What are you going to learn?

Content

Apply the properties of relations, functions, and sequences to complete operations on discrete structures such as sets, functions, relations, and sequences. Verify the correctness of an argument using propositional logic, predicate logic, and truth tables. Construct mathematical proofs using counter-examples, direct proofs, proof by contrapositive, proof by contradiction, case analysis, and mathematical induction. Evaluate Boolean functions and simplify expressions using the properties of Boolean algebra. Apply counting techniques and combinatorics to determine discrete probability. Model relationships using graphs and trees. Model using graphs, directed graphs and trees, basic concepts, properties and definitions. Combinations, permutations. Model computer systems using FSM.

Chapter 1. Logic

• Statements and logical Connectives. Truth Tables

• Predicates Logics and Quantifiers

• Proof Techniques

• Introduction. Notation

• Operations

• Denumerability

Chapter 2. Sets

Chapter 3. Relations and Functions

• Binary Relations

• Ordering

• Functions

Chapter 4. Combinatorics

• Counting Principles

• Sampling and Selecting

• Permutations and Combinations

Chapter 5. Graphs

• Introduction

• Graphs Terminology

• Directed and Undirected Graphs

• Trees

• Digraphs and Connectivity Problems

Chapter 6. Boolean Algebra and Computer Logic

• Introduction

• Logic Circuits. Gates

• Combinational Circuits

• Karnaugh Maps

Chapter 7. Algebraic Structures

• Definition

• Smigroups, Monoids

• Groups

• Applications to Error Correcting Codes

Chapter 8. Finite State Machines (FSM)

• Definition

• State Tables and Graphs

• FSM as Transducers and Recognizers

• Discussion of Limitations of FSM

• Introduction to Formal Languages

Bibliography

1. Gersting, J L. Mathematical Structures for Computers Science. 7th ed. W. H. Freeman and Company, 2014.

2. Rosen, K. Discrete Mathematics and its Applications. 7th. Ed. McGraw-Hill, 2007.

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