Real Analysis

University of Otago

Course Description

  • Course Name

    Real Analysis

  • Host University

    University of Otago

  • Location

    Dunedin, New Zealand

  • Area of Study

    Calculus, Mathematics

  • Language Level

    Taught In English

  • Prerequisites

    MATH 170

  • Course Level Recommendations

    Upper

    ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

    Hours & Credits

  • Credit Points

    18
  • Recommended U.S. Semester Credits
    3 - 4
  • Recommended U.S. Quarter Units
    4 - 6
  • Overview

    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.

    Course 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

    Learning Outcomes
    Students will learn how to formulate and test rigorous mathematical concepts.

Course Disclaimer

Courses and course hours of instruction are subject to change.

Eligibility for courses may be subject to a placement exam and/or pre-requisites.

Some courses may require additional fees.

Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.

Please reference fall and spring course lists as not all courses are taught during both semesters.

Availability of courses is based on enrollment numbers. All students should seek pre-approval for alternate courses in the event of last minute class cancellations

Please note that some courses with locals have recommended prerequisite courses. It is the student's responsibility to consult any recommended prerequisites prior to enrolling in their course.