This course introduces the key concepts of modern real analysis. The philosophy of this course is that modern analysis play a fundamental role in mathematics itself and in applications to areas such as physics, computer science, economics and engineering. This course will have shared lectures with MATH2320 but will have different tutorials and assessment which will emphasise the application of techniques.
Topics to be covered include:
Review of the real number system, the foundations of calculus, elementary set theory; metric spaces, sequences, series and power series, uniform convergence, continuity, the contraction mapping principle; foundations of multidimensional calculus, applications to the calculus of variations, integral equations and differential equations.

Note: This is an Honours Pathway Course. It emphasises the sophisticated application of deep mathematical concepts.

On satisfying the requirements of this course, students will have the knowledge and skills to:

1. Explain the fundamental concepts of real analysis and their role in modern mathematics and applied contexts
2. Demonstrate accurate and efficient use of real analysis techniques
3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from real analysis
4. Apply problem-solving using real analysis techniques applied to diverse situations in physics, engineering and other mathematical contexts

Assessment will be based on:

• Tutorials (15%; LO 1-4)
• Assignments (15%; LO 1-4)
• Final exam (70%; LO 1-4)