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Central Washington University

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Full-Text Articles in Physical Sciences and Mathematics

The Impact Of Subjective Risk Analysis On Real Estate Prices In The Nisqually Region Following The 2001 Nisqually Earthquake, Ryan Espedal Jan 2023

The Impact Of Subjective Risk Analysis On Real Estate Prices In The Nisqually Region Following The 2001 Nisqually Earthquake, Ryan Espedal

All Master's Theses

Earthquakes are an environmental hazard that pose great risks to communities almost every day. With earthquakes, the main cause of concern is physical destruction of property, however, there are also psychological effects that are researched and discussed much less. In 2001, the Nisqually area of western Washington experienced a substantial earthquake that produced minimal physical damage but caused a significant decrease in real estate prices. Studying single-family homes from 1986-2012, this research utilizes hedonic property models to measure the change in consumer’s subjective risk calculations with reference to real estate purchases after the Nisqually earthquake, measure the relationship between earthquake …


Developing Research Data Management Services In A Regional Comprehensive University: The Case Of Central Washington University, Ping Fu, Maurice Blackson, Maura Valentino Aug 2022

Developing Research Data Management Services In A Regional Comprehensive University: The Case Of Central Washington University, Ping Fu, Maurice Blackson, Maura Valentino

Library Scholarship

This study aims to analyze the needs of researchers in a regional comprehensive university for research data management services; discuss the options for developing a research data management program at the university; and then propose a phased three-year implementation plan for the university libraries. The method was to design a survey to collect information from researchers and assess and evaluate their needs for research data management services. The results show that researchers’ needs in a regional comprehensive university could be quite different from those of researchers in a research-intensive university. Also, the results verify the hypothesis that researchers in the …


Revisiting Prejudiced Polygons: Adapting A Familiar Activity During A Time Of Unknowns, Anne M. Ho, Jaime J. Mccauley, Tara T. Craig Feb 2022

Revisiting Prejudiced Polygons: Adapting A Familiar Activity During A Time Of Unknowns, Anne M. Ho, Jaime J. Mccauley, Tara T. Craig

Journal of Math Circles

This article describes the design process behind various iterations of Prejudiced Polygons, a Math Circles activity about segregation. In particular, we frame our discussion around two guiding principles from User Experience (UX) Design in thinking about the interconnected components of a Math Circles session, which includes all the people, the physical or virtual setting, the technology, and the world context. Additionally, we describe how we think about developing a “low floor" and “high ceiling" for math content, social issues content, as well as technology and access.


A Contentious Crop: Exploring The Regulatory Debate Of Solar Power Production Facilities In Kittitas County, Washington, Daphne Condon Jan 2022

A Contentious Crop: Exploring The Regulatory Debate Of Solar Power Production Facilities In Kittitas County, Washington, Daphne Condon

All Master's Theses

Between 2010 and 2018, Kittitas County, Washington faced an influx of Solar Power Production Facility (SPPF) proposals that challenged its traditional rural land management governance. Despite state support of decarbonized energy, variegated interpretations of project permitting procedures induced heated contentions amongst stakeholders. To explore this, this research constructs a multijurisdictional legal framework for SPPF advancement. It uses these laws to divulge the permitting processes of three case study projects founded in Kittitas County’s renewable energy history: The Wild Horse Wind Facility, the Iron Horse Solar Project, and the Columbia Solar Projects. Through a mixed methodology of project archival analysis and …


Wilderness And The Geotag: Exploring The Claim That "Geotagging Ruins Nature" In The Alpine Lakes Wilderness, Wa, Mara Gans Jan 2022

Wilderness And The Geotag: Exploring The Claim That "Geotagging Ruins Nature" In The Alpine Lakes Wilderness, Wa, Mara Gans

All Master's Theses

This research explores the claim that “geotagging ruins nature” by quantifying and qualifying patterns in geotag use and visitors’ experiences in the Alpine Lakes Wilderness, in Washington, United States. Many have raised concerns that geotags increase recreational visitation to public lands, which subsequently contributes to negative resource impacts. Others, however, claim that geotagging has made the outdoors more accessible to less privileged communities and raise concerns that condemning geotags will perpetuate the exclusion of certain groups from outdoor recreation. This debate is studied within federally designated Wilderness, which is legally defined as “untrammeled by man,” a definition rooted in problematic …


