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Active Prelude to Calculus: Empowering the Next Generation of Innovators
By Dr. Evelyn Reed, PhD
Dr. Evelyn Reed is a Professor of Mathematics Education at Stanford University, specializing in innovative teaching methodologies and the application of mathematics in STEM fields. She has authored several textbooks and published extensively on the pedagogical benefits of active learning in mathematics.
Published by: Springer Nature – A leading global scientific publisher with a strong reputation for high-quality research and educational materials.
Edited by: Dr. Mark Johnson, PhD – A seasoned editor with over 15 years of experience in mathematics publishing and a proven track record of producing impactful educational resources.
Abstract: This article explores the transformative impact of an "active prelude to calculus" approach on student learning and its significant implications for various industries. We delve into the benefits of hands-on, inquiry-based learning in preparing students for the rigors of calculus and beyond, highlighting its contributions to problem-solving skills, critical thinking, and a deeper understanding of fundamental mathematical concepts. We examine how this active approach fosters a more robust and applicable mathematical foundation crucial for success in STEM-related careers.
What is an Active Prelude to Calculus?
Traditional calculus instruction often focuses on rote memorization and procedural techniques. This passive approach can leave students struggling to grasp the underlying concepts and apply them to real-world problems. An "active prelude to calculus" dramatically shifts this paradigm. It emphasizes active learning strategies, collaborative problem-solving, and real-world applications to build a solid foundation before formal calculus instruction. This prelude isn't simply a pre-calculus course; it's a fundamentally different approach to learning the foundational concepts necessary for calculus success.
This active prelude to calculus utilizes various pedagogical techniques, including:
Inquiry-based learning: Students actively participate in investigating mathematical concepts through exploration and experimentation, rather than passively receiving information.
Collaborative problem-solving: Group work and peer interaction are encouraged, fostering teamwork and communication skills crucial in many industries.
Real-world applications: Problems are contextualized within relevant fields, demonstrating the practical utility of mathematical concepts. This connects abstract ideas to tangible situations, making learning more engaging and meaningful.
Technology integration: Tools like graphing calculators and dynamic geometry software are used to visualize concepts and facilitate exploration.
Formative assessment: Continuous feedback and assessment are integrated into the learning process, allowing students to track their progress and identify areas for improvement.
The Benefits of an Active Prelude to Calculus
The benefits of an active prelude to calculus are far-reaching and extend beyond improved calculus performance. Students who engage in this approach often exhibit:
Increased conceptual understanding: A deeper grasp of fundamental mathematical concepts, leading to greater problem-solving proficiency.
Enhanced critical thinking skills: The ability to analyze complex situations, identify patterns, and develop creative solutions.
Improved problem-solving abilities: Greater confidence and competence in tackling challenging mathematical problems.
Stronger mathematical communication skills: Improved ability to articulate mathematical ideas clearly and concisely, both verbally and in writing.
Increased self-efficacy: Greater belief in their own mathematical abilities and potential.
Industry Implications of an Active Prelude to Calculus
The impact of an active prelude to calculus extends far beyond the classroom, significantly influencing various industries that rely heavily on mathematical reasoning and problem-solving. Specifically, it strengthens the foundation for success in:
Engineering: Engineers rely heavily on calculus for design, analysis, and problem-solving. A strong foundation built through an active prelude to calculus ensures greater competence in these areas.
Data Science: The ability to analyze and interpret data effectively is crucial in data science. The critical thinking and problem-solving skills developed through this approach are directly transferable to this field.
Computer Science: Calculus forms the basis of many algorithms and computational techniques. A solid understanding of mathematical concepts improves the ability to design efficient and effective software.
Finance: Financial modeling and risk assessment often involve complex mathematical calculations. The analytical skills nurtured by an active prelude to calculus are essential for financial professionals.
Physics: Physics is deeply intertwined with calculus, and a strong mathematical foundation is vital for understanding and applying physical principles.
Preparing Students for the Demands of the Future
In an increasingly complex world driven by technological advancements, the need for individuals with strong mathematical and analytical skills is paramount. An active prelude to calculus provides a crucial stepping stone, empowering students with the skills and confidence to thrive in various STEM fields and beyond. This approach doesn't merely prepare students for calculus; it equips them with a flexible and adaptable mindset that serves them throughout their academic and professional journeys. It is an investment in a future workforce capable of tackling complex challenges with innovation and ingenuity.
Conclusion
The adoption of an active prelude to calculus marks a significant shift in mathematics education, offering substantial benefits for both students and industry. By fostering a deeper understanding of mathematical concepts, strengthening critical thinking skills, and promoting problem-solving abilities, this approach prepares students for success in various STEM fields and beyond. As we continue to navigate an increasingly data-driven and technologically advanced world, the importance of an active prelude to calculus cannot be overstated.
FAQs
1. What is the difference between a traditional pre-calculus course and an active prelude to calculus? A traditional pre-calculus course primarily focuses on procedural skills. An active prelude emphasizes conceptual understanding and problem-solving through active learning strategies.
2. How does an active prelude to calculus improve problem-solving skills? It encourages students to actively engage with problems, explore different approaches, and learn from their mistakes, leading to enhanced problem-solving abilities.
3. Is an active prelude to calculus suitable for all students? Yes, it caters to diverse learning styles by offering multiple avenues for engagement and understanding.
4. What types of technology are typically used in an active prelude to calculus? Graphing calculators, dynamic geometry software, and online learning platforms are frequently used.
5. How is formative assessment implemented in an active prelude to calculus? Formative assessments are integrated throughout the learning process, providing regular feedback to students and instructors.
6. What are the long-term benefits of an active prelude to calculus beyond college? It equips students with critical thinking, problem-solving, and analytical skills highly valued in various industries.
7. How can educators implement an active prelude to calculus in their classrooms? By incorporating inquiry-based learning, collaborative projects, and real-world applications into their teaching.
8. Are there any resources available to support teachers in implementing an active prelude to calculus? Yes, numerous professional development opportunities and teaching materials are available.
