Understanding exponential growth is of critical importance in sustainability, resource conservation, and economics. This work contains a collection of practice problems and realistic case studies developed for the teaching of sustainability science and conservation, with an emphasis on learning and applying the concepts of exponential growth. The exercises are designed to foster quantitative competence (numeracy) as well as critical thinking and systems thinking. Students learn to work with tools such as spreadsheet software and online databases and practice the application of basic but powerful quantitative analyses techniques. The case studies are based on recent, high quality data and explore questions of high relevance for the study and application of sustainability science. This work is related to the Growth in a finite world presentation (http://www.slideshare.net/amenning/growth-in-a-finite-world-sustainability-and-the-exponential-function).]]>

Understanding exponential growth is of critical importance in sustainability, resource conservation, and economics. This work contains a collection of practice problems and realistic case studies developed for the teaching of sustainability science and conservation, with an emphasis on learning and applying the concepts of exponential growth. The exercises are designed to foster quantitative competence (numeracy) as well as critical thinking and systems thinking. Students learn to work with tools such as spreadsheet software and online databases and practice the application of basic but powerful quantitative analyses techniques. The case studies are based on recent, high quality data and explore questions of high relevance for the study and application of sustainability science. This work is related to the Growth in a finite world presentation (http://www.slideshare.net/amenning/growth-in-a-finite-world-sustainability-and-the-exponential-function).]]>

Understanding exponential growth is of critical importance in sustainability, resource conservation, and economics. This article provides a rigorous yet accessible introduction to this essential concept. It also provides a selection of practice problems that will help students apply and deepen their understanding of the material. This article accompanies my lecture presentation "Growth in a Finite World - Sustainability and the Exponential Function" (http://www.slideshare.net/amenning/growth-in-a-finite-world-sustainability-and-the-exponential-function). Also refer to Case Studies for Sustainability Education: Understanding Exponential Growth (http://www.slideshare.net/amenning/exponential-growth-casestudies).]]>

Understanding exponential growth is of critical importance in sustainability, resource conservation, and economics. This article provides a rigorous yet accessible introduction to this essential concept. It also provides a selection of practice problems that will help students apply and deepen their understanding of the material. This article accompanies my lecture presentation "Growth in a Finite World - Sustainability and the Exponential Function" (http://www.slideshare.net/amenning/growth-in-a-finite-world-sustainability-and-the-exponential-function). Also refer to Case Studies for Sustainability Education: Understanding Exponential Growth (http://www.slideshare.net/amenning/exponential-growth-casestudies).]]>

A lecture in Quantitative Sustainability It is often claimed that agricultural productivity needs to be increased in order to feed a growing world population. Food security depends on several factors besides the productivity, including waste/efficiency, energy crops, meat consumption, and global justice and equity. This lecture explores the issue of food security in its many dimensions and teaches how to use a high-level systems approach in sustainability science.]]>

A lecture in Quantitative Sustainability It is often claimed that agricultural productivity needs to be increased in order to feed a growing world population. Food security depends on several factors besides the productivity, including waste/efficiency, energy crops, meat consumption, and global justice and equity. This lecture explores the issue of food security in its many dimensions and teaches how to use a high-level systems approach in sustainability science.]]>

The problems below are a selection of real world problems developed for the teaching of sustainability/conservation related College classes. The exercises are designed to foster quantitative competence (numeracy) as well as critical thinking and systems thinking. They are basic but realistic and all data used are taken from the published scientific literature and from public online databases maintained by official organizations such as FAO and EIA. No advanced Mathematics is required, yet these problems are challenging for most students. Many students need help to overcome a certain math anxiety or even phobia. These exercises must be accompanied by intensive discussion, assistance, and feedback. Students who complete these assignments successfully experience the power of even basic quantitative methods. They learn that informed citizens do not have to rely solely upon the advice of experts – with reasonable effort they can gather and interpret information and come up with approximate answers to important, non-trivial real world questions.]]>

The problems below are a selection of real world problems developed for the teaching of sustainability/conservation related College classes. The exercises are designed to foster quantitative competence (numeracy) as well as critical thinking and systems thinking. They are basic but realistic and all data used are taken from the published scientific literature and from public online databases maintained by official organizations such as FAO and EIA. No advanced Mathematics is required, yet these problems are challenging for most students. Many students need help to overcome a certain math anxiety or even phobia. These exercises must be accompanied by intensive discussion, assistance, and feedback. Students who complete these assignments successfully experience the power of even basic quantitative methods. They learn that informed citizens do not have to rely solely upon the advice of experts – with reasonable effort they can gather and interpret information and come up with approximate answers to important, non-trivial real world questions.]]>

A helix is a curve that in every point makes a constant angle with a fixed direction, and a slant helix is a curve with a principal normal that has this property. In this paper, the natural equations of the slant helix are developed and an explicit parametrization of its Frenet apparatus is given. To this goal, a general method is presented for transforming a Frenet space curve into a successor curve, which has the predecessor’s tangent as principal normal. Helices are exactly the successor curves of plane curves and slant helices are the successor curves of helices. By the same method, an infinite series of successor curves can be constructed. The new method is not restricted to curves with positive curvature. To achieve maximal generality, the paper first gives a generalization of conventional Frenet theory. Bishop frames are examined along with Frenet frames as a useful tool in the theory of space curves.]]>

