Digital Commons Network^™

The Development Of Calculus In The Kerala School, Phoebe Webb

The Mathematics Enthusiast

The Kerala School of mathematics, founded by Madhava in Southern India, produced many great works in the area of trigonometry during the fifteenth through eighteenth centuries. This paper focuses on Madhava's derivation of the power series for sine and cosine, as well as a series similar to the well-known Taylor Series. The derivations use many calculus related concepts such as summation, rate of change, and interpolation, which suggests that Indian mathematicians had a solid understanding of the basics of calculus long before it was developed in Europe. Other evidence from Indian mathematics up to this point such as interest in …

Pursuing Coherence Among Proportionality, Linearity, And Similarity: Two Pathways From Preservice Teachers’ Geometric Representations, Hyung Sook Lee, Jaehoon Yim

The Mathematics Enthusiast

The importance of using multiple representations of a mathematical concept and connecting the representations has been discussed in learning and teaching mathematics. The Common Core State Standards further the discussion with an emphasis on focus and coherence in teaching mathematical concepts across grades. Preservice teachers in our problem solving class were asked to use geometric representations to solve a problem that required proportional reasoning. They were also asked to sequence the works of their peers as well as their own from a developmental perspective. Sequencing geometric representations with various levels was challenging because it required showing a coherent understanding of …

Tme Volume 11, Number 3

The Mathematics Enthusiast

No abstract provided.

Editorial: Is Every Tme Issue Special?, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

The Miracle Of Applied Mathematics, Frank Blume

The Mathematics Enthusiast

We provide an outline of a college-level lecture on systems of differential equations that is intended to offer an alternative, integrative view of the subject. Particular emphasis is placed on the fact that very elementary concepts and insights can be employed to gain access to a very wide range of important applications, including the Schr¨odinger equation, the Klein-Gordon equation, the Laplace equation, and the Poisson equation.

Generalizing Cantor-Schroeder-Bernstein: Counterexamples In Standard Settings, Tien Chih

The Mathematics Enthusiast

The Cantor-Schroeder-Bernstein theorem states that any two sets that have injections into each other have the same cardinality, i.e. there is a bijection between them. Another way to phrase this is if two sets A;B have monomorphisms from A to B and B to A, then they are isomorphic in the setting of sets. One naturally wonders if this may be extended to other commonly studied systems of sets with structure and functions which preserve that structure. Given two objects with injective structure preserving maps between them are the structures of these objects the same? In other words, would these …

A Study On Malaysian Mathematicians’ Way Of Knowing, Lim Chap Sam

The Mathematics Enthusiast

“Can you name me a mathematician?” “Einstein??”

“Do you wish to become a mathematician one day?”

If these questions were asked to the public or any school students, the most likely answer to both questions might be a big ‘No!’. Why is this so?

The director of the Public Understanding of Mathematics Forum, Gene Kloz (1996) claims that the mathematics profession is the most misunderstood in all of academia. According to him, the public thinks that mathematicians contemplate ancient proofs and work as lonely recluses. Moreover, the most common public image of a mathematician has been furnished by a physicist …

Reasoning-And-Proving Within Ireland’S Reform-Oriented National Syllabi, Jon Davis

The Mathematics Enthusiast

As educational systems around the world attempt to reform their mathematics programs to increase students’ opportunities to engage in processes central to the practice of mathematics such as proof, it is important to understand how this mathematical act is portrayed in national curriculum documents that drive that change. This study examined the presence of reasoning-and-proving (RP) in Ireland’s national reform-oriented secondary syllabi for junior cycle (ages 12-15) and senior cycle (ages 15-18) students. The analyses reveal that there were no differences among direct and indirect RP learning outcomes within each syllabus, but statistically significant differences did exist across syllabi in …

Difficulties In Solving Context-Based Pisa Mathematics Tasks: An Analysis Of Students’ Errors, Ariyadi Wijaya, Marja Van Den Heuvel-Panhuizen, Michiel Doorman, Alexander Robitzsch

The Mathematics Enthusiast

The intention of this study was to clarify students’ difficulties in solving context-based mathematics tasks as used in the Programme for International Student Assessment (PISA). The study was carried out with 362 Indonesian ninth- and tenth-grade students. In the study we used 34 released PISA mathematics tasks including three task types: reproduction, connection, and reflection. Students’ difficulties were identified by using Newman’s error categories, which were connected to the modeling process described by Blum and Leiss and to the PISA stages of mathematization, including (1) comprehending a task, (2) transforming the task into a mathematical problem, (3) processing mathematical procedures, …

Scholastic Standards In The United States – The Discussion Concerning The ‘Common Core’, Alan H. Schoenfeld, Günter Törner

The Mathematics Enthusiast

Preface: This article has been developed based on a personal discussion between the German author Günter Törner and Alan Schoenfeld, who is an expert in the field of mathematical didactics. Basically there are three reasons for us to share our insights with the public:

(1) Readers, having subscribed to Jerry Becker’s e-mail information network, have received numerous messages over the past few months; what do we need to know about this fact in Germany?

