MATH 227A LEC A: MATH-COMP BIOLOGY (45060)

Math 227A, Mathematics and Computational Biology

Fall 2019 

Instructor: Natalia Komarova, Email: komarova@uci.edu

Instructor's website:  https://www.math.uci.edu/~komarova/

Class Room: RH 340N 

Day and Time: MWF 9am-9:50am

Office Hours: Monday 11-11:30, Wed 11-11:30

Texts (the students are not required to buy these texts):

1) Dynamical System Models in the Life Sciences, Fred Y.M. Wan, World Scientific, 2018.

2) Dynamics of cancer: mathematical foundations of oncology.  Dominik Wodarz and Natalia Komarova, World Scientific, 2014.

 

Premise of the Course: This course is intended as an introduction to the main mathematical concepts used in mathematical modeling in life sciences. The goal is to develop an appreciation for dynamical systems, and to learn what analytical tools are available to study them.  The following topics will be covered:

- Ordinary differential equations (ODEs), initial value problems.

- Equilibrium solutions and their stability. 

- Bifurcations.

- Systems of linear ODEs: solutions, equilibria and stability.

- Nonlinear ODEs, linear stability analysis.  

- Phase plane in 2D, bifurcations, time scale separation.

- Boundary value problems.

As time allows, we will also talk about related subjects such as  optimization/calculus of variations, transport equations, and stochastic processes related to population dynamics. Examples from real biological problems will be provided, which illustrate the mathematical methods covered in class.

Homework: Several homework assignments will be given throughout the course. The lowest assignment score is dropped for the purposes of the grade.

Presentations: Each student will be required to deliver a short (~15 minutes including discussion) presentation in class, in lieu of the final. The purpose of the presentations is  (1) to allow each student to connect the course material with a biological topic of their interest, (2) to apply the knowledge obtained in class, and (3) to work on their presentation skills, as well as participation in a discussion. Presentations will take place on Nov 25, Dec 2, Dec 4, and Dec 6. The deadline to submit the paper title is Mon, Nov 18. A short paper (1-2 pages) for each presentation is due Dec 6, at 9am.

The presentation should be based on a published article on mathematical biology, which uses ODEs to describe a biological system/phenomenon. The presentation and the paper must contain the following information: (1) Present the biological question; (2) Specify what ODEs were used and explain their parameters and variables; (3) Explain how the ODEs were solved/analyzed; (4) How did this help advance our understanding of the biological problem. In addition to delivering their own presentations, students are expected to participate in the discussion of other students' presentations.

 

Midterm: Wed, October 30. Presentations: Nov 25, Dec 2, Dec 4, and Dec 6.

 

The grade:

Final (presentation) 40%

Midterm 40%

Homework 30%

 

Academic Integrity: Students are responsible for informing themselves of UCI’s policies regarding academic dishonesty. Students found in violation of the code are subject to penalties ranging from loss of credit for work involved to a grade of F in the course, and possible risk of suspension or probation. The academic dishonesty policy will be enforced in all areas of the course, including homework, quizzes, and exams. For more information about the academic dishonesty policy and procedures, including information about your rights and responsibilities as a student, see https://aisc.uci.edu/students/academic-integrity/index.php