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- Title
- A Computational Introduction to Number Theory and Algebra.
- Abstract/Description
- All of the mathematics required beyond basic calculus is developed “from scratch.” Moreover, the book generally alternates between “theory” and “applications”: one or two chapters on a particular set of purely mathematical concepts are followed by one or two chapters on algorithms and applications; the mathematics provides the theoretical underpinnings for the applications, while the applications both motivate and illustrate the mathematics. Of course, this dichotomy between theory and applications is not perfectly maintained: the chapters that focus mainly on applications include the development of some of the mathematics that is specific to a particular application, and very occasionally, some of the chapters that focus mainly on mathematics include a discussion of related algorithmic ideas as well. The mathematical material covered includes the basics of number theory (including unique factorization, congruences, the distribution of primes, and quadratic reciprocity) and of abstract algebra (including groups, rings, fields, and vector spaces). It also includes an introduction to discrete probability theory—this material is needed to properly treat the topics of probabilistic algorithms and cryptographic applications. The treatment of all these topics is more or less standard, except that the text only deals with commutative structures (i.e., abelian groups and commutative rings with unity) — this is all that is really needed for the purposes of this text, and the theory of these structures is much simpler and more transparent than that of more general, non-commutative structures. • There are a few sections that are marked with a “(∗),” indicating that the material covered in that section is a bit technical, and is not needed else- where. • There are many examples in the text, which form an integral part of the book, and should not be skipped. • There are a number of exercises in the text that serve to reinforce, as well as to develop important applications and generalizations of, the material presented in the text. • Some exercises are underlined. These develop important (but usually simple) facts, and should be viewed as an integral part of the book. It is highly recommended that the reader work these exercises, or at the very least, read and understand their statements. • In solving exercises, the reader is free to use any previously stated results in the text, including those in previous exercises. However, except where otherwise noted, any result in a section marked with a “(∗),” or in §5.5, need not and should not be used outside the section in which it appears. • There is a very brief “Preliminaries” chapter, which fixes a bit of notation and recalls a few standard facts. This should be skimmed over by the reader. • There is an appendix that contains a few useful facts; where such a fact is used in the text, there is a reference such as “see §An,” which refers to the item labeled “An” in the appendix.
- Date Issued
- 2009
- Title
- Algebra and Trigonometry.
- Abstract/Description
- Algebra and Trigonometry provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensure that the book meets the needs of a variety of courses. Algebra and Trigonometry offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.
- Date Issued
- 2-13-2015
- Title
- Algebra and Trigonometry 2e.
- Abstract/Description
- Algebra and Trigonometry 2e provides a comprehensive exploration of mathematical principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensure that the book addresses the needs of a variety of courses. Algebra and Trigonometry 2e offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned. The Algebra and Trigonometry 2e revision focused on improving relevance and representation as well as mathematical clarity and accuracy. Introductory narratives, examples, and problems were reviewed and revised using a diversity, equity, and inclusion framework. Many contexts, scenarios, and images have been changed to become even more relevant to students’ lives and interests. To maintain our commitment to accuracy and precision, examples, exercises, and solutions were reviewed by multiple faculty experts. All improvement suggestions and errata updates from the first edition were considered and unified across the different formats of the text. The first edition of Algebra and Trigonometry by OpenStax is available in web view here.
- Date Issued
- 12-21-2021
- Title
- Applied Probability.
