Topology : Math 440

Day-Time: Monday, Wednesday, Friday – 11:00 am to 11:50 am

Location: KAP 147

Instructor:  Soham Chanda

Office: KAP 438A

Office Hours: Wednesday 12:30pm to 1:30pm or by appointment.

Contact Info: sohamcha[at]usc{dot}edu

Course-webpage: https://sites.google.com/view/sohamc/teaching/topology-math-440 (recursive link)

Office Hours for super-grader : (Math Center, KAP 263)

Monday 2-3pm

Tuesday 11am - 12 noon

Wednesday 4-5pm

Announcements

• Midterm date has been moved to Oct 9th, Wednesday, in class.

Course Description

Topology  provides the fundamentals of the language of modern geometry . This course is an introduction to pointset topology, which formalizes the notion of a shape (via the notion of a topological space), notions of ``closeness'' (via open and closed sets, convergent sequences), properties of topological spaces (compactness, completeness, and so on), as well as relations between spaces (via continuous maps).

Textbook: The official course text is Topology (2nd edition) by James R. Munkres. Within this text, we will focus on Part I, particularly Chapters 1-3.

Prerequisite: This is a very proof-based course, and students are expected to have some familiarity and comfort with writing proofs.

Course Notes

Course notes will be posted after each class on my course webpage and on Brightspace.

Grading Breakdown

·       30% Homework 

·       25% Midterm Exam 

·       20% Project 

·       25% Final Exam

Assignment Submission Policy

Math 440 will have weekly homework assignments, posted on the course webpage and brightspace. You can handwrite your solutions, but you are encouraged to consider typing your solutions with LaTeX. You are encouraged to work with others and consult references (including the course textbook), but the homework you turn in must be written by you independently, in your own language, and you must cite your sources and collaborators.

Late homeworks will not be accepted. In order to accomodate exceptional situations, your lowest homework score will be dropped at the end of the semester.

Your homework should not only be graded for mathematical correctness, it will also include how readable they are. A good guiding policy to check if your writeup is readable is to imagine your reader is a fellow student who just learnt about the material required to do the homework.

For further advice on writing your homework (and project paper), see: 

·       Prof. J. Munkres' Comments on Style.

·       Prof. K. Conrad's guide to (common) Errors in Mathematical Writing.

·       Prof. M. Hutchings' Introduction to mathematical arguments (including a review of logic and common types of proofs).

Attendance

Attendance is mandatory. Classes will be in person. In case a class has to be over zoom, you will be informed in advance and you can connect to the meeting through the course Brightspace page.

Course Notes

 You can find course-notes here.

Project

A portion of your class grade will be based upon a project exploring an aspect of topology beyond the topics covered in class. Concretely, with a small group of 2-3 students, you will be asked to write a short expository article (around 4-6 pages, typed up using LaTeX), and give an in-class 20 min presentation. The topic of study will be chosen in consultation with the Instructor.

Exams

The midterm will be on Oct 9th, Wednesday, in class, 11:00am to 11:50am.

The final exam will be on December 11th, Wednesday, 11:00am to 1pm.

The exams are closed book and no electronic aid (such as but not restricted to laptop,tabs) permitted. The final exam is cumulative but will focus more on materials covered after midterm.

Academic Integrity

The University of Southern California is foremost a learning community committed to fostering successful scholars and researchers dedicated to the pursuit of knowledge and the transmission of ideas. Academic misconduct is in contrast to the university’s mission to educate students through a broad array of first-rank academic, professional, and extracurricular programs and includes any act of dishonesty in the submission of academic work (either in draft or final form).  

This course will follow the expectations for academic integrity as stated in the USC Student Handbook. All students are expected to submit assignments that are original work and prepared specifically for the course/section in this academic term. You may not submit work written by others or “recycle” work prepared for other courses without obtaining written permission from the instructor(s). Students suspected of engaging in academic misconduct will be reported to the Office of Academic Integrity.

Other violations of academic misconduct include, but are not limited to, cheating, plagiarism, fabrication (e.g., falsifying data), knowingly assisting others in acts of academic dishonesty, and any act that gains or is intended to gain an unfair academic advantage.

Academic dishonesty has a far-reaching impact and is considered a serious offense against the university. Violations will result in a grade penalty, such as a failing grade on the assignment or in the course, and disciplinary action from the university itself, such as suspension or even expulsion.

For more information about academic integrity see the student handbook or the Office of Academic Integrity’s website, and university policies on Research and Scholarship Misconduct.

Course Content Distribution and Synchronous Session Recordings Policies 

USC has policies that prohibit recording and distribution of any synchronous and asynchronous course content outside of the learning environment.

Recording a university class without the express permission of the instructor and announcement to the class, or unless conducted pursuant to an Office of Student Accessibility Services (OSAS) accommodation. Recording can inhibit free discussion in the future, and thus infringe on the academic freedom of other students as well as the instructor. (Living our Unifying Values: The USC Student Handbook, page 13).

Distribution or use of notes, recordings, exams, or other intellectual property, based on university classes or lectures without the express permission of the instructor for purposes other than individual or group study. This includes but is not limited to providing materials for distribution by services publishing course materials. This restriction on unauthorized use also applies to all information, which had been distributed to students or in any way had been displayed for use in relation to the class, whether obtained in class, via email, on the internet, or via any other media. Distributing course material without the instructor’s permission will be presumed to be an intentional act to facilitate or enable academic dishonestly and is strictly prohibited. (Living our Unifying Values: The USC Student Handbook, page 13).

Disclaimer

This syllabus is not a contract, and the Instructor reserves the right to make some changes during the semester.

Statement on University Academic and Support Systems 

Students and Disability Accommodations: 

USC welcomes students with disabilities into all of the University’s educational programs. The Office of Student Accessibility Services (OSAS) is responsible for the determination of appropriate accommodations for students who encounter disability-related barriers. Once a student has completed the OSAS process (registration, initial appointment, and submitted documentation) and accommodations are determined to be reasonable and appropriate, a Letter of Accommodation (LOA) will be available to generate for each course. The LOA must be given to each course instructor by the student and followed up with a discussion. This should be done as early in the semester as possible as accommodations are not retroactive. More information can be found at osas.usc.edu. You may contact OSAS at (213) 740-0776 or via email at osasfrontdesk@usc.edu. 

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To be eligible for certain kinds of financial aid, students are required to maintain Satisfactory Academic Progress (SAP) toward their degree objectives. Visit the Financial Aid Office webpage for undergraduate- and graduate-level SAP eligibility requirements and the appeals process. 

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