6) Let p in U that pass through p have the same length. It is known that a convex planar U can have at most one equichordal point.
But the proof is very abstract and extremely difficult Scholars enrolled in the bachelor's, master's and Ph.D. degree level programmes of Mathematics, and having Calculus as one of their subjects can take our Calculus assignment help for completing their dissertation, coursework, homework, thesis, reports, etc., on the concepts related to Calculus. Also, you can choose from .
Problem 2: What is true in dimension three? Problem 3: What is true for non-convex domains?1) The Berry-Esseen Theorem. It is still of current interest to determine the maximal error of the asymptotic normal approximation to the scaled sample mean as specified by a central limit theorem.
Recent results related to the bound in the Berry-Esseen theorem, for summands of both i. and non-identically distributed observations, are to due Shevtsova (2010, 2011).
This project would involve studying the methods used to obtain such bounds and investigating the accuracy using simulated data. 2) Post-Selection Inference for Linear Regression.
Inferential correctness for testing hypotheses about regression coefficients after a variable selection procedure has been utilized requires a careful evaluation of the effects of the selection procedure on the final inference. This project involves studying, in real-data examples, how classical inference procedures are invalidated by the use of selection procedures.
The performance of inference procedures designed to control, respectively, selective type I error and familywise error rates (FWER) will be compared in theory and practice. Inference in curved exponential families, following a principled approach, requires construction of exact or approximate ancillary statistics. Examples include the gamma hyperbola model, the bivariate normal correlation model, and ARMA(p,q) models used in time series analysis.
This project involves motivating a principled, accurate approach to inference in such models, and real-data comparisons with conventional inference procedures which do not respect such statistical principles. 4) The double bootstrap and the warp-speed double bootstrap.
The double bootstrap was proposed as a technique to improve the coverage accuracy of confidence intervals constructed via conventional single-bootstrap methods This workshop will introduce basic principles of writing proposals across a range of writing. 2. To help you understand the rhetorical situation of the thesis proposal and common elements of such proposals. 3. To introduce practical rhetorical The Introduction: Creating a Research Space / Defining Your Contribution..
The warp-speed double-bootstrap attempts to achieve this using a single double-bootstrap sample for each bootstrap sample, drastically reducing the computational costs.
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This project investigates the source of this discrepancy using large-scale simulations in different model settings of practical interest. 1) If a1,a2, are integers with gcd = 1, then the Eulidean algorithm implies that there exists a (n x n)-matrix A with integer entries, with first row = (a1,a2,.
Serre for polynomial rings over a field, with the a's being polynomials in several variables.
This fundamental question generated an enormous amount of mathematics (giving birth to some new fields) and was finally settled almost simultaneously by D. Now, there are fairly elementary proofs of this which require only some knowledge of polynomials and a good background in linear algebra. This could be an excellent project for someone who wants to learn some important and interesting mathematics.
(These results seem to be of great interest to people working in control theory. Though I am not an expert, I'm willing to learn with a motivated student. )2) A basic question in number theory and theoretical computer science is to find a "nice" algorithm to decide whether a given number is prime or not.
This has important applications in secure transmissions over the internet and techniques like RSA cryptosystems.
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All the methods availabe so far has been known to take exponential time Calculus assignment help casinodelille com Best college admission essay myers mcginty Writing dissertation WBUR Buy college essay th grade Essay writing. When you are applying for a job a cover letter is usually expected to accompany your resume Writing one can seem like a huge task and figuring out what .
There are probabilistic methods to determine whether a number is prime, which take only polynomial time.
The drawback is that there is a small chance of error in these methods. So, computer scientists have been trying for the last decade to find a deterministic algorithm which works in polynomial time.
Recently, this has been achieved by three scientists from IIT, Kanpur, India. A copy of their article can be downloaded from A nice project would be to understand their arguments (which are very elementary and uses only a little bit of algebra and number theory) and maybe to do a project on the history of the problem and its ramifications.
