MAT 1101: Algebra II, Winter 2022
Instructor: Florian Herzig;
my last name at math dot toronto dot edu
Office Hours (online/zoom): by appointment
TA: Enrique Nuñez Lon-wo
Lectures: Tuesdays 2-4pm, Thursdays 2-3pm (online/zoom)
Official syllabus
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Fields: Algebraic and transcendental extensions, normal and separable extensions, fundamental theorem of Galois theory, solution of equations by radicals.
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Commutative Rings: Noetherian rings, Hilbert basis theorem, invariant theory, Hilbert Nullstellensatz, primary decomposition, affine algebraic varieties.
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Structure of semisimple algebras, application to representation theory of finite groups.
Useful books for reference (I will not really follow any of them)
- Grillet, Abstract algebra (click link for online access; this book might be the closest to my course)
- Dummit and Foote, Abstract Algebra, 3rd ed.
- Jacobson, Basic Algebra, Volumes I and II.
- Lang, Algebra, 3rd ed.
For representation theory:
- Serre, Linear representations of finite groups
- Alperin and Bell, Groups and representations
- Webb, A Course in Finite Group Representation Theory (available online)
Grading scheme
Homework: 30%
Term test: 30%
Final: 40%
There will be 5 homework assignments. Your lowest homework score will not count towards your grade.
Drop deadline: Sun, Feb 20, 2022
Term test: Tue, Feb 15, 2:10-4:00pm (instead of class).
There will be no makeup test! If you miss the test for a valid reason, the grade will be reweighted as 45% homework and 55% final.
Final: Wed, Apr 20, 2-5pm
Homework (tentative schedule)
Assignments will be posted and solutions will be collected via Gradescope (gradescope.ca, not gradescope.com!).
- Assignment 1, due Fri Feb 4
- Assignment 2, due Tue Mar 1
- Assignment 3, due Fri Mar 11
- Assignment 4, due Fri Mar 25
- Assignment 5, due Fri Apr 8
Links