Introduction to Computational Thinking

Communication 1

Books: Computational Thinking and Programming book (official book of the course - it includes more than 100 exercises with keys!) + accompanying book How To Code in Python

Other material: available in the GitHub repository of the course at https://github.com/comp-think/2021-2022/

Communication 2

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Communication 3

We will use the GitHub repository of the course for a series of activities, such as exercises and raising issues

Thus, please, create a new account on GitHub: https://github.com/join

Communication 4

Video of previous lectures:

1. Introduction to the course

Communication 5

As you should already know, a non-mandatory workshop will be held immediately after the last lecture, where the students are asked to organise themself in groups of 3-4 people (max. score: 4)

Max. score you can obtain from it: 4 points

We need to decide the date – my suggestion is
21 December 2021, 9:30-12:30

Any question about the previous lecture?

Historic hero: Noam Chomsky

Founders of the cognitive science field

Father of the modern linguistics

Provided a classification for formal grammars

A formal grammar is a mathematical tool for defining a language (e.g. English) according to a finite set of production rules, that allows one to construct any syntactic valid sentence of such language

Types of formal grammars

• regular grammars (the least expressive)

• context-free grammars

• context-sensitive grammars

• recursively enumerable grammars (the most expressive)

All specify constraints on the way one can use terminal and non-terminal symbols

• terminals are elementary symbols of the language (e.g. words), e.g. "write"

• non-terminals (e.g. <sentence>) can be replaced by a combination of terminal and non-terminal symbols

Example of formal grammar

A simple grammar defined using the Backus-Naur form

<sentence> ::= <pronoun> "write"
<pronoun> ::= "I"
<pronoun> ::= "you"

<sentence> ⇒
<pronoun> "write" ⇒
"I" "write"

Meaning: part 1

Computational Thinking and Programming

Definition of computational (Oxford Dictionary): using or relating to computers

A computer (today): electronic device

A computer (before advent of electronic computers): a person who performs mathematical calculations

Human computers

Groups of people who have to undertake long calculations for specific experiments or measurements

In astronomy: used for calculating astronomical coordinates of non-terrestrial things – such as the calculation of passages of Halley's Comet by Alexis Claude Clairaut and colleagues

In commerce: Napoleon imposed the creation of mathematical tables to convert quantities from the old imperial system of measurements to the new metric system

Towards electronic computers

In 1822, Charles Babbage developed the Difference Engine and then the Analytical Engine - the latter one was programmable, making it the very first mechanical general-purpose computer in history

Babbage's Difference Engine

Babbage's Analytical Engine

Electronic computers

The ideas presented in the Analytical Engine were developed in a physical machine only one century later, since computing technology has had a drastic change as a consequence of World War II

In 1946, US developed the Electronic Numerical Integrator and Computer (ENIAC), a programmable computer through patch cables and switches - the fixed point in time that generated all modern computers

Our take

In this course, with computer we mean any information-processing agent (i.e. a person or a machine acting mechanically if appropriately instructed) that can make calculations and produce some output starting from input

Meaning: part 2

Computational Thinking and Programming

The word programming stands for programming language

Natural language vs Programming language

Natural language

An ordinary language (e.g. English), either written or oral, that has evolved naturally in humans, usually without a specific and premeditated planning

Usually, natural languages are very expressive but intrinsically ambiguous

Programming language

A formal-born language, defined using Chomsky's context-free languages, usually

They oblige to specific syntactic rules that avoid possible ambiguous statements, mainly by restricting the expressiveness of the language

All the sentences in such language are conveying just one possible meaning

Kinds of languages 1/2

100010110101010000100100000010001000001111111010000000000111011100000110101110000000000000000000000000000000000011000011100000111111101000000010011101110000011010111000000000010000000000000000000000001100001101010011101110110000000100000000000000000000000010111001000000010000000000000000000000001000110100000100000110011000001111111010000000110111011000000111100010111101100110001001110000010100101011101011111100010101101111000011

fib:
    mov edx, [esp+8]
    cmp edx, 0
    ja @f
    mov eax, 0
    ret
    
    @@:
    cmp edx, 2
    ja @f
    mov eax, 1
    ret
    
    @@:
    push ebx
    mov ebx, 1
    mov ecx, 1

    @@:
        lea eax, [ebx+ecx]
        cmp edx, 3
        jbe @f
        mov ebx, ecx
        mov ecx, eax
        dec edx
    jmp @b
    
    @@:
    pop ebx
    ret

Kinds of languages 2/2

unsigned int fib(unsigned int n) {
    if (n <= 0) return 0;
    else if (n <= 2) return 1;
    else {
        unsigned int a,b,c;
        a = 1;
        b = 1;
        while (1) {
            c = a + b;
            if (n <= 3) return c;
            a = b;
            b = c;
            n--;
        }
    }
}

The function for calculating the nth Fibonacci number takes as input an integer “n”. If “n” is less than or equal to 0, then 0 is returned as a result. Otherwise, if “n” is less than or equal to 2, then 1 is returned. Otherwise, in all the other cases, associate the value “1” to two distinct variables “a” and “b”. Then, repeat the following operations indefinitely. Set the variable “c” as the sum of “a” plus “b”. If “n” is less than or equal to “3” then return “c”, otherwise assign the value of “b” to “a” and the value of “c” to “b”, and finally decrease the value of “n” by 1 before repeating.

Meaning: part 3

Computational Thinking and Programming

To think (definition, Oxford Dictionary): use one's mind actively to form connected ideas

Addressed in the previous lecture! Some lesson learnt:

• Leaving out unneeded material

• Trial-and-error prodedure may be effective

• Recognising similarity of a problem to one already solved makes the problem easier to solve

• Use of patterns provided by experience is the most rapid way of solving problems

Human-computer communication

Writing a program: communicating to a computer in a (formal) language that such a computer and the human instructor can both understand

What we need:

1. agree on which language to use for the communication between us and a computer (either human or machine)

2. think about possible instructions that, if followed systematically by the computer, can enable it to return the expected result to a certain problem

What are they?

Two objects, each composed by a stack of usually rectangular pages (346 and 288 respectively) made of paper oriented with one edge fixed together and then bound to the flexible spine of a protective cover of heavier material, containing a text written by someone (Lewis Carroll) in a natural language (Italian and English respectively)

Abstraction is the key

The process of leaving out of consideration one or more properties of a complex object or situation by extracting common features from specific examples

What is Computational Thinking

An approach for solving problems, designing systems and understanding human behaviour that draws on concepts fundamental to computing

Reshape the abstractions we have ingested as consequence of our life experiences – that we are unconsciously reusing

Being again fully conscious of such abstractions, we can use an appropriate language for making them understandable to a computer, in order to automatise them

Final goal of Computational Thinking: to complement the other thinking strategies one has already learnt in the past with another tool to describe reality