- discuss objects and relationships between them
- set is collection of distinct objects
- every set is contained by itself
- difference - set of elements in A but not in B
- union - set of elements in A or B
- intersection - set of elements in A and B
- symmetric difference - set of elements in A or B but not in both
- cartesian product - set of all ordered pairs (a, b) where a is in A and b is in B
- function is rule from A to B. A is domain, B is codomain.
- cardinality - number of elements in a set
- a group is a set with a binary operation that satisfies four properties: closure, associativity, identity, and invertibility
- abelian group - commutative group under binary operation
- function is homomorphism if it preserves the group operation
- isomorphism - bijective homomorphism
- group is cyclic if there exists an element g in the group such that every element in the group can be written as g^n for some integer n
- structure - set R with two binary operations, add and mul
- abelian, monoid, distributive
- ideal of a ring is subset a - b is in I for all a, b in I
- fiest is set with 2 binary operations, usually add and mul
- finite fields are galois fields
- field E containing F as subfield.
- tower of field extensions - is seq of fields
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