Learning Targets

Logic and Set Theory

L1:	I can use quantified logic to express English sentences and mathematical concepts.
L2:	I can correctly simplify logical expressions which include quantifiers, negations (NOT), conjunctions (AND), disjunctions (OR), and implications.
L3:	I can use rules of logical inference to determine whether a conclusion follows logically from a set of premises.
S1:	I can describe sets using roster, set-builder, and set-generator notations.
S2:	I can perform operations on sets (including union, intersection, difference, complement, cartesian product, and power set) and determine the cardinality of a set.

Proof-Writing

PF1:	I can use the element method to prove that one set is a subset of another, or that two sets are equal.
PF2:	I can prove mathematical statements using proof-by-contradiction.
PF3:	I can correctly state the base case and inductive hypothesis in a proof by weak induction.
PF4:	I can prove the base case and inductive hypothesis in a proof by weak induction when they are supplied to me.
PF5:	I can write a complete proof by weak induction.
PF6:	I can write a complete proof by strong induction.
FR1:	I can prove that a supplied relation is or is not 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.
R1:	I can describe a mathematical process or algorithm using a recurrence relation.
R2:	I can use the tree method to determine the asymptotic runtime of a recursive algorithm.

Probability

PR1:	I can evaluate marginal, and joint probabilities of events on discrete sample spaces.
PR2:	I can use Bayes’ Theorem to evaluate conditional probabilities.
PR3:	I can evaluate expectations of random variables on discrete sample spaces.

Graphs

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

© Phil Chodrow, 2024