Physical Sciences and Mathematics Commons^™

Introduction To Mathematical Analysis I - 3rd Edition, Beatriz Lafferriere, Gerardo Lafferriere, Mau Nam Nguyen

PDXOpen: Open Educational Resources

Video lectures explaining problem solving strategies are available

Our goal in this set of lecture notes is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.

The lecture notes contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. In addition, the notes include many carefully selected exercises of various levels …

An Introduction To Number Theory, J. J. P. Veerman

PDXOpen: Open Educational Resources

These notes are intended for a graduate course in Number Theory. No prior familiarity with number theory is assumed.

Chapters 1-14 represent almost 3 trimesters of the course. Eventually we intend to publish a full year (3 trimesters) course on number theory. The current content represents courses the author taught in the academic years 2020-2021 and 2021-2022.

It is a work in progress. If you have questions or comments, please contact Peter Veerman (veerman@pdx.edu).

Relativity Lite: A Pictorial Translation Of Einstein’S Theories Of Motion And Gravity, Jack C. Straton

PDXOpen: Open Educational Resources

Relativity Lite is designed for the General Astronomy sequence (PH 361-2U, SCI 315-6U) whose primary book glosses over Special Relativity and General Relativity while trying to explain the Cosmology that is based on those subjects. Relativity Lite translates the mathematical equations conventional relativity texts rely upon into pictures that are readily understood and contain within them the mathematical essentials. This book provides the comprehensive coverage needed to understand, in sufficient depth, these three linked areas of our reality.

Readers seeking this knowledge on their own, and those in other courses for nonscientists, may also find it helpful.

Adopt/Adapt
If you …

Lectures On Mathematical Computing With Python, Jay Gopalakrishnan

PDXOpen: Open Educational Resources

This open resource is a collection of class activities for use in undergraduate courses aimed at teaching mathematical computing, and computational thinking in general, using the python programming language. It was developed for a second-year course (MTH 271) revamped for a new undergraduate program in data science at Portland State University. The activities are designed to guide students' use of python modules effectively for scientific computation, data analysis, and visualization.

Adopt/Adapt
If you are an instructor adopting or adapting this open educational resource, please help us understand your use by filling out this form

Climate Toolkit: A Resource Manual For Science And Action - Version 2.0, Frank Granshaw

PDXOpen: Open Educational Resources

The Climate Toolkit is a resource manual designed to help the reader navigate the complex and perplexing issue of climate change by providing tools and strategies to explore the underlying science. As such it contains a collection of activities that make use of readily available on-line resources developed by research groups and public agencies. These include web-based climate models, climate data archives, interactive atlases, policy papers, and “solution” catalogs. Unlike a standard textbook, it is designed to help readers do their own climate research and devise their own perspective rather than providing them with a script to assimilate and repeat. …

Modeling Post-Fire Successional Trajectories Under Climate Change In Interior Alaska Using Landis Ii, Shelby A. Weiss

Systems Science Friday Noon Seminar Series

Alaska boreal forest ecosystems are experiencing a greater frequency of wildfire relative to the region’s historic fire regime. These increases in fire frequency, as well as annual burned area, increase the probability of forests re-burning within shorter intervals than were experienced historically. Such changes to the fire regime have the potential to shift successional trajectories in this ecosystem. To better understand potential changes in vegetation composition following short-interval, repeat fires, we are using LANDIS-II, a forest landscape model, to simulate changes in forest composition in response to climate change and increasing fire frequency. This seminar will include a description of …

Statistical Analysis Of Social Network Change, Teresa D. Schmidt

Systems Science Friday Noon Seminar Series

We explore two statistical methods that infer social network structures and statistically test those structures for change over time: regression-based differential network analysis (R-DNA) and information theory-based differential network analysis (I-DNA). RDNA is adapted from bioinformatics and I-DNA employs reconstructability analysis. Both methods are used to analyze Medicaid claims data from one-year periods before and after the formation of the Health Share of Oregon Coordinated Care Organization (CCO). We hypothesized that Health Share’s CCO formation would be followed by several changes in the healthcare delivery network.

