Physical Sciences and Mathematics Commons^™

Nonparametric Methods For Data In Infinite Dimensional Space., Anirvan Chakraborty Dr.

Doctoral Theses

For univariate as well as finite dimensional multivariate data, there is an extensive literature on nonparametric statistical methods. One of the reasons for the popularity of nonparametric methods is that it is often difficult to justify the assumptions (e.g., Gaussian distribution of the data) made in the models used in parametric methods. Nonparametric procedures use more flexible models, which involve less assumptions. So, they are more robust against possible departures from the model assumptions, and are applicable to a wide variety of data. Nonparametric methods outperform their parametric competitors in many situations, where the assumptions required for the parametric methods …

2015: "Go With The Flow", Paul Nebres '16, Kushagra Gupta '16, Jason Chen '16, Noor Michael '16

Distinguished Student Work

In a famous incident in August 2010, a Chinese traffic jam stretched for over 100 kilometers and stranded drivers took over two weeks to get from one side to the other. Stemming from a routine lane closure for road maintenance, the traffic jam soon spiraled out of control, as cars piling up at the jam greatly outnumbered those leaving the other end. Sadly, in todays overpopulated world, these sorts of nightmare scenarios are only becoming more and more common, from chronic traffic jams in congested Chinese cities to Carmageddon in Los Angeles. For drivers, these extensive traffic jams can be …

2015: "No Safety, Know Pain : Know Safety, No Pain", Brice Wang '16, Joy Qiu '16, Daniel Sohn '16, Angad Garg '16

Distinguished Student Work

In the world we live in today, many people live in urban or suburban areas. For this reason, residents of these metropolitan areas should be aware of the safety of the city they live in so they can take necessary precautions and educate youth about what actions are safe. In addition, judging the safety of a city allows the government of the city to analyze what factors and laws make other cities safer, and how they can replicate these conditions to make their city a safer place as well.

Contribution And Citation Impact Of Panjab University In Mathematics Research During 2005-14, Madhu Bansal, Jivesh Bansal, Harinder Singh Saini, B M. Gupta

Library Philosophy and Practice (e-journal)

This paper analyzes 230 research publications of the Panjab University in mathematics during ten years (2005-14), as covered in Scopus International database. The study quantifies publication data in various aspects of performance, such as the publication growth, research impact and quality, national and international collaboration, contribution and impact of authors, major areas of research, preferred channels of research communications and characteristics of higher cited papers. The findings reveal that Panjab University total publications in mathematics has increased at an annual average growth rate of 17.15% and registered an average citation impact per paper of 2.92 and impact factor per paper …

Mathematics In Contemporary Society Chapter 1, Patrick J. Wallach

Open Educational Resources

Mathematics in Contemporary Society is the textbook that corresponds to MA-321, the course of the same name. The course is designed to provide students with mathematical ideas and methods found in the social sciences, the arts, and in business. Topics will include fundamentals of statistics, scatterplots, graphics in the media, problem solving strategies, dimensional analysis, mathematics in music and art, and mathematical modeling. EXCEL is used to explore real world applications.

The textbook was posted in weekly installments:

• Chapter 1
• Chapter 2
• Chapter 3
• Chapter 4
• Chapter 5
• Chapter 6
• Chapter 7
• Chapter 8
• Chapter 9
• Chapter 10
• Chapter 11

Mathematics In Contemporary Society Chapter 6, Patrick J. Wallach

Open Educational Resources

Mathematics in Contemporary Society is the textbook that corresponds to MA-321, the course of the same name. The course is designed to provide students with mathematical ideas and methods found in the social sciences, the arts, and in business. Topics will include fundamentals of statistics, scatterplots, graphics in the media, problem solving strategies, dimensional analysis, mathematics in music and art, and mathematical modeling. EXCEL is used to explore real world applications.

The textbook was posted in weekly installments:

• Chapter 1
• Chapter 2
• Chapter 3
• Chapter 4
• Chapter 5
• Chapter 6
• Chapter 7
• Chapter 8
• Chapter 9
• Chapter 10
• Chapter 11

Mathematics In Contemporary Society Chapter 7, Patrick J. Wallach

Open Educational Resources

Mathematics in Contemporary Society is the textbook that corresponds to MA-321, the course of the same name. The course is designed to provide students with mathematical ideas and methods found in the social sciences, the arts, and in business. Topics will include fundamentals of statistics, scatterplots, graphics in the media, problem solving strategies, dimensional analysis, mathematics in music and art, and mathematical modeling. EXCEL is used to explore real world applications.

