Mondays and Wednesdays 11:25-12:40
Location: ??-TBD
This course is cross-listed for undergraduate and graduate students. Official course syllabi for each, along with learning objectives, can be found here.
In this course we will discuss systems of polynomial equations (ideals), their solution sets (varieties), and how these objects can be effectively manipulated (algorithms). This is a theoretical course with view toward applications, treating structure, properties and relationships of these objects. Writing and communicating mathematical concepts is an important part of the course.
Math 230 Introduction to Discrete Mathematics or Math 332 Elementary Linear Algebra. In particular, familiarity with proofs and mathematical structures.
(Note: our textbook says it assumes knowledge of linear algebra. If you have not taken 332 yet and are worried about matrices - you probably met a matrix or two in your calculus courses. You should be able to catch up on the concepts needed in our text; ask, and you will be provided background information on such topics if they arise.)
Sonja Petrović
Office: the Tower, 18th floor, office 186C-1.
Office hours: Time to be determined, most likely on Wednesdays after class. Likely located at the Kaplan Institute.
e-contact: The best way to e-communicate with the instructor is via Canvas. If you must email, please use sonja.petrovic@illinoistech.edu and put the course number in the subject line. Your message will generally be answered within 1-2 business/teaching days.
Components of the final grade: homework completion (5%), homework group oral check-in (15%), attendance (5%), midterm exam (25%), final exam (30%), project (20%). More information in the drop-down. >>This information is subject to change until the first day of classes.<<
The grading scale will be no more strict than A:90-100, B:78-89, C: 65-77, D:53-64.
Regular class attendance and class participation is important and expected. You are expected to come to lectures, participate in discussions, read the textbook (including examples not covered in class), and ask questions. Students are responsible for all announcements and supplements given within any lecture. It is totally acceptable to miss a class or two; but missing more than 20% of the lectures will result in losing attendance points.
Are you shy, but want to participate actively?
Participation can have two components: in-class activities and asynchronous activities on Canvas. Details will be shared during the first week of classes. We will use Canvas discussion board for participation, class discussion, chats, Q&A, etc. The system is highly catered to getting you help fast and efficiently from classmates, the TA, and myself. Rather than emailing questions to the teaching staff, I encourage you to post your questions on the appropriate channels in Canvas.
Homework problem sets will be posted online at least one week before the due date. Typically, there will be weekly homework, with possible exceptions around exam time. There may also be reading assignments to which you will be asked to respond.
Important note on written work and oral check-ins: Homework is graded for completion only — since this is a small course without a teaching assistant or grader, this keeps things manageable. However, keeping up with the homework is essential: three times during the semester (as announced on the course schedule), class time will be used for a group check-in. In groups of 3–4, you will work through a problem drawn from recent homework topics — on the spot, together. Each student will also receive individual follow-up questions. These sessions are scored 0 / 3 / 5 per round; three rounds × 5 pts = 15% of your final grade. Students who have been doing the homework will find these sessions straightforward.
Since this is expected to be a small course and we will have no teaching assistant or grader due to university funding, the homework grading policy has updated from the standard full grading of the paper homework submissions. All oral check-ins are based solely on your HW work submitted.
There will be a regular "in-class" exam sometime mid-semester, the date to be determined at least two weeks in advance. Exam dates and topics covered will be announced on the course homepage and in class. Make-up exams will be given only in case of a documented emergency. A comprehensive final exam will be given during the IIT final exam week.
Exams will generally consist of three types of problems: (1) examples, counterexamples, definitions; (2) algorithms, computations and applications; (3) proofs (some routine, some of moderate difficulty).
Exam topics
No surprises. Everything from the book, notes, syllabus.
Students are required to work on an independent project, typically during the second half of the semester. The project will involve studying a class-related topic, and writing a short summary paper on this subject, which will go through several stages of revision. Your paper should be self-contained and accessible to the other participants in the class. Achieving this should take about 5 pages (Path A: 4–5pp, Path B: 5–6pp). Toward the end of the course, you will read a referee report written by another student in the class, and you will also write such a report about the paper of another student. A list of possible topics will be posted in September.
It is expected that the project will be done in groups of two, sometimes three students (math 431) or individually (math 530); but this information will be determined after the start of the semester, based on final class size.
Graduate Requirement: Students enrolled in MATH 530 are required to deliver a 15-minute oral presentation on their project. This presentation is a mandatory component of the final grade and is not required for MATH 431 students.