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A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically students will have taken calculus, but it is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form. Determinants and eigenvalues are covered along the way. A unique feature of this book is that chapters, sections and theorems are labeled rather than numbered. For example, the chapter on vectors is labeled "Chapter V" and the theorem that elementary matrices are nonsingular is labeled "Theorem EMN." Another feature of this book is that it is designed to integrate SAGE, an open source alternative to mathematics software such as Matlab and Maple. The author includes a 45-minute video tutorial on SAGE and teaching linear algebra. This textbook has been used in classes at: Centre for Excellence in Basic Sciences, Westmont College, University of Ottawa, Plymouth State University, University of Puget Sound, University of Notre Dame, Carleton University, Amherst College, Felician College, Southern Connecticut State University, Michigan Technological University, Mount Saint Mary College, University of Western Australia, Moorpark College, Pacific University, Colorado State University, Smith College, Wilbur Wright College, Central Washington U (Lynwood Center), St. Cloud State University, Miramar College, Loyola Marymount University.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Algebras Linear
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- e-book
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e-book
Teaching Mathematics is nothing less than a mathematical manifesto. Arising in response to a limited National Curriculum, and engaged with secondary schooling for those aged 11 ̶ 14 (Key Stage 3) in particular, this handbook for teachers will help them broaden and enrich their students’ mathematical education. It avoids specifying how to teach, and focuses instead on the central principles and concepts that need to be borne in mind by all teachers and textbook authors—but which are little appreciated in the UK at present. This study is aimed at anyone who would like to think more deeply about the discipline of ‘elementary mathematics’, in England and Wales and anywhere else. By analysing and supplementing the current curriculum, Teaching Mathematics provides food for thought for all those involved in school mathematics, whether as aspiring teachers or as experienced professionals. It challenges us all to reflect upon what it is that makes secondary school mathematics educationally, culturally, and socially important.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics -- Study teaching (Secondary)
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- e-book
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e-book
The pedagogical approach is anchored in formal definitions/proof of security, but in a way that I believe is more accessible than what is "traditional" in crypto. All security definitions are written in a unified and simplified "game-based" style. For an example of what security definitions look like in this style, see the index of security definitions (which will make more sense after reading chapters 2 & 4).
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Cryptography
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- e-book
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This book is written for students who have taken calculus and want to learn what “real mathematics" is. We hope you will find the material engaging and interesting, and that you will be encouraged to learn more advanced mathematics. This is the second edition of our text. It is intended for students who have taken a calculus course, and are interested in learning what higher mathematics is all about. It can be used as a textbook for an "Introduction to Proofs" course, or for self-study. Chapter 1: Preliminaries, Chapter 2: Relations, Chapter 3: Proofs, Chapter 4: Principles of Induction, Chapter 5: Limits, Chapter 6: Cardinality, Chapter 7: Divisibility, Chapter 8: The Real Numbers, Chapter 9: Complex Numbers. The last 4 chapters can also be used as independent introductions to four topics in mathematics: Cardinality; Divisibility; Real Numbers; Complex Numbers.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Logic Symbolic mathematical Textbooks
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- e-book
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e-book
A Cool, Brisk Walk Through Discrete Mathematics, an innovative and non-traditional approach to learning Discrete Math, is available for low cost from Blurb or via free download.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics Textbooks Computer science -- Mathematics
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- e-book
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e-book
Game theory is an excellent topic for a non-majors quantitative course as it develops mathematical models to understand human behavior in social, political, and economic settings. The variety of applications can appeal to a broad range of students. Additionally, students can learn mathematics through playing games, something many choose to do in their spare time! This text also includes an exploration of the ideas of game theory through the rich context of popular culture. It contains sections on applications of the concepts to popular culture. It suggests films, television shows, and novels with themes from game theory. The questions in each of these sections are intended to serve as essay prompts for writing assignments. Ancillary material are available to verified course instructors by emailing jfirkins@linfield.edu
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Game theory
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- e-book
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e-book