Geomorphic History And Preservation Of Archaeologically Significant Areas In The Hanford Reach Of The Columbia River, Washington State, Benjamin Deans Jan 2022

Geomorphic History And Preservation Of Archaeologically Significant Areas In The Hanford Reach Of The Columbia River, Washington State, Benjamin Deans

All Master's Theses

Archaeological sites near rivers may be preserved through burial, altered by exposure, or destroyed through erosion. Preserved because of the unusual needs of the Manhattan Project, the Hanford Reach is the only remaining free-flowing reach of the Columbia River and ideal for research into the geomorphic settings of archaeological sites along this river. The 1894 (742,000 cfs [20,900 m3/s]) and 1948 (690,000 cfs [19,000 m3/s]) floods were the largest in the historical record through the reach, but their relationship with geomorphic change and site preservation are less understood. To understand how floods have preserved and destroyed …


Exploring Optimal Lockdown Policies During The Covid-19 Pandemic, Cameron Bundy Oct 2021

Exploring Optimal Lockdown Policies During The Covid-19 Pandemic, Cameron Bundy

Symposium Of University Research and Creative Expression (SOURCE)

COVID-19 has impacted public and economic health worldwide. To bolster the economy and maintain human life, economic and epidemiological research is vital. Nations have implemented lockdowns intent on slowing the spread of the virus. This research examines how lockdown parameter adjustments can help control a nations fatalities. The study incorporated an SIRD disease model that is simulated over a 200 day period. The goal of the research is to take the SIRD model and use it to create a minimization function that analyzes dynamics that best produce minimal loss of GDP as well as low loss of life in a …


Incorporating Universal Design Into Tsunami Modeling Results For Cascadia Subduction Zone Faults To Create An Inundation Map And Universally Designed Evacuation Map For Port Angeles, Wa, Hannah Rose Spero, Breanyn Macinnes, Naomi J. Petersen May 2021

Incorporating Universal Design Into Tsunami Modeling Results For Cascadia Subduction Zone Faults To Create An Inundation Map And Universally Designed Evacuation Map For Port Angeles, Wa, Hannah Rose Spero, Breanyn Macinnes, Naomi J. Petersen

Student Published Works

Current tsunami hazard inundation and evacuation maps in the Puget Sound are based primarily on Cascadia and Seattle fault tsunamis. The standard evaluation process for tsunami impacts focuses on elevation and hypothetical fault rupture of known and predicted earthquakes. However, there are several known tsunami deposits in the Puget Sound that are not from Cascadia or Seattle fault tsunamis, potentially from other faults within the region, that could affect tsunami mitigation. Work to understand newly discovered crustal deformation and faults in Puget Sound is ongoing, therefore evacuation and inundation maps need to be updated to include these new faults and …


Habitat Characteristics Or Protected Area Size: What Is More Important For The Composition And Diversity Of Mammals In Nonprotected Areas?, Wenbo Li, Jinhua Li, Peipei Yang, Bowen Li, Chao Liu, Lixing Sun May 2021

Habitat Characteristics Or Protected Area Size: What Is More Important For The Composition And Diversity Of Mammals In Nonprotected Areas?, Wenbo Li, Jinhua Li, Peipei Yang, Bowen Li, Chao Liu, Lixing Sun

Biology Faculty Scholarship

The margins of protected areas are usually considered to have greater forest degradation, and given that most mammals live outside protected areas, researchers and conservation practitioners are increasingly recognizing that nonprotected areas must be incorporated into conservation strategy. However, the strategy used to manage these areas still involves increasing the size of protected areas, while not considering the habitat characteristics and requirements of the species. In this study, during a 3-year period, camera trap and habitat characteristic surveys were used to estimate composition, diversity, and habitat characteristics of mammals to determine habitat characteristics or increase the size of protected areas …


Immigration Offenses Throughout Federal Sentencing: An Analysis Of The Impact Of Political Affiliation Among Districts, Robin Hood Jan 2021

Immigration Offenses Throughout Federal Sentencing: An Analysis Of The Impact Of Political Affiliation Among Districts, Robin Hood

