BIOINF 501 001 FA 2024
Fall 2024 BIOINF 501
Mathematical Foundations for Bioinformatics
Overview
The course covers some of the mathematical prerequisites to understand fundamental techniques in bioinformatics, biomedical research, and machine learning. The goal is to introduce students to a wide variety of topics, so that they will be able to understand their applications in future courses and/or they will have a basic understanding to build upon should they need to dig deeper into certain topics. Each module contains topics normally covered over an entire semester, so we inevitably won't be able to delve into every detail. On the other hand, the focus will be on computations and using software to solve problems.
Topics include: 1) introduction to multi-variable calculus, complex numbers, and probability; 2) foundations of linear algebra, such as linear systems, eigenvalues and eigenvectors, matrix algebra, least square solutions, singular value decomposition and applications; 3) introduction to differential equations and dynamical systems, such as existence and uniqueness of solutions, linear systems, bifurcations; 4) optimization methods, such as free and constrained optimization, Lagrange multipliers, data denoising using optimization and heuristic methods. Demonstrations using MATLAB, R, and Python will be included throughout the course.
All classes are in person.
Instructors
Cristian Minoccheri
Links to an external site. and Ivo Dinov OH (Fridays 9AM
Links to an external site., pass: 2212)
TA: Elysia Chou Links to an external site.
Start Time, End Time and Location
Lecture: Mon and Wed 1:30PM - 3:00PM, Rm. 3813 Med Sci II Bldg Links to an external site..
Lab/Discussion: Mondays @ 3:00 – 4:00 PM in Rm. 3813 Med Sci II Bldg Links to an external site..
This course will be an in-person class.
Topics/Modules
Module 1: Multivariable Calculus and Probability
Introduction to multivariable functions, gradients, matrix and vector calculus, multiple integrals
Axioms of probability
Conditional probability, sum and product rules, Bayes formula
Discrete and continuous distributions, joint distributions
Conditional distributions, sum and product rules for distributions
Expectation
Taught by: Cristian Minoccheri Links to an external site.
Duration: about 5 lectures
Module 2: Linear Algebra
Linear systems, Matrix algebra,Linear transformations
Linear subspaces, dimension, linear projections
Orthogonality, least squares solutions
Determinants, eigenvalues and eigenvectors, rank
Markov chains
Symmetric matrices and diagonalization
Singular value decomposition and applications
Principal component analysis
Spectral graph theory
Taught by: Cristian Minoccheri Links to an external site.
Duration: about 10 lectures
Module 3: Differential Equations
Introduction to differential equations
Systems of linear equations
Dynamical systems, introduction to bifurcation theory
Taught by: Cristian Minoccheri Links to an external site.
Duration: about 3 lectures
Module 4: Optimization ( Links to an external site.November 11 – December 4, 2024)
Free (unconstrained) optimization vs. Constrained Optimization Links to an external site.
Foundations of R (Introduction) 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: 8 lectures
Software tools: Matlab, R, Python, and open-science tools.
Course Summary:
Date | Details | Due |
---|---|---|
Tue Sep 5, 2023 | Calendar Event Kayvan's Office Hours | 8am to 9am |
Wed Sep 6, 2023 | Calendar Event BIOINF 501 FA 2023 GSI Office Hours | 5pm to 6pm |
Mon Sep 11, 2023 | Calendar Event BIOINF 501 LAB | 3pm to 4pm |
Tue Sep 12, 2023 | Calendar Event Kayvan's Office Hours | 8am to 9am |
Wed Sep 13, 2023 | Calendar Event BIOINF 501 FA 2023 GSI Office Hours | 5pm to 6pm |
Tue Sep 19, 2023 | Calendar Event Kayvan's Office Hours | 8am to 9am |
Wed Sep 20, 2023 | Calendar Event BIOINF 501 FA 2023 GSI Office Hours (zoom only) | 5pm to 6pm |
Tue Sep 26, 2023 | Calendar Event Kayvan's Office Hours | 8am to 9am |
