Math 308 Final Exam Review
The final exam will be held Tuesday, May 5, at 8:30-11:30 a.m. in Yost 300.
The exam will be about twice the length of each midterm, with about half
of the exam covering material which was not on the midterms.
Material which was covered on the midterms is listed on the midterm review
pages. The more recent material is from sections 22-24, 26-27, 29, and
31-33 of the textbook.
You will be asked for complete definitions (including appropriate
context) of some subset of the following terms.
- relation
- function
- partition
- equivalence relation
- binary operation
- commutative
- associative
- identity element
- inverse element
- group
- subgroup
- cyclic subgroup
- Cayley digraph
- permutation
- symmetric group
- even/odd permutation
- coset (be able to distinguish between left and right cosets)
- direct product of groups
- (group) homomorphism
- (group) isomorphism
- kernel
- normal
- factor group / quotient group
- action
- orbit (in the context of group actions)
- ring
- (ring) homomorphism
- (ring) isomorphism
- integral domain
- characteristic
- field of quotients
- polynomial with coefficients in R
- evaluation homomorphism
- zero of a polynomial
- irreducible polynomial
- endomorphism
- group ring
- ideal
- factor ring / quotient ring
- maximal ideal
- prime ideal
- prime field
- principal ideal
- extension field
- algebraic element
- transcendental element
- irreducible polynomial of an element
- simple extension
- algebraic extension
- finite extension
- algebraically closed
- algebraic closure
- constructible
- Galois field
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