Math 100A (abstract algebra)
Contact information
- Instructor: Aaron Pollack; apollack@ucsd.edu
- TA: Jacob Keller; jjkeller@ucsd.edu
Office hours
- Pollack: M 10am-11am; W 10am-11am; F 2pm-3pm
- Keller: Tu 4pm-6pm; Th 4pm-6pm
Lecture Topics
Recorded lectures can be found on Canvas
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Friday 2 October: Lecture 1 Section 2.1: laws of composition
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Monday 5 October: Lecture 2 Section 2.1 and Section 2.2: groups
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Wednesday 7 October: Lecture 3 Section 2.2 and Section 2.3: the symmetric group, subgroups
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Friday 9 October: Lecture 4 Section 2.3: subgroups of the integers
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Monday 12 October: Lecture 5 Section 2.4, 2.5: examples of groups; cyclic groups; homomorphisms
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Wednesday 14 October: Lecture 6 Section 2.5, 2.6: homomorphisms, normal subgroups, isomorphisms
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Friday 16 October: Lecture 7 Section 2.4, 2.5: more on cyclic groups; the map S_4 to S_3
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Monday 19 October: Lecture 8 Section 2.7: equivalence relations and partitions; cosets
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Wednesday 21 October: Lecture 9 Section 2.8: cosets, Lagrange's Theorem
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Friday 23 October: Lecture 10 Section 2.8, 2.9: cosets, modular arithmetic
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Monday 26 October: Lecture 11 Section 2.12: quotient groups
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Wednesday 28 October: Lecture 12 examples of groups
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Friday 30 October: Lecture 13 generators and relations; section 2.10: the correspondence theorem
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Monday 2 November: Lecture 14 Section 2.11: product groups
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Wednesday 4 November: Lecture 15 Section 6.2: isometries
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Friday 6 November: Lecture 16 Section 6.2, 6.3: isometries and isometries of the plane
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Monday 9 November: Lecture 17 Section 6.3: isometries of the plane
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Wednesday 11 November: No lecture (Veterans Day)
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Friday 13 November: Lecture 18 Section 6.4: finite subgroups of O_2
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Monday 16 November: Lecture 19 Section 6.5: discrete groups of isometries
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Wednesday 18 November: Lecture 20 Section 6.5, 6.7: discrete groups of isometries, group actions
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Friday 20 November: Lecture 21 Section 6.7, 6.8: group actions, the action on cosets
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Monday 23 November: Lecture 22 Section 6.9: the counting formula; semidirect products
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Wednesday 25 November: Lecture 23 semidirect products
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Friday 27 November: No lecture (Thanksgiving)
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Monday 30 November: Lecture 24 Section 6.11, 7.1, 7.2, 7.3: permutation representations, Cayley's theorem, the class equation, p-groups
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Wednesday 2 December: Lecture 25 Section 7.7: Sylow theorems, classification of groups of order pq
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Friday 4 December: Lecture 26 Section 7.6, 7.7: normalizers; proof of Sylow theorems
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Monday 7 December: Lecture 27 Section 10.1: representations, examples of representations
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Wednesday 9 December: Lecture 28 Section 10.2: direct sum of representations, irreducible representations
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Friday 11 December: Lecture 29 Section 10.3, 10.4: unitary representations, Maschke's theorem, characters
Homework Assignments
Quizzes