1) DNA methylation DNA methylation in vertebrates typically occurs at CpG sites and results in the conversion of the cytosine to 5-methylcytosine. Human DNA has about 80%-90% of CpG sites methylated.
Methylation is important to embryonic development and cancer. With the current next-generation sequencing (NGS) technology, people identify regions with different methylation levels under different disease status to understand the mechanism of cancer and other disorders.
NGS data from methylation experiments process complicated strictures and impose challenges to statisticians. We are developing statistical tools for theanalysis of NGS data from such experiments.
2) Statistical analysis for anesthesiology data Anesthesiology is a very important part of surgery and many other medical practice. Anesthesiologists are still in debate about proper ways to monitor patients' anesthetic status.
A recent publication on the New England Journal of Medicine (vol 365, pages 591-600) suggest that a device approved by the Food and Drug Administration (FDA) to reduce the risk that patients will recall their surgery does not lower the risk of the problem, known as intraoperative awareness, any more than a less expensive method. Statistical analysis will help to find better ways of anesthetic practice. 3) Statistical analysis for spatial cognition It is intriguing to understand how people construct the memorized maps after seeing a real map.
Statistical tools are crucial to understanding the transformation from the reality to the map in people's memory.
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1) Fluid Dynamics Consider a cylindrical tube, open at one end Help writing calculus dissertation proposal. Help writing dissertation proposal nativeagle com Custom Essay Writing Service Fresh Essays. Assistance for research proposal. Computer science dissertation example Online Multivariable Calculus Homework Help Services Essay Help Essay Basics multivariable calculus. Key .
At the closed end, a small quantity of gas is injected.
It diffuses out the other end at a predictable rate. Now, suppose the quantity of gas injected is increased.
The flow will not scale linearly, as the effect of the pressure of the introduced gas must be considered. I have a project with Professor Gregory Yablonksky in the Chemical Engineering department to model this flow.
2) Linear Matrix Inequalities A computer vision problem posed by Professor Robert Pless in the Computer Science Department. Imagine a large number of cameras arranged around a central object.
One wants to match up the pictures, but there is some error in the measurement. Mathematically, the problem becomes approximating a large symmetric matrix by a rank 3 matrix that has 1's on the diagonal.
It ties in to an active research area in systems theory: solving a linear matrix inequality with a rank constraint. 3) Applied Statistics/Public Health The "French paradox" is the claim that, despite having a high fat diet, French people have a low rate of heart disease. I believe this is a statistical artifact, due principally to cultural differences in filling out death certificates.
I would be willing to supervise an undergraduate who wished to hunt down the data and analyze it. 4) Galapagos Tortoises My friend Stephen Blake has collected movement data on Galapagos Tortoises for two years. We would like to understand more about the tortoises's movement, for example what makes them migrate, how are they influenced by climate changes, why smaller tortoises don't migrate, how they choose routes, etc.
For more information about the tortoises, see Anne the Tortoise1) Computation in topological combinatorics Topological combinatorics includes the study of simplicial complexes (that is, geometric objects built from possibly higher dimensional analogues of the unit interval, the equilateral triangle and the equilateral tetrahedron) whose faces are indexed by combinatorial objects such as graphs Thesis Writing Services. research proposal dissertation. essay-writer.org. do my descriptive writing for high school students. how to write essay. blog writing services uk. high school help. research writing service. legit essay writing companies. buy college paper online. where can i find someone to write essays for me..
Welker has been used to investigate the structure of such complexes.
There are many adjustments and additions which could be made to improve the program, the most ambitious of which is to make it amenable to parallel processing. 2) Order complexes of subgroup lattices The set of subgroups of a group G is partially ordered by inclusion.
There are interesting open questions and proven theorems about relating the algebraic structure of G to the combinatorial structure of this partially ordered set. For any partially ordered set P, the set of all totally ordered subsets of P determines a simplicial complex.
The topological structure of this complex is related to the combinatorial structure of P. One can hope to use this relationship productively when P is the set of subgroups of G.
This area is appropriate for both reseach and expository projects. 3) Symmetric functions A symmetric function is a power series of bounded degree in infinitely many variables which is not changed by any permutation of the variables.
