Introduction to Algorithms by Thomas H. Cormen, Charles E. Leiserson and Ronald L. Rivest and Clifford Stein : Chapter 9

The authors defined $i^{th}$ order statistic of a set of $n$ elements as the $ i^{th} $ smallest element. The $ \lfloor\frac{n+1}{2}\rfloor $ is called lower median and $ \lceil\frac{n+1}{2}\rceil $ is called upper median. The authors then define selection problem as follows:
A set $A$ of $n$ (distinct) numbers and a number $i$, with $ 1 <= i <= n $. The element $ x \in A $ that is larger than exactly $ i-1 $ other elements of $A$. The authors discuss that finding minimum and maximum from a set of $n$ element requires $n-1$ comparisons. The authors also prove that simultaneous finding of maximum and minimum can be done in at most $ 3 \times \lfloor \frac{n}{2} \rfloor $ comparisons. The authors then provide a randomized algorithm to find $ i^{th} $ order statistic using the quick-sort randomized partition algorithm. The authors also prove that the algorithm's average running time is $ O(n) $. The authors defined dynamic sets as the sets which change when they are manipulated by algorithms. The authors then define two kinds of operations on dynamic sets, queries that return information about the set and modifications which change the set as follows:

1. SEARCH
2. INSERT
3. DELETE
4. MINIMUM
5. MAXIMUM
6. SUCCESSOR
7. PREDECESSOR