MAT 333 Abstract Algebra, Section 01, CN 45122 Fall 2021


Class meets online via zoom MWF 11:30 AM - 12:45 PM, the zoom meeting information will be announced on Blackboard


Instructor: Serban Raianu, office: NSM E-108, office phoner: (310) 243-3139, cell phone: (657) 204-5612

e-mail address:, URL:;

office hours (same zoom link as classes): Monday, Wednesday: 8:20 AM - 9:50 AM, Friday: 11:30 AM 12:30 PM, or by appointment.



Course Description: MAT 333, Abstract Algebra, covers material from the first two chapters of the textbook: sets, groups, rings, polynomial rings, fields.


Text: Algebra I: Groups, Rings, & Arithmetic, by Serban Raianu, PDF available online at


Objectives: After completing MAT 333 the student should be able to: state definitions of basic concepts (e.g., congruence, groups, rings, integral domains, fields, subrings, homomorphisms, ideals); understand and use the Euclidean algorithm; understand and use modular arithmetic; state major theorems (e.g., the division algorithm, the unique factorization theorem, the remainder theorem, the factor theorem, the isomorphism theorems) and be able to identify the structures to which each theorem applies (e.g. the integers, integral domains, polynomial rings F[x] where F is a field, groups, etc.) ; find examples of objects that satisfy given algebraic properties (a noncommutative ring, a commutative ring but not an integral domain, etc)


Prerequisites: MAT 271 or equivalent with a grade of "C" or better.


Grades: Grades will be based on two zoom video meetings 15-minutes examinations (50% total), a comprehensive final examination (20%), and quizzes, homework, video and other assignments (30%) for the remainder.

The exact grading system for your section is the following:


An oral examination will consist in giving a definition or a statement for a notion or result studied in class, and explaining two homework problems from the homework assignments. A list of the possible definitions and statements is posted on Blackboard. A definition or a statement will be chosen by selecting a random number from 1 to the number of definitions and statements on the list. The homework problems will be selected by choosing randomly the lecture number, then a problem number from 1 to the total number of problems in the assignment corresponding to that lecture. For example, the definition/statement number 5 will refer to the fifth item on the list of possible definitions or statements on the list. The homework problem (1,13) will refer to problem 9 in Section 1.3 in CLP-1: this is the 13th problem in the homework assignment for Lecture 1.1. Each of the two oral exams will be graded on a 100 scale, then the sum of the scores is divided by 4 and denoted by E.


Homework will be due every week, the day before quiz days, and each homework is worth 10 points. Each week two of the problems from the homework due for that week will be selected and graded on a scale from 0 to 3. The remaining 4 points will be awarded for completeness of the homework assignment. Submitting solutions copied from the back of the book will bring little or no credit, since copying solutions will not prepare you for answering questions during the oral examinations. The average of all homework scores is denoted by H. Homework will be submitted as a pdf with your paper work on Gradescope. There is no need to match the pages with the problems when submitting the homework, see

Gradescope can be accessed from the link in Content in your Blackboard course, and you can practice submitting your work on Gradescope using the assignment called Submission practice, which will remain open throughout the semester. You might be asked to explain your work on a submitted problem. Failure to provide an explanation might result in a score of zero for the entire homework assignment. No late homework will be accepted.



15 minutes quizzes will be given every week, and will be graded on a scale from 1 to 10. The average of the quizzes scores is denoted by Q. While taking the quiz the video camera on zoom needs to be on and you need to be in the frame. Each quiz will consist of one problem, similar but not necessarily identical to one of the homework problems assigned for that week. The quiz will be taken on Gradescope, where you will read the problem and submit your written answers. No makeup quizzes will be offered.


There are also 10 points awarded for explaining one homework problem on video. This portion of the grade is denoted by V. Videos will be due the day before quiz days and will have to be uploaded on Flipgrid

The homework problems from which to choose one problem to explain on video appear in boldface in the schedule below. No late submissions will be accepted.



The final exam, which will consist of fifteen problems similar to problems assigned as homework throughout the semester, will be graded out of a maximum possible 200, then the score is divided by 10 and denoted by F. The final exam will be taken on Gradescope, and the camera on zoom needs to be on (with you in the frame) for the duration of the final exam. When submitting the work for the final exam pages and problems will have to be matched, failure to do that might result in points deducted. Webcams can be requested from the IT department if necessary.


To determine your final grade, compute E+H+Q+V+F. The maximum is 100, and the grade will be given by the rule:

A: 93‑100; A‑: 90‑92; B+: 87‑89; B: 83‑86; B‑: 80‑82

C+: 77‑79; C: 73‑76; C‑: 70‑72; D+: 67‑69; D: 60‑66; F: Less than 60. You will be able to follow your progress in the class in Blackboard under Grade Center throughout the semester.


