In [1]:

# 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!

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.

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?)¶

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.

Motivation¶

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

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.

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.

In [12]:

more_than_1

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
/var/folders/pd/w73mdrsj2836_7gp0brr2q7r0000gn/T/ipykernel_15712/3210039468.py in <module>
----> 1 more_than_1

NameError: name 'more_than_1' is not defined

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

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

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

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

The following "assignment statements" are invalid ❌.

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.

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

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

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

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

Aside: hit `tab` to autocomplete a set name¶

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.

Some functions can take a variable number of arguments¶

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

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

Nested evaluation¶

We can nest many function calls to evaluate sophisticated expressions.

...how did that work?

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.

It also has constants built-in!

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

What's the difference? 🧐¶

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.

In [49]:

2 ** 3000

Out[49]:

1230231922161117176931558813276752514640713895736833715766118029160058800614672948775360067838593459582429649254051804908512884180898236823585082482065348331234959350355845017413023320111360666922624728239756880416434478315693675013413090757208690376793296658810662941824493488451726505303712916005346747908623702673480919353936813105736620402352744776903840477883651100322409301983488363802930540482487909763484098253940728685132044408863734754271212592471778643949486688511721051561970432780747454823776808464180697103083861812184348565522740195796682622205511845512080552010310050255801589349645928001133745474220715013683413907542779063759833876101354235184245096670042160720629411581502371248008430447184842098610320580417992206662247328722122088513643683907670360209162653670641130936997002170500675501374723998766005827579300723253474890612250135171889174899079911291512399773872178519018229989376

`float`¶

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

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!).

In [55]:

2.0 ** 3000

---------------------------------------------------------------------------
OverflowError                             Traceback (most recent call last)
/var/folders/pd/w73mdrsj2836_7gp0brr2q7r0000gn/T/ipykernel_15712/1310821553.py in <module>
----> 1 2.0 ** 3000

OverflowError: (34, 'Result too large')

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.

Aside: Jupyter memory model¶

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

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.

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¶

Concept Check ✅ – Answer at cc.dsc10.com ¶

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`¶

Concept Check ✅ – Answer at cc.dsc10.com ¶

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

`int`¶

`float`¶

The pitfalls of `float`¶

Type coercion between `int` and `float`¶