9. How does an active prelude to calculus benefit students who struggle with mathematics? It provides a more supportive and engaging learning environment, allowing students to build confidence and a stronger foundation.
Related Articles:
1. "The Efficacy of Inquiry-Based Learning in Pre-Calculus": This article investigates the effectiveness of inquiry-based learning in improving student understanding and performance in pre-calculus concepts.
2. "Collaborative Learning in Mathematics: A Meta-Analysis": This meta-analysis examines the impact of collaborative learning on student achievement in mathematics, focusing on various learning strategies.
3. "The Role of Technology in Enhancing Mathematics Education": This article explores the use of technology in enhancing mathematics education, specifically in pre-calculus and calculus courses.
4. "Real-World Applications of Calculus in Engineering": This article showcases the practical applications of calculus within different engineering disciplines, demonstrating its relevance to real-world problems.
5. "Developing Critical Thinking Skills in Mathematics through Problem-Solving": This article discusses strategies for fostering critical thinking skills in mathematics through engaging problem-solving activities.
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8. "Bridging the Gap: Connecting Pre-Calculus to Calculus Concepts": This article focuses on strategies for making the transition from pre-calculus to calculus smoother and more effective.
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| active prelude to calculus: Active Prelude to Calculus Matthew Boelkins, 2019-07-28 Active Prelude to Calculus is designed for college students who aspire to take calculus and who either need to take a course to prepare them for calculus or want to do some additional self-study. Many of the core topics of the course will be familiar to students who have completed high school. At the same time, we take a perspective on every topic that emphasizes how it is important in calculus. This text is written in the spirit of Active Calculus and is especially ideal for students who will eventually study calculus from that text. The reader will find that the text requires them to engage actively with the material, to view topics from multiple perspectives, and to develop deep conceptual understanding of ideas.Many courses at the high school and college level with titles such as college algebra, precalculus, and trigonometry serve other disciplines and courses other than calculus. As such, these prerequisite classes frequently contain wide-ranging material that, while mathematically interesting and important, isn't necessary for calculus. Perhaps because of these additional topics, certain ideas that are essential in calculus are under-emphasized or ignored. In Active Prelude to Calculus, one of our top goals is to keep the focus narrow on the following most important ideas. Those most important ideas include: functions as processes; average rate of change; a library of basic functions; families of functions that model important phenomena; the sine and cosine are circular functions; inverses of functions; exact values versus approximate ones; and long-term trends, unbounded behavior, and limits of functions. See more in the preface of the text at https: //activecalculus.org/prelude/preface-our-goals.html.The text is available in three different formats: HTML, PDF, and print, each of which is available via links on the landing page at https: //activecalculus.org/. The first two formats are free. |
| active prelude to calculus: Active Calculus 2018 Matthew Boelkins, 2018-08-13 Active Calculus - single variable is a free, open-source calculus text that is designed to support an active learning approach in the standard first two semesters of calculus, including approximately 200 activities and 500 exercises. In the HTML version, more than 250 of the exercises are available as interactive WeBWorK exercises; students will love that the online version even looks great on a smart phone. Each section of Active Calculus has at least 4 in-class activities to engage students in active learning. Normally, each section has a brief introduction together with a preview activity, followed by a mix of exposition and several more activities. Each section concludes with a short summary and exercises; the non-WeBWorK exercises are typically involved and challenging. More information on the goals and structure of the text can be found in the preface. |
| active prelude to calculus: Precalculus Sheldon Axler, 2017-08-21 Sheldon Axler's Precalculus: A Prelude to Calculus, 3rd Edition focuses only on topics that students actually need to succeed in calculus. This book is geared towards courses with intermediate algebra prerequisites and it does not assume that students remember any trigonometry. It covers topics such as inverse functions, logarithms, half-life and exponential growth, area, e, the exponential function, the natural logarithm and trigonometry. |
| active prelude to calculus: Advanced Calculus Harold M. Edwards, 1994-01-05 This book is a high-level introduction to vector calculus based solidly on differential forms. Informal but sophisticated, it is geometrically and physically intuitive yet mathematically rigorous. It offers remarkably diverse applications, physical and mathematical, and provides a firm foundation for further studies. |
| active prelude to calculus: Active Calculus Multivariable 2018 Steven Schlicker, David Austin, Matt Boelkins, 2018-07-30 Active Calculus Multivariable is different from most existing texts in at least the following ways: The style of the text requires students to be active learners; there are very few worked examples in the text, with there instead being 3 or 4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus ideas. Each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class. There are several WeBWorK exercises in each section along with additional challenging exercises. The book is open source and can be used as a primary or supplemental text. |
| active prelude to calculus: Precalculus Jay Abramson, 2018-01-07 Precalculus is adaptable and designed to fit the needs of a variety of precalculus courses. It is a comprehensive text that covers more ground than a typical one- or two-semester college-level precalculus course. The content is organized by clearly-defined learning objectives, and includes worked examples that demonstrate problem-solving approaches in an accessible way. Coverage and Scope Precalculus contains twelve chapters, roughly divided into three groups. Chapters 1-4 discuss various types of functions, providing a foundation for the remainder of the course. Chapter 1: Functions Chapter 2: Linear Functions Chapter 3: Polynomial and Rational Functions Chapter 4: Exponential and Logarithmic Functions Chapters 5-8 focus on Trigonometry. In Precalculus, we approach trigonometry by first introducing angles and the unit circle, as opposed to the right triangle approach more commonly used in College Algebra and Trigonometry courses. Chapter 5: Trigonometric Functions Chapter 6: Periodic Functions Chapter 7: Trigonometric Identities and Equations Chapter 8: Further Applications of Trigonometry Chapters 9-12 present some advanced Precalculus topics that build on topics introduced in chapters 1-8. Most Precalculus syllabi include some of the topics in these chapters, but few include all. Instructors can select material as needed from this group of chapters, since they are not cumulative. Chapter 9: Systems of Equations and Inequalities Chapter 10: Analytic Geometry Chapter 11: Sequences, Probability and Counting Theory Chapter 12: Introduction to Calculus |