This book covers the standard material for a one-semester course in multivariable calculus. The topics include curves, differentiability and partial derivatives, multiple integrals, vector fields, line and surface integrals, and the theorems of Green, Stokes, and Gauss. Roughly speaking the book is organized into three main parts corresponding to the type of function being studied: vector-valued functions of one variable, real-valued functions of many variables, and finally the general case of vector-valued functions of many variables. As is always the case, the most productive way for students to learn is by doing problems, and the book is written to get to the exercises as quickly as possible. The presentation is geared towards students who enjoy learning mathematics for its own sake. As a result, there is a priority placed on understanding why things are true and a recognition that, when details are sketched or omitted, that should be acknowledged. Otherwise the level of rigor is fairly normal. Matrices are introduced and used freely. Prior experience with linear algebra is helpful, but not required.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Vector valued functions Calculus Textbooks
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- e-book
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e-book
This text is intended to support courses that bridge the divide between mathematics typically encountered in U.S. high school curricula and the practical problems that natural resource students might engage with in their disciplinary coursework and professional internships.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Problem solving Applied mathematics Textbooks Numerical analysis
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- e-book
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e-book
This book, which presupposes familiarity only with the most elementary concepts of arithmetic (divisibility properties, greatest common divisor, etc.), is an expanded version of a series of lectures for graduate students on elementary number theory. Topics include: Compositions and Partitions; Arithmetic Functions; Distribution of Primes; Irrational Numbers; Congruences; Diophantine Equations; Combinatorial Number Theory; and Geometry of Numbers. Three sections of problems (which include exercises as well as unsolved problems) complete the text.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Number theory Textbooks
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- e-book
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e-book
Introduction to Financial Mathematics: Concepts and Computational Methods serves as a primer in financial mathematics with a focus on conceptual understanding of models and problem solving. It includes the mathematical background needed for risk management, such as probability theory, optimization, and the like. The goal of the book is to expose the reader to a wide range of basic problems, some of which emphasize analytic ability, some requiring programming techniques and others focusing on statistical data analysis. In addition, it covers some areas which are outside the scope of mainstream financial mathematics textbooks. For example, it presents marginal account setting by the CCP and systemic risk, and a brief overview of the model risk. Inline exercises and examples are included to help students prepare for exams on this book.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Business mathematics Textbooks
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e-book
Motivated by questions in cosmology, the open-content text Geometry with an Introduction to Cosmic Topology uses Mobius transformations to develop hyperbolic, elliptic, and Euclidean geometry - three possibilities for the global geometry of the universe. The text, written for students who have taken vector calculus, also explores the interplay between the shape of a space and the type of geometry it admits. Geometry is suitable for a semester course in non-Euclidean geometry or as a guide to independent study, with over 200 exercises and several essays on topics including the history of geometry, parallax and curvature, and research aimed at determining the shape of the universe.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Cosmic magnetic fields Topology Textbooks Geometry
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- e-book
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e-book
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. For students who need a review of basic mathematical concepts before beginning "epsilon-delta"-style proofs, the text begins with material on set theory (sets, quantifiers, relations and mappings, countable sets), the real numbers (axioms, natural numbers, induction, consequences of the completeness axiom), and Euclidean and vector spaces; this material is condensed from the author's Basic Concepts of Mathematics, the complete version of which can be used as supplementary background material for the present text.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematical analysis Textbooks
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- e-book
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This textbook was born of a desire to contribute a viable, free, introductory Numerical Analysis textbook for instructors and students of mathematics. The ultimate goal of Tea Time Numerical Analysis is to be a complete, one-semester, single-pdf, downloadable textbook designed for mathematics classes. Now includes differential equations. Over 350 pages Over 1000 lines of code Over 200 figures Open source
- Subjects:
- Mathematics and Statistics
- Keywords:
- Numerical analysis -- Data processing Textbooks
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- e-book
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e-book
This is a free textbook teaching introductory statistics for undergraduates in Psychology. This textbook is part of a larger OER course package for teaching undergraduate statistics in Psychology, including this textbook, a lab manual, and a course website. All of the materials are free and copiable, with source code maintained in Github repositories.
