MATH 3230 – Abstract Algebra 1

**In Fall 2021, the mode of instruction for this class will be in-person.**


Course Description:

The fundamental topics of modern algebra including elementary number theory, groups, rings, polynomials and fields.

Prerequisites: A grade of C or better in MATH 2710 or 2142Q. Recommended preparation: MATH 2144Q or 2210Q. Cannot be taken after passing MATH 3231.
Credits: 3
Meets: Tuesdays, and Thursdays, 2-3:15, at MONT 414.


About the Instructor: Álvaro Lozano-Robledo

Alvaro Lozano-Robledo in action (Shawn Kornegay/UConn Photo)
Alvaro Lozano-Robledo in action (Shawn Kornegay/UConn Photo), see this UConn Today’s article.

I’m a Professor of mathematics at the University of Connecticut and the Director of Undergraduate Studies in the Department of Mathematics.

Office hours: Mondays 11-12 and Fridays 2:30-3:30 (online, via Webex) or by appointment (in person at MONT 233).


About the Book and Other Resources

    I will be following the main reference: Tom Judson’s “Abstract Algebra: Theory and Applications” (2020 Annual Edition) which you can find for free at the author’s website or you can purchase an inexpensive hard-copy. There are many other excellent references on abstract algebra, but I will only point out Prof. Keith Conrad’s website which contains many expository papers that you may find very useful.

    During the course we will discuss computability aspects of the theory, so it is helpful for students to familiarize themselves with computer packages that can handle computations on elliptic curves:


    Homework

    Homework sets will be due every other week. Most of what you learn in this course will be the result of working exercises that are designed to reinforce key concepts, develop skills, and test your understanding of the material. There will be textbook exercises due at the end of every other week on lecture material. Some of the exercises are straightforward, others are very complex. In general homework is due every other Thursday.

    Late homework will not be accepted. Although it should be done daily, it will only be collected once every other week, on Thursdays, in my office (MONT 233) *before* 3:30PM. The first assignment is due on Thursday 9/9.

    You are encouraged to talk with your classmates about the homework. If you have difficulties, do not waste time — get help! Please come to office hours!

    All problems numbers below refer to the online version of the book.

    Homework assignments:

    • Homework Set 1 (due 9/9):
      • Ch 1: 29.
      • Ch 2: 2, 5, 15 (a and b), 16, 17
      • Ch 3: 1 (b and f), 2, 4, 7, 10, 14, 17, 31, 41.
    • Homework Set 2 (due 9/23):
      • Ch 4: 1, 2 (you may use a calculator or computer!), 4 (b and d), 6 (note: D4 has 8 elements), 7 (the quaternions are defined in Example 3.15 in the book), 10, 22(only part (a) and definitely use a calculator/computer to proceed like in Section 4.3), 23, 26, 31, 34, 39.
      • Ch 5: 1(b and d), 2(b, d, and f), 5.
    • Homework Set 3 (due 10/7):
      • Ch 5: 6, 8, 13, [17, 18, and 19 — all three are related], 27.
      • Ch 6: 1, 2, 5(a and b), 7, 8 (suppose there is such an x value and raise it to the p-1), 9, 17, 21 (here phi is the Euler phi function).
    • Homework Set 4 (due 10/21):
      • Ch 9: 4, 5, 8, 10, 11, 12, 14, 18, 22, 24, 25, 34, 35, 41, 50.
    • Homework Set 5 (due 10/4):
      • Ch 10: 1(d), 4, 5, 7, 8, 9, 13, 14.
      • Ch 11: 2(b and c), 3, 5, 7, 9, 12, 16.

    Information about exams and grading for your class:

    Your grade in the course will be determined by your performance on the two midterm exams, a final exam, and your lecture grade. The lecture grade consists primarily of homework and class participation. Your entire grade is out of 550 points (see below):

    Here you will find information about midterms and exams.

      • FIRST EXAM: Tuesday, September 28th (in-class)
      • SECOND EXAM: Thursday, November 11th (in-class)
      • FINAL EXAM:
        • Take-home exam with open book/notes policy.

    The final exam will cover material from the entire course, but there will be an emphasis on material covered after the second prelim. No calculators are allowed on exams.

    Grade: The grading will be based on Prelim 1 (100 points), Prelim 2 (125 points), the final exam (175 points) and a lecture grade (150 points). The lecture grade will be based on homework and class participation.