| active prelude to calculus: Mathematics and Computation Avi Wigderson, 2019-10-29 From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography |
| active prelude to calculus: Introduction to Soergel Bimodules Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson, 2020-09-26 This book provides a comprehensive introduction to Soergel bimodules. First introduced by Wolfgang Soergel in the early 1990s, they have since become a powerful tool in geometric representation theory. On the one hand, these bimodules are fairly elementary objects and explicit calculations are possible. On the other, they have deep connections to Lie theory and geometry. Taking these two aspects together, they offer a wonderful primer on geometric representation theory. In this book the reader is introduced to the theory through a series of lectures, which range from the basics, all the way to the latest frontiers of research. This book serves both as an introduction and as a reference guide to the theory of Soergel bimodules. Thus it is intended for anyone who wants to learn about this exciting field, from graduate students to experienced researchers. |
| active prelude to calculus: Iterated Maps on the Interval as Dynamical Systems Pierre Collet, J.-P. Eckmann, 2009-08-25 Iterations of continuous maps of an interval to itself serve as the simplest examples of models for dynamical systems. These models present an interesting mathematical structure going far beyond the simple equilibrium solutions one might expect. If, in addition, the dynamical system depends on an experimentally controllable parameter, there is a corresponding mathematical structure revealing a great deal about interrelations between the behavior for different parameter values. This work explains some of the early results of this theory to mathematicians and theoretical physicists, with the additional hope of stimulating experimentalists to look for more of these general phenomena of beautiful regularity, which oftentimes seem to appear near the much less understood chaotic systems. Although continuous maps of an interval to itself seem to have been first introduced to model biological systems, they can be found as models in most natural sciences as well as economics. Iterated Maps on the Interval as Dynamical Systems is a classic reference used widely by researchers and graduate students in mathematics and physics, opening up some new perspectives on the study of dynamical systems . |
| active prelude to calculus: Precalculus James Stewart, L. Redlin, Saleem Watson, 2002 In this best selling Precalculus text, the authors explain concepts simply and clearly, without glossing over difficult points. This comprehensive, evenly-paced book provides complete coverage of the function concept and integrates substantial graphing calculator materials that help students develop insight into mathematical ideas. This author team invests the same attention to detail and clarity as Jim Stewart does in his market-leading Calculus text. |
| active prelude to calculus: Convex Optimization & Euclidean Distance Geometry Jon Dattorro, 2005 The study of Euclidean distance matrices (EDMs) fundamentally asks what can be known geometrically given onlydistance information between points in Euclidean space. Each point may represent simply locationor, abstractly, any entity expressible as a vector in finite-dimensional Euclidean space.The answer to the question posed is that very much can be known about the points;the mathematics of this combined study of geometry and optimization is rich and deep.Throughout we cite beacons of historical accomplishment.The application of EDMs has already proven invaluable in discerning biological molecular conformation.The emerging practice of localization in wireless sensor networks, the global positioning system (GPS), and distance-based pattern recognitionwill certainly simplify and benefit from this theory.We study the pervasive convex Euclidean bodies and their various representations.In particular, we make convex polyhedra, cones, and dual cones more visceral through illustration, andwe study the geometric relation of polyhedral cones to nonorthogonal bases biorthogonal expansion.We explain conversion between halfspace- and vertex-descriptions of convex cones,we provide formulae for determining dual cones,and we show how classic alternative systems of linear inequalities or linear matrix inequalities and optimality conditions can be explained by generalized inequalities in terms of convex cones and their duals.The conic analogue to linear independence, called conic independence, is introducedas a new tool in the study of classical cone theory; the logical next step in the progression:linear, affine, conic.Any convex optimization problem has geometric interpretation.This is a powerful attraction: the ability to visualize geometry of an optimization problem.We provide tools to make visualization easier.The concept of faces, extreme points, and extreme directions of convex Euclidean bodiesis explained here, crucial to understanding convex optimization.The convex cone of positive semidefinite matrices, in particular, is studied in depth.We mathematically interpret, for example,its inverse image under affine transformation, and we explainhow higher-rank subsets of its boundary united with its interior are convex.The Chapter on Geometry of convex functions,observes analogies between convex sets and functions:The set of all vector-valued convex functions is a closed convex cone.Included among the examples in this chapter, we show how the real affinefunction relates to convex functions as the hyperplane relates to convex sets.Here, also, pertinent results formultidimensional convex functions are presented that are largely ignored in the literature;tricks and tips for determining their convexityand discerning their geometry, particularly with regard to matrix calculus which remains largely unsystematizedwhen compared with the traditional practice of ordinary calculus.Consequently, we collect some results of matrix differentiation in the appendices.The Euclidean distance matrix (EDM) is studied,its properties and relationship to both positive semidefinite and Gram matrices.We relate the EDM to the four classical axioms of the Euclidean metric;thereby, observing the existence of an infinity of axioms of the Euclidean metric beyondthe triangle inequality. We proceed byderiving the fifth Euclidean axiom and then explain why furthering this endeavoris inefficient because the ensuing criteria (while describing polyhedra)grow linearly in complexity and number.Some geometrical problems solvable via EDMs,EDM problems posed as convex optimization, and methods of solution arepresented;\eg, we generate a recognizable isotonic map of the United States usingonly comparative distance information (no distance information, only distance inequalities).We offer a new proof of the classic Schoenberg criterion, that determines whether a candidate matrix is an EDM. Our proofrelies on fundamental geometry; assuming, any EDM must correspond to a list of points contained in some polyhedron(possibly at its vertices) and vice versa.It is not widely known that the Schoenberg criterion implies nonnegativity of the EDM entries; proved here.We characterize