M230 WINTER 2019 MIDTERM INSTRUCTIONS
1. There will be 5 problems: 2 easy, 2 intermediate, and one more challenging.
2. The topics will cover the material in the book discussed in the
lecture/discussions starting from Section 7.1 all the way up to Section 8.3,
including. Nothing from Chapter 9 will be on the midterm.
3. There will be no question asking to reproduce a proof of a theorem from
the book, instead, the problems will ask to use the theory we went through
so far to
(a) solve some given problems about concrete rings and ideals.
(b) prove some simple general facts about rings and ideals.
The problems will be similar to homework problems and to recommended problems
suggested on the homework assignment website.
4. Here are some topics to focus on:
(a) Basic knowledge about concrete rings we went through:
various number rings, including quadratic fields and quadratic integer
rings, polynomial rings, matrix rings
(b) Homomorphisms and quotient constructions; isomorphism theorems
(c) Principal ideals, prime ideals, maximal ideals and properties of
associated quotients.
(d) Irreducibles and primes.
(e) Euclidean domains, Principal ideal domains, Unique factorization
domains.
(f) Norms.
(g) Chinese remainder theorem.
5. It will be important that you express yourself clearly and correctly. It
will be expected that you write your arguments rigorously, but include just the
right amount of information. Please take this into account when preparing for
the midterm.
M230
Last Modified: February 8, 2019