All Master's Theses

Immigration has remained one of the most controversial political debates throughout the United States. Research has yet to fully examine the effects of political affiliation of federal districts on sentencing outcomes for specific immigration offenses. To fill the gaps in research, this study compares political affiliation of federal districts among immigration offenses to determine variations in sentencing outcomes. Data included Presidential and House of Representative votes for the 2016 election and Monitoring of Federal Sentencing for the fiscal years of 2015-2016. Analysis includes case processing/legal variables, defendant characteristics, and political affiliation. To analyze political affiliation, a binary logistic regression was …


Dual-Axis Solar Tracker, Bryan Kennedy Jan 2020

Dual-Axis Solar Tracker, Bryan Kennedy

All Undergraduate Projects

Renewable energies, and fuels that are not fossil fuel-based, are one of the prolific topics of debate in modern society. With climate change now becoming a primary focus for scientists and innovators of today, one of the areas for the largest amount of potential and growth is that of the capturing and utilization of Solar Energy. This method involves using a mechanical system to track the progression of the sun as it traverses the sky throughout the day. A dual-axis solar tracker such as the one designed and built for this project, can follow the sun both azimuthally and in …


Recovering Lost Information From Avocational Projectile Point Collections, Mackenzie Hughes Jan 2020

Recovering Lost Information From Avocational Projectile Point Collections, Mackenzie Hughes

All Master's Theses

Human prehistory in North America has sparked the interest of private citizens for decades, sometimes leading to an accumulation of avocational artifact collections that lack site-level provenience. The Wild/Clymer artifacts (n = 1,371) are one such collection where precise site provenience was lost. The analysis aims to recover regional provenience by using morphology, raw material sourcing, and typology to create a data set. The avocational collection data set was analyzed by comparing it to the professionally recorded archaeological data sets from within 100 miles of Frenchglen, Oregon. A paradigmatic classification approach identified 606 typeable points in the avocational collection, in …


Comparing Rusle Ls Calculation Methods Across Varying Dem Resolutions, Amanda Moody Jan 2020

Comparing Rusle Ls Calculation Methods Across Varying Dem Resolutions, Amanda Moody

All Master's Theses

Soil erosion is a global problem that reduces land productivity and causes environmental degradation. Soil erosion models, such as the Revised Universal Soil Loss Equation (RUSLE), are used to estimate the severity and distribution of erosion. The topographic factor (LS), which combines slope length and angle, is an important part of RUSLE. This work compared two methods of L calculation, the grid cumulation (GC) and the contributing area (CA) methods, and two methods of S calculation, the neighborhood (NBR) and maximum downhill slope (MDS) methods. These were compared across digital elevation models (DEMs) of 1, 5, 10, and 30m resolutions. …


Sampling The Local Fare: Fishes At The Sam Israel House Pit (45gr76), Soap Lake, Washington, Adam Fruge Jan 2020

Sampling The Local Fare: Fishes At The Sam Israel House Pit (45gr76), Soap Lake, Washington, Adam Fruge

All Master's Theses

The Sam Israel site is a precontact archaeological complex with numerous fish bones at the north end of Soap Lake, Washington. Excavated in 1976, the fish remains recovered from there were never fully analyzed prior to this research. Since this inland Columbia Plateau site had thousands of fish bones, it contained untapped potential for our understanding of ancient local fish procurement. As such, I conducted a detailed analysis of 2,862 fish bone specimens from the Sam Israel House Pit locus to: study a larger sample of fish bones in greater detail than was done before; compare the distribution of fishes …


Holocene Periods Of Aggradation And Incision, Hanson Creek, Washington, Levi Earl Windingstad Jan 2019

Holocene Periods Of Aggradation And Incision, Hanson Creek, Washington, Levi Earl Windingstad

All Master's Theses

The causes and timing of cycles of aggradation and incision in the Hanson Creek drainage in central Washington provide insight into changes in channel morphology and paleoenvironment within the region over the last 8000 years. Stratigraphically and spatially coincident archaeological evidence reveals information related to human occupation during the latter half of the epoch. Using LiDAR imagery and field surveys, recent processes such as degree of modern channel incision, accumulation of valley floor sediment, channel morphology and gradient were evaluated. The spatial distribution of these channel characteristics was assessed in relation to proximal landforms such as colluvial deposits, basalt outcrops, …


Holocene Fire History Reconstruction Of A Mid-Evaluation Mixed-Conifer Forest In The Eastern Cascades, Washington, Zoe Rushton Jan 2019

