Courses

Introduction to Neural Coding and Computation

Introduces computational neuroscience, grounded in neuronal and synaptic biophysics. Works through mathematical description of how neurons encode information, and how neural activity is produced dynamically. Uses and teaches Matlab as a programming language to implement models of neuronal dynamics and to perform coding analysis.

Prerequisites:

Math 125

Course Web Page

Computational Modeling of Biological Systems

Fundamental models that arise in biology and their analysis through modern scientific computing. Discrete and continuous-time dynamics, in deterministic and stochastic settings, with applications from molecular biology to neuroscience to population dynamics. Statistical analysis of experimental data. MATLAB or R programming taught from scratch.

Prerequisites:

Either a course in differential equations or permission of the instructor

Course Web Page (Autumn 2017)

Mathematical Analysis in Biology and Medicine

This course focuses on developing and analyzing mechanistic, dynamic models of biological systems and processes, to better understand their behavior and function. Applications are drawn from many branches of biology and medicine. Students will gain experience in applying differential equations, difference equations, and dynamical systems theory to biological problems.

Prerequisites:

Either courses in differential equations and probability and statistics, or permission of the instructor

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Course Web Page (Winter 2018)

Mathematical Theory of Cellular Dynamics

Biological cells are biochemical systems that obey the laws of physics. This course develops a coherent mathematical theory for processes inside living cells. It focuses on analyzing dynamics leading to functions of cellular components (gene regulation, signaling biochemistry, metabolic networks, cytoskeletal biomechanics, epigenetic inheritance) using deterministic and stochastic models.

Prerequisites:

Either courses in dynamical systems, partial differential equations, and probability, or permission of the instructor

Course Web Page (Winter 2014)

Dynamics of Neurons and Networks

Mathematical analysis and computational modeling on three interconnected scales -- neurons, networks, and populations -- including (1) oscillations and synchrony, (2) role of network structure and symmetry, (3) statistical mechanics tools for large-scale models, (4) bifurcation and reduction methods for biophysical models. Emphasizes links between system dynamics and signal processing.

Prerequisites:

Either familiarity with dynamical systems and probability or permission of the instructor

Course Web Page (Winter 2020)

Mathematical Ecology

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.

Prerequisites:

Either a course in differential equations or permission of the instructor

Course Web Page (Spring 2019)

Mathematical Modeling of Cancer

Introduces stochastic and deterministic methods for mathematical modeling of cancer evolution. Particular emphasis on branching process models of cancer initiation, progression and response to therapy, and their relationship to clinical, epidemiological and sequencing data. The course introduces both analytic and computational approaches for modeling cancer, and gets students acquainted with the current research in the field.

Prerequisite:

Previous experience with calculus, probability, ODEs and programming or permission of instructor.