Digital Commons Network^™

Geo 491.02: Geological Mapping In Virtual Reality, Natalie Bursztyn

University of Montana Course Syllabi, 2021-2025

No abstract provided.

Stepping Stone Problem On Graphs, Rory O'Dwyer

The Mathematics Enthusiast

This paper formalizes the stepping stone problem introduced Ladoucer and Rebenstock [G] to the setting of simple graphs. This paper considers the set of functions from the vertices of our graph to N, which assign a fixed number of 1’s to some vertices and assign higher numbers to other vertices by adding up their neighbors’ assignments. The stepping stone solution is defined as an element obtained from the argmax of the maxima of these functions, and the maxima as its growth. This work is organized into work on the bounded and unbounded degree graph cases. In the bounded case, sufficient …

A General Expression For Hermite Expansions With Applications, Tom P. Davis

The Mathematics Enthusiast

Hermite polynomials arise when dealing with functions of normally distributed variables, and are commonly thought of as the analog of the simple polynomials on functions of regular variables. Therefore the Hermite expansion should be an analog of the Taylor expansion. Indeed there is a strong connection between the two – the general coefficient in the Hermite expansion is the weighted integral of the nth derivative, as compared to the nth derivative evaluated at zero in the case of Taylor. This fact can be used to derive the Hermite expansion for the integral and the derivative of a function. Furthermore, it …

The Tradition Of Large Integers In Historical Arithmetical Textbooks, Franka Miriam Bruckler, Vladimir Stilinovic

The Mathematics Enthusiast

After the Hindu-Arabic decimal positional system was introduced in Europe, throughout many centuries textbooks on elementary arithmetic, intended for beginners, had a more or less fixed organization of content, usually starting with chapters on numeration. These chapters, as a rule, contained one or more examples of large integers the purpose of which was simply to be named (read out loud), sometimes also vice versa. This tradition apparently began with the two first texts that significantly contributed to the spread of the decimal system in Europe—the Latin translations of al- Khwarizmi’s treatise on decimal arithmetic, and Leonardo’s Liber Abaci, containing examples …

Will They Automatically Work Together? Cooperation Among Non-Fools In Hobbes´S Leviathan, Karim Pluma

The Mathematics Enthusiast

Thomas Hobbes´s State of War is commonly imagined as a harrowing condition where hostile interactions are the rule and non-hostile encounters are the rare exception. However, while it is generally true that Hobbes purposely outlined his famed condition of anarchy as a condition of perennial conflict, it is also equally true that cooperative behavior was not uncommon. In fact, by only taking into account cooperative behavior, as presented in Leviathan, the anarchic humans leave the absolute uncertainties of the State of War and create the Commonwealth for their safety and well-being. Over the past fifty years or so, several exits …

An Examination Of The Factors And Characteristics That Contribute To The Success Of Putnam Fellows, Robert A. J. Stroud, Thomas C. Defranco

The Mathematics Enthusiast

The William Lowell Putnam Mathematical Competition is an intercollegiate mathematics competition for students in the United States and Canada and is regarded as the most prestigious and challenging mathematics competition in North America (Alexanderson, 2004; AMS, 2020; Grossman, 2002; Reznick, 1994; Schoenfeld, 1985). Students who earn the five highest scores on the examination are named Putnam Fellows. Since its inception in 1938, only 306 individuals have won the competition and a select few have won multiple times. Clearly, being named a Putnam Fellow is a remarkable achievement and therefore, understanding the factors and characteristics that contribute to their success is …

The Construction Of Figured Numbers In Geogebra Software Using Algebraic Properties, Francisco Evamar Barros, Francisco Regis Vieira Alves, Paula Maria Machado Cruz Catarino, Renata Teofilo De Sousa

The Mathematics Enthusiast

Figured numbers are sequences of natural numbers that, when represented by dots, form geometric configurations. The immediate sequence of figured numbers presents in its configuration the equilateral triangles, being the basis for finding several others, as long as a relationship between them is discovered. This article shows the construction of polygonal, stellar and three-dimensional figured numbers that can be constructed using the GeoGebra software as a resource to visualize the properties that relate these numbers to the triangular numbers. It is a way of observing the relationship that the figures shown have to each other, how we can understand the …

Tagging Opportunities To Learn: A Coding Scheme For Student Tasks, Janet Heine Barnett, Cihan Can, Daniel E. Otero

The Mathematics Enthusiast

This article describes the development of a coding scheme for analyzing mathematical tasks in Primary Source Projects (PSPs), curriculum materials based on primary historical sources designed for teaching standard topics from today’s undergraduate mathematics curriculum. Our scheme attends to social-cultural aspects of mathematical learning while focusing on the student actions expected as they work tasks. We exemplify our scheme with tasks drawn from a diverse set of PSPs and report results from its application to these projects. We conclude with comments on how our work can assist instructors, curriculum developers, and researchers, including those who are interested in other types …

On The Even Distribution Of Odd Primes: An On-Ramp To Mathematical Research, James Quinlan, Michael Todd Edwards

The Mathematics Enthusiast

The authors consider a conjecture by Chebyshev in 1853 on the distribution of odd primes among those that are one more than a multiple of four and those three more than a multiple of four—and use technology to explore the cardinality of these subsets. Generalizations are presented for student exploration along with several sources for more in-depth research.

