Class meetings: Monday and Wednesday, 1:00 – 2:15, LL 513
Office: LL 817B
E-mail: hmoon8 at fordham.edu
Course webpage: https://fordham.blackboard.com
Office hours: Thursday 2:00 – 4:00, or by appointment
Text: Topology of Surfaces, C. Kinsey, ISBN-13: 978-0387941028, ISBN-10: 0387941029.
Course objective
This course is an introduction to the topological structure and its applications. Topology is concerned with the properties of spaces that are preserved under continuous deformations, such as stretching, twisting, bending. In this course, we investigate how mathematicians understand and study the concept of ‘space’.
This course has two phases. In the first stage, we discuss basic topological notions such as open set, closed set, connected set, compact set, continuous function, and homeomorphism with emphasis on metric spaces. In the second phase, we study how ideas from topology and linear algebra can help us to distinguish different spaces. We discuss simplicial complex, homology group, Betti number, and Euler characteristic. If time permitted, we will discuss how abstract mathematical ideas in topology can be used in practical applications, by skimming the basic ingredients of topological data analysis.
Prerequisite
Math 2001 (Discrete Math), Math 2004 (Multivariable Calculus I), and Math 2006 (Linear Algebra I), or permission of the instructor.
Grading
I grade on a curve. Final grades will be computed according to the following breakdown:
| Homework | 25 % |
| Midterm Exams | 2 x 20 % |
| Final | 35 % |
Test
There will be two midterm exams and one final exam. The final exam is cumulative. Make up exams will not be given unless you have a documented reason.
Homework
There will be weekly homework assignments. It will be collected on Monday, before the class starts. The homework assignment for this class will be different from other math classes in two ways. First of all, you have to typeset your homework. I will not accept handwriting. However, if you have some technical difficulty to input some mathematical formulas or graphs, please come to me to discuss how to input mathematical formula. Secondly, you are not allowed to use any incomplete sentences or abbreviation. Your solution must consist of full sentences. I don’t accept any late submission or e-mail submission unless there is some medical/family emergency.
Attendance
Based on Fordham’s academic policy, coming to every class during the official academic term is required. It is your own responsibility to know what happens in class. I may not penalize for each of your absences, but if you make five unexcused absences, then you will get an F.
During the lecture
Except the purpose of note taking, use of any electronic device, including cell phones, tablets, and laptops is not allowed.
Expectation
The federal definition of “credit hour” requires that for a four-credit course, you should spend 12 hours per week (including class time) on it. I expect that you study at least 9 hours per week to prepare this class. Otherwise it would not be easy to pass this course. The preparation includes completing your homework, reading your textbook/lecture notes, and solving exercise problems.
Collaboration
I highly recommend you to work in groups and help each other. It would be essential to collaborate for doing your homework, reading your textbook, and preparing your tests. I expect that you can learn how to work together during your learning experience. It would be really, really important for studying higher mathematics.
However, do not copy someone’s homework. You must understand how to solve the problems, and need to write with your own language. If I notice any plagiarism, the whole homework set will be void and you may get 0 credit.
Additional materials
I will post course lecture notes and solutions of homework/tests on the course web- page. Check the course webpage regularly, at least once in a week. It is always advisable to work as many additional problems from the book as you have time for. Each week I will post on the course webpage a list of recommended problems. You don’t need to submit a solution of recommended problems, but studying them will be very helpful to improve your mathematical understanding.
Calculator or computer
Only calculators are permitted on midterm tests and the final. Use of computers, smartphone or any other electronic devices is not allowed.
Math Help Room
A great deal of help is available and I strongly encourage to use them. Math Help Room is where you can get free help. The new Math Help Room is located in QuinnX library which is located in the basement of LL building. The hours for QuinnX is M–Th 11am – 7pm and F 11am – 6pm. Faculty members and upper class math majors will stay and help you. I am going to hold my office hours in Math Help Room. The staffing schedule of Math Help Room will be e-mailed to you soon. We encourage you to use the Math Help Room for getting help in math or just discussing math with your peers.
Academic integrity
As a Fordham University student, you have agreed to abide by the University’s aca- demic integrity policy. All academic work must meet the standards described in http://www.fordham.edu/info/20322/academic_advising/3030/academic_integrity. Lack of knowledge of the academic integrity policy is not a reasonable explanation for a violation. Questions related to course assignments and the academic integrity policy should be directed to the instructor.
Disability Services for Students
If you are a student with a documented disability and require academic accommodations, you need to register with the Office of Disability Services for Students (ODS) in order to request academic accommodations for your courses. Please contact the main ODS office at Rose Hill at 718-817-0655 to arrange services. Staff at ODS can walk you through the process and arrange appointments depending on which campus you take courses at. Accommodations are not retroactive, so you need to register with ODS prior to receiving your accommodations. Please see me after class or during office hours if you have questions or would like to submit your academic accommodation letter to me if you are already registered for accommodations with Fordham.
Disclaimer
The course syllabus is a general plan for the course; deviations announced to the class by the instructor may be necessary.