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-1-1A First Course in Linear Algebra
https://www.merlot.org/merlot/viewMaterial.htm?id=297792
A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically such a student will have taken calculus, but this 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.<br><br>
PDF versions are available to download for printing or on-screen viewing, an online version is available, and physical copies may be purchased from the print-on-demand service at Lulu.com. <br><br>
GNU Free Documentation LicenseThu, 13 Mar 2008 19:39:13 GMTRobert Beezer University of Pugent SoundAlgebra: Abstract and Concrete
https://www.merlot.org/merlot/viewMaterial.htm?id=313490
The book provides a thorough introduction to "modern'' or "abstract'' algebra at a level suitable for upper-level undergraduates and beginning graduate students. The book addresses the conventional topics: groups, rings, fields, and linear algebra, with symmetry as a unifying theme.Fri, 30 May 2008 07:37:12 GMTFrederick Goodman University of IowaThe Math Open Reference Project
https://www.merlot.org/merlot/viewMaterial.htm?id=350875
A free interactive math textbook on the web. Initially covering high-school geometry.Mon, 17 Nov 2008 19:36:54 GMTJohn Page Math Open Reference ProjectDimensions (geometry)
https://www.merlot.org/merlot/viewMaterial.htm?id=350912
<p>This is a free, online textbook that provides information on dimensions, from longtitude and latitude to the proof of a theorem of geometry. There are 9 chapters, each 13 minutes long. The book contains a total of 117 minutes of video, but can also be read as an ordinary textbook.</p><p>The film can be enjoyed by anyone, provided the chapters are well-chosen. There are 9 chapters, each 13 minutes long. Chapters 3-4, 5-6 and 7-8 are double chapters, but apart from that, they are more or less independent of each other.</p>Mon, 17 Nov 2008 19:53:36 GMTMultiple others in credits http://www.dimensions-math.org/Dim_merci_E.htm; Étienne Ghys; Jos Leys; Aurélien Alvarez Multiple international sponsorsA First Course in Linear Algebra
https://www.merlot.org/merlot/viewMaterial.htm?id=76448
<p style="margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%;"><span style="color: #00000a;"><span style="font-family: 'arial' , serif;">This text, originally by K. Kuttler, has been redesigned by the Lyryx editorial team as a first course in linear algebra for science and engineering students who have an understanding of basic algebra.</span></span></p>
<p style="margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%;"><span style="color: #00000a;"><span style="font-family: 'arial' , serif;">All major topics of linear algebra are available in detail, as well as proofs of important theorems. In addition, connections to topics covered in advanced courses are introduced. The text is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile.</span></span></p>
<p style="margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%;"><span style="color: #00000a;"><span style="font-family: 'arial' , serif;">Each chapter begins with a list of student learning outcomes, and examples and diagrams are given throughout the text to reinforce ideas and provide guidance on how to approach various problems. Suggested exercises are included at the end of each section, with selected answers at the end of the text.</span></span></p>
<p style="margin-bottom: 0cm; line-height: 100%;"><span style="color: #00000a;">Lyryx develops and supports open texts, with editorial services to adapt the text for each particular course. In addition, Lyryx provides</span><span style="color: #00000a;">content-specific formative online assessment, a wide variety of supplements, and in-house support available 7 days/week for both students and instructors.</span></p>Thu, 07 Mar 2002 08:00:00 GMTK. Kuttler, Adapted by Lyryx Learning Lyryx LearningAlgebra
https://www.merlot.org/merlot/viewMaterial.htm?id=813968
<p>'The Boundless Algebra textbook is a college-level, introductory textbook that covers the important subject of Algebra -- one of the basic building blocks of studies in higher mathematics. Boundless works with subject matter experts to select the best open educational resources available on the web, review the content for quality, and create introductory, college-level textbooks designed to meet the study needs of university students.</p>
