Nam Hung Tran Nguyen

1. The number of PhD/Graduate students at some US universities    Many US universities indicated all of their graduate students on their websites. For example, the following image shows the list of graduate students in mathematics at Harvard University.     Based on these lists, I just counted the number of graduate students at some universities and got the following result(s): MIT has 122 students, Cornell University has 80 students, Texas A&M University has 105 students, Stanford University has 65 students, Harvard University has 64 students, Yale University has 46 students, University of Utah has 90 students, The University of Chicago has 81 students, City University of New York has 76 students and University of California, Berkeley (UCB) has 175 students.  2. The number of PhD/Graduate students from several universities who later became speakers at International Congress of Mathematicians    Being invited at International Congress of Mathe...

As you may have known before, graphs and other related structures (e.g. trees, binary trees, etc.) help us to construct effective methods to store and search for data. In fact, linked list and its variations can also be viewed graph-theoretically.  1. Directed graph A directed graph is an ordered pair G = (V, A), where V is the vertex set and A is a family of ordered pairs of elements from V. In a directed graph, adjacency is not symmetric or mutual. For example, in the following directed graph, 1 is adjacent to 2 but 2 is not adjacent to 1.  2. Linked list and the associated directed graph A linked list is a list of objects constructed as follows: starting from an object, called the head , we continuingly insert the succeeding objects until we reach the final object, called the tail . In this list, an object is linked to its succeeding object. More clearly, this list consists of n objects, namely o(1), o(2), ..., o(n) such that for each i = 1, 2, ..., n - 1, o(i) is linked t...