Logic, sets, graph theory, and mathematical reasoning for computer science
← Back to Computer ScienceFoundation of mathematical reasoning using logical statements and operations.
Express complex mathematical statements using predicates and quantifiers.
Master various methods for constructing mathematical proofs.
Understand collections of objects and operations on sets.
Study mappings between sets and relationships within sets.
Count arrangements, selections, and combinations of objects.
Analyze networks, connections, and graph structures.
Explore properties of integers and divisibility.
Study ordered lists and their sums in discrete settings.
Apply Boolean logic to digital circuit design.
Explore advanced concepts in graph theory and algorithms.
Connect combinatorics with basic probability theory.
Introduction to computational models and formal language theory.
Apply discrete mathematics concepts to real computer science problems.
Build the foundation of mathematical reasoning using logical statements and operations.
Understand declarative statements that are either true or false, form the basis of logical reasoning.
Master AND (∧), OR (∨), NOT (¬), implication (→), and biconditional (↔) operators.
Systematically evaluate compound propositions and determine logical equivalences.
Identify statements that are always true (tautologies) or always false (contradictions).
Analyze argument structure, distinguish between valid and invalid reasoning patterns.
Apply modus ponens, modus tollens, and other logical rules to construct valid arguments.
Convert logical expressions to conjunctive normal form (CNF) and disjunctive normal form (DNF).
Work with Boolean variables and operations, foundation for digital circuit design.
Express complex mathematical statements using predicates and quantifiers.
Understand functions that return true/false values and their domains of discourse.
Express statements about all elements in a domain using "for all" quantification.
Express statements about the existence of elements using "there exists" quantification.
Handle multiple quantifiers in a single statement, understand order importance.
Apply De Morgan's laws to quantifiers, convert between ∀ and ∃ in negations.
Convert natural language statements into precise logical notation using predicates.
Identify equivalent statements involving quantifiers and apply transformation rules.
Construct proofs using universal instantiation, existential generalization, and other rules.
Master various methods for constructing rigorous mathematical proofs.
Prove implications P → Q by assuming P and showing Q follows logically.
Prove P → Q by proving the contrapositive ¬Q → ¬P instead.
Assume the negation of what you want to prove and derive a contradiction.
Break the problem into exhaustive cases and prove each case separately.
Prove statements about natural numbers using base case and inductive step.
Use all previous cases in the inductive hypothesis, not just the immediate predecessor.
Prove that objects with certain properties exist and are unique.
Develop intuition for choosing appropriate proof techniques for different problems.
Understand collections of objects and fundamental operations on sets.
Learn set notation, roster and set-builder notation, empty set, and universal set.
Master union (∪), intersection (∩), difference (-), and symmetric difference (⊕).
Visualize set relationships and operations using overlapping circles and regions.
Apply commutative, associative, distributive, and De Morgan's laws for sets.
Understand the set of all subsets of a given set and its cardinality properties.
Form ordered pairs and n-tuples from multiple sets, basis for relations.