GitHub Repository: dsc-courses/dsc10-2022-fa
Path: blob/main/lectures/lec03/lec03.ipynb
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Kernel: Python 3 (ipykernel)

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# Don't worry about what this code does, but make sure to run it if you're following along.

from IPython.display import IFrame
def show_nested_eval():
    src = 'https://docs.google.com/presentation/d/e/2PACX-1vQpW0NzwT3LjZsIIDAgtSMRM1cl41Gp_Lf8k9GT-gm5sGAIynw4rsgiEFbIybClD6QtxarKaVKLbR9U/embed?start=false&loop=false&delayms=60000" frameborder="0" width="960" height="569" allowfullscreen="true" mozallowfullscreen="true" webkitallowfullscreen="true"'
    width = 960
    height = 569
    return IFrame(src, width, height)

Lecture 3 – Expressions and Data Types

DSC 10, Fall 2022

Announcements

Lab 1 is released and is due Saturday at 11:59PM.
- It contains a video 🎥 towards the end, Navigating DataHub and Jupyter Notebooks. Watching this video should be a worthwhile investment of your time ⌚!
- Post on EdStem or come to office hours for help!
Homework 1 is released and is due Tuesday at 11:59PM.
- Finish the lab before you work on the homework!
Issues with DataHub? See here. Issues with Gradescope? See here. Other issues? Post on EdStem.

Agenda

What is code? What are Jupyter Notebooks?
Expressions.
Variables.
Call expressions.
Data types.

Lots of programming – follow along in the notebook by clicking the "Expressions and Data Types" link on the course website.

What is code? What are Jupyter Notebooks? 💻

What is code?

Instructions for computers are written in programming languages, and are referred to as code.
“Computer programs” are nothing more than recipes: we write programs that tell the computer exactly what to do, and it does exactly that – nothing more, and nothing less.

Why Python?

Popular.
Variety of uses.
- Web development.
- Data science and machine learning.
- Not really used for developing applications.
Easy to dive right in!

Jupyter Notebooks 📓

Often, but not in this class, code is written in a text editor and then run in a command-line interface.

Jupyter Notebooks allow us to write and run code within a single document. They also allow us to embed text and code. We will be using Jupyter Notebooks throughout the quarter.
DataHub is a server that allows you to run Jupyter Notebooks from your web browser without having to install any software locally.

Aside: lecture slides

The lecture slides you're viewing right now are also in the form of a Jupyter Notebook – we're just using an extension (called RISE) to make them look like slides.
When you click a "lecture" link on the course website, you'll see the lecture notebook in regular notebook form.
To view it in slides form, click the bar chart button in the toolbar.

This button!

Expressions

Python as a calculator

An expression is a combination of values, operators, and functions that evaluates to some value.

For now, let's think of Python like a calculator – it takes expressions and evaluates them.

We will enter our expressions in code cells. To run a code cell, either:
- Hit shift + enter (or shift + return) on your keyboard (strongly preferred), or
- Press the "▶ Run" button in the toolbar.

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-1 + 3.14

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2 ** 3

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(17 - 14) / 2

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# Only one value is displayed. Why?
3 * 4
5

Arithmetic operations

| Operation | Operator | Example | Value | | --- | --- | --- | --- | | Addition | + | 2 + 3 | 5 | | Subtraction | - | 2 - 3 | -1 | | Multiplication | * | 2 * 3 | 6 | | Division | / | 7 / 3 | 2.66667 | | Remainder | % | 7 % 3 | 1 | | Exponentiation | ** | 2 ** 0.5 | 1.41421 |

Python uses the typical order of operations – PEMDAS (BEDMAS?)

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3 * 2 ** 2

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(3 * 2) ** 2

Activity

In the cell below, replace the ellipses with an expression that's equivalent to

(19 + 6 \cdot 3) - 15 \cdot \left(\sqrt{100} \cdot \frac{1}{30}\right) \cdot \frac{3}{5} + \frac{4^2}{2^3} + \left( 6 - \frac{2}{3} \right) \cdot 12

Try to use parentheses only when necessary.

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...

Variables

Motivation

Below, we compute the number of seconds in a year.

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60 * 60 * 24 * 365

If we want to use the above value later in our notebook to find, say, the number of seconds in 12 years, we'd have to copy-and-paste the expression. This is inconvenient, and prone to introducing problems.

