Good books on higher mathematics?

Question

Books

Due to a recent question about ships and torpedoes, I decided to refresh and improve knowledge in this area.
Can anyone recommend good books on differential calculus, discrete mathematics?
Books with typical (and not so) tasks will especially please. Books with tasks related to programming will bring tons of happiness.
Language: Russian, English - English preferred

Answer 1

If you really need understanding:
Tasks and theorems from analysis. ( In 2 parts ) Georg Polia, Gabor Szege
The book is a task book, where tasks are selected so that on the basis of the previous ones the next one can be solved. What is fundamental is that the entire course of higher algebra and functional analysis is itself derived from these problems.
Such study is not “you are taught” but “you will know for yourself”. The level of understanding is much higher.
You really need to understand that these are books from the beginning of the last century. Some things were then read from a different angle, but the way these books educate the brain is worth it.
If you need an understandable book:
Course of differential and integral calculus, Fikhtengolts 3 volumes
Course of mathematical analysis. In 3 volumes. Kudryavtsev also 3 volumes.
Both books have a detailed scrupulous description of the differential and integral calculus. Written in different styles, some like one, some the other.
I am not aware of a general course in discrete mathematics. At MIPT they teach one thing, friends at Mekhmati and VMK teach another.
I would advise
N.K. Vereshchagin, A. Shen. "Lectures on Mathematical Logic and the Theory of Algorithms" - a good introduction to the discret
Aho, Ulman - Theory of parsing of translation and compilation. - how the first stages of the compiler work are arranged. There is a whole science behind this.
And in general, all the books where the authors include Aho and Ulman made me happy. e.g.
Aho, Ullman, Compilers. Principles, technologies, tools”- the best book on compilers known to me (already code generation itself).
The last two have the original in English.

Answer 2

To refresh the course, Fichtenholtz is suitable.
If you want hardcore knowledge?
Then read Vladimir Antonovich Zorich.
http://www.ozon.ru/context/detail/id/3422686/
In English - I haven’t read anything on this topic myself, but I can only recommend the book [Calculus by Woods] , on which Richard Feynman studied differential calculus .

Answer 3

Dmitry Pimenny writes well, I remember at the university I understood a lot from his books.
www.ozon.ru/context/detail/id/6835826/
www.ozon.ru/context/detail/id/4008464/

Answer 4

Ilyin V.A. Poznyak E.G. Linear algebra
Demidovich B.P. A collection of tasks and exercises in mathematical analysis - I think many people know this useful book)

Answer 5

I study discrete mathematics using this book, everything seems to be very clear.

Answer 6

Structure and Interpretation of Classical Mechanics
Both difurs and programming.