2. Recommended Books
• Discrete Mathematics with Applications (second edition) by
Susanna S. Epp
• Discrete Mathematics and Its Applications (sixth edition) by
Kenneth H. Rosen
• Discrete Mathematics by Ross and Wright• Discrete Mathematics by Ross and Wright
3. MAIN TOPICS
1. Logic
2. Sets & Operations on sets
3. Relations & Their Properties
4. Functions
5. Sequences & Series
6. Recurrence Relations
7. Combinatorics
8. Probability
9. Graphs
10. Trees
4. What is Discrete Mathematics?
• Discrete mathematics is the study of mathematical structures
that are fundamentally discrete rather than continuous. In
contrast to real numbers that have the property of varying
"smoothly", the objects studied in discrete mathematics –
such as integers, graphs, and statements in logic– do not vary
smoothly in this way, but have distinct, separated values.smoothly in this way, but have distinct, separated values.
5. What is Discrete Mathematics?
• Discrete mathematics focuses on problems that are not over a
continuous domain. For example, is it possible to visit 3 islands
in a river with 6 bridges without crossing any bridge more than
once? That is a discrete math problem (because there are a
finite (fixed, discrete) number of bridges). Or, what is the
smallest number of telephone lines needed to connect 200smallest number of telephone lines needed to connect 200
cities? The numbers can be large and the logic can be
complex, but these type of problems are different from
finding an optimal value for a function where the domain can
be 3, 3.14, 3.14159, or any real value.
6. What is Discrete Mathematics?
• Discrete Mathematics concerns processes that consist of a
sequence of individual steps.
7. Logic
Logic is the study of the principles and methods that
distinguishes between a valid and an invalid argument.