(2) Scholastic standards – a keyword that sounds very familiar to us in terms of educational policy… But it is also a hot topic in other …

Development Of The Binary Number System And The Foundations Of Computer Science, Daniel R. Lande

The Mathematics Enthusiast

This paper discusses the formalization of the binary number system and the groundwork that was laid for the future of digital circuitry, computers, and the field of computer science. The goal of this paper is to show how Gottfried Leibniz formalized the binary number system and solidified his thoughts through an analysis of the Chinese I Ching. In addition, Leib-niz’s work in logic and with computing machines is presented. This work laid the foundation for Boolean algebra and digital circuitry which was continued by George Boole, Augustus De Mor-gan, and Claude Shannon in the centuries following. Some have coined Leibniz …

Ion Composition In Interchange Injection Events In Saturn's Magnetosphere, M. F. Thomsen, Daniel B. Reisenfeld, R. J. Wilson, M. Andriopoulou, F. J. Crary, G. B. Hospodarsky, C. M. Jackman, X. Jia, K. K. Khurana, C. Paranicas, E. Roussos, N. Sergis, R. L. Tokar

Physics and Astronomy Faculty Publications

Interchange injection events are commonly observed by the Cassini spacecraft in the region between about 6 and 12 R_s (1 R_s = 60,268 km) and even frequently beyond. In this study, 13 examples of interchange injection events are identified in Cassini-Cassini Plasma Spectrometer data under special conditions such that time-of-flight (TOF) mass spectra could be obtained from entirely within the events. Using the TOF data to separate the main ion species H⁺, H₂⁺, and W⁺, approximate densities of each species are calculated under the assumption that all distributions were isotropic. The …

Cold Magnetically Trapped 2DG Scandium Atoms. I. Interaction Potential, Tijs Karman, Xi Chu, Gerrit C. Groenenboom

Chemistry and Biochemistry Faculty Publications

We present a first principles description of the interaction of two ground-state scandium atoms. Scandium has a ²D_g ground state. Thirty molecular states correlate to the lowest dissociation limit of the dimer. In the short range, potential energy curves are calculated using second-order n-electron valence state perturbation theory. The first-order long-range interaction is calculated at the complete active space self-consistent field level. We determine the second-order long-range dispersion interaction from atomic dynamic polarizabilities at imaginary frequencies. These polarizabilities are calculated using time-dependent density functional theory. We merge the short-range approach with the long-range model to obtain a physical …

The Minimization Process In The Correlation Estimation System (Ces) Compared To Least Squares In Linear Regression, Rudy Gideon

Mathematical Sciences Faculty Publications

This presentation contains a new system of estimation, starting with correlation coefficients, that rivals least squares and for much data does better. One example of SAT and ACT data is used to illustrate minimization through the Correlation Estimation System (CES) in a two-variable linear regression; in this example the CES results give a better representation of the meaning of the data. All the regression model parameters, including variation and location, are estimated by this general CES process. The results from this example are completely typical; the example was not cherry-picked. If you are a least squares-bible toting statistician then what …

Separation Of The Ribbon From Globally Distributed Energetic Neutral Atom Flux Using The First Five Years Of Ibex Observations, N. A. Schwadron, E. Moebius, S. A. Fuselier, D. J. Mccomas, H. O. Funsten, Paul H. Janzen, Daniel B. Reisenfeld, H. Kucharek, M. A. Lee, K. Fairchild, F. Allegrini, M. Dayeh, G. Livadiotis, M. Reno, M. Bzowski, J. M. Sokol, M. A. Kubiak, E. R. Christian, R. Demajistre, P. Frisch, A. Galli, P. Wurz, M. Gruntman

Physics and Astronomy Faculty Publications

The Interstellar Boundary Explorer (IBEX) observes the IBEX ribbon, which stretches across much of the sky observed in energetic neutral atoms (ENAs). The ribbon covers a narrow (∼20^◦–50^◦) region that is believed to be roughly perpendicular to the interstellar magnetic field. Superimposed on the IBEX ribbon is the globally distributed flux that is controlled by the processes and properties of the heliosheath. This is a second study that utilizes a previously developed technique to separate ENA emissions in the ribbon from the globally distributed flux. A transparency mask is applied over the ribbon and …

A Regional Look At Hanpp: Human Consumption Is Increasing, Npp Is Not, Steven W. Running

Ecosystem and Conservation Sciences Faculty Publications

Abdi et al (2014 Environ. Res. Lett. 9 094003), have adapted the concept of comparing supply and demand of annual plant production known as human appropriation of net primary production (HANPP) to a region of the Sahel with rapid population growth. They found that HANPP more than doubled over the study period of 2000–2010, from 19% to 41%, suggesting increasing vulnerability of these populations to food insecurity.