<p><br />This textbook covers:<br /><br /><strong>The Building Blocks of Algebra</strong> -- Real Numbers, Exponents, Scientific Notation, Order of Operations, Working with Polynomials, Factoring, Rational Expressions, Radical Notation and Exponents, Basics of Equation Solving<br /><br /><strong>Graphs, Functions, and Models</strong> -- Graphing, Functions: An Introduction, Modeling Equations of Lines, Functions Revisited, Algebra of Functions, Transformations<br /><br /><strong>Functions, Equations, and Inequalities</strong> -- Linear Equations and Functions, Complex Numbers, Quadratic Equations, Functions, and Applications, Graphs of Quadratic Functions, Further Equation Solving, Working with Linear Inequalities<br /><br /><strong>Polynomial and Rational Functions</strong> -- Polynomial Functions and Models, Graphing Polynomial Functions, Polynomial Division; The Remainder and Factor Theorems, Zeroes of Polynomial Functions and Their Theorems, Rational Functions, Inequalities, Variation and Problem Solving<br /><br /><strong>Exponents and Logarithms</strong> -- Inverse Functions, Graphing Exponential Functions, Graphing Logarithmic Functions, Properties of Logarithmic Functions, Growth and Decay; Compound Interest<br /><br /><strong>Systems of Equations and Matrices</strong> -- Systems of Equations in Two Variables, Systems of Equations in Three Variables, Matrices, Matrix Operations, Inverses of Matrices, Determinants and Cramer's Rule, Systems of Inequalities and Linear Programming, Partial Fractions<br /><br /><strong>Conic Sections</strong> -- The Parabola, The Circle and the Ellipse, The Hyperbola, Nonlinear Systems of Equations and Inequalities<br /><br /><strong>Sequences, Series and Combinatorics</strong> -- Sequences and Series, Arithmetic Sequences and Series, Geometric Sequences and Series, Mathematical Inductions, Combinatorics, The Binomial Theorem, Probability'</p>Wed, 20 Nov 2013 18:04:24 GMTBoundlessCalculus - Class Notes, Practice Tests, and Worksheets with Solutions
https://www.merlot.org/merlot/viewMaterial.htm?id=408892
<p>A collection of Class Notes, Practice Tests, and Worksheets for Calculus. Full solutions are provided. Recommended for Calculus I courses.</p>Sun, 04 Oct 2009 00:41:02 GMTTeodoru Gugoiu La Citadelle, Ontario, CanadaCourse of Linear Algebra and Multidimensional Geometry
https://www.merlot.org/merlot/viewMaterial.htm?id=447773
<p>This is a free, online textbook that can be downloaded as a pdf file. According to the site, "This is a textbook for the course of multidimensional geometry and linear algebra. This course is a part of the basic mathematical education. Therefore, it is taught at Physical and Mathematical Departments in all Universities of Russia during one or two semesters."</p>Tue, 27 Apr 2010 19:42:26 GMTRuslan SharipovLinear algebra via exterior products
https://www.merlot.org/merlot/viewMaterial.htm?id=447307
<p>This is a free, online textbook. According to Textbook Revolution, "Really explains abstract vectors, tensors, exterior products, determinants, Pfaffians, and more - linear algebra without cumbersome matrix calculations. Suitable as a second course of intermediate to advanced linear algebra. Exercises and example calculations provided."</p>Mon, 26 Apr 2010 21:18:30 GMTSergei Winitzki University of MuenchenLinear Algebra with Applications
https://www.merlot.org/merlot/viewMaterial.htm?id=1374974
<p style="font-weight: normal;">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.</p>
<p>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.</p>
<p>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).</p>
<p>Ancillary Materials:</p>
<p>Online Homework System (Lyryx Learning)</p>
<p style="font-weight: normal;">Partial Student Solution Manual, Instructor Solution Manual, Lecture Slides, LaTeX Source Files (all Creative Commons licensed)</p>
<p style="margin-bottom: 0cm; font-weight: normal; line-height: 100%;"> </p>Thu, 05 Apr 2018 19:49:38 GMTW. Keith NicholsonMathematical Reasoning: Writing and Proof
https://www.merlot.org/merlot/viewMaterial.htm?id=800960