- Subjects:
- Psychology and Mathematics and Statistics
- Keywords:
- Statistics Social sciences -- Statistical methods Textbooks Psychology
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- e-book
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e-book
It is increasingly clear that the shapes of reality – whether of the natural world, or of the built environment – are in some profound sense mathematical. Therefore it would benefit students and educated adults to understand what makes mathematics itself ‘tick’, and to appreciate why its shapes, patterns and formulae provide us with precisely the language we need to make sense of the world around us. The second part of this challenge may require some specialist experience, but the authors of this book concentrate on the first part, and explore the extent to which elementary mathematics allows us all to understand something of the nature of mathematics from the inside. The Essence of Mathematics consists of a sequence of 270 problems – with commentary and full solutions. The reader is assumed to have a reasonable grasp of school mathematics. More importantly, s/he should want to understand something of mathematics beyond the classroom, and be willing to engage with (and to reflect upon) challenging problems that highlight the essence of the discipline. The book consists of six chapters of increasing sophistication (Mental Skills; Arithmetic; Word Problems; Algebra; Geometry; Infinity), with interleaved commentary. The content will appeal to students considering further study of mathematics at university, teachers of mathematics at age 14-18, and anyone who wants to see what this kind of elementary content has to tell us about how mathematics really works.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics Textbooks
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- e-book
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First Semester in Numerical Analysis with Julia presents the theory and methods, together with the implementation of the algorithms using the Julia programming language (version 1.1.0). The book covers computer arithmetic, root-finding, numerical quadrature and differentiation, and approximation theory. The reader is expected to have studied calculus and linear algebra. Some familiarity with a programming language is beneficial, but not required. The programming language Julia will be introduced in the book. The simplicity of Julia allows bypassing the pseudocode and writing a computer code directly after the description of a method while minimizing the distraction the presentation of a computer code might cause to the flow of the main narrative.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Numerical analysis -- Data processing Mathematics Julia (Computer programming language) Textbooks
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- e-book
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e-book
A college (or advanced high school) level text dealing with the basic principles of matrix and linear algebra. It covers solving systems of linear equations, matrix arithmetic, the determinant, eigenvalues, and linear transformations. Numerous examples are given within the easy to read text. This third edition corrects several errors in the text and updates the font faces.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Matrices Algebra Textbooks
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- e-book
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e-book
This text was written as a prequel to the APEXCalculus series, a three–volume series on Calculus. This text is not intended to fully prepare students with all of the mathematical knowledge they need to tackle Calculus, rather it is designed to review mathematical concepts that are often stumbling blocks in the Calculus sequence. It starts basic and builds to more complex topics. This text is written so that each section and topic largely stands on its own, making it a good resource for students in Calculus who are struggling with the supporting mathemathics found in Calculus courses. The topics were chosen based on experience; several instructors in the Applied Mathemathics Department at the Virginia Military Institute (VMI) compiled a list of topics that Calculus students commonly struggle with, giving the focus of this text. This allows for a more focused approach; at first glance one of the obvious differences from a standard Pre-Calculus text is its size.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Precalculus Trigonometry Algebra Textbooks
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- e-book
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e-book
This version of YAINTT has a particular emphasis on connections to cryptology. The cryptologic material appears in Chapter 4 and §§5.5 and 5.6, arising naturally (I hope) out of the ambient number theory. The main cryptologic applications – being the RSA cryptosystem, Diffie-Hellman key exchange, and the ElGamal cryptosystem – come out so naturally from considerations of Euler’s Theorem, primitive roots, and indices that it renders quite ironic G.H. Hardy’s assertion [Har05] of the purity and eternal inapplicability of number theory. Note, however, that once we broach the subject of these cryptologic algorithms, we take the time to make careful definitions for many cryptological concepts and to develop some related ideas of cryptology which have much more tenuous connections to the topic of number theory. This material therefore has something of a different flavor from the rest of the text – as is true of all scholarly work in cryptology (indeed, perhaps in all of computer science), which is clearly a discipline with a different culture from that of “pure”mathematics. Obviously, these sections could be skipped by an uninterested reader, or remixed away by an instructor for her own particular class approach.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Number theory Textbooks
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- e-book
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e-book
This is a first draft of a free (as in speech, not as in beer, [Sta02]) (although it is free as in beer as well) textbook for a one-semester, undergraduate statistics course. It was used for Math 156 at Colorado State University–Pueblo in the spring semester of 2017.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Statistics Textbooks
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- e-book
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e-book
