Ask HN: How can I learn to read mathematical notation?

Tests and deadlines provide motivation to do the actual work.

Having a curriculum means that the content is laid out in a logical order that the professor believes should be achievable.

There is a stupid amount of information out there. Breaking it down into a progression that students can follow in order to learn and understand it is incredibly important.

If you're motivated enough then sure maybe you can just buy and read the textbook, although sometimes professors deviate from that when it's wrong.

> Class populations are so large that if everyone had asked clarifying questions, we wouldn't have completed the readings.

Good thing not everybody asks, and those that do ask are generally asking questions shared by a good chunk of the class.

The format was like this: the classes were 2h long, and the professor would begin with an exposition: first a short recap of the previous class, then introducing the new material for the day, new concepts, definitions, the starting point for the day's class. This could take anywhere from 5 minutes to up to 30 or 40.

After that, we were handed a work-sheet. It contained the definitions/summary of the concepts that were just introduced, then a series of exercises. Now this is the core of it: the main part of the class was working through these in order. The exercises were structured so that the rest of the material was learned by doing, by working out through the exercises. They would e.g. ask to prove interesting consequences, or important theorems that followed from the definitions at the start. The professor would point out an exercise, read it aloud, comment on the "meaning" of the problem or what it's meant to demonstrate or similar remarks, then give us some time to figure it out. After a bit, he would ask someone that completed it to present his/her reasoning. Now note that this part required real effort from the part of the professor. I tremendously admire him for this because it required him to listen carefully and think through the proof presented by the student, something which is more difficult than, say, presenting and explaining his own proof on the blackboard. Anyway, he would listen to it, comment ("you could have simplified here", "you didn't consider this case there", etc.), perhaps ask some other students for alternative approaches, or maybe give an alternative approach himself if necessary. By doing this we would learn the rest of the material by working it out from those principles; in a way in a sort of "narrative" that had a thematic "chapter" in each class and an overarching "story" for the whole class.

In summary, only about 10 minutes at the start would be real exposition. This usually amounted to stating definitions or axioms to work with for the rest of the class. The rest of the material -- any theorems, conclusions, etc. -- were worked out.

I have some difficulty concentrating even on 1h or 1h30 lectures. These were 2h and I would be effortlessly engaged for the whole duration. It kind of pains me that maybe the best class I've taken in university wasn't even one in my degree :^)

The secret to reading papers in unfamiliar field is to not get discouraged just because you don't get it immediately. Instead, I will research each concept I encounter that I don't understand well.

Let's assume I want to understand something in a field I am not familiar with. It is important to understand that this typically means I have to get at least somewhat familiar with the field. I don't expect to read a paper and get it just from that single read!

I will open the paper and first just read what I can from start to end without stopping to research anything. This gives me some idea what the paper is about and what are some of the concepts that are important and how they are used later. I call this scanning.

I will go back to the start and slowly go researching EVERYTHING, ABSOLUTELY EVERYTHING that I don't understand. This is most of the work. I will keep the paper open and have something to mark where I currently am. I will research meaning of every symbol and every piece of notation, every concept being introduced, until I am confident I understand it.

This may take multiple days to advance a single line as I will frequently spend time on tagents or just getting up to speed with the basics.

Once I go through entire paper I will get back to start and now read it again. Now that I know the language of the paper I can focus on the matter at hand. I may do this few times until I am satisfied I got everything I could.

Again, I want to stress it, don't expect to understand a paper in unfamiliar field on the first reading. It is completely unrealistic. Use materials, ask people to explain, research on the Internet, rinse and repeat.

but in their defense, i was a difficult student.