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Programming Language Processing: tokenization, parsing and semantic analysis, graph representations, syntactic transformations. Smartphone and Web Programming: multi-threading, asynchronous event-handling, permissions.

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Program Analysis: static and dynamic analysis of concurrent programs, model checking, information flow analysis for security, random testing. Probabilistic Models of Source Code: program embeddings, probabilistic grammars, statistical language models, structural models. Applications of Machine Learning e. Blake Meike and Masumi Nakamura. Programming Android. O'Reilly, David Harman.

Effective JavaScript. Addison-Wesley, Steve Souders. Even Faster Websites. Deep Learning. MIT Press, Research papers. Spectral graph algorithms are very popular in theoretical computer science and machine learning, as they provide polynomial time approximations to several hard computational problems. This course will cover some basic topics in spectral graph theory and algorithms with some applications to network analysis.

This course emphasizes rigorous analysis of algorithms. Andries E. Brouwer, Willem H. Haemers, Spectra of graphs, Springer The design and implementation of scalable, reliable and secure software systems is critical for many modern applications. Numerous program analyses are designed to aid the programmer in building such systems and significant advances have been made in recent years.

The objective of the course includes introduction of the practical issues associated with programming for modern applications, the algorithms underlying these analyses, and applicability of these approaches to large systems. There will be special emphasis on practical issues found in modern software. The course project will be geared towards building the programming skills required for implementing large software systems. References: Course material available from the webpage; research papers. Vector Spaces : Subspaces, Linear independence, Basis and dimension, orthogonality.

Matrices : Solutions of linear equations, Gaussian elimination, Determinants, Eigenvalues and Eigenvectors, Characteristic polynomial, Minimal polynomial, Positive definite matrices and Canonical forms. Singular Value Decomposition, Applications.

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Combinatorial design

Vertex cover, matching, path cover, connectivity, hamiltonicity, edge colouring, vertex colouring, list colouring; Planarity, Perfect graphs; other special classes of graphs; Random graphs, Network flows, Introduction to Graph minor theory. Bondy and U. Murty, "Graph Theory", Springer B. Bollabas, "Modern Graph Theory", Springer Vesztergombi: Discrete Mathematics, Springer Herstein I N : Topics in Algebra, 2 ed.

Finite-state automata, including the Myhill-Nerode theorem, ultimate periodicity, and Buchi's logical characterization. Turing machines and undecidability, including Rice's theorem and Godel's incompleteness theorem.

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References: Hopcroft J. Addison Wesley, Dexter Kozen: Automata and Computability. Springer Edmund M. Prerequisites Basics of data structures, algorithms, and automata theory. The aim of this course is to give a basic introduction to this field. Starting with the basic definitions and properties, we intend to cover some of the classical results and proof techniques of complexity theory.

Design theory

Lecture notes of similar courses as and when required. More importantly, some mathematical maturity with an inclination towards theoretical computer science. Design and Analysis of Algorithms, Greedy algorithms, divide and conquer strategies, dynamic programming, max flow algorithms and applications, randomized algorithms, linear programming algorithms and applications, NP-hardness, approximation algorithms, streaming algorithms. Limits of sequence of random variables, Introduction to Statistics, Hypothesis testing.

Kishor S. Vijay K. Rohatgi, A. Dataflow analysis: Lattices, computing join-over-all-paths information as the least solution to a set of equations that model the program statements, termination of dataflow analysis, analysis of multi-procedure programs.


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Abstract interpretation of programs: Galois connections, correctness of dataflow analysis. Pointer analysis of imperative programs. Program dependence graphs, and program slicing. Assertional reasoning using Hoare logic. Type Systems: Monomorphic and polymorphic type systems, Hindley-Milner's type inference algorithm for functional programs.

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Prerequisites Exposure to programming, and the basics of mathematical logic and discrete structures. Basic combinatorial numbers, selection with repetition, pigeon hole principle, Inclusion-Exclusion Principle, Double counting; Recurrence Relations, Generating functions; Special combinatorial numbers: Sterling numbers of the first and second kind, Catalan numbers, Partition numbers; Introduction to Ramsey theory; Combinatorial designs, Latin squares; Introduction to Probabilistic methods, Introduction to Linear algebra methods.

References: R. Grimaldi, B.


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Vanlint, R. Spencer, P. Prerequisites None. A very basic familiarity with probability theory and linear algebra is preferred, but not a must. The required concepts will be introduced quickly in the course. Need for unconstrained methods in solving constrained problems. Necessary conditions of unconstrained optimization, Structure of methods, quadratic models. Methods of line search, Armijo-Goldstein and Wolfe conditions for partial line search. Global convergence theorem, Steepest descent method.

Conjugate-direction methods: Fletcher-Reeves, Polak-Ribierre. Derivative-free methods: finite differencing.

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Restricted step methods. Methods for sums of squares and nonlinear equations. Linear and Quadratic Programming. Duality in optimization. References: Fletcher R. References: Ideals, Varieties and Algorithms by D. Algorithmic Algebra by Bhubaneswar Mishra, Springer, Probability spaces and continuity of probability measures, random variables and expectation, moment inequalities, multivariate random variables, sequence of random variables and different modes of convergence, law of large numbers, Markov chains, statistical hypothesis testing, exponential models, introduction to large deviations.