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Development Of Cfl-Free, Explicit Schemes For Multidimensional Advection-Reaction Equations, Hong Wang, Jiangguo Liu

Faculty Publications

We combine an Eulerian–Lagrangian approach and multiresolution analysis to develop unconditionally stable, explicit, multilevel methods for multidimensional linear hyperbolic equations. The derived schemes generate accurate numerical solutions even if large time steps are used. Furthermore, these schemes have the capability of carrying out adaptive compression without introducing mass balance error. Computational results are presented to show the strong potential of the numerical methods developed.

Chords Of Longest Circuits Of Graphs, Xuechao Li

Graduate Theses, Dissertations, and Problem Reports

This thesis is on a long standing open conjecture proposed by one of the most prominent mathematicians, Dr. C. Thomassen: Every longest circuit of 3-connected graph has a chord. In 1987, C. Q. Zhang proved that every longest circuit of a 3-connected planar graph G has a chord if G is cubic or if the minimum degree is at least 4. In 1997, Carsten Thomassen proved that every longest circuit of 3-connected cubic graph has a chord.;In this dissertation, we prove the following three independent partial results: (1) Every longest circuit of a 3-connected graph embedded in a projective plane …

An Analysis Of The Academic Success Achieved By Five Freshman Cohorts Through A Community College Developmental Education Program., Nancy K. Gray-Barnett

Electronic Theses and Dissertations

The challenge of underprepared students' entering America's colleges and universities is not new. Because of their "open door" policies, community colleges are more likely to enroll students who are not college prepared. This retrospective study focused on the performance of students who had completed required developmental education courses compared to the performance of students without developmental requirements. The study examined developmental education success measures for five cohorts of first-time degree-seeking freshmen each tracked for a six-year period enrolled at Walters State Community College located in Tennessee.

The success measures compared included grade point averages earned in college-level mathematics and English …

Helping At-Risk Students Add Up: Motivational Lessons For Students In High School Mathematics, Karen Beckner

Mahurin Honors College Capstone Experience/Thesis Projects

No abstract provided.

What We Can Learn From Timss: Comparison Of Australian And Russian Timss-R Results In Algebra, Alla Routitsky, Susan Zammit

Dr Alla Routitsky

No abstract provided.

Literary Evidence For Roman Arithmetic With Fractions, David W. Maher, John F. Makowski

Classical Studies: Faculty Publications and Other Works

No abstract provided.

Affinity Learning In Mathematics, Arthur I. Zygielbaum, Neal Grandgenett

Teacher Education Faculty Proceedings & Presentations

Teaching complex subjects such as mathematical modeling is intrinsically challenging. It is more so in a typical classroom setting. In this paper, we explore the use of technology to provide an electronic tutor that interacts with both teacher and student to provide a personalized and focused learning experience. Affinity Learning is an environment that captures the skills of a master teacher in a dynamic but simple technical embodiment and presents lessons and assessments online to a student. Initial results not only indicate that learning has occurred, but also distinguish male from female performance and give interesting insight into the learning …

Math Major, Math Major, Arthur T. Benjamin

All HMC Faculty Publications and Research

Sung to the tune of "Matchmaker" from Fiddler on the Roof:

Math major, math major, make me some math.

Find me a prime, sketch me a path.

Math major, math major look through your books,

And make me some perfect math.

Dynamic Coloring Of Graphs, Bruce Montgomery

Graduate Theses, Dissertations, and Problem Reports

In this dissertation, we introduce and study the idea of a dynamic coloring of a graph, a coloring in which any multiple-degree vertex of the graph must be adjacent to at least two color classes.;As parts of the overall research, we study (for some interesting subjects of colorings) the corresponding subjects of dynamic colorings, we compare the chromatic number and dynamic chromatic number, and we study some problems unique to dynamic colorings. Also, we introduce and briefly study a generalization of dynamic coloring.;The interesting subjects of colorings we consider are the chromatic number of important graphs, upper bounds of the …

Set-Theoretic And Algebraic Properties Of Certain Families Of Real Functions, Krzysztof Plotka

Graduate Theses, Dissertations, and Problem Reports

Given two families of real functions F1 and F2 we consider the following question: can every real function f be represented as f = f 1 + f2, where f1 and f2 belong to F1 and F2 , respectively? This question leads to the definition of the cardinal function Add: Add( F1,F2 ) is the smallest cardinality of a family F of functions for which there is no function g in F1 such that g + F is contained in F2 . This work is devoted entirely to the study of the function Add for different pairs of families of …

How Many Blocks To The Empire State Building? : An Original Story, Enakshi Bose

Graduate Student Independent Studies

Presents a children's story for eight and nine year old children that poses several mathematical questions, including the central one of how many blocks it is from the 215th Street subway station in Inwood to the Empire State Building. Photographs and maps enhance the mathematical concepts involved. Discusses the developmental appropriateness of the book's content and how the material meets various standards in mathematics.

