tag:open.umn.edu,2005:/opentextbooks/textbooks?commit=Go&page=6&term=algebra&utf8=%E2%9C%93Open Textbook Library - Search results for "algebra"2019-06-22T16:27:43Zhttps://open.umn.edu/assets/common/favicon/favicon-1594c2156c95ca22b1a0d803d547e5892bb0e351f682be842d64927ecda092e7.icohttps://open.umn.edu/assets/library/otl_logo-f9161d5c999f5852b38260727d49b4e7d7142fc707ec9596a5256a778f957ffc.png7272019-06-22T16:27:43Z2024-01-22T14:52:18ZTeaching Mathematics at Secondary Level<img alt="Read more about Teaching Mathematics at Secondary Level" title="Teaching Mathematics at Secondary Level cover image" class="cover " width="160" height="241" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NjcyLCJwdXIiOiJibG9iX2lkIn19--51c74badf4924aaec35a5887a99ce98fd890dbc0/9781783741397.jpg" />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.7262019-06-22T15:18:00Z2024-01-22T14:52:18ZThe Essence of Mathematics Through Elementary Problems<img alt="Read more about The Essence of Mathematics Through Elementary Problems" title="The Essence of Mathematics Through Elementary Problems cover image" class="cover " width="160" height="241" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NjcxLCJwdXIiOiJibG9iX2lkIn19--9f3a78a492e1bf2038fdeea38f1397b4f92bd0e9/9781783747016.jpg" />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.7102019-05-15T23:37:43Z2024-03-05T02:11:42ZFirst Semester in Numerical Analysis with Julia<img alt="Read more about First Semester in Numerical Analysis with Julia" title="First Semester in Numerical Analysis with Julia cover image" class="cover " width="155" height="200" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NjU2LCJwdXIiOiJibG9iX2lkIn19--ad942b5e610404311068b8a80f91f2b196c098d3/0000FSNumAnJu.jpg" />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.6422018-11-17T23:55:20Z2024-01-22T14:52:06ZBusiness Math: A Step-by-Step Handbook<img alt="Read more about Business Math: A Step-by-Step Handbook" title="Business Math: A Step-by-Step Handbook cover image" class="cover " width="1275" height="1650" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6Mjc3OSwicHVyIjoiYmxvYl9pZCJ9fQ==--efbe7d78f26171d06a6f77beca690afef66ca5cb/Lyryx_Business%20Math_2021B.jpg" />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.5742018-09-07T17:22:11Z2024-01-22T14:52:15ZOperational Amplifiers & Linear Integrated Circuits: Theory and Application - 3e<img alt="Read more about Operational Amplifiers & Linear Integrated Circuits: Theory and Application - 3e" title="Operational Amplifiers & Linear Integrated Circuits: Theory and Application - 3e cover image" class="cover " width="272" height="344" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NDk3LCJwdXIiOiJibG9iX2lkIn19--64f1f26c9a9e45282220148751f099c1d6eba646/0000OpeAmpLIC.png" />The goal of this text, as its name implies, is to allow the reader to become proficient in the analysis and design of circuits utilizing modern linear ICs. It progresses from the fundamental circuit building blocks through to analog/digital conversion systems. The text is intended for use in a second year Operational Amplifiers course at the Associate level, or for a junior level course at the Baccalaureate level. In order to make effective use of this text, students should have already taken a course in basic discrete transistor circuits, and have a solid background in algebra and trigonometry, along with exposure to phasors. Calculus is used in certain sections of the text, but for the most part, its use is kept to a minimum. For students without a calculus background, these sections may be skipped without a loss of continuity. (The sole exception to this being Chapter Ten, Integrators and Differentiators, which hinges upon knowledge of calculus.) There is also a lab manual for this textbook.5732018-09-07T17:22:11Z2024-01-22T14:52:15ZSemiconductor Devices: Theory and Application<img alt="Read more about Semiconductor Devices: Theory and Application" title="Semiconductor Devices: Theory and Application cover image" class="cover " width="373" height="480" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NDk2LCJwdXIiOiJibG9iX2lkIn19--a9765616c46ea4cd39030eaffcac6398502ce084/0000SemDevThA.png" />The goal of this text, as its name implies, is to allow the reader to become proficient in the analysis and design of circuits utilizing discrete semiconductor devices. It progresses from basic diodes through bipolar and field effect transistors. The text is intended for use in a first or second year course on semiconductors at the Associate or Baccalaureate level. In order to make effective use of this text, students should have already taken coursework in basic DC and AC circuits, and have a solid background in algebra and trigonometry along with exposure to phasors. Calculus is used in certain sections of the text but for the most part it is used for equation derivations and proofs, and is kept to a minimum. For students without a