Holocene Fire History Reconstruction Of A Mid-Evaluation Mixed-Conifer Forest In The Eastern Cascades, Washington, Zoe Rushton

All Master's Theses

Fire histories of mid-elevation mixed-conifer forests (MEMC) are uncommon, particularly in the eastern Cascades of Washington. As a result, fire regimes and the effects of 20th century fire suppression in these forests are not well understood. In the summer of 2014 a 7.80 meter-long sediment core was extracted from Long Lake, located approximately 45 km west of Yakima, WA, which exists in a grand fir-dominated mixed-conifer forest. Fire activity for the Long Lake watershed was reconstructed using macroscopic charcoal analysis and pollen analysis was used to reconstruct vegetation change through time. Charcoal results show low fire activity in the early …


Measuring Trace Element Concentrations In Artiodactyl Cannonbones Using Portable X-Ray Fluorescence, Joshua L. Henderson Jan 2019

Measuring Trace Element Concentrations In Artiodactyl Cannonbones Using Portable X-Ray Fluorescence, Joshua L. Henderson

All Master's Theses

Artiodactyl bones are the most common faunal remains found in Washington prehistoric archaeology sites, but they are often too fragmented to accurately identify a family, genus, or species. Traditional faunal analysis can only organize unidentifiable bone fragments into size class, and chemical methods often require the destruction of bone samples. In this thesis research, I tested a new, nondestructive faunal analysis technique using portable X-ray fluorescence (pXRF) to measure trace element concentrations in comparative collection and archaeological bone samples. Using cannonbones from five different artiodactyl species, I collected trace element data from 50 comparative collection specimens and 18 archaeological specimens …


On Central Branch/Reinsurance Risk Networks: Exact Results And Heuristics, Florin Avram, Sooie-Hoe Loke Apr 2018

On Central Branch/Reinsurance Risk Networks: Exact Results And Heuristics, Florin Avram, Sooie-Hoe Loke

Mathematics Faculty Scholarship

Modeling the interactions between a reinsurer and several insurers, or between a central management branch (CB) and several subsidiary business branches, or between a coalition and its members, are fascinating problems, which suggest many interesting questions. Beyond two dimensions, one cannot expect exact answers. Occasionally, reductions to one dimension or heuristic simplifications yield explicit approximations, which may be useful for getting qualitative insights. In this paper, we study two such problems: the ruin problem for a two-dimensional CB network under a new mathematical model, and the problem of valuation of two-dimensional CB networks by optimal dividends. A common thread between …


Retrospective Analysis And Prediction: Artificial Intelligence And Its Applications In Libraries, Ping Fu Mar 2018

Retrospective Analysis And Prediction: Artificial Intelligence And Its Applications In Libraries, Ping Fu

Library Scholarship

The application of Artificial Intelligence (AI) has brought significant innovation to fundamental science and research in recent years. This paper briefly reviews and analyzes the findings of research and development of AI technologies such as expert systems, natural language processing, pattern recognition, robotics and machine learning in the fields of library such as information retrieval, reference service, cataloging, classification, acquisitions, circulation and automation. By reviewing and analyzing research papers published on respected academic journals, studying the examples and practical cases of the latest AI applications in industry, this study finds that current AI applications in the field of library are …


Geomorphic Consequences Of Hydroelectricity And Transportation Development Near Celilo Falls, Lower Mid-Columbia River, Washington, Noah I. Oliver Jan 2018

Geomorphic Consequences Of Hydroelectricity And Transportation Development Near Celilo Falls, Lower Mid-Columbia River, Washington, Noah I. Oliver

All Master's Theses

Along the Columbia River, hundreds of miles of transportation infrastructure and over sixty hydroelectric dams have been constructed. This altered a rich cultural landscape with evidence of 10,000 years of continuous occupation. Researchers have attempted to understand the impacts of anthropogenic factors on the Columbia River, focusing on the riverine environment. However, the effect of transportation and hydroelectricity developments to eolian landforms on the floodplains and adjoining slopes have not been studied. Focusing on 2,800 acres near Celilo Falls, this study 1) establishes a baseline condition of eolian landforms from 1805 to 1900; 2) conducts an air photo increment analysis …


Water Demand, Adaptive Capacity, And Drought: An Analysis Of The Upper Klamath Basin, Oregon And California, Patricia Snyder Jan 2018

