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Details for MAT302 Mathematical Analysis

Essential for students in the B.Ed. (Secondary) program, this unit focusing on the properties of real numbers, topological concepts, and the structure of metric and function spaces. Students will learn to apply axioms and theorems, developing proof techniques like induction and contradiction. This subject not only enhances problem-solving skills but also integrates a philosophical approach to mathematics informed by Christian values.

Quick Stats

  • Currently offered by Alphacrucis: Yes
  • Course code: MAT302
  • Credit points: 10

Subject Coordinator

Contact studentsupport@ac.edu.au for more information.

Prerequisite

Unit Content

Outcomes

  1. 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;
  2. Describe complete metric and function spaces; have a working understanding of bases, countability, separation, and compactness;  
  3. 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;
  4. 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;
  5. Develop a personal philosophy in using the theoretical formulation of reasoning and problem solving skills learnt in context that is informed by Christian values.
  6. 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

Please consult your course prospectus or enquire about how and when this course will be offered next at Alphacrucis University College.

Assessment Methods

  • Worksheets (30%)
  • Online Exam/Activities (30%)
  • Final Examination (40%) 

Prescribed Text

  • Primary readings provided