Prior knowledge of elementary calculus
In this course, students will learn to formulate mathematical models leading to rate equations, transport equations, and variational principles. They will also learn techniques for extracting qualitative and quantitative information from those models. In particular, they will study phase line analysis, phase plane analysis, the method of characteristics, dimensional analysis, and methods for constructing similarity solutions.
B18 Methods of Mathematical Modeling I
In this course, students will learn to apply regular and singular perturbation methods to ordinary and partial differential equations. They will also be exposed to boundary-layer theory, long-wave asymptotic methods for partial differential equations, methods for analyzing weakly nonlinear oscillators and systems with multiple time scales, the method of moments, the Turing instability, pattern formation, and Taylor dispersion.
No prior knowledge assumed
This course will provide an introduction to Evolutionary Biology focusing on the developmental process of multicellular organisms for students with and without an undergraduate background in this field. Two major goals in this course will be to understand evolutionary changes in development and to learn modern creatures and technologies employed for addressing issues in evolutionary developmental biology.This course presents the basic principles and recent findings in evolutionary developmental biology.
Biology, chemistry, or physics at undergraduate levels
Description: Students will learn several basic concepts of biophysics including thermal conformational fluctuation and thermal diffusion, and how cells might take advantage of these physical processes to enable their functions. As a biological paradigm, the cellular membrane system (and their functions), with a special attention paid to signal transduction in the plasma membrane, will be extensively covered.
Prerequisite courses and assumed knowledge: Basic computer skill with Windows, MacOS, or Linux is assumed. Each student will bring in a laptop provided by the Graduate School. Knowledge of basic mathematics, such as the calculus of vectors and matrices and the concept of differential equations, is assumed, but pointers for self-study are given if necessary.
The course starts with basic programming using Python, with some notes on other computing frameworks. Students then get acquainted with data manipulation and visualization using “numpy” and “matplotlib.” After learning how to define one’s own function, students learn iterative methods for solving algebraic equations and dynamic simulation of differential equations. The course also covers basic concepts in stochastic sampling, distributed computing, and software management.
Assumes general knowledge in biology; ideally follow-on course from B16 Ecology and Evolution
Life sciences have been greatly influenced by the progress of DNA sequencing technologies. The field of Evolutionary Biology is no exception, and increasingly relies upon fast generation of DNA sequences, that are analysed using fast evolving bioinformatics tools.
This is a basic level course, that will be adjusted accordingly to the interests of enrolled students. No prior knowledge assumed.
The course will start from the mechanisms of animal movement, including the evolutionary, ecological and energetic aspects; we will explore the anatomical and mechanical features of the body machinery (such as muscles, bones and tendons) before investigating the structure and dynamic function of the neuronal circuits driving and controlling movements.
Students work in the laboratory of the Professor under whom they wish to conduct their thesis research. They undertake and write up preliminary research work, complete an in-depth literature review and prepare a research plan. The preliminary research work should include methods the students will use in their thesis research. The literature review should be in the area of their thesis topic and be of publishable quality.
This course aims to develop knowledge and skills important for leadership in scientific research and education. The three main components of the course are (1) weekly seminars covering basic principles of research conduct and ethics, scientific communication, and aspects of science in society, (2) a cross-disciplinary group project, and (3) practical experience to develop presentation and teaching skills.