# Summary of Course

## Class 1 Introduction

1. What is Computer Science about?(The introduction).
2. The basic framework and conception of the programs.
• The purpose.
• What the programs to do with real-world.
• Input
• State
• Initial state
• Domain events
• Output
3. Pseudo code
4. Program Evaluation

## Class 2 Programming Languages

1. Define of the programming languages.
2. Syntax.
3. Semantics.
5. Mathematics models and the programming.
6. Safety-critical system.

## Class 3 Programs and Models

1. Five models:
• Visualizations
• Building a physical model
• Reinstatement of problems
• Use of analogy
• Mathematical model
We should to get the advantage and the disadvantage of these five models.

## Class 4 Flow Chart

1. Two informal way to model system behavior
2. Flow Chart
• Define
• Main symbols
• How to write a flow chart

## Class 5 Set Theory

1. Tuples
2. Set
• Set membership
• Special set
• Cardinality
• Venn diagrams
• Set builder notation
• With the programs
• Relation with the set
• Unary Set Operation
• Powerset
• Binary set operations
• Union
• Intersection
• Difference A-B or A\B
• Cartesian product AXB
• Disjoint sets
• Properties of operations

## Class 6 Relations and Functions

1. Relation
• Directed graph
• Domain of a relation
• Range of a relation
• Inverse
• Complement
• Relation on a set
• Totality properties
• Left-total
• right-total
• Injective
• Functional
• One to one(Bijective)
2. Function
• Types
• Partial Function

## Class 7 Values and Types

1. Type of values
• Primitive types
• Composite types
• Cartesian Product
2. Mappings
• Array with map
• Function with map

## Class 8 Types

1. Copy Semantics
2. Reference Semantics
3. Static and Dynamic
4. Expressions
5. Variables and Storage
6. Total update and Selective update
7. Flexibel Array
9. Heap variables

## Class 9 StackHeapMemoryEx

1. Heap and the Stack

## Class 10 Propositional Logic

1. Logic
2. Propositional logic
3. Proposition / Compound proposition
4. Logical operator
• Conjunction
• Disjunction
• Negation
• Exclusive or
• Conditional(implication)
• Biconditional(bi-implications)
5. Truth table
6. Tautology
8. Continency
9. Syllogisms
10. Validating Rules

## Class 11 Prog Correntness

1. Correctness of Program
• Preconditon
• postcondition
• Strengthened
• Weakened
2. Conjunction Rule
3. Disjunction Rule
4. Concatenation Rule
5. Modified Concatenation Rule
6. Assignment Rule

## Class 12 If Statements

1. Rule for Conditions(no else clause)

## Class 13 Loops Correctness

1. Invariant and Invariant for the loop’

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