QERM: An Interdisciplinary Graduate Program


Degree Programs

Master's Degree Coursework

Master of Science (M.S.) degree coursework is divided into core and elective courses. Electives are selected with the guidance of the M.S. supervisory committee. A Plan of Study form documenting the recommended electives is completed and approved by the M.S. supervisory committee.

QERM Master's Degree Core Coursework

Autumn Quarter

STAT 516 Stochastic Modeling of Scientific Data (3 credits)
Markovian and semi-Markovian models, point processes, cluster models, queuing models, likelihood methods, estimating equations. Prerequisite: STAT 511 or STAT 396.

IND E 599 (Section D) Introduction to Optimization (3 credits)
**OR**
IND E 513 Linear Optimization Models in Engineering

QERM 597 QERM Fall Seminar (2 credits)

Winter Quarter

STAT 517 Stochastic Modeling of Scientific Data (3 credits)
Markovian and semi-Markovian models, point processes, cluster models, queuing models, likelihood methods, estimating equations. Prerequisite: STAT 516. Offered: W.

BIOL 567/CFR 567/FISH 567 Topics in Advanced Ecology (3, max. 6)
Discusses literature on active research areas or controversies in different branches of ecology. Offered: jointly with CFR 567/FISH 567; W.

QERM 597 - QERM Winter Seminar (2 credits)
All students register for this course; students in year 2 and above present their research to QERM students and faculty. Schedule of presentations - QERM 597

Spring Quarter

QERM 514 - Analysis of Ecological and Environmental Data (4 credits) Overview of generalized linear models (GLMs), their use in forestry, fisheries, wildlife ecology, and environmental monitoring. Analysis of the statistical tests that fall under GLMs: chi-square tests on contingency tables, t-tests, analysis of variances, etc. Statistical software S+/R used throughout. (Instructor class description - QERM 514)

SEFS 540 - Optimization Techniques for Natural Resources (5 credits ) Studies optimization techniques for natural resource managers including spatial optimization; linear, integer, and multi-objective programming; and stochastic and combinatorial optimization. Emphasizes model building rather than on algorithmic concepts. Prerequisite: MATH 308 or permission of instructor.

* AMATH 523 - Mathematical Analysis in Biology and Medicine(5 credits)
This course focusxes on developing and analyzing mechanistic, dynamic models of biological systems and processes, to better understand their behavior and funciton. Applications are drawn from many brances of biology and medicine. Students will gain experience in applying differential equations, difference equations, and dynamical systems theory to biological problems. Prerequisites: Background equivalent to AMATH 351, AMATH 422 or MATH 307.
**OR**
* AMATH 535 - Mathematical Ecology (5 credits)
This course considers models, methods, and issues in population ecology. Topics include the effects of density dependence, delays, demographic stochasticity, and age structure on population growth; population interactions (predation, competition, and mutualism); and applications of optimal control theory to the management of renewable resources. Prerequisite: AMATH 402 or AMATH 423 or permission of the instructor.

OTHER

Ecology Elective (from list of recommended ecology electives) - recommended to be taken fall quarter
QSCI 486 - Experimental Design (not required, but recommended during years when the course is offered) Topics in analysis of variance and experimental designs: choice of designs, comparison of inefficiency, power, sample size, pseudoreplication, factor structure. Prerequisite: QSCI 482; recommended: QSCI 483. Offered even years.
QERM 600 - Independent Study (variable credits)
QERM 700 - Masters Thesis Credits (minimum of 9 credits required)

* Students are encouraged to take AMATH 535 instead of AMATH 523 in the years when AMATH 535 is offered.

After completing the core coursework outlined above the student selects additional coursework in collaboration with their supervisory committee.

A student’s supervisory committee may also recommend a course in scientific writing (TC 509 (Writing the Scientific Article), FISH 521 (Grant Proposal Writing for Graduate Students).

DESCRIPTION OF SUGGESTED ELECTIVES

STATISTICS ELECTIVES:

STAT 512 Statistical Inference (4)
Review of random variables; transformations, conditional expectation, moment generating functions, convergence, limit theorems, estimation; Cramer-Rao lower bound, maximum likelihood estimation, sufficiency, ancillarity, completeness. Rao-Blackwell theorem. Hypothesis testing: Neyman-Pearson lemma, monotone likelihood ratio, likelihood-ratio tests, large-sample theory. Contingency tables, confidence intervals, invariance. Introduction to decision theory. Prerequisite: STAT 395 and STAT 421, STAT 423, STAT 504, or BIOST 512 (concurrent registration permitted for these three). Offered: A.

