Math 290 Textbook: A First Course in Linear Algebra (FCLA)
Conceived as open-source, free to copy/modify/distribute

• December 2003: Initiated for Spring sabbatical
• December 2004: Reasonably complete
• December 2006: Version 1.0
• December 2006: (X)HTML Version
• July 2008: jsMath Version
• Summer/Fall 2012: Conversion to XML, full HTML version
• May 2013: Initiated MathBook XML project

• 2010-14: National Science Foundation Undergraduate Education Grant
  • UTMOST: Undergraduate Teaching of Mathematics with Open Software and Textbooks
  • William Stein (UW): Sage, SageMathCloud
  • Jason Grout + Students (Drake University): Sage Cell
  • Tom Judson (UPS - 2000): Abstract Algebra textbook
  • David Farmer (AIM): Knowls, FCLA CSS
  • Kiran Kedlaya
  • RAB: Converted FCLA to Sage Notebooks via tex4ht
• May 2013: Shuttleworth Foundation Flash Grant
  • MathBook XML project

A textbook (esp. in mathematics) is a highly structured document:

• Chapter, Section, Subsection (e.g. Subsection 2.3.8)
• Theorem, Lemma, (w/ Proof), Definition (e.g. Axiom 5.17)
• Table and Figure (e.g. Table 4.2.4)
• Example, Remark, inline Exercise (e.g. Exercise 5.115)
• Exercise sections (per chapter, per section, etc.?)
• Bibliography (one, or per chapter?) (e.g. [3, Theorem 6])
• Equation (e.g. Equation (5.2.3))

Image from tex.stackexchange.com/questions/95963

Navigation

• Table of Contents
• Index
• Numbering (hierachical)

Extras

• Notation List
• Hints, Solutions for Exercises
• List of Figures, etc.

How does this all change online (HTML)?

• A printed book presents a linear, or depth-first search, version of the structure
• HTML allows expressing the tree structure with multiple pages, enhanced navigation

Image from interactivepython.org

• Express data (sentences, words) in a hierarchy
• “eXtensible” — can define new elements (“tags”)
• Simple syntax, very few reserved characters
  (ampersand is the worst)
• XML does not have to be ugly!
  (bad reputation: data exchange, automated production)

MathBook XML is a new “XML application” for structured documents (with mathematics documents described first)

<book>
	<title>A First Course in Linear Algebra</title>
	<chapter>
		<title>Systems of Linear Equations</title>
		<section>
			<title>Reduced Row Echelon Form</title>
			<p>When analyzing systems of equations...</p>
		</section>
		<section>
			<title>Homogeneous Systems</title>
			<p>The special case of ...</p>
		</section>
	</chapter>
</book>

• Design a presentation-neutral XML specification
• Allow for conversion to a variety of outputs:
  • \(\LaTeX\), then to PDF/print (safety net)
  • HTML, tree of webpages
  • Sage Notebooks, iPython notebooks, SageMathCloud worksheets
  • EPUB (ebooks for ereaders)
  • Whatever may come next
• Easy and natural for authors to use
• Converters demonstrate feasibility (reference design)

• “\(\LaTeX\) is great between the dollar signs”
• \(\LaTeX\) in <m>, <me>, <md>+<mrow> elements
• Pass-through to \(\LaTeX\) output
• Configure MathJax JavaScript library for HTML output

The Cauchy-Bunyakovsky-Schwarz Inequality:\[\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)\]

• Knowls — collapsible snippets of text, fully supported
• Google Fonts — in use
• Google Code Prettifier — for static program listings
• Sage Cell — program execution, fully implemented
• GeoGebra — Geometry canvas/playground (needs work)
• Video, Audio players — video partially implemented
• WeBWorK online homework — feasible
• Skulpt: in-browser Python execution — feasible

<theorem xml:id="theorem-finite-extension">
<statement>
	<p>Every finite extension field <m>E</m> of a field 
	   <m>F</m> is an algebraic extension.</p>
</statement>
<proof>
	<p>Let <m>\alpha \in E</m>....</p>
</proof>
/theorem>

• Recently converted to XML from \(\LaTeX\) (nearly done)
  • Text, Conversion: Tom Judson
  • Production, Conversion: RAB
  • HTML and CSS design: David Farmer
  • CSS and JavaScript implementation: Michael DuBois, UPS '14
• Improving the \(\LaTeX\), HTML and Sage Notebook conversions
• Link

• Conversion to SageMathCloud, iPython worksheets
• EPUB — MathJax now makes good scalable SVG's
• Compile xsltproc for Windows?
• Lists and tables need work
• Static versions of dynamic elements?
• Slideshows?

<slide>
	<title>To Do, Questions</title>
	<ul>
		<li>Conversion to SageMathCloud, iPython worksheets</li>
		<li>EPUB <mdash /> MathJax now makes <em>good</em>
		    scalable SVG's</li>
		<li>Compile <c>xsltproc</c> for Windows?</li>
		<li>Lists and tables need work</li>
		<li>Static versions of dynamic elements?</li>
		<li>Slideshows?</li>
	</ul>
</slide>

• Code: GitHub, GPL'ed
• Discussion: Google Groups' mathbook-xml-support
• Website: mathbook.pugetsound.edu

Thanks for listening!