Overview
MATH104 develops the mathematical language, structures, and reasoning methods used in computer science, data analysis, software engineering, cybersecurity, networks, and related technical disciplines. The course emphasizes finite, countable, and structured objects, with applications to algorithms, databases, and computational problem-solving.
Topics include propositions, predicate logic, logical equivalence, quantifiers, sets, functions, relations, equivalence relations, partial orders, direct proof, contradiction, contrapositive, mathematical induction, strong induction, counterexamples, counting principles, permutations and combinations, the pigeonhole principle, inclusion-exclusion, recurrence relations, introductory probability, and asymptotic reasoning. Graph theory includes graph terminology and representations, paths, cycles, connectivity, trees, spanning trees, bipartite graphs, directed graphs, and network applications. Additional material may include Boolean algebra, modular arithmetic, elementary number theory, and finite-state concepts.
Learning Outcomes
- Translate verbal statements into precise mathematical notation using propositions, predicates, quantifiers, sets, functions, and relations.
- Construct clear and logically valid direct, contrapositive, contradiction, inductive, and strong inductive proofs.
- Evaluate mathematical arguments for validity and construct counterexamples to disprove universal claims.
- Perform operations involving sets, functions, relations, Boolean expressions, and modular arithmetic.
- Solve elementary counting, probability, and recurrence-relation problems using appropriate discrete methods.
- Model practical systems and processes using graphs, trees, directed graphs, relations, and other discrete structures.
- Analyze basic algorithms and computational processes using recurrence relations and introductory asymptotic reasoning.
- Communicate discrete mathematical reasoning accurately using appropriate notation, definitions, diagrams, and proof conventions.
Timetable
| Type | Length | Frequency | Period |
|---|---|---|---|
| Lecture | 2 hours | Weekly | All semester |
| Tutorial | 1 hour | Weekly | All semester |
| Workshop | 2 hours | Fortnightly | All semester |
Assessment Schedule
| Type | Description | Weighting |
|---|---|---|
| Assignment | Problem sets (8 × 5%) | 40.00% |
| Assignment | Proof-writing exercises (2 × 5%) | 10.00% |
| Quiz | Quizzes (4 × 2.5%) | 10.00% |
| Deliverable | Applied discrete-structure modeling task | 10.00% |
| Test | Mid-semester test | 15.00% |
| Exam | Final examination | 15.00% |
Prerequisites
- Requirement 14 NCEA Level 2 Mathematics credits, externally assessed
Teaching Staff & Programs
This course is delivered jointly by faculty from the participating programs listed below. In line with the Douchewater Way, the University of Sexology tailors core instruction directly to each cohort's specific discipline — adapting curriculum to program needs rather than forcing students into a one-size-fits-all model. Learn more about our approach at The Douchewater Way.
