Assignment Schedule for Mat375

Day Date Activity Assignment (due one week from assignment date, unless otherwise stated)
Mon1/13 Welcome/Intro For next time: give me your one-pager on which athlete has the better right to be acclaimed champion cross-country runner:

  1. What have you tried, or considered?
  2. What else would you like to know?
  3. Who's better? (Your best guess so far)
Wed1/15 Cross Country Competition Discussion of our preliminary work, and move to a plan. Homework: Carry out the plan that we devise today. Provide a one page summary of your decision on Friday.
Fri1/17 Cross Country Competition -- the end! Let's see what we've done... For Wednesday, please read Riegel's paper, and prepare to discuss it.
Mon1/20 MLK Day No Class! Already? Enjoy!
Wed1/22 Empirical Modeling: Linear Regression -- fitting a line For next time: please read the final report of the cross country problem. Then for Monday,

  1. Verify my calculations of $\alpha$ in the final report.

  2. Use Riegel's model to estimate Thad and Thomas's times on the 100 meter dash, and on a marathon (42.2 km).

  3. Use the same procedure discussed in class to find a power rule for the world-class women close to what Riegel found.

Fri1/24 A linear regression challenge Please read over the Bestiary of functions, from Ben Bolker's Ecological Models and Data in R (for Monday). Note in particular the reasons for using these particular functions as models for different phenomena. You might want to add this to your notebook, in case you might find it useful on an exam.

For Friday, 1/31: your group will write a three-page report (or so), typed, on Dave's stick: what is it, and why is it marked the way it is? You should be able to reconstruct any marking on the stick.

Mon1/27 Regression: The basic problem, and misadventures  
Wed1/29 Univariate and Multivariate Derivation, continued  
Fri1/31 Linear Regression derivation Use the Stewart version of the Keeling data (it's available in that Mathematica file) to
  1. compute the center of mass $(\overline{x},\overline{y})$.
  2. the equation of the regression line -- all "by hand" (i.e. by calculator).
  3. Plot -- by hand -- the data, the center of mass, and the regression line.
  4. What is the minimal value of the sum of squared residuals?

Please submit that on Wednesday, 2/5.
Mon2/3 Linear Regression Derivation Your next group projects (due Wednesday, 2/19 -- revised):

Using the most recent Keeling CO2 data, and using linear regression,

  1. produce (and evaluate) models of monthly CO2 trend that are

    • linear in time (decimal date),

    • quadratic in time,

    • exponential in time,

  2. Then produce and evaluate a model that is (your favorite of the three types above), with the addition of terms of the form $\sin\left({\frac{t}{T}}\right)$ and $\cos\left({\frac{t}{T}}\right)$ (where $t$ is again decimal date). These sinusoidal terms will capture the oscillations. What value should you choose for $T$?

  3. Ultimately you should determine the decimal date at which the model predicts CO2 to first surpass 450 ppm -- the point at which we lock in 2 degrees C of global warming (per the National Academy of Sciences).

In addition, for Friday, 2/7: I want each (stick) group to submit one more thing: all the markings missing from Dave's stick for a 10 foot log, obtained using a stated equation.

You can see some of the 10 foot markings on this scanned image, to verify your calculations.

Wed2/5 Linear Regression Diagnostics Due Monday, 2/10:

We need to evaluate our work. For the project ("Dave's Stick"), please hand me one to two pages, typed, and which will be kept strictly anonymous (i.e. no one else will ever see it):

  1. Evaluate your own report, especially comparing it to other reports.
  2. Compare your partner(s) and your contributions to the report. Perhaps you took different roles, which you can describe.
  3. Feel free to compliment your partners, if that's appropriate.
  4. Suggest how you would divide the effort put into the report by each member (divide 100% -- e.g. Bob, 20%; Lulu, 50%; Stan, 30%).

Notes:

  • You all have different backgrounds and skills. Some of you have already done some advanced statistics, or perhaps some math modeling. I'm not focused on that so much, as to make sure that everyone is contributing, and that everyone is doing good quality work (which will only improve as we go along, I'm quite sure).

  • I will continue to ask these questions of you and your partners for the rest of the course. You have at least one more small group project (Keeling), plus the final project -- with different partners. So you will be evaluated by different people.

    First, be a good partner yourself!:)

    Second, do a fair and honest appraisal of others.

    I will issue you a participation grade at the end, which reflects only the synthesis of the reports, and I won't share individual comments to protect reviewers.

    If you ever felt that I were being unfair in this assessment, you could request an audit by any faculty member from our department of your own choosing, who would review my methodology, and whose grade would overrule my own, if it differed.

Fri2/7 Linear Regression Diagnostics  
Mon2/10 Linear Regression with non-linear curves  
Wed2/12 Linear Regression with non-linear curves  
Fri2/14 Climate Strike No class
Mon2/17 Work on Keeling Project  
Wed2/19 Review  
Fri2/21 Midterm 1  
Mon2/24 Major project outline

  • There is exam redemption! You all can retake exam 1, at your leisure, and I'll average your two scores.

  • You may discuss the problems with each other, and with me.

  • These will be due Friday, 2/28.

In addition, for our first main project assignment:

  • Enter the data into a spreadsheet with 366 entries (due Friday, 2/28).

