Daniel Arreola, Office Hours: Tue and Thu 3–4:30pm in Carver 438.
Time and Place
Lectures: MWF 9:55pm–10:45pm in Carver 282
Texts and Resources
Main text: Hungerford, Abstract Algebra: An Introduction, 3rd Edition (available from the University Bookstore in both hardcopy and electronic format, and on Amazon)
The class will require weekly homework submissions, 2 in-class exams, and a final exam. Class components will be weighted as follows:
Homework: 45%
(Oct 2, 2023) Exam 1: 15%
(Nov 6, 2023) Exam 2: 15%
(Dec 13 at 7:30–9:30am) Final Exam: 25%
Your homework should be neat and stapled. Problems should be listed in order and proofs given in complete sentences with correct notation. Use of LaTeX is encouraged but not at all required. For each homework question you must:
Write out the statement of the question – ideally you will paraphrase the given question, highlighting key points while removing any irrelevant details.
Explain your solution with a complete and logical succession of ideas. Each problem will be graded on the following 4 point scale:
4=Very Good - Correct mathematics that is carefully thought out and thoroughly explained with complete sentences.
3=Good - Correct mathematics with some minor gaps in explanation.
2=Basic - Partial solution with errors in understanding or computation.
1=Emerging - Work that has some merit but also has significant shortcomings in the mathematics or explanation.
0=No Credit - No work submitted or no serious attempt.
Homework
Homework sets will be posted here. They are due most Wednesdays. First homework is due August 30.
We will cover Appendix A,B,C,D and Chapters 1–5, 7 and Section 8.1. A short summary of each lecture will be posted here.
Appendix A - Logic and Proof
Appendix B - Sets and Functions
1.1 - The Division Algorithm
1.2 - Divisibility: The greatest common divisor
1.2 - Divisibility: Euclid's Algorithm
1.3 - Primes and Unique Factorization
(Labor day)
2.1 - Congruence in \(\mathbb{Z}\)
Appendix C - Well-ordering and Induction
Appendix D - Equivalence Relations and 2.2 - Modular Arithmetic
2.3 - Structure of \(\mathbb{Z}_n\)
3.1 - Definition and Examples of Rings
3.1 - (continued)
3.2 - Basic Properties of Rings
3.2 - (continued)
3.3 - Isomorphisms and Homomorphisms
3.3 - (continued)
Review for Exam 1
(Oct 2) Exam 1
4.1 - Polynomial Rings \(R[x]\)
4.2 - Divisibility in \(F[x]\)
4.3 - Irreducibles and Unique Factorization
4.4 - Polynomial Functions, Roots, Reducibility
4.4 (contd.) and 4.5 - Irreducibility in \(\mathbb{Q}[x]\)
4.5 (contd.)
4.6 - Irreducibility in \(\mathbb{R}[x]\) and \(\mathbb{C}[x]\)
5.1 - Congruence in \(F[x]\)
5.2 - Arithmetic in \(F[x]/(p(x))\)
5.3 - Structure of \(F[x]/(p(x))\)
extra/review/examples of \(F[x]/(p(x))\)
7.1 - Definition and Examples of Groups
7.2 - Basic Properties of Groups
Review for Exam 2
(Nov 6) Exam 2 on Sections 3.3, 4.1–4.6 and 5.1–5.3.
7.2 - (contd.)
7.3 - Subgroups
7.3 (contd.) Center and Cyclic Groups
7.4 - Isomorphisms and Homomorphisms
7.4 - (contd.)
(after break) 7.5 - The Symmetric and Alternating Groups
7.5 – 8.1 - Congruence and Lagrange's Theorem
8.1 - (contd.)
Extra/Review
Extra/Review
Extra/Review
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