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For me, it has always been the terminology. The basic theorems are relatively easy to understand... once you can remember the vast number of algebra-specific de

by gh02t 11y ago

For me, it has always been the terminology. The basic theorems are relatively easy to understand... once you can remember the vast number of algebra-specific definitions. The field also has a proclivity for umm "colorful" choices of names. It's not unlike say Haskell, which IMO is pretty straightforward once you have a feel for all the terminology.

goalieca 11y ago
Like this from wikipedia on Monoid? Suppose that S is a set and • is some binary operation S × S → S, then S with • is a monoid if it satisfies the following two axioms: Associativity For all a, b and c in S, the equation (a • b) • c = a • (b • c) holds. Identity element There exists an element e in S such that for every element a in S, the equations e • a = a • e = a hold. In other words, a monoid is a semigroup with an identity element. It can also be thought of as a magma with associativity and identity. The identity element of a monoid is unique.[1] A monoid in which each element has an inverse is a group.
- cmrx64 11y ago
  It seems to me that the definition presented there is relatively free of jargon, except the "in other words" section which links it to other (linked) structures.
  - gh02t 11y ago
    > except the "in other words" section which links it to other (linked) structures. That's what I was getting at. I took a few classes in AA and its sibling topology, including at graduate level. Most of the time was spent defining things, because there's so many terms with very specific definitions. Only after maybe 2/3rds of a course do you really start getting into deeper material. In my brain, reading definitions was always a process like: read through, substitute definitions for jargon terms, read through, substitute... iterate until you hit a fixed point. That's standard for math, but AA is particularly well known for its colorful choice of names. Some people enjoy it, but I was always more attracted to the analysis-family areas of math. I've always found the other name for category theory amusing though: https://en.wikipedia.org/wiki/Abstract_nonsense https://en.wikipedia.org/wiki/Abstract_nonsense
    - cmrx64 11y ago
      Fair enough! My biggest struggle taking AA was also remembering the definitions of everything. There are so many things all tied together.
- kmill 11y ago
  I think I only finally remembered what a monoid was when I realized it was a category with one object ("mono-"). Or that a groupoid is a category where every arrow is an isomorphism, so then a category which is both a monoid and a groupoid is a "group."

by gh02t 11y ago

goalieca 11y ago

Like this from wikipedia on Monoid? Suppose that S is a set and • is some binary operation S × S → S, then S with • is a monoid if it satisfies the following two axioms: Associativity For all a, b and c in S, the equation (a • b) • c = a • (b • c) holds. Identity element There exists an element e in S such that for every element a in S, the equations e • a = a • e = a hold. In other words, a monoid is a semigroup with an identity element. It can also be thought of as a magma with associativity and identity. The identity element of a monoid is unique.[1] A monoid in which each element has an inverse is a group.

cmrx64 11y ago
It seems to me that the definition presented there is relatively free of jargon, except the "in other words" section which links it to other (linked) structures.
- gh02t 11y ago
  > except the "in other words" section which links it to other (linked) structures. That's what I was getting at. I took a few classes in AA and its sibling topology, including at graduate level. Most of the time was spent defining things, because there's so many terms with very specific definitions. Only after maybe 2/3rds of a course do you really start getting into deeper material. In my brain, reading definitions was always a process like: read through, substitute definitions for jargon terms, read through, substitute... iterate until you hit a fixed point. That's standard for math, but AA is particularly well known for its colorful choice of names. Some people enjoy it, but I was always more attracted to the analysis-family areas of math. I've always found the other name for category theory amusing though: https://en.wikipedia.org/wiki/Abstract_nonsense https://en.wikipedia.org/wiki/Abstract_nonsense
  - cmrx64 11y ago
    Fair enough! My biggest struggle taking AA was also remembering the definitions of everything. There are so many things all tied together.
kmill 11y ago
I think I only finally remembered what a monoid was when I realized it was a category with one object ("mono-"). Or that a groupoid is a category where every arrow is an isomorphism, so then a category which is both a monoid and a groupoid is a "group."