    You should triple enter the data -- that is, each person should enter it separately, then compare to make sure that it was accurately entered.

    You might build a common spreadsheet (like this perhaps), so that it's easy to compare.

Wed2/26 Non-linear modeling  
Fri2/28 Non-linear modeling II Please revise your Keeling reports (due next Friday). I want to feature one report to give you an idea of some things that I'd like you to shoot for....

Please also include confidence intervals for amplitude $A$ and phase $t_0$.

I'll grade based more on the final paper than on the original.

Mon3/2 Non-linear regression Homework (due Friday):

  1. Use Newton's method to find roots of the following, starting from the value $x_0$ given.

    1. $f(x)=\ln(x)-1.23$, with $x_0=1.2$.
    2. $f(x)=\cos(x)-.23$, with $x_0=1.2$.
    3. $f(x)=x(x^2-1)$, with $x_0=.4$.

    Graph the functions in the vicinity of $x_0$. Compute 4 iterates, by hand (show your work, but use a calculator). Use software to solve for the "true solution", and compare your answer to the value obtained. Are the iterates approaching the solution, and, if so, how (and how quickly)?

  2. Use non-linear regression to fit the models \[ at^2+bt+c+A\sin\left(2 \pi \frac{t-t_0}{T}\right) \] and \[ at^2+bt+c+(\alpha + \beta t) \sin\left(2 \pi \frac{t-t_0}{T}\right) \] to the NOAA Keeling data.

    1. This file will load the data into Mathematica for you, to get you started.
    2. Discuss both models. How well do they fit? Compare. One model is a generalization of the other, of course.
    3. Are we justified in taking $T=1$?
    4. Are we justified in believing that the amplitude is changing in time?

Wed3/4 non-linear Corn Growth and ODEs  
Fri3/6 Hare and Lynx: Tyson, et al. Suppose that there is no climate change for Wood County. Then what would we expect of our data?

If the globe were warming, then one thing we concluded is that we should see more MaxMax years-of-occurence on the recent side (toward 1992), and fewer on the earlier side (toward 1854).

So in order to test a null hypothesis of "No climate change" against an alternative of "Global warming", we could test the distribution of MaxMax years-of-occurence by decades, and see if it's uniform: all decades are the same.

Please do the following (on your own, but feel free to share ideas and results within your group):

  1. Describe what you would expect for the other series -- MinMax, MaxMin, MinMin.

  2. For your time series, create a histogram showing how many years occurred in each decade (1854-1863,1864-1873, etc.). Draw this by hand.

    Jon and Proctor -- you did the first three months of the year. Please do the same, but for all extremes in the first three months of the year.

  3. Climate is usually defined as the average of thirty years of weather. Also create a histogram using three-decade-long bins (example: 1854-1883,1884-1913,1914-1943,1944-1973,1974-1992 -- check out that last one! How would you adjust for it?). Draw this by hand.

  4. Describe how one might decide if your histograms are "abnormal" (and so we might "reject the null"), given the null hypothesis of no climate change.

Come prepared to share your results on Monday following break.
Mon3/09 Spring Break  
Wed3/11 Spring Break  
Fri3/13 Spring Break  
Mon3/16 Spring Break (imprevu)  
Wed3/18 Spring Break (imprevu)  
Fri3/20 Spring Break (imprevu)  
Mon3/23 Hare and Lynx: Tyson, et al. Your assignment concerning the major project is due today.

Carry out labPP.html, and submit the results to me by Wednesday, 3/25.

Wed3/25 Hare and Lynx: Tyson, et al.

Carry out labPP2.html, and submit the results to me by Friday, 3/27.

Fri3/27 Some readings for the Fletcher project. Your homework is described in the day's agenda, day26.

Due Monday, 3/30!

Mon3/30 Hare and Lynx: Tyson, et al. Your lab is due on Friday, 4/3.
Wed4/1 Temperatures of Wood County and climate change Homework: by Friday, reproduce the figures as requested in the day 27 agenda.
Fri4/3 SIR models: Coronavirus Please do the first lab in our SIR modeling unit by Monday, 4/6.
Mon4/6 SIR models: Flattening the Curve Please do the second lab in our SIR modeling unit before Friday, 4/10: i.e., due Thursday, 4/9.
Wed4/8 Back to the Fletcher project, for a catch-up. Your homework is laid out in the day's agenda (due Monday, 4/13).
Fri4/10 SIR models: Coronavirus in Italy Please do the second lab in our SIR modeling unit before Friday, 4/10: i.e., due Tuesday, 4/14.
Mon4/13 Summary and review of SIR and predator/prey models Take a listen to the summaries of the labs, and look over the "keys" that I've provided for othem. These are in the day32 agenda.
Wed4/15 Review  
Fri4/17 Midterm 2  
Mon4/20 Temperatures of Wood County and climate change I've given you some problems to work on in today's agenda. These are not formal assignments, but I'm hoping that someone can come up with something....
Wed4/22 Temperatures of Wood County and climate change I've given you some homework in today's agenda (due Sunday night). Nothing big.
Fri4/24 Temperatures of Wood County and climate change  
Mon4/27 Temperatures of Wood County and climate change Presentations
Wed4/29 Review  
Fri5/1 Review  
Mon5/4 Final 8:00 am

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