Introduction to Mathematical Analysis

This course provides a path towards an honours degree for those students who have not taken the honours first year calculus course MATH1010.03. The course MATH3210.03, which is required for several honours programmes, has this course as an alternative to MATH1010.03 as a prerequisite.

Some of the topics that will be discussed in this course are functions, the real numbers, least upper bounds, sequences, and limits of sequences and functions. The course will emphasize the theoretical aspects of the subject. A principal objective of the course is that students learn to understand the various definitions and to use them to prove basic properties of the objects being defined. The structure of proofs and the basic logic underlying these proofs will be carefully considered. Relatively little effort will be devoted to problems involving calculations, except when they are useful for explaining the concepts.

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The grading will be based on homework, one or two tests and a final examination.