\documentclass{beamer}[10pt]
\usepackage{beamerthemesplit}
\usetheme{Warsaw}
%\usepackage{verbatim}
\usepackage{color}
%\usepackage{media9}
\usepackage{fontspec}
\setmainfont[Script=Devanagari]{Sanskrit 2003}

\newfontfamily \dv[Script=Devanagari]{Sanskrit 2003}

\title{\textcolor{yellow}{Algorithms in Ancient India}}
\author{Amba Kulkarni}
\institute{ Department of Sanskrit Studies, \\University of Hyderabad}
\date{13-14th February 2018}

\begin{document}
\setbeamertemplate{footline}[frame number]
%===================================slide 1=========================%
\begin{frame}

\titlepage

\end{frame}
%============================================================%
\begin{frame}
\'{S}ikh{\=a} (hair tied in a knot)\\
\vspace{0.5cm}
{\dv पदोत्तरां जटामेव शिखामार्याः प्रचक्षते} \textbar \textbar 11 \textbar \textbar\\
\vspace{0.5cm}
\'{S}ikh{\=a} has the same pattern as that of Ja\d{t}{\=a} with next word added at the end of the pattern.
If there are 5 words then the \'{s}ikh{\=a} will be as follows\\
\vspace{0.5cm}
1 2 2 1 1 2 3; \\
2 3 3 2 2 3 4; \\
3 4 4 3 3 4 5; \\
4 5 5 4 4 5; \\
5 iti 5\\
\end{frame}
%============================================================%
\begin{frame}
Rekh{\=a} (line)\\
\vspace{0.5cm}
{\dv क्रमाद् द्वित्रिच्तुःपञ्चपदक्रममुदाहरेत्}\textbar\\
{\dv पृथक्पृथग्विपर्यस्य रेखामाहुः पुनः क्रमात्}\textbar \textbar 12 \textbar \textbar \\
\vspace{0.5cm}
If there are 7 words, then the Rekh{\=a} is as follows\\
1 2; 2 1; 1 2; \\
2 3 4; 4 3 2; 2 3; 3 4;\\
4 5 6 7; 7 6 5 4; 4 5; 5 6; 6 7; 7 iti 7\\
\end{frame}
%============================================================%
\begin{frame}
Dhvaja (Flag)\\
\vspace{0.5cm}
{\dv ब्रूयादादौ क्रमं सम्यगन्तादुत्तारयेदिति}\texttbar\\
{\dv वर्गे वा ऋचि वा यस्य पठनं स ध्वजः स्मृतः}\textbar \textbar 13 \textbar \textbar\\
\vspace{0.5cm}
If there are 9 words, then the Dhvaja will be as follows:\\
1 2; 9 iti 9; \\
2 3; 8 9;\\
3 4; 7 8;\\
4 5; 6 7;\\
5 6; 5 6;\\
6 7; 4 5;\\
7 8; 3 4;\\
8 9; 2 3;\\
9 iti 9; 1 2\\
\vspace{0.5cm}
Note: This is similar to the kramam{\=a}l{\=a} except that in kramam{\=a}l{\=a} the second pair is in reverse order while here it is in normal order.
\end{frame}
%============================================================%
\begin{frame}
Da\d{n}\d{d}a (rod) \\
{\dv क्रममुक्त्वा विपर्यस्य पुनश्च क्रममुत्तरम्} \textbar\\
{\dv अर्धर्चादेवमुक्तोक्तैः क्रमदण्डोभिधीयते} \textbar \textbar 14 \textbar \textbar\\
\vspace{0.5cm}
If there are 6 words in a \d{r}c and at the 3rd word half \d{r}c ends, then the  da\d{n}\d{d}a is\\
1 2; 2 1; \\
1 2; 2 3; 3 2 1; \\
1 2; 2 3; 3 4; 3 iti 3; 4 3 2 1; \\
1 2; 2 3; 3 4; 3 iti 3; 4 5; 5 4 3 2 1;\\
1 2; 2 3; 3 4; 3 iti 3; 4 5; 5 6; 6 5 4 3 2 1;\\
1 2; 2 3; 3 4; 3 iti 3; 4 5; 5 6; 6 iti 6\\
\vspace{0.5cm}
Note that the last line of the da\d{n}\d{d}a is same as that of the kramap{\=a}\d{t}ha.
\end{frame}
%============================================================%
\begin{frame}
Ratha (Chariot)\\
{\dv पादशोर्धर्चशो वापि सहोक्त्या दण्डवद्रथः} \textbar \textbar 15 \textbar \textbar \\