The textbook was posted in weekly installments:

• Chapter 1
• Chapter 2
• Chapter 3
• Chapter 4
• Chapter 5
• Chapter 6
• Chapter 7
• Chapter 8
• Chapter 9
• Chapter 10
• Chapter 11

Mathematics In Contemporary Society Chapter 10, Patrick J. Wallach

Open Educational Resources

Mathematics in Contemporary Society is the textbook that corresponds to MA-321, the course of the same name. The course is designed to provide students with mathematical ideas and methods found in the social sciences, the arts, and in business. Topics will include fundamentals of statistics, scatterplots, graphics in the media, problem solving strategies, dimensional analysis, mathematics in music and art, and mathematical modeling. EXCEL is used to explore real world applications.

The textbook was posted in weekly installments:

• Chapter 1
• Chapter 2
• Chapter 3
• Chapter 4
• Chapter 5
• Chapter 6
• Chapter 7
• Chapter 8
• Chapter 9
• Chapter 10
• Chapter 11

Mathematics In Contemporary Society Chapter 9, Patrick J. Wallach

Open Educational Resources

Mathematics in Contemporary Society is the textbook that corresponds to MA-321, the course of the same name. The course is designed to provide students with mathematical ideas and methods found in the social sciences, the arts, and in business. Topics will include fundamentals of statistics, scatterplots, graphics in the media, problem solving strategies, dimensional analysis, mathematics in music and art, and mathematical modeling. EXCEL is used to explore real world applications.

The textbook was posted in weekly installments:

• Chapter 1
• Chapter 2
• Chapter 3
• Chapter 4
• Chapter 5
• Chapter 6
• Chapter 7
• Chapter 8
• Chapter 9
• Chapter 10
• Chapter 11

Foliations With Geometric Structures: An Approach Through H-Principle., Sauvik Mukherjee Dr.

Doctoral Theses

A foliation on a manifold M can be informally thought of as a partition of M into injectively immersed submanifolds, called leaves. In this thesis we study foliations whose leaves carry some specific geometric structures.The thesis consists of two parts. In the first part we classify foliations on open manifolds whose leaves are either locally conformal symplectic or contact manifolds. These foliations can be described by some higher geometric structures - namely the Poisson and the Jacobi structures. In the second part of the thesis, we consider foliations on open contact manifolds whose leaves are contact submanifolds of the ambient …

On The Analysis Of Some Recursive Equations In Probability., Arunangshu Biswas Dr.

Doctoral Theses

This thesis deals with recursive systems used in theoretical and applied probability. Recursive systems are stochastic processes {Xn}n≥1 where the Xn depends on the earlier Xn−1 and also on some increment process which is uncorrelated with the process Xn. The simplest example of a recursive system is the Random Walk, whose properties have been extensively studied. Mathematically a recursive system takes the form Xn = f(Xn−1, n), is the increment/ innovation procedure and f(·, ·) is a function on the product space of xn and n. We first consider a recursive system called Self-Normalized sums (SNS) corresponding to a sequence …

Work Integrated Learning In Stem In Australian Universities: Final Report: Submitted To The Office Of The Chief Scientist, Daniel Edwards, Kate Perkins, Jacob Pearce, Jennifer Hong

Dr Daniel Edwards

The Australian Council for Educational Research (ACER) undertook this study for the Office of the Chief Scientist (OCS). It explores the practice and application of Work Integrated Learning (WIL) in STEM, with a particular focus on natural and physical sciences, information technology, and agriculture departments in Australian universities. The project involved a detailed ‘stocktake’ of WIL in practice in these disciplines, with collection of information by interview, survey instruments, consultation with stakeholders and literature reviews. Every university in Australia was visited as part of this project, with interviews and consultation sessions gathering insight from more than 120 academics and support …

Work Integrated Learning In Stem In Australian Universities: Final Report: Submitted To The Office Of The Chief Scientist, Daniel Edwards, Kate Perkins, Jacob Pearce, Jennifer Hong

