Learning Targets

Targets LS1-3 are introduced on Quiz 1. Targets PF1, PF2, and FR1 are introduced on Quiz 2. Targets C1, C2, and R1 are introduced on Quiz 3. Targets G1, P1, and P2 are introduced on Quiz 4.

Logic and Sets

• LS1: I can simplify and evaluate logical expressions that include quantifiers and boolean operations.
• LS2: I can represent sets in set-builder notation; determine whether an object is an element of a set; and prove that one set is equal to or a subset of another.
• LS3: I can perform operations on sets (intersection, union, complement, difference, Cartesian product) and determine the cardinality of a set.

Proofs

• PF1: I can use direct proof, proof by cases, and proof-by-contradiction to prove mathematical statements.
• PF2: I can choose between weak and strong induction and write correct inductive proofs that include both a base case and an inductive step.

Functions and Relations

• FR1: I can determine whether or not a given relation is an equivalence relation.

Counting

• C1: I can use the principles of addition, multiplication, and inclusion-exclusion to solve counting problems.
• C2: I can use permutations and combinations to count the number of candidate solutions to a given problem.

Recursion and Recurrence Relations

• R1: I can use recurrence relations to model and analyze simple mathematical processes and algorithms.

Graphs

• G1: I can write correct proofs of simple mathematical propositions about the structure of graphs.

Probability

• PR1: I can evaluate marginal, joint, and conditional probabilities of events on discrete sample spaces.
• PR2: I can evaluate expectations of random variables on discrete sample spaces.