Abstract Algebra 1 - Spring 2017
Instructor: Christopher Sadowski
Email: csadowski at ursinus dot edu
Office: Pfahler Hall 101A
Office Hours: Monday and Wednesday 1:30-3:00, Tuesday 9:00-10:00, Friday 1:30-2:30, and by appointment.
Text: Contemporary Abstract Algebra, Ninth Edition, by Joseph A. Gallian.
Course Objectives: Students will learn the basic ideas and techniques of multivariable calculus. Students will be required to know:
- Groups: definition and examples, finite and infinite groups, abelian groups
- Subgroups: definitions and defining relations
- Permutations: Symmetric groups, dihedral groups, cycles and transpositions, alternating groups
- Homomorphisms and Isomorphisms: Definitions and properties, kernel, isomorphism theorems
- Cyclic groups: properties, definitions, and examples
- Quotient groups: definitions and properties, normal subgroups
- Sylow Theorems: theorems and applications
Learning Goals: This course will meet the following departmental learning goals:
- Organize and synthesize evidence to identify patterns and formulate conjectures
- Demonstrate mastery of standard proof techniques
- Communicate to technical and non-technical audiences, and work independently and in groups
Location: Pfahler 109
Meeting times: MWF 9:00-9:50
Grading:
-30% Homework
-15% Midterm 1
-15% Midterm 2
-15% Midterm 3
-25% Final Exam
Exams: Exams will be announced 2 weeks in advance. Make up exams will require documentation as proof of absence, and will be assessed on a case-by-case basis. The following dates are tentative:
Exam 1: 2/24/17
Exam 2: 3/24/17
Exam 3: 4/28/17
Final Exam:
Homework: There will be weekly homework assigned each Friday, to be completed online and finished by the following Friday.
Academic Honesty: Students may work together and discuss assignments with one another, but all work handed in must be solely the student's. Any incident of cheating on a quiz or exam will results in a grade of 0 for the assignment, with no make-up allowed. A second incident of cheating will result in a failing grade for the course. All incidents of cheating will be reported to the Dean's Office. Please refer to the Student Handbook on Academic Honesty and the Statement on Plagiarism.
Attendance: Students are expected to attend all classes. If you are unable to attend class for a legitimate reason, please email me before class.
Inclement Weather Policy: Students will be emailed in the event that class is cancelled due to inclement weather.Ac
Accommodations Policy: Students requiring accommodations should provide me with the appropriate paperwork from the Accommodations Office at the beginning of the semester.
SPTQ: Towards the end of the semester, students will be reminded to fill out SPTQ forms. These forms are invaluable to both the instructor and the department, since they provide valuable feedback to the instructor on how to improve the course, and provide evaluation information to the department chair. Honest constructive feedback (both positive and negative!) is appreciated.
Inclusive climate in the classroom: In this class we will work to promote an environment where everyone feels safe and welcome, even during uncomfortable conversations. Every voice in the classroom has something of value to contribute to class discussion. Because the class will represent a diversity of individual beliefs, backgrounds, and experiences, every member of this class must show respect for every other member of this class. You are encouraged to not only take advantage of opportunities to express your own ideas, but also, learn from the information and ideas shared by other students.
Syllabus (subject to change as the course progresses):
Week 1 (week of 1/16/17)
Chapter 0: Mathematical Preliminaries
Week 2: (week of 1/23/17)
Chapter 0: Mathematical Preliminaries
Chapter 1: Introduction to Groups
Week 3: (week of 1/30/17)
Chapter 2: Groups
Week 4: (week of 2/6/17)
Chapter 3: Finite Groups, Subgroups
Week 5: (week of 2/13/17)
Chapter 4: Cyclic Groups
Week 6: (week of 2/20/17)
Chapter 5: Permutation Groups
Week 7: (week of 2/27/17)
Chapter 6: Isomorphisms
SPRING BREAK
Week 8: (week of 3/13/17)
Chapter 7: Cosets and Lagrange's Theorem
Week 9: (week of 3/20/17)
Chapter 8: External Direct Products
Week 10: (week of 3/27/17)
Chapter 9: Normal Subgroups and Factor Groups
Week 11: (week of 4/3/17)
Chapter 10: Group Homomorphisms
Week 12: (week of 4/10/17)
Chapter 11: Fundamental Theorem of Finite Abelian Groups
Week 13: (week of 4/17/17)
Chapter 24: Sylow Theorems
Week 14: (week of 4/24/17)
Chapter 25: Finite Simple Groups
Week 15: (week of 5/1/17)
Chapter 26: Generators and Relations
Last day of classes is 5/3/17