Network science is a vibrant, multidisciplinary field of contemporary scientific research. Networks can help us understand an abundance of phenomena such as brain activity, the spread of diseases (and malware), the proliferation of viral memes, and the emergence of forest fires. In this course, you will learn about the mathematical foundations of network theory, and creatively explore a variety of models through small projects and computer simulations.
Together we will study a variety of real-world networks, and use these concrete examples to introduce techniques used by mathematicians and computer scientists to model and analyze complex systems. Emphasis will be given to interesting applications, with opportunities for you to focus on phenomena they find most compelling. Starting from simulating specific examples, we will explore how mathematical thinking can help us understand networks. This will be accomplished through in-class exploratory assignments and small projects that will help students build mathematical understanding and proficiency in computer simulations. We will also learn about how networks are used in applications by reading accessible examples of modern STEM research. Moreover, you will practice communicating mathematical concepts in a supportive environment through class discussions and short presentations.
Learning to creatively use mathematical tools is a key step in transitioning from high school level math — which often stresses learning formulas and specific techniques — to college-level math. This course will guide you through such transition by encouraging and empowering you to use concepts from network theory to formulate your own models and gain a better understanding of real-world systems that affect their daily lives.
In this course, you will learn to:
• Identify how foundational concepts in network science come into play in systems that directly impact the students’ daily lives
• Creatively use mathematical ideas to model a variety of phenomena
• Employ programming tools to simulate real-world networks; use these simulations to build a better understanding of the systems taken into consideration, and make predictions
• Utilize probability and statistics to handle uncertainty and complexity in realistic mathematical models
• Effectively communicate nuanced mathematical ideas to their peers
These learning goals will help establish a solid foundation for further study in a variety of STEM fields, where networks come into play extensively. This course will be particularly helpful for students who are considering studying mathematics or computer science, as it will help those students become familiar with creative mathematical thinking and problem-solving.
Students are required to be proficient in Algebra (basic arithmetic, equations, inequalities, proportions, and percents). Any mathematical knowledge beyond that is not required, but it is still welcome in this class and will enable you to explore more sophisticated models. Some basic knowledge of probability will be particularly helpful. A little familiarity with computer programming is also helpful, but not required. All programming skills necessary for this course will be covered in class. This course recommends a laptop for course-related programming, games/simulations, etc. Please note that some devices (e.g., Chromebooks) do not allow software downloads onto a desktop and so will not accommodate the specific needs of this course. If you have questions about this requirement please reach out to [email protected]
Online sections of Pre-College courses are offered in one of the following modalities: Asynchronous, Mostly asynchronous, or Blended. Please review full information regarding the experience here.