Math 435, Basic Abstract Algebra - Spring 2020

Instructor: Jack Huizenga

Jack Huizenga
Office: 324 McAllister
  • Meeting times: MWF 3:35-4:25
  • Location: 215 Armsby Building
  • First meeting: Monday, January 13
  • Office hours: Monday 4:30-5:30, Wednesday 4:30-5:30, or by appointment.
  • 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.
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 the webpage most Fridays, and they are due in class the following Friday. 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. Please write your solutions clearly and carefully, using complete sentences to explain all steps of your proofs or computations.

If you have to miss class on the due date, you can turn in your assignment early to my box in the McAllister building. 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, Wednesday Feb. 19
Week 11: Exam 2, Friday Apr. 3
Final exam: 6:50 PM Tuesday, May 5 - 8:40 PM Thursday, May 7

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 80/70/60 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: All make-up exams for permissible excuses must be requested in advance of the exam. Travel scheduled on an exam date is not a permissible excuse. There will be no make-up exams for unexcused abscences. At the instructor's discretion, in the case of a missed midterm your other exam scores may be used to determine your grade.

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: All Penn State policies regarding ethics and honorable behavior apply to this course.
Disability Statement: Penn State welcomes students with disabilities into the University's educational programs. The Office for Disability Services Web site provides contact information for every Penn State campus: . For further information, please visit the Office for Disability Services Web site: .
Homework assignments (Solutions available on Canvas) :