|On the Reconstruction Conjecture
||"Every graph of order three or more is reconstructible." Frank Harary restated one of the most famous unsolved problems in graph theory. In the early 1900's, while one was working on his doctoral dissertation, two mathematicians made a conjecture abo...
|On the Quadratic Sieve
||Factoring large integers has long been a subject that has interested mathematicians. And although this interest has been recently increased because of the large usage of cryptography, the thought of factoring integers that are hundreds of digits in l...
|Reducible Configurations and So On: The Final Years of the Four Color Theorem
||The Four Color Theorem is in a set of mathematical questions that are very simple to state but amazingly complex to answer. It goes as follows, "given any map, are any more than 4 colors required to color the map in such a way that no two areas which...
|On the Hausdorff Dimension of the Boundary of a Self-Similar Tile
||In our everyday experiences, we have developed a concept of dimension, neatly expressed as integers, i.e. a point, line, square and cube as 0-, 1-, 2-, and 3-dimensional, respectively. Less intuitive are dimensions of sets such as the Koch Curve and ...
|Elliptic curves and factoring.
||The Elliptic Curve Method (ECM) is a powerful and widely used algorithm for factorization which can be implemented with several different forms of elliptic curves. We will give some general background on the theory of elliptic curves and the ideas be...