General information | Course description | Lecture notes | Assignments | Homework schedule | Grading | Links | Fine print

**Lectures:** Wednesday and Friday, 15:05 – 16:20, Physics Building 227

**Text:** *Abstract Algebra*,
by David S. Dummit and Richard M. Foote (third edition)

**Secondary texts:**

- Artin:
*Algebra* - Lang:
*Algebra* - Herstein:
*Topics in Algebra*

**Name:** Professor Ezra Miller
**Address:** Mathematics Department,
Duke University, Box 90320,
Durham, NC 27708-0320
**Office:** Physics 209
**Phone:** (919) 660-2846
**Email:** *ezramath.duke.edu*
**Webpage:**
*https://math.duke.edu/people/ezra-miller*
**Course webpage:** you're already
looking at it... but it's
*https://services.math.duke.edu/~ezra/501/501.html*
**Office hours:**
Tuesday 14:00 – 15:00 &
Wednesday 12:00 – 13:15, in Physics 209

**Course content:**

- groups
- subgroups
- homomorphisms
- cosets
- quotient groups
- symmetry
- group actions
- permutation representations
- Sylow theorems
- rings
- ideals
- polynomials
- fractions
- modules
- structure theorem over PID

Rings combine two operations: addition and multiplication. In familiar situations, particularly the integers and univariate polynomials, interactions between the two operations lead to fundamental theorems concerning factorization into primes. What results is a main goal of the course: a single structure theorem that classifies all finite abelian groups and also produces Jordan canonical forms of linear transformations.

**Prerequisites:**
Math 501 is a demanding course. Students are expected to have
a firm grasp of linear algebra before beginning the course. In
addition, it is expected that every student begins the course
comfortable and proficient at writing rigorous mathematical
arguments (proofs).

**Reading assignments**are included at the top of each homework and midterm.- Due dates for the five homework assignments this semester are listed in the table below.
- All assignments, including the midterms, will be
take-home.
**All are due at the start of class time on the due date**. **All solutions you turn in, including midterms, homework, and term projects, must be typewritten using the provided LaTeX template.**Communicating your ideas is an integral part of mathematics. In addition to the usual PDF files, LaTeX source files for each of the homework assignments as well as each of the midterms will be provided. You should use these as LaTeX templates for your solutions, by filling in your responses in those files. I am happy to answer any questions you might have about LaTeX, although you should ask your classmates first.**Turn in your homework solutions to me by email**. Send at least your .tex file (the grader or I may comment on your TeX usage); if you include your .pdf file as well then it can serve as verification that your system produces the same output as ours do.**Do not email your midterm solutions to the grader**; email them only to me.**Collaboration on homework is encouraged**, as long as each person understands the solutions, writes them up using their own words, and indicates—on the homework page—who their collaborators were.- In contrast,
**no collaboration or consultation of human or electronic sources—except for the "Text" listed above"—is allowed for either of the two midterms or the final exam.** **You must cite sources in your solutions.**If you rely on so-and-so's theorem, then you must state the theorem and tell me where you found it. Be specific: "the dual rank theorem" is not precise; in contrast, "[Climenhaga, Theorem 5.10]" is. Theorems are often known by many names, so I'm likely not to recognize many theorems by names you might attach.

Assignment | Due Date | Problems | Reading |
---|---|---|---|

Homework #1 | Wed. 13 September | in PDF or LaTeX | §1.1–1.6, §2.1, §2.3 |

Homework #2 | Wed. 27 September | in PDF or LaTeX | §2.2, §2.4, §3.1–3.3, §5.1 |

Midterm 1 | Wed. 4 October | in PDF or LaTeX | §1.7, §4.1, §3.5 |

Homework #3 | Fri. 20 October | in PDF or LaTeX | §4.2–4.6, §5.3–5.5, §6.3 |

Homework #4 | Fri. 3 November | in PDF or LaTeX | §7.1–7.4, §7.6 |

Midterm 2 | Fri. 10 November | in PDF or LaTeX | §8.1–8.3, §7.5 |

Homework #5 | Fri. 1 December | in PDF or LaTeX | §10.1–10.3, §10.5, §12.1 |

Final exam | Wed. 13 December, noon |

- 50% Homework
- 30% Midterms
- 20% Final exam

- list of all courses given in the Math Department in Fall 2017.
- Official University calendar for academic year 2017–2018.
- Fundamental University policies concerning academic dishonesty and related matters.

Many thanks are due to Jeremy Martin and Vic Reiner, who provided templates for this webpage many years ago.

The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by Duke University.

*ezramath.duke.edu*

*Fri Nov 17 04:54:50 EST 2017*

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