Dr. Sarah's Math 4140/5530 Differential Geometry Tentative Calendar - Fall 2015

The best way to contact me outside of class is during office hours or on the ASULearn Forum, as I usually check the posts daily, even on weekends.
  • Office Hours this week
    in person during finals: Wed 6th 12:45, Tues 12th 10:00 and 1:30, Thur 14th 10:30
    8pm Zoom Conferencing: Thur 7th, Fri 8th, Mon 11th, Wed 13th and on the ASULearn Forums
  • Class highlights A daily overview
  • Syllabus and Grading Policies
    DUE Date

    Dates are subject to change and additional homework will fill in what is listed. WORK IS DUE at the beginning of class unless otherwise noted.
    7 Dec - Mon
  • Final Project Presentations our assigned time is 3-5:30. Mandatory to pass the class.
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    3 Dec - Thur
  • Read Relativity by David Brink on ASULearn
  • Skim Selections from 8.5 on Curvatures: p. 412 - Exercise 8.4.9 on p. 413, p. 416-421, and p. 425 starting at "To end this section"-429
  • 1 Dec - Tues
  • Test corrections (turn in original test too)
  • Work on the final project
  • Use class time as a research day to work on the final project. I will be in the class to help, as an open office hour, although you may work from elsewhere, and I'll be in office hours as posted and on the forums as usual.
  • 24 Nov - Tues
  • Homework 7: Research and Investigate a Metric Form
    Topics are approved on first-come-first-served basis on the whole class discussion forum on ASULearn
    Alcubierre metric or warp drive metric: Aneisy, James and Robert
    Anti-de Sitter metric: Josh Huffstetler
    Eddington-Finkelstein metric: Anna
    Friedmann-Lemaitre-Robertson-Walker (FLRW) metric: Ian
    Godel Metric: Ben
    Kerr metric: Josh Cox
    Kerr-Newman rotating charged Black Hole metric: Daniel and Kelcey
    Reissner-Nordstrom metric: Matt and Zach
    Schwarzschild metric: Janie
    Taub-NUT metric: Callum
    Wormhole metric: Sam
  • 19 Nov - Thur
  • Read How to Create Your Own Universe in Three Easy Steps by Lawrence Brenton. Math Horizons April 2011, pp. 5-9. on ASULearn
  • Continue working on Homework 7
  • 17 Nov - Tues
  • Read p. 397 A Glimpse at Higher Dimensions, and p. 409-411 Christoffel Symbols
  • Read through Homework 7 and write down any questions. Begin working on the homework. Topics are approved on first-come-first-served basis on the whole class discussion forum on ASULearn
  • 12 Nov - Thur
  • Continue thinking about a Final Project topic
  • Read p. 124-126 A Formula for Gauss Curvature, and 5.2 The Geodesic Equations starting on p. 215-the pictures opposite p. 218.

  • 10 Nov - Tues
  • Test 2 on Surfaces study guide
  • 5 Nov - Thur
  • Read through the Final Project and write down any questions. Start thinking about a final project topic.
  • Study for test 2 via the study guide and write down any questions you have.
  • Use class time as a study day for test 2. I will be in the class to answer any questions, as an open office hour, although you may study from elsewhere, and I'll be in office hours as posted and on the forums as usual.
  • 3 Nov - Tues
  • Read 5.4 Surfaces not in R^3 starting on p. 226- Exercise 5.4.10 on p. 230 and write down any questions
  • 5530 students: Choose two terms in the surfaces glossary to post on ASULearn. First come first served.
  • 29 Oct - Thur
  • Homework 6: Research and Investigate a Surface
    Topics are approved on first-come-first-served basis on the whole class discussion forum on ASULearn
    Enneper's surface - Aneisy, Anna and Russell
    Helicoid - James and Robert
    Hyperboloid of 1 sheet - Matt and Zach
    Hyperbolic paraboloid - Janie
    Kuen's surface - Ian
    Mobius strip - Josh H.
    Pseudosphere - Daniel and Kelcey
    Scherk's surface(s) - Sam
    Torus - Callum and Ben
  • 27 Oct - Tues
  • Read through A Quick Introduction to Non-Euclidean Geometry by Bob Gardner, focusing especially on the last page, and write down any questions.
  • Continue working on homework 6
  • 22 Oct - Thur
  • Begin working on homework 6
  • Read p. 275 - 277 (stop at Definition 6.1.6) and write down any questions.
  • 20 Oct - Tues
  • Read p. 84-86 and 88, 107, 111, Example 3.2.8 on p. 112-114, and Figure 4.4 on p. 169, and write down any questions
  • 13 Oct - Tues
  • Homework 5: Flat Donuts and Round Donuts
  • 8 Oct - Thur
  • Read 2.2 p. 79-80, 2.3 p. 86-87, and p. 212-215 in 5.1 and write down any questions
  • Begin working on Homework 5
  • 6 Oct - Tues
  • Read through 2.1 and the first page of 2.2 (on p. 77) and write down any questions
  • In 2.4 and 2.5 look at the pictures but ignore the text for now (until we cover the shape operator and first fundamental form E, F, G next week)
  • Test corrections
  • 1 Oct - Thur
  • Homework 4: Intrinsic Geometry of Cones
  • If you have a ball or something else spherical, bring that with you.
  • 29 Sep - Tues
  • Read p. 67 and p. 209 in the book and write down any questions
  • Begin working on Homework 4
  • 24 Sep - Thur
  • Read the Surfaces reading on ASULearn. Look up pictures of any surfaces mentioned there that you are not familar with, and take notes (or highlight) any terms that are mentioned in both the article and the glossary on surfaces.
  • Read p. 248-250 in the book, but don't worry about the Maple code.
  • 22 Sep - Tues
  • Open your eyes to surfaces in our world. Find, either in person or in a picture, a surface which interests you and be prepared to share where it arises and what significance it has.