The Chain Rule Does Not Have To Be A Pain Rule, Elizabeth Beeman, Jennifer Runge, Lauren Holden, Devon Maxwell, Yi-Yin (Winnie) Ko

The Mathematics Enthusiast

Relational and instrumental understanding of the Chain Rule can help teachers provide students a deeper and more meaningful calculus experience.

The Monty Brawl And Other Unexpected Consequences Of Mathematical Instruction, Francesco Beccuti

The Mathematics Enthusiast

No abstract provided.

Using Gardner's Three-Squares Problem For A Group Project In A Mathematical Problem Solving Module, Jonathan Hoseana

The Mathematics Enthusiast

Consider a 1 x 3 grid whose top-left vertex is connected to the bottom-right vertex of each of the unit squares. What is the sum of the three acute angles formed by the connecting segments with the unit squares' bases? This is the so-called three-squares problem, often attributed to Gardner. In a recent academic year, the author used a video on this problem, produced by the YouTube channel Numberphile, for a group project in a first-semester undergraduate module: Mathematical Problem Solving. The project involved collaborative writing on the problem and individual completion of a peer-assessment form. We report the outcomes …

Going Off On A Tangent: An Inclusion-Exclusion Identity, Aloysius Bathi Kasturiarachi

The Mathematics Enthusiast

Undergraduate research in tertiary education offers mathematics students a pathway to engage in high-impact practices. Using a simple sum equals product identity from number theory as a motivator, we build a series of inclusion-exclusion identities for convex polygons using the symmetry inherent in the tangent function. The techniques used are simple and accessible, illuminating and generalizable, in a manner that rejects a singular line of inquiry in favor of a plurality of mathematical ideas.

Investigating Problems Posed By Pre-Service Mathematics Teachers For The Four Operations In Fractions, Yasemin Kiymaz

The Mathematics Enthusiast

This study investigates 40 preservice middle school teachers’ problems posed for two given fractions. Pre-service teachers were asked to pose three problems (farea, length and set model) for each of the operations of addition, subtraction, multiplication and division with these fractions. 12 problems posed by each pre-service teacher were examined in terms of their suitability for the given operation, the targeted model and real life relevance. Errors in the posed problems were also examined. As a result of the analysis, it was observed that the model in which pre-service teachers were the most unsuccessful in posing problems was the set …

On Convincing Power Of Counterexamples, Orly Buchbinder, Rina Zazkis

The Mathematics Enthusiast

Despite plethora of research that attends to the convincing power of different types of proofs, research related to the convincing power of counterexamples is rather slim. In this paper we examine how prospective and practicing secondary school mathematics teachers respond to different types of counterexamples. The counterexamples were presented as products of students’ arguments, and the participants were asked to evaluate their correctness and comment on them. The counterexamples varied according to mathematical topic: algebra or geometry, and their explicitness. However, as we analyzed the data, we discovered that these distinctions were insufficient to explain why teachers accepted some counterexamples, …

A Role For Affect In The Future Of Mathematics Education (With Thoughts On Intelligence), Marcelo Almora Rios

The Mathematics Enthusiast

A Review of:

1. Alan Schoenfeld, Heather Fink, Alyssa Sayavedra, Anna Weltman, & Sandra Zuñiga-Ruiz’s (2023) Mathematics Teaching on Target, Routledge, 164pp. ISBN (HB): 978-1-0324-4167-2;

2. Alan Schoenfeld, Heather Fink, Sandra Zuñiga-Ruiz, Siqi Huang, Xinyu Wei, & Brantina Chirinda’s (2023) Helping Students Become Powerful Mathematics Thinkers, Routledge, 272pp. ISBN (HB): 978-1-0324-4168-9.

Montana Kaimin, January 25, 2024, Students Of The University Of Montana, Missoula

Montana Kaimin, 1898-present

Student newspaper of the University of Montana, Missoula.

Documents From The January 24, 2024 Meeting Of The Associated Students Of The University Of Montana (Asum), University Of Montana--Missoula. Associated Students

Senate Meeting Agendas and Minutes, 2007-Present

Agenda and meeting minutes from the January 24, 2024 meeting of the Associated Students of the University of Montana (ASUM).

Sb01_23-24 Resolution To Achieve Equal Pay Throughout The Montana University System With Addendum, Trey Magnuson

University of Montana Staff Senate Resolutions

Staff Senate urged UM's Administration and Human Resource Services, the Office of the Commissioner of Higher Education, the Board of Regents, the Montana Governor’s Office, and bargaining unions (e.g., Montana Federation of Public Employees) to examine data regarding pay equity across the Montana University System in order to recruit and retain talented staff.

