Calculus for the Life Sciences: A Modeling Approach

Calculus for the Life Sciences: A Modeling Approach

Author: James L. Cornette

Publisher: American Mathematical Soc.

ISBN: 9781470451424

Category: Calculus

Page: 713

View: 838

Calculus for the Life Sciences is an entire reimagining of the standard calculus sequence with the needs of life science students as the fundamental organizing principle. Those needs, according to the National Academy of Science, include: the mathematical concepts of change, modeling, equilibria and stability, structure of a system, interactions among components, data and measurement, visualization, and algorithms. This book addresses, in a deep and significant way, every concept on that list. The book begins with a primer on modeling in the biological realm and biological modeling is the theme and frame for the entire book. The authors build models of bacterial growth, light penetration through a column of water, and dynamics of a colony of mold in the first few pages. In each case there is actual data that needs fitting. In the case of the mold colony that data is a set of photographs of the colony growing on a ruled sheet of graph paper and the students need to make their own approximations. Fundamental questions about the nature of mathematical modeling—trying to approximate a real-world phenomenon with an equation—are all laid out for the students to wrestle with. The authors have produced a beautifully written introduction to the uses of mathematics in the life sciences. The exposition is crystalline, the problems are overwhelmingly from biology and interesting and rich, and the emphasis on modeling is pervasive. An instructor's manual for this title is available electronically to those instructors who have adopted the textbook for classroom use. Please send email to [email protected] for more information. Online question content and interactive step-by-step tutorials are available for this title in WebAssign. WebAssign is a leading provider of online instructional tools for both faculty and students.

Undergraduate Mathematics for the Life Sciences

Undergraduate Mathematics for the Life Sciences

Author: Glenn Ledder

Publisher: MAA

ISBN: 9780883851913

Category: Biomathematics

Page: 228

View: 196

There is a gap between the extensive mathematics background that is beneficial to biologists and the minimal mathematics background biology students acquire in their courses. The result is an undergraduate education in biology with very little quantitative content. New mathematics courses must be devised with the needs of biology students in mind. In this volume, authors from a variety of institutions address some of the problems involved in reforming mathematics curricula for biology students. The problems are sorted into three themes: Models, Processes, and Directions. It is difficult for mathematicians to generate curriculum ideas for the training of biologists so a number of the curriculum models that have been introduced at various institutions comprise the Models section. Processes deals with taking that great course and making sure it is institutionalized in both the biology department (as a requirement) and in the mathematics department (as a course that will live on even if the creator of the course is no longer on the faculty). Directions looks to the future, with each paper laying out a case for pedagogical developments that the authors would like to see.

Mathematics for the Life Sciences

Mathematics for the Life Sciences

Author: Erin N. Bodine

Publisher: Princeton University Press

ISBN: 9780691150727

Category: Mathematics

Page: 630

View: 454

An accessible undergraduate textbook on the essential math concepts used in the life sciences The life sciences deal with a vast array of problems at different spatial, temporal, and organizational scales. The mathematics necessary to describe, model, and analyze these problems is similarly diverse, incorporating quantitative techniques that are rarely taught in standard undergraduate courses. This textbook provides an accessible introduction to these critical mathematical concepts, linking them to biological observation and theory while also presenting the computational tools needed to address problems not readily investigated using mathematics alone. Proven in the classroom and requiring only a background in high school math, Mathematics for the Life Sciences doesn't just focus on calculus as do most other textbooks on the subject. It covers deterministic methods and those that incorporate uncertainty, problems in discrete and continuous time, probability, graphing and data analysis, matrix modeling, difference equations, differential equations, and much more. The book uses MATLAB throughout, explaining how to use it, write code, and connect models to data in examples chosen from across the life sciences. Provides undergraduate life science students with a succinct overview of major mathematical concepts that are essential for modern biology Covers all the major quantitative concepts that national reports have identified as the ideal components of an entry-level course for life science students Provides good background for the MCAT, which now includes data-based and statistical reasoning Explicitly links data and math modeling Includes end-of-chapter homework problems, end-of-unit student projects, and select answers to homework problems Uses MATLAB throughout, and MATLAB m-files with an R supplement are available online Prepares students to read with comprehension the growing quantitative literature across the life sciences A solutions manual for professors and an illustration package is available

A Radical Approach to Real Analysis

A Radical Approach to Real Analysis

Author: David Bressoud

Publisher: American Mathematical Society

ISBN: 9781470469047

Category: Mathematics

Page: 339

View: 247

In this second edition of the MAA classic, exploration continues to be an essential component. More than 60 new exercises have been added, and the chapters on Infinite Summations, Differentiability and Continuity, and Convergence of Infinite Series have been reorganized to make it easier to identify the key ideas. A Radical Approach to Real Analysis is an introduction to real analysis, rooted in and informed by the historical issues that shaped its development. It can be used as a textbook, as a resource for the instructor who prefers to teach a traditional course, or as a resource for the student who has been through a traditional course yet still does not understand what real analysis is about and why it was created. The book begins with Fourier's introduction of trigonometric series and the problems they created for the mathematicians of the early 19th century. It follows Cauchy's attempts to establish a firm foundation for calculus and considers his failures as well as his successes. It culminates with Dirichlet's proof of the validity of the Fourier series expansion and explores some of the counterintuitive results Riemann and Weierstrass were led to as a result of Dirichlet's proof.

