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%\part{Algorithm and Data-Structure Notes}
%\input{Algorithms}
\part{Coding Questions}
\input{Coding}
%\part{Game Design Notes}
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%\part{Linear Algebra Notes}
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%\part{Finite Element Method}
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\begin{appendices}
\part{Mathematical Concepts in Algorithms}
\input{AppendixAlgoMaths}
\end{appendices}
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\chapter{Mathematical Concepts in Algorithms}
\markright{}
\label{algomaths}
\section{Summations}
\label{algo-summations}
When an algorithm contains iterative control constructs like \texttt{while} or \texttt{for} loops, we can express its running times in terms of sum of times spent in the loops. When we evaluate these summations, we obtain performance bounds ($O$, $\Theta$ or $\Omega$). This section contains some of the concepts of these summations. For a list of $n$ numbers $a_0, a_1, a_2, \dots, a_{n-1}$, we can designate their sum as $\sum\limits_{i=0}^{n-1} a_i$. When the sequence is infinite, the sum becomes $\sum\limits_{i=0}^{\infty} a_i$ or $$\lim_{i\to\infty}$$ $\sum\limits_{i=0}^{n-1} a_i$. If the limit exists, then the series \textbf{converges}; otherwise, it \textbf{diverges}.\\
\textbf{Linearity}\\
For any real number $c$ and finite sequences $a_0, a_1, a_2, \dots, a_{n-1}$ and $b_0, b_1, b_2, \dots, b_{n-1}$,
\begin{equation}
\sum\limits_{i=0}^{n-1} (ca_i + b_i) = c\sum\limits_{i=0}^{n-1} a_i + \sum\limits_{i=0}^{n-1} b_i
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No file Notes.ptc.
[21] [22] (./AppendixAlgoMaths.tex
Appendix A.
<use "Pictures/chapter_head_2.pdf" >
! Missing number, treated as zero.
<to be read again>
A
l.1 \chapter{Mathematical Concepts in Algorithms}If someone can shed some light on this, I would be much obliged.