STAT 513 Statistical Inference (4)
Review of random variables; transformations, conditional expectation, moment generating functions, convergence, limit theorems, estimation; Cramer-Rao lower bound, maximum likelihood estimation, sufficiency, ancillarity, completeness. Rao-Blackwell theorem. Hypothesis testing: Neyman-Pearson lemma, monotone likelihood ratio, likelihood-ratio tests, large-sample theory. Contingency tables, confidence intervals, invariance. Introduction to decision theory. Prerequisite: STAT 512. Offered: W.

STAT 570 Advanced Applied Statistics and Linear Models (3)
Generalized linear models, REML in mixed models for randomized blocks, split plots, longitudinal data. Generalized estimating equations, empirical model building, cross validation, recursive partitioning, generalized additive models, projection pursuit. Prerequisite: STAT 513; STAT 533 or STAT 421 and STAT 423, and a course in matrix algebra for STAT 570. Offered: jointly with BIOST 570; A.

STAT 571 Advanced Applied Statistics and Linear Models (3)
Generalized linear models, REML in mixed models for randomized blocks, split plots, longitudinal data. Generalized estimating equations, empirical model building, cross validation, recursive partitioning, generalized additive models, projection pursuit. Prerequisite: STAT 570. Offered: jointly with BIOST 571; W.

Biology/Ecology Electives:

BIOL 429 Models in Biology (4) NW
Explores use of models in biology in a wide range of topics, including morphogenesis, nerve signals, ecological interactions, population biology, and evolutionary theory. Emphasis on the biological insights models can provide rather than mathematical techniques. Prerequisite: either MATH 146, MATH 390, MATH 395, STAT 342, or STAT 391. 

BIOL 433 Marine Ecology (5) NW
Study of marine ecological processes such as recruitment, disturbance, competition, and predation, and their effects on the structure and diversity of marine communities. Weekend field trips to local intertidal habitats required. Prerequisite: either BIOL 356, BIOL 472, or a minimum grade of 3.4 in BIOL 180. Offered: Sp, odd years.

BIOL 472 Community Ecology (5) NW
Covers the complexity of biological communities as influenced by biotic and abiotic factors, as well as the impact of human activities (like global warming) on communities. Prerequisite: BIOL 356.

BIOL 476 Conservation Biology (5) NW
Explores biological, managerial, economic, and ethical concepts affecting survival of species. Applications of ecology, biogeography, population genetics, and social sciences for the preservation of species in the face of widespread global habitat modification, destruction, and other human activities. Prerequisite: BIOL 180.

BIOL 497 Special Topics in Biology (1-5, max. 10) NW

BIOL 560 Seminar in Ecology (1-3, max. 15)
Weekly discussions of past and current scientific literature in ecology, reviews of the state of the field, and presentation of research results. Discussions may cover the full breadth of the discipline or focus on selected topics. Graduate status required, or permission of instructor for undergraduates. 

BIOL 561 Topics in Ecology (1-3, max. 15)
Focused discussion of on-going research in ecology occurring in the instructor's laboratory. Graduate status required, or permission of instructor for undergraduates.

BIOL 563 Experimental Evolutionary Ecology (5) NW
Explores experimentally approachable questions in ecology and evolution through lectures, lab, and field experiments. Topics may include evolution of bacterial antibiotic resistance, the evolution of virulence, seed predation, plant biodiversity, and others. Offered: A; concurrent with BIOL 481. 

FISH 458 Modeling and Estimation in Conservation and Resource Management (4) NW
Explores the use of models in the evaluation of alternative management polices for natural resources, including modeling approaches, fitting models to data, and evaluating alternative management polices. Emphasizes calculating risk of extinction, and design of biological reserves. Recommended: either Q SCI 454 or FISH 454. Offered: jointly with Q SCI 458;  

FISH 557 Estimation of Population Parameters (4)
Statistical analysis of population data; design and analysis of mark-recapture experiments on natural populations; laboratory work on computers. Recommended: probability theory and Q SCI 292 and 483.

FISH 558 Decision Analysis in Natural Resource Management (4)
Focuses on age and size-structured population models; Bayesian methods; Sample Importance Resample algorithm; Markov chain Monte Carlo algorithm; policy evaluation; and risk analysis and uncertainty in fisheries management. Recommended: FISH 557, or permission of instructor. 

FISH 559 Numerical Computing for the Natural Resources (4)
Focuses on age and size-structured population models; Bayesian methods; Sample Importance Resample algorithm; Markov chain Monte Carlo algorithm; policy evaluation; and rask analysis and uncertainty in fisheries management. Recommended: FISH 557, or permission of Instructor.

