Discrete Mathematics - IIITB

By Prof. Ashish Choudhury   |   IIIT Bangalore
Learners enrolled: 3335
Discrete mathematics is the study of mathematical structures that are discrete in the sense that they assume only distinct, separate values, rather than in a range of values. It deals with the mathematical objects that are widely used in all most all fields of computer science, such as programming languages, data structures and algorithms, cryptography, operating systems, compilers, computer networks, artificial intelligence, image processing, computer vision, natural language processing, etc. The subject enables the students to formulate problems precisely, solve the problems, apply formal proof techniques and explain their reasoning clearly.

INTENDED AUDIENCE
The course is intended for any student from the computer science discipline
PREREQUISITES : None
INDUSTRIES  SUPPORT     : None
Summary
 Course Status : Completed Course Type : Core Duration : 12 weeks Category : Computer Science and Engineering Foundations of Computing Credit Points : 3 Level : Undergraduate/Postgraduate Start Date : 18 Jan 2021 End Date : 09 Apr 2021 Enrollment Ends : 01 Feb 2021 Exam Date : 25 Apr 2021 IST

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.

Course layout

Week 1:Logic: Proposition and Predicate Logic, introduction to proof techniques
Week 2:Advanced proof techniques, resolution, induction
Week 3: Set theory and relations
Week 4:Various types of relations and functions
Week 5:Combinatorics Part I: permutations, combinations, sum rule, product rule, pigeon-hole principle, Ramsey numbers
Week 6:Combinatorics Part II: Combinatorial proofs, Catalan numbers, counting using recursion, principal of inclusion-exclusion, advanced counting techniques
Week 7: Recurrence equations and various methods of solving recurrence equations
Week 8:Cardinality theory, countable and uncountable sets, Cantor’s diagonalization, uncomputable functions
Week 9:Graph theory Part I: basic definitions, Euler’s theorem, bipartite graphs and matching, Hall’s marriage theorem, various operations on graphs
Week 10:Graph theory part II: isomorphism, vertex-connectivity, edge-connectivity, Euler graphs and Hamiltonian graphs, various characterizations, vertex and edge coloring
Week 11: Abstract algebra: groups, rings, fields
Week 12:Basic number theory: modular arithmetic, prime numbers and properties, GCD, Chinese remainder theorem, Fermat’s little theorem, RSA cryptosystem

Books and references

1. Discrete Mathematics and Its Applications, Kenneth Rosen
2. Discrete and Combinatorial Mathematics, Ralph Grimaldi
3. Elements of Discrete Mathematics, C. L. Liu

Prof. Ashish Choudhury

IIIT Bangalore
Dr. Ashish Choudhury is currently an Associate Professor at IIIT Bangalore. He did his MS and PhD in Computer science from IIT Madras, followed by postdoc at ISI Kolkata and University of Bristol. His research work is focused on the foundation of cryptographic protocols for real-world problems. His current projects aim to design efficient protocols in the asynchronous network model which can be realized in practice. In general he is interested in secure distributed computing and all areas of theoretical computer science.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 25 April 2021 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Madras .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team