"So why is it a totally different course?"
This question is independent of how the machine actually works.
"Would you have to see it because it was very complex subjects, or did more or less use of mathematical algorithms?"
There is no computation without algorithms that use math ... The quantity or size is related to the algorithm itself, it depends on what it will do, but both AI will define a whole range of behaviors and interpretations as the ML that will absorb these definitions, will use a reasonable amount of complexity.
I have no doubt that they are closely related terms and that ML is a subcategory of AI.
The difference in my view, since I affirm that ML is sub-category of AI, is that AI is more linked to the cognitive functions inherent to the human being, and that ML uses these concepts to learn and execute. >
In my opinion it is as if AI were the theory and ML the practice.
Then answering your question, "Why Artificial Intelligence and Machine Learning are different matters?" ...
They are not different materials, they are complementary materials ...
Here you can see that ML is a subcategory of AI, of course it is wiki, but by logic we can agree that yes ...
Machine learning is a sub-field of computer science that has evolved from the study of pattern recognition and the theory of computational learning in artificial intelligence.
And here can see you a bit more through the mind of one of the precursors of AI.