You will be expected to perform an independent study project involving analysis of a data set, equivalent to a term paper, on a subject of your choice. Your project should involve study beyond the level of the brief general discussions in Numerical Recipes. You should prepare a written report of length no more than ~5 pages OR a website with equivalent content OR a 10-minute presentation for class. Presentations will occupy the last class session. For information on how to create a website, see http://www.washington.edu/computing/web/publishing/.
Many students will want to select a problem related to their job or personal research interests. You should be careful to define a problem that can be dealt with adequately in the time available, for which a reasonable and manageable data set is readily available. The topic must also require application of numerical methods in an area covered by the course, and at an appropriate level of difficulty. All projects must use data that can be released as public information.
To make sure your topic is suitable, you must submit a proposal describing your topic, the nature of the data set, and a preliminary list of references and sources you will use. This proposal should be submitted by email to wilkes@u.washington.edu no later than the date specified on the class calendar.
Students who do not have a ready-made topic in mind may select one of the following, for which I can supply data sets. These serve as examples to illustrate the sort of topics needed for those who want to define their own problem.
1) Fits to cosmic ray energy spectrum
Astrophysicists are interested in the energy spectrum of primary cosmic ray protons ("primary" means measured at the top of the atmosphere). Parameters of interest are the intensity and the slope of the spectrum (how fast does the particle flux diminish with energy). In particular, there is an open question in the research community regarding the presence of a change in slope around energies of 1015 eV. You can use maximum likelihood techniques to find the best fit and errors on the slope and intensity for data from a balloon flight experiment which recorded proton and alpha-particle fluxes.
2) Detection of acoustical signals in noise
A common problem in marine science applications is to identify signals from an acoustical beacon. Given digitized data from a recording of acoustical signals, apply Fourier correlation techniques to search for pings with known features in noisy hydrophone data, and determine their arrival times. Analogous problems exist in many areas of signal processing, of course.
3) Sunspot data
Since the 1840's, careful records have been kept of the number of sunspots visible as a function of time. The possibilities here are endless. Find periodicity and correlations in simultaneous measurements of sunspot numbers and cosmic ray fluxes at the earth's surface (neutron monitor data), or correlate the sunspot numbers with other phenomena you may have data for: people have claimed correlations with stock market performance (if anyone has access to a file of daily Dow-Jones Average closing prices for a long period of time, please let me know), weather, the number of Republican Senators, homicide rates, etc etc. You can also compare the performance of various fitting, smoothing or averaging techniques on the detailed time series. For data, see ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/SUNSPOT_NUMBERS/ ; for an explanation look at the file read.me; see http://www.ngdc.noaa.gov/stp/SOLAR/SSN/ssn.html for additional information.
4) Phototube pulse parameters
Photomultiplier tubes provide electrical pulses in response to light input (as low as a single photon). One perennial problem is finding a way of extracting a number nicely proportional to the light collected from a record of the pulse shape (voltage vs time). Pulse area is the best estimator but it is expensive to measure (in terms of hardware cost) with fast analog-to-digital electronics. People try various quick measurements, like pulse width (time over a given threshold -- which threshold is best?) and peak height. I have lots of PMT pulse voltage-vs-time records; you can compute their area and then try to find correlations between area and any other parameter or combination of parameters.
5) Electron cascade simulation
When a high energy gamma ray strikes a block of lead, it can convert itself into an electron and a positron (pair production); each of these can in turn shake off additional gamma rays (bremsstrahlung) which continue the process -- but not ad infinitum. The total number of charged particles in the cascade increases, but of course the energy per particle decreases due to energy conservation. Eventually the mean photon energy falls below the threshold for pair production (energy < mass of electron + positron). Then the number of particles decreases as electrons bounce off atoms and lose energy by ionization. This leads to a characteristic shape for a plot of the number of charged particles present as a function of depth in Pb, called the "transition curve", or shower curve. The process is of great interest because it provides a good technique for measuring the energy of gamma rays (or electrons), called "ionization calorimetry": since pair production and bremsstrahlung just involve an exchange of energy between particles and photons, the only real energy LOSS mechanism is ionization. Thus one can relate the area under the shower curve, called the "track length" (why?) to the energy of the initiating particle. Use monte carlo techniques to perform a simplified simulation of electron-photon cascades initiated by a high energy gamma ray in Pb, and compare your results to standard shower curves. I can provide a separate handout with more details.