One thing to do during Christmas break in Germany: Reading others' (non-mathematical) writing
As the 2-week Christmas break began, I realized that there are a wealth of stuffs that I needed to learn: professionalized LaTeX (as I usually had difficulties memorizing "unfamiliar" symbols such as \models, ...), English, German, mathematical writing skills (as I sometimes failed to take note the stuffs written on the blackboard due to the fast dynamics of the lecture), or even some preliminaries knowledge in Geometry/Topology, ...
Analogously to "All roads lead to Rome", I would say (almost) all roads lead to this blog. My friend introduced this blog to me a few months ago, but I did not notice until I spend the whole night delving into the contents of these posts. I was impressed by the experiences that the author mentioned, which were quite similar to those of myself to a certain extain.
Example: In a post, the author talked about flashcards - a method that he used to apply. He even showed what he wrote on one sample flashcard and explained how/why he realized that it was ... a wrong approach. While I have not used flashcards for memorizing mathematical terms, I could apply his story to "criticize" my other wrong/ineffective learning techniques. I did intend to write a post on this blog about some of the learning techniques that I am applying, but his post about flashcards made me realize that my approach might be wrong, thus such a post should be written later. By later, I mean when I successfully tested the effectiveness of these techniques via ... the final exams (in February 2026).
(Perhaps my last comment was inspired by a similar one given by Professor Markus Hausmann during his lecture on Topology 1: "By later, I mean Topology 2", which means that he advertised a content that will be talked in detail in Topology 2 - the next subject after Topology 1).
He even uploaded the lecture notes of many courses in Bonn, which were worthwhile resources for me to (re)learn the preliminaries knowledge (about covering map/space, for example) and discover some interesting topics offered at Bonn. One of these lecture notes was written in German. While my A1-level German was obviously not good enough to understand this material, I still managed to have a grasp of the mathematical definitions/arguments given thanks to my mathematical sense (i.e. guess the content) and Google translation. During the process, I also noted some German words/sayings, especially those that I found interesting.
Example: After defining what a (point-set) topology on a set is, the professor said that "Das ist alles ein bisschen abstrakter Yoga - noch ist nichts passiert!". As far as I could understand (after using Google translations and knowing that "passiert" means "happen"), it means that the definition is too "simple" that it might fail to show how "complicated" the story is. I wish I was told about this as soon as I knew the definition of a topology.
Not only did I read this blog but I also spent time discovering some other resources that talked about the stories behind studying mathematics. Perhaps it is a good idea to take note or listen to these stories on the remaining days of the break. And finding an analog of such stories for myself should be an incredible but good idea, especially when it comes to pedagogical/tutorial activities. Here are some resources that I found out:
- Podcast "On a Tangent": this 7-episode series was made by Simone Ramello, an Italian PhD student at Universität Münster from 2020 to 2024. It was somewhat sad that this series is too short. But delving into these stories should be a nice experience. I was impressed by a story about a girl who is from Africa and managed to switch from statistics to (geometric) group theory.
Analogously to "All roads lead to Rome", I would say (almost) all roads lead to this blog. My friend introduced this blog to me a few months ago, but I did not notice until I spend the whole night delving into the contents of these posts. I was impressed by the experiences that the author mentioned, which were quite similar to those of myself to a certain extain.
Example: In a post, the author talked about flashcards - a method that he used to apply. He even showed what he wrote on one sample flashcard and explained how/why he realized that it was ... a wrong approach. While I have not used flashcards for memorizing mathematical terms, I could apply his story to "criticize" my other wrong/ineffective learning techniques. I did intend to write a post on this blog about some of the learning techniques that I am applying, but his post about flashcards made me realize that my approach might be wrong, thus such a post should be written later. By later, I mean when I successfully tested the effectiveness of these techniques via ... the final exams (in February 2026).
(Perhaps my last comment was inspired by a similar one given by Professor Markus Hausmann during his lecture on Topology 1: "By later, I mean Topology 2", which means that he advertised a content that will be talked in detail in Topology 2 - the next subject after Topology 1).
He even uploaded the lecture notes of many courses in Bonn, which were worthwhile resources for me to (re)learn the preliminaries knowledge (about covering map/space, for example) and discover some interesting topics offered at Bonn. One of these lecture notes was written in German. While my A1-level German was obviously not good enough to understand this material, I still managed to have a grasp of the mathematical definitions/arguments given thanks to my mathematical sense (i.e. guess the content) and Google translation. During the process, I also noted some German words/sayings, especially those that I found interesting.
Example: After defining what a (point-set) topology on a set is, the professor said that "Das ist alles ein bisschen abstrakter Yoga - noch ist nichts passiert!". As far as I could understand (after using Google translations and knowing that "passiert" means "happen"), it means that the definition is too "simple" that it might fail to show how "complicated" the story is. I wish I was told about this as soon as I knew the definition of a topology.
Not only did I read this blog but I also spent time discovering some other resources that talked about the stories behind studying mathematics. Perhaps it is a good idea to take note or listen to these stories on the remaining days of the break. And finding an analog of such stories for myself should be an incredible but good idea, especially when it comes to pedagogical/tutorial activities. Here are some resources that I found out:
- Podcast "On a Tangent": this 7-episode series was made by Simone Ramello, an Italian PhD student at Universität Münster from 2020 to 2024. It was somewhat sad that this series is too short. But delving into these stories should be a nice experience. I was impressed by a story about a girl who is from Africa and managed to switch from statistics to (geometric) group theory.
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