https://www.peasantmaths.com//Peasant MathsDaily reminder to drink more water 2024-03-19T10:16:43+08:00 Ben Zhang https://www.peasantmaths.com// Jekyll © 2024 Ben Zhang /assets/img/favicons/favicon.ico /assets/img/favicons/favicon-96x96.png Calculus III - Lecture 82024-02-29T00:00:00+08:00 2024-02-29T00:00:00+08:00 https://www.peasantmaths.com//posts/calc3_9/ Ben Zhang 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 Meth No meth today, just all technicalities. Calculus III - Lecture 82024-02-29T00:00:00+08:00 2024-02-29T00:00:00+08:00 https://www.peasantmaths.com//posts/calc3_8/ Ben Zhang 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 equivalent to the domain of their function. We provide a physical understanding of this category. We do calculus on them. Please introduce mengnifolds next lecture… Meth Pure maths is much easie... Calculus III - Lecture 72024-02-27T00:00:00+08:00 2024-02-27T00:00:00+08:00 https://www.peasantmaths.com//posts/calc3_7/ Ben Zhang 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 want to say something, I don’t care either. (This might suggest that I absolutely think mathematics is truth and am very firm on this, or I don’t think mathematics is truth. Whatever.)) Throughout earl... Calculus III - Lecture 62024-02-22T00:00:00+08:00 2024-02-22T00:00:00+08:00 https://www.peasantmaths.com//posts/calc3_6/ Ben Zhang 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 past two lectures. Physics books rarely give precise definitions. You just grow used to them. Mathematics is different. Symmetry is something you should always keep in mind. My personal research is a... Calculus III - Lecture 52024-02-20T00:00:00+08:00 2024-02-20T00:00:00+08:00 https://www.peasantmaths.com//posts/calc3_5/ Ben Zhang 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 thought that the universe is three dimensional, with a centre. The Greek philosopher Aristotle had a concept of space and time in the form of $(\mathbb{E}^3,O)\times \mathbb{E}^1$. Newton believed that ...