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 DEPARTMENT OF MATHEMATICS
 AND STATISTICS
1999 - 2000 MINICALENDAR
 Faculty of Arts
 Faculty of Pure and Applied Science

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AS/SC/AK/ MATH 3210 3.0 W

Principles of Mathematical Analysis

      Rigorous presentation, with proofs, of fundamental concepts of analysis: limits, continuity, differentiation, integration, fundamental theorem, power series, uniform convergence.
      The origins of some ideas of mathematical analysis are lost in antiquity. About 300 years ago, Newton and Leibniz independently created the calculus. This was used with great success, but for the most part uncritically, for about 200 years. In the last century, mathematicians began to examine the foundations of analysis, giving the concepts of function, continuity, convergence, derivative and integral the firm basis they required. These developments continue today, for example with the study of calculus on infinite dimensional spaces.
      This course is a continuation of first and second year calculus. The material will be presented in a rigorous manner, putting emphasis on careful mathematical arguments, proofs and illustrative examples. The objectives of the course include improved skill at understanding and writing mathematical arguments as well as understanding of the concepts of the course. The course will provide a useful theoretical background for a variety of higher level and graduate courses including those in analysis, probability, topology, mathematical statistics, and numerical analysis.
      The textbook will be Bartle and Sherbert, Introduction to Real Analysis.

Prerequisite:At least one of the following four courses or course combinations: (1) AS/SC/MATH 2010 3.0, (2) AS/SC/AK/MATH 3110 3.0, (3) AS/SC/AK/MATH 2310 3.0 and AS/SC/MATH 1010 3.0, (4) AS/SC/MATH 2015 3.0 and AS/SC/MATH 1010 3.0.

Coordinator: T. Salisbury

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