Application of R-DNA and I-DNA to claims data involves three steps: (a) the inference …

A Computational Model For Recovery From Brain Injury, Wayne Wakeland

Systems Science Friday Noon Seminar Series

A computational simulation model calculates recovery trajectories following traumatic brain injury (TBI). Prior publications include a multi-scale framework for studying concussion and a systems-level causal loop diagram (CLD) and discussion of feedback processes. The scope of the computational model goes beyond concussion to include all severities of TBI. A set of first order ordinary differential equations and their associated parameters determines recovery trajectories. While highly speculative, the model serves to demonstrate the potential utility of computational models in this context. Much more research will be needed to create a properly supported research model that could be used for clinical trial …

Systems Thinking As A Design Process, Elizabeth Lockwood

Systems Science Friday Noon Seminar Series

During my master’s degree I analyzed sustainable practices in the built environment. What came from that work was a deep level of understanding that the current practices and rating systems appeared to be technical approaches to a larger system at play. I realized I have a gift to see hidden connections and find links between systems. Currently I use systems mapping as part of the design process to unearth the hidden elements in a system. I believe it is important to understand where designers, clients and stakeholders can insert themselves into a system. Part of this understanding is having empathy …

The Complexities Of Open Data, Hector Dominguez

Systems Science Friday Noon Seminar Series

Hector Dominguez is the current Open Data Coordinator at the City of Portland, and there are several lessons learned and strategies developed in the several months of work in this position. Hector will share some challenges on creating trusted and reliable data and information services, as well as the opportunities to work with Urban Data to resolve city challenges and to support achieving the City's goals in the coming years.

In this talk, Hector will share how modeling and defining the right metrics are not the only factors to implementing a citywide program, but rather, how ethics, communications and strategy …

Latent Space Models For Temporal Networks, Jasper Alt

Systems Science Friday Noon Seminar Series

In many contexts we may expect the structure of networks to be derived from some kind of abstract distance between actors. We refer to this phenomenon as homophily: like nodes connect to like. For example, people with similar beliefs may be more likely to form social relations.

We formalize this notion by positioning the nodes in a latent space representing the possible values of the homophilous attributes. Realistically, we should expect latent attributes like beliefs to change over time in some nontrivial way, and the structures of temporal networks to evolve accordingly. We introduce a model of latent space dynamics …

Systems Evolution And Engineering Thermodynamics, Terry Bristol

Systems Science Friday Noon Seminar Series

Despite impressive contributions, the philosophical foundations of systems theory remain in flux. In the practical context, the proper understanding of the relation of the systems framework to classical mechanics and quantum theory remains unresolved.

I argue our understanding of systems theory is advanced by recognizing the crucial link to engineering and thermodynamics. Engineering thermodynamics is more general than the historically dominant ‘rational mechanical’ thermodynamics of Clausius, Boltzmann, the Entropy Cult (viz. Jaynes’s MEP) and the recent information theory.

That systems theory’s philosophical foundations are in a philosophy of engineering and an engineering worldview should be no surprise, given the modern …

How To Be A Successful Organic Chemist, Alexander H. Sandtorv

PDXOpen: Open Educational Resources

How to be a successful organic chemist is meant as an introductory text for undergraduates taking organic chemistry teaching labs. The text is a clear and practical introduction to safety, chemical handling, organic chemistry techniques, and lab reports.

Adopt/Adapt
If you are an instructor adopting or adapting this PDXOpen textbook, please help us understand your use by filling out this form

Introduction To Mathematical Analysis I - 2nd Edition, Beatriz Lafferriere, Gerardo Lafferriere, Mau Nam Nguyen

PDXOpen: Open Educational Resources

Video lectures explaining problem solving strategies are available

Our goal in this set of lecture notes is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.

The lecture notes contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. The lecture notes also contain many well-selected exercises of various levels. Although …

Prediction: The Quintessential Model Validation Test, Wayne Wakeland

Systems Science Friday Noon Seminar Series

It is essential to objectively test how well policy models predict real world behavior. The method used to support this assertion involves the review of three SD policy models emphasizing the degree to which the model was able to fit the historical outcome data and how well model-predicted outcomes matched real world outcomes as they unfolded. Findings indicate that while historical model agreement is a favorable indication of model validity, the act of making predictions without knowing the actual data, and comparing these predictions to actual data, can reveal model weaknesses that might be overlooked when all of the available …

Mapping Human-Environment Connections On The Olympic Peninsula: An Atlas Of Landscape Values, Rebecca J. Mclain, Lee Cerveny, Diane Besser, David Banis, Alexa Todd, Stephanie Rohdy, Corinna Kimball-Brown

Occasional Papers in Geography

Occasional Papers in Geography Publication No. 7

The advent of computerized mapping has land managers’ ability to map the biophysical services provided by forested ecosystems. However, mapping the cultural services of those systems is more challenging. Human ecology mapping (HEM), which provides spatially-explicit depictions of the complex connections between humans and their environment, is an approach that can be used to improve understandings of the cultural services associated with landscapes. This atlas provides an overview of what HEM is and draws on experiences with a pilot project on the Olympic Peninsula in western Washington to illustrate what HEM data looks …