Business Mathematics was written to meet the needs of a twenty-first century student. It takes a systematic approach to helping students learn how to think and centers on a structured process termed the PUPP Model (Plan, Understand, Perform, and Present). This process is found throughout the text and in every guided example to help students develop a step-by-step problem-solving approach. This textbook simplifies and integrates annuity types and variable calculations, utilizes relevant algebraic symbols, and is integrated with the Texas Instruments BAII+ calculator. It also contains structured exercises, annotated and detailed formulas, and relevant personal and professional applications in discussion, guided examples, case studies, and even homework questions.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Business mathematics Textbooks
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- e-book
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e-book
The precursors to what we study today as Trigonometry had their origin in ancient Mesopotamia, Greece and India. These cultures used the concepts of angles and lengths as an aid to understanding the movements of the heavenly bodies in the night sky. Ancient trigonometry typically used angles and triangles that were embedded in circles so that many of the calculations used were based on the lengths of chords within a circle. The relationships between the lengths of the chords and other lines drawn within a circle and the measure of the corresponding central angle represent the foundation of trigonometry - the relationship between angles and distances.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Precalculus Trigonometry Textbooks
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- e-book
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e-book
This College Algebra text will cover a combination of classical algebra and analytic geometry, with an introduction to the transcendental exponential and logarithmic functions. If mathematics is the language of science, then algebra is the grammar of that language. Like grammar, algebra provides a structure to mathematical notation, in addition to its uses in problem solving and its ability to change the appearance of an expression without changing the value.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Trigonometry Algebra Textbooks
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- e-book
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e-book
Learning Statistics with R covers the contents of an introductory statistics class, as typically taught to undergraduate psychology students, focusing on the use of the R statistical software. The book discusses how to get started in R as well as giving an introduction to data manipulation and writing scripts. From a statistical perspective, the book discusses descriptive statistics and graphing first, followed by chapters on probability theory, sampling and estimation, and null hypothesis testing. After introducing the theory, the book covers the analysis of contingency tables, t-tests, ANOVAs and regression. Bayesian statistics are covered at the end of the book.
- Subjects:
- Psychology and Mathematics and Statistics
- Keywords:
- Statistics Social sciences -- Statistical methods Textbooks Statistics -- Computer programs R (Computer program language)
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- e-book
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e-book
This brief book provides a noncomprehensive introduction to GNU Octave, a free open source alternative to MatLab. The basic syntax and usage is explained through concrete examples from the mathematics courses a math, computer science, or engineering major encounters in the first two years of college: linear algebra, calculus, and differential equations.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Programming (Mathematics) Textbooks GNU Octave Computer science -- Mathematics
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- e-book
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e-book
We hope readers will take away three ideas from this book in addition to forming a foundationof statistical thinking and methods. (1) Statistics is an applied field with a wide range of practical applications. (2) You don't have to be a math guru to learn from real, interesting data. (3) Data are messy, and statistical tools are imperfect. But, when you understand the strengths and weaknesses of these tools, you can use them to learn about the real world. Textbook overviewThe chapters of this book are as follows: 1. Data collection. Data structures, variables, and basic data collection techniques. 2. Summarizing data. Data summaries and graphics. 3. Probability. The basic principles of probability. 4. Distributions of random variables. Introduction to key distributions, and how the normal model applies to the sample mean and sample proportion. 5. Foundation for inference. General ideas for statistical inference in the context of estimating the population proportion. 6. Inference for categorical data. Inference for proportions using the normal and chisquare distributions. 7. Inference for numerical data. Inference for one or two sample means using the t distribution, and comparisons of many means using ANOVA. 8. Introduction to linear regression. An introduction to regression with two variables. Instructions are also provided in several sections for using Casio and TI calculators.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Statistics Textbooks
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- e-book
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e-book
We hope readers will take away three ideas from this book in addition to forming a foundation of statistical thinking and methods. (1) Statistics is an applied field with a wide range of practical applications. (2) You don't have to be a math guru to learn from interesting, real data. (3) Data are messy, and statistical tools are imperfect. However, when you understand the strengths and weaknesses of these tools, you can use them to learn interesting things about the world. Textbook overview The chapters of this book are as follows: 1. Introduction to data. Data structures, variables, summaries, graphics, and basic data collection techniques. 2. Foundations for inference. Case studies are used to introduce the ideas of statistical inference with randomization and simulations. The content leads into the standard parametric framework, with techniques reinforced in the subsequent chapters.1 It is also possible to begin with this chapter and introduce tools from Chapter 1 as they are needed. 3. Inference for categorical data. Inference for proportions using the normal and chi-square distributions, as well as simulation and randomization techniques. 4. Inference for numerical data. Inference for one or two sample means using the t distribution, and also comparisons of many means using ANOVA. A special section for bootstrapping is provided at the end of the chapter. 5. Introduction to linear regression. An introduction to regression with two variables. Most of this chapter could be covered immediately after Chapter 1. 6. Multiple and logistic regression. An introduction to multiple regression and logistic regression for an accelerated course. Appendix A. Probability. An introduction to probability is provided as an optional reference. Exercises and additional probability content may be found in Chapter 2 of OpenIntro Statistics at openintro.org. Instructor feedback suggests that probability, if discussed, is best introduced at the very start or very end of the course.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Statistics Textbooks
