# 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.

© Phil Chodrow, 2023