Wed Sep 27, 2023 | Calendar Event BIOINF 501 FA 2023 GSI Office Hours (canceled) | 5pm to 6pm |
Tue Oct 3, 2023 | Calendar Event Kayvan's Office Hours | 8am to 9am |
Wed Oct 4, 2023 | Calendar Event BIOINF 501 FA 2023 GSI Office Hours | 5pm to 6pm |
Tue Oct 10, 2023 | Calendar Event Kayvan's Office Hours | 8am to 9am |
Wed Oct 11, 2023 | Calendar Event BIOINF 501 FA 2023 GSI Office Hours (zoom only) | 5pm to 6pm |
Tue Oct 17, 2023 | Calendar Event Kayvan's Office Hours | 8am to 9am |
Wed Oct 18, 2023 | Calendar Event BIOINF 501 FA 2023 GSI Office Hours | 5pm to 6pm |
Tue Oct 24, 2023 | Calendar Event Kayvan's Office Hours | 8am to 9am |
Wed Oct 25, 2023 | Calendar Event BIOINF 501 FA 2023 GSI Office Hours(zoom only) | 5pm to 6pm |
Tue Oct 31, 2023 | Calendar Event Kayvan's Office Hours | 8am to 9am |
Wed Nov 1, 2023 | Calendar Event BIOINF 501 FA 2023 GSI Office Hours | 5pm to 6pm |
Tue Nov 7, 2023 | Calendar Event Kayvan's Office Hours | 8am to 9am |
Wed Nov 8, 2023 | Calendar Event BIOINF 501 FA 2023 GSI Office Hours | 5pm to 6pm |
Tue Nov 14, 2023 | Calendar Event Kayvan's Office Hours | 8am to 9am |
Wed Nov 15, 2023 | Calendar Event BIOINF 501 FA 2023 GSI Office Hours | 5pm to 6pm |
Tue Nov 21, 2023 | Calendar Event Kayvan's Office Hours | 8am to 9am |
Wed Nov 22, 2023 | Calendar Event BIOINF 501 FA 2023 GSI Office Hours | 5pm to 6pm |
Tue Nov 28, 2023 | Calendar Event Kayvan's Office Hours | 8am to 9am |
Wed Nov 29, 2023 | Calendar Event BIOINF 501 FA 2023 GSI Office Hours | 5pm to 6pm |
Tue Dec 5, 2023 | Calendar Event Kayvan's Office Hours | 8am to 9am |
Wed Dec 6, 2023 | Calendar Event BIOINF 501 FA 2023 GSI Office Hours | 5pm to 6pm |
Wed Dec 13, 2023 | Calendar Event BIOINF 501 FA 2023 GSI Office Hours | 5pm to 6pm |
Wed Dec 20, 2023 | Calendar Event BIOINF 501 FA 2023 GSI Office Hours | 5pm to 6pm |
Fri Sep 6, 2024 | Calendar Event BIOINF 501 GSI Office Hours | 3:30pm to 4:30pm |
Mon Sep 9, 2024 | Calendar Event BIOINF 501 Lab | 3pm to 4pm |
Fri Sep 13, 2024 | Calendar Event BIOINF 501 GSI Office Hours | 3:30pm to 4:30pm |
Sun Sep 15, 2024 | Assignment Module1_Assignment1 | due by 11:59pm |
Thu Sep 19, 2024 | Calendar Event BIOINF 501 GSI Office Hours | 5:30pm to 6:30pm |
Mon Sep 23, 2024 | Calendar Event BIOINF 501 Lab | 3pm to 4pm |
Fri Sep 27, 2024 | Calendar Event BIOINF 501 GSI Office Hours | 3:30pm to 4:30pm |
Sun Sep 29, 2024 | Assignment Module1_Assignment2 | due by 11:59pm |
Fri Oct 4, 2024 | Calendar Event BIOINF 501 GSI Office Hours | 3:30pm to 4:30pm |
Mon Oct 7, 2024 | Calendar Event BIOINF 501 Lab | 3pm to 4pm |
Fri Oct 11, 2024 | Calendar Event BIOINF 501 GSI Office Hours | 3:30pm to 4:30pm |
Sun Oct 13, 2024 | Assignment Module2_Assignment1 | due by 11:59pm |
Fri Oct 18, 2024 | Calendar Event BIOINF 501 GSI Office Hours | 3:30pm to 4:30pm |
Mon Oct 21, 2024 | Calendar Event BIOINF 501 Lab | 3pm to 4pm |
Fri Oct 25, 2024 | Calendar Event BIOINF 501 GSI Office Hours | 3:30pm to 4:30pm |
Sun Oct 27, 2024 | Assignment Module2_Assignment2 | due by 11:59pm |
Fri Nov 1, 2024 | Calendar Event BIOINF 501 GSI Office Hours | 3:30pm to 4:30pm |
Mon Nov 4, 2024 | Calendar Event BIOINF 501 Lab | 3pm to 4pm |
Fri Nov 8, 2024 | Calendar Event BIOINF 501 GSI Office Hours | 3:30pm to 4:30pm |
Sun Nov 10, 2024 | Assignment Module3_Assignment | due by 11:59pm |
Fri Nov 15, 2024 | Calendar Event BIOINF 501 GSI Office Hours | 3:30pm to 4:30pm |
Mon Nov 18, 2024 | Calendar Event BIOINF 501 Lab | 3pm to 4pm |
Fri Nov 22, 2024 | Calendar Event BIOINF 501 GSI Office Hours | 3:30pm to 4:30pm |
Sun Dec 1, 2024 | Assignment Module2_Assignment3 | due by 11:59pm |
Mon Dec 2, 2024 | Calendar Event BIOINF 501 Lab | 3pm to 4pm |
Fri Dec 6, 2024 | Calendar Event BIOINF 501 GSI Office Hours | 3:30pm to 4:30pm |
Mon Dec 9, 2024 | Calendar Event BIOINF 501 Lab | 3pm to 4pm |
Tue Dec 10, 2024 | Assignment Homework 4 (Optimization) | due by 11:59pm |
