Course Syllabus
Fall 2018 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: 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
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
Location: Medical Science 2 - 3733
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 | Due |
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