Available in 2021
Course code



10 units


2000 level

Course handbook


Abstraction and generalisation are at the core of mathematics. Formal algebraic and epsilon-delta proofs underpin many areas of modern mathematics. This course dives deeper into the formal structures of linear algebra and calculus. You will practice your formal proof techniques both algebraically and analytically and see examples of modern applications of linear algebra, thus further developing your logical, analytical and critical thinking skills. On completion of this course, you will have developed the necessary skills and theoretical knowledge to work with real-valued functions and with linear algebra, in both theoretical and applied contexts.

Availability2021 Course Timetables


  • Semester 2 - 2021

Learning outcomes

On successful completion of the course students will be able to:

1. Solve mathematical problems using advanced linear algebra.

2. Solve mathematical problems using real analysis.

3. Carefully state and prove key theorems in linear algebra and calculus using the associated techniques.

4. Construct and communicate rigorous mathematical arguments.


  • Operators on Inner-Product Spaces, Orthogonality
  • Jordan Canonical Form and Singular Value Decomposition
  • Differentiability and Mean Value Theorem
  • Riemann integral and the Fundamental Theorems of Calculus

Assumed knowledge


Assessment items

Formal Examination: Final Exam

In Term Test: Midsemester Test

Written Assignment: Assignments

Contact hours



Face to Face On Campus 3 hour(s) per Week for 12 Weeks starting in week 1


Face to Face On Campus 1 hour(s) per Week for 12 Weeks starting in week 2

The University of Newcastle acknowledges the traditional custodians of the lands within our footprint areas: Awabakal, Darkinjung, Biripai, Worimi, Wonnarua, and Eora Nations. We also pay respect to the wisdom of our Elders past and present.