Math 270 Team Projects
This 4-unit course will meet only 3 hours per week. In place of the fourth hour, you will complete 2 team projects. In addition, you will actively listen to 16 presentations by other teams.
Objectives
- deepen your understanding of key concepts and methods
- stimulate your interest in real-world applications of differential equations
- encourage fluency with various capabilities of Mathematica software
- further your ability to work well on a team
- develop your oral and visual presentation skills
Presentation
Each team of 3 people will be assigned a time to present a 12- to 15-minute slide presentation to the class on an assigned topic. Each person on a team should speak for approximately the same amount of time.
3 weeks before: choosing/finding a problem
Teams will choose from recommended problems on a particular day in class, or may locate a problem of their own choosing and request approval by the professor at least 3 weeks before their presentation.
1 week before: seeking help
If a team needs help understanding their problem, or creating Mathematica visualizations, they must seek help from the professor at least 1 week before their presentation.
2 days before: rehearsal
A team must rehearse their slide presentation with the instructor at least 2 days prior to their scheduled classroom presentation. You are responsible for scheduling this meeting with me.
The following class: evaluation and reflection
Upon completion of the presentation, each team member must complete the “Team Project Self/Peer-Evaluation” and “Team Project Reflection” (forms below) and submit a printed copy during the following class period.
Team Project 1 Topics
Section / References / Topic / Problems / Presentation DaySL p. 31 / 1.3 / The bones of Olduvai: Potassium-argon dating / 3 / 1a
1.4 / Viscous damping: Longer to rise or to fall? / 15 / 1a
SL p. 37 / 1.4 / Multicompartment medication models: Tetracycline in the body / 11 / 1a
2.4 / Using slope fields to bound solutions / 25 / 1b
SL p. 122 / 2.3, 2.4 / Approximate numerical solutions / 3, 4, 5 / 1bc
SL p. 137 / 2.1-2.4 / Sensitivity to input frequency: Will the message get through? / 14, 15 / 1bc
SL p. 137 / 2.1-2.4 / Steady states: Periodic forced oscillations / 16, 19 / 1bc
SL p. 145 / 2.5 / Pursuit models: A ferryboat in a current / 36 / 1c
SL p. 145 / 2.5 / Pursuit models: A goose and a moving nest / 38 / 1c
2.6 / Harvesting a predator-prey community to extinction / 8 / 1c
2.6 / Predator-prey systems: Linearizing to estimate the periods of cycles / 9 / 1c
2.6 / Regulating harvesting rates and season to maximize sustainable yield / 10 / 1c
2.6 / Orbits of the Lotka-Volterra system are cycles / 11 / 1c
Team Project 2 Topics
Section / References / Topic / Problems / Presentation Day3.4 / Gravity-driven rapid transit / 24 / 2abc
3.6 / Inside-outside temperature lag / 34 / 2abc
3.6 / Higher order ODEs and operator identities / 37, 38, 45, 48 / 2abc
SL p. 251 / 1.3, 3.7 / Einstein's field equations of general relativity / 1 / 2abc
4.1 / Creeping bugs on a square table / 10 / 2abc
4.2 / Beat frequencies and engineering functions / 21 / 2abc
5.2 / The Laplace transform for difference equations / 34 / 2abc
6.3 / 3x3 system matrices with a deficient eigenspace / 40 / 2c
6.4 / Small-amplitude oscillations of a double pendulum / 27 / 2c
Grading Criteria
Your score on the project will be computed based upon 5 criteria.
Your team members will receive the same grade for the first 3 criteria, unless your self/peer-evaluations necessitate adjustments to take into account unequal effort.
2 pointsDepth of mathematical content presented
2 pointsFollowing guidelines on readability of slides (see below)
3 pointsAppropriate and substantial use of Mathematica, including use of the “Manipulate” command if at all possible
You will receive an individual grade for the final 2 criteria.
2 pointsClear explanation of mathematical content (did you effectively communicate the big picture of your problem, its solution, and the implications?)
1 pointLength and thoughtfulness of your “Team Project Reflection”
10 pointsTotal
An unexcused absence on other teams’ presentation day will subtract 1 point from your individual score.
Readability of Slides
To ensure that your audience is able to comprehend your slides, follow these guidelines:
- If there is a diagram or equation which you want the audience to be able to see for the entire presentation, you may wish to write this on the board at the beginning. You should not do any algebraic manipulations on the board. For anything you write on the board, please submit to me a neatly written copy of it after your presentation.
- While it is important for you to understand all the details of how to solve any differential equations involved in your problem, it is usually not best to show all of the details during your presentation. If it took you an hour to understand the details, the class will not be able to digest them in 3 minutes. Break up the solution process into the important steps. Put only the results of these important steps on your slides, and help the class to understand the broad outline of the solution process and why it works. Give them enough insight so that they could try to solve it on their own later on. To convey the big picture, as opposed to a sequence of small steps, will actually require a deeper understanding on your part.
- You should rarely have more than 4 or 5 lines of text on a single slide. Use a large font.
- Your equations must be properly formatted, or they will be very difficult for your audience to digest. Please follow the suggestions on the next page.
Presenting in PowerPoint: (3 options)
1)(recommended)Type an equation using the equation editor in Microsoft Word 2007, then cut and paste it into PowerPoint. Make sure the font size of the equation is big enough in Word before you copy it, so that the image in PowerPoint will not be pixelated (the shortcut is to highlight text, then Control Shift > or Control Shift <, or for more fine control, Control ] or Control [ ).
2)Use Insert -> Object -> Microsoft Equation 3.0 to type an equation directly within PowerPoint. This option tends to be less user-friendly/powerful than option (1).
3)Type an equation in Mathematica, highlight it, increase the size (Alt = to increase, Alt - to decrease), then use File -> Save Selection As, and save the equation in some image format (.png seems to work well). Then you can copy and paste the image file into your PowerPoint.
Presenting in Mathematica:
Be sure to enter text in the correct "Style". Click "Window -> Show Toolbar" to make the styles easier to access. Better yet, use the keyboard shortcuts, which can be found under "Format -> Style". Relevant "styles" for your presentation include title, section, text, inline formula, and display formula. It seems to work better to highlight an entire cell when choosing a style, rather than just highlighting a piece of text within a cell.
If you choose to present in Mathematica, you should use the “Slide Show” functionality.
Presenting in LaTeX:
Most professional math presentations and papers (and many science ones) are typeset using LaTeX software. If you want an example of a typeset paper and presentation, see the research section of my website. For presentations, there is an add-on to LaTeX called Beamer. This software is all available online for free. If you want to go to graduate school in math (and perhaps in science as well), you should learn LaTeX at some point while you are an undergraduate. If you want to learn, I'm happy to get you started. I can show you the basics, and you can borrow my LaTeX handbook if you like. Before long, you may find yourself typesetting your homework too!
Team Project Self/Peer-Evaluation
Please write your team members’ names, grade their effort, and describe how they contributed to your team’s success.
You:______
Effort: ___Poor ___Below average ___Average ___Above Average ___Exceptional
Contribution:
Member: ______
Effort: ___Poor ___Below average ___Average ___Above Average ___Exceptional
Contribution:
Member: ______
Effort: ___Poor ___Below average ___Average ___Above Average ___Exceptional
Contribution:
Team Project Reflection
Your responses should be typed, and should approximately fill this page (single spaced).
1)As you worked on this project, what is the most significant thing you learned about working on a team, or about your personal strengths or weaknesses?
2)Describe your personal mathematical learning process as you worked on this project, including any key mathematical insights at which you arrived.