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List of Practicals
Write the programs for the following using SCILAB
1. Set Theory
a. Inclusion Exclusion principle.
b. Power Sets
c. Mathematical Induction
2. Functions and Algorithms
a. Recursively defined functions
b. Cardinality
c. Polynomial evaluation
d. Greatest Common Divisor
3. Counting
a. Sum rule principle
b. Product rule principle
c. Factorial
d. Binomial coefficients
e. Permutations
f. Permutations with repetitions
g. Combinations
h. Combinations with repetitions
i. Ordered partitions
j. Unordered partitions
4. Probability Theory
a. Sample space and events
b. Finite probability spaces
c. Equiprobable spaces
d. Addition Principle
e. Conditional Probability
f. Multiplication theorem for conditional probability
g. Independent events
h. Repeated trials with two outcomes
5. Graph Theory
a. Paths and connectivity
b. Minimum spanning tree
c. Isomorphism
6. Directed Graphs
a. Adjacency matrix
b. Path matrix
7. Properties of integers
a. Division algorithm
b. Primes
c. Euclidean algorithm
d. Fundamental theorem of arithmetic
e. Congruence relation
f. Linear congruence equation
8. Algebraic Systems
a. Properties of operations
b. Roots of polynomials
9. Boolean Algebra
a. Basic definitions in Boolean Algebra
b. Boolean algebra as lattices
10. Recurrence relations
a. Linear homogeneous recurrence relations with constant coefficients
b. Solving linear homogeneous recurrence relations with constant coefficients
c. Solving general homogeneous linear recurrence relations