**Instructor**: Paul Jenkins

**Office**: 320 TMCB, 801-422-5868

**Email**: jenkins@math.byu.edu

**Lecture**: 11:00-11:50 AM MWF, 135 TMCB

**Office hours**: 3:00-3:50 PM MWF or by appointment

**Textbook**: Galois Theory, Third Edition, Ian Stewart, Chapman & Hall/CRC, ISBN 1-58488-393-6. Please note the list of known errors in the textbook online at http://flash.lakeheadu.ca/~avantuyl/courses/oldcourses/Stewart_Corrections.pdf and mark your book accordingly.

**Grading**: Homework and projects 30%, reading assignments 10%, two midterms 15% each, final exam 30%. Grades will be available on BYU Gradebook.

**Exams**: Two midterm exams in the testing center on October 7-9 and November 18-20. A study guide for the first exam is available here. A study guide for the second exam is available here. The final exam is scheduled for 11:00 AM-2:00 PM on Thursday December 19. The final exam will cover all material studied this semester.

**Homework**: Homework will be due on Mondays, Wednesdays, and Fridays at 5 PM in the box outside my office door. Homework assignments will be posted on the course website. Your homework should be neat and should include enough detail that another student from the class could follow your arguments. Homework that is not stapled, is excessively sloppy, or is written on paper torn from a spiral notebook may receive less than full credit. Late homework will not be accepted. Working in groups on homework is encouraged, but each student should write up each problem, without looking at other students’ written solutions. The three homework assignments with the lowest scores will be dropped.

**Prerequisite Course**: Math 371.

**Course Description**: This is a second course in abstract algebra focusing on field theory. The course is aimed at undergraduate mathematics majors, and it is strongly recommended for students intending to complete a graduate degree in mathematics. In addition to being an important branch of mathematics in its own right, abstract algebra is now an essential tool in number theory, geometry, topology, and, to a lesser extent, analysis. Outside of mathematics, algebra also has applications in cryptography, coding theory, quantum chemistry, and physics.

**Minimal Learning Outcomes**: Students should achieve mastery of the topics listed below. This means that they should know all relevant definitions, correct statements of the major theorems (including their hypotheses and limitations), and examples and non-examples of the various concepts. The students should be able to demonstrate their mastery by solving non-trivial problems related to these concepts, and by proving simple (but non-trivial) theorems about the below concepts, related to, but not identical to, statements proven by the text or instructor.

- Ring Theory
- Ideals and ring homomorphisms
- Quotient rings
- Prime and maximal ideals
- Polynomial rings over fields
- Factorization in polynomial rings
- Irreducible polynomials
- Polynomial division algorithm

- Field Theory
- Extensions of fields
- Field extensions via quotients in polynomial rings
- Automorphisms of fields
- Finite fields
- Fields of characteristic 0 and prime characteristic
- Splitting fields
- Galois extensions and Galois groups
- The Galois correspondence
- Independence of characters
- Fundamental Theorem of Galois Theory
- Fundamental Theorem of Algebra
- Roots of unity
- Solvability by radicals
- Ruler and compass constructions
- Insolvability of the quintic

This is a 3 credit class. The BYU Catalog states that “The expectation for undergraduate courses is three hours of work per week per credit hour for the average student who is appropriately prepared; much more time may be required to achieve excellence.” Thus, an average student should expect to spend at least 6 hours per week outside of lecture on working problems, reading the textbook, reviewing concepts, and completing assignments.

**Electronic devices**: On exams, only testing center calculators may be used. Do not use mobile phones or permit them to ring during class.

**Preventing Sexual Harassment**: Title IX of the Education Amendments of 1972 prohibits sex discrimination against any participant in an educational program or activity that receives federal funds. The act is intended to eliminate sex discrimination in education and pertains to admissions, academic and athletic programs, and university-sponsored activities. Title IX also prohibits sexual harassment of students by university employees, other students, and visitors to campus. If you encounter sexual harassment or gender-based discrimination, please talk to your professor, contact the Equal Employment Office at 801-422-5895 or 1-888-238-1062 (24 hours) or http://www.ethicspoint.com, or contact the Honor Code Office (4440 WSC) at 801-422-2847.

**Students with Disabilities**: BYU is committed to providing reasonable accommodation to qualified persons with disabilities. If you have any disability that may adversely affect your success in this course, please contact the University Accessibility Center office (2170 WSC) at 422-2767. Services deemed appropriate will be coordinated with the student and instructor by that office.

**Honor Code**: In keeping with the principles of the BYU Honor Code, students are expected to be honest in all of their academic work. Academic honesty means, most fundamentally, that any work you present as your own must in fact be your own work and not that of another. Violations of this principle may result in a failing grade in the course and additional disciplinary action by the university. Students are also expected to adhere to the Dress and Grooming Standards. It is the university's expectation, and my own expectation in class, that each student will abide by all Honor Code standards. Please call the Honor Code Office (4440 WSC) at 801-422-2847 if you have questions about those standards.