Discrete Mathematics (2016)

Discrete Mathematics (2016)

Discrete Mathematics (2016)

Curriculum

Duration:
March 1 2016 - Jun 30 2017


Eligibility:
Course is FREE. Anybody can register. Click on your University below and select your college to see full course listing. Then click on the course Register link.
Students with Non-listed University or College can choose ANY University and its Base Course with closest matching Syllabi, and register.


Authors: Bhavana Kanukurthi, Nishanth Chandran, Neeraj Kayal

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Bhavana Kanukurthi is an Assistant Professor in the Department of Computer Science and Automation at the Indian Institute of Science, Bangalore. Her research, in the area of cryptography and security, focuses on obtaining efficient solutions for securing data and computation on the cloud. She has published at leading conferences such as STOC, CRYPTO, Eurocrypt and TCC.
Prior to joining IISc, Bhavana worked as a post-doctoral researcher at UCLA. She obtained her PhD in Computer Science in 2011 from Boston University, where she was the recipient of the 2010 Research Excellence Award.

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Nishanth Chandran is a researcher at Microsoft Research, India. His research interests are in cryptography, security, and algorithms. Nishanth received his Ph.D. and M.S. in Computer Science from UCLA and his B.E. in Computer Science and Engineering from Anna University, Chennai. He publishes regularly in top computer science conferences and journals such as CRYPTO, TCC, Journal of the ACM, and SIAM Journal of Computing. Nishanth's research work has been covered by the MIT Technology Review and by the science journal, Nature. He is a recipient of the Chorafas Award for Excellence in Research and has served on numerous program committees. Prior to joining Microsoft Research, India, Nishanth was a researcher with AT&T Security Research Centre, New York.

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Neeraj Kayal’s main interests include algebra, geometry, number theory and their applications in Computer Science. His recent work has been focused on optimal ways of computing arithmetic functions. Previously, Neeraj Kayal was part of the team that discovered the first provably efficient algorithm for testing Primality. He is a recipient of the Gödel prize and the Fulkerson Prize for the same along with his co-authors. He was also given the Distinguished Alumnus Award of Indian Institute of Technology Kanpur for his work in computational complexity theory.


Syllabus(Outline):

Unit 1 Proofs
a. Well-ordering principle (Weeks 1 -2) b. Contradiction
c. Contraposition d. Logic
e. Sets f. Induction (Weeks 2 - 3)
g. Pigeonhole Principle (Week 4)
Unit 2 Combinatorics and Probability Theory: (4 weeks)
a. Permutations b. Combinations
c. Counting d. Basic Probability
e. Expectation – linearity f. Union Bound
g. Chernoff Bounds
Unit 3 Number Theory and Modular Arithmetic: (Weeks 9 - 10)
a. Polynomials b. Euclids Algorithm
c. Secret Sharing d. Fermat’s Little Theorem
e. Reed Solomon Codes f. RSA Cryptosystem
Unit 4 Graph Theory: (Weeks 11 - 13)
a. Degree, path, cycle, connectivity b. Eulerian walks and Hamiltonian cycles
c. Trees d. Graph problems: TSP, matching problem, vertex cover, Konig’s Theorem


Schedule:

Quiz Dates
Quiz Schedule 5 QUIZZES (postings will be notified to registered MEC email addresses)
Certificate Eligibility
Course Participation Certificate View 80% of Course Lessons & Score at least 70% Aggregate Average (or 280 points) from Top 4 Quizzes

Universities

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