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60 * 60 * 24 * 365 * 12

It would be great if we could store the initial value and refer to it later on!

Variables and assignment statements

A variable is a place to store a value so that it can be referred to later in our code. To define a variable, we use an assignment statement.

\overbrace{\texttt{myvariable}}^{\text{name}} = \overbrace{\texttt{2 + 3}}^{\text{any expression}}

An assignment statement changes the meaning of the name to the left of the = symbol.

The expression on the right-hand side of the = symbol is evaluated before being assigned to the name on the left-hand side.
- e.g. myvariable is bound to 5 (value) not 2 + 3 (expression).

Note that before we use it in an assignment statement, more_than_1 has no meaning.

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more_than_1

After using it in an assignment statement, we can ask Python for its value.

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# Note that an assignment statement doesn't output anything!
more_than_1 = 15 - 5

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more_than_1

Anytime we use more_than_1 in an expression, 10 is substituted for it.

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more_than_1 * 2

Note that the above expression did not change the value of more_than_1, because we did not re-assign more_than_1!

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more_than_1

Naming variables

Generally, give your variables helpful names so that you know what they refer to.
Variable names can contain uppercase and lowercase characters, the digits 0-9, and underscores.
- They cannot start with a number.
- They are case sensitive!

The following assignment statements are valid, but use poor variable names 😕.

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six = 15

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i_45love_chocolate_9999 = 60 * 60 * 24 * 365

The following assignment statements are valid, and use good variable names ✅.

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seconds_per_hour = 60 * 60
hours_per_year = 24 * 365
seconds_per_year = seconds_per_hour * hours_per_year

The following "assignment statements" are invalid ❌.

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6 = 15

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3 = 2 + 1

Assignment statements are not mathematical equations!

Unlike in math, where $x = 3$ means the same thing as $3 = x$ , assignment statements are not "symmetric".
An assignment statement assigns (or "binds") the name on the left of = to the value to the right of =, nothing more.

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x = 3
x

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4 = x

A variable's value is set at the time of assignment

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uc = 2
sd = 3 + uc

Assignment statements are not promises – the value of a variable can change!

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uc = 7

Note that even after changing uc, we did not change sd, so it is still the same as before.

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sd

A helpful analogy

A common metaphor is that variables are like boxes or containers (source).
Another analogy: an assignment statement is like placing a sticker on a value.

Concept Check ✅ – Answer at cc.dsc10.com

Assume you have run the following three lines of code:

side_length = 5
area = side_length ** 2
side_length = side_length + 2

What are the values of side_length and area after execution?

A. side_length = 5, area = 25

B. side_length = 5, area = 49

C. side_length = 7, area = 25

D. side_length = 7, area = 49

E. None of the above

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Aside: hit `tab` to autocomplete a set name

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...

Call expressions 📞

Algebraic functions

In math, functions take in some input and return some output.

f(x, y) = 2x^2 + 3xy - 1

We can determine the output of a function even if we pass in complicated things.

f\left(\frac{1+2}{3+4}, (-1)^{15}\right)

Call expressions

Call expressions in Python invoke functions – they tell a function to "run its recipe".
Functions in Python work the same way functions in math do.
The inputs to functions are called arguments.

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abs(-12)

Some functions can take a variable number of arguments

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max(3, -4)

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max(2, -3, -6, 10, -4)

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# Only two arguments!
max(4 + 5, 5 - 4)

Use the `?` after a function to see the documentation for a function

Or, use the help function, e.g. help(max).

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max?

Example: `round`

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my_number = 1.22
round(my_number)

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round?

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round(1.22222, 3)

Nested evaluation

We can nest many function calls to evaluate sophisticated expressions.

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min(abs(max(-1, -2, -3, min(4, -2))), max(5, 100))

...how did that work?

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show_nested_eval()

Import statements

Python doesn't have everything we need built in.
In order to gain additional functionality, we import modules via import statements.
Modules can be thought of as collections of Python functions and values.
Call these functions using the syntax module.function(), called "dot notation".

Example: `import math`

sqrt, log, pow, etc.

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import math

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math.sqrt(9)

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math.pow(3, 2)

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# What base is log?
math.log?

