MATH 5410 Analysis for Teachers

In mathematics the concept of a real number comprises a rigorous treatment of the intuitive notion of `quantity'. The intuitive idea of a `relation' between quantities is encapsulated in rigorous mathematical terms by the

concept of a function of a real variable. The study of real numbers and functions of a real variable, together with higher concepts built upon them---such as measure and integration, metric spaces, families of functions, and so forth---is collectively referred to as analysis. Complex numbers and functions of a complex variable are closely related to real numbers and functions of a real variable, and study of the former is also referred to as analysis, or, more precisely , complex analysis.

MATH 5410 aims to convey a flavor of analysis as seen from a more sophisticated mathematical perspective than that of the Ontario high school curriculum, in the hopes that teachers will gain a new, enriched understanding that allows them to view the high school curriculum as part of a bigger picture.

Another objective of MATH 5410, is to convey a sense of the place of mathematics within the wider world. After all, why should math be taught as a basic subject from primary through secondary school? It turns out that the information age which is now upon us is largely based on the fact that a mathematically rigorous treatment of `quantity' is applicable to just

about anything: sounds, images, language, music, motion. The particular branch of mathematics that treats the `quantification' of sounds, pictures and communication is known as information theory, and it is the basis for digital communication as manifest in the world wide web, with its myriad applications such as youtube and iTunes, as well as cellular telephones and other wireless (and wired) media. But in order to have anything beyond a superficial understanding of information theory, one has to have a mastery of basic analysis. Any technical discussion of mp4 or coding theory, for

example, makes use of concepts from analysis. It is thus hoped that teachers who take MATH 5410 will be better equipped to convey to their students the place of mathematics in the broader world.

The format of the course will be weekly lectures and worksheets, with evaluation based on regular assignments, two in-class

tests, and a presentation.

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