**Instructor**: Paul Jenkins

**Office**: 282 TMCB, 801-422-5868

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

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

**Office hours**: 1:00-1:50 PM MWF or by appointment

**Textbook**: Abstract Algebra, An Introduction, Second Edition, Thomas W. Hungerford, Brooks/Cole, ISBN 978-0-03-010559-3, or Abstract Algebra, An Introduction, Third Edition, Thomas W. Hungerford, Brooks/Cole, ISBN 978-1-111-56962-4.

**TA:** Daniel Adams, adamsdan@mathematics.byu.edu

Office hours: 3-3:50 MWF, 4-4:50 TTh, location TMCB 330

**Grading**: Homework 25%, reading assignments 10%, three midterms 15% each, final exam 20%. Grades will be available on BYU Learning Suite.

**Exams**: In the testing center on September 26-27, October 26-27, and November 28-29. The final exam will be on Tuesday December 13 from 11 AM-2 PM. The final exam will cover all material studied this semester.

**Homework**: Homework will be assigned each day throughout the semester, and will be due at 4:30 PM in the box outside my office on the class day after it is assigned. Homework assignments will be posted on the course webpage. 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 lowest three homework assignments will be dropped.

**Electronic devices**: Do not use mobile phones or permit them to ring during class. Calculators may be used on homework; if you use a calculator or computer, you should indicate this. Calculators will probably not be very helpful on many problems. Only testing center calculators may be used on exams.

**Prerequisites**: Math 290 (Fundamentals of Mathematics) and Math 313 (Elementary Linear Algebra). Many problems in this course will be theoretical and will involve proofs, so it is essential that a student be familiar with methods of mathematical proof. Other topics you should be familiar with from prior courses include basic logic and set theory, functions, mathematical induction, and equivalence relations.

**Minimal learning outcomes**: See https://www.math.byu.edu/wiki/index.php/Math_371:_Abstract_Algebra_1. 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.

- Group Theory
- Basic Definitions
- Examples of groups
- Subgroups
- Lagrange's Theorem
- Homomorphisms
- Normal Subgroups
- Quotient Groups
- Isomorphism Theorems
- Cauchy's Theorem
- Direct Products
- The Symmetric Group
- Even and odd Permutations
- Cycle Decompositions

- Ring Theory
- Basic Definitions
- Examples of rings (both commutative and noncommutative)
- Ideals
- Ring homomorphisms
- Quotient rings
- Prime and maximal ideals
- Polynomial rings
- Factorization in polynomial rings
- Field of fractions of a domain

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.

**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 801-422-2767. 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.