Math 310, Winter 2005

Midterm Topics & Overview

 

Midterm: Wednesday, February 2nd, in class, 50 minutes

You may bring a sheet of notes, but it should not include full proofs (templates are fine).

Test covers sections 1-9 of the text.

 

Review sessions: in class Monday and optionally Tuesday, 4:30-6 in THO 211

 

Study: Textbook sections 1-9 (including examples and proofs), class notes, all assigned homework (collected or not).

Bring questions to reviews or office hours.

 

Main topics per section:

 

  1. The Language of Mathematics: Statements, Connectives (and, or, not).
  2. Implications.
  3. Direct Proofs and proof by cases.
  4. Proof by contradiction.
  5. Induction (skip 5.4 Strong Induction).
  6. Sets: elements, ways to define/notation, subsets, empty set, operations on sets (union, intersection, difference), power set of a set, complement of a set.
    Thm 6.3.4: results and how to prove them.
    Know how to prove a set is a subset of another, or that two sets are equal.
    Understand difference between an element and a subset.
  7. Quantifiers: universal and existential.
    Understand what they are and how to use them. Understand combinations of more than one quantifier, and negations of such. How to prove and disprove statements involving quantifiers.
    Cartesian product: definition and how to use it.
  8. Functions (skip 8.3)
    Definitions & understand: functions, domain, codomain, image, graph, composition of functions.
    Be able to come up with examples.
  9. Functions: Injections, Surjections and Bijections. (skip 9.3)

Definitions & understand: when a function is injective, surjective, bijective, and invertible; inverse of a function.

Also: understand inequalities and proofs involving inequalities.

 

Midterm questions may include computational questions (e.g. truth tables, or function compositions), definitions, multiple choice, short questions like “give the converse of the following statement”, finding errors in an argument, a couple short proofs (e.g. set equality, function injectivity), one “serious” proof.