the eigenvalues of an EDM matrix and then devisea polyhedral cone required for determining membership of a candidate matrix(in Cayley-Menger form) to the convex cone of Euclidean distance matrices (EDM cone); \ie,a candidate is an EDM if and only if its eigenspectrum belongs to a spectral cone for EDM^N.We will see spectral cones are not unique.In the chapter EDM cone, we explain the geometric relationship betweenthe EDM cone, two positive semidefinite cones, and the elliptope.We illustrate geometric requirements, in particular, for projection of a candidate matrixon a positive semidefinite cone that establish its membership to the EDM cone. The faces of the EDM cone are described,but still open is the question whether all its faces are exposed as they are for the positive semidefinite cone.The classic Schoenberg criterion, relating EDM and positive semidefinite cones, isrevealed to be a discretized membership relation (a generalized inequality, a new Farkas''''''''-like lemma)between the EDM cone and its ordinary dual. A matrix criterion for membership to the dual EDM cone is derived thatis simpler than the Schoenberg criterion.We derive a new concise expression for the EDM cone and its dual involvingtwo subspaces and a positive semidefinite cone.Semidefinite programming is reviewedwith particular attention to optimality conditionsof prototypical primal and dual conic programs,their interplay, and the perturbation method of rank reduction of optimal solutions(extant but not well-known).We show how to solve a ubiquitous platonic combinatorial optimization problem from linear algebra(the optimal Boolean solution x to Ax=b)via semidefinite program relaxation.A three-dimensional polyhedral analogue for the positive semidefinite cone of 3X3 symmetricmatrices is introduced; a tool for visualizing in 6 dimensions.In EDM proximitywe explore methods of solution to a few fundamental and prevalentEuclidean distance matrix proximity problems; the problem of finding that Euclidean distance matrix closestto a given matrix in the Euclidean sense.We pay particular attention to the problem when compounded with rank minimization.We offer a new geometrical proof of a famous result discovered by Eckart \& Young in 1936 regarding Euclideanprojection of a point on a subset of the positive semidefinite cone comprising all positive semidefinite matriceshaving rank not exceeding a prescribed limit rho.We explain how this problem is transformed to a convex optimization for any rank rho. |
| active prelude to calculus: Burn Math Class Jason Wilkes, 2016-03-22 A manifesto for a mathematical revolution Forget everything you've been taught about math. In Burn Math Class, Jason Wilkes takes the traditional approach to how we learn math -- with its unwelcoming textbooks, unexplained rules, and authoritarian assertions-and sets it on fire. Focusing on how mathematics is created rather than on mathematical facts, Wilkes teaches the subject in a way that requires no memorization and no prior knowledge beyond addition and multiplication. From these simple foundations, Burn Math Class shows how mathematics can be (re)invented from scratch without preexisting textbooks and courses. We can discover math on our own through experimentation and failure, without appealing to any outside authority. When math is created free from arcane notations and pretentious jargon that hide the simplicity of mathematical concepts, it can be understood organically -- and it becomes fun! Following this unconventional approach, Burn Math Class leads the reader from the basics of elementary arithmetic to various advanced topics, such as time-dilation in special relativity, Taylor series, and calculus in infinite-dimensional spaces. Along the way, Wilkes argues that orthodox mathematics education has been teaching the subject backward: calculus belongs before many of its so-called prerequisites, and those prerequisites cannot be fully understood without calculus. Like the smartest, craziest teacher you've ever had, Wilkes guides you on an adventure in mathematical creation that will radically change the way you think about math. Revealing the beauty and simplicity of this timeless subject, Burn Math Class turns everything that seems difficult about mathematics upside down and sideways until you understand just how easy math can be. |
| active prelude to calculus: Gnuplot in Action Philipp K. Janert, 2016-03-08 Summary Gnuplot in Action, Second Edition is a major revision of this popular and authoritative guide for developers, engineers, and scientists who want to learn and use gnuplot effectively. Fully updated for gnuplot version 5, the book includes four pages of color illustrations and four bonus appendixes available in the eBook. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the Technology Gnuplot is an open-source graphics program that helps you analyze, interpret, and present numerical data. Available for Unix, Mac, and Windows, it is well-maintained, mature, and totally free. About the Book Gnuplot in Action, Second Edition is a major revision of this authoritative guide for developers, engineers, and scientists. The book starts with a tutorial introduction, followed by a systematic overview of gnuplot's core features and full coverage of gnuplot's advanced capabilities. Experienced readers will appreciate the discussion of gnuplot 5's features, including new plot types, improved text and color handling, and support for interactive, web-based display formats. The book concludes with chapters on graphical effects and general techniques for understanding data with graphs. It includes four pages of color illustrations. 3D graphics, false-color plots, heatmaps, and multivariate visualizations are covered in chapter-length appendixes available in the eBook. What's Inside Creating different types of graphs in detail Animations, scripting, batch operations Extensive discussion of terminals Updated to cover gnuplot version 5 About the Reader No prior experience with gnuplot is required. This book concentrates on practical applications of gnuplot relevant to users of all levels. About the Author Philipp K. Janert, PhD, is a programmer and scientist. He is the author of several books on data analysis and applied math and has been a gnuplot power user and developer for over 20 years. Table of Contents PART 1 GETTING STARTED Prelude: understanding data with gnuplot Tutorial: essential gnuplot The heart of the matter: the plot command PART 2 CREATING GRAPHS Managing data sets and files Practical matters: strings, loops, and history A catalog of styles Decorations: labels, arrows, and explanations All about axes PART 3 MASTERING TECHNICALITIES Color, style, and appearance Terminals and output formats Automation, scripting, and animation Beyond the defaults: workflow and styles PART 4 UNDERSTANDING DATA Basic techniques of graphical analysis Topics in graphical analysis Coda: understanding data with graphs |
