# Course Description

# Course Name

**Real Analysis**

**Session: VDNS3121**

# Hours & Credits

18 Credit Points

# Prerequisites & Language Level

**Taught In English**

- There is no language prerequisite for courses at this language level.

# 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 content subject to change