Course Syllabus

Fall 2018 BIOINF 501

Mathematical Foundations for Bioinformatics

 

Instructors:

Topics/Modules: Kayvan Najarian, Daniel Burns, Jonathan Gryak, Indika Rajapakse, and Ivo Dinov

 

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: Kayvan Najarian and 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

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

Taught by: Ivo Dinov

Duration: 6 lectures

 

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

 

Start Time, End Time and Location

Wed Sep 5, 2018, 1:30 PM 3:00 PM ET Medical Science 2 - 3733

 

Mon Sep 10, 2018, 1:30 PM 3:00 PM ET Medical Science 2 - 3733

 

Wed Sep 12, 2018, 1:30 PM 3:00 PM ET Taubman Health Sciences Library - 5330

 

Mon Sep 17, 2018, 1:30 PM 3:00 PM ET Medical Science 2 - 3733

 

Wed Sep 19, 2018, 1:30 PM 3:00 PM ET Medical Science 2 - 3733

 

Mon Sep 24, 2018, 1:30 PM 3:00 PM ET Medical Science 2 - 3733

 

Wed Sep 26, 2018, 1:30 PM 3:00 PM ET Taubman Health Sciences Library - 6215

 

Mon Oct 1, 2018, 1:30 PM 3:00 PM ET Medical Science 2 - 3733

 

Wed Oct 3, 2018, 1:30 PM 3:00 PM ET Medical Science 2 - 3733

 

Mon Oct 8, 2018, 1:30 PM 3:00 PM ET Medical Science 2 - 3733

 

Wed Oct 10, 2018, 1:30 PM 3:00 PM ET Medical Science 2 - 3733

 

Wed Oct 17, 2018, 1:30 PM 3:00 PM ET Medical Science 2 - 3733

 

Mon Oct 22, 2018, 1:30 PM 3:00 PM ET Medical Science 2 - 3733

 

Wed Oct 24, 2018, 1:30 PM 3:00 PM ET Medical Science 2 - 3733

 

Mon Oct 29, 2018, 1:30 PM 3:00 PM ET Medical Science 2 - 3733

 

Wed Oct 31, 2018, 1:30 PM 3:00 PM ET Medical Science 2 - 3733

 

Mon Nov 5, 2018, 1:30 PM 3:00 PM ET Medical Science 2 - 3733

 

Wed Nov 7, 2018, 1:30 PM 3:00 PM ET Medical Science 2 - 3733

 

Mon Nov 12, 2018, 1:30 PM 3:00 PM ET Medical Science 2 - 3733

 

Wed Nov 14, 2018, 1:30 PM 3:00 PM ET Medical Science 2 - 3733

 

Mon Nov 19, 2018, 1:30 PM 3:00 PM ET Medical Science 2 - 3733

 

Wed Nov 21, 2018, 1:30 PM 3:00 PM ET Medical Science 2 - 3733

 

Mon Nov 26, 2018, 1:30 PM 3:00 PM ET Medical Science 2 - 3733

 

Wed Nov 28, 2018, 1:30 PM 3:00 PM ET Medical Science 2 - 3733

 

Mon Dec 3, 2018, 1:30 PM 3:00 PM ET Medical Science 2 - 3733

 

Wed Dec 5, 2018, 1:30 PM 3:00 PM ET Medical Science 2 - 3733

 

Mon Dec 10, 2018, 1:30 PM 3:00 PM ET Medical Science 2 - 3733

Course Summary:

Date Details