Abstracts Of Papers, 79th Annual Meeting Of The Virginia Academy Of Science, May 22-25, 2001, James Madison University, Harrisonburg, Virginia

Virginia Journal of Science

Abstracts of papers that were presented at the 79th Annual Meeting of the Virginia Academy of Science, May 22-25, 2001, James Madison University, Harrisonburg, Virginia.

Approximating Eigenvalues For Double Well Potentials., Chad Fulk

Student Work

One dimensional double well potentials usually refer to those potentials which have two equivalent or non-equivalent minima. They have been used to model diverse systems ranging from the electronic structure of diatomic molecules to electron-lattice coupling in high temperature superconductors [1][2]. However, one difficulty to the utility of these models is that exact analytical solutions for almost all double well potentials have not been found, in spite of the fact that this type of potential is constantly utilized as an illustra­tive example in the literature. Despite intensive research into this problem, only a few types of double wells have been …

Geometry In Action: A Curriculum Unit Utilizing Dynamic Geometry Software To Enhance Students’ Comprehension, Cynthia A. Mignini

Critical and Creative Thinking Capstones Collection

The paper identifies two critical obstacles to student success in a traditional geometry classroom and examines the role dynamic geometry software can play in overcoming these obstacles.

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

Mathematical Constance (A Poem Dedicated To Constance Reid), Arthur T. Benjamin

All HMC Faculty Publications and Research

Mathematical Constance (A Poem Dedicated to Constance Reid)

I think that I shall never see

A constant lovelier than e,

Whose digits are too great too state,

They're 2.71828…

And e has such amazing features

It's loved by all (but mostly teachers).

With all of e's great properties

Most integrals are done with … ease.

Theorems are proved by fools like me

But only Euler could make an e.

I suppose, though, if I had to try

To choose another constant, I

Might offer i or phi or pi.

But none of those would satisfy.

Of all the …

There Really Are No Contradictions: A Response, Calvin Jongsma

Faculty Work Comprehensive List

Response to "There are no Contradictions" by T.G. Ammon in The College Mathematics Journal, Vol. 31, No. 1 (Jan., 2000), pp. 48-49 which was part of the "Fallacies, Flaws, and Flimflam" column edited by Ed Barbeau of the Department of Mathematics at the University of Toronto.

Mathematics Achievement In Tennessee Schools In The Context Of Opportunity To Learn., Richard Lee Kitzmiller

Electronic Theses and Dissertations

This study examines the relationship of student achievement in mathematics and factors purported to influence such achievement. The factors utilized in the study were selected from those contained in accountability reports issued by the state of Tennessee in 1995-96. The student achievement measures were based on four high school end-of-course mathematics tests. Student performance on these tests is examined both in terms of actual scores and value-added measures. This study organizes the available accountability measures in an Opportunity-to-Learn (OTL) framework for the purpose of determining relationships that can inform practice and give policy guidance.

The study examined 65 (of 139) …

Incorporating Technology In Mathematics Education: A Suite Of E-Activities For The Modem Mathematics Classroom, Jennifer E. Youngberg

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

National studies indicate major deficiencies in students' understanding of mathematics. Research suggests that students tend to view mathematics as a set of computational rules rather than a process of discovery and a tool for problem-solving. Most students fail to grasp the concepts behind the computations.

Technology provides a partial solution to this problem. Over the past decade, computers have emerged as a powerful tool in education. Computers place the control of action in the learning process with the student. They allow students to experiment with, explore, and discover mathematics at their own pace. With computers, students can consider more examples …

Some Problem In Homogenization., M. Rajesh Dr.

Doctoral Theses

No abstract provided.

Abstracting Aristotle’S Philosophy Of Mathematics, John J. Cleary

Research Resources

In the history of science perhaps the most influential Aristotelian division was that

between mathematics and physics. From our modern perspective this seems like an unfortunate deviation from the Platonic unification of the two disciplines, which guided Kepler and Galileo towards the modern scientific revolution. By contrast, Aristotle’s sharp distinction between the disciplines seems to have led to a barren scholasticism in physics, together with an arid instrumentalism in Ptolemaic astronomy. On the positive side, however, astronomy was liberated from commonsense realism for the conceptual experiments of Aristarchus of Samos, whose heliocentric hypothesis was not adopted by later astronomers because …

Analysis Of The Change In Math Placement Test Instruments, Sharon Schmidtz, Carl Simpson

Office of Institutional Effectiveness

In May of 2000 a new Math Placement Test (MPT) instrument was put into use and new cut-off scores inplemented. This report analyses the effectiveness of this change.

Stochastic Comparision And Dependence Among Order Statistics,Spacing And Concomitants Of Order Statistics., Baha-Eldin Khaledi Dr.