Symmetric functions appear in many areas of mathematics, including combinatorics and representation theory (which involves studying a group G by understanding homomorphisms from G to various matrix groups). There are lots of interesting open combinatorial problems involving symmetric functions (many appear in the exercises after Chapter 7 of R. Stanley's book, Enumerative Combinatorics, Volume 2).
This area is also appropriate for expository projects The aim is not only to aid in the development of a well written paper, but also to help students begin to think about mathematical writing. I am greatly indebted to a wonderful booklet, How to Write Mathematics, which provided much of the substance of this essay. I will reference many direct quotations, especially from the .
1) Learn about propensity analysis as a means of establishing causality and write your thesis using real data (which I can supply). 2) Learn about zero-inflated and double-hurdle models, and apply them to real data.
(Both deal with the idea that certain variables predict whether a response is necessarily zero, and if the response is not necessarily zero, then other variables might predict its value. ) A student worked on this last year, but you can extend what he did.
The classic example is electro- convulsive therapy for depression.
The machine typically has about five fixed charge levels (in Coulombs), and the charge is stepped up until the patient has a seizure. We thus know coarse lower and upper bounds on the seizure threshold, and the task is to estimate the exact seizure threshold.
4) Learn about GIS and write an application that maps pollution, river flows, drought, etc. SAS has a GIS application, but we also have special-purpose software on the public machines in Eads.
5) Learn about analysis of complex survey data (stratification, clusters, and weight) and analyze a real data set. Most large public-access data sets have this complex structure.
This was covered in a course - Math 438 I think - but that was so long ago it's not listed in the catalog. There are, in fact, two forms of complex data, the "classic" form in which each stratum has exactly two clusters, and the "certainty PSU" form.
6) Learn about census data, and how census info can be merged by tract with special-purpose data. I have a friend who has some pathological gambling data, who has extracted most of the obvious results from her data, but might be looking for help in digging out some remaining gems. 7) Learn about the relationship between the jackknife and the bootstrap, and be able to illustrate what Bradley Efron meant when he said: "What actually happened was that Rupert Miller in our department was working on the jackknife.
He had written a paper called the "Trustworthy Jackknife" in which he tried to figure out when the jackknife method gave dependable variance estimates.
It worked, but nobody could figure out why it worked You can also feel free to contact other faculty, or to propose other ideas with individual faculty members. You might suggest ideas for In working out examples, the latter boils down to some surprisingly entertaining 3-dimensional linear algebra which ultimately tells you how to draw a triangulation. Mirror symmetry comes .
What I thought was that the jackknife must be a differential, local kind of approximation for something else. And so when I started looking for the something else I came up with the bootstrap.
In calculus, we learn that there are curves that do not have tangent lines.
In this project, we will study geometry of singular spaces which are generalizations of singular curves.
One class of such singular spaces that are interesting to us is called orbifold. It is an important object in both mathematics and physics.
We will mainly focus on orbifolds and compute some useful invariants about them. In mathematics, the shape of a donut is called torus. Noncommutative torus is the quantization of the usual torus, and appears naturally in both mathematics and physics.
We will study some interesting applications of noncommutative tori in physics. 3) Can you comb the hair on a coconut? The answer is ``no". There is an interesting mathematics theory related to this answer, which is called index theory.
We will apply index theory to study some interesting properties on geometric spaces.
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Then implement the Euclidean algorithm for Laurent polynomials described in the paper.
(Thus, you will use ideas in abstract algebra and Fourier analysis to write an efficient computer program that is part of the JPEG-2000 image compression algorithm. 67-101) of my book "Adapted Wavelet Analysis," and also Strang, "The Discrete Cosine Transform" (SIAM Review 41:1(1999),135-147). Synthesize a proof that the discrete Hartley transform is orthogonal.
(Thus, you will see how the Sturm-Liouville theorem from differential equations can save many tedious computations in the verification that a basis, such as one used in the JPEG (1990) image compression algorithm, is orthonormal.
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