sta4ana analysis of real numbers and functions
ANALYSIS OF REAL NUMBERS AND FUNCTIONS
STA4ANA
2018
Credit points: 15
Subject outline
The subject introduces the basic mathematical methods for statistics. It covers selected topics in classical analysis of functions that are essential for a proper understanding of the material in many statistics subjects. The limits of sequences and limits of functions are studied in this subject. We also study series and various tests are derived to determine the convergence or otherwise of these series. We then extend the basic idea of limit to include sequences of functions and sequences of sets in metric spaces. A powerful theorem called The Contraction Mapping Theorem will be derived. This theorem plays a fundamental role in analysis and its applications. We will use it to establish the existence and uniqueness of solutions to certain differential equations. Various applications in statistics will be discussed.
SchoolSchool Engineering&Mathematical Sciences
Credit points15
Subject Co-ordinatorYuri Nikolayevsky
Available to Study Abroad StudentsYes
Subject year levelYear Level 4 - UG/Hons/1st Yr PG
Exchange StudentsYes
Subject particulars
Subject rules
Prerequisites (MAT1NLA and MAT1CDE) or MAT1CLA
Co-requisitesN/A
Incompatible subjects MAT2ANA
Equivalent subjectsN/A
Special conditionsN/A
Graduate capabilities & intended learning outcomes
01. Calculate limits of certain sequences and functions and justify these calculations.
- Activities:
- Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
02. Prove the convergence or otherwise of certain series by applying appropriate tests.
- Activities:
- Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
03. Manipulate bounds and least upper bounds
- Activities:
- Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
04. Perform calculations involving function and metric spaces.
- Activities:
- Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
05. Apply the contraction map theorem in various situations.
- Activities:
- Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
06. Communicate your understanding of analysis using both words and precise mathematical symbolism.
- Activities:
- Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
07. Explain mathematical arguments to other students.
- Activities:
- Opportunities are provided in practice classes
08. Independently apply mathematical conepts and tools for statistical derivations.
- Activities:
- Students are introduced to mathematical concepts in the lectures. These concepts are then applied in assignments. This assessment requires independent research into statistical problems.
Subject options
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Melbourne, 2018, Semester 1, Day
Overview
Online enrolmentNo
Maximum enrolment sizeN/A
Enrolment information
Subject Instance Co-ordinatorYuri Nikolayevsky
Class requirements
LectureWeek: 10 - 22
Two 1.0 hours lecture per week on weekdays during the day from week 10 to week 22 and delivered via face-to-face.
PracticalWeek: 10 - 22
Two 1.0 hours practical per week on weekdays during the day from week 10 to week 22 and delivered via face-to-face.
Assessments
| Assessment element | Comments | % | ILO* |
|---|---|---|---|
| Fortnightly written assignments | 30 | 01, 02, 03, 04, 05, 06, 07, 08 | |
| Three-hour exam | 70 | 01, 02, 03, 04, 05, 06, 08 |