Academics

  /  

Courses

  /  

Descriptions

ES_APPM 395: Selected Topics in Applied Mathematics

Description

From Physics to data-driven modeling: With applications in genomic, cellular, developmental, ecological and neuro biology

Course textbook: 
If you wish to purchase it and a free pdf that the authors have kindly shared with us for the purpose of teaching. Please do not circulate this without express authorization from the authors directly. Github repository for tutorials.

Why am I teaching this course and what is it about? 
I teach what I wish to learn. The most important and powerful models in history have not been data-driven. Perhaps they have been data-constrained or data-inspired. But, there does seem to be a new brand of models that are more data-driven than in the past. My knee-jerk reaction is that the overwhelming majority of these more data-driven (insert AI/ML blah blah) modeling is of little general scientific or even engineering value in the long run. All that being said, how can we argue with the potential power of these approaches. So perhaps theory needs to evolve. Perhaps we go through a historical phase where theory and modeling is more data-driven. And,, following that, there will be a middle ground where the two philosophical paradigms will find a (un?)happy marriage? The book we will be following provides a starting point, a first map, that I hope helps us organize the various threads of this new approach to modeling. As is clear from this brief description, this course is not a course in biology. Instead, examples from biology will be the basis of tutorials and assignments. I will introduce the biological background needed in class, assuming that you have none of it. We will be assuming that you know how to code, and how to code in python. We will also be assuming that you have seen, and perhaps even have some level of mastery, over the basic building blocks of mathematics: calculus, linear algebra, and probability. Since this is the first time we are teaching this course we ask for your patience and help in building it. What I would like is for people to read sections of the book/pdf ahead of class and come ready to lectures for my attempt in trying to present the ideas. I hope we can collectively converge towards having insights into the material covered in this book. I will be adding additional sections on generative deep learning and unsupervised dimensionality reduction.

-------------------------------------------------------------------------------------------------------------------