The resolution passed during the January 10, 2024 University of Montana Staff Meeting. Subsequently, a data error was found, and a correction was made. Due to the change in data and revised statement associated with the data point, the resolution was brought back up on a special …

Montana Kaimin, January 18, 2024, Students Of The University Of Montana, Missoula

Montana Kaimin, 1898-present

Student newspaper of the University of Montana, Missoula.

Documents From The January 10, 2024 Meeting Of The University Of Montana Staff Senate, University Of Montana--Missoula. Staff Senate

University of Montana Staff Senate Meeting Minutes

Agenda and meeting minutes from the January 10, 2024 meeting of the University of Montana Staff Senate. The following resolutions were discussed during the meeting:

SB01_23-24 Resolution to Achieve Equal Pay Throughout the Montana University System with Addendum

Other highlights include Sustainability Office Updates with Eva Rocke, Sustainability Director, Academic Playbook Overview with Provost Andrea Lawrence and Vice Provost John DeBoer, and Community Outreach Ideas.

The Role Of Sociopolitical Workplace Networks In Involuntary Employee Turnover, Theresa M. Floyd, Alexandra Gerbasi, Giuseppe (Joe) Labianca

Management and Marketing Faculty Publications

While poor performance is one reason employees are fired, previous research suggests it plays a limited role in explaining terminations. We argue that sociopolitical concerns play a role in determining who is terminated. Using field data from a U.S. health care company and experimental data using participants with supervisory experience, we show how the supervisor’s political concerns with the focal employee, which are contingent on the supervisor-employee political relationship and the way it is embedded within the workplace network, are related to dismissal decisions. Not only do we expect that a supervisor will be less likely to terminate an employee …

Voter Information Pamphlet, 2024, Montana. Secretary Of State

The Montana Constitution Collection

Voter information pamphlet for the general election, November 5, 2024.

‘Something Beyond’ And ‘Unspeakable’: A Passage To India As A Vedantic Novel, Ruth Vanita

Global Humanities and Religions Faculty Publications

No abstract provided.

Multidimensional Cognitive-Communication Assessment For Concussion, Catherine A. Off

University Grant Program Reports

The long-term purpose of this research is to explore an ecologically valid, multidimensional assessment protocol that can identify and characterize persisting yet subtle, cognitive-communication symptoms following concussion.

British Translators, Bhagat Singh, And ‘Atheism’: How ‘Reverse Translation’ Alters The Meaning Of Philosophical Concepts, Ruth Vanita

Global Humanities and Religions Faculty Publications

This chapter is a preliminary enquiry into a process for which I have invented the term ‘reverse translation’ since there seems to be no specific term available for it. Reverse translation is the process by which the meaning of a Hindu philosophical concept changes in Indian languages because of a process of incorrect translation to and from English.

Estimation Of Probability Of Habitat Use Of Roosevelt Elk On The Olympic Peninsula, Vincent Michael Gugliotti

Undergraduate Theses, Professional Papers, and Capstone Artifacts

Estimating the probability of habitat use for a particular species is crucial to the direct management and conservation of that species. Without knowledge of habitat preferences, managers cannot effectively focus efforts on vital resources or landscape types. However, modelling probability of habitat use can be done in several ways which leaves room for variation and uncertainty in the estimates produced by each method. This study is an examination of the variation between two estimates of probability of habitat use while focusing on a particular subspecies of elk that inhabits a unique ecosystem relative to other elk subspecies. I modeled elk …

Nike's Product Recommendation System And Incorporation Of Ai, Quinton Truman Lamers

Undergraduate Theses, Professional Papers, and Capstone Artifacts

No abstract provided.

Somewhere In-Between: My Evolving Understanding Of Wilderness, Sebastian J. Driver

Undergraduate Theses, Professional Papers, and Capstone Artifacts

Wilderness has many definitions and is a concept that means something different to everyone. According to the Wilderness Act of 1964, "Wilderness is an area where the earth and its community of life are untrammeled by man, where man himself is a visitor who does not remain." In recent years, the definition of wilderness is under debate as it fails to excludes the indigenous perspective. Due to the exclusion of Native Americans some have called for the removal of the word wilderness altogether. However, I propose that instead of removing the word altogether that we can redefine it to make …

Social Story Interventions: Promoting Positive Preschool Behaviors, Emma Meyer

Undergraduate Theses, Professional Papers, and Capstone Artifacts

This action research study investigates the effectiveness of social story interventions in enhancing positive behaviors among children within the Learning and Belonging (LAB) Preschool setting. The study focuses on an individual child to assess the impact of social stories on behaviors related to self-regulation, resiliency, and whole-group behaviors. Data-collection involves observational periods before and after the implementation of social story interventions using an interval timing method. The observational data highlights specific behaviors and challenges faced by the targeted child, informing the development of tailored social stories. The intervention period includes the creation and implementation of two social story scripts targeting …