Teaching Statistics Using Baseball

Teaching Statistics Using Baseball

Author: Jim Albert

Publisher: American Mathematical Society

ISBN: 9781470469382

Category: Mathematics

Page: 257

View: 996

Teaching Statistics Using Baseball is a collection of case studies and exercises applying statistical and probabilistic thinking to the game of baseball. Baseball is the most statistical of all sports since players are identified and evaluated by their corresponding hitting and pitching statistics. There is an active effort by people in the baseball community to learn more about baseball performance and strategy by the use of statistics. This book illustrates basic methods of data analysis and probability models by means of baseball statistics collected on players and teams. Students often have difficulty learning statistics ideas since they are explained using examples that are foreign to the students. The idea of the book is to describe statistical thinking in a context (that is, baseball) that will be familiar and interesting to students. The book is organized using a same structure as most introductory statistics texts. There are chapters on the analysis on a single batch of data, followed with chapters on comparing batches of data and relationships. There are chapters on probability models and on statistical inference. The book can be used as the framework for a one-semester introductory statistics class focused on baseball or sports. This type of class has been taught at Bowling Green State University. It may be very suitable for a statistics class for students with sports-related majors, such as sports management or sports medicine. Alternately, the book can be used as a resource for instructors who wish to infuse their present course in probability or statistics with applications from baseball. The second edition of Teaching Statistics follows the same structure as the first edition, where the case studies and exercises have been replaced by modern players and teams, and the new types of baseball data from the PitchFX system and fangraphs.com are incorporated into the text.

Geometry Illuminated

Geometry Illuminated

Author: Matthew Harvey

Publisher: The Mathematical Association of America

ISBN: 9781939512116

Category: Mathematics

Page: 561

View: 352

Geometry Illuminated is an introduction to geometry in the plane, both Euclidean and hyperbolic. It is designed to be used in an undergraduate course on geometry, and as such, its target audience is undergraduate math majors. However, much of it should be readable by anyone who is comfortable with the language of mathematical proof. Throughout, the goal is to develop the material patiently. One of the more appealing aspects of geometry is that it is a very "visual" subject. This book hopes to takes full advantage of that, with an extensive use of illustrations as guides. Geometry Illuminated is divided into four principal parts. Part 1 develops neutral geometry in the style of Hilbert, including a discussion of the construction of measure in that system, ultimately building up to the Saccheri-Legendre Theorem. Part 2 provides a glimpse of classical Euclidean geometry, with an emphasis on concurrence results, such as the nine-point circle. Part 3 studies transformations of the Euclidean plane, beginning with isometries and ending with inversion, with applications and a discussion of area in between. Part 4 is dedicated to the development of the Poincaré disk model, and the study of geometry within that model. While this material is traditional, Geometry Illuminated does bring together topics that are generally not found in a book at this level. Most notably, it explicitly computes parametric equations for the pseudosphere and its geodesics. It focuses less on the nature of axiomatic systems for geometry, but emphasizes rather the logical development of geometry within such a system. It also includes sections dealing with trilinear and barycentric coordinates, theorems that can be proved using inversion, and Euclidean and hyperbolic tilings.

Thinking Geometrically

Thinking Geometrically

Author: Thomas Q. Sibley

Publisher: The Mathematical Association of America

ISBN: 9781939512086

Category: Mathematics

Page: 586

View: 579

Thinking Geometrically: A Survey of Geometries is a well written and comprehensive survey of college geometry that would serve a wide variety of courses for both mathematics majors and mathematics education majors. Great care and attention is spent on developing visual insights and geometric intuition while stressing the logical structure, historical development, and deep interconnectedness of the ideas. Students with less mathematical preparation than upper-division mathematics majors can successfully study the topics needed for the preparation of high school teachers. There is a multitude of exercises and projects in those chapters developing all aspects of geometric thinking for these students as well as for more advanced students. These chapters include Euclidean Geometry, Axiomatic Systems and Models, Analytic Geometry, Transformational Geometry, and Symmetry. Topics in the other chapters, including Non-Euclidean Geometry, Projective Geometry, Finite Geometry, Differential Geometry, and Discrete Geometry, provide a broader view of geometry. The different chapters are as independent as possible, while the text still manages to highlight the many connections between topics. The text is self-contained, including appendices with the material in Euclid’s first book and a high school axiomatic system as well as Hilbert’s axioms. Appendices give brief summaries of the parts of linear algebra and multivariable calculus needed for certain chapters. While some chapters use the language of groups, no prior experience with abstract algebra is presumed. The text will support an approach emphasizing dynamical geometry software without being tied to any particular software.

