Engineering 1020: Introduction to Programming

Lecture 1: Expressions

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Last time

Introduction to Introduction to Programming

Computer structure

Knowledge and Computation

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A simple algorithm

e.g., find the sum of the set $S = 4, 7, 2, 11, 5, 8, 1$

Mathematically:

$\sum_{i = 1}^{n} S_{1. . n}$

Algorithmically?

(do this as an exercise)

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Suggested methodology:

work out an example or two
break it into steps
explain the steps to someone else (pretend they're a computer)

Software

Description of instructions for a computer

You express meaning using a programming language

Python:

y = x / 2
if (2 * y == x):
    print(x, 'is even')

C++:

int y = x / 2;
if (2 * y == x)
    cout << x << " is even\n";

Also:

Assembly, C, C#, Go, Java, Matlab, Perl, R, Rust, Scala, SPIN...

Your code is translated into machine instructions

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What is software?

Softer than hardware?

There's also "firmware", but...

Software, whether written in C++, Java, Python or another programming language, is a way of describing algorithms to a computer. Consider the following implementations of the algorithm from above that checks whether or not a number is even.

You should note that these two code snippets look a bit different, as the details of the two programming languages are different, but the fundamentals of algorithms are the same.

In both the Python and C++ examples, a program has to translate the programmer-readable source code into computer-readable machine code for the CPU to execute. This process will happen mostly transparently to us as we work with Python via online Python environments or integrated development environments (IDEs). I have provided information about getting started with Python tools on the tools page.

Programming languages5 / 22

Programming languagesvs natural languageslike natural languages
unlike natural languages
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Like natural languages, a medium for expressing semantics

Unlike natural languages, highly constrained (more like math). Allows succinct yet powerful constructions.

Programming languagesvs natural languageslike natural languages
unlike natural languages
Syntax and semantics5 / 22

Like natural languages, a medium for expressing semantics

Unlike natural languages, highly constrained (more like math). Allows succinct yet powerful constructions.

Programming languagesvs natural languageslike natural languages
unlike natural languages
Syntax and semanticssyntax: rules of well-formed language
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Like natural languages, a medium for expressing semantics

Unlike natural languages, highly constrained (more like math). Allows succinct yet powerful constructions.

Programming languagesvs natural languageslike natural languages
unlike natural languages
Syntax and semanticssyntax: rules of well-formed language
semantics: the meaning of it all
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Like natural languages, a medium for expressing semantics

Unlike natural languages, highly constrained (more like math). Allows succinct yet powerful constructions.

Write some softwareYes, right now!6 / 22

Write some softwareYes, right now!Think about a problem
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Write some softwareYes, right now!Think about a problem, e.g., what is 1+2×3−4?
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Write some softwareYes, right now!Think about a problem, e.g., what is 1+2×3−4?
Compute an answer
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Write some software

Yes, right now!

Think about a problem, e.g., what is $1 + 2 \times 3 - 4$ ?
Compute an answer
Check your answer with Python

Type 1 + 2 * 3 - 4 into pythonmorsels.com/repl, then press Enter

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What did you just do?7 / 22

What did you just do?Wrote an expression7 / 22

What did you just do?Wrote an expressionExpression was evaluated7 / 22

What did you just do?Wrote an expressionExpression was evaluatedWhat is an expression?Algebra:7 / 22

What did you just do?Wrote an expressionExpression was evaluatedWhat is an expression?Algebra: values, operators that evaluate7 / 22

What did you just do?Wrote an expressionExpression was evaluatedWhat is an expression?Algebra: values, operators that evaluate to a value7 / 22

What did you just do?Wrote an expressionExpression was evaluatedWhat is an expression?Algebra: values, operators that evaluate to a valueProgramming:7 / 22

What did you just do?Wrote an expressionExpression was evaluatedWhat is an expression?Algebra: values, operators that evaluate to a valueProgramming: the same!7 / 22

What did you just do?Wrote an expressionExpression was evaluatedWhat is an expression?Algebra: values, operators that evaluate to a valueProgramming: the same! (even operator precedence)7 / 22

Exercise 0Submit a Python expression that evaluates to 42Not:
Python 3.9.1
>>> x = 21
>>> y = 21
>>> x + y
42

Or:
x = 21
y = 21
print(x + y)

Just:
21 + 21

Or even:
42

See: "Resources" > "Tools"
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ExpressionsValues and operations that evaluate to a value9 / 22

ExpressionsValues and operations that evaluate to a valueLet's consider each of these words in turn9 / 22