calculus background these sections may be skipped without a loss of continuity. There is also a lab manual for this textbook.5702018-09-07T17:22:10Z2024-01-22T14:52:22ZMathematics for Elementary Teachers<img alt="Read more about Mathematics for Elementary Teachers" title="Mathematics for Elementary Teachers cover image" class="cover " width="1275" height="1651" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NDkzLCJwdXIiOiJibG9iX2lkIn19--ebfb89d9ebaeb41b0da25bffeb5dd09186bbbe50/0000MatEleTea.png" />This book will help you to understand elementary mathematics more deeply, gain facility with creating and using mathematical notation, develop a habit of looking for reasons and creating mathematical explanations, and become more comfortable exploring unfamiliar mathematical situations.The primary goal of this book is to help you learn to think like a mathematician in some very specific ways. You will:• Make sense of problems and persevere in solving them. You will develop and demonstrate this skill by working on difficult problems, making incremental progress, and revising solutions to problems as you learn more.• Reason abstractly and quantitatively. You will demonstrate this skill by learning to represent situations using mathematical notation (abstraction) as well as creating and testing examples (making situations more concrete).• Construct viable arguments and critique the reasoning of others. You will be expected to create both written and verbal explanations for your solutions to problems. The most important questions in this class are “Why?” and “How do you know you're right?” Practice asking these questions of yourself, of your professor, and of your fellow students.Throughout the book, you will learn how to learn mathematics on you own by reading, working on problems, and making sense of new ideas on your own and in collaboration with other students in the class.5362018-09-07T17:22:08Z2024-01-22T14:51:57ZQuantitative Research Methods for Political Science, Public Policy and Public Administration (With Applications in R) - 3rd Edition<img alt="Read more about Quantitative Research Methods for Political Science, Public Policy and Public Administration (With Applications in R) - 3rd Edition" title="Quantitative Research Methods for Political Science, Public Policy and Public Administration (With Applications in R) - 3rd Edition cover image" class="cover " width="2550" height="3300" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NDYxLCJwdXIiOiJibG9iX2lkIn19--b57d3b79613ad7c81ee5def561e24ff81bb284fc/0000QuaResMet.png" />The focus of this book is on using quantitative research methods to test hypotheses and build theory in political science, public policy and public administration. It is designed for advanced undergraduate courses, or introductory and intermediate graduate-level courses. The first part of the book introduces the scientific method, then covers research design, measurement, descriptive statistics, probability, inference, and basic measures of association. The second part of the book covers bivariate and multiple linear regression using the ordinary least squares, the calculus and matrix algebra that are necessary for understanding bivariate and multiple linear regression, the assumptions that underlie these methods, and then provides a short introduction to generalized linear models.The book fully embraces the open access and open source philosophies. The book is freely available in the SHAREOK repository; it is written in R Markdown files that are available in a public GitHub repository; it uses and teaches R and RStudio for data analysis, visualization and data management; and it uses publically available survey data (from the Meso-Scale Integrated Socio-geographic Network) to illustrate important concepts and methods. We encourage students to download the data, replicate the examples, and explore further! We also encourage instructors to download the R Markdown files and modify the text for use in different courses.5082018-09-07T17:22:06Z2024-03-25T13:07:03ZElementary College Geometry - 2021 ed.<img alt="Read more about Elementary College Geometry - 2021 ed." title="Elementary College Geometry - 2021 ed. cover image" class="cover " width="402" height="562" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6Mzk4NCwicHVyIjoiYmxvYl9pZCJ9fQ==--e77af57592fcbd3f4af559dfa1772beec1a3109c/Screen%20Shot%202022-09-05%20at%203.49.40%20PM.png" />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.4632018-09-07T17:22:03Z2024-01-22T14:51:56ZA Primer of Real Analysis<img alt="Read more about A Primer of Real Analysis" title="A Primer of Real Analysis cover image" class="cover " width="825" height="839" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MzkxLCJwdXIiOiJibG9iX2lkIn19--864c61adae81eab2962f3b4d6c0f8f391a65765f/0000PriReaAna.png" />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.
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