- Abstract/Description
- This is a "first course" in the sense that it presumes no previous course in probability. The mathematical prerequisites are ordinary calculus and the elements of matrix algebra. A few standard series and integrals are used, and double integrals are evaluated as iterated integrals. The reader who can evaluate simple integrals can learn quickly from the examples how to deal with the iterated integrals used in the theory of expectation and conditional expectation. Appendix B provides a convenient compendium of mathematical facts used frequently in this work. And the symbolic toolbox, implementing MAPLE, may be used to evaluate integrals, if desired. In addition to an introduction to the essential features of basic probability in terms of a precise mathematical model, the work describes and employs user defined MATLAB procedures and functions (which we refer to as m-programs, or simply programs) to solve many important problems in basic probability. This should make the work useful as a stand-alone exposition as well as a supplement to any of several current textbooks. Most of the programs developed here were written in earlier versions of MATLAB, but have been revised slightly to make them quite compatible with MATLAB 7. In a few cases, alternate implementations are available in the Statistics Toolbox, but are implemented here directly from the basic MATLAB program, so that students need only that program (and the symbolic mathematics toolbox, if they desire its aid in evaluating integrals). Since machine methods require precise formulation of problems in appropriate mathematical form, it is necessary to provide some supplementary analytical material, principally the so-called minterm analysis. This material is not only important for computational purposes, but is also useful in displaying some of the structure of the relationships among events.
- Date Issued
- 2009
- Title
- Beginning and Intermediate Algebra.
- Date Issued
- 2020
- Title
- Collaborative Statistics.
- Abstract/Description
- Collaborative Statistics was written by Barbara Illowsky and Susan Dean, faculty members at De Anza Collegein Cupertino, California. The textbook was developed over several years and has been used in regularand honors-level classroom settings and in distance learning classes. Courses using this textbook have beenarticulated by the University of California for transfer of credit. The textbook contains full materials forcourse offerings, including expository text, examples, labs, homework, and projects. A Teacher's Guide iscurrently available in print form and on the Connexions site at and supplemental course materials including additional problem sets and video lectures are available. The on-line text for each of these collections collections willmeet the Section 508 standards for accessibility. An on-line course based on the textbook was also developed by Illowsky and Dean. It has won an awardas the best on-line California community college course. The on-line course will be available at a later dateas a collection in Connexions, and each lesson in the on-line course will be linked to the on-line textbookchapter. The on-line course will include, in addition to expository text and examples, videos of courselectures in captioned and non-captioned format. The original preface to the book as written by professors Illowsky and Dean, now follows: This book is intended for introductory statistics courses being taken by students at two– and four–yearcolleges who are majoring in fields other than math or engineering. Intermediate algebra is the only prerequisite.The book focuses on applications of statistical knowledge rather than the theory behind it. Thetext is named Collaborative Statistics because students learn best by doing. In fact, they learn best byworking in small groups. The old saying “two heads are better than one” truly applies here. Our emphasis in this text is on four main concepts: thinking statistically incorporating technology working collaboratively writing thoughtfully These concepts are integral to our course. Students learn the best by actively participating, not by justwatching and listening. Teaching should be highly interactive. Students need to be thoroughly engagedin the learning process in order to make sense of statistical concepts. Collaborative Statistics providestechniques for students to write across the curriculum, to collaborate with their peers, to think statistically,and to incorporate technology. This book takes students step by step. The text is interactive. Therefore, students can immediately applywhat they read. Once students have completed the process of problem solving, they can tackle interestingand challenging problems relevant to today's world. The problems require the students to apply theirnewly found skills. In addition, technology (TI-83 graphing calculators are highlighted) is incorporatedthroughout the text and the problems, as well as in the special group activities and projects. The book alsocontains labs that use real data and practices that lead students step by step through the problem solvingprocess. At De Anza, along with hundreds of other colleges across the country, the college audience involves alarge number of ESL students as well as students from many disciplines. The ESL students, as well asthe non-ESL students, have been especially appreciative of this text. They find it extremely readable andunderstandable. Collaborative Statistics has been used in classes that range from 20 to 120 students, and inregular, honor, and distance learning classes
- Date Issued
- 2021
- Title
- College Algebra.
- Abstract/Description
- College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.
- Date Issued
- 2-13-2015
- Title
- College Algebra: Version (π) Corrected Edition.
- Date Issued
- 2013
- Title
- Concepts in Statistics.
