1.Discrete Probability
a.An Introduction to Discrete Probability
b.Probability Theory
c.Bayes’ Theorem
d.Expected Value and Variance
2. Advanced Counting Techniques
a.Applications of Recurrence Relations.
b.Solving Linear Recurrence Relations.
c.Divide-and-Conquer Algorithms and Recurrence Relations.
d.Generating Functions.
e.Inclusion–Exclusion.
f.Applications of Inclusion–Exclusion.
3. Relations
a.Relations and Their Properties.
b.n-ary Relations and Their Applications .
c. Representing Relations.
d.Closures of Relations.
e.Equivalence Relations.
f.Partial Orderings.
4. Graphs
a.Graphs and Graph Models.
b.Graph Terminology and Special Types of Graphs. .
c.Representing Graphs and Graph Isomorphism.
d.Connectivity.
e.Euler and Hamilton Paths.
f.Shortest-Path Problems.
g.Planar Graphs
h.Graph Coloring
5.Trees
a.Introduction to Trees
b.Applications of Tree
c.Tree Traversal
d.Spanning Trees
e.Minimum Spanning Trees
6. Linked List, Stack, and Queue
7. Induction
a.Mathematical Induction
b.Weak and strong induction
c.Recursive definitions of functions and sequences
d.Recurrence relation
8. Relations
a.Reflexivity, symmetry, transitivity
b.Operations, union, intersection, complement, projection, join
c.Composition and exponentiation
d. Equivalence relations and equivalence classes
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