This document provides an overview of the topics covered in a discrete structures course, including logic, sets, relations, functions, sequences, recurrence relations, combinatorics, probability, and graphs. It defines discrete mathematics as the study of mathematical structures that have distinct, separated values rather than varying continuously. Some examples given are problems involving a fixed number of islands/bridges or connecting a set number of cities with telephone lines. Logic is introduced as the study of valid vs. invalid arguments, and basic logical concepts like statements, truth values, compound statements, logical connectives, negation, and truth tables are outlined.

1. Discrete StructuresDiscrete Structures
MT217
Lecture 01

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.

8. Statement

9. Examples

10. TRUTH VALUES of Propositions

11. Examples

12. Examples

13. Not Propositions

14. Rule

15. Example

16. Example

17. Understanding Statements

18. Understanding Statements

19. Compound Statement

20. Symbolic Representation

21. Logical Connectives

22. Examples

23. Translating from English to
Symbols

24. Translating from English to
Symbols

25. Translating from English to
Symbols

26. Translating from English to
Symbols

27. Translating from English to
Symbols

28. Negation (~)

29. Truth Table

30. Truth Table for

31. Conjunction (^)

32. Truth Table for

33. Disjunction (ᴠ)

34. Truth Table for

35. Summary