In [1]:
# Run this cell to set up packages for lecture.
from lec02_imports import *

Lecture 2 – Expressions and Data Types¶

DSC 10, Spring 2024¶

Announcements¶

  • Everything you need for this class is at dsc10.com. This class does not use Canvas.
    • If you recently enrolled, you should get access to Gradescope and DataHub in about 24 hours.
  • Discussion is today at 2PM, 3PM, or 4PM in Center 109. Today's section will focus on Python basics and Jupyter notebooks. Come to any section.
  • Lab 0 is out, due on Saturday, April 6 at 11:59PM.
    • Watch the 🎥 video towards the end on how to navigate DataHub and Jupyter notebooks.
  • Please fill out the Welcome Survey as soon as possible; here you can let us know your time preferences for quizzes.
    • We'll get back to you by Monday to let you know your assigned quiz time.
  • The office hours schedule is now posted, and office hours start today in HDSI 155. Please visit!
  • Join Ed and post questions!

Python Bootcamp¶

Next week, the student organization Diversity in Data Science is hosting a Python bootcamp specifically for students in DSC 10 who are new to programming. Feel free to sign up!

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.
In [2]:
23
Out[2]:
23
In [3]:
-15 + 2.718
Out[3]:
-12.282
In [4]:
4 ** 3
Out[4]:
64
In [5]:
(2 + 3 + 4) / 3
Out[5]:
3.0
In [6]:
# Only one value is displayed. Why?
9 + 10
13 / 4
21
Out[6]:
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? 🛏️)¶

In [7]:
5 * 2 ** 3
Out[7]:
40
In [8]:
(5 * 2) ** 3
Out[8]:
1000

Activity¶

In the cell below, write 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.

In [ ]:

Variables¶

Motivation¶

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

In [9]:
60 * 60 * 24 * 365
Out[9]:
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.

In [10]:
60 * 60 * 24 * 365 * 12
Out[10]:
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!¶

In [11]:
# Note: This is an assignment statement, not an expression.
# Assignment statements don't output anything!
a = 1
In [12]:
a = 2
In [13]:
b = 2

Example¶

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

In [15]:
triton

---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[15], line 1
----> 1 triton

NameError: name 'triton' is not defined

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

In [16]:
triton = 15 - 5
In [17]:
triton
Out[17]:
10

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

In [18]:
triton * -4
Out[18]:
-40

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

In [19]:
triton
Out[19]:
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 😕.

In [20]:
six = 15
In [21]:
i_45love_chocolate_9999 = 60 * 60 * 24 * 365

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

In [22]:
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 ❌.

In [23]:
7_days = 24 * 7

  Cell In[23], line 1
    7_days = 24 * 7
     ^
SyntaxError: invalid decimal literal
In [24]:
3 = 2 + 1

  Cell In[24], 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.
In [25]:
x = 3
In [26]:
3 = x

  Cell In[26], line 1
    3 = x
    ^
SyntaxError: cannot assign to literal

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

In [27]:
uc = 2
sd = 3 + uc

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

In [28]:
uc = 7

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

In [29]:
sd
Out[29]:
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¶

In [ ]:

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.
In [30]:
abs(-23)
Out[30]:
23

Some functions can take a variable number of arguments¶

In [31]:
max(4, -8)
Out[31]:
4
In [32]:
max(2, -3, -6, 10, -4)
Out[32]:
10
In [33]:
max(9)

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In[33], line 1
----> 1 max(9)

TypeError: 'int' object is not iterable
In [34]:
# Only two arguments!
max(9 + 10, 9 - 10)
Out[34]:
19

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

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

In [35]:
round(1.45678)
Out[35]:
1
In [36]:
round?
In [37]:
round(1.45678, 3)
Out[37]:
1.457

Nested evaluation¶

We can nest many function calls to evaluate sophisticated expressions.

In [38]:
min(abs(max(-1, -2, -3, min(4, -2))), max(5, 100))
Out[38]:
1

...how did that work?

In [39]:
show_nested_eval()
Out[39]:

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.

In [40]:
import math
In [41]:
math.sqrt(16)
Out[41]:
4.0
In [42]:
math.pow(2, 5)
Out[42]:
32.0
In [43]:
# What base is log?
math.log?
In [44]:
# Tab completion for browsing.
math.

  Cell In[44], line 2
    math.
         ^
SyntaxError: invalid syntax

math also has constants built in!

In [45]:
math.pi
Out[45]:
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? For the ones that don't error, try to determine what they evaluate to!

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? 🧐¶

In [46]:
4 / 2
Out[46]:
2.0
In [47]:
5 - 3
Out[47]:
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.
In [48]:
7 - 15
Out[48]:
-8
In [49]:
type(7 - 15)
Out[49]:
int
In [50]:
2 ** 300
Out[50]:
2037035976334486086268445688409378161051468393665936250636140449354381299763336706183397376
In [51]:
2 ** 3000
Out[51]:
1230231922161117176931558813276752514640713895736833715766118029160058800614672948775360067838593459582429649254051804908512884180898236823585082482065348331234959350355845017413023320111360666922624728239756880416434478315693675013413090757208690376793296658810662941824493488451726505303712916005346747908623702673480919353936813105736620402352744776903840477883651100322409301983488363802930540482487909763484098253940728685132044408863734754271212592471778643949486688511721051561970432780747454823776808464180697103083861812184348565522740195796682622205511845512080552010310050255801589349645928001133745474220715013683413907542779063759833876101354235184245096670042160720629411581502371248008430447184842098610320580417992206662247328722122088513643683907670360209162653670641130936997002170500675501374723998766005827579300723253474890612250135171889174899079911291512399773872178519018229989376

float¶

  • A float is specified using a decimal point.
  • A float might be printed using scientific notation.
In [52]:
3.2 + 2.5
Out[52]:
5.7
In [53]:
type(3.2 + 2.5)
Out[53]:
float
In [54]:
# The result is in scientific notation: e+90 means "times 10^90".
2.0 ** 300
Out[54]:
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.
In [55]:
1 + 0.2
Out[55]:
1.2
In [56]:
1 + 0.1 + 0.1
Out[56]:
1.2000000000000002
In [57]:
2.0 ** 3000

---------------------------------------------------------------------------
OverflowError                             Traceback (most recent call last)
Cell In[57], line 1
----> 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.
In [58]:
2.0 + 3
Out[58]:
5.0
In [59]:
12 / 2
Out[59]:
6.0
In [60]:
# Want an integer back.
int(12 / 2)
Out[60]:
6
In [61]:
# int chops off the decimal point!
int(-2.9)
Out[61]:
-2

Aside: Jupyter memory model¶

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

In [62]:
triton
Out[62]:
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!