Pgcs syllabus

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Pgcs syllabus

  1. 1. Chennai Mathematical Institute MSc/PhD Computer ScienceTopics covered in entrance examination • Discrete Mathematics Sets and relations, elementary counting techiniques, pigeon hole principle, partial or- ders, • Elementary probability theory • Automata Theory Regular expressions, non deterministic and deterministic finite automata, subset con- struction, regular languages, non regularity (pumping lemma), context free grammars, basic ideas about computable and noncomputable functions. • Algorithms O notation, recurrence relations, time complexity of algorithms, sorting and searching (bubble sort, quick sort, merge sort, heap sort). • Data structures Lists, queues, stacks, binary search trees, heaps. • Graphs Basic definitions, trees, bipartite graphs, matchings in bipartite graphs, breadth first search, depth first search, minimum spanning trees, shortest paths. • Algorithmic techniques Dynamic programming, divide and conquer, greedy. • Logic Boolean logic, truth tables, boolean circuits — and, or, not, and, nand gates.Suggested reading material 1. Frank Harary: Graph Theory, Narosa. 2. John Hopcroft and Jeffrey D Ullman: Introduction to Automata, Languages and Com- putation, Narosa. 3. Jon Kleinberg and Eva Tardos: Algorithm Design, Pearson. 4. C. Liu: Elements of Discrete Mathematics, Tata McGraw-Hill.

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