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About the Course
About the Course
I taught Discrete Math and Theory (CS2120/2102) for four years at the University of Virginia.
I inherited a strong curriculum that I continually adjusted over the course of each semester, culminating in a very different class than the one I started out teaching via Zoom, Fall Semester, 2020.
The curriculum posted here is a slightly abbreviated Summer Session course that I taught in July 2024.
Featured Exams & Worksheets
Featured Exams & Worksheets
The_Cumulative_Operators.pdfThe Cumulative Operators
I think this was probably my favorite worksheet I ever made, and it was accompanied by a lecture I really enjoyed giving as well, so enjoy it? :)
eq_rules.pdfEquivalence Rules
equivalence_proof_ws.pdfEquivalence Proofs
Practicing_Counterexamples_with_Relations.pdfBinary Relations
CS2120FinalSpring24.pdfSample Final Exam
Course Slidesets
Course Slidesets
Summer Session Slideset 1.pptxSlideset 1
Sets and Course Foundations
Course overview · defining sets · membership, curly-brace notation · no-order/no-duplicates · nested sets
Summer Session Slideset 2.pptxSlideset 2
Propositional Logic
Propositions and truth values · connectives (not / and / or / xor / implies / iff) · combining operators · truth tables · DeMorgan's Law
Summer Session Slideset 3.pptxSlideset 3
Predicates and First-Order Logic
Predicates · universal (∀) and existential (∃) quantifiers · nested quantifiers · negating quantified statements
Summer Session Slideset 4.pptxSlideset 4
Relations and Functions
Binary relations and properties (reflexive, symmetric, transitive, anti-symmetric) · functions, domain, codomain · injective, surjective, bijective · counter-examples
Summer Session Slideset 5.pptxSlideset 5
Proofs and Intro to Number Theory
Proof by contradiction · rational numbers · integers, factors, primes · Fundamental Theorem of Arithmetic · GCD and coprimality
Summer Session Slideset 6.pptxSlideset 6
Well-Ordering and Mathematical Induction
Well-ordering principle · induction outline (base case + inductive step) · summation identities · practice progression from guided to independent
Summer Session Slideset 7.pptxSlideset 7
Combinatorics
Cartesian products · counting characters, license plates, phone numbers · product notation and factorials · permutations vs combinations · shufflings of repeated letters
Summer Session Slideset 8.pptxSlideset 8
Logarithms and Irrationality Proofs
Log identities (product, quotient, power, change-of-base) · log-rewrite practice · proofs that log₂(3), log₈(9) are irrational · log_{n+2}(n+1) ∉ ℤ
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