Accommodations for Students with Disabilities: California State University, Dominguez Hills adheres to all applicable federal, state, and local laws, regulations, and guidelines with respect to providing reasonable accommodations for students with temporary and permanent disabilities. If you have a disability that may adversely affect your work in this class, I encourage you to register with Student disAbility Resource Center (SdRC) and to talk with me about how I can best help you. All disclosures of disabilities will be kept strictly confidential. Please note: no accommodation may be made until you register with the SdRC in WH D-180. For information call (310) 243-3660 or to use telecommunications Device for the Deaf, call (310) 243-2028.


Academic Integrity: The mathematics department does not tolerate cheating. Students who have questions or concerns about academic integrity should ask their professors or the counselors in the Student Development Office, or refer to the University Catalog for more information. (Look in the index under "academic integrity".) Using homework solving or derivative/integral computing websites, or collaborating in chat rooms during tests in this class is prohibited, the penalty for being caught is an automatic F in the class and referral for disciplinary action.


Exam and quiz rules: Students must email a picture of their CSUDH student ID at the beginning of the semester, then they have to be on zoom with the camera on for the duration of the quiz/exam. Cell phones, headphones, and browsing the internet (other than connecting to Gradescope) may not be used at all during tests.










Tentative schedule and homework assignments


M 8/23:           Lecture 1.1: 1.1 Sets and functions: 1.1.2,1.1.6,1.1.7,1.1.8,1.1.11,1.1.12 (6 problems)

W 8/25:           Lecture 1.2:  1.1 Sets and functions: 1.1.13,1.1.15,1.1.16,1.1.17 (4 problems)

M 8/30:           Lecture 1.3: 1.2 The integers: 1.2.3,1.2.4,1.2.6,1.2.9,1.2.12 (5 problems)

W 9/1:             Lecture 1.4: 1.2 The integers: 1.2.14,1.2.16,1.2.17,1.2.18,1.2.26  (5 problems)

M 9/6:             Labor Day

W 9/8:             Lecture 1.5: 1.3 Equivalence relations and factor sets: 1.3.3, 1.3.5  (2 problems)

M 9/13:           Lecture 1.6: 1.3 Equivalence relations and factor sets: 1.3.9,1.3.12 (2 problems)

W 9/15:           Lecture 1.7: 1.3 Equivalence relations and factor sets: 1.3.19 (1 problem)

M 9/20:           Lecture 1.8: 1.4 Groups and morphisms of groups: 1.4.3,1.4.4,1.4.5 (3 problems)      

W 9/22:           Lecture 1.9:  1.4 Groups and morphisms of groups 1.4.6,1.4.7,1.4.8,1.4.11,1.4.13

(5 problems)

M 9/27:           Lecture 1.10:  1.5 Subgroups and normal subgroups: 1.5.3,1.5.4,1.5.6,1.5.8 (4 problems)

W 9/29:           Lecture 1.11:  1.5 Subgroups and normal subgroups: 1.5.13,1.5.15 (2 problems)

M 10/4:           Lecture 1.12:  1.6 Factor groups: 1.6.2,1.6.4 (2 problems)

W 10/6:           Review             

M 10/11:         Oral Exam Week 1

W 10/13:         Oral Exam Week 1

M 10/18:         Lecture 2.1: 1.6 Factor groups: 1.6.16,1.6.17 (2 problems)

W 10/20:         Lecture 2.2: 1.7 Finite groups and the Lagrange theorem:1.7.3,1.7.7,1.7.8,1.7.10,1.7.11 (5 problems)

M 10/25:         Lecture 2.3: 1.7 Finite groups and the Lagrange theorem: 1.7.14,1.7.19,1.7.20,1.7.21 (4 problems)

W 10/27:         Lecture 2.4:  2.1 Rings and morphisms of rings: 2.1.2, 2.1.4,2.1.6,2.1.7,2.1.8, 2.1.13

 (6 problems)

M 11/1:           Lecture 2.5: 2.2 Subrings and ideals: 2.2.2,2.2.3,2.2.5,2.2.6 (4 problems)

W 11/3:           Lecture 2.6: 2.2 Subrings and ideals: 2.2.7,2.2.8,2.2.10,2.2.12 (4 problems)

M 11/8:           Lecture 2.7: 2.3 Factor rings: 2.3.4,2.3.6,2.3.8,2.3.10,2.3.16 (5 problems)

W 11/10:         Lecture 2.8: 2.4 Prime and maximal ideals: 2.4.2,2.4.3,2.4.5,2.4.10,2.4.12,2.4.15 (6 problems)

M 11/15:         Lecture 2.9:  2.6 Polynomial rings: 2.6.3,2.6.6,2.6.7(3 problems)

W 11/17:         Lecture 2.10:  2.6 Polynomial rings: 2.6.9,2.6.10 (2 problems)

M 11/22:         Lecture 2.11:  2.6 Polynomial rings: 2.6.11,2.6.12 (2 problems) 

W 11/24:         Review

M 11/29:         Oral Exam Week 2

W 12/1:           Oral Exam Week 2




Final examination: Wednesday, December 8, 11:30 AM - 1:30 PM.














Important Dates:





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