\vspace{0.5cm}
Here, 2 or 3 or 4 units of a \d{r}c are uttered simultaneously in the order of da\d{n}\d{d}a.
So suppose 11 12 13 14 15 16 are the words in the 1st quarter, and 21 22 23 24 25 26 are the words in the second quarter, then the ratha is:

11 12; 12 11; \\
21 22; 22 21; \\

11 12; 12 13; 13 12 11; \\
21 22; 22 23; 23 22 21; \\

11 12; 12 13; 13 14; 13 iti 13; 14 13 12 11; \\
21 22; 22 23; 23 24; 23 iti 23; 24 23 22 21; \\

11 12; 12 13; 13 14; 13 iti 13; 14 15; 15 14 13 12 11;\\
21 22; 22 23; 23 24; 23 iti 23; 24 25; 25 24 23 22 21;\\

11 12; 12 13; 13 14; 13 iti 13; 14 15; 15 16; 16 15 14 13 12 11;\\
21 22; 22 23; 23 24; 23 iti 23; 24 25; 25 26; 26 25 24 23 22 21;\\

11 12; 12 13; 13 14; 13 iti 13; 14 15; 15 16; 16 iti 16\\
21 22; 22 23; 23 24; 23 iti 23; 24 25; 25 26; 26 iti 26\\
\end{frame}
%============================================================%
\begin{frame}
Ghana (hard)\\
\vspace{0.3cm}
These are of two types:\\
{\dv अन्तात् क्रमं पठेत पूर्वमादिपर्यन्तमानयेत} \textbar\\
{\dv आदिक्रमं जयेदन्तं घनमाहुरमनीषिणः} \textbar \textbar 16 \textbar \textbar \\

\vspace{0.3cm}
{\dv शिखामुक्त्वा विपर्यस्य पुनस्त्रिपदमाहरेत} \textbar\\
{\dv अथ घन इति प्रोक्त इत्यष्टौ विकृतिः पठेत} \textbar \textbar 17 \textbar \textbar\\

\'{S}ikh{\=a}: \\
1 2 2 1 1 2 3; \\
2 3 3 2 2 3 4; \\
3 4 4 3 3 4 5; ...\\
Ghana: \\
1 2 2 1 1 2 3 3 2 1 1 2 3; \\
2 3 3 2 2 3 4 4 3 2 2 3 4; \\
3 4 4 3 3 4 5 5 4 3 3 4 5; ...\\
\end{frame}
%============================================================%
\begin{frame}
\frametitle{G{\=a}yatri mantra}
{\dv ॐ भूर्भुव: स्व: तत्सवितुर्वरेण्यं । भर्गो देवस्य धीमहि, धीयो यो न: प्रचोदयात् ।।   } \\
\vspace{1cm}
We meditate on the effulgent glory of the divine Light; may he inspire our understanding (S Radhakrishnan)
\end{frame}
%============================================================%
\begin{frame}
\frametitle{G{\=a}yatri mantra Ghanap{\=a}\d{t}ha}

