tag:open.umn.edu,2005:/opentextbooks/subjects/pure?page=3Open Textbook Library - Pure Textbooks2019-06-22T16:27:43Zhttps://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.6752019-02-28T18:22:20Z2024-01-22T14:52:03ZFundamentals of Matrix Algebra<img alt="Read more about Fundamentals of Matrix Algebra" title="Fundamentals of Matrix Algebra cover image" class="cover " width="557" height="798" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NjIxLCJwdXIiOiJibG9iX2lkIn19--68a82c3c6d917ada6531531a815d9f73b32cd890/0000FunMatAlg.png" />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.6742019-02-28T17:39:48Z2024-03-25T13:11:24ZAPEX PreCalculus<img alt="Read more about APEX PreCalculus" title="APEX PreCalculus cover image" class="cover " width="641" height="833" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NjE5LCJwdXIiOiJibG9iX2lkIn19--e024b479ad3a18cf736ee2dd390243d1bf373b19/0000APEPreCal.png" />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.6702019-02-13T18:03:29Z2024-01-22T14:52:15ZLies, Damned Lies, or Statistics: How to Tell the Truth with Statistics<img alt="Read more about Lies, Damned Lies, or Statistics: How to Tell the Truth with Statistics" title="Lies, Damned Lies, or Statistics: How to Tell the Truth with Statistics cover image" class="cover " width="655" height="848" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NjE0LCJwdXIiOiJibG9iX2lkIn19--5c7fd4cc2b95bd755021797b60c907b5002b260a/0000LieDamSta.png" />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 2017.6492018-12-14T23:32:20Z2024-02-12T14:09:22ZOpen Resources for Community College Algebra<img alt="Read more about Open Resources for Community College Algebra" title="Open Resources for Community College Algebra cover image" class="cover " width="142" height="227" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NzE4LCJwdXIiOiJibG9iX2lkIn19--7d8e5467dc11c2ef2afe078f5fc9fee850b021a7/ORCCAbrandlogo.png" />Open Resources for Community College Algebra (ORCCA) is an open-source, openly-licensed textbook package (eBook, print, and online homework) for basic and intermediate algebra. At Portland Community College, Part 1 is used in MTH 60, Part 2 is used in MTH 65, and Part 3 is used in MTH 95.6112018-09-16T18:13:09Z2024-01-22T14:52:01ZTrigonometry<img alt="Read more about Trigonometry" title="Trigonometry cover image" class="cover " width="645" height="833" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NTM3LCJwdXIiOiJibG9iX2lkIn19--f63c3626153e21ac5dfaf3dbfe0caf4cc3905d48/0000Trigonome.PNG" />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.6102018-09-16T17:45:37Z2024-01-22T14:52:01ZCollege Algebra & Trigonometry<img alt="Read more about College Algebra & Trigonometry" title="College Algebra & Trigonometry cover image" class="cover " width="648" height="834" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NTM2LCJwdXIiOiJibG9iX2lkIn19--f2a5e683dc84d820ff8096d0bd5df979135c76c1/0000CollegAlg.PNG" />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.5572018-09-07T17:22:10Z2024-01-22T18:54:25ZIntroduction to GNU Octave: A brief tutorial for linear algebra and calculus students<img alt="Read more about Introduction to GNU Octave: A brief tutorial for linear algebra and calculus students" title="Introduction to GNU Octave: A brief tutorial for linear algebra and calculus students 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/eyJfcmFpbHMiOnsiZGF0YSI6NDgwLCJwdXIiOiJibG9iX2lkIn19--d84822615a72b4a50f7edc601d27f4d86886aa5d/0000IntroGNUO.png" />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.5292018-09-07T17:22:08Z2024-01-22T14:52:01ZIntermediate Algebra - 2e<img alt="Read more about Intermediate Algebra - 2e" title="Intermediate Algebra - 2e cover image" class="cover " width="478" height="522" data-controller="common--cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MTQ2MSwicHVyIjoiYmxvYl9pZCJ9fQ==--f0eaaa59707ceecd1959730fdcd41bf4541da150/LinearAlg.PNG" />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.
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