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
Module 4: Optimization Links to an external site.
Free (unconstrained) optimization vs. Constrained Optimization Links to an external site.
Foundations of R Links to an external site.
Equality and Inequality constraints Links to an external site.
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 Links to an external site. (supervised classification & unsupervised clustering)
Instructor: Ivo Dinov Links to an external site.
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 |
|---|---|---|
| Mon Sep 24, 2018 | Assignment Module 1 | due by 11:59pm |
| Wed Sep 26, 2018 | Assignment Module 2 - Linear Algebra, Linear Algebra Part 1 - Homework 1 | due by 1:30pm |
| Mon Oct 8, 2018 | Assignment Module 2 - Linear Algebra, Linear Algebra Part 1 - Homework 2 | due by 1:30pm |
| Wed Oct 31, 2018 | Assignment Module 2 - Linear Algebra, Linear Algebra Part 2 - Homework 1 | due by 11:59pm |
| Tue Nov 6, 2018 | Assignment Module 3, Part 1 - Differential Equations, Part 1 - Homework 1 | due by 1:30pm |
| Wed Nov 14, 2018 | Assignment Module 3, Part 1 - Differential Equations, Part 1 - Homework 2 | due by 1:30pm |
| Mon Nov 19, 2018 | Assignment Module 3.2 - Differential Equations, Part 2 | due by 11:59pm |
| Tue Dec 11, 2018 | Assignment Module 4 (Optimization) | due by 11:59pm |
| Wed Dec 12, 2018 |
Assignment
Central Campus Fall 2018 Evaluation
(Central Campus Fall 2018 Evaluation)
|
due by 11:59pm |
| Assignment Central Campus Fall 2018 Evaluation | due by 11:59pm |