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e-book
This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader’s attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics Algebra Textbooks Geometry
- Resource Type:
- e-book
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e-book
As currently taught in the United States, introductory courses in analytical chemistry emphasize quantitative (and sometimes qualitative) methods of analysis along with a heavy dose of equilibrium chemistry. Analytical chemistry, however, is much more than a collection of analytical methods and an understanding of equilibrium chemistry; it is an approach to solving chemical problems. Although equilibrium chemistry and analytical methods are important, their coverage should not come at the expense of other equally important topics. The introductory course in analytical chemistry is the ideal place in the undergraduate chemistry curriculum for exploring topics such as experimental design, sampling, calibration strategies, standardization, optimization, statistics, and the validation of experimental results. Analytical methods come and go, but best practices for designing and validating analytical methods are universal. Because chemistry is an experimental science it is essential that all chemistry students understand the importance of making good measurements. My goal in preparing this textbook is to find a more appropriate balance between theory and practice, between “classical” and “modern” analytical methods, between analyzing samples and collecting samples and preparing them for analysis, and between analytical methods and data analysis. There is more material here than anyone can cover in one semester; it is my hope that the diversity of topics will meet the needs of different instructors, while, perhaps, suggesting some new topics to cover.
- Subjects:
- Chemistry
- Keywords:
- Chemistry Analytic -- Quantitative Textbooks
- Resource Type:
- e-book
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e-book
Astronomy is designed to meet the scope and sequence requirements of one- or two-semester introductory astronomy courses. The book begins with relevant scientific fundamentals and progresses through an exploration of the solar system, stars, galaxies and cosmology. The Astronomy textbook builds student understanding through the use of relevant analogies, clear and non-technical explanations, and rich illustrations. Mathematics is included in a flexible manner to meet the needs of individual instructors.
- Subjects:
- Cosmology and Astronomy
- Keywords:
- Textbooks Astronomy
- Resource Type:
- e-book
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e-book
This free online textbook (e-book in webspeak) is a one semester course in basic analysis. This book started its life as my lecture notes for Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in the fall semester of 2009, and was later enhanced to teach Math 521 at University of Wisconsin-Madison (UW-Madison). A prerequisite for the course is a basic proof course. It should be possible to use the book for both a basic course for students who do not necessarily wish to go to graduate school, but also as a first semester of a more advanced course that also covers topics such as metric spaces.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Functions of real variables Mathematical analysis Textbooks
- Resource Type:
- e-book
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e-book
This text is intended to provide an in-depth introduction to the key ideas in chemistry. We have designed the book to show how these ideas are developed from simple to complex systems and how they relate to each other. We consider three ideas central to an understanding of chemistry: the structure of matter, the properties of matter, and the energy changes involved in the reorganization of matter; all are connected by the interactions or forces that cause matter to interact. We aim to provide compelling reasons why you will find yourself wanting to learn chemistry and to illustrate what you will be able to do with this knowledge once you have learned it.
- Subjects:
- Chemistry
- Keywords:
- Chemistry Organic Chemistry Textbooks
- Resource Type:
- e-book
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e-book
"In 2013, Lyryx forked the now-popular Calculus open textbook written by David Guichard. Michael Cavers of the University of Calgary, together with the Lyryx editorial team, further redeveloped the content, examples, diagrams, and overall look-and-feel of the book, making it more accessible to first year college and university students. Additional contributors have helped improve the content, including Mark Blenkinsop of Carleton University. In particular, there was the addition of an introductory chapter reviewing the fundamental topics required in a first semester Calculus course, and the paring down of topics that are typically beyond the scope of math and engineering service courses. Currently, the book covers the standard Calculus I and II courses, with Calculus III under development."--Open Textbook Library.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Textbooks
- Resource Type:
- e-book
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e-book
Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 1 covers functions, limits, derivatives, and integration. OpenStax College has compiled many resources for faculty and students, from faculty-only content to interactive homework and study guides.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Textbooks
- Resource Type:
- e-book
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e-book
Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Textbooks
- Resource Type:
- e-book
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e-book
Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Textbooks
- Resource Type:
- e-book
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e-book
"Chemistry: Atoms First is a peer-reviewed, openly licensed introductory textbook produced through a collaborative publishing partnership between OpenStax and the University of Connecticut and UConn Undergraduate Student Government Association. This title is an adaptation of the OpenStax Chemistry text and covers scope and sequence requirements of the two-semester general chemistry course. Reordered to fit an atoms first approach, this title introduces atomic and molecular structure much earlier than the traditional approach, delaying the introduction of more abstract material so students have time to acclimate to the study of chemistry. Chemistry: Atoms First also provides a basis for understanding the application of quantitative principles to the chemistry that underlies the entire course."--Open Textbook Library.
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e-book
Discrete Mathematics: An Open Introduction is a free, open source textbook appropriate for a first or second year undergraduate course for math majors, especially those who will go on to teach. The textbook has been developed while teaching the Discrete Mathematics course at the University of Northern Colorado. Primitive versions were used as the primary textbook for that course since Spring 2013, and have been used by other instructors as a free additional resource. Since then it has been used as the primary text for this course at UNC, as well as at other institutions.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics Textbooks Computer science -- Mathematics
- Resource Type:
- e-book
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e-book
This is a forest measurements textbook written for field technicians. Silvicultural applications and illustrations are provided to demonstrate the relevance of the measurements. Special “technique tips” for each skill are intended to help increase data collection accuracy and confidence. These include how to avoid common pitfalls, effective short cuts and essentials for recording field data correctly. The emphasis is on elementary skills; it is not intended to be a timber cruising guide.
