Week 1
Assignment for the first week of Math 505
Explore this website. Find out about the
text, coverage, and requirements of this course.
Review the following
basic material. (Just do it; you don't need to turn anything in.)
- Equivalence relations are ubiquitous in mathematics.
Know the definition of an equivalence relation on a set. Show that an
equivalence relation partitions the set into equivalence
classes. Give several examples of equivalence relations. This
Wikipedia article contains everything you need to know and
much more.
- Basic Number Theory. Look through Section 0.1 of the
text. Most
of this material should be familiar to you from undergraduate
courses, especially that up to 0.1.5. Review as needed. We
will review some of this stuff as it comes up during the
semester.
- Group Theory Basics. Read Sections 1.1 and 1.2 of the
text. Know the definition of group, abelian group, subgroup, group
isomorphism, and
understand the important examples discussed there: integers, integers
modulo n, cyclic groups, permutation groups, symmetric group,
alternating group, dihedral group.
- Be ready to hit the decks running on Tuesday, August 30th. We'll
move right into Section 1.3.
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