[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.

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

*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,


*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

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