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# Tab completion for browsing
math.

It also has constants built-in!

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math.pi

Concept Check ✅ – Answer at cc.dsc10.com

Assume you have run the following statements:

x = 3
y = -2

Which of these examples results in an error?

A. abs(x, y)

B. math.pow(x, abs(y))

C. round(x, max(abs(y ** 2)))

D. math.pow(x, math.pow(y, x))

E. More than one of the above

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Data types

What's the difference? 🧐

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4 / 2

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5 - 3

To us, 2.0 and 2 are the same number, $2$ . But to Python, these appear to be different! 😱

Data types

Every value in Python has a type.
- Use the type function to check a value's type.
It's important to understand how different types work with different operations, as the results may not always be what we expect.

Two numeric data types: `int` and `float`

int : An integer of any size.
float: A number with a decimal point.

`int`

If you use these operations between ints (+, -, *, **), the result will be another int.
ints have arbitrary precision in Python, meaning that your calculations will always be exact.

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3 + 5

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type(3 + 5)

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2 ** 300

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2 ** 3000

`float`

A float is specified using a decimal point.
A float might be printed using scientific notation.

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2.0 + 3.2

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type(2.0 + 3.2)

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2.0 ** 300

The pitfalls of `float`

floats have limited size (but the limit is huge).
floats have limited precision of 15-16 decimal places.
After arithmetic, the final few decimal places can be wrong in unexpected ways (limited precision!).

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1 + 0.2

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1 + 0.1 + 0.1

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2.0 ** 3000

Type coercion between `int` and `float`

By default, Python changes an int to a float in a mixed expression involving both types.
- Note that the division of two ints automatically returns a float value.
A value can be explicity coerced (i.e. converted) using the int and float functions.

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2.0 + 3

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2 / 1

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# Want an integer back
int(2 / 1)

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# int chops off the decimal point, effectively rounding DOWN
int(3.9)

Aside: Jupyter memory model

Our notebook still remembers all of the variables we defined earlier in the lecture.

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more_than_1

However, if you come back to your notebook after a few hours, it will usually "forget" all of the variables it once knew about.
When this happens, you will need to run the cells in your notebook again.
See Navigating DataHub and Jupyter Notebooks for more.

Summary, next time

Summary

Expressions evaluate to values. Python will display the value of the last expression in a cell by default.
Python knows about all of the standard mathematical operators and follows PEMDAS.
Assignment statements allow us to bind values with variables.
We can call functions in Python similar to how we call functions in math.
- Python knows some functions by default, and import statements allow us to bring additional functionality from modules.
All values in Python have a data type.
- ints and floats are numbers.
- ints are integers, while floats contain decimal points.

Next time

We'll learn about strings, a data type in Python designed to store text. We'll also learn how to store many pieces of information in a single value, using arrays.

Note: We will introduce some code in labs and homeworks as well. Not everything will be in lecture. You will learn by doing!

Lecture 3 – Expressions and Data Types

DSC 10, Fall 2022

Announcements

Agenda

What is code? What are Jupyter Notebooks? 💻

What is code?

Why Python?

Jupyter Notebooks 📓

Aside: lecture slides

Expressions

Python as a calculator

Arithmetic operations

Python uses the typical order of operations – PEMDAS (BEDMAS?)

Activity

Variables

Motivation

Variables and assignment statements

Naming variables

Assignment statements are not mathematical equations!

A variable's value is set at the time of assignment

A helpful analogy

Concept Check ✅ – Answer at cc.dsc10.com

Aside: hit tab to autocomplete a set name

Call expressions 📞

Algebraic functions

Call expressions

Some functions can take a variable number of arguments

Use the ? after a function to see the documentation for a function

Example: round

Nested evaluation

Import statements

Example: import math

Concept Check ✅ – Answer at cc.dsc10.com

Data types

What's the difference? 🧐

Data types

Two numeric data types: int and float

int

float

The pitfalls of float

Type coercion between int and float

Aside: Jupyter memory model

Summary, next time

Summary

Next time

Aside: hit `tab` to autocomplete a set name

Use the `?` after a function to see the documentation for a function

Example: `round`

Example: `import math`

Two numeric data types: `int` and `float`

`int`

`float`

The pitfalls of `float`

Type coercion between `int` and `float`