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,
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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Prerequisites: AS/SC/MATH2010.03 or AS/SC/MATH3110.03.
Coordinator: T. Salisbury