Computation
Last updated
Last updated
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.
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 should launch an interactive session.
Computing platforms
Computing languages
Arithmetic operations
Variables
Functions
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
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 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
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.
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
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.
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.
Markup and Markdown
Markup and LaTeX
Python
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
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
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
For example
will turn into
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
