This course continues on from MATH1115, providing an in-depth development of fundamental concepts of calculus and linear algebra, with a particular emphasis on the underlying foundations of mathematics. The use and understanding of proof and abstract ideas, will allow students to develop analytical skills which will form a base for further study in fundamental mathematics as well as providing a foundation for a wide range of quantitative areas such as computer science, engineering, economics, statistics and physics. 

Topics to be covered include:

Analysis - logic, axioms for the real numbers, completeness, sequences and convergence, continuity, existence of extrema, infinite series, convergence tests, power series, Taylor series, binomial series, complex power series, vectors, dot product, cross product, planes and lines in 3-space, vector functions, curves and parametrization, Kepler’s laws, functions of several variables, chain rule, gradients and directional derivatives, Quadratic forms, extreme values, Lagrange multipliers;

Algebra – induction, theory and application of Euclidean vector spaces, vector spaces, linear independence, bases and dimension, eigenvalues and eigenvectors, orthogonality and least squares.

Note: This is a HPC. It involves extra material and emphasizes the use and understanding of proof and abstract ideas to a deeper conceptual level than MATH1014.

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

Assessment will be based on:

• Tutorials (5%; LO 1-4)
• Five assignments (25% in total: LO 1-4)
• Mid-semester test (25%; LO 1-4)
• Final examination (45%; LO 1-4)

A mark of 60 or more in MATH1021 or MATH1115.

with MATH1002, MATH1004, MATH1014, MATH1012, MATH1022 and ENGN1222