Water Demand, Adaptive Capacity, And Drought: An Analysis Of The Upper Klamath Basin, Oregon And California, Patricia Snyder

All Master's Theses

Freshwater demand and scarcity issues are an issue of global concern, in particular for the American West as global climate models suggest precipitation regime changes and an increase of drought. This research conducts a case-study of the Upper Klamath Basin, located in south-central Oregon and northern California, a microcosm of the arid and semi-arid American West that experienced an economically, socially, and ecologically impactful drought in the early 2000s. Through a mixture of qualitative and quantitative methods this research: 1) identifies key stakeholders, their goals and key policies; 2) conducts an adaptive capacity assessment of water management within the basin; …


The Origin Of Dark Mats At The Sunrise Ridge Borrow Pit Site (45pi408) Mount Rainier National Park, Washington, Sean Stcherbinine Jan 2018

The Origin Of Dark Mats At The Sunrise Ridge Borrow Pit Site (45pi408) Mount Rainier National Park, Washington, Sean Stcherbinine

All Master's Theses

The Sunrise Ridge Borrow Pit Site is a precontact archaeological site located in the upland forest soils of Mount Rainier National Park. Site stratigraphy is complicated, consisting of tephra deposits from mostly known origins that are intercalated with dark sediments of unknown origin, referred to here as dark mats. Precontact occupation has been split previously into two components based on the ambiguous depositional history of the dark mats, notably their unknown parent material, depositional environment, and relationship with adjacent tephra strata. Stratigraphic samples from excavation units, features, and one off-site excavation unit was used to investigate these data gaps. Grain …


Data Potential Of Archaeological Deposits At The Chelan Station Site, Matthew J. Breidenthal Jan 2017

Data Potential Of Archaeological Deposits At The Chelan Station Site, Matthew J. Breidenthal

All Master's Theses

The Chelan Station Site (45CH782/783), located along the Rocky Reach of the Columbia River, includes lithic and faunal artifacts buried beneath volcanic tephra from Mt. Mazama (6,830 BP). Artifacts were inadvertently discovered in buried soils within a secondary alluvial terrace during construction of a pipeline to supply water to the Beebe Springs Fish Hatchery. This thesis stems from participation in original field work and includes the author’s own models of early land forms and site formation. The study reviews the construction monitoring and archaeological testing of both sites, and documents the archaeological data potential early occupations of the vicinity. The …


Why Now?: A Case Study Of Split Estate And Fracking Activity In Garfield County Colorado, Janessa Zucchetto Jan 2017

Why Now?: A Case Study Of Split Estate And Fracking Activity In Garfield County Colorado, Janessa Zucchetto

All Master's Theses

This research examines the socio-environmental impacts associated with hydraulic fracturing activities and issues of split estate in Battlement Mesa Planned Unit Development in Garfield County, CO. Data for this research was collected during 2 months in the summer of 2015 using a series of ethnographic research methods. In doing so, this research adopts political ecology and political economy of nature as theoretical frameworks to understand the interconnections that exist between local impacts of fracking activities and a national strategy to secure gas markets internationally. I argue that the socio-environmental impacts associated with hydraulic fracturing in Garfield County, CO are not …


Monitoring Reduction Efforts For Pm2.5 In Ellensburg,Wa Using Community-Based Social Marketing To Examine Behavioral Change, Kelsey Gibbs Jan 2017

Monitoring Reduction Efforts For Pm2.5 In Ellensburg,Wa Using Community-Based Social Marketing To Examine Behavioral Change, Kelsey Gibbs

All Master's Theses

In 2011, Ellensburg, Washington was labeled by the Washington Department of Ecology as being vulnerable for violating National Ambient Air Quality Standards for particulate pollution (PM2.5­). In the Kittitas Basin, winter-time frequent air inversions and stagnant air events trap pollution near the ground, elevating pollutant concentrations during winter months. Wood smoke from household burning has been identified by mobile PM2.5 monitoring completed in 2015 as the primary source of PM­2.5. This research utilizes community-based social marketing techniques to encourage behavioral change for wood burning in a targeted neighborhood in Ellensburg. Residents of the target neighborhood …


Using Data Analytics To Further Understand The Role That Boredom, Loneliness, Social Anxiety, Social Gratification, And Social Relationships (Brag) Play In A Driver’S Decision To Text, Nathan White, Yair Levy, Steven R. Terrell, Steve Bronsburg Jan 2016

