# 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&rm=minimal" frameborder="0" width="960" height="569" allowfullscreen="true" mozallowfullscreen="true" webkitallowfullscreen="true"'
    width = 960
    height = 569
    return IFrame(src, width, height)

Lecture 2 – Expressions and Data Types

DSC 10, Fall 2023

Announcements

• Everything you need for this class is at dsc10.com. This class does not use Canvas.
• The solutions to the pretest are now posted. See how you did and watch the 🎥 video at the end to learn more about important test-taking skills.
• Lab 0 is out and is now due on Saturday, October 7 at 11:59PM.
  • It's worthwhile to watch the 🎥 video towards the end on how to navigate DataHub and Jupyter Notebooks.
• The office hours schedule is now posted, and office hours start today in HDSI 155. Please visit!
• Post on Ed with any questions.
• It was great seeing so many of you on Friday at our Meet the Professors event. We made it on the HDSI Instagram!

Opportunities

• There are two events coming up this week that may interest you:
  1. Python Bootcamp for DSC 10 students new to programming. Tomorrow and Thursday 1-3pm on Zoom. Sign up here!
  2. HDSI Undergraduate Social. Thursday, October 5th from 4-6pm on the HDSI Patio.
• We'll post events like this on our "Opportunities" thread on Ed. Check it out periodically!

Discussion sections

• There is no discussion today, or any Monday. We are only holding discussions on Wednesday afternoons:
  • Section A: Wednesday 3-3:50PM in Pepper Canyon Hall 109.
  • Section B: Wednesday 4-4:50PM in Pepper Canyon Hall 109.
  • Section C: Wednesday 5-5:50PM in Mandeville B-210.
• Please fill out the Welcome Survey as soon as possible; here you can request to change discussions or get assigned to a discussion if you're enrolled in Section D.

Agenda

• What is code? What are Jupyter Notebooks?
• Expressions.
• Variables.
• Calling functions.
• Data types.

There will be 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?

• It's popular!

• It has a variety of use cases. Some examples:
  • Web development.
  • Data science and machine learning.
  • Scripting and automation.

• It's (relatively) 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 (or both steps are done in an IDE).

• 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 DataHub 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.

23

23

-15 + 2.718

-12.282

4 ** 3

64

(2 + 3 + 4) / 3

3.0

# Only one value is displayed. Why?
9 + 10
13 / 4
21

21

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? 🛏️)

5 * 2 ** 3

40

(5 * 2) ** 3

1000

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.

Variables

Motivation

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

60 * 60 * 24 * 365

31536000

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 errors.

60 * 60 * 24 * 365 * 12

378432000

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.

$$ \overbrace{\texttt{zebra}}^{\text{name}} = \overbrace{\texttt{23 - 14}}^{\text{any expression}} $$

• 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. zebra is bound to 9 (value) not 23 - 14 (expression).

Think of variable names as nametags!

# Note: This is an assignment statement, not an expression.
# Assignment statements don't output anything!
a = 1

a = 2

b = 2

Example

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

triton

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
/var/folders/pd/w73mdrsj2836_7gp0brr2q7r0000gn/T/ipykernel_14415/521444765.py in <module>
----> 1 triton

NameError: name 'triton' is not defined

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

triton = 15 - 5

triton

10

Any time we use triton in an expression, 10 is substituted for it.

triton * -4

-40

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

triton

10

Naming variables

• 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 😕.

six = 15

i_45love_chocolate_9999 = 60 * 60 * 24 * 365

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

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 ❌.

7_days = 24 * 7

  File "/var/folders/pd/w73mdrsj2836_7gp0brr2q7r0000gn/T/ipykernel_14415/3229775372.py", line 1
    7_days = 24 * 7
     ^
SyntaxError: invalid decimal literal

3 = 2 + 1

  File "/var/folders/pd/w73mdrsj2836_7gp0brr2q7r0000gn/T/ipykernel_14415/2449763097.py", line 1
    3 = 2 + 1
    ^
SyntaxError: cannot assign to literal

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.