A helix is a curve that in every point makes a constant angle with a fixed direction, and a slant helix is a curve with a principal normal that has this property. In this paper, the natural equations of the slant helix are developed and an explicit parametrization of its Frenet apparatus is given. To this goal, a general method is presented for transforming a Frenet space curve into a successor curve, which has the predecessor’s tangent as principal normal. Helices are exactly the successor curves of plane curves and slant helices are the successor curves of helices. By the same method, an infinite series of successor curves can be constructed. The new method is not restricted to curves with positive curvature. To achieve maximal generality, the paper first gives a generalization of conventional Frenet theory. Bishop frames are examined along with Frenet frames as a useful tool in the theory of space curves.]]>

Basic ideas in Ecological Economics]]>

Basic ideas in Ecological Economics]]>

A treatise in classical curve theory featuring the development of the complete theory of Frenet frames and the Frenet equations, and the derivation of explicit representations of important curve classes (Helices, Curves of Constant Precession, Slant Helices)]]>

A treatise in classical curve theory featuring the development of the complete theory of Frenet frames and the Frenet equations, and the derivation of explicit representations of important curve classes (Helices, Curves of Constant Precession, Slant Helices)]]>

Geographically referenced US census data provide a large amount of information about the extent of urbanization and land consumption. Population count, the number of housing units and their vacancy rates, and demographic and economic parameters such as racial composition and household income, and their change over time, can be examined at different levels of geographic resolution to observe patterns of urban flight, suburbanization, and reurbanization. This paper will review the literature on prior application of census data in a geospatial setting. It will identify strengths and weaknesses and address methodological challenges of census-based approaches to the study of urbanization. Of special interest will be literature comparing and/or integrating census data with alternative methodologies, e.g. based on Remote Sensing. The general purpose of this paper is to lay the groundwork for the optimal use of high resolution census data in studying urbanization in the United States. Review paper by Toni Menninger, 2012 ]]>

Geographically referenced US census data provide a large amount of information about the extent of urbanization and land consumption. Population count, the number of housing units and their vacancy rates, and demographic and economic parameters such as racial composition and household income, and their change over time, can be examined at different levels of geographic resolution to observe patterns of urban flight, suburbanization, and reurbanization. This paper will review the literature on prior application of census data in a geospatial setting. It will identify strengths and weaknesses and address methodological challenges of census-based approaches to the study of urbanization. Of special interest will be literature comparing and/or integrating census data with alternative methodologies, e.g. based on Remote Sensing. The general purpose of this paper is to lay the groundwork for the optimal use of high resolution census data in studying urbanization in the United States. Review paper by Toni Menninger, 2012 ]]>

The "Tragedy of the Commons" is one of the most influential scientific publications ever yet it is widely misunderstood. The short presentation provides a critical appraisal and links to read more.]]>

The "Tragedy of the Commons" is one of the most influential scientific publications ever yet it is widely misunderstood. The short presentation provides a critical appraisal and links to read more.]]>

]]>

]]>

A presentation about the Human Population Challenge developed for students in sustainability, including current data, basic demographic concepts, and a discussion of sustainability related issues. The presentation "Growth in a Finite World" is closely related and precedes this lecture. The presentation "Energy Sustainability" is also suitable as a follow-up lecture.]]>

A presentation about the Human Population Challenge developed for students in sustainability, including current data, basic demographic concepts, and a discussion of sustainability related issues. The presentation "Growth in a Finite World" is closely related and precedes this lecture. The presentation "Energy Sustainability" is also suitable as a follow-up lecture.]]>

This presentation is an introduction to the sustainable energy challenge. It gives an overview over fossil fuels, the laws of energy, energy efficiency and conservation, and renewable energy sources. The focus is on providing students with the scientific tools for understanding the magnitude of the challenge and analyzing potential solutions.]]>

This presentation is an introduction to the sustainable energy challenge. It gives an overview over fossil fuels, the laws of energy, energy efficiency and conservation, and renewable energy sources. The focus is on providing students with the scientific tools for understanding the magnitude of the challenge and analyzing potential solutions.]]>

This presentation, accessible to the general public and specifically designed for students of sustainability, explores the dramatic growth of the human sphere on planet Earth with its limited resources, and presents the mathematical tools for understanding the exponential function. The lecture is accompanied by the article "Exponential Growth, Doubling Time, and the Rule of 70" (http://www.slideshare.net/amenning/exponential-growthmath) and a collection of practice problems and case studies (http://www.slideshare.net/amenning/exponential-growth-casestudies). The presentation "The Human Population Challenge" is suitable as a follow-up lecture.]]>

This presentation, accessible to the general public and specifically designed for students of sustainability, explores the dramatic growth of the human sphere on planet Earth with its limited resources, and presents the mathematical tools for understanding the exponential function. The lecture is accompanied by the article "Exponential Growth, Doubling Time, and the Rule of 70" (http://www.slideshare.net/amenning/exponential-growthmath) and a collection of practice problems and case studies (http://www.slideshare.net/amenning/exponential-growth-casestudies). The presentation "The Human Population Challenge" is suitable as a follow-up lecture.]]>

]]>

]]>

]]>

]]>