Math 4220, Exam 1 Study Guide
The rst exam will cover material from sections 0-4. Recall that we only looked at 0 briey, but
there may still be questions on that section. The exam will be in the testing center, make sure you
are aware of the operating hours. I expect most students to be able to nish the exam in under 2
hours.
You will need to know basic denitions. I will ask you to state some formal denitions, and you
will need to know others in order to use them in proving other problems. Here is a list of some of
the important denitions:
• one-to-one
• group
• associative
• onto
• subgroup
• commutative
• f (A)
• binary operation
• identity
• equivalence relation
• closure
• inverses
Note that there may be additional terms I expect you to know (e.g. a mod n).
You should know specic examples of groups, with the appropriate operation, such as:
• Z
• Q
• R∗
• C∗
• Zn
• Q∗
• Rn
• Dn
• U (n)
• R
• C
• GL(2, R)
You should know the statements of named theorems. You do not need to know the number, but
you need to be able to write the statement down accurately (as with the denitions above).
• The One-Step Subgroup Test (3.1)
• The Two-Step Subgroup Test (3.2)
You also should know important theorems, lemmas, and corollaries. You do not need to know the
number (or whether it is a theorem or corollary), but be able to state that there is a theorem that
tells us . . . . Here are some of the more important ones so far.
• 2.1
• 3.1
• 4.1 Cor 1, 2
• 2.2
• 3.2
• 4.2
• 2.3
• 3.4
• 4.2 Cor 1, 3, 4
• 2.4
• 4.1
• 4.3
• 4.3 Cor
You need to be able to use the theorems and denitions to prove other results. You may need a
variety of proof techniques, including induction and contradiction.