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functions, Functions between POSETS, Order isomorphism.

UNIT-II: Lattices (12 Hours)
Lattice as a POSET, Lattice as an algebra and their equivalence, Bounded lattices, Sublattices,
Interval in a lattice, Products and homomorphism of lattices, Isomorphism of lattices;
Distributive, Complemented, Partition and pentagonal lattices.
UNIT-III: Boolean Algebra and Switching Circuits (15 Hours)

Boolean algebra, De Morgan‘s laws, Boolean expressions, Truth tables, Logic diagrams,
Boolean functions, Disjunctive normal forms (as join of meets), Minimal forms of Boolean
polynomials, Quine Mc-Cluskey method, Karnaugh maps, Switching circuits, Applications of
switching circuits.

*TUTORIAL (15 Hours (1 Hour per week))

SUGGESTED READING:

1. Rudolf Lidl, & Gunter Pilz (2004). Applied Abstract Algebra (2nd ed.). Undergraduate
text
2. in Mathematics, Springer (SIE), Indian Reprint.
3. Bernard Kolman, Robert C. Busby, & Sharon Cutler Ross (2009). Discrete Mathematical
4. Structures (6th ed.). Pearson education Inc., Indian reprint.
5. Rosen, Kenneth H. (2017). Discrete Mathematics and its applications with combinatorics
and Graph Theory (7th ed.). McGraw Hill Education.

Math.322 Linear Programming 3+1*

LEARNING OBJECTIVES:

The primary objective of this course is to introduce:
 The solution of linear programming problem using simplex method.
 The solution of transportation and assignment problems.
 Game theory which makes possible the analysis of the decision-making process of two
25. interdependent subjects.

LEARNING OUTCOMES:

This course will enable the students to:
 Learn about the simplex method used to find optimal solutions of linear optimization
 problems subject to certain constraints.
 Write the dual of a linear programming problem.
 Solve the transportation and assignment problems.
 Learn about solution of rectangular games using graphical method and dominance.
 Formulate game to a pair of associated prima-dual linear programming problems.

THEORY (45 Hours)

UNIT-I: Linear Programming Problem, Simplex Method, and Duality (18 Hours)
Standard form of the LPP, graphical method of solution, basic feasible solutions, and
convexity; Introduction to the simplex method: Optimality criterion and unboundedness,
Simplex tableau and examples, Artificial variables; Introduction to duality, Formulation of the
dual problem with examples.

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