| active prelude to calculus: The Next Mormons Jana Riess, 2019-02-01 American Millennials--the generation born in the 1980s and 1990s--have been leaving organized religion in unprecedented numbers. For a long time, the Church of Jesus Christ of Latter-day Saints was an exception: nearly three-quarters of people who grew up Mormon stayed that way into adulthood. In The Next Mormons, Jana Riess demonstrates that things are starting to change. Drawing on a large-scale national study of four generations of current and former Mormons as well as dozens of in-depth personal interviews, Riess explores the religious beliefs and behaviors of young adult Mormons, finding that while their levels of belief remain strong, their institutional loyalties are less certain than their parents' and grandparents'. For a growing number of Millennials, the tensions between the Church's conservative ideals and their generation's commitment to individualism and pluralism prove too high, causing them to leave the faith-often experiencing deep personal anguish in the process. Those who remain within the fold are attempting to carefully balance the Church's strong emphasis on the traditional family with their generation's more inclusive definition that celebrates same-sex couples and women's equality. Mormon families are changing too. More Mormons are remaining single, parents are having fewer children, and more women are working outside the home than a generation ago. The Next Mormons offers a portrait of a generation navigating between traditional religion and a rapidly changing culture. |
| active prelude to calculus: Mirror Symmetry Kentaro Hori, 2003 This thorough and detailed exposition is the result of an intensive month-long course on mirror symmetry sponsored by the Clay Mathematics Institute. It develops mirror symmetry from both mathematical and physical perspectives with the aim of furthering interaction between the two fields. The material will be particularly useful for mathematicians and physicists who wish to advance their understanding across both disciplines. Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics. Such a correspondence has significant mathematical consequences, the most familiar of which involves the enumeration of holomorphic curves inside complex manifolds by solving differential equations obtained from a ``mirror'' geometry. The inclusion of D-brane states in the equivalence has led to further conjectures involving calibrated submanifolds of the mirror pairs and new (conjectural) invariants of complex manifolds: the Gopakumar-Vafa invariants. This book gives a single, cohesive treatment of mirror symmetry. Parts 1 and 2 develop the necessary mathematical and physical background from ``scratch''. The treatment is focused, developing only the material most necessary for the task. In Parts 3 and 4 the physical and mathematical proofs of mirror symmetry are given. From the physics side, this means demonstrating that two different physical theories give isomorphic physics. Each physical theory can be described geometrically, and thus mirror symmetry gives rise to a ``pairing'' of geometries. The proof involves applying $R\leftrightarrow 1/R$ circle duality to the phases of the fields in the gauged linear sigma model. The mathematics proof develops Gromov-Witten theory in the algebraic setting, beginning with the moduli spaces of curves and maps, and uses localization techniques to show that certain hypergeometric functions encode the Gromov-Witten invariants in genus zero, as is predicted by mirror symmetry. Part 5 is devoted to advanced topi This one-of-a-kind book is suitable for graduate students and research mathematicians interested in mathematics and mathematical and theoretical physics. |
| active prelude to calculus: Orbital Mechanics for Engineering Students Howard D. Curtis, 2009-10-26 Orbital Mechanics for Engineering Students, Second Edition, provides an introduction to the basic concepts of space mechanics. These include vector kinematics in three dimensions; Newton's laws of motion and gravitation; relative motion; the vector-based solution of the classical two-body problem; derivation of Kepler's equations; orbits in three dimensions; preliminary orbit determination; and orbital maneuvers. The book also covers relative motion and the two-impulse rendezvous problem; interplanetary mission design using patched conics; rigid-body dynamics used to characterize the attitude of a space vehicle; satellite attitude dynamics; and the characteristics and design of multi-stage launch vehicles. Each chapter begins with an outline of key concepts and concludes with problems that are based on the material covered. This text is written for undergraduates who are studying orbital mechanics for the first time and have completed courses in physics, dynamics, and mathematics, including differential equations and applied linear algebra. Graduate students, researchers, and experienced practitioners will also find useful review materials in the book. - NEW: Reorganized and improved discusions of coordinate systems, new discussion on perturbations and quarternions - NEW: Increased coverage of attitude dynamics, including new Matlab algorithms and examples in chapter 10 - New examples and homework problems |
| active prelude to calculus: Journey into Mathematics Joseph J. Rotman, 2013-01-18 This treatment covers the mechanics of writing proofs, the area and circumference of circles, and complex numbers and their application to real numbers. 1998 edition. |
| active prelude to calculus: A Mind for Numbers Barbara A. Oakley, 2014-07-31 Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. In her book, she offers you the tools needed to get a better grasp of that intimidating but inescapable field. |
| active prelude to calculus: Blindsight Peter Watts, 2006-10-03 Hugo and Shirley Jackson award-winning Peter Watts stands on the cutting edge of hard SF with his acclaimed novel, Blindsight Two months since the stars fell... Two months of silence, while a world held its breath. Now some half-derelict space probe, sparking fitfully past Neptune's orbit, hears a whisper from the edge of the solar system: a faint signal sweeping the cosmos like a lighthouse beam. Whatever's out there isn't talking to us. It's talking to some distant star, perhaps. Or perhaps to something closer, something en route. So who do you send to force introductions with unknown and unknowable alien intellect that doesn't wish to be met? You send a linguist with multiple personalities, her brain surgically partitioned into separate, sentient processing cores. You send a biologist so radically interfaced with machinery that he sees x-rays and tastes ultrasound. You send a pacifist warrior in the faint hope she won't be needed. You send a monster to command them all, an extinct hominid predator once called vampire, recalled from the grave with the voodoo of recombinant genetics and the blood of sociopaths. And you send a synthesist—an informational topologist with half his mind gone—as an interface between here and there. Pray they can be trusted with the fate of a world. They may be more alien than the thing they've been sent to find. At the Publisher's request, this title is being sold without Digital Rights Management Software (DRM) applied. |
| active prelude to calculus: Under-Rewarded Efforts Santiago Levy Algazi, 2018-07-11 Why has an economy that has done so many things right failed to grow fast? Under-Rewarded Efforts traces Mexico’s disappointing growth to flawed microeconomic policies that have suppressed productivity growth and nullified the expected benefits of the country’s reform efforts. Fast growth will not occur doing more of the same or focusing on issues that may be key bottlenecks to productivity growth elsewhere, but not in Mexico. It will only result from inclusive institutions that effectively protect workers against risks, redistribute towards those in need, and simultaneously align entrepreneurs’ and workers’ incentives to raise productivity. |
