Algebraic Topology is the study of topological spaces (e.g. subspaces of ℝn) by means of associated algebraic objects that encode particular topological features. In this introductory course, we will focus mainly on the fundamental group, which is a group defined from closed paths in a given topological space. We will define simplicial complexes, study free groups as fundamental groups of graphs, prove the Seifert–van Kampen Theorem and study the correspondence between subgroups and covering maps. We will see many examples along the way, including graphs, surfaces and 3-manifolds.
Basic Information
Lectures are held Tue./Thu., 12:00pm–1:15pm in 302 Joyce Cummings Center (JCC).
- Instructor: Nima Hoda
- Email: nima.hoda@tufts.edu
- Office hours: Wed./Thu., 2:00pm–3:30pm in JCC 588.
- TA: Mingyang Zhou
- Office hours:
- Tue., 1:30pm–2:30pm in JCC 574 (Math Library).
- Fri., 11:00am–12:00pm in JCC 510 (Fishbowl).
- Office hours:
- Texts:
- Learning objectives: 1bcd, 2, 6
Piazza
We will use Piazza as an online forum for discussing homework and lecture material. Course announcements will also be made via Piazza so please ensure that you are registered and enable email notifications.
Evaluation
Your grade will be based on your homework submissions and two in-person exams: a midterm and a final.
- 30%: Homework (submitted on Gradescope)
- 30%: Midterm exam, Thu. Mar. 6 (in class)
- 40%: Final exam
Your lowest two homework grades will be dropped.
Homework
Homework assignments are due Fridays at 11:00pm on Gradescope, almost every week. You are highly encouraged to discuss homework problems with your fellow students but your solutions must be written independently.
A subset of the homework problems will be graded.
Submission policy
Occasionally technical or other issues may cause temporary submission problems. In order to accommodate for such situations, homework may be submitted up to 24h after the deadline late without penalty. After this grace period, homework will no longer be accepted. Exceptions may be made in extraordinary circumstances at the instructor's discretion.
Additional resources and information
Accommodations for Students with Disabilities:
Tufts University values the diversity of our students, staff, and faculty and recognizes the important contribution each student makes to our unique community. Tufts is committed to providing equal access and support to all qualified students through the provision of reasonable accommodations so that each student may fully participate in the Tufts experience. If you have a disability that requires reasonable accommodations, please contact the StAAR Center (formerly Student Accessibility Services) at StaarCenter@tufts.edu or 617-627-4539 to make an appointment with an accessibility representative to determine appropriate accommodations. Please be aware that accommodations cannot be enacted retroactively, making timeliness a critical aspect for their provision.
Academic Support at the StAAR Center:
The StAAR Center (formerly the Academic Resource Center and Student Accessibility Services) offers a variety of resources to all students (both undergraduate and graduate) in the Schools of Arts and Science, Engineering, the SMFA and Fletcher; services are free to all enrolled students. Students may make an appointment to work on any writing-related project or assignment, attend subject tutoring in a variety of disciplines, or meet with an academic coach to hone fundamental academic skills like time management or overcoming procrastination. Students can make an appointment for any of these services by visiting the StAAR Center website (go.tufts.edu/StAARCenter).
Student Suport, Including Mental Health:
As a student, there may be times when personal stressors or emotional difficulties interfere with your academic performance or well-being. The Counseling and Mental Health Service (CMHS) provides confidential consultation, brief counseling, and urgent care at no cost for all Tufts undergraduates as well as for graduate students who have paid the student health fee. To make an appointment, call 617-627-3360. Please visit the CMHS website (go.tufts.edu/Counseling) to learn more about their services and resources.
Diversity, Equity, Inclusion:
We would like to create a learning environment that is respectful of diversity: gender identity, sexuality, disability, age, socioeconomic status, ethnicity, race, nation- ality, religion, and culture. Your suggestions are encouraged and appreciated. If something said or done in the classroom, by ourselves or other students, causes discomfort or offense, please let us know, through a third party such as a trusted friend if necessary. Please see the Tufts math department page on reporting discrimination.
Religious Accommodations:
Tufts University faculty, staff, and administration highly value and acknowledge the religious diversity of its student body. Students seeking religious accommoda- tions related to their holy days are encouraged to collaborate with faculty to make arrangements during the first week of each semester. The religious holy days calendar, including the holy days policy from the Faculty Handbook, is available here for your reference. Students seeking additional support may refer to the University Religious Accommodations Policy, available here. The University Chaplaincy is also available to respond to questions on religious observances; their contact information is available here.