$$
% create the definition symbol
\def\bydef{\stackrel{\Delta}{=}}
%\def\circconv{\otimes}
\def\circconv{\circledast}
\newcommand{\qed}{\mbox{ } \Box}
\newcommand{\infint}{\int_{-\infty}^{\infty}}
% z transform
\newcommand{\ztp}{ ~~ \mathop{\mathcal{Z}}\limits_{\longleftrightarrow} ~~ }
\newcommand{\iztp}{ ~~ \mathop{\mathcal{Z}^{-1}}\limits_{\longleftrightarrow} ~~ }
% fourier transform pair
\newcommand{\ftp}{ ~~ \mathop{\mathcal{F}}\limits_{\longleftrightarrow} ~~ }
\newcommand{\iftp}{ ~~ \mathop{\mathcal{F}^{-1}}\limits_{\longleftrightarrow} ~~ }
% laplace transform
\newcommand{\ltp}{ ~~ \mathop{\mathcal{L}}\limits_{\longleftrightarrow} ~~ }
\newcommand{\iltp}{ ~~ \mathop{\mathcal{L}^{-1}}\limits_{\longleftrightarrow} ~~ }
\newcommand{\ftrans}[1]{ \mathcal{F} \left\{#1\right\} }
\newcommand{\iftrans}[1]{ \mathcal{F}^{-1} \left\{#1\right\} }
\newcommand{\ztrans}[1]{ \mathcal{Z} \left\{#1\right\} }
\newcommand{\iztrans}[1]{ \mathcal{Z}^{-1} \left\{#1\right\} }
\newcommand{\ltrans}[1]{ \mathcal{L} \left\{#1\right\} }
\newcommand{\iltrans}[1]{ \mathcal{L}^{-1} \left\{#1\right\} }
% coordinate vector relative to a basis (linear algebra)
\newcommand{\cvrb}[2]{\left[ \vec{#1} \right]_{#2} }
% change of coordinate matrix (linear algebra)
\newcommand{\cocm}[2]{ \mathop{P}\limits_{#2 \leftarrow #1} }
% Transformed vector set
\newcommand{\tset}[3]{\{#1\lr{\vec{#2}_1}, #1\lr{\vec{#2}_2}, \dots, #1\lr{\vec{#2}_{#3}}\}}
% sum transformed vector set
\newcommand{\tsetcsum}[4]{{#1}_1#2(\vec{#3}_1) + {#1}_2#2(\vec{#3}_2) + \cdots + {#1}_{#4}#2(\vec{#3}_{#4})}
\newcommand{\tsetcsumall}[4]{#2\lr{{#1}_1\vec{#3}_1 + {#1}_2\vec{#3}_2 + \cdots + {#1}_{#4}\vec{#3}_{#4}}}
\newcommand{\cvecsum}[3]{{#1}_1\vec{#2}_1 + {#1}_2\vec{#2}_2 + \cdots + {#1}_{#3}\vec{#2}_{#3}}
% function def
\newcommand{\fndef}[3]{#1:#2 \to #3}
% vector set
\newcommand{\vset}[2]{\{\vec{#1}_1, \vec{#1}_2, \dots, \vec{#1}_{#2}\}}
% absolute value
\newcommand{\abs}[1]{\left| #1 \right|}
% vector norm
\newcommand{\norm}[1]{\left|\left| #1 \right|\right|}
% trans
\newcommand{\trans}{\mapsto}
% evaluate integral
\newcommand{\evalint}[3]{\left. #1 \right|_{#2}^{#3}}
% slist
\newcommand{\slist}[2]{{#1}_{1},{#1}_{2},\dots,{#1}_{#2}}
% vectors
\newcommand{\vc}[1]{\textbf{#1}}
% real
\newcommand{\Real}[1]{{\Re \mit{e}\left\{{#1}\right\}}}
% imaginary
\newcommand{\Imag}[1]{{\Im \mit{m}\left\{{#1}\right\}}}
\newcommand{\mcal}[1]{\mathcal{#1}}
\newcommand{\bb}[1]{\mathbb{#1}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\Q}{\mathbb{Q}}
\newcommand{\R}{\mathbb{R}}
\newcommand{\C}{\mathbb{C}}
\newcommand{\I}{\mathbb{I}}
\newcommand{\Th}[1]{\mathop\mathrm{Th(#1)}}
\newcommand{\intersect}{\cap}
\newcommand{\union}{\cup}
\newcommand{\intersectop}{\bigcap}
\newcommand{\unionop}{\bigcup}
\newcommand{\setdiff}{\backslash}
\newcommand{\iso}{\cong}
\newcommand{\aut}[1]{\mathop{\mathrm{Aut(#1)}}}
\newcommand{\inn}[1]{\mathop{\mathrm{Inn(#1)}}}
\newcommand{\Ann}[1]{\mathop{\mathrm{Ann(#1)}}}
\newcommand{\dom}[1]{\mathop{\mathrm{dom} #1}}
\newcommand{\cod}[1]{\mathop{\mathrm{cod} #1}}
\newcommand{\id}{\mathrm{id}}
\newcommand{\st}{\ |\ }
\newcommand{\mbf}[1]{\mathbf{#1}}
\newcommand{\enclose}[1]{\left\langle #1\right\rangle}
\newcommand{\lr}[1]{\left( #1\right)}
\newcommand{\lrsq}[1]{\left[ #1\right]}
\newcommand{\op}{\mathrm{op}}
\newcommand{\dotarr}{\dot{\rightarrow}}
%Category Names:
\newcommand{\Grp}{\mathbf{Grp}}
\newcommand{\Ab}{\mathbf{Ab}}
\newcommand{\Set}{\mathbf{Set}}
\newcommand{\Matr}{\mathbf{Matr}}
\newcommand{\IntDom}{\mathbf{IntDom}}
\newcommand{\Field}{\mathbf{Field}}
\newcommand{\Vect}{\mathbf{Vect}}
\newcommand{\thm}[1]{\begin{theorem} #1 \end{theorem}}
\newcommand{\clm}[1]{\begin{claim} #1 \end{claim}}
\newcommand{\cor}[1]{\begin{corollary} #1 \end{corollary}}
\newcommand{\ex}[1]{\begin{example} #1 \end{example}}
\newcommand{\prf}[1]{\begin{proof} #1 \end{proof}}
\newcommand{\prbm}[1]{\begin{problem} #1 \end{problem}}
\newcommand{\soln}[1]{\begin{solution} #1 \end{solution}}
\newcommand{\rmk}[1]{\begin{remark} #1 \end{remark}}
\newcommand{\defn}[1]{\begin{definition} #1 \end{definition}}
\newcommand{\ifff}{\LeftRightArrow}
<!-- For the set of reals and integers -->
\newcommand{\rr}{\R}
\newcommand{\reals}{\R}
\newcommand{\ii}{\Z}
\newcommand{\cc}{\C}
\newcommand{\nn}{\N}
\newcommand{\nats}{\N}
<!-- For terms being indexed.
Puts them in standard font face and creates an index entry.
arg: The term being defined.
\newcommand{\pointer}[1]{#1\index{#1}} -->
<!-- For bold terms to be index, but defined elsewhere
Puts them in bold face and creates an index entry.
arg: The term being defined. -->
\newcommand{\strong}[1]{\textbf{#1}}
<!-- For set names.
Puts them in italics. In math mode, yields decent spacing.
arg: The name of the set. -->
\newcommand{\set}[1]{\textit{#1}}
$$