Dr Jacob Pearce

The Australian Council for Educational Research (ACER) undertook this study for the Office of the Chief Scientist (OCS). It explores the practice and application of Work Integrated Learning (WIL) in STEM, with a particular focus on natural and physical sciences, information technology, and agriculture departments in Australian universities. The project involved a detailed ‘stocktake’ of WIL in practice in these disciplines, with collection of information by interview, survey instruments, consultation with stakeholders and literature reviews. Every university in Australia was visited as part of this project, with interviews and consultation sessions gathering insight from more than 120 academics and support …

Ambiguity In Speaking Chemistry And Other Stem Content: Educational Implications, Mick D. Isaacson, Michelle Michaels

Journal of Science Education for Students with Disabilities

Ambiguity in speech is a possible barrier to the acquisition of knowledge for students who have print disabilities (such as blindness, visual impairments, and some specific learning disabilities) and rely on auditory input for learning. Chemistry appears to have considerable potential for being spoken ambiguously and may be a barrier to accessing knowledge and to learning. Educators in chemistry may be unaware of, or have limited awareness of, potential ambiguity in speaking chemistry and may speak chemistry ambiguously to their students. One purpose of this paper is to increase awareness of potential ambiguity in speaking chemistry and other STEM fields …

Some Issues In Unsupervised Feature Selection Using Similarity., Partha Pratim Kundu Dr.

Doctoral Theses

Pattern recognition is what humans do most of the time, without any conscious effort, and fortunately excel in. Information is received through various sensory organs, processed simultaneously in the brain, and its source is instantaneously identified without any perceptible effort. The interesting issue is that recognition occurs even under non-ideal conditions, i.e., when information is vague, imprecise or incomplete. In reality, most human activities depend on the success in performing various pattern recognition tasks. Let us consider an example. Before boarding a train or bus, we first select the appropriate one by identifying either the route number or its destination …

Quantization Of Two Types Of Multisymplectic Manifolds, Baran Serajelahi

Electronic Thesis and Dissertation Repository

This thesis is concerned with quantization of two types of multisymplectic manifolds that have multisymplectic forms coming from a Kahler form. In chapter 2 we show that in both cases they can be quantized using Berezin-Toeplitz quantization and that the quantizations have reasonable semiclassical properties.

In the last chapter of this work, we obtain two additional results. The first concerns the deformation quantization of the (2n-1)-plectic structure that we examine in chapter 2, we make the first step toward the definition of a star product on the Nambu-Poisson algebra (C^{\infty}(M),{.,...,.}). The second result concerns the algebraic properties of the generalized …

Infographics And Mathematics: A Mechanism For Effective Learning In The Classroom, Ivan Sudakov, Thomas Bellsky, Svetlana Usenyuk, Victoria V. Polyakova

Physics Faculty Publications

This work discusses the creation and use of infographies in an undergraduate mathematics course. Infographies are a visualization of information combining data, formulas, and images. This article discusses how to form an infographic and uses infographics on topics within mathematics and climate as examples. It concludes with survey data from undergraduate students on both the general use of infographics and on the specific infographics designed by the authors.

Wavelet Analysis On Local Fields Of Positive Characteristic., Quiser Jahan Dr.

Doctoral Theses

In this chapter, we will give a brief history of wavelet analysis on R. We will also list some bask results on local felds which will be used in subvequent chapters.1.1 Wavelets on RWe fiest start with a brief history of wavelets und some basic defnitions and results conceming the orthonormal wavekts on R.1.1.1 A brief historyIn the last few decades vaveler theory has growa extensively and has drawn great atlention sot only in mathematies bu also in engineering, pitysics, computer science and many other fields. In signal and image processing, wavelets play a very important role.In 1910, A. Haar …

Euler Class Groups Of Polynomial And Sub Integral Extensions Of A Noetherian Ring., Md. Ali Zinna Dr.

Doctoral Theses

ObjectiveThe main objectives of this thesis are the following:(i) To investigate the behaviour of the Euler class groups under integral and subintegral extensions. More precisely, given a subintegral (or integral) extension R+ S of Noetherian rings, we are interested in finding out the relationship between the Euler class group of R and the Euler class group of S.(ii) To develop a theory (namely, an extension of the theory of Euler class group to the Euler class group of R[T) relative to a projective R[T|-module L of rank 1) in order to detect the precise obstruction for a projective R[T]-module P …

Course Proposal For A Mathematical Modeling Course In A High School Curriculum, Thomas P. Marlowe

Masters Essays

In the winter of 2015, I will be piloting a course on mathematical modeling at Hawken School, an independent high school in Gates Mills, OH. As I develop all elements of this course, such as lesson plans, assessments, and rubrics, I will be mindful of factors such as the newly adopted Common Core mathematics standards, the variety of student backgrounds in such a course, and how various mathematical societies and organizations such as SIAM, MAA, and COMAP can help in implementing it. However, there is one basic question driving my interest in and design of this course: “when am I …

Infinity In The High School Mathematics Classroom, Alyssa Hoslar

Masters Essays

No abstract provided.

Mittag-Leffler Therorem, Elizabeth O. Agyeman

Masters Essays

No abstract provided.

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

Work Integrated Learning In Stem In Australian Universities: Final Report: Submitted To The Office Of The Chief Scientist, Daniel Edwards, Kate Perkins, Jacob Pearce, Jennifer Hong

Higher education research

The Australian Council for Educational Research (ACER) undertook this study for the Office of the Chief Scientist (OCS). It explores the practice and application of Work Integrated Learning (WIL) in STEM, with a particular focus on natural and physical sciences, information technology, and agriculture departments in Australian universities. The project involved a detailed ‘stocktake’ of WIL in practice in these disciplines, with collection of information by interview, survey instruments, consultation with stakeholders and literature reviews. Every university in Australia was visited as part of this project, with interviews and consultation sessions gathering insight from more than 120 academics and support …

Some Problems In Differential And Subdifferential Calculus Of Matrices., Priyanka Grover Dr.

Doctoral Theses

A central problem in many subjects like matrix analysis, perturbation theory, numerical analysis and physics is to study the effect of small changes in a matrix A on a function f(A). Among much studied functions on the space of matrices are trace, determinant, permanent, eigenvalues, norms. These are real or complex valued functions. In addition, there are some interesting functions that are matrix valued. For example, the (matrix) absolute value, tensor power, antisymmetric tensor power, symmetric tensor power.When a function is differentiable, one of the ways to study the above problem is by using the derivative of f at A, …

Some Studies On Selected Stream Ciphers Analysis Fault Attack & Related Results., Subhadeep Banik Dr.

Doctoral Theses

Stream Ciphers are important Symmetric Cryptological primitives, built for the purpose of providing secure message encryption. As no formal security proofs exist, our confidence in these algorithms is largely based on the fact that intense cryptanalysis has been carried out over several years without revealing any weakness. This thesis makes some independent contributions to the cryptanalysis of a selection of stream ciphers.In this thesis, we take a closer look at two stream ciphers viz. RC4+ designed by Maitra et al. at Indocrypt 2008 and GGHN designed by Gong et al. at CISC 2005. Both these ciphers were designed as viable …

The Implications Of Self-Driving Cars On Insurance, Amanda Lobello

Honors Projects in Mathematics

Self-driving cars, also known as autonomous vehicles, are being researched and tested by automakers, technology industry leaders, and other institutions. Lawmakers and politicians are discussing the legislation that will affect the fate of such technology. Primary benefits include safety, mobility, free time, less traffic, and green effects. However, there are also obstacles to the implementation of self-driving vehicles including consumer acceptance, legal liability, and cost. With the potential shift in responsibility from driver to automaker, rating factors for insurance may change, weighing more heavily on the model of the car as a factor. The fate of auto insurance is in …

Counting On R-Fibonacci Numbers, Arthur Benjamin, Curtis Heberle

All HMC Faculty Publications and Research

We prove the r-Fibonacci identities of Howard and Cooper using a combinatorial tiling approach.

Book Review: How To Bake Pi: An Edible Exploration Of The Mathematics Of Mathematics, Darren B. Glass

Math Faculty Publications

If you think about it, mathematics is really just one big analogy. For one example, the very concept of the number three is an drawing an analogy between a pile with three rocks, a collection of three books, and a plate with three carrots on it. For another, the idea of a group is drawing an analogy between adding real numbers, multiplying matrices, and many other mathematical structures. So much of what we do as mathematicians involves abstracting concrete things, and what is abstraction other than a big analogy? [excerpt]

Teaching Algebra: A Comparison Of Scottish And American Perspectives, Brittany Munro

Undergraduate Honors Theses

A variety of factors influence what teaching strategies an educator uses. I analyze survey responses from algebra teachers in Scotland and Appalachia America to discover how a teacher's perception of these factors, particularly their view of mathematics itself, determines the pedagogical strategies employed in the classroom.