CS-173 / CS-227: Continuous Algorithms

• Instructor: Prof. Rahul Simha

• Office Hours: TBA

• Class Time/Place: TBA

• Prerequisites: CS-123, CS-143

• Course description: Overview of structures in continuous mathematics from a computational viewpoint. Main topics include simulation, computational modeling, machine learning, neural networks, decision trees, text classification, statistical language processing, robot control algorithms.

• What the course is about: To understand what this course is about and why you should consider taking it, let's first examine the standard CS algorithms course. What do we learn in that course? We cover topics such as data structures (trees, tries, hashing), graph algorithms (DFS, BFS, Dijkstra), discrete optimization and NP-completeness. Almost any textbook on algorithms has these topics at its core. The problem-solving paradigms we learn have to do with divide-and-conquer, dynamic programming, recursion and the use of appropriate data structures.

  Yet, there is a whole world of algorithms that are both important and are fundamentally different. These algorithms include:

  • Algorithms that simulate physical reality, for example the motion of objects or interactions between chemicals, or complex systems such as transportation networks.
  • Algorithms that reason about probability, or that work with probabilistic quantities (We call them simulations).
  • Algorithms that control robots, both at the low level (controlling movement) as well as at the high level (planning a path).
  • Algorithms that involve learning or recognition, for example, face-recognition or handwriting recognition.
  • Algorithms that involve understanding natural languages.
  What is common to all these algorithms, and what differentiates them from algorithms in the standard course, is that they are all based on continuous structures or continuous mathematics. Thus, while graph algorithms are based on discrete structures (graphs), a simulation involves real numbers.

  The purpose of this course is to give you an overview of this area, introduce you to key ideas, and along the way, stimulate interest in the very different types of problems you can solve with this approach.

• A note about grads vs. undergrads. Undergrads will be graded on a different scale, and will possibly work in teams. Yes, we recognize that you are taking an elective course.

• Textbooks: There is no single book that covers all the material we need. We will go with these:
  • Pattern Classification. By R.O.Duda, P.E.Hart and D.G.Stork.
  • Neural Networks: Algorithms, Applications and Programming Techniques. By J.A.Freeman and D.M.Skapura.
  • Statistical Language Learning. By E.Charniak.

• Coursework: This will be a project-oriented course. The idea is to see if we can apply the concepts learned to some practical problem. Students may potentially propose projects, and may choose to participate in a robot-control competition.