Is it worth touching Pismenny's lecture notes at all?

Question

IT education

Now the task is to learn mathematics again. And now I am faced with the choice of textbooks. On the one hand, there are proven books on mathematics, statistics, and other mathematical disciplines. But they are relatively large. And there are written notes, they are shorter, they provide the necessary basics, but when I read it, I had the feeling that they were not telling me something. Are there people here who have studied the written language? What are your impressions, is it enough of what it gives if you are not going to work in pure mathematics, but mathematics is rather a useful application. And no, I'm not lazy, I'm just thinking about how best to spend my time.

Answer 1

When I wanted to improve mathematics, I decided that it was worth adding these notes to my personal library (higher mathematics in 2 parts and a separate note on probability theory), since their content and method of presenting material coincided by about 95% with my university course.
The coverage of topics is standard, strict definitions of the main mathematical concepts and concepts are given with proofs, there are relevant practical examples. It is convenient to use them not as textbooks, but as reference books that you can turn to if you need to understand some issue, and if at the same time you do not mind getting to the essence of phenomena through strict formal definitions.
Is it possible to learn mathematics by studying them from cover to cover? I doubt. For this purpose, it is rather necessary to perform a lot of practical tasks. But for help in solving these problems, you can refer to the lectures. So my recipe is: a good problem book + lecture notes in the form of reference material + lots and lots and lots of practice. And in order not to lose motivation from all this "dryness" to read popular science books on mathematics, which really tell about it in an interesting way (although sometimes in a simplified form) and really captivate to do it. Fortunately, there are many such books.

Answer 2

Can you advice? Mathematics can be comprehended in two ways:
1. Theoretically
2. In practice
In the first option, you will not only have to read and comprehend all the works in the chosen direction (some of the mathematicians use their own mathematics).
Second, applied, i.e. you learn what you need.
Your question shows that you have not yet chosen, think about what you are interested in.