Studying online
There are now 2 possible online modes for units:
Units with modes Online timetabled and Online flexible are available for any student to self-enrol and study online.
Click on an offering mode for more details.
Unit Overview
- Description
This unit provides students with foundations in metric spaces and measure theory. Topics include norms and metrics, metric spaces, completeness, compactness, the contraction mapping principle and its consequences, Lebesgue measure, measurable sets, sigma-algebras, repeated integration, product measure, Fatou's Lemma, Dominated Convergence Theorem, Monotone Convergence Theorem, Lebesgue points, differentiation Theorem, convolution and approximation of the identity.
- Credit
- 6 points
- Offering
(see Timetable) Availability Location Mode Semester 1 UWA (Perth) Face to face - Details for undergraduate courses
- Level 2 core unit in the Mathematics major sequence
- Level 2 option in the Mathematics major sequence
- Outcomes
Students are able to (1) explain and exploit the notions of measure; (2) provide examples of measurable and non measurable sets; (3) utilize the notion of product measure and the theorems of Fubini and Tonelli; (4) exploit Fatou's Lemma, Dominated Convergence Theorem and Monotone Convergence Theorem to compute limits of sequence of functions; and (5) exploit the notion of Lebesgue points and the differentiation theorem to detect the density of a measure.
- Assessment
Indicative assessments in this unit are as follows: (1) tests and (2) final exam. Further information is available in the unit outline.
Student may be offered supplementary assessment in this unit if they meet the eligibility criteria.
- Unit Coordinator(s)
- Professor Serena Dipierro
- Unit rules
- Prerequisites
- and
- Incompatibility
- MATH2031 Introduction to Pure Mathematics
- Contact hours
- lectures: 3 hours per week
workshops: 2 hours per week
- The availability of units in Semester 1, 2, etc. was correct at the time of publication but may be subject to change.
- All students are responsible for identifying when they need assistance to improve their academic learning, research, English language and numeracy skills; seeking out the services and resources available to help them; and applying what they learn. Students are encouraged to register for free online support through GETSmart; to help themselves to the extensive range of resources on UWA's STUDYSmarter website; and to participate in WRITESmart and (ma+hs)Smart drop-ins and workshops.
- Visit the Essential Textbooks website to see if any textbooks are required for this Unit. The website is updated regularly so content may change. Students are recommended to purchase Essential Textbooks, but a limited number of copies of all Essential Textbooks are held in the Library in print, and as an ebook where possible. Recommended readings for the unit can be accessed in Unit Readings directly through the Learning Management System (LMS).
- Contact hours provide an indication of the type and extent of in-class activities this unit may contain. The total amount of student work (including contact hours, assessment time, and self-study) will approximate 150 hours per 6 credit points.
Face to face
Predominantly face-to-face. On campus attendance required to complete this unit. May have accompanying resources online.
Online flexible
100% Online Unit. NO campus face-to-face attendance is required to complete this unit. All study requirements are online only. Unit is asynchronous delivery, with NO requirement for students to participate online at specific times.
Online timetabled
100% Online Unit. NO campus face-to-face attendance is required to complete this unit. All study requirements are online only. Unit includes some synchronous components, with a requirement for students to participate online at specific times.
Online Restricted
Not available for self-enrolment. Students access this mode by contacting their student office through AskUWA. 100% Online Unit.
NO campus face-to-face attendance. All study and assessment requirements are online only. Unit includes some timetabled activities, with a requirement for students to participate online at specific times. In exceptional cases (noted in the Handbook) students may be required to participate in face-to-face laboratory classes when a return to UWA’s Crawley campus becomes possible in order to be awarded a final grade.
External
No attendance or regular contact is required, and all study requirements are completed either via correspondence and/or online submission.
Off-campus
Regular attendance is not required, but student attends the institution face to face on an agreed schedule for purposes of supervision and/or instruction.
Multi-mode
Multiple modes of delivery. Unit includes a mix of online and on-campus study requirements. On campus attendance for some activities is required to complete this unit.