- Keywords:
- Textbooks Forests forestry -- Measurement
- Resource Type:
- e-book
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e-book
"This is a forest measurements textbook written for field technicians. Silvicultural applications and illustrations are provided to demonstrate the relevance of the measurements. Special "technique tips" for each skill are intended to help increase data collection accuracy and confidence. These include how to avoid common pitfalls, effective short cuts, and essentials for recording field data correctly. The emphasis is on elementary skills
- Keywords:
- Textbooks Forests forestry -- Measurement
- Resource Type:
- e-book
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e-book
Our goal with this textbook is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs. The lecture notes contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. The lecture notes also contain many well-selected exercises of various levels. Although these topics are written in a more abstract way compared with those available in some textbooks, teachers can choose to simplify them depending on the background of the students. For instance, rather than introducing the topology of the real line to students, related topological concepts can be replaced by more familiar concepts such as open and closed intervals. Some other topics such as lower and upper semicontinuity, differentiation of convex functions, and generalized differentiation of non-differentiable convex functions can be used as optional mathematical projects. In this way, the lecture notes are suitable for teaching students of different backgrounds. The second edition includes a number of improvements based on recommendations from students and colleagues and on our own experience teaching the course over the last several years. In this edition we streamlined the narrative in several sections, added more proofs, many examples worked out in detail, and numerous new exercises. In all we added over 50 examples in the main text and 100 exercises (counting parts).
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematical analysis Textbooks
- Resource Type:
- e-book
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e-book
The exercises in this laboratory manual are designed to engage students in hand-on activities that reinforce their understanding of the microbial world. Topics covered include: staining and microscopy, metabolic testing, physical and chemical control of microorganisms, and immunology. The target audience is primarily students preparing for a career in the health sciences, however many of the topics would be appropriate for a general microbiology course as well.
- Subjects:
- Laboratory Techniques and Safety and Biology
- Keywords:
- Microbiology Laboratory manuals Textbooks
- Resource Type:
- e-book
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e-book
We believe the entire book can be taught in twenty five 50-minute lectures to a sophomore audience that has been exposed to a one year calculus course. Vector calculus is useful, but not necessary preparation for this book, which attempts to be self-contained. Key concepts are presented multiple times, throughout the book, often first in a more intuitive setting, and then again in a definition, theorem, proof style later on. We do not aim for students to become agile mathematical proof writers, but we do expect them to be able to show and explain why key results hold. We also often use the review exercises to let students discover key results for themselves; before they are presented again in detail later in the book. The book has been written such that instructors can reorder the chapters (using the La- TeX source) in any (reasonable) order and still have a consistent text. We hammer the notions of abstract vectors and linear transformations hard and early, while at the same time giving students the basic matrix skills necessary to perform computations. Gaussian elimination is followed directly by an “exploration chapter” on the simplex algorithm to open students minds to problems beyond standard linear systems ones. Vectors in Rn and general vector spaces are presented back to back so that students are not stranded with the idea that vectors are just ordered lists of numbers. To this end, we also labor the notion of all functions from a set to the real numbers. In the same vein linear transformations and matrices are presented hand in hand. Once students see that a linear map is specified by its action on a limited set of inputs, they can already understand what a basis is. All the while students are studying linear systems and their solution sets, so after matrices determinants are introduced. This material can proceed rapidly since elementary matrices were already introduced with Gaussian elimination. Only then is a careful discussion of spans, linear independence and dimension given to ready students for a thorough treatment of eigenvectors and diagonalization. The dimension formula therefore appears quite late, since we prefer not to elevate rote computations of column and row spaces to a pedestal. The book ends with applications–least squares and singular values. These are a fun way to end any lecture course. It would also be quite easy to spend any extra time on systems of differential equations and simple Fourier transform problems.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Algebras Linear
- Resource Type:
- e-book
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e-book
This text covers the standard material for a US undergraduate first course: linear systems and Gauss's Method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues, as well as additional topics such as introductions to various applications. It has extensive exercise sets with worked answers to all exercises, including proofs, beamer slides for classroom use, and a lab manual for computer work. The approach is developmental. Although everything is proved, it introduces the material with a great deal of motivation, many computational examples, and exercises that range from routine verifications to a few challenges. Ancillary materials are available at the publisher link.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Algebras Linear
- Resource Type:
- e-book
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e-book
Linear Regression Using R: An Introduction to Data Modeling presents one of the fundamental data modeling techniques in an informal tutorial style. Learn how to predict system outputs from measured data using a detailed step-by-step process to develop, train, and test reliable regression models. Key modeling and programming concepts are intuitively described using the R programming language. All of the necessary resources are freely available online.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Linguistics -- Statistical methods R (Computer program language) Mathematical linguistics
- Resource Type:
- e-book
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e-book
Microbiology covers the scope and sequence requirements for a single-semester microbiology course for non-majors. The book presents the core concepts of microbiology with a focus on applications for careers in allied health. The pedagogical features of the text make the material interesting and accessible while maintaining the career-application focus and scientific rigor inherent in the subject matter. Microbiology's art program enhances students' understanding of concepts through clear and effective illustrations, diagrams, and photographs.
- Subjects:
- Biology
- Keywords:
- Microbiology Textbooks
- Resource Type:
- e-book
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e-book
My Math GPS: Elementary Algebra Guided Problem Solving is a textbook that aligns to the CUNY Elementary Algebra Learning Objectives that are tested on the CUNY Elementary Algebra Final Exam (CEAFE). This book contextualizes arithmetic skills into Elementary Algebra content using a problem-solving pedagogy. Classroom assessments and online homework are available from the authors.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Algebra Textbooks
- Resource Type:
- e-book