BIOINF 501 001 FA 2019

BIOINF 501 001 FA 2019

Fall 2019 BIOINF 501

Mathematical Foundations for Bioinformatics

 

Instructors:
Kayvan Najarian, Daniel Burns, Jonathan Gryak, Indika Rajapakse, and Ivo Dinov

 

Topics/Modules:

Module 1: Review of Some Basic Methods in Mathematics

               Review of multi-variable calculus

               Probability functions

               Review of complex variables and functions

Taught by: Kayvan Najarian

Duration: 4 lectures

 

Module 2: Linear Algebra

Part I

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

Taught by: Jonathan Gryak

Duration: 5 lectures

 

Part II

Singular value decomposition

Principal component analysis

Spectral graph theory

Taught by: Daniel Burns

Duration: 5 lectures

 

Module 3: Differential Equations

Part I

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

Taught by: Jonathan Gryak

Duration: 4 lectures

 

Part II

Cellular dynamics: Biological background. A gene network that acts as clock. Networks that act as a switch

A brief introduction to numerical methods to solve differential equations

Taught by: Indika Rajapakse

Duration: 2 lectures

 

Module 4: Optimization

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

Free (unconstrained) optimization vs. Constrained Optimization

Foundations of R

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

Location: TBD

 

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

 

Start Time, End Time and Location

MW 1:30PM - 3:00PM, Room TBD

Course Summary:

Date Details
CC Attribution Share Alike This course content is offered under a CC Attribution Share Alike license. Content in this course can be considered under this license unless otherwise noted.