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- e-book
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e-book
After being traditionally published for many years, this formidable text by W. Keith Nicholson is now being released as an open educational resource and part of Lyryx with Open Texts! Supporting today's students and instructors requires much more than a textbook, which is why Dr. Nicholson opted to work with Lyryx Learning. Overall, the aim of the text is to achieve a balance among computational skills, theory, and applications of linear algebra. It is a relatively advanced introduction to the ideas and techniques of linear algebra targeted for science and engineering students who need to understand not only how to use these methods but also gain insight into why they work. The contents have enough flexibility to present a traditional introduction to the subject, or to allow for a more applied course. Chapters 1–4 contain a one-semester course for beginners whereas Chapters 5–9 contain a second semester course. The text is primarily about real linear algebra with complex numbers being mentioned when appropriate (reviewed in Appendix A).
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Algebras Linear
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- e-book
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e-book
Intermediate Algebra 2e is designed to meet the scope and sequence requirements of a one-semester intermediate algebra course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. The material is presented as a sequence of clear steps, building on concepts presented in prealgebra and elementary algebra courses. The second edition contains detailed updates and accuracy revisions to address comments and suggestions from users. Dozens of faculty experts worked through the text, exercises and problems, graphics, and solutions to identify areas needing improvement. Though the authors made significant changes and enhancements, exercise and problem numbers remain nearly the same in order to ensure a smooth transition for faculty.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Algebra Textbooks
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- e-book
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e-book
Esta comunidad tiene como fin construir un texto base, que pretende ser la puerta de entrada al mundo de las matemáticas superiores y sus aplicaciones en el campo de las Ciencias de la Ingeniería.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Integral Calculus Differential calculus Textbooks
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- e-book
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e-book
This text is intended for a brief introductory course in plane geometry. It covers the topics from elementary geometry that are most likely to be required for more advanced mathematics courses. The only prerequisite is a semester of algebra. The emphasis is on applying basic geometric principles to the numerical solution of problems. For this purpose the number of theorems and definitions is kept small. Proofs are short and intuitive, mostly in the style of those found in a typical trigonometry or precalculus text. There is little attempt to teach theorem-proving or formal methods of reasoning. However the topics are ordered so that they may be taught deductively. The problems are arranged in pairs so that just the odd-numbered or just the even-numbered can be assigned. For assistance, the student may refer to a large number of completely worked-out examples. Most problems are presented in diagram form so that the difficulty of translating words into pictures is avoided. Many problems require the solution of algebraic equations in a geometric context. These are included to reinforce the student's algebraic and numerical skills, A few of the exercises involve the application of geometry to simple practical problems. These serve primarily to convince the student that what he or she is studying is useful. Historical notes are added where appropriate to give the student a greater appreciation of the subject. This book is suitable for a course of about 45 semester hours. A shorter course may be devised by skipping proofs, avoiding the more complicated problems and omitting less crucial topics.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Geometry
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- e-book
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e-book
This trigonometry textbook is different than other trigonometry books in that it is free to download, and the reader is expected to do more than read the book and is expected to study the material in the book by working out examples rather than just reading about them. So this book is not just about mathematical content but is also about the process of learning and doing mathematics. That is, this book is designed not to be just casually read but rather to be engaged. Since this can be a difficult task, there are several features of the book designed to assist students in this endeavor. In particular, most sections of the book start with a beginning activity that review prior mathematical work that is necessary for the new section or introduce new concepts and definitions that will be used later in that section. Each section also contains several progress checks that are short exercises or activities designed to help readers determine if they are understanding the material. In addition, the text contains links to several interactive Geogebra applets or worksheets. These applets are usually part of a beginning activity or a progress check and are intended to be used as part of the textbook.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Precalculus Trigonometry Textbooks
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- e-book
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e-book
