Fall 2023 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, eigenvalues and eigenvectors, matrix algebra, least square solutions, singular value decomposition and applications, 3) basics of differential equations, such as existence and uniqueness of solutions and linear systems, 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 are in person.

Instructors
Kayvan Najarian, Cristian Minoccheri, and Ivo Dinov

TA: Shiting Li

 

Start Time, End Time and Location

Lecture: Mon and Wed 1:30PM - 3:00PM, Rm. 3813 Med Sci II Bldg.

Lab/Discussion: Mondays @ 3:00 – 4:00 PM in Rm. 3813 Med Sci II Bldg.

This course will be an in-person class.

 

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 algebra

The inverse of a linear transformation

Linear subspaces and dimension

Linear projections

Orthogonality

Least square solutions

Determinants, eigenvalues and eigenvectors, rank

Symmetric matrices and diagonalization

Singular value decomposition and applications

Principal component analysis

Linear models

Taught by: Cristian Minoccheri

Duration: 12 lectures

 

Module 3: Differential Equations

First and second order linear equations

Systems of linear equations

Discrete and continuous dynamical systems

Taught by: Cristian Minoccheri

Duration: 3 lectures

 

Module 4: Optimization (November 13 – December 6, 2023)

Data Science and Predictive Analytics EBook (University of Michigan Library)

Free (unconstrained) optimization vs. Constrained Optimization

Foundations of R (Introduction)

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: 8 lectures

 

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Software tools: Matlab, R, Python, and open-science tools.