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Course Summary

This class is offered as CS6505 at Georgia Tech where it is a part of the Online Masters Degree (OMS). Taking this course here will not earn credit towards the OMS degree.

In this course, we will ask the big questions, “What is a computer? What are the limits of computation? Are there problems that no computer will ever solve? Are there problems that can’t be solved quickly? What kinds of problems can we solve efficiently and how do we go about developing these algorithms?” Understanding the power and limitations of algorithms helps us develop the tools to make real-world computers smarter, faster and safer.

Why Take This Course?

You will learn a wealth of tools and techniques that will help you recognize when problems you encounter in the real-world are intractable and when there an efficient solution. This can save you countless hours that otherwise would have been spent on a fruitless endeavor or in re-inventing the wheel.

Prerequisites and Requirements

Students are expected to have a solid grasp of the basics of discrete mathematics. Discrete Mathematics and Its Applications by Ken Rosen provides an excellent background for this course.

If you answer “no” to any of the following questions, it may be beneficial to acquire background knowledge concurrently or prior to taking the course.

  1. Can you show that the sum of the first n numbers is n(n+1)/2? Can you give the proof as an induction on n?
  2. Can you give an O(n log n) algorithm for sorting n numbers?
  3. Can you describe the difference between breadth-first and depth-first search?
  4. Given an nxn matrix A and an n-dimensional vector b, can you give a polynomial-time algorithm to find a vector x such that Ax=b?

See the Technology Requirements for using Udacity.

Syllabus

Lesson 1: Computability

  • Languages & Countability
  • Turing Machines
  • The Church-Turing Thesis
  • Universality
  • Undecidability

Lesson 2: Complexity

  • P and NP
  • NP-Completeness
  • NP-Complete Problems
  • The Golden Ticket

Lesson 3: Algorithms

  • Dynamic Programming
  • Fast Fourier Transform
  • Maximum Flow
  • Maximum Bipartite Matching
  • Linear Programming
  • Duality
  • Randomized Algorithms
  • Approximation Algorithms

Instructors & Partners

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Charles Brubaker

Charles Brubaker earned his PhD in Computer Science from Georgia Tech in 2009. He then taught high school computer science and coached basketball at Pace Academy in Atlanta for 4 years. In 2012, inspired by Udacity, he began recording his lectures on a tablet, creating online quizzes, and automatically grading assignments to give his students instant feedback. The success of this enterprise convinced him that Udacity represented the wave of the future in education, and he joined the company in the summer of 2013.

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Lance Fortnow

Lance Fortnow is professor and chair of the School of Computer Science of the College of Computing at the Georgia Institute of Technology. His research focuses on computational complexity and its applications to economic theory.

Fortnow received his Ph.D. in Applied Mathematics at MIT in 1989 under the supervision of Michael Sipser. Before he joined Georgia Tech in 2012, Fortnow was a professor at Northwestern University, the University of Chicago, a senior research scientist at the NEC Research Institute and a one-year visitor at CWI and the University of Amsterdam. Since 2007, Fortnow holds an adjoint professorship at the Toyota Technological Institute at Chicago.

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Hariharan Venkateswaran

H. Venkateswaran obtained his Ph.D. in Computer Science from the University of Washington in 1986. He then joined the faculty of Georgia Institute of Technology as an Assistant Professor, where he has pursued his research interests in Complexity Theory, Information Security, and Parallel Computation. A renowned teacher on campus, he was awarded "The William A “Gus” Baird Faculty Teaching Award" in 2008.