References etc.

chapter24.tex

@@ -359,7 +359,8 @@ The expected value for $X$ in a geometric distribution is
 
 \index{Markov chain}
 
-A \key{Markov chain} is a random process
+A \key{Markov chain}\footnote{A. A. Markov (1856--1922)
+was a Russian mathematician.} is a random process
 that consists of states and transitions between them.
 For each state, we know the probabilities
 for moving to other states.
@@ -516,7 +517,9 @@ It turns out that we can find order statistics
 using a randomized algorithm without sorting the array.
 The algorithm is a Las Vegas algorithm:
 its running time is usually $O(n)$
-but $O(n^2)$ in the worst case.
+but $O(n^2)$ in the worst case\footnote{C. A. R. Hoare
+discovered both this algorithm, known as \key{quickselect} \cite{hoa61b},
+and a similar sorting algorithm, known as \key{quicksort} \cite{hoa61a}.}.
 
 The algorithm chooses a random element $x$
 in the array, and moves elements smaller than $x$
@@ -561,7 +564,8 @@ answer would by easier than to calculate it from scratch.
 
 It turns out that we can solve the problem
 using a Monte Carlo algorithm whose
-time complexity is only $O(n^2)$.
+time complexity is only $O(n^2)$\footnote{This algorithm is sometimes
+called \index{Freivalds' algoritm} \key{Freivalds' algorithm} \cite{fre77}.}.
 The idea is simple: we choose a random vector
 $X$ of $n$ elements, and calculate the matrices
 $ABX$ and $CX$. If $ABX=CX$, we report that $AB=C$,