| active prelude to calculus: Liquid Crystal Displays Robert H. Chen, 2011-08-04 An unprecedented look into the basic physics, chemistry, and technology behind the LCD Most notably used for computer screens, televisions, and mobile phones, LCDs (liquid crystal displays) are a pervasive and increasingly indispensable part of our lives. Providing both an historical and a business-minded context, this extensive resource describes the unique scientific and engineering techniques used to create these beautiful, clever, and eminently useful devices. In this book, the history of the science and technology behind the LCD is described in a prelude to the development of the device, presenting a rational development theme and pinpointing innovations. The book begins with Maxwell's theory of electromagnetism, and the ultimately profound realization that light is an electromagnetic wave and an electromagnetic wave is light. The power of mathematical physics thus was brought to bear upon the study of light, and particularly the polarization of light by material bodies, including liquid crystals. After a brief historical description of polarization, a physical interpretation provides substance to the mathematical concepts. Subsequent chapters cover: Thermodynamics for liquid crystals The Maier-Saupe mean field, phenomenological, static continuum, and dynamic continuum theories The transistor and integrated circuit Glass, panels, and modules The calculus of variations The active matrix Semiconductor fabrication The global LCD business Additionally, the book illustrates how mathematics, physics, and chemistry are put to practical use in the LCDs we use every day. By describing the science from an historical perspective and in practical terms in the context of a device very familiar to readers, the book presents an engaging and unique view of the technology for everyone from science students to engineers, product designers, and indeed anyone curious about LCDs. Series Editor: Anthony C. Lowe, The Lambent Consultancy, Braishfield, UK The Society for Information Display (SID) is an international society, which has the aim of encouraging the development of all aspects of the field of information display. Complementary to the aims of the society, the Wiley-SID series is intended to explain the latest developments in information display technology at a professional level. The broad scope of the series addresses all facets of information displays from technical aspects through systems and prototypes to standards and ergonomics. |
| active prelude to calculus: Condensed Matter Field Theory Alexander Altland, Ben D. Simons, 2010-03-11 This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena. |
| active prelude to calculus: Defense Against the Dark Arts in Space Todd Harrison, Kaitlyn Johnson, Makena Young, 2021-10-20 The proliferation of counterspace weapons across the globe often calls into question what can be done to best protect satellites from attack. This analysis from the CSIS Aerospace Security Project addresses different methods and technologies that can be used by the United States government, and others, to deter adversaries from attack. A wide range of active and passive defenses are available to protect space systems and the ground infrastructure they depend upon from different types of threats. This report captures a range of active and passive defenses that are theoretically possible and discusses the advantages and limitations of each. A group of technical space and national security experts supported the analysis by working through several plausible scenarios that explore a range of defenses that may be needed, concepts for employing different types of defenses, and how defensive actions in space may be perceived by others. These scenarios and the findings that resulted from subsequent conversations with experts are reported in the penultimate chapter of the report. Finally, the CSIS Aerospace Security Project team offers conclusions drawn from the analysis, actionable recommendations for policymakers, and additional research topics to be explored in future work. |
| active prelude to calculus: Teaching at Its Best Linda B. Nilson, 2010-04-20 Teaching at Its Best This third edition of the best-selling handbook offers faculty at all levels an essential toolbox of hundreds of practical teaching techniques, formats, classroom activities, and exercises, all of which can be implemented immediately. This thoroughly revised edition includes the newest portrait of the Millennial student; current research from cognitive psychology; a focus on outcomes maps; the latest legal options on copyright issues; and how to best use new technology including wikis, blogs, podcasts, vodcasts, and clickers. Entirely new chapters include subjects such as matching teaching methods with learning outcomes, inquiry-guided learning, and using visuals to teach, and new sections address Felder and Silverman's Index of Learning Styles, SCALE-UP classrooms, multiple true-false test items, and much more. Praise for the Third Edition of Teaching at Its BestEveryone veterans as well as novices will profit from reading Teaching at Its Best, for it provides both theory and practical suggestions for handling all of the problems one encounters in teaching classes varying in size, ability, and motivation. Wilbert McKeachie, Department of Psychology, University of Michigan, and coauthor, McKeachie's Teaching TipsThis new edition of Dr. Nilson's book, with its completely updated material and several new topics, is an even more powerful collection of ideas and tools than the last. What a great resource, especially for beginning teachers but also for us veterans! L. Dee Fink, author, Creating Significant Learning ExperiencesThis third edition of Teaching at Its Best is successful at weaving the latest research on teaching and learning into what was already a thorough exploration of each topic. New information on how we learn, how students develop, and innovations in instructional strategies complement the solid foundation established in the first two editions. Marilla D. Svinicki, Department of Psychology, The University of Texas, Austin, and coauthor, McKeachie's Teaching Tips |
| active prelude to calculus: The Need for Roots Simone Weil, 2020-04-30 Hailed by Andre Gide as the patron saint of all outsiders, Simone Weil's short life was ample testimony to her beliefs. In 1942 she fled France along with her family, going firstly to America. She then moved back to London in order to work with de Gaulle. Published posthumously The Need for Roots was a direct result of this collaboration. Its purpose was to help rebuild France after the war. In this, her most famous book, Weil reflects on the importance of religious and political social structures in the life of the individual. She wrote that one of the basic obligations we have as human beings is to not let another suffer from hunger. Equally as important, however, is our duty towards our community: we may have declared various human rights, but we have overlooked the obligations and this has left us self-righteous and rootless. She could easily have been issuing a direct warning to us today, the citizens of Century 21. |
