20180613

From Ben: You can view all the problems at once by clicking on the schedule and then selecting Schedule.AllProblems. The entire semester will appear in one page. Feel free to use this to study. Here is a list of topics we have studied.

• Lower and upper bounds for a set.
• Infimum and supremum of a set.
• Limit points of a set.
• Showing two sets are equal by showing each is a subset of the other.
• The principle of mathematical induction.
• Truth tables and logically equivalent statements. Negations of statements.
• Implication, converse, inverse, contrapositive.
• Union, intersection, of two sets, as well as lots of properties related to them.
• Relation between limit points and subsets, as well as relationship between subsets and infimums.
• The quantifiers $\forall$ and $\exists$. Order matters, and negating them.
• Relationship between max and sup.
• Set complements and cartesian products, as well as lots of properties related to them.
• Lots of problems has you practice using $\forall$ and $\exists$, often without you even noticing it. We've seen lots of definitions given using these quantifiers (lower bound, infimum, upper bound, supremum, limit point, function, injective, surjective, open set, limit of a sequence, periodic, etc.) I strongly suggest you practice writing the definition of each of these words using these quantifiers. Then write the negation of each definition, using these quantifiers. You should be able to do this flawlessly by the end of the semester. If you practice doing it now, and ask for feedback on how you are doing, you'll get there and be completely ready for real analysis.