## Mission

Scientific content increasingly relies on the presentation and authoring of complex multimedia diagrams and figures, sometimes interactive, to convey information in a non-textual way. Wikis and user-generated hyper-linked content have both been very successful in the case for text---this is what we aim to do for mathematical diagrams.

Many professors in higher education who write textbooks know TeX, however, they don't often know how to program the Web. The future of building interactive user interfaces should lie not in the hands of programmers, but in the hands of the expert of a given field---the goal of this project is to supply math, physics, and engineering professors with a platform to express mathematical concepts to students to provide immersive learning environments.

Ideally, this projects serves twofold: First, in closing the gap for non-web-technical authors to express ideas and concepts through Web technology without the knowledge of coding or user interface design, by mapping a typesetting language to interactive programming. Second, in providing deep, educational experiences for our youth to engage more in the sciences, and begin to use exploration and creativity in learning through interactive textbooks.

The loose structure and nature of user interface design poses a problem for documenting science and related interfaces in a consistent manner. TeX provides us with some "laws" to obey in order to design the output of a text and graphical language around. Hence, we can attempt to create a synthesis of a structured user interface specification (TeX) and a structured functional specification (HTML5) to provide a publishing platform for the current and next generation.

The Art is where we can blend these two standards bodies; higher levels of abstraction allow people to express their ideas without having to worry about the mechanisms by which the technology is rendering their works. It is in these environments when people can express themselves freely.

## Team

The digital textbook platform was created by Dan Lynch, working with his advisor, Babak Ayazifar.

### Dan Lynch

Dan's interest in mathematics and music inspired him to transfer into the college of engineering to learn about Fourier analysis at UC Berkeley. Since then, Dan has authored over 300 pages of signal processing documentation that is used by the EECS department, and has now applied that experience to build the mathapedia digital textbook platform with Babak.

Remember, you are a function of the sum of living things...

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LinkedIn

### Babak Ayazifar

Dr. Babak Ayazifar received his undergraduate education at the California Institute of Technology, and his Master's and doctoral training at the Massachusetts Institute of Technology (MIT), all in Electrical Engineering (EE). From 1992-1994 he was an Associate Member of the Technical Staff in the Communications Research Laboratory of the David Sarnoff Research Center in Princeton, New Jersey. He participated in the development of DirecTV and contributed to the U.S. HDTV Grand Alliance. Following his stint with Sarnoff, he returned to MIT to pursue his Ph.D. studies in EE. He was appointed Senior Lecturer in the spring of 2002, prior to receiving his doctorate, to teach a graduate-level course in digital signal processing. From 2003-2005, Babak was involved in patent prosecution as a Technical Specialist in the Intellectual Property & Technology Group for the corporate law and litigation firm of Ropes & Gray in Boston. Since spring 2005, when he joined the Berkeley EECS faculty as a Lecturer, Babak has taught Structure and Interpretation of Systems and Signals (EE 20N); Signals and Systems (EE 120); and Teaching Techniques for Electrical Engineering (EE 301). In all cases, his teaching effectiveness ratings have been consistently high, as one might expect given his considerable, and award-winning, teaching experience at MIT. His teaching honors and awards include the Goodwin Medal (1999), MIT's top teaching award for graduate students; and promotion to Instructor-G (1996), the highest rank in the MIT EECS Department to which a graduate student could be promoted and which entailed teaching assignments ordinarily reserved for faculty. Babak was also the recipient of the Harold L. Hazen Teaching Award (1995), another Departmental award given annually to a graduate-student instructor in acknowledgment of outstanding teaching ability and performance. Babak is co-inventor on one patent, Method and apparatus for providing scalable compressed video signal ( U.S. Patent no. 5,387,940). He is a member of Tau Beta Pi, the national engineering honor society, and Eta Kappa Nu, the electrical engineering honor society.

Homepage

## Special Thanks

Thank you to the great team who built MathJax, the math rendering engine of the web: