: an example covering ALL group theory concepts!! | Essence of Group Theory
10:51
Chapter 7: Group actions, symmetric group and Cayley’s theorem | Essence of Group Theory
13:41
Two opposite games involving golden ratio (ft. Tom Rocks Maths)
12:47
Chapter 6: Homomorphism and (first) isomorphism theorem | Essence of Group Theory
12:37
Chapter 5: Quotient groups | Essence of Group Theory
09:41
How will the COVID-19 (coronavirus) epidemic end?
12:03
Chapter 4: Conjugation, normal subgroups and simple groups | Essence of Group Theory
13:40
Chapter 3: Lagrange's theorem, Subgroups and Cosets | Essence of Group Theory
12:27
Chapter 2: Orbit-Stabiliser Theorem | Essence of Group Theory
06:07
Chapter 1: Symmetries, Groups and Actions | Essence of Group Theory
07:25
Power rule of integrals not using integration; definition of e | DIw/oI #7
03:40
How do I love math? (Part II - Proof without words)
06:52
How is pi calculated to trillions of digits?
04:39
Why does R(4,4)=18?
05:28
Proof of Ramsey's theorem
14:02
Rhapsody on Ramsey numbers (and aliens?)
10:02
15-year-old did mathematical research?! What was my thinking process back then?
06:30
The art of generalization in Mathematics | DDC #4
10:03
More ways of deriving Catalan numbers | DDC #3
11:13
Catalan numbers are not in Catalan | DDC #2
11:28
Crash Course in Combinatorics | DDC #1
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About
Hi, I am Trevor. This channel discusses maths (or physics) concepts that I am passionate about, and tackles them in a novel perspective. For example, most people introduced Green's functions with lots of DE concepts, but my video on the topic did so from electrostatics, providing a vivid image of point charges. The new perspectives are not meant to be "easier" to understand, and I have never intended the videos to be pedagogical; the videos are just some interesting concepts and arguments you have not heard before on YouTube (maybe anywhere).
For those who are wondering, I don't use coding to produce my videos, and while stylistically similar to 3Blue1Brown, I don't use Manim (Grant's mathematical animation Python library) to produce my videos. I actually use PowerPoint, GeoGebra and (sometimes) Mathematica to produce my videos.
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