Expression: values and operations that evaluate to a value

Values

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Expression: values and operations that evaluate to a value

Values

For now, just one kind:

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Expression: values and operations that evaluate to a value

Values

For now, just one kind:

A literal value

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Expression: values and operations that evaluate to a value

Literals

Literally mean what they literally say

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Expression: values and operations that evaluate to a value

Literals

Literally mean what they literally say

42 : an integer literal

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Expression: values and operations that evaluate to a value

Literals

Literally mean what they literally say

42 : an integer literal
3.14 : a real-number (floating-point) literal

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Expression: values and operations that evaluate to a value

Literals

Literally mean what they literally say

42 : an integer literal
3.14 : a real-number (floating-point) literal
'hello' : a string literal

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Expression: values and operations that evaluate to a value

Literals

Literally mean what they literally say

42 : an integer literal
3.14 : a real-number (floating-point) literal
'hello' : a string literal
True : a logical (Boolean) literal

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Expression: values and operations that evaluate to a value

Integer literals

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Expression: values and operations that evaluate to a value

Integer literals

`1`, `2`, `42`... (ok, so like math!)

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Expression: values and operations that evaluate to a value

Integer literals

`1`, `2`, `42`... (ok, so like math!)

`1_000_000` (ok, so a bit like math...)

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You can use underscores in the middle of a Python integer literal to help group numbers and keep things clear. These underscores can go anywhere: they're not tied to thousands, so be careful! (e.g., 1_00_000 looks a lot like 1_000_000, but its meaning is quite different)

Expression: values and operations that evaluate to a value

Integer literals

`1`, `2`, `42`... (ok, so like math!)

`1_000_000` (ok, so a bit like math...)

`0b10`, `0o10`, `0x10` (what!?)

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We'll come back to what these different ways of writing integers mean when we get to talking about how numbers are represented. For now, just know that there are lots of ways to write integers! (exercise for the keen: what do these "funny" integer literals evaluate to?)

Expression: values and operations that evaluate to a value

Floating-point literals

`3.0` — is this the same as `3`?

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Expression: values and operations that evaluate to a value

Floating-point literals

`3.0` — is this the same as `3`?

`3.1` — ok, definitely not the same as `3`

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Expression: values and operations that evaluate to a value

Floating-point literals

`3.0` — is this the same as `3`?

`3.1` — ok, definitely not the same as `3`

`3.1415927` — definitely not the same as `3`

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Expression: values and operations that evaluate to a value

Floating-point literals

`3.0` — is this the same as `3`?

`3.1` — ok, definitely not the same as `3`

`3.1415927` — definitely not the same as `3`

(Professor Frink notwithstanding)

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Expression: values and operations that evaluate to a value

Floating-point literals

`3.0` — is this the same as `3`?

`3.1` — ok, definitely not the same as `3`

`3.1415927` — definitely not the same as `3`

(Professor Frink notwithstanding)

Scientific notation: `3.14e0`, `1e100`...

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Expression: values and operations that evaluate to a value

Imaginary literals

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Expression: values and operations that evaluate to a value

Imaginary literals

With integer prefix: `1j`, `2j`, ...

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Expression: values and operations that evaluate to a value

Imaginary literals

With integer prefix: `1j`, `2j`, ...

With floating-point prefix: `1.0j`, `1.1j`...

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Expression: values and operations that evaluate to a value

Imaginary literals

With integer prefix: `1j`, `2j`, ...

With floating-point prefix: `1.0j`, `1.1j`...

Not complex literals, imaginary literals

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Expression: values and operations that evaluate to a value

Imaginary literals

With integer prefix: `1j`, `2j`, ...

With floating-point prefix: `1.0j`, `1.1j`...

Not complex literals, imaginary literals

1+2j is actually an expression

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Expression: values and operations that evaluate to a value

Variables

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Expression: values and operations that evaluate to a value

Variables

Named values

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Expression: values and operations that evaluate to a value

Variables

Named values

Actually, it's slightly more complicated than that, but...

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We'll talk more about variables in later lectures when we talk about how to create them. For now we will just focus on using them.

Expression: values and operations that evaluate to a value

Variables

Named values

Actually, it's slightly more complicated than that, but...

>>> from math import *
>>> pi
3.141592653589793
>>> 2j * pi
6.283185307179586j

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We'll talk more about variables in later lectures when we talk about how to create them. For now we will just focus on using them.

Expression: values and operations that evaluate to a value

Variables

Named values

Actually, it's slightly more complicated than that, but...