The Lebesgue Integral for Undergraduates

The Lebesgue Integral for Undergraduates

Author: William Johnston

Publisher: The Mathematical Association of America

ISBN: 9781939512079

Category: Mathematics

Page: 297

View: 358

In 1902, modern function theory began when Henri Lebesgue described a new "integral calculus." His "Lebesgue integral" handles more functions than the traditional integral-so many more that mathematicians can study collections (spaces) of functions. For example, it defines a distance between any two functions in a space. This book describes these ideas in an elementary accessible way. Anyone who has mastered calculus concepts of limits, derivatives, and series can enjoy the material. Unlike any other text, this book brings analysis research topics within reach of readers even just beginning to think about functions from a theoretical point of view.

Common Sense Mathematics

Common Sense Mathematics

Author: Ethan D. Bolker

Publisher: The Mathematical Association of America

ISBN: 9781939512109

Category: Mathematics

Page: 329

View: 453

Common Sense Mathematics is a text for a one semester college-level course in quantitative literacy. The text emphasizes common sense and common knowledge in approaching real problems through popular news items and finding useful mathematical tools and frames with which to address those questions. We asked ourselves what we hoped our students would remember about this course in ten year’s time. From that ten year perspective thoughts about syllabus–“what topics should we cover?"–seemed much too narrow. What matters more is our wish to change the way our students' minds work–the way they approach a problem, or, more generally, the way they approach the world. Most people “skip the numbers" in newspapers, magazines, on the web and (more importantly) even in financial information. We hope that in ten years our students will follow the news, confident in their ability to make sense of the numbers they find there and in their daily lives. Most quantitative reasoning texts are arranged by mathematical topics to be mastered. Since the mathematics is only a part of what we hope students learn, we've chosen another strategy. We look at real life stories that can be best understood with careful reading and a little mathematics.

A TeXas Style Introduction to Proof

A TeXas Style Introduction to Proof

Author: Ron Taylor

Publisher: American Mathematical Soc.

ISBN: 9781470450465

Category: Proof theory

Page: 161

View: 808

A TeXas Style Introduction to Proof is an IBL textbook designed for a one-semester course on proofs (the “bridge course”) that also introduces TeX as a tool students can use to communicate their work. As befitting “textless” text, the book is, as one reviewer characterized it, “minimal.” Written in an easy-going style, the exposition is just enough to support the activities, and it is clear, concise, and effective. The book is well organized and contains ample carefully selected exercises that are varied, interesting, and probing, without being discouragingly difficult.

Math through the Ages: A Gentle History for Teachers and Others Expanded Second Edition

Math through the Ages: A Gentle History for Teachers and Others Expanded Second Edition

Author: William P. Berlinghoff

Publisher: American Mathematical Soc.

ISBN: 9781470464561

Category: Education

Page: 331

View: 937

Where did math come from? Who thought up all those algebra symbols, and why? What is the story behind π π? … negative numbers? … the metric system? … quadratic equations? … sine and cosine? … logs? The 30 independent historical sketches in Math through the Ages answer these questions and many others in an informal, easygoing style that is accessible to teachers, students, and anyone who is curious about the history of mathematical ideas. Each sketch includes Questions and Projects to help you learn more about its topic and to see how the main ideas fit into the bigger picture of history. The 30 short stories are preceded by a 58-page bird's-eye overview of the entire panorama of mathematical history, a whirlwind tour of the most important people, events, and trends that shaped the mathematics we know today. “What to Read Next” and reading suggestions after each sketch provide starting points for readers who want to learn more. This book is ideal for a broad spectrum of audiences, including students in history of mathematics courses at the late high school or early college level, pre-service and in-service teachers, and anyone who just wants to know a little more about the origins of mathematics.

A Comprehensive Physically Based Approach to Modeling in Bioengineering and Life Sciences

A Comprehensive Physically Based Approach to Modeling in Bioengineering and Life Sciences

Author: Riccardo Sacco

Publisher: Academic Press

ISBN: 9780128125199

Category: Technology & Engineering

Page: 854

View: 541

A Comprehensive Physically Based Approach to Modeling in Bioengineering and Life Sciences provides a systematic methodology to the formulation of problems in biomedical engineering and the life sciences through the adoption of mathematical models based on physical principles, such as the conservation of mass, electric charge, momentum, and energy. It then teaches how to translate the mathematical formulation into a numerical algorithm that is implementable on a computer. The book employs computational models as synthesized tools for the investigation, quantification, verification, and comparison of different conjectures or scenarios of the behavior of a given compartment of the human body under physiological and pathological conditions. Presents theoretical (modeling), biological (experimental), and computational (simulation) perspectives Features examples, exercises, and MATLAB codes for further reader involvement Covers basic and advanced functional and computational techniques throughout the book