<p>'Mathematical Reasoning: Writing and Proof is designed to be a text for the ﬁrst course in the college mathematics curriculum that introduces students to the pro-cesses of constructing and writing proofs and focuses on the formal development of mathematics. The primary goals of the text are as follows:</p><p>To help students learn how to read and understand mathematical deﬁnitions and proofs;</p><p>To help students learn how to construct mathematical proofs;</p><p>To help students learn how to write mathematical proofs according to ac-cepted guidelines so that their work and reasoning can be understood by others; and</p><p>To provide students with material that will be needed for their further study of mathematics.'</p>Mon, 14 Oct 2013 22:21:09 GMTTed Sundstrom Grand Valley State UniversityTrigonometry
https://www.merlot.org/merlot/viewMaterial.htm?id=511968
<p>According to The Orange Grove, "This book covers elementary trigonometry. It is suitable for a one-semester course at the college level, though it could also be used in high schools. The prerequisites are high school algebra and geometry. Contents: 1) Right Triangle Trigonometry. 2) General Triangles. 3) Identities. 4) Radian Measure. 5) Graphing and Inverse Functions. 6) Additional Topics. Appendix A) Answers and Hints to Selected Exercises. Appendix B) Graphing with Gnuplot."</p>Thu, 06 Jan 2011 20:47:03 GMTMichael CorralDifferential Equations
https://www.merlot.org/merlot/viewMaterial.htm?id=556384
<p>"Here are my online notes for my differential equations course that I teach here at Lamar University. Despite the fact that these are my “class notes”, they should be accessible to anyone wanting to learn how to solve differential equations or needing a refresher on differential equations.</p><p>I’ve tried to make these notes as self contained as possible and so all the information needed to read through them is either from a Calculus or Algebra class or contained in other sections of the notes."</p><p> </p>Fri, 10 Jun 2011 18:53:50 GMTPaul Dawkins Lamar UniversityOpen SUNY Textbooks Initiative
https://www.merlot.org/merlot/viewMaterial.htm?id=1067658
<p>Open SUNY Textbooks Initiative (2012) is an open access textbook initiative by the State University of New York (SUNY) libraries and supported by SUNY Innovative Instruction Technology Grants for developing and publishing at least thirty high-quality, cost-effective, college level open textbooks by various faculty authors. Ten open textbooks (Phase 1) are currently availabe for global use by educators and students, with an additional 16 open textbooks (Phase 2) coming soon. </p>Mon, 28 Sep 2015 10:46:16 GMTKate Pitcher (Editor); Allison Brown (Editor/PM); et al. SUNY/SUNY Libraries/SUNY Press and Affiliated MembersA Gentle Introduction to the Art of Mathematics
https://www.merlot.org/merlot/viewMaterial.htm?id=800958
<p>'This book is designed for the transition course between calculus and differential equations and the upper division mathematics courses with an emphasis on proof and abstraction. The book has been used by the author and several other faculty at Southern Connecticut State University. There are nine chapters and more than enough material for a semester course. Student reviews are favorable.</p><p>It is written in an informal, conversational style with a large number of interesting examples and exercises, so that a student learns to write proofs while working on engaging problems.'</p>Mon, 14 Oct 2013 22:13:53 GMTJoseph E. FieldsA simplified introduction to LaTeX
https://www.merlot.org/merlot/viewMaterial.htm?id=447678
<p>This is a free, online textbook. The table of contents can be found here: <a href="http://samizdat.mines.edu/latex/latextoc.ps" target="_blank" rel="nofollow"></a><a href="http://samizdat.mines.edu/latex/latextoc.ps" target="_blank" rel="nofollow">http://samizdat.mines.edu/latex/latextoc.ps</a></p>Tue, 27 Apr 2010 20:40:20 GMTHarvey J. Greenberg University of Colorado at DenverA youtube Calculus Workbook (Part I)
https://www.merlot.org/merlot/viewMaterial.htm?id=803561
<p>This is a free textbook offered by BookBoon.</p><p>'<span>This book is a guide through a playlist of Calculus instructional videos. The format, level of details and rigor, and progression of topics are consistent with a semester long college level first Calculus course, or equivalently an AP Calculus AB course. The book further provides simple summary of videos, written definitions and statements, worked out examples--even though fully step-by-step solutions are to be found in the videos-- and an index. The playlist and the book are divided into 15 thematic learning modules. At the end of each learning module, one or more quiz with full solutions is provided. Every 3 or 4 modules, a mock test on the previous material, with full solutions, is also provided. This will help you test your knowledge as you go along. The book can be used for self study, or as a textbook for a Calculus course following the “flipped classroom” model.'</span></p>Tue, 22 Oct 2013 20:55:35 GMTFrédéric Mynard Georgia Southern UniversityActive Calculus
