Math 435, Basic Abstract Algebra - Fall 2020

Instructor: Jack Huizenga

Jack Huizenga
  • Meeting times: MWF 3:35-4:25
  • Location: Zoom, link on Canvas
  • First meeting: Monday, August 24
  • Office hours: Immediately after class each day or by appointment. Aditionally, we will schedule an evening problem session in coordination with the homework.
  • Textbook: John B. Fraleigh, A First Course In Abstract Algebra, 7th edition. The book Charles Pinter, A Book of Abstract Algebra, might also be useful for a second point of view.
Brief course description: We will cover the first six chapters of the textbook. This is a first course in abstract algebra, focusing on the three main topics of study in algebra: groups, rings, and fields. On the one hand, groups explore the concept of symmetry in mathematics; on the other hand, rings and fields generalize the familiar concept of number to more abstract settings. The interplay between these two seemingly different ideas is incredibly important in modern mathematics. Students will learn to analyze concrete examples of these objects, as well as to reason abstractly and provide their own proofs of theorems in abstract algebra.
Prerequisites: Math 311W, Concepts of Discrete Mathematics is the only formal prerequisite. On the other hand, this is one of the more challenging 400-level math courses, and it will be helpful to have seen other material at a similar level before. If for example you plan on taking Math 436 (Linear Algebra) at some point, it would be natural to take that before taking this course, as it is generally an easier course that will prepare you well for the more challenging topics in this course. Familiarity with proof writing will certainly be helpful, although one of the main goals of this course is to become more proficient in proof writing.
Course Delivery: The course will be presented online via Zoom in a remote synchronous mode. Students are strongly encouraged to both ask and answer questions by "raising their hand" within Zoom. The instructor will record lecture notes on a tablet device and post the notes from class each day. Recordings of lectures will also be posted after class, but in-class attendance is strongly encouraged whenever feasible. You and other students will and *should* have many questions to be answered, and you should always feel free to interrupt when something is not clear. If you have a question, many of your fellow students probably have the same question, and we can save a great deal of time and confusion by addressing it.
Homework: Homework is by far the most important part of the course. The only way to learn advanced mathematics is to do advanced mathematics. Weekly homework assignments will be posted on Canvas most Fridays, and you will upload a pdf of your homework on Canvas by the next Friday at class time. A typical homework set will consist of a reading assignment, 5 exercises to be turned in, and a list of additional textbook exercises that you should complete for yourself. You should expect the homework to take 5-10 hours per week to complete. Please write your solutions clearly and carefully, using complete sentences and paragraphs to explain all steps of your proofs or computations.

Solutions to homework will be posted after class on the day it is due, so late homework will not be accepted for any reason. Your lowest score will be dropped at the end of the semester.

Collaboration: You are encouraged to discuss homework problems with your fellow students. However, you have to write up your solutions by yourselves and show originality. Please write the names of any students you collaborated with on your assignment.
Exams: We will tentatively have exams on the following dates.

Week 6: Exam 1, Friday Oct. 2
Week 11: Exam 2, Friday Nov. 6
Final exam: To be announced

Grading: The homework and exams will count for the following portions of your grade.

Homework: 20%
Exam 1: 20%
Exam 2: 20%
Final: 40%

Letter grades will be assigned based on the cumulative score; the ranges corresponding to letter grades will be determined based on the difficulty of the exams and the following rubric.

A: Able to perform basic computations in algebra and recite the definitions from the course. Demonstrates solid understanding of the theoretical aspects of the course.
B: Able to perform basic computations in algebra and recite the definitions from the course. Demonstrates some understanding of the theoretical aspects of the course.
C: Able to perform basic computations in algebra and recite the definitions from the course.
D/F: Fails to meet the expectations for a C.

Cumulative scores of 85/75/65 will receive at least an A-/B-/C-; however, the final breakpoints may be lowered slightly. Grade ranges will be discussed in more detail after each exam.

Make-up exams: Any conflict with scheduled exams should be discussed with the instructor as soon as possible. No accomodations will be provided for missed exams without a valid excuse.

Final exam scheduling: Conflicts for the final exam are determined by scheduling; they cannot be scheduled through the Mathematics Department. A student with a final exam conflict must take action to request a conflict exam through eLion during the final exam conflict filing period.

Academic Integrity Statement: Academic integrity is the pursuit of scholarly activity in an open, honest and responsible manner. Academic integrity is a basic guiding principle for all academic activity at The Pennsylvania State University, and all members of the University community are expected to act in accordance with this principle. Consistent with this expectation, the University’s Code of Conduct states that all students should act with personal integrity, respect other students’ dignity, rights and property, and help create and maintain an environment in which all can succeed through the fruits of their efforts.

Academic integrity includes a commitment by all members of the University community not to engage in or tolerate acts of falsification, misrepresentation or deception. Such acts of dishonesty violate the fundamental ethical principles of the University community and compromise the worth of work completed by others.
Disability Statement: Penn State welcomes students with disabilities into the University’s educational programs. Every Penn State campus has an office for students with disabilities. Student Disability Resources (SDR) website provides contact information for every Penn State campus. For further information, please visit the Student Disability Resources website.

In order to receive consideration for reasonable accommodations, you must contact the appropriate disability services office at the campus where you are officially enrolled, participate in an intake interview, and provide documentation. See documentation guidelines. If the documentation supports your request for reasonable accommodations, your campus disability services office will provide you with an accommodation letter. Please share this letter with your instructors and discuss the accommodations with them as early as possible. You must follow this process for every semester that you request accommodations.

Counseling and Psychological Services Statement:

Many students at Penn State face personal challenges or have psychological needs that may interfere with their academic progress, social development, or emotional wellbeing. The university offers a variety of confidential services to help you through difficult times, including individual and group counseling, crisis intervention, consultations, online chats, and mental health screenings. These services are provided by staff who welcome all students and embrace a philosophy respectful of clients’ cultural and religious backgrounds, and sensitive to differences in race, ability, gender identity and sexual orientation.

Counseling and Psychological Services at University Park  (CAPS): 814-863-0395

Counseling and Psychological Services at Commonwealth Campuses

Penn State Crisis Line (24 hours/7 days/week): 877-229-6400
Crisis Text Line (24 hours/7 days/week): Text LIONS to 741741

Educational Equity Statement: Penn State takes great pride to foster a diverse and inclusive environment for students, faculty, and staff. Acts of intolerance, discrimination, or harassment due to age, ancestry, color, disability, gender, gender identity, national origin, race, religious belief, sexual orientation, or veteran status are not tolerated and can be reported through Educational Equity via the Report Bias webpage.