**Instructor**: Paul Jenkins

**Office**: 279 TMCB, 801-422-5868

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

**Lecture**: 11:00-11:50 AM MWF, 112 TMCB

**Office hours**: 3:00-3:50 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:** Clayton Williams, clayton.williams@mathematics.byu.edu, 254 TMCB

Office hours: 2:00-2:50 PM Monday-Friday (may move to 205 TMCB if 254 is too crowded)

**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 February 2-4 (study guide here), March 2-4 (study guide here), and April 4-6 (study guide here). The final exam will be on Saturday April 16 from 11 AM-2 PM in room 112 TMCB. 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 11:00 AM on Gradescope on the class day after it is assigned. Homework assignments will be posted on the course webpage and Learning Suite. Your homework should be neat and should include enough detail that another student from the class could follow your arguments. Homework that is is excessively sloppy or is not readable 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 permit mobile phones 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.

**Prerequisites**: Math 290 (Fundamentals of Mathematics) and Math 213 or 313 (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 Registration Policy 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.

**COVID-19:** While COVID-19 conditions persist and until further notice, students and faculty are required to wear masks at all times during class; faculty are not at liberty to waive this expectation. Students who feel sick, including exhibiting symptoms commonly associated with COVID-19 (fever; cough; shortness of breath/difficulty breathing; chills; muscle pain; sore throat; new loss of taste or smell; etc.) should not attend class and should work with their instructor to develop a study plan for the duration of the illness.

**Preventing & Responding to Sexual Misconduct**: Brigham Young University prohibits all forms of sexual harassment—including sexual assault, dating violence, domestic violence, and stalking on the basis of sex—by its personnel and students and in all its education programs or activities. University policy requires all faculty members to promptly report incidents of sexual harassment that come to their attention in any way and encourages reports by students who experience or become aware of sexual harassment. Incidents should be reported to the Title IX Coordinator at t9coordinator@byu.edu or (801) 422-8692 or 1085 WSC. Reports may also be submitted online at https://titleix.byu.edu/report or 1-888-238-1062 (24-hours a day). BYU offers a number of resources and services for those affected by sexual harassment, including the university's confidential Sexual Assault Survivor Advocate. Additional information about sexual harassment, the university's Sexual Harassment Policy, reporting requirements, and resources can be found in the University Catalog, by visiting http://titleix.byu.edu, or by contacting the university's Title IX Coordinator.

**Student Disability**: Brigham Young University is committed to providing a working and learning atmosphere that reasonably accommodates qualified persons with disabilities. A disability is a physical or mental impairment that substantially limits one or more major life activities. Whether an impairment is substantially limiting depends on its nature and severity, its duration or expected duration, and its permanent or expected permanent or long-term impact. Examples include vision or hearing impairments, physical disabilities, chronic illnesses, emotional disorders (e.g., depression, anxiety), learning disorders, and attention disorders (e.g., ADHD). If you have a disability which impairs your ability to complete this course successfully, please contact the University Accessibility Center (UAC), 2170 WSC or 801-422-2767 to request a reasonable accommodation. The UAC can also assess students for learning, attention, and emotional concerns. If you feel you have been unlawfully discriminated against on the basis of disability, please contact the Equal Opportunity Office at 801-422-5895, eo_manager@byu.edu, or visit https://hrs.byu.edu/equal-opportunity for help.

**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. Adherence demonstrates respect for yourself and others and ensures an effective learning and working environment. It is the university's expectation, and every instructor's expectation in class, that each student will abide by all Honor Code standards. Please call the Honor Code Office at 422-2847 if you have questions about those standards.