I want recommendations that follow this morale:
The minimum _sufficiency_ of axiomatic studies for the _efficient_ understanding of practical mathematical theories.
Because I'm burned out of of these retarded lectures, staring at theorems that have a proof easy to understand but hard to come up with; explained over and over for an hour by a teacher. I'm dying inside being there while I have an actual drive for knowledge.
Case in point: Axiomatic Set Theory books with dozens of exercises. The majority of Mathematicians work without such knowledge in mainstream PURE mathematical subjects.
Read: https://arxiv.org/abs/1212.6543
8 pages, more than you possibly need to know about sets. Many very recommended books, probably 90% of undergraduate education is done without being able to state more than 3 axioms of Set Theory.
This is not something that teachers talk about nor do authors of abstract non-sense tell you when you start their book. It's as if you were expected to follow a bunch of stupid reasoning like a tool for no reward. Their motivation sometimes is written like "you will be able to understand more abstract non-sense that has applications on one (1) single technological field which by the way is stale and in no need of further improvement". If that kind of description rings the bell of a math subject, please mention it here so I don't lose my time. I'm interested in Algebra because it supposedly has some applications in Physics. I am also interested in Analysis because I don't like the use of differentials without a good definition, but I actually want to know some Physics.
I unironically feel like killing myself over this, nothing is really surprising nor useful so far and I'm in third year. I'm a third year undergraduate in Math, if I go Physics I feel it'd be lacking a lot of explanations; using results before they are properly understood gives me a bit anxiety or feeling of dishonesty. Anything south of Physics is even worse.
The minimum _sufficiency_ of axiomatic studies for the _efficient_ understanding of practical mathematical theories.
Because I'm burned out of of these retarded lectures, staring at theorems that have a proof easy to understand but hard to come up with; explained over and over for an hour by a teacher. I'm dying inside being there while I have an actual drive for knowledge.
Case in point: Axiomatic Set Theory books with dozens of exercises. The majority of Mathematicians work without such knowledge in mainstream PURE mathematical subjects.
Read: https://arxiv.org/abs/1212.6543
8 pages, more than you possibly need to know about sets. Many very recommended books, probably 90% of undergraduate education is done without being able to state more than 3 axioms of Set Theory.
This is not something that teachers talk about nor do authors of abstract non-sense tell you when you start their book. It's as if you were expected to follow a bunch of stupid reasoning like a tool for no reward. Their motivation sometimes is written like "you will be able to understand more abstract non-sense that has applications on one (1) single technological field which by the way is stale and in no need of further improvement". If that kind of description rings the bell of a math subject, please mention it here so I don't lose my time. I'm interested in Algebra because it supposedly has some applications in Physics. I am also interested in Analysis because I don't like the use of differentials without a good definition, but I actually want to know some Physics.
I unironically feel like killing myself over this, nothing is really surprising nor useful so far and I'm in third year. I'm a third year undergraduate in Math, if I go Physics I feel it'd be lacking a lot of explanations; using results before they are properly understood gives me a bit anxiety or feeling of dishonesty. Anything south of Physics is even worse.
