Principles of Mathematical Analysis

The origins of some ideas of mathematical analysis are lost in antiquity. 300 years ago, Newton and Leibniz independently created what we call the calculus. This was used with great success, but for the most part uncritically, for nearly two hundred years. In the 19th century mathematicians began to examine the foundations of analysis, giving such concepts as ``function", ``continuity", ``convergence", ``derivative" and ``integral" the firm basis they required. These developements continue today. For example, one of the major themes in 20th century mathematics has been the study of "functional analysis", or calculus in infinite dimensional spaces. The course is a prerequisite, or at least a good background, for several 4000-level courses,including MATH4010.06, MATH4030.06, MATH4080.06, and MATH4210.06.

The topics of the course will include limits, continuity, derivatives and integrals, picking up where calculus courses leave off. Notions such as uniform continuity and uniform convergence will play a central role. The emphasis will be on rigorous mathematical argument, proofs and examples, and the development of the skills required in the study of advanced mathematics.

The course is a natural continuation of the first and second year honours calculus courses. An alternate route into the course is to take the ordinary calculus courses, and follow them by MATH3110. The latter will not cover all topics in the same depth as the honours calculus courses, but it does provide sufficient background and exposure to rigorous mathematical argument to prepare students for MATH3210.

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