>>> from math import *
>>> pi
3.141592653589793
>>> 2j * pi
6.283185307179586j

r1 + r2

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We'll talk more about variables in later lectures when we talk about how to create them. For now we will just focus on using them.

ExpressionsValues and operations that evaluate to a value16 / 22

ExpressionsValues and operations that evaluate to a valueValues ✔literals ✔
variables ✔
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ExpressionsValues and operations that evaluate to a valueValues ✔literals ✔
variables ✔
Operations16 / 22

OperationsStarting with arithmetic operators:17 / 22

OperationsStarting with arithmetic operators:

Symbol
Meaning
Usage
Math


+
addition
1 + 2
1+2

-
subtraction
3 - 4
3−4

*
multiplication
5 * 6
5×6

/
division
7 / 8
7÷8 or 78


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Symbol	Meaning	Usage	Math
`+`	addition	`1 + 2`	$1 + 2$
`-`	subtraction	`3 - 4`	$3 - 4$
`*`	multiplication	`5 * 6`	$5 \times 6$
`/`	division	`7 / 8`	$7 \div 8$ or $\frac{7}{8}$

Evaluation: precedence

Operation
Kind

()
parenthetical

*, /
multiplicative

+, -
additive

Order of operations mattersJust like math!18 / 22

Operation	Kind
`()`	parenthetical
`*`, `/`	multiplicative
`+`, `-`	additive

Evaluation: precedence

Operation
Kind

()
parenthetical

*, /
multiplicative

+, -
additive

Order of operations mattersJust like math! (for now)18 / 22

Operation	Kind
`()`	parenthetical
`*`, `/`	multiplicative
`+`, `-`	additive

Top Hat question: Order of Operations (literals only)

Division operator19 / 22

Division operatorx÷y19 / 22

Division operatorx÷y or y)x―19 / 22

Division operatorx÷y or y)x―Integers and real (floating-point) numbers19 / 22

We can perform division on integers and real numbers. It doesn't make sense to divide, say, a string and an integer. Syntactically, x / y is valid, but it could be semantically nonsense.

Q: what is $7 \div 2$ ?

Division operator

$x \div y$ or $y \overset{―}{) x}$

Integers and real (floating-point) numbers

>>> 7 / 2
3.5

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We can perform division on integers and real numbers. It doesn't make sense to divide, say, a string and an integer. Syntactically, x / y is valid, but it could be semantically nonsense.

Q: what is $7 \div 2$ ?

How about in long division?

When performing long division, we will often leave the result as 3 with a remainder of 1.

Division operator

$x \div y$ or $y \overset{―}{) x}$

Integers and real (floating-point) numbers

>>> 7 / 2
3.5

>>> 7 // 2
3
>>> 7 % 2
1

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We can perform division on integers and real numbers. It doesn't make sense to divide, say, a string and an integer. Syntactically, x / y is valid, but it could be semantically nonsense.

Q: what is $7 \div 2$ ?

How about in long division?

When performing long division, we will often leave the result as 3 with a remainder of 1.

Exponentiation20 / 22

Q: what's your favourite equation?

ExponentiationEuler's identity: ejπ=−120 / 22

Q: what's your favourite equation?

Exponentiation

Euler's identity: $e^{j π} = - 1$ †

† Since $e^{j x} = \cos x + j \sin x$ ... but that's for another course!

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Q: what's your favourite equation?

Exponentiation

Euler's identity: $e^{j π} = - 1$ †

† Since $e^{j x} = \cos x + j \sin x$ ... but that's for another course!

In Python: the `**` operator

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Q: what's your favourite equation?

Exponentiation

Euler's identity: $e^{j π} = - 1$ †

† Since $e^{j x} = \cos x + j \sin x$ ... but that's for another course!

In Python: the `**` operator

$x^{y}$ in Python is `x**y`

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Q: what's your favourite equation?

Exponentiation

Euler's identity: $e^{j π} = - 1$ †

† Since $e^{j x} = \cos x + j \sin x$ ... but that's for another course!

In Python: the `**` operator

$x^{y}$ in Python is `x**y`

>>> from math import *
>>> e ** (1j * pi)
(-1+1.2246467991473532e-16j)

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Q: what's your favourite equation?

Note that the answer isn't precisely -1: it's $- 1 + 1.22646 \times 10^{- 16} j$ . This is due to the way that floating-point numbers are represented in a computer, and it's emblematic of the limits of computation.

Questions?21 / 22

(here endeth the lesson)

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