1 00:00:00,371 –> 00:00:04,311 Hello and welcome back to the bright side of mathematics.

2 00:00:04,371 –> 00:00:10,035 In this video here I want to show you the learning path I envisioned for my videos

3 00:00:10,235 –> 00:00:13,379 and which you can also use to learn mathematics.

4 00:00:13,657 –> 00:00:19,657 For this you can use my webpage here. Which is thebrightsideofmathematics.com

5 00:00:19,857 –> 00:00:26,756 and usually it’s for my Steady supporters, Patreon supporters and the members on YouTube to find additional material.

6 00:00:26,814 –> 00:00:30,898 However, the things I want to show you now are completely for free :)

7 00:00:31,098 –> 00:00:40,215 So what you should do here is, you either click overview network or on this button “get started”, to see the network of my videos.

8 00:00:40,457 –> 00:00:47,058 So the idea here is that each node represents a playlist on YouTube, a whole series

9 00:00:47,258 –> 00:00:53,348 and each arrow here, each edge shows you in which order you should go through these videos,

10 00:00:53,714 –> 00:01:00,987 but maybe for the first step, just ignore the arrows altogether and just read the picture from top to bottom.

11 00:01:01,187 –> 00:01:06,780 Which means you first have to understand the things on the top to understand the things downstairs

12 00:01:07,114 –> 00:01:09,971 and there we immediately see the foundation,

13 00:01:10,013 –> 00:01:17,401 the language we need to learn first to understand mathematics is given here in my start learning mathematics series

14 00:01:17,971 –> 00:01:24,468 and moreover if things are on the same level, it’s best to go through them left to right.

15 00:01:24,668 –> 00:01:29,371 This means here you first should understand how basic logic works in mathematics

16 00:01:29,436 –> 00:01:36,043 and then you can go through the sets and in the end you understand how we construct the number sets.

17 00:01:36,543 –> 00:01:42,757 By the way, you can just click on a node to find the corresponding videos on YouTube.

18 00:01:43,286 –> 00:01:50,019 Here for example we have the start learning sets series and this button here brings you to YouTube

19 00:01:50,219 –> 00:01:52,685 and to the first video in the series

20 00:01:53,243 –> 00:02:00,621 and here I can already tell you learning how sets work is very important for the rest of the courses altogether.

21 00:02:01,186 –> 00:02:05,863 Ok, then next in the list after my whole start mathematics series,

22 00:02:06,063 –> 00:02:11,299 we find almost on the same level, linear algebra and real analysis

23 00:02:11,499 –> 00:02:15,636 and there you might already know, these are very important courses,

24 00:02:15,836 –> 00:02:19,825 because in linear algebra you learn how to deal with vectors

25 00:02:19,843 –> 00:02:23,715 and in real analysis you learn how to calculate with functions

26 00:02:23,915 –> 00:02:29,164 and this knowledge is indeed needed to understand all the topics below.

27 00:02:29,364 –> 00:02:35,429 So for example, functional analysis needs the knowledge from linear algebra and real analysis.

28 00:02:36,157 –> 00:02:44,320 But in the best case you also have knowledge about all these topics that are before on top of functional analysis on this level here

29 00:02:44,520 –> 00:02:50,229 and if I say knowledge it doesn’t mean that you have to watch every video in the series above,

30 00:02:50,329 –> 00:02:54,783 it just means, if there is a question that occurs while watching functional analysis,

31 00:02:54,983 –> 00:03:00,494 maybe you have to go back to some specific video in the series above.

32 00:03:00,800 –> 00:03:05,416 So for example if you start with the complex analysis series here,

33 00:03:05,616 –> 00:03:09,150 you might follow that easily with your knowledge of complex numbers,

34 00:03:09,350 –> 00:03:11,470 but at some point you might think:

35 00:03:11,514 –> 00:03:19,040 “I should refresh my knowledge about multivariable calculus to understand the partial derivatives that occur there.”

36 00:03:19,471 –> 00:03:27,128 Ok, so there we have it. This is the map for my videos and you can use it for free, for your own learning path

37 00:03:27,700 –> 00:03:33,308 and if you want to support me, you can do that on Steady, Patreon or here on YouTube.

38 00:03:33,314 –> 00:03:37,143 Thank you very much and see you next time. Bye-bye!