- Abstract/Description
- Using highly interactive learning design, this Concepts in Statistics course provides students with a strong understanding of fundamental principles that guide the study of statistical inference. Drawing from Open Learning Initiative (OLI) source content, this course’s simulations and lab-style synthesis activities invite hands-on exploration of statistical concepts. Students learn to summarize data graphically and numerically; examine relationships among quantitative data; understand the role of probability and probability distributions; link probability to statistical inference; and conduct foundational statistical calculations and analyses.
- Title
- Elementary Algebra v. 1.0 (Saylor Academy).
- Abstract/Description
- It is essential to lay a solid foundation in mathematics if a student is to be competitive in today’s global market. The importance of algebra, in particular, cannot be overstated, as it is the basis of all mathematical modeling used in applications found in all disciplines. Traditionally, the study of algebra is separated into a two parts, elementary algebra and intermediate algebra. This textbook, Elementary Algebra, is the first part, written in a clear and concise manner, making no assumption of prior algebra experience. It carefully guides students from the basics to the more advanced techniques required to be successful in the next course. This text is, by far, the best elementary algebra textbook offered under a Creative Commons license. It is written in such a way as to maintain maximum flexibility and usability. A modular format was carefully integrated into the design. For example, certain topics, like functions, can be covered or omitted without compromising the overall flow of the text. An introduction of square roots in Chapter 1 is another example that allows for instructors wishing to include the quadratic formula early to do so. Topics such as these are carefully included to enhance the flexibility throughout. This textbook will effectively enable traditional or nontraditional approaches to elementary algebra. This, in addition to robust and diverse exercise sets, provides the base for an excellent individualized textbook instructors can use free of needless edition changes and excessive costs!
- Date Issued
- 2011
- Title
- Fundamentals of Mathematics.
- Abstract/Description
- Fundamentals of Mathematics is a work text that covers the traditional study in a modern prealgebra course, as well as the topics of estimation, elementary analytic geometry, and introductory algebra. It is intended for students who: have had previous courses in prealgebra, wish to meet the prerequisites of higher level courses such as elementary algebra, need to review fundamental mathematical concenpts and techniques. This text will help the student devlop the insight and intuition necessary to master arithmetic techniques and manipulative skills. It was written with the following main objectives: to provide the student with an understandable and usable source of information, to provide the student with the maximum oppurtinity to see that arithmetic concepts and techniques are logically based, to instill in the student the understanding and intuitive skills necessary to know how and when to use particular arithmetic concepts in subsequent material cources and nonclassroom situations, to give the students the ability to correctly interpret arithmetically obtained results. We have tried to meet these objects by presenting material dynamically much the way an instructure might present the material visually in a classroom. (See the development of the concept of addition and subtraction of fractions in section 5.3 for examples) Intuition and understanding are some of the keys to creative thinking, we belive that the material presented in this text will help students realize that mathematics is a creative subject.
- Date Issued
- 2008
- Title
- Galilieo Open Leanring Materials.
- Date Issued
- 04/2021
- Title
- Intermediate Algebra.
- Abstract/Description
- Intermediate Algebra is a textbook for students who have some acquaintance with the basic notions of variables and equations, negative numbers, and graphs, although we provide a "Toolkit" to help the reader refresh any skills that may have gotten a little rusty. In this book we journey farther into the subject, to explore a greater variety of topics including graphs and modeling, curve-fitting, variation, exponentials and logarithms, and the conic sections. We use technology to handle data and give some instructions for using a graphing calculator, but these can easily be adapted to any other graphing utility.
- Date Issued
- 2020
- Title
- Intermediate Algebra 1e (OpenStax).
- Abstract/Description
- Intermediate Algebra 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. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics.
- Date Issued
- 05/14/2017
- Title
- Intermediate Algebra 2e.
- Abstract/Description
- 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.
- Date Issued
- 05/06/2020
- Title
- Intermediate Algebra BC Campus.
- Abstract/Description
- This OpenStax book was imported into Pressbooks on October 3, 2019, to make it easier for instructors to edit, build upon, and remix the content. Intermediate Algebra 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.
