MATH 6180
MATH 4020
MATH 1190 3.0
MATH 6181


Current and Recent Courses

Math 1025 3.0 (Winter 2017) Applied Linear Algebra

        For Information on this course throughout the term visit  "Moodle @ York University"

Math 4020 6.0 (Fall/Winter 2006/07) Algebra II
Math 1190 3.0 (Fall 2006) Introduction to Sets and Logic
Math 6180 3.0 (Winter 2017) Category Theory
Math 6181 3.0 (Winter 2008) Categorical Topology


Math 6182 3.0 (Winter 2009) Topos- and Sheaf-Theory

NOTE: Lectures will start on March 31 and will be held Tuesdays and Thursdays 10-11:30 in 2005VH. I have prepared lecture notes covering the first third of the course. Please email me to request a copy.

Sheaf theory is one of the key elements in Grothendieck's rewriting of
modern algebraic geometry. It led him to the notion of topos which was subsequently
generalized by Lawvere and Tierney who established an astonishing link
between geometry and logic. The course provides some basic elements of topos
and sheaf theory. Beyond the applications to geometry and logic we will also
discuss the role of topos theory in quantum physics and computing.

Although basic categorical notions and tools will be reviewed as needed,
students without prior knowledge of basic elements of category theory are
advised to undertake some reading prior to the course. MATH 6120 is a co-requisite.

Evaluation will be based at 50% on 5 home work assignments; 20 % on a special individual project, 30 % on a final test.

Here are some useful books on the subject of the course (ordered alphabetical:

F. Borceux: Handbook of Categorical Algebra, vol. 3. Cambridge University Press 1994.
R. Goldblatt: Topoi - The Categorical Analysis of Logic. Elsevier 1984. Reprint: Dover 2006.

P. T. Johnstone: Topos Theory. Academic Press, London 1977.
S. MacLane and I. Moerdijk: Sheaves in Geometry and Logic, A First Intorduction
to Topos Theory. Springer 1992.
C. McLarty: Elementary Categories, Elementary Toposes. Oxford University Press 1992
M.-C. Pedicchio, W. Tholen (editors): Catgorical Foundations. Cambridge University Press 2004. (Chapter VII only, by C. Centazzo and E. Vitale.)




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