University of Technology Sydney

37438 Modern Analysis with Applications

6cp; Forms of attendance in this subject have changed to enable social distancing and reduce the risks of spreading COVID-19 in our community. There may also have been changes to the assessment requirements. Consequently, the Subject Outline information for this subject has changed. Details of the changes may be published in an Addendum to the Subject Outline which is available through your LMS (Blackboard or Canvas)
Requisite(s): (35232 Advanced Calculus OR 37234 Advanced Calculus) AND (35212 Computational Linear Algebra OR 37233 Linear Algebra)
These requisites may not apply to students in certain courses.
There are course requisites for this subject. See access conditions.
Anti-requisite(s): 35322 Advanced Analysis


This subject introduces some of the most important and powerful mathematical tools developed over the last one hundred years. These are essential for the modern theory of probability and stochastic processes that underpin the pricing of derivative securities traded in international financial markets as well as the mathematical foundations of quantum physics. Topics include measure spaces; Lebesgue measure; borel sets and sigma algebra; Lebesgue integrals; product measures; probability as a measure; metric spaces; normed linear spaces; Banach spaces; Hilbert spaces; Lp spaces; applications to problems in probability and Fourier series.

Typical availability

Spring session, City campus

Detailed subject description.

Access conditions

Note: The requisite information presented in this subject description covers only academic requisites. Full details of all enforced rules, covering both academic and admission requisites, are available at access conditions and My Student Admin.