Abstract Algebra deals with the structure of algebraic systems. The familiar algebraic operations on numbers are distilled into mathematical entities called groups, rings and fields. This greatly widens the scope, utility and generality of algebra. The course is designed to expose you to some key algebraic ideas used in advanced mathematics, as well as to sharpen your abstract reasoning and theorem-proving skills. Although abstract algebra has many applications, our approach is primarily theoretical. You will write lots of proofs. You may have to think about things in new and challenging ways. This can require lots of time, hard work, deep thought and imagination. Prerequisites: MATH 300 and MATH 310, with a minimum grade of C. It is expected that you are familiar with material from these courses, including: elementary set theory, direct proof, contrapositive proof, proof by contradiction, if-and-only-if proof, induction, existence proof, counterexamples, relations, equivalence relations, partitions, integers modulo n, functions, matrix multiplication and inverses, determinants, vector spaces, subspaces, etc. The course covers selections from the first 21 chapters of the text. Your grade is determined by quizzes, participation, two tests and a final exam. Text: Abstract Algebra: Theory and Applications (2023 edition), By Thomas J. Judson (ISBN 978-1-9443251-8-3) Available at VCU's Bookstore or online outlets, or get a FREE PDF version here: https://judsonbooks.org/abstract-algebra-theory-and-applications/ Quizzes: There will be a short (10 minute) quiz most weeks, as posted on the Course Calendar. Quiz problems will be taken from an Exercise List. Tests: There will be two tests. Each is in-class and closed-book. Use of calculators is not allowed during tests. In writing the tests, I assume that you have been studying the material at least 6 hours per week outside of class. Test dates are listed on the Course Calendar. Many test questions will be selected from the Exercise List. Participation: Participation means that you in some way demonstrate intellectual involvement in the course. It does not necessarily mean that you ask questions or volunteer answers. Active participation may include your working lots of exercises and displaying preparedness, dedication and intellectual curiosity. Final Exam: The final exam is scheduled for 8:00-10:50 am, December 14. This closed-book exam is comprehensive, covering all material discussed in class. In writing the final exam, I will assume that you have been studying the material at least 6 hours per week outside of class, throughout the entire semester.
Attendance: I do not take attendance, but I do notice if you are not attending class. If your grades are high, I do not mind if you miss class occasionally; otherwise excessive absences may result in a reduced participation score. As a matter of courtesy, you should arrive punctually and stay for the entire duration of each class you attend. Please inform me ahead of time if you must leave early. I may administratively drop or withdraw from the course any student who has not attended class for four consecutive weeks without explanation. Make-up Work: I do not give makeup tests or quizzes. I will drop your lowest test grade and three low quiz grades. If you miss a test or quiz, then that counts as the dropped grade, up to the number of grades dropped. If you miss the final exam for a legitimate reason (i.e. a documented illness or emergency) then, following University protocol, you can request a grade of Incomplete (I) for the course, and you will need to make up the missed exam by the deadline set by the University. Notice: If I have questions about your work on any quiz or test, I may request a meeting to discuss the issues before returning the graded work. Important: All exams and quizzes are on campus, in-class and in-person. Generative AI: Neither the students nor the instructor will use generative AI in this course. Devices: In class, you are expected to be connected with the course. All devices not related to coursework (phones, etc.) should be muted and put away for the entire duration of any class. Smartwatches or Wearables that are voice or data connected (i.e. iOS and/or Android enabled devices such Apple watches, Meta glasses, etc.) are not permitted during quizzes and tests. Violation will be considered an honor offense. Recordings and Photography: Because of privacy considerations for all class members, recording video or audio in class is not allowed, except with documented approval by VCU's SAEO office. Please do not take photos in class. Office: Please feel free visit my office whenever you have a question, or if you just want to chat. If my posted hours are inconvenient, I will be happy to schedule an appointment. Tell me if you are having trouble. Catching up can be difficult once you get behind, so let me know as soon as you think there is a problem. Webpage: Information about this course is posted on my web page (not on Canvas). Go to https://richardhammack.github.io/Math401/. There you will find the syllabus, a calendar, copies of old tests, and other materials. Solutions for all graded work (quizzes and tests) will be posted after the due dates. Email: Any email correspondence concerning this course should be through VCU email. (University policy discourages communication about classes through other email addresses.) I may send email messages either to the whole class or individuals in the class. It is your responsibility to check your VCU email regularly. Exercises: For each chapter we cover, you should work as many of the exercises as possible for practice. Answers or hints can be found at the end of the text. Many of these problems will be used for the quizzes, tests and final exam. Keep in mind that there can be many correct approaches for some proof-oriented questions, so the fact that your solution does not match a given solution does not necessarily mean it is wrong. Ask me if you are ever unsure about the validity of your solution. Deadline to Withdraw: Friday, October 30. Boilerplate: Use VCU Libraries to find and access library resources, spaces, technology and services that support and enhance all learning opportunities at the university. (https://www.library.vcu.edu/) Read VCU's syllabus statements at https://faculty.provost.vcu.edu/faculty-resources/syllabus-resources/for-students// | |||||||||||||||||||||||||||||||