  • 17 Sep - Thur
  • Test 1 on Curves study guide
  • 15 Sep - Tues
  • Find as many people as you can related to the creation of the Frenet formulas and the years of their contributions, including Bartels, Darboux, Frenet, Pagani, and Serret.
  • Study for test 1 and write down any questions you have.
  • 10 Sep - Thur
  • Homework 3: More Curves
  • 8 Sep - Tues
  • Read p. 34-35 in 1.5 and begin working on Homework 3.
  • 5530 students: Choose two terms in the glossary on curves to post on ASULearn. First come first served.
  • 3 Sep - Thur
  • Read 1.2, 1.3 and How Flies Fly: Kappatau Space Curves by Rudy Rucker, and write down any questions you have.
  • 1 Sep - Tues
  • Homework 2: Curves
    Maple Applet spacecurve.mw that calculates the Velocity, Acceleration, Jerk, Speed, ArcLength, Curvature, and Torsion
    Maple Applet TNBapplet.mw that animates the Frenet Frame
    Both of these files are by past graduate student Nathan Crowder
  • 27 Aug - Thur
  • Skim through homework 1 solutions on ASULearn, including the Maple commands I used for plotting.
  • Read the Curves reading on ASULearn by Dogan Comez, myself and Jill Thomley and prepare to discuss it.
  • Continue working on homework 2.
  • 25 Aug - Tues
  • Search google for Dr. Sarah, click on my page, and click on the 4140/5530 link and then read through the Syllabus Write down any questions.
  • Read section 1.1 in the book, and write down any questions you have.
  • On ASULearn and send me a posting in the private forum (only you and Dr. Sarah): what you would like to be called (your nickname / first name); your phone number; your major; any additional academic concentrations/minors; what you might like to do as a career; your non-academic interests and hobbies; anything else you want me to know
  • On ASULearn add a picture of yourself (Profile) so that it is easier to get to know each other.
  • Begin working on homework 2 (9/1 due date).
  • 5530 students: Choose two terms in the review glossary to post on ASULearn. First come first served. You can claim a term by posting something for it, and then add more later. I've put up curvature as a sample, although you may use your own style.
  • 20 Aug - Thur
  • Homework 1: Review. I am happy to help in office hours or as an ASULearn forum message. You may wish to review concepts via web pages such as: Paul's Online Calculus III Notes, Jeff Knisley's Multivariable Calculus Online, or Carlos Rodriguez's Multivariate Calculus
  • Purchase the textbook, which is available in the bookstore: Differential Geometry and Its Applications (Classroom Resource Materials)
    The Mathematical Association of America Edition in 2007 [The one with "The Bat" surface on the cover]
    John Oprea, 469 pp., hardbound, 2007
    ISBN: 978-0883857489
  • Purchase the i-clicker from the bookstore [if you have one from the past or another class, one suffices], and bring it to all classes
  • 18 Aug - Tues
  • First day of class