Syllabus

MATH:6000:0001 - Introduction to Algebra I, Fall 2018

This course plan may be modified during the semester. Such modifications will be announced in advance during class periods. Every student is responsible for keeping abreast of such changes.

Instructor: Prof. Frauke Bleher

Office: 225K MLH (second floor, north wing), 335-1514

Email address: frauke-bleher@uiowa.edu

Office hours: 8:00-9:15AM TTh in 225K MLH

Lectures:

3:30-4:45PM TTh in 207 PH (Phillips Hall)

Course Web page:

http://homepage.divms.uiowa.edu/~fbleher/math6000.html
Check this for announcements, lecture schedule and homework, take-home exams, and other information about the course.

Prerequisites:

MATH:5000-5010 (Master's Level Abstract Algebra I/II) or equivalent, or consent of instructor

IMPORTANT: It is assumed that you know the basics about groups, rings, modules and fields, as taught in MATH:5000-5010.

Description of the Course:

This course is the first course of a two-semester course sequence MATH:6000-6010. In these two semesters we will discuss topics in group theory, category theory, module theory, ring theory, Galois theory, representation theory and algebraic geometry.

Objectives and Goals of the Course:

The main goal is to obtain general knowledge of abstract algebra needed for research specialization in algebra or for applications in other areas of mathematics. The objective is to provide a more rigorous discussion of selected topics in abstract algebra.

Texts:

We will mainly use the following texts for MATH:6000. You are not required to buy any of these books. These books have all been put on reserve in the media/reserve area at the south end of the first floor of the Main Library.

• David S. Dummit and Richard M. Foote: Abstract Algebra, 3rd Edition, John Wiley and Sons.
• Serge Lang: Algebra, Revised Third Edition, Springer Verlag (Graduate Texts in Mathematics No. 211).
• Joseph J. Rotman: Advanced Modern Algebra, Prentice Hall.

Other useful texts: (These have also been put on reserve in the media/reserve area at the south end of the first floor of the Main Library.)

• Charles W. Curtis and Irving Reiner: Methods of representation theory, Volume 1, John Wiley and Sons.
• Thomas W. Hungerford: Algebra, Springer Verlag (Graduate Texts in Mathematics No. 73).

Topics to be covered:

Topics from group theory (composition series, Jordan-Hölder, ... )

Topics from category theory (categories, free objects, products/coproducts, functors, natural transformations, ... )

Topics from module theory (products/coproducts, free modules, Hom functors, tensor product functors, projective/injective modules, flat modules, ... )

Topics from ring theory (Noetherian/Artinian rings and modules, Jacobson radical, simple and semisimple rings, Wedderburn's structure theorem, ... )

Homework:

Homework problems will be posted on the course web page under Lecture Schedule and Homework. It is anticipated that there will be a homework assignment every 1-2 weeks.

Please take homework seriously. You may collaborate on homework (discussing mathematics with your peers is an important skill), but you must write your own solutions. Your homework solutions should be literate. It is important that you explain your method, not just obtain an answer.

The expectation is that your homework is legible. The best way to ensure this is to either write neatly or to use LaTeX or something equivalent to write your homework.

Exams:

There will be a take-home midterm exam and a take-home final exam, the latter will be cumulative.

Take-home midterm exam: due at the beginning of the class on Thursday, October 18.

Take-home final exam: due by 11AM on Monday, December 10, in Prof. Bleher's mailbox.

The expectation is that your solutions to the exams are legible. The best way to ensure this is to either write neatly or to use LaTeX or something equivalent to write your solutions to the tests.

Getting help:

You are very welcome to see Prof. Bleher during her office hours or to make an appointment.

If you come outside of office hours and she is not in her office, the best way to reach her or to ask questions is by e-mail. Usually, Prof. Bleher will respond within a day or two.

Please take advantage of the help offered to you and come to office hours early if you feel you have problems following the course.

Attendance:

Regular attendance will be expected. Attendance will be taken at the beginning of each class.

If you must miss a class, please excuse yourself. If you have an acceptable excuse (such as illness, family emergency, attending a math conference, having a job interview, etc), you will be recorded as attending. You will be responsible for the material missed in class.

You are responsible for announcements made in class, which may concern changes in assignments, syllabus, etc.

Grades:

Grading Weights:

40% -- Attendance and Homework

30% -- Take-home Midterm Exam

30% -- Take-home Final Exam (cumulative)

Grades will be assigned on a curve that depends on the class.

Policy regarding late homework or late take-home exams:

Unexcused late homework or late take-home exams will not be accepted. Exceptions are illness and other serious and verifiable reasons.

If for any reason you are not able to submit your homework or take-home exams on time, please let Prof. Bleher know as soon as possible. If your reason is acceptable, Prof. Bleher may arrange with you for a different time to submit your work.

College of Liberal Arts and Sciences Policies and Procedures

• The Department of Mathematics has offices in 14 MLH. To make an appointment to speak with the departmental executive officer (DEO), also known as the Chair, call 335-0714 or contact the Departmental Secretary in 14 MLH.

• Administrative Home of the Course: The College of Liberal Arts and Sciences (CLAS) is the administrative home of this course and governs its add/drop deadlines, the second-grade-only option, and other policies. These policies vary by college (https://clas.uiowa.edu/students/handbook).

• Electronic Communication: Students are responsible for official correspondences sent to their University of Iowa email address (uiowa.edu) and must use this address for all communication within the University of Iowa (Operations Manual, III.15.2. Scroll down to k.11).

• Accommodations for Disabilities: The University of Iowa is committed to an educational experience that is accessible to all students. A student may request academic accommodations for a disability (such as mental health, attention, learning, vision, and physical or health-related condition) by registering with Student Disability Services (SDS). The student should then discuss accommodations with the course instructor (https://sds.studentlife.uiowa.edu/).

• Nondiscrimination in the Classroom: The University of Iowa is committed to making the classroom a respectful and inclusive space for all people irrespective of their gender, sexual, racial, religious or other identities. Toward this goal, students are invited to optionally share their preferred names and pronouns with their instructors and classmates. The University of Iowa prohibits discrimination and harassment against individuals on the basis of race, class, gender, sexual orientation, national origin, and other identity categories set forth in the University’s Human Rights policy. For more information, contact the Office of Equal Opportunity and Diversity at diversity@uiowa.edu or diversity.uiowa.edu.

• Academic Integrity: All undergraduates enrolled in courses offered by CLAS have, in essence, agreed to the College's Code of Academic Honesty. Misconduct is reported to the College, resulting in suspension or other sanctions, with sanctions communicated with the student through the University of Iowa email address.

• CLAS Final Examination Policies: The final exam schedule for each semester is announced around the fifth week of classes; students are responsible for knowing the date, time, and place of a final exam. Students should not make travel plans until knowing this final exam information. No exams of any kind are allowed the week before finals. (https://clas.uiowa.edu/faculty/teaching-policies-resources-examination-policies.)

• Making a Complaint: Students with a complaint should first visit with the instructor or course supervisor and then with the departmental executive officer (DEO), also known as the Chair. Students may then bring the concern to CLAS (https://clas.uiowa.edu/students/handbook/student-rights-responsibilities).

• Understanding Sexual Harassment: Sexual harassment subverts the mission of the University and threatens the well-being of students, faculty, and staff. All members of the University of Iowa community must uphold the University of Iowa mission and contribute to a safe environment that enhances learning. Incidents of sexual harassment must be reported immediately. For assistance, definitions, and the full University policy, see https://osmrc.uiowa.edu/.