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44348.591J / 7.81J / 9.531J Systems Biology
http://www.merlot.org/merlot/viewMaterial.htm?id=555004
This course introduces the mathematical modeling techniques needed to address key questions in modern biology. An overview of modeling techniques in molecular biology and genetics, cell biology and developmental biology is covered. Key experiments that validate mathematical models are also discussed, as well as molecular, cellular, and developmental systems biology, bacterial chemotaxis, genetic oscillators, control theory and genetic networks, and gradient sensing systems. Additional specific topics include: constructing and modeling of genetic networks, lambda phage as a genetic switch, synthetic genetic switches, circadian rhythms, reaction diffusion equations, local activation and global inhibition models, center finding networks, general pattern formation models, modeling cell-cell communication, quorum sensing, and finally, models for Drosophila development.Global Focus on Knowledge 2007 / the World of Mathematics
http://www.merlot.org/merlot/viewMaterial.htm?id=556042
2007 Summer Semester "the World of Mathematics״Mathematics has the history of more than 2,000 years. It is the field still studied actively today, and developments are made rapidly in. Profound nature of numbers and figures, structures of functions and spaces are discovered one after another, and now, Fermat's last theorem, which had been the mystery of 350 years, or Poincare conjecture left pending for 100 years are solved. Recent proceedings of mathematics is quite spectacular. Also, since it allows free thinking and has a wide versatility, mathematics is applied to fundamental science, engineering, economics, sociology, and other disciplines as the common language of science. Sometimes, mathematics has the power to change all over the sociey, as it did when the principle of computer was discovered. Mathematics cannot be divided artificially. However, we are accustomed to, for the sake of convenience, separate it into four fields; algebra, geometry, analysis and applied mathematics. Plus, mathematical science includes mathematics for practical applications to analyze natural and social phenomena In this lecture series, themes characteristic to each fields are discussed by the experts working internationally. They navigate you for your further studies, by focusing mathematics from a wide perspective. Mathematics students learn in the first and second grade would be the basis of further studies. These lectures are expected to provide you with an outlook for the future.Introductory Modeling in Biology
http://www.merlot.org/merlot/viewMaterial.htm?id=379362
Introductory course in quantitative biology for lower division undergraduates. A range of biological topics are covered including plant pathology, ion channels, HIV, primate sexuality, and protein phylogenetics. Students are assumed to have completed one year of undergraduate calculus, and an introductory statistics class is useful. Math skills used include graphing, probability, correlation, arrays, logarithms, and ordinary differential equations. The discrete teaching modules are designed to be self-contained lab exercises. The modules are written as Mathcad documents that the students complete for credit. Thus, students must have access to Mathcad (version 13 or higher). PDF versions of the modules are also provided for demonstration purposes.Quantitative topics in Animal Behavior
http://www.merlot.org/merlot/viewMaterial.htm?id=379434
Undergraduate computer lab designed to teach quantitative thinking in the context of Animal Behavior. Ideally, this lab would be taught as a supplement to a concurrent lecture course. Students are assumed to have completed one year of undergraduate calculus, and an introductory statistics class is useful.Topics include bird song analysis (spectrograms), stochastic movement (diffusion and biased random walks), optimization of foraging strategies, evolutionary stable strategies (ess), spatial models of foraging, neural circuits, and frequency-dependent fitness. Math skills used include graphing, probability, arrays, logarithms, discrete-time models, and phase plane analysis.The modules are designed to be self-contained lab exercises. They are Mathcad documents that the students complete for credit. Thus, students must have access to Mathcad (version 13 or higher). PDF versions of the modules are also provided for demonstration purposes.Quantitative topics in Biochemistry
http://www.merlot.org/merlot/viewMaterial.htm?id=379488
Undergraduate lab series designed to familiarize students with using computer models to answer biochemical questions. Ideally, this lab would be taught as a supplement to a concurrent lecture course. Students are assumed to have completed one year of undergraduate calculus.Topics include acid-base chemistry, Gibbs free energy, Michaelis-Menten kinetics, enzyme inhibition, hemoglobin, and the Bohr effect. Math skills used include graphing (2-D and 3-D), algebra, logarithms, and numerical solutions to systems of equations.The modules are designed to be self-contained lab exercises. They are Mathcad documents that the students complete for credit. Thus, students must have access to Mathcad (version 13 or higher). PDF versions of the modules are also provided for demonstration purposes.Quantitative Topics in Neurobiology
http://www.merlot.org/merlot/viewMaterial.htm?id=379494
Undergraduate computer lab designed to teach quantitative thinking in the context of neurobiology. Ideally, this lab would be taught as a supplement to a concurrent lecture course. Students are assumed to have completed one year of undergraduate calculus.Topics include Nernst equation, GHK equation, passive electrical spread, voltage clamp, action potentials, synaptic currents, reciprocal inhibition, lateral inhibition, and the swimming circuit of Tritonia. Math skills used include graphing, logarithms, differential equations, and discrete-time models.The modules are designed to be self-contained lab exercises. They are Mathcad documents that the students complete for credit. Thus, students must have access to Mathcad (version 13 or higher). PDF versions of the modules are also provided for demonstration purposes.Transportation and Spatial Modelling
http://www.merlot.org/merlot/viewMaterial.htm?id=591345
The objective is to get insight and practice in the design and use of mathematical models for the estimation of transport demand in the framework of major strategic transportation planning. The course consists of a number of lectures and several exercises. Study Goals: 1. Insight in the function of mathematical models in transportation and spatial planning; 2. Knowledge of theoretical backgrounds of models; 3. Knowledge of application areas of models; 4. Ability to develop one's own plan of analysis for model computations; 5. Ability to apply models on planning problems; 6. Ability to present outcomes of model computations..