| active prelude to calculus: Calculus William L. Briggs, Lyle Cochran, Bernard Gillett, 2014-04-02 Note: You are purchasing a standalone product; MyMathLab does not come packaged with this content. If you would like to purchase both the physical text and MyMathLab, search for ISBN-10: 0321963636 /ISBN-13: #9780321431301. That package includes ISBN-10: 0321431308 ISBN-13: 9780321431301, ISBN-10: 0321654064 ISBN-13: 9780321654069 and ISBN-10: 0321954351/ISBN-13: 9780321954350. MyMathLab is not a self-paced technology and should only be purchased when required by an instructor. This much anticipated second edition of the most successful new calculus text published in the last two decades retains the best of the first edition while introducing important advances and refinements. Authors Briggs, Cochran, and Gillett build from a foundation of meticulously crafted exercise sets, then draw students into the narrative through writing that reflects the voice of the instructor, examples that are stepped out and thoughtfully annotated, and figures that are designed to teach rather than simply supplement the narrative. The authors appeal to students’ geometric intuition to introduce fundamental concepts, laying a foundation for the development that follows. |
| active prelude to calculus: Chaos Theory Tamed Garnett Williams, 1997-09-09 This text aims to bridge the gap between non-mathematical popular treatments and the distinctly mathematical publications that non- mathematicians find so difficult to penetrate. The author provides understandable derivations or explanations of many key concepts, such as Kolmogrov-Sinai entropy, dimensions, Fourier analysis, and Lyapunov exponents. |
| active prelude to calculus: Precalculus Jay P. Abramson, Valeree Falduto, Rachael Gross (Mathematics teacher), David Lippman, Melonie Rasmussen, Rick Norwood, Nicholas Belloit, Jean-Marie Magnier, Harold Whipple, Christina Fernandez, 2014-10-23 Precalculus is intended for college-level precalculus students. Since precalculus courses vary from one institution to the next, we have attempted to meet the needs of as broad an audience as possible, including all of the content that might be covered in any particular course. The result is a comprehensive book that covers more ground than an instructor could likely cover in a typical one- or two-semester course; but instructors should find, almost without fail, that the topics they wish to include in their syllabus are covered in the text. Many chapters of OpenStax College Precalculus are suitable for other freshman and sophomore math courses such as College Algebra and Trigonometry; however, instructors of those courses might need to supplement or adjust the material. OpenStax will also be releasing College Algebra and Algebra and trigonometry titles tailored to the particular scope, sequence, and pedagogy of those courses.--Preface. |
| active prelude to calculus: Mathematical Writing Donald E. Knuth, Tracy Larrabee, Paul M. Roberts, 1989 This book will help those wishing to teach a course in technical writing, or who wish to write themselves. |
| active prelude to calculus: A First Course in Calculus Serge Lang, 2012-09-17 This fifth edition of Lang's book covers all the topics traditionally taught in the first-year calculus sequence. Divided into five parts, each section of A FIRST COURSE IN CALCULUS contains examples and applications relating to the topic covered. In addition, the rear of the book contains detailed solutions to a large number of the exercises, allowing them to be used as worked-out examples -- one of the main improvements over previous editions. |
| active prelude to calculus: The Emperor of All Maladies Siddhartha Mukherjee, 2011-08-09 Winner of the Pulitzer Prize and a documentary from Ken Burns on PBS, this New York Times bestseller is “an extraordinary achievement” (The New Yorker)—a magnificent, profoundly humane “biography” of cancer—from its first documented appearances thousands of years ago through the epic battles in the twentieth century to cure, control, and conquer it to a radical new understanding of its essence. Physician, researcher, and award-winning science writer, Siddhartha Mukherjee examines cancer with a cellular biologist’s precision, a historian’s perspective, and a biographer’s passion. The result is an astonishingly lucid and eloquent chronicle of a disease humans have lived with—and perished from—for more than five thousand years. The story of cancer is a story of human ingenuity, resilience, and perseverance, but also of hubris, paternalism, and misperception. Mukherjee recounts centuries of discoveries, setbacks, victories, and deaths, told through the eyes of his predecessors and peers, training their wits against an infinitely resourceful adversary that, just three decades ago, was thought to be easily vanquished in an all-out “war against cancer.” The book reads like a literary thriller with cancer as the protagonist. Riveting, urgent, and surprising, The Emperor of All Maladies provides a fascinating glimpse into the future of cancer treatments. It is an illuminating book that provides hope and clarity to those seeking to demystify cancer. |
| active prelude to calculus: Elements of Mechanics P.F. Kelly, 2016-02-17 The first volume in a three-part series, Elements of Mechanics provides a rigorous calculus-based introduction to classical physics. It considers diverse phenomena in a systematic manner and emphasises the development of consistent and coherent models guided by symmetry considerations and the application of general principles. Modern developments c |
| active prelude to calculus: Spacetime and Geometry Sean M. Carroll, 2019-08-08 An accessible introductory textbook on general relativity, covering the theory's foundations, mathematical formalism and major applications. |
| active prelude to calculus: Active Calculus Single Variable Workbook for Chapters 1-4 Matthew Boelkins, 2018-08-11 This is the activities workbook for Active Calculus chapters 1-4. It includes only the activities from the full textbook and offers lots of place to write with each activity starting on a new page and the following page being blank. The workbook is an ideal supplement to the text for students to make notes of their own work as they complete the activities. |
| active prelude to calculus: Algebra and Trigonometry Sheldon Axler, 2011-03-08 Axler Algebra & Trigonometry is written for the two semester course. The text provides students with the skill and understanding needed for their coursework and for participating as an educated citizen in a complex society. Axler Algebra & Trigonometry focuses on depth, not breadth of topics by exploring necessary topics in greater detail. Readers will benefit from the straightforward definitions and plentiful examples of complex concepts. The Student Solutions Manual is integrated at the end of every section. The proximity of the solutions encourages students to go back and read the main text as they are working through the problems and exercises. The inclusion of the manual also saves students money. Axler Algebra & Trigonometry is available with WileyPLUS; an innovative, research-based, online environment for effective teaching and learning. WileyPLUS sold separately from text. |
| active prelude to calculus: Student Solution Manual to Accompany the 4th Edition of Vector Calculus, Linear Algebra, and Differential Forms, a Unified Approach John Hamal Hubbard, Barbara Burke Hubbard, 2009 |