Active Calculus Multivariable is the continuation of Active Calculus to multivariable functions. The Active Calculus texts are different from most existing calculus texts in at least the following ways: the texts are free for download by students and instructors in .pdf format; in the electronic format, graphics are in full color and there are live html links to java applets; the texts are open source, and interested instructors can gain access to the original source files upon request; the style of the texts requires students to be active learners — there are very few worked examples in the texts, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; 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; the exercises are few in number and challenging in nature.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Functional analysis Textbooks
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- e-book
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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
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- e-book
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e-book
This is a short introduction to the fundamentals of real analysis. Although the prerequisites are few, I have written the text assuming the reader has the level of mathematical maturity of one who has completed the standard sequence of calculus courses, has had some exposure to the ideas of mathematical proof (including induction), and has an acquaintance with such basic ideas as equivalence relations and the elementary algebraic properties of the integers.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematical analysis Textbooks
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- e-book
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e-book
I intend this book to be, firstly, a introduction to calculus based on the hyperrealnumber system. In other words, I will use infinitesimal and infinite numbers freely. Just as most beginning calculus books provide no logical justification for the real number system, I will provide none for the hyperreals. The reader interested in questions of foundations should consult books such asAbraham Robinson's Non-standard Analysis or Robert Goldblatt's Lectures onthe Hyperreals. Secondly, I have aimed the text primarily at readers who already have somefamiliarity with calculus. Although the book does not explicitly assume any prerequisites beyond basic algebra and trigonometry, in practice the pace istoo fast for most of those without some acquaintance with the basic notions of calculus.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Textbooks
- Resource Type:
- e-book
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e-book
This is a new approach to an introductory statistical inference textbook, motivated by probability theory as logic. It is targeted to the typical Statistics 101 college student, and covers the topics typically covered in the first semester of such a course. It is freely available under the Creative Commons License, and includes a software library in Python for making some of the calculations and visualizations easier.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematical statistics 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
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e-book
Elementary Algebra is designed to meet the scope and sequence requirements of a one-semester elementary algebra course. The book's organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Algebra Textbooks
- Resource Type:
- e-book
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e-book
This book is meant to be rigorous, conservative, elementary and minimalist. At the same time it includes about the maximum what students can absorb in one semester. Approximately one-third of the material used to be covered in high school, but not any more.The present book is based on the courses given by the author at the Pennsylvania State University as an introduction to the foundations of geometry. The lectures were oriented to sophomore and senior university students. These students already had a calculus course. In particular,they are familiar with the real numbers and continuity. It makes it possible to cover the material faster and in a more rigorous way than it could be done in high school.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Geometry Plane Textbooks
- Resource Type:
- e-book
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e-book
Calculus: Early Transcendentals, originally by D. Guichard, has been redesigned by the Lyryx editorial team. Substantial portions of the content, examples, and diagrams have been redeveloped, with additional contributions provided by experienced and practicing instructors. This approachable text provides a comprehensive understanding of the necessary techniques and concepts of the typical Calculus course sequence, and is suitable for the standard Calculus I, II and III courses. To practice and develop an understanding of topics, this text offers a range of problems, from routine to challenging, with selected solutions. As this is an open text, instructors and students are encouraged to interact with the textbook through annotating, revising, and reusing to your advantage. Suggestions for contributions to this growing textbook are welcome. Lyryx develops and supports open texts, with editorial services to adapt the text for each particular course. In addition, Lyryx provides content-specific formative online assessment, a wide variety of supplements, and in-house support available 7 days/week for both students and instructors.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Textbooks
- 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
Applied Finite Mathematics covers topics including linear equations, matrices, linear programming, the mathematics of finance, sets and counting, probability, Markov chains, and game theory.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics Textbooks
- Resource Type:
- e-book
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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
The book "Introductory Business Statistics" by Thomas K. Tiemann explores the basic ideas behind statistics, such as populations, samples, the difference between data and information, and most importantly sampling distributions. The author covers topics including descriptive statistics and frequency distributions, normal and t-distributions, hypothesis testing, t-tests, f-tests, analysis of variance, non-parametric tests, and regression basics. Using real-world examples throughout the text, the author hopes to help students understand how statistics works, not just how to "get the right number."