OCEAN 539 Seminar in Biological Oceanography (*, max. 24)
Lectures, discussions, and work on selected problems of current interest. Prerequisite: permission of instructor. Offered: AWSp.

FORESTRY/ECOLOGY ELECTIVES:

CFR 501 Forest Ecosystems-Community Ecology (5)
Community ecology of forest ecosystems. Quantitative methods of community description. Role of limiting factors, competition and disturbance in determining community composition, structure and stability. Introduction to forest ecosystem productivity. History and application of successional theory. Prerequisite: basic ecology course or permission of instructor. Offered: A.

ESRM 425 Ecosystem Management (5) NW
Scientific and social basis for ecological forestry. Forest practices to achieve integrated environmental and economic goals based upon material models of disturbance and stand development including alternative harvesting methods; adaptive management and monitoring; certification and global issues. Offered: A. 

CFR 526 Seminar in Advanced Silviculture (3)
Seminar on current and emerging silvicultural issues and underlying biological principles. Topics include: stand management to enhance wildlife, biodiversity and high productivity in sub-tropical and tropical regions; computer simulation of stand growth; adaptation to changes in management objectives; soil conditions and productivity during stand rotation; and minimizing effects of catastrophic disruption. Prerequisite: ESRM 428. Offered: W.

CFR 541 Advanced Landscape Ecology (5)
Investigates the causes and consequences of spatial patterns in ecology. Concentrates on applied questions and approaches, covering topics such as scaling, landscape processes, pattern measurement, biogeography, landscape modeling, and conservation planning. Prerequisite: CFR 501. Offered: W.

MODELING ELECTIVES:

IND E 410 Linear and Network Programming (4)
Modeling and optimization of linear network problems. Topics inclucde: optimization of linear systems, mathematical model design, simplex method, primal-dual algorithms, parametric programming, goal programming, network problems and algoithms, and PERT/CPM. Prerequisite: either MATH 136 or MATH 308; CSE 142. Offered: A. 

IND E 411 Stochastic Models and Decision Analysis (4)
Stochastic systems analysis to industrial engineering problems. Topics include: Markov chains, queueing theory, queueing applications, and decision analysis. Prerequisite: IND E 315; IND E 410. Offered: W.

IND E 412 Integer and Dynamic Programming (4)
Modeling and optimization of problems and dynamic programming approach to optimization. Topics include: integer programming formulation techniques, linear and Lagrangian relaxation, branch-and-bound and cutting-plane methods, integer programming applications, and dynamic programming. Prerequisite: IND E 411. Offered: Sp.

IND E 508 Stochastic Processes in Engineering (3)
Non-measure theoretic introduction to stochastic processes. Topics include Poisson processes, renewal processes, Markov and semi-Markov processes, Brownian motion, and martingales, with applications to problems in queuing, supply chain management, signal processing, control, and communications. Prerequisite: E E 505. Offered: jointly with E E 508; AWSp.

IND E 513 Linear Optimization Models in Engineering (3)
Advanced formulation techniques to expand applications of linear programming to large-scale models. Appreciation of role of optimization models in engineering applications through introduction of techniques such as decomposition. Individual engineering projects. Prerequisite: IND E 410 and MATH 308 or permission of instructor.

OPTIMIZATION ELECTIVES:

MATH 407 Linear Optimization (3) NW
Maximization and minimization of linear functions subject to constraints consisting of linear equations and inequalities; linear programming and mathematical modeling. Simplex method, elementary games and duality. Prerequisite: either 2.0 in MATH 136, 2.0 in MATH 308, 2.0 in MATH 318, or 2.0 in AMATH 352. Offered: AWS.

MATH 408 Nonlinear Optimization (3) NW
Maximization and minimization of nonlinear functions, constrained and unconstrained; nonlinear programming problems and methods. Lagrange multipliers; Kuhn-Tucker conditions, convexity. Quadratic programming. Prerequisite: either 2.0 in MATH 308 or 2.0 in MATH 318; either 2.0 in MATH 327 or 2.0 in MATH 334. Offered: W.

MATH 409 Discrete Optimization (3) NW
Maximization and minimization problems in graphs and networks (shortest paths, minimum spanning trees, maximum flows, minimum cost flows); transportation and trans-shipment problems, NP-completeness. Prerequisite: 2.0 in MATH 407. Offered: Sp.

MATH 514/AMATH 514  Networks and Combinatorial Optimization (3)
Networks and directed graphs. Paths and trees. Feasible and optimal flows and potentials. Transportation problems, matching and assignment problems. Algorithms and applications. Prerequisite: MATH 308 or AMATH 352 and MATH 324. Offered: jointly with AMATH 514.

 

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