Introduction

Administrative trivia

  • Laptop policy
  • Course material on web page and Avenue to Learn
  • Expectations of professor and students
  • Textbook (optional); Gries et al. Practical Programming 3d ed. (see outline)
  • also see resources

Course content

reasonable balance among

  • nitty-gritty practical programming instruction:

    … I just sat down in front of a text editor, with nothing but thoughts, and ended up with a program that did exactly what I wanted it to a few hours later … (ankit panda)

  • conceptual foundations of computing/computer science
  • context/culture of mathematical/scientific computing

  • interesting applications

Installing Python

Overview of math/sci computing

Using computers in math and science

  • math users vs. understanders vs. developers
  • develop conjectures; draw pictures; write manuscripts
  • mathematical proof (e.g. four-colo(u)r theorem and other examples); computer algebra
  • applied math: cryptography, tomography, logistics, finance, fluid dynamics, …
  • applied statistics: bioinformatics, Big Data/analytics, …
  • discrete vs. continuous math

Running Python

Fun!

Hello, world (always the first program you write in a new computer language)

print('hello, python world!')
## hello, python world!

Python as a fancy calculator (REPL, Read-Evaluate-Print-Loop)

print(62**2*27/5+3)
## 20760.6

reference: Python intro section 3.1.1

Interlude: about Python

the “prime walk” (from math.stackexchange.com)

  1. start at the origin, heading right, counting up from 1
  2. move forward one space, counting up, until you find a prime
  3. turn 90\({}^\circ\) clockwise
  4. repeat steps 2 and 3 until you get bored

code here (bbolker.github.io/math1mp/code/primewalk.py)

Note:

  • easier to understand/modify than write from scratch
  • build on existing components (modules)

Interfaces

  • integrated development environment (IDE), command line/console (Spyder)
  • programming editor
  • notebooks
  • not MS Word! skull

Features

  • syntax highlighting, bracket-matching, hot-pasting
  • integrated help
  • integrated debugging tools

  • integrated project management tools

  • most important: maintain reproducibility; well-defined workflows

Assignment and types (PP \(\S2.4\))

  • superficially simple
    • set aside memory space, create a symbol that points to that space
    • = is the assignment operator (“gets”, not “equals”)
    • <variable> = <value>
    • variable names
      • what is legal? (names include letters, numbers, underscores, must start with a letter)
      • what is customary? convention is variables_like_this (“snake case”)
      • what works well? v vs. temporary_variable_for_loop
      • same principles apply to file, directory/folder names
  • variables are of different types
    • built-in: integer (int), floating-point (float), complex, Boolean (bool: True or False),
    • dynamic typing
      • Python usually “does what you mean”, converts types when sensible
    • strong typing
      • try print(type(x)) for different possibilities (x=3; x=3.0; x="a")
      • what happens if you try x=a?
      • don’t be afraid to experiment!

Examples

x=3
y=3.0
z="a"
q=complex(1,2)
type(x+y)  ## mixed arithmetic
type(int(x+y))  ## int(), float() convert explicitly
type(x+z)
type(q)
type(x+q)
type(True)
type(True+1) ## WAT

[^2](As Dive into Python says in a similar context, “Ew, ew, ew! Don’t do that. Forget I even mentioned it.”)

Check out the Python tutor for these examples

Arithmetic operators, precedence

  • exponentiation (**)
  • negation (“unary minus”) (-)
  • multiplication/division (*,/,//=integer division,%=remainder (“modulo”))
  • addition/subtraction (+, - (“binary”))

Use parentheses when in doubt!

Puzzle: what is -1**2? Why?

Logical operators (PP \(\S5.1\))

  • comparison: (==, !=)
  • inequalities: >, <, >=, <=,
  • basic logic: (and, or, not)
  • remember your truth tables, e.g. not(a and b) equals (not a) or (not b)
a = True; b = False; c=1; d=0
a and b
not(a and not b)
a and not(b>c)
a==c  ## careful!
not(d)
not(c)

operator precedence

From CodingBat:

We have two monkeys, a and b, and the parameters a_smile and b_smile indicate if each is smiling. We are in trouble if they are both smiling or if neither of them is smiling. Return True if we are in trouble.

monkey_trouble(True, True) → True
monkey_trouble(False, False) → True
monkey_trouble(True, False) → False

Truth tables

A B A and B A or B not A
True True True True False
True False False True False
False True False True True
False False False False True

Logical expressions

  • The logical expression: not not a and not b or a is equivalent to ((not (not a)) and (not b)) or a since the operator not takes precedence over the operators and and or.

  • So if a = True and b = False this evaluates to True
  • Since not not a is equivalent to a, we can simplify the expression to just (a and not b) or a.

  • Can we simplify this further?

What can we do with not a and not b ?

String operations (PP chapter 4)

reference: Python intro section 3.1.2

  • Less generally important, but fun
  • + concatenates
  • * replicates and concatenates
  • in searches for a substring
a = "xyz"
b = "abc"
a+1  ## error
a+b
b*3
(a+" ")*5
b in a

CodingBat problems:

One more useful string operation: len(s) returns the length (number of characters)

Indexing and slicing

Indexing

  • Extracting elements is called indexing a list
  • Indexing starts from zero
  • Negative indices count backward from the end of the string
    (-1 is the last element)
  • Indexing a non-existent element gives an error
slicing

slicing

Slicing

  • Extracting (consecutive) sets of elements is called slicing
  • Slicing non-existent element(s) gives a truncated result
  • Slicing specifies start, end, step (or “stride”)
  • Leaving out a bit goes from the beginning/to the end
  • Slicing works on strings too!
x[:]        # everything
x[a:b]      # element a (zero-indexed) to b-1
x[a:]       # a to end
x[:b]       # beginning to b-1
x[a:b:n]    # from a to b-1 in steps of n
  • generate a list of odd numbers from 3 to 15
  • reverse a string?

String slicing practice

From CodingBat:

Methods

  • Objects in Python have classes (string, integer, etc.)
  • Classes have methods - things you can to do the objects
  • You use a method by calling .()
    • yes, this seems weird at first.
  • methods may or may not have arguments

String methods: examples

Strings have lots of methods, for example:

x = "abcdef"
x.upper()
## 'ABCDEF'
x.capitalize()
## 'Abcdef'
x.endswith("f")
## True
x.startswith("qrs")
## False
x.islower()
## True