- Subjects:
- Management and Mathematics and Statistics
- Keywords:
- Industrial management -- Statistical methods Commercial statistics Textbooks
- Resource Type:
- e-book
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e-book
You are probably asking yourself the question, "When and where will I use statistics?". If you read any newspaper or watch television, or use the Internet, you will see statistical information. There are statistics about crime, sports, education, politics, and real estate. Typically, when you read a newspaper article or watch a news program on television, you are given sample information. With this information, you may make a decision about the correctness of a statement, claim, or "fact." Statistical methods can help you make the "best educated guess."
- Subjects:
- Management and Mathematics and Statistics
- Keywords:
- Industrial management -- Statistical methods Commercial statistics 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
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
Applied Combinatorics is an open-source textbook for a course covering the fundamental enumeration techniques (permutations, combinations, subsets, pigeon hole principle), recursion and mathematical induction, more advanced enumeration techniques (inclusion-exclusion, generating functions, recurrence relations, Polyá theory), discrete structures (graphs, digraphs, posets, interval orders), and discrete optimization (minimum weight spanning trees, shortest paths, network flows). There are also chapters introducing discrete probability, Ramsey theory, combinatorial applications of network flows, and a few other nuggets of discrete mathematics. Applied Combinatorics began its life as a set of course notes we developed when Mitch was a TA for a larger than usual section of Tom's MATH 3012: Applied Combinatorics course at Georgia Tech in Spring Semester 2006. Since then, the material has been greatly expanded and exercises have been added. The text has been in use for most MATH 3012 sections at Georgia Tech for several years now. Since the text has been available online for free, it has also been adopted at a number of other institutions for a wide variety of courses. In August 2016, we made the first release of Applied Combinatorics in HTML format, thanks to a conversion of the book's source from LaTeX to MathBook XML. An inexpensive print-on-demand version is also available for purchase. Find out all about ways to get the book. Since Fall 2016, Applied Combinatorics has been on the list of approved open textbooks from the American Institute of Mathematics. Applied Combinatorics is open source and licensed under the Creative Commons Attribution-ShareAlike 4.0 International License (CC-BY-SA).
- Subjects:
- Mathematics and Statistics
- Keywords:
- Combinatorial analysis Graph theory Textbooks
- Resource Type:
- e-book
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e-book
Think Bayes is an introduction to Bayesian statistics using computational methods. The premise of this book, and the other books in the Think X series, is that if you know how to program, you can use that skill to learn other topics. Most books on Bayesian statistics use mathematical notation and present ideas in terms of mathematical concepts like calculus. This book uses Python code instead of math, and discrete approximations instead of continuous mathematics. As a result, what would be an integral in a math book becomes a summation, and most operations on probability distributions are simple loops. I think this presentation is easier to understand, at least for people with programming skills. It is also more general, because when we make modeling decisions, we can choose the most appropriate model without worrying too much about whether the model lends itself to conventional analysis. Also, it provides a smooth development path from simple examples to real-world problems.
- Subjects:
- Computing and Mathematics and Statistics
- Keywords:
- Bayesian statistical decision theory Python (Computer program language) Textbooks
- Resource Type:
- e-book