https://www.peasantmaths.com//Peasant MathsDaily reminder to drink more water 2024-09-09T16:52:44+08:00 Ben Zhang https://www.peasantmaths.com// Jekyll © 2024 Ben Zhang /assets/img/favicons/favicon.ico /assets/img/favicons/favicon-96x96.png Mengology - Advanced Algebra I - Lecture 32024-09-09T00:00:00+08:00 2024-09-09T00:00:00+08:00 https://www.peasantmaths.com//posts/advalg3/ Ben Zhang 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? Then we set some conventions. The most important theorems in mathematics are those that are EASY to prove. Let other people do the unnatural things, and you do the natural thing, then life is much e... 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...