Math 100C (Abstract algebra 3)
Contact information
- Instructor: Aaron Pollack; apollack@ucsd.edu
- TA: Hargun Bhatia; hpbhatia@ucsd.edu
Office hours
- Pollack: Mondays,Wednesdays 1:25-2:25 pm in APM 7349
- Bhatia: Thursdays 3-5pm in HSS 3073
Lecture Topics
Recorded lectures can be found on Canvas
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Monday 1 April: Introduction to course
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Wednesday 3 April: Review of 100A, 100B; vector spaces
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Friday 5 April: Vector spaces and linear algebra
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Monday 8 April: Vector spaces and linear algebra
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Wednesday 10 April: the matrix of a linear transformation; Rank-Nullity theorem
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Friday 12 April: Change of basis; algebraic elements of field extensions
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Monday 15 April: algebraic extensions of fields; the degree of an extension
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Wednesday 17 April: degree of extension; ruler and compass contsruction
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Friday 19 April: ruler and compass constructions
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Monday 22 April: adjoining roots; the derivative
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Wednesday 24 April: the derivative
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Friday 26 April: finite fields
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Monday 29 April: primitive elements
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Wednesday 1 May: Exam 1
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Friday 3 May: symmetric functions
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Monday 6 May: the discriminant; splitting fields, the splitting theorem
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Wednesday 8 May: uniqueness of splitting fields up to isomorphism
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Friday 10 May: fixed fields; the fixed field theorem
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Monday 13 May: Galois extensions
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Wednesday 15 May: The main theorem of Galois theory
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Friday 17 May: Galois theory of cubic polynomials; roots of unity
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Monday 20 May: Group representations: Definitions
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Wednesday 22 May: Irreducible representations
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Friday 24 May: Unitary Representations
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Monday 27 May: No lecture (Memorial Day)
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Wednesday 29 May: No lecture (Exam 2)
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Friday 31 May: Characters; One-dimensional representations
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Monday 3 June: One-dimensional representations; Schur's lemma
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Wednesday 5 June: Proof of orthogonality relations
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Friday 7 June: Modern algebraic number theory
Homework Assignments
Homework is due by 10:00pm Pacific time on Gradescope on the days listed below
Exams