This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking. Examples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a two-quarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, real-world framework. In all cases, the focus is clear: how does the math help us understand the science?
Developing Advanced Proficiency in Chinese through Debate provides lesson plans for holding high-level debates in the classroom. The lesson plans in this textbook were created based on the standards of the Oral Proficiency Interview held by the American Council on the Teaching of Foreign Languages. These lesson plans train students in advanced language tasks such as giving thorough descriptions and narrations, comparing abstract concepts, and establishing hypotheses. The lesson plans in this textbook will train students in dialectical thinking and give them opportunities to improve their ability to summarize, make inductions, and contrast hypotheses. The debate topics of each lesson plan emphasize areas that are familiar to the lives and interests of Western students while still allowing them to engage with differences between Chinese and Western culture. The lesson plans address a wide range of topics, such as employment, financial management, psychoactive drugs, and artificial intelligence. Furthermore, every lesson plan includes material to help students practice listening and contains lesson-specific vocabulary, discussion questions, debate prompts, debate tactics, and grammar practices. Accompanying e-resources are available at https://advancedchinese.byu.edu/. This book is suitable for students who have acquired high levels of proficiency in Chinese or who have taken at least three years of college level study of Chinese as their second language. Teachers will also be able to use the structure of the lesson plans in this textbook to assist them as they design assessments for their students.
This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking. Examples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a two-quarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, real-world framework. In all cases, the focus is clear: how does the math help us understand the science?
Developing Advanced Proficiency in Chinese through Debate provides lesson plans for holding high-level debates in the classroom. The lesson plans in this textbook were created based on the standards of the Oral Proficiency Interview held by the American Council on the Teaching of Foreign Languages. These lesson plans train students in advanced language tasks such as giving thorough descriptions and narrations, comparing abstract concepts, and establishing hypotheses. The lesson plans in this textbook will train students in dialectical thinking and give them opportunities to improve their ability to summarize, make inductions, and contrast hypotheses. The debate topics of each lesson plan emphasize areas that are familiar to the lives and interests of Western students while still allowing them to engage with differences between Chinese and Western culture. The lesson plans address a wide range of topics, such as employment, financial management, psychoactive drugs, and artificial intelligence. Furthermore, every lesson plan includes material to help students practice listening and contains lesson-specific vocabulary, discussion questions, debate prompts, debate tactics, and grammar practices. Accompanying e-resources are available at https://advancedchinese.byu.edu/. This book is suitable for students who have acquired high levels of proficiency in Chinese or who have taken at least three years of college level study of Chinese as their second language. Teachers will also be able to use the structure of the lesson plans in this textbook to assist them as they design assessments for their students.
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