Weeks
Fifteen Mondays
Each card opens a week: objectives, notes, the wow moment, the lab and where to go deeper.
Propositional Logic
p → q- 01Propositional Logic Sep 21
Welcome: What Is Discrete Mathematics?
The course, the plan for the semester, and why computer science is built on discrete, countable things rather than smooth curves.
Notes ready - 02Propositional Logic Sep 28
Propositional Logic: Propositions, Connectives, Truth Tables
What counts as a proposition, the five connectives, truth tables, and the most misunderstood operator in computer science: the conditional.
+ lab Notes ready - 03Propositional Logic Oct 5
Logical Equivalences and Boolean Circuits
Biconditional and XOR in depth, the laws of logic, proving and simplifying with equivalences, satisfiability, and how the same laws build the adder inside your CPU.
+ lab Notes ready
Predicate Logic and Quantifiers
∀x ∃y- 04Predicate Logic Oct 12
Predicates and Quantifiers
Statements with variables: predicates, domains, “for all” and “there exists”, translating English into logic and back, and negating quantified statements correctly.
+ lab Notes ready - 05Predicate Logic Oct 19
Nested Quantifiers and Specifications
Statements with two quantifiers, why their order changes everything, how to negate them step by step, and how engineers use them to write precise specifications.
+ lab Notes ready
Reasoning and Proof
∴- 06Proofs Oct 26
Rules of Inference
Valid arguments, modus ponens and friends, resolution, and how machines draw conclusions.
+ lab - 07Proofs Nov 2
Introduction to Proofs
Direct proof, contrapositive, contradiction, cases and counterexamples. How to be certain.
+ lab - 08Proofs Nov 9
Midterm Exam
Written midterm on weeks 1–7: propositional logic, predicate logic, rules of inference and proofs.
Exam
Sets, Relations and Functions
A ∩ B- 09Discrete Structures Nov 16
Sets and Set Operations
Sets, subsets, power sets, Cartesian products, and the algebra of sets.
+ lab - 10Discrete Structures Nov 23
Relations and Functions
Relations and their properties, equivalence relations, and functions: injective, surjective, bijective.
+ lab - 11Discrete Structures Nov 30
Sequences, Sums and the Sizes of Infinity
Sequences and recurrences, summation formulas, and why some infinite sets are bigger than others.
+ lab
Induction, Recursion and Counting
n → n+1- 12Induction & Counting Dec 7
Induction, Recursion and Growth of Functions
Mathematical and strong induction, recursive definitions, and Big-O for comparing algorithms.
+ lab - 13Induction & Counting Dec 14
Counting and the Pigeonhole Principle
Product and sum rules, permutations, combinations, and the pigeonhole principle.
+ lab
Graphs and Trees
G = (V, E)- 14Graphs Dec 21
Graphs: Models, Terminology and Representations
Graphs as models of networks, degree and the handshake theorem, special graphs, representations and isomorphism.
+ lab - 15Graphs Dec 28
Connectivity, Coloring and Trees · Project Demo Day
Paths and connectivity, graph coloring, and trees. Project demos in the second half.
+ lab