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This award-winning text carefully leads the student through the basic topics of Real Analysis. Topics include metric spaces, open and closed sets, convergent sequences, function limits and continuity, compact sets, sequences and series of functions, power series, differentiation and integration, Taylor's theorem, total variation, rectifiable arcs, and sufficient conditions of integrability. Well over 500 exercises (many with extensive hints) assist students through the material.
This textbook attempts to provide you with an overview of the commonly used basic mathematical models, as well as a wide range of applications. It offers a perspective that brings you back to the modeling process and the assumptions that go into it.
Mathematical Reasoning: Writing and Proof is designed to be a text for the first course in the college mathematics curriculum that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics. The primary goals of the text are to help students:
· Develop logical thinking skills and to develop the ability to think more abstractly in a proof oriented setting.
· Develop the ability to construct and write mathematical proofs using standard methods of mathematical proof including direct proofs, proof by contradiction, mathematical induction, case analysis, and counterexamples.
· Develop the ability to read and understand written mathematical proofs.
· Develop talents for creative thinking and problem solving.
· Improve their quality of communication in mathematics. This includes improving writing techniques, reading comprehension, and oral communication in mathematics.
· Better understand the nature of mathematics and its language.
This text also provides students with material that will be needed for their further study of mathematics.
Word Count: 27961
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Mathematics for Biomedical Physics is an open textbook, published by the Wayne State University Library System, geared to introduce several mathematical topics at the rudimentary level so that students can appreciate the applications of mathematics to the interdisciplinary field of biomedical physics. Most of the topics are presented in their simplest but rigorous form so that students can easily understand the advanced form of these topics when the need arises. Several end-of-chapter problems and chapter examples relate the applications of mathematics to biomedical physics. After mastering the topics of this book, students would be ready to embark on quantitative thinking in various topics of biology and medicine.
This book will help you to understand elementary mathematics more deeply, gain facility with creating and using mathematical notation, develop a habit of looking for reasons and creating mathematical explanations, and become more comfortable exploring unfamiliar mathematical situations.
The primary goal of this book is to help you learn to think like a mathematician in some very specific ways. You will:
• Make sense of problems and persevere in solving them. You will develop and demonstrate this skill by working on difficult problems, making incremental progress, and revising solutions to problems as you learn more.
• Reason abstractly and quantitatively. You will demonstrate this skill by learning to represent situations using mathematical notation (abstraction) as well as creating and testing examples (making situations more concrete).
• Construct viable arguments and critique the reasoning of others. You will be expected to create both written and verbal explanations for your solutions to problems. The most important questions in this class are “Why?” and “How do you know you're right?” Practice asking these questions of yourself, of your professor, and of your fellow students.
Throughout the book, you will learn how to learn mathematics on you own by reading, working on problems, and making sense of new ideas on your own and in collaboration with other students in the class.
Math in Society is a free, open textbook. This book is a survey of contemporary mathematical topics, most non-algebraic, appropriate for a college-level topics course for liberal arts majors. The text is designed so that most chapters are independent, allowing the instructor to choose a selection of topics to be covered. Emphasis is placed on the applicability of the mathematics. Core material for each topic is covered in the main text, with additional depth available through exploration exercises appropriate for in-class, group, or individual investigation. This book is appropriate for Math 107 (Washington State Community Colleges common course number).
We dedicate this book to our students. May you have greater ease in paying for college and grow your proficiency and confidence in math.
This lesson will require students to practice measuring real-world objects in different units and evaluate the most effective units to use for solving problems.
This lesson will require students to practice measuring real-world objects in different units and evaluate the most effective units to use for solving problems.
Students will identify which unit of measure inch, foot or yard is best for measuring various items in the outdoor learning lab. They will then apply the use of the appropriate tool to measure a variety of objects to the nearest marker.
Students will develop measurement vocabulary and fluency by comparing the different heights of plants.
Students will develop measurement vocabulary and fluency by comparing the different heights of plants.
In this lesson, students will build fluency using the language of measurement by collecting data about various plants in the outdoor classroom.
In this lesson, students will build fluency using the language of measurement by collecting data about various plants in the outdoor classroom.
Students will develop measurement vocabulary and fluency by comparing the different heights of plants.
In this lesson, students to practice measuring real-world objects in different units and evaluate which are the most effective units for solving particular problems.
This lesson will require students to practice measuring real-world objects in different units and evaluate which are the most effective units for solving particular problems.