# Learning Targets

Targets LS1-3 are introduced on Quiz 1. Targets PF1, PF2, and FR1 are introduced on Quiz 2. Targets CR1-3 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 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 and Recursion

• CR1: I can use the principles of addition, multiplication, and inclusion-exclusion to solve counting problems.
• CR2: I can use permutations and combinations to count the number of candidate solutions to a given problem.
• CR3: I can prove that a recurrence relation describes a simple algorithm’s runtime and use this relation to determine the big-oh asymptotic runtime.

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 and conditional expectations of random variables on discrete sample spaces.