Ideas in Mathematics The idea of continuity. We have a beautiful formula [\lvert B^A \rvert = \lvert B \rvert ^ {\lvert A \rvert}.] But what happens when at least one of $A$ and $B$ are empty? Th...

# Mengology - Advanced Algebra I - Lecture 3

# Calculus III - Lecture 8

Lecture highlights: More details about the construction of our category of mappings between subsets of Euclidean spaces The velocity functor Pushforward map Definition of smooth manifold ...

# Calculus III - Lecture 8

Lecture highlights: We just talk about the category of smooth maps between subsets of Euclidean spaces in this lecture. We prove that these maps indeed form a category. Graphs are naturally ...

# Calculus III - Lecture 7

Lecture highlights: $T$ is a functor A big picture for what is to come. Meth Few meth today, mostly the cold hard truth. Well is mathematics truth? I don’t know. (For the few of you who wa...

# Calculus III - Lecture 6

Lecture highlights: symmetries quadrics high school mathematics multivariable calculus high school mathematics Meth Obviously he like these stuff, that’s why he mething a lot these p...

# Calculus III - Lecture 5

Lecture highlights: Euclidean structure Categories and functors Meth He methed a lot this lecture! In the Greek times, they believed that the Earth is the centre of the universe. They tho...

# Calculus III - Lecture 4

Today we talk about affine spaces. We only care about stuff over the real numbers in this course. Lecture highlights: Definition We have a ‘dictionary’ between vector space and affine space ...

# This Week I Learned - W06 - 2024

Update 2024-09-09: Look at how this went. p-adic distance ultra-metric $\sigma$-finite measure: the measure space can be decomposed into a countable sequence of sets with finite measure c...

# Calculus III - Lecture 3

I cannot claim to have a summary of the whole lecture, that’s why I switched the wording to ‘highlights’ Lecture highlights: tensor algebra graded vector space determinants M: Do abstrac...

# Calculus III - Lecture 2

Calculus on Mengnifolds I have no idea what happened this lecture. Lecture highlights: Notations Review of linear algebra The set of bases of $V$ may be naturally identified with the set ...