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Use symbolic logic to express and apply formal reasoning
Assessment Strategies
by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the grading scale contained on the syllabus
through active participation in class discussions and activities
Criteria
translate English sentences into logical statements, including compound and conditional statements, and statements using predicates and quantifiers
construct truth tables for the above types of statements
identify logically equivalent statements
identify valid and invalid arguments
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Write formal proofs
Assessment Strategies
by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the grading scale contained on the syllabus
through active participation in class discussions and activities
Criteria
construct clear, concise, and valid arguments using direct proof
construct clear, concise, and valid arguments using counter examples
construct clear, concise, and valid arguments using contradiction
you construct clear, concise, and valid arguments using contraposition
you construct clear, concise, and valid arguments using proof by induction
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Explore sequences and recursion
Assessment Strategies
by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the grading scale contained on the syllabus
through active participation in class discussions and activities
Criteria
understand and construct formulas for sequences
use isummation and product notation
understand and construct recursively defined sequences
solve recurrence relations by iteration
prove propositions about sequences and recursion
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Explore sets, functions, and relations
Assessment Strategies
by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the grading scale contained on the syllabus
through active participation in class discussions and activities
Criteria
know and apply the definitions of sets, subsets, partitions, the empty set, power sets, and Cartesian products
know and apply the definitions of functions defined on general sets
determine whether a function is one-to-one and/or onto
know and apply the definitions of a relation and its inverse
determine whether relations are reflexive, symmetric, and/or transitive
know and apply the definitions of equivalence relations and equivalence classes
prove propositions about sets, functions, and relations
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Apply the fundamental techniques of counting
Assessment Strategies
by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the grading scale contained on the syllabus
through active participation in class discussions and activities
Criteria
use possibility trees and the multiplication rule to count events
use formulas to count permutations
use formulas to count combinations
count elements of disjoint sets using the addition rule
apply the Pigeonhole Principle
prove propositions involving counting
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Explore graphs and trees
Assessment Strategies
by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the grading scale contained on the syllabus
through active participation in class discussions and activities
Criteria
know and apply the basic terminology of a graph
translate relations into directed graphs
apply the concept of degree
determine whether a graph is a tree
prove propositions about graphs and trees
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Apply the concepts of elementary number theory
Assessment Strategies
by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the grading scale contained on the syllabus
through active participation in class discussions and activities
Criteria
prove properties of divisibility
use the Unique Factorization of Integers Theorem
use the Quotient-Remainder Theorem
use the Triangle Inequality
know and apply the definitions of div and mod