Course Syllabus

Fall 2019 BIOINF 501

Mathematical Foundations for Bioinformatics

 

Instructors:
Kayvan Najarian, Daniel Burns, Jonathan Gryak, Reza Soroushmehr, and Ivo Dinov

Start Time, End Time and Location

MW 1:30PM - 3:00PM, Room: # Palmer Hall 2036 

 

Topics/Modules:

Module 1: Review of Some Basic Methods in Mathematics

Probability functions

Review of complex variables and functions

Taught by: Kayvan Najarian

Duration: 2 lectures

            

Review of multi-variable calculus

Taught by: Reza Soroushmehr

Duration: 2 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: Jonathan Gryak

Duration: 3 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

Differential equations for compartmental modeling of biomedical systems

Taught by: Reza Soroushmehr

Duration: 4 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

 

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