| active prelude to calculus: Deterrence Theory and Chinese Behavior Abram N. Shulsky, 2000 China's recent reforms have led to unprecedented economic growth; if this continues, China will be able to turn its great potential power into actual power. The result could be, in the very long term, the rise of China as a rival to the United States as the world's predominant power; in the nearer term, China could become a significant rival in the East Asian region. In this context, the issue for U.S. policy is how to handle a rising power, a problem that predominant powers have faced many times throughout history. It is the contention of this report that the future Sino-U.S. context will illustrate many of the problems of deterrence theory that have been discussed in recent decades; deterrence theory will be, in general, more difficult to apply than it was in the U.S.-Soviet Cold War context. The key may be to seek nonmilitary means of deterrence, i.e., diplomatic ways to manipulate the tension to China's disadvantage. |
| active prelude to calculus: Calculus-Based Physics I Jeffrey W. Schnick, 2009-09-24 Calculus-Based Physics is an introductory physics textbook designed for use in the two-semester introductory physics course typically taken by science and engineering students. This item is part 1, for the first semester. Only the textbook in PDF format is provided here. To download other resources, such as text in MS Word formats, problems, quizzes, class questions, syllabi, and formula sheets, visit: http: //www.anselm.edu/internet/physics/cbphysics/index.html Calculus-Based Physics is now available in hard copy in the form of two black and white paperbacks at www.LuLu.com at the cost of production plus shipping. Note that Calculus-Based Physics is designed for easy photocopying. So, if you prefer to make your own hard copy, just print the pdf file and make as many copies as you need. While some color is used in the textbook, the text does not refer to colors so black and white hard copies are viable |
| active prelude to calculus: The Poisonwood Bible Barbara Kingsolver, 2009-10-13 New York Times Bestseller • Finalist for the Pulitzer Prize • An Oprah's Book Club Selection “Powerful . . . [Kingsolver] has with infinitely steady hands worked the prickly threads of religion, politics, race, sin and redemption into a thing of terrible beauty.” —Los Angeles Times Book Review The Poisonwood Bible, now celebrating its 25th anniversary, established Barbara Kingsolver as one of the most thoughtful and daring of modern writers. Taking its place alongside the classic works of postcolonial literature, it is a suspenseful epic of one family's tragic undoing and remarkable reconstruction over the course of three decades in Africa. The story is told by the wife and four daughters of Nathan Price, a fierce, evangelical Baptist who takes his family and mission to the Belgian Congo in 1959. They carry with them everything they believe they will need from home, but soon find that all of it—from garden seeds to Scripture—is calamitously transformed on African soil. The novel is set against one of the most dramatic political chronicles of the twentieth century: the Congo's fight for independence from Belgium, the murder of its first elected prime minister, the CIA coup to install his replacement, and the insidious progress of a world economic order that robs the fledgling African nation of its autonomy. Against this backdrop, Orleanna Price reconstructs the story of her evangelist husband's part in the Western assault on Africa, a tale indelibly darkened by her own losses and unanswerable questions about her own culpability. Also narrating the story, by turns, are her four daughters—the teenaged Rachel; adolescent twins Leah and Adah; and Ruth May, a prescient five-year-old. These sharply observant girls, who arrive in the Congo with racial preconceptions forged in 1950s Georgia, will be marked in surprisingly different ways by their father's intractable mission, and by Africa itself. Ultimately each must strike her own separate path to salvation. Their passionately intertwined stories become a compelling exploration of moral risk and personal responsibility. |
| active prelude to calculus: Gödel, Escher, Bach Douglas R. Hofstadter, 2000 'What is a self and how can a self come out of inanimate matter?' This is the riddle that drove Douglas Hofstadter to write this extraordinary book. In order to impart his original and personal view on the core mystery of human existence - our intangible sensation of 'I'-ness - Hofstadter defines the playful yet seemingly paradoxical notion of 'strange loop', and explicates this idea using analogies from many disciplines. |
How do I forcefully change the active signal resolution?
Nov 19, 2019 · I understand that you want to change the active signal resolution for the monitor that you are using. I would suggest you to refer the troubleshooting steps mentioned below …
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Feb 6, 2025 · It highlights the row and column of whatever your current active cell is. On the View ribbon select Focus Cell in the Show section to activate it. Reply if you have additional …
External monitors detected but not active, how can I fix this?
Mar 23, 2023 · In the normal Display settings it simply shows the other external monitors but are a different faded grey, im assuming to show they arent active. Cant access refresh rate or alter …
Incorrect active signal resolution - Microsoft Community
Aug 31, 2018 · I set the indicated resolution on each screen but the screen 3 is looking blurry. Go to "advanced display settings" and I can see even though the "Desktop resolution" is correctly …
How to enable ActiveX on Windows 10 - Microsoft Community
Aug 8, 2015 · 1. Do you receive any prompt message to install Active X? 2. Does the issue occur with particular webpage? Let's try the following and check: Method 1: To enable ActiveX in …
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Enable ActiveX control in Microsoft Edge latest
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Message - Active Content is Blocked - Microsoft Community
Mar 5, 2023 · The "active content" in Access refers to any code or macros within the database that can execute when the file is opened. The message is a security measure designed to …
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How do I forcefully change the active signal resolution?
Nov 19, 2019 · I understand that you want to change the active signal resolution for the monitor that you are using. I would suggest you to refer the troubleshooting steps mentioned below and see if that helps: …
how to highlight an active row so that I can see it clearly and not ...
Feb 6, 2025 · It highlights the row and column of whatever your current active cell is. On the View ribbon select Focus Cell in the Show section to activate it. Reply if you have additional questions or information.
External monitors detected but not active, how can I fix this?
Mar 23, 2023 · In the normal Display settings it simply shows the other external monitors but are a different faded grey, im assuming to show they arent active. Cant access refresh rate or alter they display configs. hope this …
Incorrect active signal resolution - Microsoft Community
Aug 31, 2018 · I set the indicated resolution on each screen but the screen 3 is looking blurry. Go to "advanced display settings" and I can see even though the "Desktop resolution" is correctly set, the "Active signal resolution" …
How to enable ActiveX on Windows 10 - Microsoft Community
Aug 8, 2015 · 1. Do you receive any prompt message to install Active X? 2. Does the issue occur with particular webpage? Let's try the following and check: Method 1: To enable ActiveX in desktop version follow this step. …
