Proofs
in calculus and analysis. Topics include sets, functions, axioms for
R,
applications of the completeness axiom, countability, sequences and their
limits, monotone sequences, limits of functions, continuity.
This course provides a path towards an honours degree for those
students who have not taken the honours first year calculus
course MATH 1010 3.0. The course MATH 3210 3.0, which is required for
several honours programmes, has this course as an alternative to
MATH 1010 3.0 as a prerequisite.
The course will emphasize
the theoretical aspects of the subject. A principal goal of
the course is learning 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 them will be carefully considered.
Relatively little effort will be devoted to problems involving
calculations, except when they are useful for explaining the
concepts.
The final grade will be based on written assignments, two class tests,
and a final examination. The exact scheme will be announced during the
first week of classes.
The text will be Bartle and Sherbert, Introduction To Real Analysis (Wiley).
Prerequisite:AS/SC/AK/MATH 1310 3.0 or AS/SC/MATH 1014 3.0.
CorequisitesAS/SC/AK/MATH 2310 3.0 or
AS/SC/MATH 2010 3.0 or AS/SC/MATH 2015 3.0;
AS/SC/MATH 2021 3.0 or AS/SC/AK/MATH 2221 3.0
or AS/SC/MATH 1025 3.0.
Exclusion:AS/SC/MATH 1010 3.0, AK/MATH 2400 6.0.
Coordinator: S.D. Promislow.
