Welcome to MAT 364 Topology and Geometry

Fall 2019 -  Syllabus


Intructor, grader, book...


Instructor : Moira Chas, office 3-113 Math Tower, e-mail: moira.chas“at”stonybrook.edu

Instructor's Office hours: Monday 11:00:00-11:00 ,  Wednesday 11:00-1:00, or by appointment.

Class meetings: MWF   10:00am-10:53amm Earth&Space; 183

Grader :Frederik Benirschke

Grader's office hours:  Office Hours:  Mon 1:00pm-2:00pm (Office 2-118 Math Tower)
                                      MLC Hours:  Tu 10:00am-12:00p

Textbook : Beginning Topology by Sue Goodman

Course Materials (slides, notes, etc) are here (Including the slides of the first day which are also part of the syllabus).

About this course

From the undergraduate bulletin

A broadly based introduction to topology and geometry, the mathematical theories of shape, form, and rigid structure. Topics include intuitive knot theory, lattices and tilings, non-Euclidean geometry, smooth curves and surfaces in Euclidean 3-space, open sets and continuity, combinatorial and algebraic invariants of spaces, higher dimensional spaces.
 
We will cove  Chapters 1,2, 3, 4, 6 from the textbook, and possibly more if time permits. The schedule will be updated with the progress of the course.

Learning outcomes

  • Understand the basic topological concepts: open, closed, compact and connected sets in a Rn and being able to apply these concepts to a given set.
  • Understand the concept of continuous function between topological spaces and being able to determine whether a given function is continuous.
  • Understand the concepts of homeomorphisms between spaces and  topological properties.
  • Compute the Euler characteristic of a space.
  • Being able to classify a given surface according to genus, orientability and number of boundary components.
  • Being able to state the four color theorem and generalization of this theorem to other surfaces.
  •  Compute the fundamental group of basic topological spaces (such as surfaces)

Exams and Grading

 
There will be two midterm exams (in class), and a cumulative final exam. The dates will be listed below. Success on the exams will require correct and efficient solutions to the more difficult of the homework problems.

Make sure that you can attend the exams at the scheduled times; make-ups will not be given.  If one midterm exam is missed because of a serious (documented) illness or emergency, the semester grade will be determined based on the balance of the work in the course. Students attending University Sponsored Events or in need to be absent for religious holidays should contact the instructor on the first two weeks of classes to discuss an appropriate plan.

Exam When and where
% of Final Grade
Midterm 1
 Friday Oct 11th
 In class 15%
Midterm 2
 Friday Nov 22nd
 In class
 15%
Final Exam Wed, Dec 18,
2:15pm-5:00pm
 To be announced. 40%
Homework Every Friday
20%
Class participation 10%





Homework

Homework will be assigned weekly and is due Wednesday before class. Homework is mandatory because it is an essential part of the course: It is nearly impossible to learn mathematics without working on problems
  • There will be about five problems each week
  • Each written problem is worth 5 points. Depending on the length of the assignment, only selected problems will be graded.
  • You are encouraged to study with and discuss problems with others from the class, but write up your own homework by yourself in your own words . All your collaborators and sources should be listed.
  • Under no circumstance you are allowed to browse in Internet trying to "fish" for solutions to the homework problems. Copying solutions to the homework problems from a website will be consider academic dishonesty and reported to the Academic Judiciary.
Rubric for grading problems (adapted from Emert - Parish book and  this website)

Points Solution Justification Conceptual understanding Mathematical errors
5 Complete and correct All steps are justified Apparent Minor
4 Almost complete and correct Most steps are justified A bit less than apparent A couple
3 Correct but unclear or some parts missing Some steps are justified Adequate Possibly many
2 Many parts missing or unclear. Little or deficient justification Less than adequate Possibly many
1 Incomplete No justification Lacking
0 Missing or makes no sense





    Written homework assignments can always be found HERE. Only hand in the boldface underlined problems.
 
  • Every homework assignment must be handed in with a header containing the assignment number and your name. (yes, this has to be said)
  • All of the homework pages must be stapled together
  • Copy the statement of each of the problems you are solving.
  • Write solutions in the same order as the problems are assigned on the schedule.
  • All problem sets must be legible and must use complete English sentences, correct grammar and correct spelling.
  • Problem sets which prove too difficult for the grader to read may be marked incorrect or may be returned to the student for rewriting (as the instructor sees fit). We mean it!
  • All steps should be clearly justified. (This is the point of the written homework, then show your work )
  • Use  the math symbols only when needed. (yes! I mean that, mathematical arguments should be written in complete sentence.)
  • Advice: Proofread what you have written before submitting.
  • The grader will  post the grades in Blackboard .
  • All questions regarding grading of a problem set must be addressed to the grader.


A recipe to succeed  in this course

  • solve all the problems listed in the schedule (and more if you see you need it)
  • make sure you understand how to solve the problems.
  • ask for help (to your instructor, the grader, your classmates) if you need to (do not wait to do this)
  • read the assigned material before each lecture (this is not just a pretty sentence, it is there for very good reasons)
  • attend to the lectures and be present.
  • spend between six and eight hours a week working on the course.
Remember: Math is tends to be well behaved with those who "treat her" well, that is, with people who puts time and effort in understanding. It is very rare to spend a working session on math without having understood something. We all learn at different ways and speeds, but we can all learn.
As in any math course, do not be discouraged if you find yourself struggling with a problem or a concept for hours. You will need to do computations in order to understanding the material, but do not waste time  in mindlessly memorizing techniques.
Note: Constructive feedback to your instructor will be always welcome.

Policies

Student Accessibility Support Center Statement

If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Student Accessibility Support Center, 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 Student Accessibility Support Center. For procedures and information go to the following website: http://www.stonybrook.edu/ehs/fire/disabilities .

Academic Integrity Statement


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. Further information about most academic matters can be found in the Undergraduate Bulletin, the Undergraduate Class Schedule, and the Faculty-Employee Handbook.



Aug 22, 2019