## Mathematics Thesis Coordinator:

**49. The Erlangen Program**

From the time that Euclid set down his axioms of geometry in the Elements in about 300 B.C. till the middle of the 19th century, mathematicians studied geometry in a so-called synthetic way, based on drawing conclusions from the given axioms. In the late 19th century, geometry was revolutionized by the realization that if Euclid's fifth axiom, the parallel postulate, was dropped, there were a number of alternate geometries that satisfied the first four axioms but that displayed behavior quite different from traditional Euclidean geometry. These geometries are called non-Euclidean geometries, and include projective, hyperbolic, and spherical geometries. As the theory of these geometries began to develop, one of the great mathematicians of the day, Felix Klein, proposed his Erlangen Program, a new method for studying and characterizing these geometries based on group theory and symmetries. A thesis in this area would study the various geometries, and the groups of transformations that define them.

Reference:

David Gans, Transformations and Geometries.

For further information, see Emily Proctor.
Do you struggle with a Master’s or PhD thesis in Math? Do you need a good plan to start writing? Well, in this article you will find helpful information on how to get ready for writing a Master’s **Mathematics thesis**.

Step # 1

First, you should choose a topic for your mathematical thesis. This is how you can do it:

The easiest way to see a sample Math thesis or essay is to ask Lee -she has recent ones available in her office. TheMath library has a collection of old Math theses, but only up to 1991.

## Is a Mathematics thesis difficult to cope with

I joined the faculty of TAMUCT in 2009. My math Ph.D. is from the University of Wisconsin/Madison under David Griffeath (1985) and my physics Ph.D. is from the University of Kentucky/Lexington under Keh-Fei Liu (1997). My math thesis focused on properties of one type of composition operator that has applications both to statistical mechanics and discrete dynamical systems. My physics thesis focused on the computation of properties of quantum fields using random methods applied to huge matrices.