    WARNINGS:

      1. If you cannot take an exam at the scheduled time, you MUST let your instructor know BEFORE the exam; you will almost certainly get an ’F’ on an exam if you miss it for any reason and then try to explain later.
      2. Incompletes will be given only under exceptional circumstances and then only to students who have a passing grade on a substantial part of the course. Do not expect to be granted an incomplete simply because you have fallen behind in the course.

    Tentative Schedule

    Week Topic
    1 Preliminaries, and Chapter 3: Groups
    2 Chapter 4: Cyclic Groups
    3 Ch. 5: Permutation Groups
    4 Ch. 6: Cosets and Lagrange’s Theorem
    5 Ch. 6: Fermat’s and Euler’s Theorems (also EXAM 1)
    6 Ch. 10: Conjugation, Factor Groups, Normal Subroups
    7 Ch. 11: Group Homomorphisms and Ch. 9: Isomorphisms
    8 Ch. 11: The Isomorphism Theorems and Ch. 9: Direct Products
    9 Ch. 13: Finite Abelian Groups
    10 Ch. 12: Matrix Groups and Symmetry
    11 Ch. 12: Symmetry (also EXAM 2)
    12 Ch. 14: Group Actions and the Class Equation
    13 Ch. 15: Sylow Groups and Theorems
    14 Ch. 15: Sylow Groups and Theorems

    University Policies

    • Policy Against Discrimination, Harassment and Related Interpersonal ViolenceThe University is committed to maintaining an environment free of discrimination or discriminatory harassment directed toward any person or group within its community – students, employees, or visitors.  Academic and professional excellence can flourish only when each member of our community is assured an atmosphere of mutual respect.  All members of the University community are responsible for the maintenance of an academic and work environment in which people are free to learn and work without fear of discrimination or discriminatory harassment.  In addition, inappropriate amorous relationships can undermine the University’s mission when those in positions of authority abuse or appear to abuse their authority.  To that end, and in accordance with federal and state law, the University prohibits discrimination and discriminatory harassment, as well as inappropriate amorous relationships, and such behavior will be met with appropriate disciplinary action, up to and including dismissal from the University.  Additionally, to protect the campus community, all non-confidential University employees (including faculty) are required to report sexual assaults, intimate partner violence, and/or stalking involving a student that they witness or are told about to the Office of Institutional Equity (OIE). Please be aware that while the information you provide will remain private, it will not be confidential and will be shared with University officials who can help.An exception to this reporting exists if students disclose information as a part of coursework submitted to an instructor in connection with a course assignment. Even in the absence of such obligation, all Employees are encouraged to contact OIE if they become aware of information that suggests a safety risk to the University community or any member thereof. The University takes all reports with the utmost seriousness.   More information, including resources and reporting options, is available at equity.uconn.edu and titleix.uconn.edu.
    • Student Conduct Code—Students are expected to conduct themselves in accordance with UConn’s Student Conduct Code.
    • Academic Integrity StatementThis course expects all students to act in accordance with the Guidelines for Academic Integrity at the University of Connecticut. Because questions of intellectual property are important to the field of this course, we will discuss academic honesty as a topic and not just a policy.  If you have questions about academic integrity or intellectual property, you should consult with your instructor.  Additionally, consult UConn’s guidelines for academic integrity.
    • CopyrightMy lectures, notes, handouts, and displays are protected by state common law and federal copyright law. They are my own original expression and I’ve recorded them prior or during my lecture in order to ensure that I obtain copyright protection. Students are authorized to take notes in my class; however, this authorization extends only to making one set of notes for your own personal use and no other use. I will inform you as to whether you are authorized to record my lectures at the beginning of each semester. If you are so authorized to record my lectures, you may not copy this recording or any other material, provide copies of either to anyone else, or make a commercial use of them without prior permission from me.
    • Students with Disabilities—The University of Connecticut is committed to protecting the rights of individuals with disabilities and assuring that the learning environment is accessible.  If you anticipate or experience physical or academic barriers based on disability or pregnancy, please let me know immediately so that we can discuss options. Students who require accommodations should contact the Center for Students with Disabilities, Wilbur Cross Building Room 204, (860) 486-2020, or http://csd.uconn.edu/.
    • Final Exam PolicyIn accordance with UConn policy, students are required to be available for their final exam and/or complete any assessment during the time stated. If you have a conflict with this time you must obtain official permission to schedule a make-up exam with the Dean of Students. If permission is granted, the Dean of Students will notify the instructor. Please note that vacations, previously purchased tickets or reservations, graduations, social events, misreading the assessment schedule, and oversleeping are not viable reasons for rescheduling a final.

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