|Course title||Randomness and Computation
|Course description||This course is to study the use of randomness in theoretical computer science. We will introduce basic probability tools (e.g. random variables, expectation, moments and derivations, tail inequalities, martingales) and probabilistic methods (e.g. first moment method, second moment method, Lovasz local lemma, semi-random method). Then we will show how these tools and methods can be used to design randomized algorithms (e.g. graph algorithms, number-theoretic algorithm, computational geometry), efficient data structures (e.g. balls and bins, hashing, load balancing), and sublinear algorithms (e.g. property testing, constant time algorithms, data streaming). We will also demonstrate how these tools and methods can be combined with other techniques, such as Markov chain and random walk (e.g. electric networks, expanders, random sampling, approximate counting), algebraic techniques (e.g. determinant method, fingerprinting, polynomial identity testing, interactive proof), and mathematical programming (e.g. linear programming, randomized rounding, semidefinite programming). Finally we study some methods of derandomization (e.g. conditional probability, k-wise independence, small-bias space, pseudorandom generator).
|Semester||1 or 2|
|Grade Descriptors||A/A-: EXCELLENT – exceptionally good performance and far exceeding expectation in all or most of the course learning outcomes; demonstration of superior understanding of the subject matter, the ability to analyze problems and apply extensive knowledge, and skillful use of concepts and materials to derive proper solutions.
B+/B/B-: GOOD – good performance in all course learning outcomes and exceeding expectation in some of them; demonstration of good understanding of the subject matter and the ability to use proper concepts and materials to solve most of the problems encountered.
C+/C/C-: FAIR – adequate performance and meeting expectation in all course learning outcomes; demonstration of adequate understanding of the subject matter and the ability to solve simple problems.
D+/D: MARGINAL – performance barely meets the expectation in the essential course learning outcomes; demonstration of partial understanding of the subject matter and the ability to solve simple problems.
F: FAILURE – performance does not meet the expectation in the essential course learning outcomes; demonstration of serious deficiencies and the need to retake the course.
|Learning outcomes||• Understanding of the use of randomness in computation.
• Skills to apply probability tools in solving problems.
(for reference only)
Homework or assignment: 50%
|Recommended Reading List||Sketching as a Tool for Numerical Linear Algebra. David Woodruff, Foundations and Trends® in Theoretical Computer Science, Vol 10, Issue 1–2, 2014.|
|CSCIN programme learning outcomes||Course mapping|
|Upon completion of their studies, students will be able to:|
|1. identify, formulate, and solve computer science problems (K/S);|
|2. design, implement, test, and evaluate a computer system, component, or algorithm to meet desired needs (K/S);
|3. receive the broad education necessary to understand the impact of computer science solutions in a global and societal context (K/V);|
|4. communicate effectively (S/V);
|5. succeed in research or industry related to computer science (K/S/V);
|6. have solid knowledge in computer science and engineering, including programming and languages, algorithms, theory, databases, etc. (K/S);|
|7. integrate well into and contribute to the local society and the global community related to computer science (K/S/V);|
|8. practise high standard of professional ethics (V);|
|9. draw on and integrate knowledge from many related areas (K/S/V);
|Remarks: K = Knowledge outcomes; S = Skills outcomes; V = Values and attitude outcomes; T = Teach; P = Practice; M = Measured|