Using Multi-Compartment Ensemble Modeling As An Investigative Tool Of Spatially Distributed Biophysical Balances: Application To Hippocampal Oriens-Lacunosum/Moleculare (O-Lm) Cellns, Vladislav Sekulic, J. Josh Lawrence, Frances K. Skinner

Biomedical and Pharmaceutical Sciences Faculty Publications

Multi-compartmental models of neurons provide insight into the complex, integrative properties of dendrites. Because it is not feasible to experimentally determine the exact density and kinetics of each channel type in every neuronal compartment, an essential goal in developing models is to help characterize these properties. To address biological variability inherent in a given neuronal type, there has been a shift away from using hand-tuned models towards using ensembles or populations of models. In collectively capturing a neuron’s output, ensemble modeling approaches uncover important conductance balances that control neuronal dynamics. However, conductances are never entirely known for a given neuron …

Ecogeomorphic Feedbacks And Flood Loss Of Riparian Tree Seedlings In Meandering Channel Experiments, Li Kui, John C. Stella, Anne Lightbody, Andrew C. Wilcox

Geosciences Faculty Publications

During floods, fluvial forces interact with riparian plants to influence evolution of river morphology and floodplain plant community development. Understanding of these interactions, however, is constrained by insufficient precision and control of drivers in field settings, and insufficient realism in laboratory studies. We completed a novel set of flume experiments using woody seedlings planted on a sandbar within an outdoor meandering stream channel. We quantified effects on local sedimentation and seedling loss to scour and burial across realistic ranges of woody plant morphologies (Populus versus Tamarix species), densities (240 plants m^-2 versus 24 m^-2), and sediment …

Aerosol Emissions From Prescribed Fires In The United States: A Synthesis Of Laboratory And Aircraft Measurements, A. A. May, G. R. Mcmeeking, T. Lee, J. W. Taylor, J. S. Craven, I. R. Burling, A. P. Sullivan, Sheryl Kashi Akagi, J. L. Collett Jr., M. Flynn, H. Coe, S. P. Urbanski, J. H. Seinfeld, Robert Yokelson, S. M. Kreidenweis

Chemistry and Biochemistry Faculty Publications

Aerosol emissions from prescribed fires can affect air quality on regional scales. Accurate representation of these emissions in models requires information regarding the amount and composition of the emitted species.Wemeasured a suite of submicron particulatematter species in young plumes emitted from prescribed fires (chaparral and montane ecosystems in California; coastal plain ecosystem in South Carolina) and from open burning of over 15 individual plant species in the laboratory. We report emission ratios and emission factors for refractory black carbon (rBC) and submicron nonrefractory aerosol and compare field and laboratory measurements to assess the representativeness of our laboratory-measured emissions. Laboratory measurements …

Department Of Mathematical Sciences Newsletter, Fall 2014, University Of Montana--Missoula. Department Of Mathematical Sciences

Newsletters from the Department of Mathematical Sciences at UM

iPads in the Classroom / Grant Swicegood -- UM Students Investigate the Elusive Relationship Between Topology and Geometry / Eric Chesebro -- Brian Steele Wins IBM Award / Dave Patterson -- Notes from the Chair / Leonid Kalachev -- (MT)² Grant / Jen Kacmarcik -- (MT)² Graduate Fellows / Jen Kacmarcik -- Math Puzzle / Matt Roscoe -- Math Enthusiast: An Eclectic Mix of Interesting Reading Material / Nikolaus Vonessen -- Alumni Reply Form -- Math Puzzle Solution -- Math Club Corner / Jennifer Nelson

Theoretical Analysis Of Steady State Genetic Algorithms, Alexandru Agapie, Alden H. Wright

Computer Science Faculty Publications

Evolutionary Algorithms, also known as Genetic Algorithms in a former terminology, are probabilistic algorithms for optimization, which mimic operators from natural selection and genetics. The paper analyses the convergence of the heuristic associated to a special type of Genetic Algorithm, namely the Steady State Genetic Algorithm (SSGA), considered as a discrete-time dynamical system non-generational model. Inspired by the Markov chain results in finite Evolutionary Algorithms, conditions are given under which the SSGA heuristic converges to the population consisting of copies of the best chromosome.

Airborne Characterization Of Smoke Marker Ratios From Prescribed Burning, A. P. Sullivan, A. A. May, T. Lee, G. R. Mcmeeking, S. M. Kreidenweis, S. K. Akagi, Robert Yokelson, S. P. Urbanski, J. L. Collett Jr.