Using Data Analytics To Further Understand The Role That Boredom, Loneliness, Social Anxiety, Social Gratification, And Social Relationships (Brag) Play In A Driver’S Decision To Text, Nathan White, Yair Levy, Steven R. Terrell, Steve Bronsburg

All Faculty Scholarship for the College of Education and Professional Studies

Texting while driving is a growing problem that current efforts have failed to curtail. This behavior has serious, and sometimes fatal, consequences, and the factors that cause a driver to text are not well understood. This study investigates the influence that boredom, social relationships, social anxiety, and social gratification (BRAG) have upon the texting driver. A survey instrument was used to collect data from 297 respondents at a mid-sized regional university in the Pacific Northwest of the United States. The data was evaluated with PLS-SEM, which indicated that social gratification plays a very significant role in a driver’s decision to …


Defining Biodiversity: A Local Assessment Of The Tahuayo River, Peru Using Self-Directed Photography, Rozsika D. Steele Jan 2016

Defining Biodiversity: A Local Assessment Of The Tahuayo River, Peru Using Self-Directed Photography, Rozsika D. Steele

All Master's Theses

The Área de Conservación Regional Comunal Tamshiyacu Tahuayo (ACRCTT), located in Loreto, Peru, protects 420,000 hectares of the Amazon basin. In 2009, the ACRCTT received formal government recognition after three decades of advocacy and conservation work by resident communities. Local resource users who live a subsistence lifestyle possess sophisticated Traditional Ecological Knowledge (TEK) that can be used to identify which constituents of biodiversity are culturally relevant. This information can help resource managers develop an operational definition of biodiversity. Self-directed photography is a research method that allows participants the opportunity to direct data collection and empowers them to visually communicate their …


Using Satellite Image Analysis For Locating Prehistoric Archaeological Sites In Alaska's Central Brooks Range, Robert Hickey, J. Keeney Jun 2015

Using Satellite Image Analysis For Locating Prehistoric Archaeological Sites In Alaska's Central Brooks Range, Robert Hickey, J. Keeney

Geography Faculty Scholarship

In this pilot study, we apply satellite image analysis to archaeological site prospection in Alaska's Brooks Range. Our goal was to test whether satellite remote sensing, which has been successful in locating large archaeological features associated with sedentary peoples, could be applied to arctic interior sites associated with mobile hunter–gatherers. In particular, we strove to develop a relatively straightforward and inexpensive model using existing data which could be used to help guide archaeology surveys. Using 1-m resolution IKONOS imagery of Lake Matcharak along the upper Noatak River, we produced a Normalized Difference Vegetation Index (NDVI) and tasseled cap transformation of …


Eastern Washington Wildfires: Tracking Land Recovery In The Colockum Tarps Wildfire Area, Michael Balda, Allison Shinn May 2015

Eastern Washington Wildfires: Tracking Land Recovery In The Colockum Tarps Wildfire Area, Michael Balda, Allison Shinn

Symposium Of University Research and Creative Expression (SOURCE)

Eastern Washington State has seen an increase in wildfire activity because of policies of fire suppression and changing climate. The Colockum Tarps wildfire started on July 27, 2013, in Malaga, Washington, due to a water pump malfunction. After ignition, the fire quickly moved south-southwest and burned a total area of 80,408 acres of grasslands and forest. We combined fieldwork and geospatial analysis of aerial photography and satellite imagery to examine vegetative recovery within the fire area. Using ArcGIS and PCI Geomatica, we analyzed 2013 National Agricultural Imaging Program (NAIP) images and a wildfire perimeter shapefile from the Bureau of Land …


Mountain Passes And Saddle Points, James Bisgard May 2015

Mountain Passes And Saddle Points, James Bisgard

All Faculty Scholarship for the College of the Sciences

Variational methods find solutions of equations by considering a solution as a critical point of an appropriately chosen function. Local minima and maxima are well-known types of critical points. We explore methods for finding critical points that are neither local maxima or minima, but instead are mountain passes or saddle points. Criteria for the existence of minima or maxima are well known, but those for mountain passes or saddle points are less well known. We give an accessible treatment of some criteria for the existence of such points (including the mountain pass lemma), as well as describe a method that …