BIOINF 501 001 FA 2021
Fall 2021 BIOINF 501
Mathematical Foundations for Bioinformatics
Overview
The course covers some of the fundamental mathematical techniques commonly used in bioinformatics and biomedical research. These include: 1) principles of multi-variable calculus, and complex numbers/functions, 2) foundations of linear algebra, such as linear spaces, eigen-values and vectors, singular value decomposition, spectral graph theory and Markov chains, 3) differential equations and their usage in biomedical system, which includes topic such as existence and uniqueness of solutions, two dimensional linear systems, bifurcations in one and two dimensional systems and cellular dynamics, and 4) optimization methods, such as free and constrained optimization, Lagrange multipliers, data denoising using optimization and heuristic methods. Demonstrations using MATLAB, R, and Python will be included throughout the course.
All classes will be online via Zoom
Instructors
Kayvan Najarian, Shuyang Cheng, Reza Soroushmehr, and Ivo Dinov
TA: Da-Wei Lin
Start Time, End Time and Location
MW 1:30PM - 3:00PM,
Only the first session - Monday, August 31 - will be both in-person and online. All other sessions will be remote only. Students are welcome to take the entire course online if they so choose.
Topics/Modules
Module 1: Review of Some Basic Methods in Mathematics
Probability functions
Review of complex variables and functions
Taught by: Kayvan Najarian
Duration: 3 lectures
Module 2: Linear Algebra
Introduction to linear systems
Matrix products
The inverse of a linear transformation
Linear spaces
Orthogonality
Determinants, eigenvalues and eigenvectors
Symmetric matrices and diagonalization
Solving systems of linear equations
Singular value decomposition
Principal component analysis
Spectral graph theory
Taught by: Shuyang Cheng
Duration: 9 lectures
Module 3: Differential Equations
Introduction to differential equations
First and second order linear equations
Existence and uniqueness of solutions
Difference equations
Systems of linear equations
Phase plane and bifurcation: diagrams and analysis
First order nonlinear systems
Differential equations for compartmental modeling of biomedical systems
Taught by: Reza Soroushmehr
Duration: 6 lectures
Data Science and Predictive Analytics EBook (University of Michigan Library)
Free (unconstrained) optimization vs. Constrained Optimization
Equality and Inequality constraints
Lagrange Multipliers
Linear and Quadratic Programming
Manual vs. Automated Lagrange Multiplier Optimization
Data Denoising: Application of computer optimization techniques in medicine and biology
Heuristic methods - Genetic algorithms, simulated annealing
Applications (supervised classification & unsupervised clustering)
Instructor: Ivo Dinov
Duration: 6 lectures
Software tools: Matlab, R, Python, and open-science tools.
Course Summary:
Date | Details | Due |
---|---|---|