# MATH201 Real Analysis

This paper is an introduction to the basic techniques of real analysis in the familiar context of single-variable calculus.

Analysis is, broadly, the part of mathematics that deals with limiting processes. The main examples students have met in school and first-year university are from calculus, in which the derivative and integral are defined using quite different limiting processes. Real analysis is about real-valued functions of a real variable - in fact, exactly the kind of functions that are studied in calculus. The methods of analysis have been developed over the past two centuries to give mathematicians rigorous methods for deciding whether a formal calculation is correct or not. This paper discusses the basic ideas of analysis and uses them to explain how calculus works. At the end of the semester, students should have a broader overview of calculus and a grounding in the methods of analysis that will prove invaluable in later years.

Paper title Real Analysis MATH201 Mathematics 0.1500 18 points First Semester \$851.85 \$3,585.00
Prerequisite
MATH 170
Restriction
MATH 353
Schedule C
Arts and Music, Science
Eligibility
MATH 201 is compulsory for the Mathematics major and is of particular relevance, also, for students majoring in Statistics, Physics or any discipline requiring a quantitative analysis of systems and how they change with space and time.
Contact
maths@otago.ac.nz
Teaching staff
Professor Iain Raeburn and Professor Astrid an Huef
Paper Structure
Main topics:
• A review of the real number system
• The completeness axiom
• Limits of sequences and the algebra of limits
• Limits of functions and the algebra of limits
• Continuous functions and their algebraic properties
• The intermediate value theorem
• Differentiable functions and the algebra of differentiation
• The mean value theorem and Taylor's theorem
• The Riemann integral
• The fundamental theorems of calculus
Textbooks
Text books are not required for this paper.
Course outline
View course outline for MATH 201
Critical thinking.
Learning Outcomes
Students will learn how to formulate and test rigorous mathematical concepts.

## Timetable

### First Semester

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
Other

#### Lecture

Stream Days Times Weeks
Attend
L1 Monday 12:00-12:50 9-15, 17-22
Wednesday 12:00-12:50 9-15, 17-22
Friday 09:00-09:50 9-14, 17-22

#### Tutorial

Stream Days Times Weeks
Attend one stream from
T1 Thursday 11:00-11:50 10-15, 17-22
T2 Thursday 14:00-14:50 10-15, 17-22

This paper is an introduction to the basic techniques of real analysis in the familiar context of single-variable calculus.

Analysis is, broadly, the part of mathematics that deals with limiting processes. The main examples students have met in school and first-year university are from calculus, in which the derivative and integral are defined using quite different limiting processes. Real analysis is about real-valued functions of a real variable - in fact, exactly the kind of functions that are studied in calculus. The methods of analysis have been developed over the past two centuries to give mathematicians rigorous methods for deciding whether a formal calculation is correct or not. This paper discusses the basic ideas of analysis and uses them to explain how calculus works. At the end of the semester, students should have a broader overview of calculus and a grounding in the methods of analysis that will prove invaluable in later years.

Paper title Real Analysis MATH201 Mathematics 0.1500 18 points First Semester Tuition Fees for 2018 have not yet been set Tuition Fees for international students are elsewhere on this website.
Prerequisite
MATH 170
Restriction
MATH 353
Schedule C
Arts and Music, Science
Eligibility
MATH 201 is compulsory for the Mathematics major and is of particular relevance, also, for students majoring in Statistics, Physics or any discipline requiring a quantitative analysis of systems and how they change with space and time.
Contact
maths@otago.ac.nz
Teaching staff
Paper Structure
Main topics:
• A review of the real number system
• The completeness axiom
• Limits of sequences and the algebra of limits
• Limits of functions and the algebra of limits
• Continuous functions and their algebraic properties
• The intermediate value theorem
• Differentiable functions and the algebra of differentiation
• The mean value theorem and Taylor's theorem
• The Riemann integral
• The fundamental theorems of calculus
Textbooks
Textbooks are not required for this paper.
Course outline
View course outline for MATH 201
Critical thinkingcritical thinking.
Learning Outcomes
Students will learn how to formulate and test rigorous mathematical concepts.

## Timetable

### First Semester

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
Other

#### Lecture

Stream Days Times Weeks
Attend
L1 Monday 12:00-12:50 9-13, 15-22
Wednesday 12:00-12:50 9-13, 15-16, 18-22
Friday 09:00-09:50 9-12, 15-22

#### Tutorial

Stream Days Times Weeks
Attend one stream from
T1 Thursday 11:00-11:50 10-13, 15-22
T2 Thursday 14:00-14:50 10-13, 15-22