Demography 250 is a course in mathematical demography with an emphasis on applications. It includes an introduction to basic techniques and theorems of mathematical demography and an overview of recent results and their practical implications. Only a limited number of proofs will be presented. Topics include probabilistic models of population growth, correlated frailty models for hazard functions, biodemographic models, mutation accumulation, life-course optimization, stochastic forecasting, population momentum, stable population theory, approach to stability, and demographic feedback models.
Demography 250 meets Tuesdays and Thursdays from 11:10 to 12:30 in Dwinelle Hall 127, with video hookup to the UCLA Videoconference Center in Haines Hall 215. It is taught jointly with Sociology 285D at UCLA.
Please note: The first class meeting will be on Tuesday, 4 September, in the second week of the Berkeley semester.
Prof. Wachter's office is in Room 208 in 2232 Piedmont Avenue. Office hours are from 11:00 to 11:50 and 1:30 to 2:45 on Wednesdays. A sign-up sheet is posted by the door. Telephone for UCLA students is 510-642-1578. Some on-site office hours at UCLA will be arranged. Visiting Professor Robert Chung will be assisting with the course and providing feedback on the exercises. His office is in 2224 Piedmont Avenue.
There will be weekly exercises illustrating points and developing skills on topics discussed in the lectures. Assignments are posted on the secure website and are due each Tuesday at the beginning of class. Arrangements will be made to mail UCLA exercises to Berkeley each week. Exercises will often be discussed in class, so no late solution sets will be accepted in normal circumstances. Students may use any computing system with which they are familiar, but advice on computing will only be available for the language R, a freeware version of the Bell Laboratories language SPLUS.
There will be no final examination. Instead, students are asked to submit a term paper, about ten pages in length, by 1 November 2007. The paper should be in the form of a written text for an expository class lecture on one of the topics in mathematical demography not been covered in depth in the course. The lecture should be designed for a 45-minute class, including appropriate graphs and examples. Suggestions for topics will be posted later in the term. Grades will be based 50\% on the exercises and 50\% on the paper. Class participation will count in your favor in the process of translating numerical scores into letter grades.
I : Aug : No Class
II : 4 Sep : Descendants, Branching Processes, and Exponential Growth
...: 6 Sep : Extinction Probabilities and Limit Laws
III : 11 Sep : Ancestors, Coalescents
... : 13 Sep : Random Rates, Random Walks, Homeostasis
IV : 18 Sep : Hazard Functions, Frailty Selection
...: 20 Sep : Markovian Vitality, Correlated Frailty
V : 25 Sep : Genetic Demography, Fixation, Hamilton Weights
... : 27 Sep : Mutation Accumulation
: >>>> : UCLA Quarter Starts
VI : 2 Oct : The Leslie Matrix, the Stable State
... : 4 Oct : Lotka's Equation and the Cumulant Expansion
VII : 9 Oct : Dependency Ratios, Promotions
... : 11 Oct : Lineal Kin, Intergenerational Transfers
VIII : 16 Oct : Reproductive Value and Momentum
... : 18 Oct : Approach to Stability; Population Waves
IX : 23 Oct : Non-Stable Populations; Hilbert's Projective Metric
... 25 Oct : The Inhomogeneous Ergodic Theorem
X : 30 Oct : The Renewal Equation, Lexis Surfaces, the McKendrick Equations
... : 1 Nov : CAL, Gaps and Lags, Variable r
XI : 6 Nov : Tempo and Quantum
... : 8 Nov : Stochastic Forecasting
XII : 13 Nov : Demographic Feedback Models
... : 15 Nov : Limit Cycles
XIII: 20 Nov : Stage dependence, Variable Environments
... : 22 Nov : THANKSGIVING
XIV : 27 Nov : Life History Optimization
... : 29 Nov : Resource Constraints
XV : 4 Dec : Selected Topics
... : 6 Dec : Review
Students taking the course will want to have or quickly acquire familiarity with
Life table functions e_x, l_x, _nL_x,
Lexis diagrams,
integration by parts,
Taylor series,
the epsilon-delta definition of limits,
representation of complex numbers with sines and cosines,
conditional expectations E Z = E ( E ( Z | y ) ),
varance of a binomial distribution,
mean and variance of an exponential distribution,
definition of matrix eigenvectors and eigenvalues.
A secure website has been established for the class. The URL is http://www.demog.berkeley.edu/250secure. (No twiddle before 250secure; sorry for the mistake in an earlier version.) Passwords will be assigned in class. Handouts, exercises, illustrative computer code, references, and other information will be posted on the secure website. We are planning to record the lectures on DVDs, which may be available for review.