Dr. Sarah's Math 4710/5710 Web Page - Spring 2010

  • Office Hours This Week
  • ASULearn (to post messages, access grades...)
  • Syllabus and Grading Policies


        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
    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
    27 Apr - Tues
  • Exercises on Compactness
  • __________ ________________________________________________________________________
    __________ ________________________________________________________________________
    22 Apr - Thur
  • Work on the compactness exercises and the final project.
  • 15 Apr - Thur
  • Continue working on the final project.
  • 13 Apr - Tues
  • Test 2 study guide
  • 8 Apr - Thur
  • Begin looking at the study guide for test 2 and write down any questions. Continue working on the final project.
  • 1 Apr - Thur
  • Exercises on homeomorphisms and connectedness.
  • 25 Mar - Thur
  • Try #4 again: Munkres p. 111 # 2
  • Work on the final project.
  • 23 Mar - Tues
  • Exercises on Closed, Continuity, and Hausdorff
  • 18 Mar - Thur
  • Continue working on the exercises due next week and on your final project.
  • 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
  • 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.
  • 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.
  • 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.
  • 18 Feb - Thur
  • Test 1 study guide
  • 17 Feb - Wed
  • Hannah has booked room 303 in the library from 5-9pm
  • 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.
  • 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).
  • 9 Feb - Tues
  • Topology Exercises
  • 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).
  • 28 Jan - Thur
  • Metric Space Exercises
  • 26 Jan - Tues
  • Begin working on Metric Space Exercises which are due on Thursday
  • 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.
  • 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.
  • 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.