Doctoral Theses

The simplest and the most common way of comparing two random variables is through their means and variances. It may happen that in some cases the median of X is larger than the median of Y, while the mean of X is smaller than the mean of Y. However, this confusion will not arise if the random variables are stochastically ordered. Similarly, the same may happen if one would like to compare the variability of X with that of Y based only on numerical measures of variability. Besides, these characteristics of distributions might not exist in some cases. In most …

Mapping Quantitative Trait Loci In Humans: Some Statistical Contributions., Saurabh Ghosh Dr.

Doctoral Theses

Maty qualitative tralts - such an, milk yield la cows, blood pressure in lumans --are known to be determined primarly, though zot exclusively, by inherited genetic luctora. It ls the of coasklerable impartance to identify chromosontal locations of tho genes that control a quantitative character. Linkage analysis (Ou 1990), which deals with the deduction of linkagn and estimation of recombination fractions among the loci controlling a qualitative/quantitative character and major loci wkoo poertions are knows aprfori, is widely used for localisation of gens. Although statistical methodologies for magplag gemen determining dichotomos qualitative charactes in humans aro well-developed, the demicrant of …

Boolean Functions With Important Cryptographic Properties., Subhamoy Maitra Dr.

Doctoral Theses

In this thesis we concentrate on properties of cryptographically significant Boolean functions.The techniques are mainly combinstorial and provide new resulta on enumeration and construction of such functions. Initially we concentrate on a partieular subset of Boolean functions called the symmetric Boolean functions. A closed form expression for the Walsh transform of an arbitrary symmetric Boolean function is presented. We completely characterize the symmetric functions with maximum nonlinearity and show that the maximum nonlinearity of n-variable symmetrie function can be 2n-1-2[n-1l2], Moreover, new classes of symmetric balanced and symmetric correlation immune functions are considered.We provide a randomised heuristic to construct balanced …

Contributions To Random Interactions And Dynamical Systems., Santanu Chakraborty Dr.

Doctoral Theses

In recent years random iterations of maps on Polish spaces has gained prominence. They are. nice examples of Markov processes whose invariant measures can be used in Computer imaging (see Berger ( 1). They also arise as random perturabations of deterministic dynamical systems.Let S be a Polish space with its Borel a-field. Let r be a collection of Borel maps from S to S. Let P be a probability on r. Then starting with a point z in S, we choose a map yn er according to the law P and move to ya(x). Then we choose 2 € r …

Conjunction And Aggregation, Saul Levmore

Michigan Law Review

This Article begins with the puzzle of why the law avoids the issue of conjunctive probability. Mathematically inclined observers might, for example, employ the "product rule," multiplying the probabilities associated with several events or requirements in order to assess a combined likelihood, but judges and lawyers seem otherwise inclined. Courts and statutes might be explicit about the manner in which multiple requirements should be combined, but they are not. Thus, it is often unclear whether a factfinder should assess if condition A was more likely than not to be present - and then go on to see whether condition B …

Topological Conjugacy And Rigidity Of Affine Actions., Siddhartha Bhattacharya Dr.

Doctoral Theses

The main theme of this thesis is topological classiication of aline Hows on homogeneous spaces and rigidity of equivariant continuous maps between such dows. Both these aspects have been extensively studied in the literature for subgroup actions (cf. [Be), [B-Dj and [Wi) and for automorphism flows of the cyclic group (cf. [Ar]. [K-R] and [C-S). We will consider similar questions in more general situations. A detailed outline is given below. For a topological group T, by a r-flow we mean pair (X,p), where X is a opological space and p is a continuous action of I on X. For any …

Routing Algorithms For Channels, Switchboxes And Mcm's In Vlsi Layout Design., Sandip Das Dr.

Doctoral Theses

The term Very Large Scale Integration (VLSI) reflects the capability of semi- conductor industry to fabricate a complex electronic circuit consisting of millions of components on a single silicon substrate. The growth of semiconductor technol- ogy in recent years has been described by "Moore's law", enunciated in the late 1960s, which projected quadrupling of components in a chip in every three to four years. Several factors contributed to this tremendous growth : (i) reduction of line width of the basic device and interconnection wires due to the development of high- resolution lithographic techniques and improved processing capabilities, (ii) increase in …

An Ellam Scheme For Multidimensional Advection-Reaction Equations And Its Optimal-Order Error Estimate, Hong Wang, Xiquan Shi, Richard E. Ewing

Faculty Publications

We present an Eulerian-Lagrangian localized adjoint method (ELLAM) scheme for initial-boundary value problems for advection-reaction partial differential equations in multiple space dimensions. The derived numerical scheme is not subject to the Courant-Friedrichs-Lewy condition and generates accurate numerical solutions even if large time steps are used. Moreover, the scheme naturally incorporates boundary conditions into its formulation without any artificial outflow boundary conditions needed, and it conserves mass. An optimal-order error estimate is proved for the scheme. Numerical experiments are performed to verify the theoretical estimate.