Book a Demo!
CoCalc Logo Icon
StoreFeaturesDocsShareSupportNewsAboutPoliciesSign UpSign In
Download

📚 The CoCalc Library - books, templates and other resources

132928 views
License: OTHER
Tweet
Share
Share
Kernel: 
%%html
<link href="http://mathbook.pugetsound.edu/beta/mathbook-content.css" rel="stylesheet" type="text/css" />
<link href="https://aimath.org/mathbook/mathbook-add-on.css" rel="stylesheet" type="text/css" />
<style>.subtitle {font-size:medium; display:block}</style>
<link href="https://fonts.googleapis.com/css?family=Open+Sans:400,400italic,600,600italic" rel="stylesheet" type="text/css" />
<link href="https://fonts.googleapis.com/css?family=Inconsolata:400,700&subset=latin,latin-ext" rel="stylesheet" type="text/css" /><!-- Hide this cell. -->
<script>
var cell = $(".container .cell").eq(0), ia = cell.find(".input_area")
if (cell.find(".toggle-button").length == 0) {
ia.after(
    $('<button class="toggle-button">Toggle hidden code</button>').click(
        function (){ ia.toggle() }
        )
    )
ia.hide()
}
</script>

Important: to view this notebook properly you will need to execute the cell above, which assumes you have an Internet connection. It should already be selected, or place your cursor anywhere above to select. Then press the "Run" button in the menu bar above (the right-pointing arrowhead), or press Shift-Enter on your keyboard.

ParseError: KaTeX parse error: \newcommand{\lt} attempting to redefine \lt; use \renewcommand

Up to this point we have studied sets with a single binary operation satisfying certain axioms, but we are often more interested in working with sets that have two binary operations. For example, one of the most natural algebraic structures to study is the integers with the operations of addition and multiplication. These operations are related to one another by the distributive property. If we consider a set with two such related binary operations satisfying certain axioms, we have an algebraic structure called a ring. In a ring we add and multiply elements such as real numbers, complex numbers, matrices, and functions.