Journal of Statistics and Mathematical Sciences an International journal publishing biannually Online on the aspect of Statistics and Mathematical Sciences for an effective scientific reading and public view with an aim to reach the world wide researchers. It is also the study of quantity, space, change and structure. Statistics is a branch of applied mathematics dealing with comprehension, analysis, assimilation and collection of data. Modern mathematics is dealing with algebraic geometry in association with complex analysis, topology and number theory.
These ideas could also be used as the basis of a senior thesis to earn Latin Honors. These suggestions may spark some other idea that interests you.
They also give you an idea about what areas interest some of our faculty. Among the ideas posted here, some are harder and some easier. In some cases, there may be an easier version special cases of a problem that is more accessible.
If one of the areas sounds interesting to you, contact the faculty member to discuss the topic and your background in more depth. You can also feel free to contact other faculty, or to propose other ideas with individual faculty members.
This list is not meant to be limiting in relation to topics or faculty member. You can also contact Dr. Blake Thornton for suggestions about faculty to talk with. Professor Renato Feres Geometry Some of following problems are meant to introduce you to advanced but well-established topics in graduate level math, others are much more open ended and may lead to original results.
Some are more "theoretical" while others invite you to do some computer exploration. A few are probably pie-in-the-sky problems that, to me at least, are amusing to contemplate.
Now roll the stone over the plane of the table so that at all times the point of contact lies on the curve, being careful not to allow the stone to slip or twist. We may equally well think that we are rolling the plane of the table over the surface of the stone along the given curve.
Mechanical systems with this type of motion are said to have "non-holonomic" constraints, and are common fare in mechanics textbooks. Now imagine a tangent vector to the plane at p.
This rolling of the plane over the surface provides a way to transport v along the curve, keeping it tangent at all times. The resulting vector field over the curve is said to be a "parallel" vector field. Show that there is a unique way to carry out this parallel translation.
Find a differential equation that describes the parallel vector field and use some appropriate existence and uniqueness theorem.
Let c be a short path joining p and q, whose velocity vector field is parallel. Show that c is the shortest path contained in the surface that joins p and q. Whether or not you fully succeed, this mechanical idea will give you a concrete way of thinking about ideas in differential geometry that might seem a bit abstract at first, such as Levi-Civita connection, parallel translation, geodesics, etc.
Also look for an engineering text on Robotic manipulators and explain why such non-holonomic mechanical systems are important in that area of engineering. In the engineering literature, A Mathematical Introduction to Robotic Manipulation is a particularly good reference.
Convex geometry Geometry in very high dimensions is full of surprises. Consider the following easy exercise as a warm-up.
Let B n,r represent the ball of radius r, centered at the origin, in Euclidian n-space. Here is a much more surprising fact that you might like to think about. Let S n-1 denote the sphere of radius 1 in dimension n.
It is the boundary of B n,1. Let f be a continuous function from S n-1 into the real line that does not increase distances, that is, f p - f q is not bigger than p - q for any two points p and q on the sphere.Aug 15, · Geometry Geometry Sites at U Tennessee Knoxsvile (Knoxsville, TN USA) [from which many items below were taken] The Center for Geometry, Analysis, Numerics, and Graphics (GANG) at U Massachusetts, Amherst (Amherst, MA USA) An interdisciplinary differential geometry research team which publishes its Preprints and plombier-nemours.com GANG Geometry Archive contains a Gallery of .
Differential Geometry and its Applications | Citations: | This journal publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in.
Below is a selection of some of my most significant research papers (the choice is of course subjective). All the rest of my papers can be found in my publication plombier-nemours.com you can also find electronic links to the journals in which these papers have been published.
Wild Egg is a mathematics education company focused on online mathematics education through a high quality book on rational trigonometry and screenshot pdfs for YouTube videos.
The Wild Egg team is N J Wildberger and Krista Ruffolo. Lindenmayer Systems, Fractals, and Plants originated as notes for the SIGRAPH course Fractals: Introduction, basics, and applications.
They were published, with minor editorial changes, as a book by Springer-Verlag, New York, in , and reprinted in Biostatistics.
Biostatistics is the branch of statistics responsible for the proper interpretation of scientific data generated in the biology, public health and other health sciences. It seeks to distinguish between correlation and causation, and to make valid inferences from known samples about the populations from which they were drawn.