MAT 401 Course Webpage Seminar in Mathematics: Algebra and Algorithms Tu Th 1PM — 2:20PM, Physics P—123 Fall 2017

Course Announcements Announcements about the course will be posted here. Please check the site regularly for announcements (which will also be given in lecture).

• There are now more details posted about the final paper.
• On Thursday, September 14th, there will be a guest lecturer. Problem Set 1 is due as scheduled.

Course Description The description in the undergraduate bulletin: "Discussions of a specific area of interest in mathematics. The work of each semester covers a different area of mathematics. May be repeated as topic changes. Prerequisites will be announced with the topic each time the course is offered." In Fall 2017 the topic is "Algebra and Algorithms": the commutative algebra of polynomials with an emphasis on effective algorithms and computational methods. We will also explore applications of these algorithms to problems in algebraic geometry, the theory of invariants for finite group actions, kinematic study of robots, and automatic theorem proving of results in plane geometry.

Prerequisites Registered students should have U3 or U4 standing. Students should also be familiar with linear algebra and abstract algebra at the level of MAT 310 and MAT 312 / 313. Students who have not passed MAT 310 and MAT 312 / 313 should speak with the instructor regarding permission to enroll.

Text The required textbook is Ideals, Varieties, and Algorithms, Third edition by David Cox, John Little, and Donal O'Shea.

Computer Algebra Software It will be useful to have access to one of the freely available computer algebra programs such as Macaulay 2 or Singular. Both of these freely available programs are included in many Linux distributions. There are versions that run under other operating systems as well. For instance, users of Windows can download these program as part of a Cygwin installation. Many of the functions of Macaulay2 and Singular are also available in commercial computer algebra packages such as Mathematica and Maple. Please check Softweb to see whether or not you have access to this software as a Stony Brook University student.

Lectures The instructor for this course is Jason Starr. After the first week, most lectures will be presented by the student participants of the seminar. There will be a sign-up sheet for speaker rotation in the first weeks of the semester. For the first rotation of speakers, the order will be randomly assigned by the instructor.

Speakers should meet with the instructor prior to their assigned lecture to discuss any questions and make sure they are focused on material that recurs later in the book. Students are also encouraged to meet with the instructor after the lecture for feedback.

Lecture is held Tuesdays and Thursdays, 1PM — 2:20PM in Physics P—123.

Office Hours

• Tuesdays 9:30AM — 10:30AM, Math Tower 4—108.
• Wednesdays 10 — 11AM, Math Tower P—143 (advising).
• Thursdays 9:30AM — 10:30AM, Math Tower 4—108.

Grading System Grading will be based on class participation (preparing and delivering lectures as well as active participation during presentations by other participants), weekly problem sets, a final paper, and a take-home final exam.

Required Syllabi Statements
The University Senate Undergraduate and Graduate Councils have authorized that the following required statements appear in all teaching syllabi (graduate and undergraduate courses) on the Stony Brook Campus.

Americans with Disabilities Act.
If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services, ECC (Educational Communications Center) Building, Room 128, (631) 632-6748. They will determine with you what accommodations, if any, are necessary and appropriate. All information and documentation is confidential.

Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information go to the following website: http://www.stonybrook.edu/ehs/fire/disabilities.

Academic Integrity Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty is required to report any suspected instances of academic dishonesty to the Academic Judiciary. Faculty in the Health Sciences Center (School of Health Technology Management, Nursing, Social Welfare, Dental Medicine) and School of Medicine are required to follow their school-specific procedures. For more comprehensive information on academic integrity, including categories of academic dishonesty please refer to the academic judiciary website at http://www.stonybrook.edu/commcms/academic_integrity/index.html.

Critical Incident Management Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of University Community Standards any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn. Faculty in the HSC Schools and the School of Medicine are required to follow their school-specific procedures.

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