Date
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WORK DUE at the beginning of class or lab
unless otherwise noted!
Be sure to follow the
Proof-Writing Samples and the
Proof-Writing Checklist
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| 30 April - Fri |
Final Project Presentations
from 12-2:30
Closed Sets, Open Sets, and Limit Points: Andrew and Travis
Compactness: Adrian and Lamonte
Connectedness and Disconnectedness: Jesse and Matt
Continuous Functions and Homeomorphisms: Hannah and Phillip
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| 27 Apr - Tues |
Exercises on Compactness
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| 22 Apr - Thur |
Work on the compactness exercises and the final project.
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| 15 Apr - Thur |
Continue working on the final project.
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| 13 Apr - Tues |
Test 2 study guide
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| 8 Apr - Thur |
Begin looking at the study guide for test 2
and write down any questions. Continue working on the final project.
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| 1 Apr - Thur |
Exercises on homeomorphisms and
connectedness.
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| 25 Mar - Thur |
Try #4 again: Munkres p. 111 # 2
Work on the final project.
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| 23 Mar - Tues |
Exercises on Closed, Continuity, and
Hausdorff
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| 18 Mar - Thur |
Continue working on the exercises due next week and on your final
project.
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| 16 Mar - Tues |
On a double-sided sheet of paper to turn in,
write up a review containing all of the topology
definitions, examples, and statements
of results that we covered in class. Short-hand abbreviations, keywords,
pictures, creative ways of conveying the ideas
are fine as long as you understand them.
Begin working on the exercises due next week
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| 4 Mar - Thur |
Read the chapters in both books that contain the first instances
of closed sets and prepare to share what you read.
Set theory exercise as assigned in class.
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| 2 Mar - Tues |
Download, order, or obtain from the library and web the references
we have corresponded about regarding your final project.
In addition, go to the library, and look at the
Handbook of the history of general topology
by
Charles E. Aull, R. Lowen, 1997
QA611.A3 H36 1997 (multivolume works)
Look through these to check for history of your topic, and look
at the nearby books too.
Also search the print copies of the Historia Mathematica
journals (Bound: v.3(1976)-v.31(2004) (Lower Mezzanine))
Prepare to report back on what you found.
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| 25 Feb - Thur |
Search for references related to the history of your final
project topic in the library and the web, and message me what you find.
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| 18 Feb - Thur |
Test 1 study guide
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| 17 Feb - Wed |
Hannah has booked room 303 in the library from 5-9pm
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| 16 Feb - Tues |
Each person in the class will choose a different proof from class
or the previous exercise sets - message me your choice on ASULearn to
obtain approval and I will list them here.
In latex, type up your proof.
Turn in your source code as well as your compiled version, which must
distinguish your proof as your own. The purpose of this assignment
is to revisit some of the previous proofs in order to improve them
and your understanding of them, and also to try latex.
Blank Proof Template
Some standard topology
and set theory symbols
Sample Proof 1: The square metric equals the
Euclidean metric on R2.
Sample Proof 2: Topology Exercises #5.
Use of math symbols and equations
Additional latex symbols
Latex fonts
To run LaTex on campus Macs, use TexShop.
To run LaTeX on campus PCs, you need to download TeXworks-setup, a free 'front-end' for LaTeX.
Click on the 'TeXworks-setup' link above to download the installer. Run the installer, then launch TeXworks. Installing TeXworks on a 'thumb drive' lets you use it on any campus PC without reinstalling each time.
Dr. Hirst's Tex resources
Approved Proofs on ASULearn:
Problem 3 on the exercises that were due on Jan 19: Phillip
Problem 1 on the Metric exercises: Travis
Problem 3 from the metric exercises: Matt
Problem 1 on the Topology exercises: Jesse
Problem 2 from the Topology exercises: Hannah
Problem 4 on the Topology exercises: Adrien
Begin looking at the study guide for test
1 and write down any questions.
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| 11 Feb - Thur |
Read Dr. Bauldry's
An
Incredibly Brief Introduction to Latex and write down any questions
Begin thinking about what proof you want to type up for next Tuesday
and have your choice approved as a message on ASULearn (first come
first served).
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| 9 Feb - Tues |
Topology Exercises
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| 4 Feb - Thur |
Read both books for information on how they introduce a topology.
What is similar and different about
the sections of the book that introduce a topology?
Continue working on the homework for next Tuesday
|
| 2 Feb - Tues |
Read through the final project and
write down any questions you have.
Read through
Motivation of
open sets in point-set topology and prepare to discuss.
Begin working on homework for next Tuesday (which is posted under
that due date).
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| 28 Jan - Thur |
Metric Space Exercises
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| 26 Jan - Tues |
Begin working on Metric Space Exercises
which are due on Thursday
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| 21 Jan - Thur |
Search for information on metric spaces in both books. Prepare to
share what you read about, including related definitions and theorems
(but not the proofs).
In addition, reflect on the similarities and differences.
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| 19 Jan - Tues |
Read p. 12-13 in Munkres.
You may work alone or in a group of up to 3 people and turn in 1 per
group. Make copies of your work so that you are prepared to present any
of the exercises after you turn it in.
1. Choose 1 of Mendelson p. 6 #1a or 1b
2. Mendelson p. 11 #3
3. Let f:A → B be a function and C1,C2 &sube A.
Prove that f(C1 &cap C2) &sube
f(C1) &cap f(C2). In addition, give an example to show that equality fails.
Finally, what assumption do we need to make about f - one-to-one, onto, or
both - in order to ensure equality holds? Prove your answer.
4. (Graduate Problem) In Munkres p. 14 #2, pick two parts to
complete.
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| 14 Jan - Thur |
Read p. 4-11 in Munkres.
Write up the following and be sure to give proper reference and credit
where it is due - turn this in to Dr. Mawhinney to give to me.
1. Research and write out a proof of the intermediate value theorem in your
own words.
2. Let Tn=(1/n, 1 - 1/n). Find the union ∪ n=2 to infinity of Tn.
(It often helps to draw a picture).
3. Let Tn=[-1/n,1 + 1/n]. Find the intersection ∩ n=2 to infinity of Tn.
4. (Graduate Problem)
No path can be found between the seven Konigsberg (now Kaliningrad, in Russia)
bridges, since this is exactly what Euler proved. Search on the web or in
a library, find useful references, and summarize why no such path
can be found.
Read through the Syllabus
which is online - search google for
Dr. Sarah, click on my page, and click on the MAT 4710/5710 link and then the
Syllabus link. Message me any questions on ASULearn -
- the university considers this a binding contract between us.
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