# MATH3570 Foundations of Calculus

MATH3570 is a Mathematics Level III course. See the course overview below.

Units of credit: 3

Prerequisites: 12 units of credit in Level II Mathematics courses

Exclusion: MATH3611

Cycle of offering: Term 1

Graduate attributes: The course will enhance your research, inquiry and analytical thinking abilities.

More information: This recent course handout (pdf) contains information about course objectives, assessment, course materials and the syllabus.

The Online Handbook entry contains up-to-date timetabling information.

If you are currently enrolled in MATH3570, you can log into UNSW Moodle for this course.

#### Course Aims

This course aims to re-examine the key ideas behind the Calculus and to give a deeper understanding of the notions of limit, continuity, differentiability and integrability. We will look at not only what is true, but also what is not true, in order to better understand why definitions are the way that they are, and why the conditions on the main theorems need to be there.

#### Course Description

What does it mean for a limit to exist? What does it mean for a function to be continuous or differentiable? There are functions which are continuous everywhere but differentiable nowhere! Are there functions whose integral does not exist? In this course, we look again at the essential concepts of limit, continuity, differentiability and integrability and try to place them on a sure footing. The syllabus includes material on sequences and series of real numbers and also of real valued functions. Although of general interest to those studying mathematics for its own sake, this course is of special relevance to those planning a career in secondary teaching.

MATH3570 is a compulsory component of the program for mathematics teachers.