Honours Bachelor of Science in Computer Science - Theory of Computation - St.George

Despite the name, Computer Science is not really a science of computers at all. Computers are quite remarkable electronic devices, but even more remarkable is what they can be made to do: simulate the flow of air over a wing, manage communication over the Internet, control the actions of a robot, synthesize realistic images, play grandmaster-level chess, learn how to automatically translate between languages, and on and on. Indeed, the application of computers in activities like these has affected most areas of modern life. What these tasks have in common has little to do with the physics or electronics of computers, what matters is that they can be formulated as some sort of computation. This is the real subject matter of Computer Science: computation, and what can or cannot be done computationally.
In trying to make sense of what we can get a computer to do, a wide variety of topics come up. There are, however, two recurring themes. The first is the issue of scale: how big a system can we specify without getting lost in the design, or how big a task can a computer handle within reasonable bounds of time, memory, and accuracy A large part of Computer Science deals with these questions in one form or another. In the area of programming languages and methodology, for example, we look for notations for describing computations, and programming methodologies that facilitate the production of manageable and efficient software. In the theory of computation area, we study resource requirements in time and memory of many basic computational tasks.
The second theme concerns the scope of computation. Computers were originally conceived as purely numerical calculators, but today, we tend to view them much more broadly. Part of Computer Science is concerned with understanding just how far computational ideas can be applied. In the area of artificial intelligence, for example, we ask how the function of the human brain can be expressed in computational terms. In the area of human-computer interaction, we ask what sorts of normal day-to-day activities of people might be supported and augmented using computers.
Theory of Computation studies the inherent complexity of fundamental algorithmic problems. On one hand, we develop ground-breaking efficient data structures and algorithms. On the other, we have yet to develop good algorithms for many problems despite decades of effort, and for these problems we strive to prove no time- or space-efficient algorithms will ever solve them. While the field has seen some successful impossibility results, there are still many problems (such as those underlying modern cryptography and security) for which we do not know either efficient algorithms or strong lower bounds. This focus takes a rigorous, mathematical approach to computational problem-solving: students will gain a deep understanding of algorithm paradigms and measures of problem complexity, and develop the skills necessary to convey abstract ideas with precision and clarity. Many of our students go on to graduate studies and sophisticated algorithmic work in industry. This focus has natural ties with many branches of mathematics and is the foundation of many computer science fields. Consequently, our students often apply their theoretical knowledge to other fields of interest.