How and what to learn?

Question

Programming

Hello. My name is Sergey, I'm 20 and I'm a Primate with almost 2 semesters of experience... Although the 2nd semester is coming to an end soon, I'm not entirely satisfied with the level of understanding. I decided to spend my free time on “vacation” (in the form of two months) further: to spend time on re-mastering the material.
The list is quite wide:

• theory and analysis of algorithms
  
• mathematical analysis;
  
• Discrete Math;
  
• linear algebra and geometry, algorithms
  
• as well as additionally planning mathematical logic (well, we didn’t have it).
  

I do not plan to be a mathematician, but I plan to have good and extensive knowledge in CS, but, apparently, knowledge of mathematics is necessary in many tasks (maybe not even directly, but definitely indirectly).
Naturally, the understanding of all this is unlikely to be within 2 months, even taking into account the fact that I understand part of it well. Therefore, I want to prioritize, but since I am just a freshman, I do not have a complete understanding of the need for a single subject.
So I turn to the habra community for advice:

1. From your experience, what would you recommend prioritizing the items listed above? For example, I doubt to prioritize linear algebra: it ends, but its understanding will be needed later in the funcan (as I understand it).
   
2. A very interesting and important question for the purpose. For learning mat. Science, it takes me more time than I plan to: read, take a piece of paper and a pen - restore concepts and objects, try to prove everything that requires proof, re-read, etc., until I make a good understanding of the chapter. But such a process is very costly in terms of time and effort, and therefore the question of optimizing this process is of interest: how to speed it up? how to read such literature? What are the tricks to remember information faster?
   

Thank you in advance :)

Answer 1

The fact is that there is no “truth” in remembering. The point is not to reproduce, but to apply. There are some people who can memorize, but this memorization is their impromptu game of the subject area thanks to a good imagination. The normal process of mastering and memorizing theories, which is exactly what game minds model, is first a task or tasks, and then application. If you are not a pure mathematician with a specific game imagination, this is why it is difficult to memorize theories. Perhaps you should first find out the areas of applied work in which these theories are needed, look for jobs in the departments.

Answer 2

I would recommend discrete mathematics, algorithms and logic to be prioritized. There will be a lot of mathematical analysis and linear algebra, but the basic theory will no longer be given, and it will be useful in the future much more than the Cauchy theorem)

Answer 3

No matter how you prioritize, in any case, do not worry. There is always an opportunity to improve knowledge. There would be a desire, as they say :)
UPD #1 And about the fact that some topics take more time than you planned, try to look for other sources of information where the material is more chewed. There is nothing to be ashamed of, the main thing is that in the end you understand what is at stake.

Answer 4

I think primacy needs more emphasis on linear algebra. It is useful not only for better assimilation of functional analysis. For example, the course of numerical methods is very difficult to study and understand without knowledge of linear algebra, and functional analysis of the same. After all, most problems are of the form: we take an infinite-dimensional space of functions, approximate it with a finite-dimensional one, then work in a finite-dimensional space using linear algebra methods.