I690 Mathematical Modeling for Complex Systems
The goal of this course is to provide students with a technical (mathematical, computational) background to describe, model and reason in quantitative terms about Complex Systems.
Although a universally accepted definition of complex system does not exist, in this course we will approach them by studying how macroscopic ordered/organized behavior emerges/derives from the local (possibly non-linear) interactions of a large number of simple “agents.” Students will learn how to describe, classify, model, and eventually better understand these macroscopic behaviors.
Through a set of carefully chosen “real-world” examples, selected models and problems I will try to show how a common set of mathematical tools allows us to recognize the underlying common features that characterize systems traditionally studied by different disciplines, from social to natural sciences. We will come to appreciate how the study of complex systems is an inherently interdisciplinary enterprise.
I201 Mathematical Foundations of Informatics (4cr)
This course is an introduction to methods of analytical, abstract, and critical thinking; deductive reasoning; and logical and mathematical tools used in informatics.
In the first part, the course focuses on three very general notions that underpin rational discourse in any discipline: 1. Analytical thinking; 2. Understanding and making valid arguments; 3. Abstract thinking. We will study, among other things, the notion of consistency, contradiction, valid argument, formal and informal proof, quantification. We will also explore the relation between logical constructs and natural language.
In the second part the course will provide a solid foundation for further study of many areas of computer science and informatics, such as cryptography, complex systems and networks, programming languages, database theory.
H201 Mathematical Foundations of Informatics, Honors session (4cr)
This course provides an introduction to the basic mathematical and logical tools that formalize the concept of valid reasoning.
While logic plays a central role in mathematics and computer science, the approach followed in this course is not steered towards any specific application or domain. It focuses on three very general notions that underpin rational discourse in any discipline: 1. analytical thinking; 2. understanding and making valid arguments; 3. abstract thinking. We will study, among other things, the notion of consistency, contradiction, valid argument, formal and informal proof, quantification. We will also explore the relation between logical constructs and natural language.
I400 Advanced Network Science
Networks are a powerful abstraction. They allow to represent the inner structure of real-world systems in a simple and elegant fashion. They allow us to discover patterns, test models, and, ultimately, to understand the macroscopic behavior of many interesting real-world systems, from transportation infrastructures to the diffusion of information in social media.
In this course we will learn to describe, analyze, and reason about networks and the real systems they represent. River networks, the Internet, traffic, diffusion of ideas, epidemics, and collective behavior are just few of the inspiring case studies we will consider.
I400 “Advanced Network Science” is the natural continuation of I300 “Introduction to Network Science” offered in fall 2015. We will revisit in more depth some of the topics discussed in that course, but we will also focus on modeling aspects of network evolution and on understanding the processes that networks support.