{\dv ॐ तत् सवितुस् सवितुस् तत् तत् सवितुर् वरेण्यं वरेण्यं सवितुस् तत् तत् सवितुर् वरेण्यम्।}\\
{\dv सवितुर् वरेण्यं वरेण्यं सवितुस् सवितुर् वरेण्यं भर्गो भर्गो वरेण्यं सवितुस् सवितुर् वरेण्यं भर्गः। }\\
{\dv वरेण्यं भर्गो भर्गो वरेण्यं वरेण्यं भर्गो देवस्य देवस्य भर्गो वरेण्यं वरेण्यं भर्गो देवस्य। }\\
{\dv भर्गो देवस्य देवस्य भर्गो भर्गो देवस्य धीमहि धीमहि देवस्य भर्गो भर्गो देवस्य धीमहि। }\\
{\dv देवस्य धीमहि धीमहि देवस्य देवस्य धीमहि धीमहि इति धीमहि। }\\
{\dv धियो यो यो धियो धियो यो नो नो यो धियो धियो यो नः। }\\
{\dv यो नो नो यो यो नः प्रचोदयात् प्रचोदयात् नो यो यो नः प्रचोदयात्। }\\
{\dv नः प्रचोदयात् प्रचोदयात् नो नः प्रचोदयात् प्रचोदयात् इति प्रचोदयात्॥ }\\
 
{\dv ॐ भू ॐ भुवः ॐ स्वः ॐ महः ॐ जनः ॐ तपः ॐ सत्यम्। }\\
{\dv ॐ तत् सवितुर्वरेण्यं भर्गो देवस्य धीमहि धियो यो नः प्रचोदयात् }\\
{\dv ॐ आपोज्योतीरसोऽमृतं ब्रह्म भूर्भुवःस्वरोम्‌॥ } \\


\end{frame}
%============================================================%
%\begin{frame}
%\frametitle{G{\=a}yatri mantra Ghanap{\=a}\d{t}ha}
%\begin{figure}[ht]
%\includemedia{GhanaPatha_Gayatri.mp4}
%\end{figure}
%\end{frame}
%============================================================%
\begin{frame}
\frametitle{Error Correction Error Detection Code}
Error Correction and Error Detection\\
for Reliable delivery of Digital Data\\
over unreliable communication channels\\
\end{frame}
%============================================================%
\begin{frame}
\frametitle{Error Correction Error Detection Code}
\begin{itemize}
\item Error Detection: Detection of errors due to noise
\item Error Correction: Construction of the original error-free data
\end{itemize}
To add some redundancy (repeat some data) so that the receiver can check for consistency.
\end{frame}
%============================================================%
\begin{frame}
\frametitle{Error Correction Error Detection Code}
Various Error Detecting Methods in Information Coding
\begin{itemize}
\item Repetition Code\\
Duplicate / Triplicate the data\\
1010 $\rightarrow$ 1010 1010 1010
\item Add Parity bits\\
Even Parity: 1010 $\rightarrow$ 01010\\
1011 $\rightarrow$ 11011\\
Good for detetcting odd number of errors.
\item CheckSum
\item Cyclic Redundancy Check
\item Hash Function\\
Adds a fixed length tag to a message.
\end{itemize}
\end{frame}
%============================================================%
\begin{frame}
\frametitle{Error Correction Error Detection Code}
Various Error Correcting Methods in Information Coding
\begin{itemize}
\item Parity bit: Single Error correction
\item Hamming Code
\item .
\item .
\end{itemize}
\end{frame}
%============================================================%
\begin{frame}
\frametitle{Understanding Vedas}
Six Veda\.ngas (Auxiliary disciplines) to understand Vedas\\
\begin{itemize}
\item \'{S}ik\d{s}{\=a}: (phonetics, phonology, pronunciation)\\
The place and articulation of various sounds, possible sounds in Sanskrit,
accent, stress, and rules of euphonic combination of words
\item Chandas: (prosody, Meter)\\
Poetic meters
\begin{itemize}
\item Ak\d{s}ara v\d{r}tta: based on fixed number of syllables per verse
\item M{\=a}tr{\=a} v\d{r}tta: based on fixed number of morae per verse
\item Ga\d{n}a v\d{r}tta: based on fixed pattern of morae per verse
\end{itemize}
\item Vy{\=a}kara\d{n}a: grammatical and linguistic analysis
\item Nirukta: etymology, explanation of words, particularly those that are archaic and have ancient uses with unclear meaning.
\item Kalpa: ritual instructions, Geometry
\item Jyoti\d{s}a: Astronomy, Astrology
\end{itemize}
\end{frame}
%============================================================%
\end{document}