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Basic Details:

  • Course Code: EM 214
  • Credits: 3
  • Pre-requisites: None
  • Compulsory/Optional: Compulsory for Computer Engineering specialization

Aim :

To solve problems related to propositional and predicate calculus, mathematical models for computing machines and algorithms using fundamentals of number theory, algebraic structures, boolean algebras and graph theory.

Intended Learning Outcomes:

On successful completion of the course, the students should be able to;

  • Apply the concepts of number theory and algebraic structures to solve advanced mathematical /physical problems.
  • Simplify and evaluate statements in propositional and predicate logic and check the validity of an argument.
  • Solve advanced mathematical and physical problems using graph theory and algorithms.

Couse Content:

set theory, relations and functions, axiomatic systems, ordinary Induction, invariants, strong induction.

Divisibility, the greatest common divisor, modular arithmetic, Fermat’s Little theorem, RSA algorithm

Monoids, groups, rings and fields.

Basic counting principles with permutations and combinations, basic combinatorics.

propositional and predicate logic, proof methods and strategy.

Graphs, representation of a graph in a computer, isomorphic graphs, Eulerian and Hamiltonian graphs, planar graphs, graph coloring, trees, spanning trees, binary trees, tree searching, Hasse diagrams.

Greedy algorithms, searching and sorting algorithms, algorithms to obtain minimum spanning tree and shortest path of a weighted graph, complexity of an algorithm.

finite state machines, finite state automata, turing machines.

Time Allocation (Hours):

Lectures
0
Assignments
0

Recommended Texts:

  • D. K. Joshi, “Foundations of Discrete Mathematics”, (1989/2015), Wiley-Inter Science.
  • D. K. Joshi, “Applied Discrete Structures”, (2001/2014), New Age International.
  • Thomas Koshy, “Discrete Mathematics with Applications”, 1st edition (2004), Elsevier Academic Press.
  • Ian Anderson, “A First Course in Discrete Mathematics”, (2001), Springer-Verlag London Limited.
  • Kenneth. H. Rossen “Discrete Mathematics and Applications”, (2002), McGraw-Hill Higher Education

Assessment:

In - course:

Tutorials/Assignments
20%
Mid Semester Examination
30%

End-semester:

50%