Analysis 1 is a foundational course in Mathematics, leading on to other areas of analysis, such as topology and measure theory, complex analysis, functional analysis, and harmonic analysis. It also provides important tools for application areas such as theoretical computer science, physics and engineering.
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 course will have shared lectures with MATH3116 but will have different tutorials and assessment which will emphasise the application of techniques.

Note: This is an HPC. It emphasises mathematical rigour and proof and develops the application of the theory to topics such as differential equations and the proofs of major theorems in multivariable calculus.

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)

A mark of 60 or more in MATH1021 or MATH1116.

MATH2021 and MATH3116.