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Anyone have a glossary or index for newbs? Like a shortcut to reading the symbolic notation? I have some expository knowledge to sets (ie. sets are denoted by

Anyone have a glossary or index for newbs? Like a shortcut to reading the symbolic notation? I have some expository knowledge to sets (ie. sets are denoted by capital letters). And some of the symbols (ie. the vertical pipe means given or 'where' and indicates a predicate assumption of sorts). Anyone have the cheat code for laypeople and undergrads?

smt1 6y ago
I recommend this book first actually to make sure you understand topology from a higher level perspective: https://www2.math.upenn.edu/~ghrist/notes.html https://www2.math.upenn.edu/~ghrist/notes.html It does a more panoramic view of topology and homological algebra, ending with category theory. I would read chapter 10.10 then appendix A first, but the rest of the book has a ton of illustrative motivational examples. IMHO, understanding the elegance of category theory is useful for understanding the connections between different types of math (that you may already know). There are a ton of types of math that don't really map that naturally to set theory, especially on computers. Learning some of the language of the commutative diagram (and functors, natural transformations, adjunctions) helps a lot IMHO since categorical structure can be found everywhere and it helps understand groups/rings/fields/homology/homotopy much easier, because it helps you learn how different math "behaves" relative to each other, and I find it more easily constructible on a computer (especially with any lang with higher order functions), you may want to think of the arrows as maps/functions/morphisms between types/interfaces/physical processes/computational states.
xyzzyz 6y ago
Sorry, there is no cheat code here. Understanding this stuff requires real and significant time investment, and is beyond arms reach (though not beyond sight) of undergrads and especially laypeople. If you put in investment, understand what is module, quotient operation, exact sequence etc, you will be able to follow. However, this is not trivial and not just an issue of notation: there are real, fundamental concepts here that one must learn to grasp.
- sharker8 6y ago
  What would be your "pareto list", ie the list of the concepts, symbols, notation, etc that would get one 80% of the way with 20% of the knowledge?
  - xyzzyz 6y ago
    I don't think that there is any, sorry.

smt1 6y ago

I recommend this book first actually to make sure you understand topology from a higher level perspective: https://www2.math.upenn.edu/~ghrist/notes.html https://www2.math.upenn.edu/~ghrist/notes.html It does a more panoramic view of topology and homological algebra, ending with category theory. I would read chapter 10.10 then appendix A first, but the rest of the book has a ton of illustrative motivational examples. IMHO, understanding the elegance of category theory is useful for understanding the connections between different types of math (that you may already know). There are a ton of types of math that don't really map that naturally to set theory, especially on computers. Learning some of the language of the commutative diagram (and functors, natural transformations, adjunctions) helps a lot IMHO since categorical structure can be found everywhere and it helps understand groups/rings/fields/homology/homotopy much easier, because it helps you learn how different math "behaves" relative to each other, and I find it more easily constructible on a computer (especially with any lang with higher order functions), you may want to think of the arrows as maps/functions/morphisms between types/interfaces/physical processes/computational states.

xyzzyz 6y ago

Sorry, there is no cheat code here. Understanding this stuff requires real and significant time investment, and is beyond arms reach (though not beyond sight) of undergrads and especially laypeople. If you put in investment, understand what is module, quotient operation, exact sequence etc, you will be able to follow. However, this is not trivial and not just an issue of notation: there are real, fundamental concepts here that one must learn to grasp.

sharker8 6y ago
What would be your "pareto list", ie the list of the concepts, symbols, notation, etc that would get one 80% of the way with 20% of the knowledge?
- xyzzyz 6y ago
  I don't think that there is any, sorry.