Math 103B (modern algebra II)
Contact information
- Instructor: Aaron Pollack; apollack@ucsd.edu
- TA: Mingjie Chen; mic181@ucsd.edu
- TA: Zilu Ma; zim022@ucsd.edu
Office hours
- Pollack: Mondays and Wednesdays 12:00pm-1:00pm
- Chen: Tuesdays 10:00am-12:00pm
- Ma: Tuesday 2:30pm-4:30pm
Lecture Topics
Recorded lectures can be found on Canvas
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Monday 29 March: Lecture 1: Introduction to course (geometric constructions)
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Wednesday 31 March: Lecture 2: Definition of rings (Chapter 12)
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Friday 2 April: Lecture 3: Properties of rings (Chapter 12)
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Monday 5 April: Lecture 4: Properties of rings and subrings (Chapter 12)
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Wednesday 7 April: Lecture 5: Integral domains (Chapter 13)
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Friday 9 April: Lecture 6: Fields (Chapter 13)
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Monday 12 April: Lecture 7: characteristic of a ring (Chapter 13), ideals (Chapter 14)
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Wednesday 14 April: Lecture 8: ideals and factor rings (Chapter 14)
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Friday 16 April: Lecture 9: ideals and factor rings continued (Chapter 14)
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Monday 19 April: Lecture 10: prime and maximal ideals (Chapter 14)
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Wednesday 21 April: Lecture 11: prime and maximal ideals (Chapter 14); ring homomorphisms (Chapter 15)
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Friday 23 April: No lecture (Exam 1)
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Monday 26 April: Lecture 12: ring homomorphisms (Chapter 15)
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Wednesday 28 April: Lecture 13: field of quotients (Chapter 15)
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Friday 30 April: Lecture 14: polynomial rings, division algorithm (Chapter 16)
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Monday 3 May: Lecture 15: polynomial rings, division algorithm (Chapter 16)
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Wednesday 5 May: Lecture 16: third isomorphism theorem; irreducibility of polynomials (Chapter 17)
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Friday 7 May: Lecture 17: irreducibility of polynomials (Chapter 17)
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Monday 10 May: Lecture 18: Gauss' Lemma, Eisenstein's criterion (Chapter 17)
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Wednesday 12 May: Lecture 19: unique factorization of polynomials (Chapter 17); vector spaces (chapter 19)
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Friday 14 May: Lecture 20: vector spaces, bases (chapter 19)
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Monday 17 May: Lecture 21: extension fields, splitting fields (chapter 20)
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Wednesday 19 May: Lecture 22: splitting fields (chapter 20)
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Friday 21 May: No lecture (Exam 2)
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Monday 24 May: Lecture 23: splitting fields (chapter 20)
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Wednesday 26 May: Lecture 24: splitting fields (chapter 20), algebraic and transcendental elements (chapter 21)
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Friday 28 May: Lecture 25: algebraic and transcendental elements, minimal polynomial (chapter 21)
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Wednesday 2 June: Lecture 26: finite extensions, degree of an extension (chapter 21)
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Friday 4 June: Lecture 27: degree of an extension (chapter 21), geometric constructions (chapter 23)
Homework Assignments
Homework is due by 10:00pm Pacific time on Gradescope on the days listed below
Exams