# 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

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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Start date between: and    Key dates

## Melbourne, 2018, Semester 1, Day

### Overview

Online enrolmentNo

Maximum enrolment sizeN/A

Enrolment information

Subject Instance Co-ordinatorYuri Nikolayevsky

### Class requirements

Lecture Week: 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.

Practical Week: 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.