Chemistry and Biochemistry Faculty Publications

A Particle-Into-Liquid Sampler – Total Organic Carbon (PILS-TOC) and fraction collector system was flown aboard a Twin Otter aircraft sampling prescribed burning emissions in South Carolina in November 2011 to obtain smoke marker measurements. The fraction collector provided 2 min time-integrated offline samples for carbohydrate (i.e., smoke markers levoglucosan, mannosan, and galactosan) analysis by high-performance anion-exchange chromatography with pulsed amperometric detection. Each fire location appeared to have a unique 1levoglucosan /1water-soluble organic carbon (WSOC) ratio (RF01/RF02/RF03/RF05 = 0.163± 0.007 μg C μg−1 C, RF08 = 0.115 ± 0.011 μg C μg−1 C, RF09A = 0.072 ± 0.028 μgC μg−1 C, …

October 2014 News Releases, University Of Montana--Missoula. Office Of University Relations

University of Montana News Releases, 1928, 1956-present

No abstract provided.

Current Unrestricted Operating Budgets, Fiscal Year 2015, University Of Montana--Missoula. Office Of Administration And Finance

University of Montana Current Unrestricted Operating Budgets, 1993-2017

The unrestricted operating budget of the University of Montana, issued by the Office of University Planning, Budgeting and Analysis under the Office of Administration and Finance.

Trace Gas Emissions From Combustion Of Peat, Crop Residue, Domestic Biofuels, Grasses, And Other Fuels: Configuration And Fourier Transform Infrared (Ftir) Component Of The Fourth Fire Lab At Missoula Experiment (Flame-4), C. E. Stockwell, R. J. Yokelson, S. M. Kreidenweis, A. L. Robinson, P. J. Demott, R. C. Sullivan, J. Reardon, K. C. Ryan, D. W.T. Griffith, L. Stevens

Chemistry and Biochemistry Faculty Publications

During the fourth Fire Lab at Missoula Experiment (FLAME-4, October-November 2012) a large variety of regionally and globally significant biomass fuels was burned at the US Forest Service Fire Sciences Laboratory in Missoula, Montana. The particle emissions were characterized by an extensive suite of instrumentation that measured aerosol chemistry, size distribution, optical properties, and cloud-nucleating properties. The trace gas measurements included high-resolution mass spectrometry, one-and two-dimensional gas chromatography, and open-path Fourier transform infrared (OP-FTIR) spectroscopy. This paper summarizes the overall experimental design for FLAME-4-including the fuel properties, the nature of the burn simulations, and the instrumentation employed-and then focuses on …

Inter-Calibration Of Satellite Passive Microwave Land Observations From Amsr-E And Amsr2 Using Overlapping Fy3b-Mwri Sensor Measurements, Jinyang Du, John S. Kimball, Jiancheng Shi, Lucas Alan Jones, Shengli Wu, Ruijing Sun, Hu Yang

Biological Sciences Faculty Publications

The development and continuity of consistent long-term data records from similar overlapping satellite observations is critical for global monitoring and environmental change assessments. We developed an empirical approach for inter-calibration of satellite microwave brightness temperature (T_b) records over land from the Advanced Microwave Scanning Radiometer for EOS (AMSR-E) and Microwave Scanning Radiometer 2 (AMSR2) using overlapping Tb observations from the Microwave Radiation Imager (MWRI). Double Differencing (DD) calculations revealed significant AMSR2 and MWRI biases relative to AMSR-E. Pixel-wise linear relationships were established from overlapping T_b records and used for calibrating MWRI and AMSR2 records to the AMSR-E …

Identification And Quantification Of Gaseous Organic Compounds Emitted From Biomass Burning Using Two-Dimensional Gas Chromatography/Time-Of-Flight Mass Spectrometry, L. E. Hatch, W. Luo, J. F. Pankow, Robert Yokelson, C. Stockwell, K. C. Barsanti

Chemistry and Biochemistry Faculty Publications

The current understanding of secondary organic aerosol (SOA) formation within biomass burning (BB) plumes is limited by the incomplete identification and quantification of the non-methane organic compounds (NMOCs) emitted from such fires. Gaseous organic compounds were collected on sorbent cartridges during laboratory burns as part of the fourth Fire Lab at Missoula Experiment (FLAME-4), with analysis by two-dimensional gas chromatography/time-of-flight mass spectrometry (GC×GC/TOFMS). The sensitivity and resolving power of GC×GC/TOFMS allowed the acquisition of the most extensive data set of BB NMOCs to date, with measure ments for 722 positively or tentatively identified compounds. Estimated emission factors (EFs) are presented …

Bfin 322.02: Business Finance, Timothy A. Manuel

University of Montana Course Syllabi

No abstract provided.

Bfin 322.01: Business Finance, Timothy A. Manuel

University of Montana Course Syllabi

No abstract provided.

Bch 595.01: Special Topics - Stem Graduate Research Fellowships, Michele A. Mcguirl

University of Montana Course Syllabi

No abstract provided.