- Date Issued
- 10-03-19
- Title
- Intermediate Algebra Libguide (FSCJ).
- Abstract/Description
- Resource for math including books, ebooks, videos, and more learning tools for Intermediate Algebra level, college mathematics.
- Date Issued
- 04/14/2023
- Title
- Intermediate Algebra Libguide(SJR State College).
- Date Issued
- 05/25/2022
- Title
- Intermediate Algebra Saylor Foundation.
- Abstract/Description
- It is essential to lay a solid foundation in mathematics if a student is to be competitive in today's global market. The importance of algebra, in particular, cannot be overstated, as it is the basis of all mathematical modeling used in applications found in all disciplines. Traditionally, the study of algebra is separated into a two parts, Elementary and Intermediate Algebra. This textbook by John Redden, Intermediate Algebra, is the second part. Written in a clear and concise manner, it carefully builds on the basics learned in Elementary Algebra and introduces the more advanced topics required for further study in applications found in most disciplines. Used as a standalone textbook, Intermediate Algebra offers plenty of review as well as something new to engage the student in each chapter. Written as a blend of the traditional and graphical approaches to the subject, this textbook introduces functions early and stresses the geometry behind the algebra. While CAS independent, a standard scientific calculator will be required and further research using technology is encouraged. Intermediate Algebra is written from the ground up in an open and modular format, allowing the instructor to modify it and leverage their individual expertise as a means to maximize the student experience and success. A more modernized element, embedded video examples, are present, but the importance of practice with pencil and paper is consistently stressed. Therefore, this text respects the traditional approaches to algebra pedagogy while enhancing it with the technology available today. The importance of Algebra cannot be overstated; it is the basis for all mathematical modeling used in all disciplines. After completing a course sequence based on Elementary and Intermediate Algebra, students will be on firm footing for success in higher-level studies at the college level.
- Date Issued
- 2012
- Title
- Introductory Statistics.
- Abstract/Description
- This book is meant to be a textbook for a standard one-semester introductory statistics course for general education students. Our motivation for writing it is twofold: 1.) to provide a low-cost alternative to many existing popular textbooks on the market; and 2.) to provide a quality textbook on the subject with a focus on the core material of the course in a balanced presentation.The high cost of textbooks has spiraled out of control in recent years. The high frequency at which new editions of popular texts appear puts a tremendous burden on students and faculty alike, as well as the natural environment. Against this background we set out to write a quality textbook with materials such as examples and exercises that age well with time and that would therefore not require frequent new editions. Our vision resonates well with the publisher’s business model which includes free digital access, reduced paper prints, and easy customization by instructors if additional material is desired. Over time the core content of this course has developed into a well-defined body of material that is substantial for a one-semester course. The authors believe that the students in this course are best served by a focus on the core material and not by an exposure to a plethora of peripheral topics.Therefore in writing this book we have sought to present material that comprises fully a central body of knowledge that is defined according to convention, realistic expectation with respect to course duration and students’ maturity level, and our professional judgment and experience. We believe that certain topics, among them Poisson and geometric distributions and the normal approximation to the binomial distribution (particularly with a continuity correction) are distracting in nature. Other topics, such as nonparametric methods, while important, do not belong in a first course in statistics. As a result we envision a smaller and less intimidating textbook that trades some extended and unnecessary topics for a better focused presentation of the central material. Textbooks for this course cover a wide range in terms of simplicity and complexity. Some popular textbooks emphasize the simplicity of individual concepts to the point of lacking the coherence of an overall network of concepts. Other textbooks include overly detailed conceptual and computational discussions and as a result repel students from reading them. The authors believe that a successful book must strike a balance between the two extremes, however difficult it may be. As a consequence the overarching guiding principle of our writing is to seek simplicity but to preserve the coherence of the whole body of information communicated, both conceptually and computationally. We seek to remind ourselves (and others) that we teach ideas, not just step-by-step algorithms, but ideas that can be implemented by straightforward algorithms.
- Date Issued
- 2012