x = 3

3 = x

  File "/var/folders/pd/w73mdrsj2836_7gp0brr2q7r0000gn/T/ipykernel_14415/3780819163.py", line 1
    3 = x
    ^
SyntaxError: cannot assign to literal

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

uc = 2
sd = 3 + uc

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

uc = 7

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

sd

5

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

Calling functions 📞

Algebraic functions

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

$$f(x, y) = \frac{x}{y} + 2x^2 + y^5$$

• We can determine the output of a function even if we pass in complicated-looking inputs.

$$f\left(\frac{5-3}{17 \cdot 2}, (4-3)^{-5}\right)$$

Python functions

• Functions in Python work the same way functions in math do.
• The inputs to functions are called arguments.
• Python comes with a number of built-in functions that we are free to use.
• Calling a function, or using a function, means asking the function to "run its recipe" on the given input.

abs(-23)

23

Some functions can take a variable number of arguments

max(4, -8)

4

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

10

max(9)

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
/var/folders/pd/w73mdrsj2836_7gp0brr2q7r0000gn/T/ipykernel_14415/60825961.py in <module>
----> 1 max(9)

TypeError: 'int' object is not iterable

# Only two arguments!
max(9 + 10, 9 - 10)

19

Put ? after a function's name to see its documentation 📄

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

round(1.45678)

1

round?

round(1.45678, 3)

1.457

Nested evaluation

We can nest many function calls to evaluate sophisticated expressions.

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

1

...how did that work?

show_nested_eval()

Import statements

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

Example: import math

Some of the many functions built into the math module are sqrt, pow, and log.

import math

math.sqrt(16)

4.0

math.pow(2, 5)

32.0

# What base is log?
math.log?

# Tab completion for browsing.
math.

math also has constants built in!

math.pi

3.141592653589793

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

Data types

What's the difference? 🧐

4 / 2

2.0

5 - 3

2

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 add (+), subtract (-), multiply (*), or exponentiate (**) ints, the result will be another int.
• ints have arbitrary precision in Python, meaning that your calculations will always be exact.

7 - 15

-8

type(7 - 15)

int

2 ** 300

2037035976334486086268445688409378161051468393665936250636140449354381299763336706183397376

2 ** 3000

1230231922161117176931558813276752514640713895736833715766118029160058800614672948775360067838593459582429649254051804908512884180898236823585082482065348331234959350355845017413023320111360666922624728239756880416434478315693675013413090757208690376793296658810662941824493488451726505303712916005346747908623702673480919353936813105736620402352744776903840477883651100322409301983488363802930540482487909763484098253940728685132044408863734754271212592471778643949486688511721051561970432780747454823776808464180697103083861812184348565522740195796682622205511845512080552010310050255801589349645928001133745474220715013683413907542779063759833876101354235184245096670042160720629411581502371248008430447184842098610320580417992206662247328722122088513643683907670360209162653670641130936997002170500675501374723998766005827579300723253474890612250135171889174899079911291512399773872178519018229989376

float

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

3.2 + 2.5

5.7

type(3.2 + 2.5)

float

# The result is in scientific notation: e+90 means "times 10^90".
2.0 ** 300

2.037035976334486e+90

The pitfalls of float

• floats have limited precision; after arithmetic, the final few decimal places can be wrong in unexpected ways.
• floats have limited size, though the limit is huge.

1 + 0.2

1.2

1 + 0.1 + 0.1

1.2000000000000002

2.0 ** 3000

---------------------------------------------------------------------------
OverflowError                             Traceback (most recent call last)
/var/folders/pd/w73mdrsj2836_7gp0brr2q7r0000gn/T/ipykernel_14415/1310821553.py in <module>
----> 1 2.0 ** 3000

OverflowError: (34, 'Result too large')

Converting between int and float

• If you mix ints and floats in an expression, the result will always be a float.
  • Note that when you divide two ints, you get a float back.
• A value can be explicity coerced (i.e. converted) using the int and float functions.

2.0 + 3

5.0

12 / 2

6.0

# Want an integer back.
int(12 / 2)

6

# int chops off the decimal point!
int(-2.9)

-2

Aside: Jupyter memory model

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

triton

10

• 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 to 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 sequences, or many pieces of information, in a single variable.

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