[ugrads] Potential course this Fall: 400-level Topology

Sara Jamshidi Zelenberg szelenberg at iit.edu
Fri Mar 1 14:29:55 CST 2019


Dear students,

I am emailing you to gauge interest in a potential undergraduate class in
topology for Fall of 2019. The department is willing to offer it, provided
enough students are willing to sign up. Would you like to sign up?

*If you are interested, please email me right away.* The schedule is being
determined now and, with enough interest, we can have it added.

To help you determine if *topology* is right for you, please see the
attached (tentative) syllabus (with schedule), the FAQ flyer, and some
additional information below.

---

*What textbook does the course use? Is the book cheap?*

The course will follow James Munkres, Topology (2nd Edition) very closely.
It's an *excellent* book *and* *very inexpensive. *Used copies are
everywhere online (ranging from $10 to $20). I believe you can get the text
on kindle for less than $10. The other book we will use is Counter Examples
in Topology (a Dover book). This, too, is excellent and is about $12 new.

*For a more detailed account of what is covered, please see the attached
preliminary syllabus.*

*What are the prerequisites?*

A completion of your 200-level math courses and a willingness to learn
proofs. The first week will exclusively cover how to understand, interpret
and write proofs. Throughout the course, we will try to highlight what a
proof is doing and what it is "hiding."

*How are you as a teacher?*

I know this is an important question but it is also a bit awkward for me to
answer. Luckily, I can provide a link to a lecture for the class I am
currently teaching---Math 251 (multivariate calculus). In my course, I use
some epsilon-delta proofs. Below is a link to the lecture discussing how
they work.
https://youtu.be/J9tL72nJR1o?t=770

I generally like to delve into topics conceptually and I like to cover
everything on the syllabus. My classes are generally fast-paced and
hands-on (meaning lots of problems). I strive to be very clear about my
expectations and I know Blackboard thoroughly--so your grades on Blackboard
will be accurate!

This will be a challenging class, but if you invest the time, you will
learn a lot. Given how fundamental topology is, I would guess that knowing
this course will make almost all subsequent math and stats courses a little
easier.

*I am still unsure if I want to sign up or not.*

I would encourage you to talk to me about this more.

Thank you for considering this class!

Warm wishes,
Sara

----


*Note regarding the origins of topology discussed in the flyer: Some argue
that topology began in 1825 with Cauchy's memoire **‘Mémoire sur les
intégrates définies prises entre des limites imaginaires’
<https://archive.org/details/mmoiresurlesin00cauc/page/n3>. It depends on
how one defines the subject of topology versus Real, Functional, and/or
Complex Analysis. *

*Reference for flyer (I reference this, but I could not find a direct link)*
B. Riemann, *Über die Anzahl der Primzahlen unter einer gegebenen
Grösse*, Monat
der Konigl. Preuss. Akad. der Wissen. zu Berlin aus der Jahre 1859 (1860)
671–680. (English translation in M.H.Edwards “Riemann’s zeta function”,
Dover 2001.)
-------------

Sara Jamshidi Zelenberg
Visiting Assistant Professor
Illinois Institute of Technology,
Department of Applied Mathematics (Rm 110)
(312) 567-8915, szelenberg at iit.edu
https://jamshidi.weebly.com/

*...**we should take pride in the fact that fifteen generations ago
calculus didn’t even exist!*
*     --Edray Goins, *
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