Mathematical Foundations of Computer Science(MA714)

Course Name: 

Mathematical Foundations of Computer Science

Programme: 

M.Tech (Others)

Semester: 

First

Category: 

Programme Core (PC)

Credits (L-T-P): 

(3-0-0) 3

Content: 

Divisibility, GCD, Prime Numbers, Fundamental Theorem of Arithmetic, Congruences, Fermat's Theorem, Euler Function, Primality Testing, Solution of Congruences, Chinese Remainder Theorem, Wilson's T heorem Groups and Subgroups, Homomorphism Theorems, Cosets and Normal Subgroups, Lagrange's Theorem, Rings, Finite Fields Polynomial Arithmetic, Quadratic Residues, Reciprocity, Discrete Logarithms, Elliptic Curve Arithmetic Fundamental Principles of Counting, Pigeonhole Principle, Countable and Uncountable Sets, Principle of Inclusion and Exclusion, Derangements, Equivalence Relations and Partitions, Partial Order, Lattices and Boolean Algebra, Generating Functions, Recurrence Relations, Solution of Recurrences Graphs, Euler Tours, Planar Graphs, Hamiltonian Graphs, Euler's Formula, Applications of Kuratowski's Theorem, Graph Coloring, Chromatic Polynomials, Trees, Weighted Trees, Shortest Path Algorithms, Spanning Trees, The Max-Flow Min-Cut Theorem.

References: 

Niven, H.S., Zuckerman and Montgomery, An Introduction to the Theory of Numbers, John Wiley New York, 1992
Grimaldi, R.P., Discrete and Combinatorial Mathematics: An Applied Introduction, Addison Wesley, 1994
Kolman, B. and Busby, R.C., Discrete Mathematical Structures for Computer Science, PHI, New Delhi, 1994

Department: 

Mathematical and Computational Sciences
 

Contact us

B R Shankar, Associate Professor and Head
Department of MACS, NITK, Surathkal
P. O. Srinivasnagar, Mangalore - 575 025
Karnataka, India.

  • Hot line: +91-0824-2474048

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