Mathematical Analysis
This subject is required in the major and minor mathematics structure of the B.Ed. (Secondary).
Quick Info
- Currently offered by Alphacrucis: Yes
- Course code: MAT302
- Credit points: 10
- Subject coordinator: Stephen Brinton
Prerequisites
The following courses are prerequisites:
Awards offering Mathematical Analysis
This unit is offered as a part of the following awards:
- Bachelor of Arts
- Bachelor of Arts and Bachelor of Applied Social Science
- Bachelor of Arts and Bachelor of Business
- Bachelor of Arts and Bachelor of Education (Secondary)
- Bachelor of Arts (Education Studies)
- Bachelor of Education (Secondary)
- Diploma of Arts
- Undergraduate Certificate in Arts
Unit Content
Outcomes
- Define and apply the algebraic, the order, and the completeness properties of ℝ and apply the supremum/infimum properties of ℝ; discuss the topology of ℝ; define a topological space, giving examples;
- Describe complete metric and function spaces; have a working understanding of bases, countability, separation, and compactness;
- Formulate the given axioms of analysis to establish major theorems in ℝ; and appreciate the abstract structural nature of real analysis and be familiar with the axiomatic method in analysis;
- Extend the knowledge to other fields in formulating a sustained mathematical argument with proofs when necessary, using direct proof, proof by contradiction and proof by induction;
- Develop a personal philosophy in using the theoretical formulation of reasoning and problem solving skills learnt in context that is informed by Christian values.
- Assess the opportunity provided in understanding the development of a substantial mathematical theory through mathematical computations and rigorous proofs;
Subject Content
- Set Theory
- Real Analysis
- Metric Spaces
- Topology
This course may be offered in the following formats
- Onsite (on campus)
- Online (e-Learning)
- Intensive
Assessment Methods
- Worksheets (30%)
- Online Exam/Activities (30%)
- Final Examination (40%)
Prescribed Text
- Primary readings provided