Overview
MATH101 introduces the language, structures, and reasoning methods required for university-level mathematics. Topics include sets, notation, intervals, functions, relations, mathematical statements, logical connectives, quantifiers, direct and indirect proof, proof by contradiction, counterexamples, mathematical induction, elementary number theory, algebraic manipulation, equations and inequalities, sequences, series, and introductory combinatorial reasoning.
Students practise translating among verbal, symbolic, graphical, and numerical representations while developing accurate mathematical notation and disciplined mathematical writing. Active problem solving, proof workshops, formative exercises, and applications connect foundational reasoning with calculus, statistics, computer science, and other quantitative fields.
Learning Outcomes
- Apply mathematical notation and terminology accurately when representing sets, functions, relations, statements, and quantitative relationships.
- Distinguish definitions, theorems, conjectures, examples, counterexamples, and invalid arguments.
- Construct and evaluate clear direct proofs, indirect proofs, contradiction proofs, and proofs using counterexamples.
- Apply mathematical induction appropriately to establish claims involving sequences, divisibility, inequalities, and other indexed structures.
- Solve and communicate solutions to algebraic, numerical, combinatorial, and elementary number-theoretic problems.
- Translate mathematical information among verbal, symbolic, graphical, and numerical representations.
- Evaluate the validity of mathematical reasoning and identify gaps, assumptions, and logical errors.
- Synthesize foundational mathematical techniques in clearly structured written solutions relevant to calculus, statistics, computer science, and other quantitative disciplines.
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 | Weekly formative problem sets (10 × 2%) | 20.00% |
| Assignment | Proof-writing assignments (2 × 10%) | 20.00% |
| Test | Mid-semester test | 20.00% |
| Deliverable | Proof and problem-solving portfolio | 15.00% |
| Exam | Final examination | 25.00% |
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.
