These positions are part of an exciting university wide initiative to further our status as one of the very best research universities in the nation. Last year the university hired approximately new faculty and will add a similar number this year to enhance teaching and research. The successful candidate will join a vibrant research department with representation across a full range of pure and applied mathematics. These non-tenure-track renewable positions can begin as early as January,

The list is by no means exhaustive. If you a potential advisor in mind, that person may well have other ideas. Or you may even have your own idea for a project. We encourage this route as well, but please be aware that this will put some additional responsibility on you to identify sources.

For further information, see Bruce Peterson. The Four Color Theorem For many years, perhaps the most famous unsolved problem in mathematics asked whether every possible map on the surface of a sphere could be colored in such a way that any two adjacent countries were distinguishable using only four colors.

It is easy to produce maps requiring at least four colors, but the proof that four colors are always sufficient did not appear until Topics for a thesis would include the history of the problem, including the mistakes made in early "proofs", extension of the problem to more complicated surfaces what for instance happens if the maps are drawn on the surface of an inner tube?

The proof itself marks a milestone in mathematics in that it is readily understandable, but impossible to check because it involves computer verification of an enormous number of special cases.

That is, anyone can check any individual step, but no one can check them all. The thesis would not involve computer work. For additional information, see Bruce Peterson.

Additive Number Theory We know a good deal about the multiplicative properties of the integers -- for example, every integer has a unique prime decomposition. For instance, in how many ways can we write an integer as the sum of two squares?

How many ways can we write the number 1 as the sum of three cubes? This theorem has recently been proved by Andrew Wiles of Princeton University. Mersenne Primes and Perfect Numbers Numbers like 6 and 28 were called perfect by Greek mathematicians and numerologists since they are equal to the sum of their proper divisors e.

Since then about B. There still remain many open questions, for example, do there exist any odd perfect numbers? Research could include some interesting computer work if desired. Recent results indicate that any "reasonable" voting procedure must either be dictatorial or subject to strategic manipulation.

For further information, see Mike Olinick. How does one fit this model to real data? How are the Lotka-Volterra models of competition and predation affected by the assumption that one species grows logistically in the absence of the other?

A typical problem in this field would ask how to maximize the present value of discounted net economic revenue associated with the hunting and capture of whales. How does an optimal strategy vary with the number of competing whaling fleets?

Brouwer proved that every continuous function from a n-cell to itself has at least one fixed point; that is, if f: There has also been much progress on the problem of computationally determining fixed points.

Joel Franklin, Methods of Mathematical Economics.Columbia Engineering researchers have built a Kerr frequency comb generator that, for the first time, integrates the laser together with the microresonator, significantly shrinking .

Lone Star College System Research Forest Drive, The Woodlands, TX - MAPS | HELP | JOBS | ACHIEVING THE DREAM | EMPLOYEE INTRANET. How to Write a PhD Thesis. How to write a thesis? This guide gives simple and practical advice on the problems of getting started, getting organised, dividing the huge task into less formidable pieces and working on those pieces.

Mathematics is at the heart of many of today’s advancements in science and technology and is contributing to progress in other fields such as industrial and architectural design, economics, biology, linguistics, data science, and psychology.

Available in PDF format (linked below) and in hard copy from the Mathematics Library (through , more recent ones available soon). For more information, see Senior Thesis Guidelines. The Euler Archive is an online resource for Leonhard Euler's original works and modern Euler scholarship.

This dynamic library and database provides access to original publications, and references to available translations and current research.

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