Introduction to Modern Algebra
3
In person
TR 9:30 - 10:50
Wachman 16
Wachman 1035
TR 2:15-3:15, W 11:00-12:00, and by appointment.
Our course textbook is the 3rd Edition of "Abstract Algebra: An Introduction" by Thomas Hungerford, published by Cengage. The ISBN number for this book is
978-1111569624.
The grade will be based on two midterm exams, one final exam, a group project, and submitted homework. Grades will be computed in a straightforward manner, dividing points earned by possible points. Course averages correspond to letter grades as follows: 0-49 F, 50-54 D-, 55-64 D, 65-69 D+, 70-72 C-, 73-76 C, 77-79 C+, 80-82 B-, 83-86 B, 87-89 B+, 90-92 A-, 93-100 A.
Math 2111 (Basic Concepts of Math)
This course will deal primarily with theory of rings and (hopefully) groups with a particular emphasis on writing mathematical proofs in these areas. Students should learn how to formulate mathematical proofs about these objects, and express their proofs in organized, coherent, and grammatically correct prose.
Chapter One: Arithmetic of the Integers Revisited
1.1: The Division Algorithm
1.2: Divisibility
1.3: Primes and Unique Factorization
Chapter Two: Integer Congruence and Modular Arithmetic
2.1: Congruence and Congruence Classes
2.2: Modular Arithmetic
2.3: The Structure of Z/nZ
Chapter Three: Rings
3.1: Definitions and Examples of Rings
3.2: Basic Properties of Rings
3.3: Isomorphisms and Homomorphisms
Chapter Four: Arithmetic in the Polynomial Ring of a Field
4.1: Polynomial Arithmetic; the Division Algorithm for Polynomials
4.2: Divisibility In F[X]
4.3: Irreducibles and Unique Factorization
4.4: Polynomial Functions, Roots, and Reducibility
4.5: Irreducibilty in Q[X] (Polynomials over the Rational Field)
4.6: Irreducibility over the Real and Complex Fields
Chapter Five: Congruence in F[X] and Congruence Class Arithmetic
5.1: Congruence in F[X] and Congruence Classes
5.2: Congruence Class Operations
5.3: The Structure of F[X]/(p(X))
Chapter Six: Ideals and Quotient Rings
6.1: Ideals and Congruence
6.2: Quotient Rings and Homomorphisms; the Isomorphism Theorems
6.3: The Structure of R/I; Prime and Maximal Ideals
Test 1 - Thursday, 19 February
Test 2 - Thursday, 9 April
Final Exam - Thursday, 30 April, (8:00-10:00).
You must set the above times aside for the tests. Students with DRS Accommodations will have their tests rescheduled automatically. Otherwise, the only exceptions will be those with documented emergencies as per the policy below.
Attendance is required. Students who miss more than 4 classes without an excuse will have their grades lowered by one notch (e.g., from B to B-). Those who miss more than 8 classes without an excuse will have their grades lowered by two notches, etc.
To achieve course learning goals, students must attend and participate in classes, according to the course requirements. However, if you have tested positive for or are experiencing symptoms of a contagious illness, you should not come to campus or attend in-person classes or activities. It is the student’s responsibility to contact me to create a plan for participation and engagement in the course as soon as you are able to do so, and to make a plan to complete all assignments in a timely fashion.
It is important to foster a respectful and productive learning environment that includes all students in our diverse community of learners. Our differences, some of which are outlined in the University's nondiscrimination statement, will add richness to this learning experience. Therefore, all opinions and experiences, no matter how different or controversial they may be perceived, must be respected in the tolerant spirit of academic discourse.
Any student who has a need for accommodations based on the impact of a documented disability or medical condition should contact Disability Resources and Services (DRS) in Howard Gittis Student Center South, Rm 420 (drs@temple.edu; 215-204-1280) to request accommodations and learn more about the resources available to you. If you have a DRS accommodation letter to share with me, or you would like to discuss your accommodations, please contact me as soon as practical. I will work with you and with DRS to coordinate reasonable accommodations for all students with documented disabilities. All discussions related to your accommodations will be confidential.
Freedom to teach and freedom to learn are inseparable facets of academic freedom. The University has adopted a policy on Student and Faculty Academic Rights and Responsibilities (Policy # 03.70.02) which can be accessed here (opens in new tab/window).
Students will be charged for a course unless dropped by the Drop/Add deadline date. Check the University calendar (opens in new tab/window) for exact dates.
During the Drop/Add period, students may drop a course with no record of the class appearing on their transcript. Students are not financially responsible for any courses dropped during this period. In the following weeks prior to or on the withdrawal date students may withdraw from a course with the grade of "W" appearing on their transcript. After the withdrawal date students may not withdraw from courses. Check the University Calendar (opens in new tab/window) for exact dates. See the full policy by clicking here (opens in new tab/window).
The use of generative AI tools (such as ChatGPT, DALL-E, etc.) is not permitted in this class unless specifically announced for a particular assignment; therefore, any use of AI tools for work in this class may be considered a violation of Temple University's Academic Honesty policy and Student Conduct Code, since the work is not your own. The use of unauthorized AI tools will result in a grade of zero on the assignment; a second offense will be reported to the Student Conduct Board.
The grade "I" (an "incomplete") is only given if students cannot complete the course work due to circumstances beyond their control. It is necessary for the student to have completed the majority of the course work with a passing average and to sign an incomplete contract which clearly states what is left for the student to do and the deadline by which the work must be completed. The incomplete contract must also include a default grade that will be used in case the "I" grade is not resolved by the agreed deadline. See the full policy by clicking here (opens in new tab/window).
The following academic support services are available to students (all links open in a new tab/window):
The Math Consulting Center
Student Success Center
University Libraries
Undergraduate Research Support
Career Center
Tuttleman Counseling Services
Disability Resources and Services
If you are experiencing food insecurity or financial struggles, Temple provides resources and support. Notably, the Temple University Cherry Pantry and the Temple University Emergency Student Aid Program are in operation as well as a variety of resources from the Division of Student Affairs.
Final Exam - Thursday, 30 April, (8:00-10:00). Exam rooms will be announced at least one week in advance of the exam. Important: please note that if you miss the final exam and do not make alternative arrangements before the grades are turned in, your grade for the course will be F.
Homework will be assigned at each class. Once a week, a subset of these exercises will be collected and graded. Most of these problems require you to write a proof. Once the assignment has been graded, you will have an opportunity for a rewrite and a corresponding grade adjustment.
Since this is a Writing Intensive course, a group project requiring research, writing a paper, and a presentation is required. Details will be given in class.
There will be no regularly scheduled make up exams. In the case of a DOCUMENTED EMERGENCY that prevents a student from taking a test as scheduled, the student must contact their instructor and the course coordinator immediately in order to discuss alternative arrangements.