Computation

Introduction

While we want to develop our intuition when we are estimating with large numbers, performing accurate calculations is also important. You will be able to calculate these numbers on a hand-held calculator, in Excel, and using scientific computing platforms like Python.

Since our calculations are often used as evidence to support an argument, they must be easy to read and have clear methods and assumptions. Using a computer to preserve the details of the calculation is often preferable to using a calculator.

We will start with concepts most familiar to you from your work with calculators and we will build more concepts on that knowledge.

Materials

You can find an interactive set of files here.

If the link above doesn't work, you can find the files here. Clicking on this icon Binder should launch an interactive session.

Basic Concepts

  • Computing platforms

  • Computing languages

  • Arithmetic operations

  • Variables

  • Functions

Computing platforms

  • You are likely most familiar with a calculator

  • You enter a series of commands

  • When you press enter or equals, they are sent to a small computer for

    evaluation

  • The results are printed for you

  • There are many computer programs that do similar things and allow much

    more power and flexibility

  • Other platforms are Mathematica and spreadsheets

Basic computations

  • Addition (+)

  • Subtraction (-)

  • Multiplication (*)

  • Division (/)

  • Exponentiation (^ or **)

To perform basic calculations with numbers, we can type numbers into the computer and use the symbols above to perform the calculation.

Computing languages

  • Computing languages allow us to instruct the computer to do things

  • As our models and computations become more complex, we will want to do

    things besides addition and multiplication

  • Using a computing language helps us achieve that

Variables

To make the details of a computation more clear, we can use readable names for our numbers and then use the names in the calculation.

power = 100
time = 30
energy = power * time

  • This makes the intention of the calculation more clear to the reader.

  • This also allows us to reuse what we have typed and change our numbers

    easily to repeat a similar calculation

Functions

You have often used functions on your calculator and you have encountered the idea in your math classes.

A function takes a number or numbers as an input and provides a number or numbers as an output.

You have probably used sine or cosine functions on your calculator.

You may want to make your own function for a calculation that you do frequently. The syntax for this often varies but the idea is usually the same.

m = 1
b = 10
f(x) = m * x + b
f(5) => 15

Print Function

Computer functions can take many things besides numbers as input and do many things besides return numbers as output. The print function is very useful. Provided with text or variables, it will output things to the screen.

estimate = 20
print('My estimate: ', estimate)

> My estimate: 20

Jupyter Concepts

  • Markup and Markdown

  • Markup and LaTeX

  • Python

  • Jupyter

Jupyter

  • Jupyter is like a word processor and spreadsheet in one program

  • By mixing words and computations together, you can clearly explain

    your approach to an estimation

  • It has blocks or cells of text that are sent to the program of your

    choice to be interpreted

  • Markdown: our word processor

  • Python: our spreadsheet or computation program

  • You press shift-enter to evaluate a cell

Markdown

  • You can think of this as a word processor

  • By selecting markdown as the type of cell, jupyter sends the text to

    markdown to be interpreted

  • Special characters are use to tell the computer to make headings or

    bold characters

LaTeX

  • This is a word processor especially for math

  • By placing dollar signs ($) around some text, it is sent to LaTeX to

    be interpreted

  • You can use this to write fractions and many other mathematical

    symbols

  • You can find some symbols at this

    link

For example

\frac{1}{2}

will turn into

12\frac{1}{2}

SageMathCloud

We use SageMathCloud to provide an easy-to-use platform for our computations

  • Create an account at Sage Math Cloud

  • Use your nice_person@sonoma.edu email address

  • We will add you to our class

  • You will be able to access class content and various tools

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