Civic Ecology: Living Community Systems For Sustainability, Tim Smith

Systems Science Friday Noon Seminar Series

Civic Ecology is a stakeholder-driven, whole systems framework for creating sustainable communities. The framework focuses on empowering citizens of all ages, cultures, and abilities to envision, create, and manage their community’s unique “software” -- the integrated energy, nutrient, water, waste, material, and food systems, as well as economic flows and cultural interactions that animate their place. Exploring and supporting these flows allows communities to enhance their local wealth (environmental, economic, and social), resilience, and competitiveness, and help them take control of designing and managing their future through collaboration and innovation. The Civic Ecology framework can be the foundation upon which …

The Intersection Between Science And Computer Science Is Almost Empty, Dick Hamlet

Systems Science Friday Noon Seminar Series

Traditionally, a science such as physics overlaps with mathematics and engineering in a way that has been astonishingly productive. The math provides precise expression for the science, which in turn supplies the engineering with the information it needs to exploit physical phenomena. Computer science naturally wishes to put itself in the center of the traditional picture as a science. Unfortunately, it won't wash. The `science' of programming is pure and simple mathematics, not science. The distinction is more than linguistic, since science and mathematics have quite distinct goals and methods. By making the wrong choice, computer science research has been …

Bayesian And Related Methods: Techniques Based On Bayes' Theorem, Mehmet Vurkaç

Systems Science Friday Noon Seminar Series

Bayes' theorem is a simple algebraic consequence of conditional probability. Yet, its consequences are critical to philosophy, society, and technology. Starting from its simple derivation, we will show how its interpretation in terms of base rates (priors) and class-conditional likelihoods illuminates everyday problems in medicine and law, and provides signal processing, communications, machine learning, model selection, and other applications of statistics with powerful classification and estimation tools. Next, we will briefly examine some of the ways in which this theorem can be adopted to include multiple attributes, contexts, hypotheses, and levels of risk. Methods derived from or related to Bayes’ …

Ecosystem Services: The Making Of A Metaphor We Live (?) By, Richard B. Norgaard

Systems Science Friday Noon Seminar Series

What started as a humble metaphor to help us think about our relation to nature has become integral to how we are addressing the future of humanity and the course of biological evolution. The metaphor of nature as a stock that provides a flow of services is insufficient for the difficulties we are in or the task ahead. Indeed, combined with the mistaken presumption that we can analyze a global problem within a partial equilibrium economic framework and reach a new economy project-by-project without major institutional change, the simplicity of the stock-flow framework blinds us to the complexity of the …

Systems Ideas For The Scientific And Societal Imperatives Of The Coastal Ocean: Case Of The Bp Oil Gusher In The Gulf Of Mexico, Spring & Summer 2010, Christopher Mooers

Systems Science Friday Noon Seminar Series

In recent decades, great progress has been made in advancing the scientific understanding of the coastal ocean (i.e., the 200 nautical mile Exclusive Economic Zone (EEZ)) across a broad set of disciplines. Simultaneously, the societal use of the coastal ocean has skyrocketed through, for example, increased shipping & boating, sports & commercial fishing, and exploitation of non-living resources, such as, oil & gas extraction and sand & gravel mining. International law and national policy assign coastal nations the responsibility for stewardship (i.e., wise management) of their respective EEZs. The scope of the stewardship and applications can be summarized as (1) …

Hardware Acceleration Of Inference Computing: The Numenta Htm Algorithm, Dan Hammerstrom

Systems Science Friday Noon Seminar Series

In this presentation I will describe the latest version of the Numenta HTM Cortical Learning Algorithm and why it is interesting for doing research into radical new computer architectures. Then I will discuss the hardware acceleration research we are doing, and briefly look at some preliminary applications development.

Integer Optimization And Computational Algebraic Topology, Bala Krishnamoorthy

Systems Science Friday Noon Seminar Series

We present recently discovered connections between integer optimization, or integer programming (IP), and homology. Under reasonable assumptions, these results lead to efficient solutions of several otherwise hard-to-solve problems from computational topology and geometric analysis. The main result equates the total unimodularity of the boundary matrix of a simplicial complex to an algebraic topological condition on the complex (absence of relative torsion), which is often satisfied in real-life applications . When the boundary matrix is totally unimodular, the problem of finding the shortest chain homologous under Z (ring of integers) to a given chain, which is inherently an integer program, can …

