# MATH 5410 6.00AY (Fall 2012 / Winter 2013)Analysis for teachers Course Outline

### Course Webpage

Public page: www.math.yorku.ca/~salt/courses/5410y12/5410.html
Wiki page: (under construction)

### Location:

Thursdays 6-9pm in Vari Hall: VH 2000 (relocated from CB120)

### Instructor/Contact Information:

Tom Salisbury
Department of Mathematics and Statistics
• Departmental office: N520 Ross Building, (416) 736-5250, FAX: (416) 736-5757
• Graduate Program office: N519 Ross Building, (416) 736-3974

### Office hours:

Wednesdays 10:30-12:30, by appointment, or ask me to stay after class.

### Text:

A radical approach to real analysis by D. Bressoud. 2nd edition, MAA (2007).

• 20% Class test (end of fall term)
• 25% Class test (end of winter term)
• 25% Assignments
• 20% Project
• 10% Participation
Students are responsible for reviewing York's policies concerning academic integrity.

### Course description:

Analysis and Algebra are the two pillars mathematics is built on. Loosely speaking, they are respectively the mathematics of the continuous, and the mathematics of the discrete. Virtually every area of mathematics uses at least a bit of both:
• Functions of a real variable, and calculus are both topics in "real analysis", and one goal of the course is to situate these seconry school topics within a broader perspective. In other words, to understand what calculus is actually for, and how it is applied.
• "Complex analysis" expands on real analysis, doing calculus and some parts of geometry in two dimensions, but using complex and imaginary numbers.
• "Functional analysis" expands the point of view even further, to infinitely many dimensions and Hilbert space.
• "Fourier analysis", "Differential equations", and parts of Probability theory are all either parts of analysis, or are based on it.
We will touch on all the above flavours of analysis.

The course is not a history course, though we will approach it historically, and will try to understand how the subject developed and where fundamental ideas came from. The course is also not a systematic undergraduate course in real analysis, though we will cover many of the concepts, calculations, and proofs that would arise in such a course. For example, we will spend time understanding why the needs of Fourier analysis forced analysts to re-examine the foundations of calculus long after the invention of the latter, and to come up with more rigorous notions of basic concepts such as the real numbers and continuity. We will pick selected interesting topics from various types of analysis, to give a broad perspective on how calculus gets applied (eg. fractals, signal processing, curvature, hyperbolic geometry, contour integration, tomography, option pricing).

The format will be weekly lectures and worksheets, with evaluation based on regular assignments, two in-class tests, and a project. Selected topic will be based on readings from a variety of sources. The foundational material from real analysis will be drawn from the course text.