How to study systematically the mathematical analysis?

Good evening,

Studying some of the materials associated with AI and machine learning - all the time faced with the fact that you have to podkidyvat calculus, numerical methods, discrete mathematics, decision-making methods, linear algebra, optimization methods, probability theory. But I'm doing it all piecewise, a knowledge of how it turned out - not in vain after the times of uni, but since then, it has evolved and understand how to systematize their knowledge on these subjects.

Maybe someone can advise how to sort through, and in what order, what topics are worth exploring in order to be guided in this field? And does it make sense? I often hear the opinion that there is nothing wrong to use some algorithms without understanding that actually they do, but my approach is always depressing, I am unable to agree with him so far.
July 2nd 19 at 17:25
2 answers
July 2nd 19 at 17:27
if a song something like this:

but seriously and thoughtfully - rutraker
July 2nd 19 at 17:29
I believe the order in which they studied mathematics in the University, is not even bad.
The first two courses, all of General mathematics, ranging from the ruler and Mat finishing of complex analysis, world Cup. Then, depending on the task pane, looking for specifics. In my experience I would say that a full understanding of 1 and 2 courses make it easy to continue the study of everything in all directions
Thank you. But can be a little detail that is included in the program 1-2 courses? - gregoria commented on July 2nd 19 at 17:32
in my case it was like this:
1st semester:
Linear algebra and analytical geometry: Matrices, vectors, the dimensions of the spaces, their properties and theorems
Calculus: sets, limits, derivatives
2nd semester:
Calculus: derivatives, integrals(analytical integration) series.
3-4 semester:
Twins: Starting from the concept of random variables and then, as understanding, this course is a bit separated from the rest
Differential equations: their types, decision
Numerical methods: what, why, numerical integration, concepts of approximation, interpolation, extrapolation
Complex analysis: the actual starting from the concept of complex numbers and operations over them, zakanchivaja difforme with complex variables.
To dwell on this not suggest, as the different specialties of mathematics can be more or less depending on the task you might be interesting to delve into the linal and Angel, or in the direction of statistics. Since you are a programmer, perhaps, benefit from more combinatorics or other science.
From the literature memorable Demidovich and fichtenholz on the Mat and Wentzel, Elena S. - the theory of probability. Otherwise, look for something that will be clearer for you. - jeramie.Lesch commented on July 2nd 19 at 17:35
: Thank you for the detailed answer!
The picture cleared up :) - gregoria commented on July 2nd 19 at 17:38

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