Systems Views Of The Economics Of Sustainable Development, Joshua Hughes

Systems Science Friday Noon Seminar Series

The mainstream economics of the 20th century (and now 21st century) has often failed to predict what will happen--or explain what has happened--in the real world, even with (or because of?) an ever-increasing reliance on quantitative and computational methods. Since the mid-20th century a number of people part of, or closely associated with, the systems community--economists among them--have provided insights about what is wrong with "traditional" economics. Systems science offers a number of alternative methods for understanding economic systems that take heed of these criticisms, especially in the context of sustainable development. Yet, while promising, few of these alternatives …

Higher-Level Application Of Adaptive Dynamic Programming/Reinforcement Learning – A Next Phase For Controls And System Identification?, George G. Lendaris

Systems Science Friday Noon Seminar Series

Humans have the ability to make use of experience while performing system identification and selecting control actions for changing situations. In contrast to current technological implementations that slow down as more knowledge is stored, as more experience is gained, human processing speeds up and has enhanced effectiveness. An emerging experience-based (“higher level”) approach promises to endow our technology with enhanced efficiency and effectiveness.

The notions of context and context discernment are important to understanding this human ability. These are defined as appropriate to controls and system-identification. Some general background on controls, Dynamic Programming, and Adaptive Critic leading to Adaptive Dynamic …

Building A Decision Aid Right-Side-Out, Barry F. Anderson

Systems Science Friday Noon Seminar Series

Tools have long been available for improving decision making, yet people who have knowledge of these tools seem reluctant to use them. I consider multiple reasons why this might be so and consider multiple solutions, then present what I believe to be the world's most user-friendly decision aid, which is now nearly ready for beta testing and available at no cost at http://wisedecider.net.

Wise Decider is believed to be unique in having the following features:

1. A creative thinking guide and a critical thinking guide that provide context-sensitive advice for problem structuring, evaluation, and implementation.
2. A decision table with cells …

Modal Logic And Its Applications, Explained Using Puzzles And Examples, Marek Perkowski

Systems Science Friday Noon Seminar Series

The talk introduces Modal Logic as an extension of classical propositional and First Order Logics. We discuss motivations of Lewis to create modal logic system, axioms and rules of proof. Several examples illustrate deriving theorems from axioms. "Muddy Children" puzzle is used to explain the principles of dealing with uncertainty problems where a temporal lack of response is used as additional information. Other examples include "Narrow Bridge" problem/game which relates to the problem of necessary evil in the world, robot planning and law and robot morality problems, especially related to military robots and use of force by police. Kripke semantics …

Some Problems And Solutions In The Experimental Science Of Technology: The Proper Use And Reporting Of Statistics In Computational Intelligence, With An Experimental Design From Computational Ethnomusicology, Mehmet Vurkaç

Systems Science Friday Noon Seminar Series

Statistics is the meta-science that lends validity and credibility to The Scientific Method. However, as a complex and advanced Science in itself, Statistics is often misunderstood and misused by scientists, engineers, medical and legal professionals and others. In the area of Computational Intelligence (CI), there have been numerous misuses of statistical techniques leading to the publishing of insupportable results, which, in addition to being a problem in itself, has also contributed to a degree of rift between the Statistics/Statistical Learning community and the Machine Learning/Computational Intelligence community. This talk surveys a number of misuses of statistical inference in CI settings, …

On The Effect Of Criticality And Topology On Learning In Random Boolean Networks, Alireza Goudarzi

Systems Science Friday Noon Seminar Series

Random Boolean networks (RBN) are discrete dynamical systems composed of N automata with a binary state, each of which interacts with other automata in the network. RBNs were originally introduced as simplified models of gene regulation. In this presentation, I will present recent work done conjointly with Natali Gulbahce (UCSF), Thimo Rohlf (MPI, CNRS), and Christof Teuscher (PSU). We extend the study of learning in feedforward Boolean networks to random Boolean networks (RBNs) and systematically explore the relationship between the learning capability, the network topology, the system size N, the training sample T, and the complexity of the computational task. …

Information Disclosure And Environmental Performance, Mark Stephan

Systems Science Friday Noon Seminar Series

Scholars and policymakers increasingly argue that information disclosure programs such as the Toxics Release Inventory (TRI) should be used to supplement conventional environmental regulation. Yet we lack a clear understanding of how such programs work as well as the empirical data to confirm their success in achieving environmental quality objectives. To better understand the impacts of environmental information disclosure on corporate decision making, this paper develops an analytic framework drawn from theories of risk perception and communication, individual and corporate decision making, and social capital. I examine the importance of the TRI for facility level behavior through an analysis of …