https://www.merlot.org/merlot/viewMaterial.htm?id=800971
<p>'Rather than detailed explanations and worked out examples, this book uses activities intended to be done by the students in order to present the standard concepts and computational techniques of calculus. The student activities provide most of the material to be assigned as homework, but since the book does not contain the usual routine exercises, instructors wanting such exercises will need to supply their own or use a homework system such as WebWork. With this approach <em>Active Calculus</em>makes it possible to teach an inquiry based learning course without severely restricting the material covered. Although this book is new, it has been class tested by the author and his colleagues both at their university and elsewhere.</p><p>From the preface:</p><blockquote>Where many texts present a general theory of calculus followed by substantial collections of worked examples, we instead pose problems or situations, consider possibilities, and then ask students to investigate and explore. Following key activities or examples, the presentation normally includes some overall perspective and a brief synopsis of general trends or properties, followed by formal statements of rules or theorems. While we often offer a plausibility argument for such results, rarely do we include formal proofs.'</blockquote>Mon, 14 Oct 2013 22:02:17 GMTMatt Boelkins Grand Valley State CollegeActive Calculus
https://www.merlot.org/merlot/viewMaterial.htm?id=1084071
<p>c'Several fundamental ideas in calculus are more than 2000 years old. As a formal subdiscipline of mathematics, calculus was first introduced and developed in the late 1600s, with key independent contributions from Sir Isaac Newton and Gottfried Wilhelm Leibniz. Mathematicians agree that the subject has been understood rigorously since the work of Augustin Louis Cauchy and Karl Weierstrass in the mid 1800s when the field of modern analysis was developed, in part to make sense of the infinitely small quantities on which calculus rests. Hence, as a body of knowledge calculus has been completely understood by experts for at least 150 years. The discipline is one of our great human intellectual achievements: among many spectacular ideas, calculus models how objects fall under the forces of gravity and wind resistance, explains how to compute areas and volumes of interesting shapes, enables us to work rigorously with infinitely small and infinitely large quantities, and connects the varying rates at which quantities change to the total change in the quantities themselves.</p>
<p>While each author of a calculus textbook certainly offers her own creative perspective on the subject, it is hardly the case that many of the ideas she presents are new. Indeed, the mathematics community broadly agrees on what the main ideas of calculus are, as well as their justification and their importance; the core parts of nearly all calculus textbooks are very similar. As such, it is our opinion that in the 21st century – an age where the internet permits seamless and immediate transmission of information – no one should be required to purchase a calculus text to read, to use for a class, or to find a coherent collection of problems to solve. Calculus belongs to humankind, not any individual author or publishing company. Thus, a main purpose of this work is to present a new calculus text that is free. In addition, instructors who are looking for a calculus text should have the opportunity to download the source files and make modifications that they see fit; thus this text is opensource. Since August 2013, Active Calculus has been endorsed by the American Institute of Mathematics and its Open Textbook Initiative: <a href="http://aimath.org/textbooks/.'" target="_blank" rel="nofollow">http://aimath.org/textbooks/.'</a></p>Mon, 30 Nov 2015 21:57:26 GMTMatthew Boelkins; David Austin; Steven Schlicker Grand Valley State University; Grand Valley State University; Grand Valley State UniversityAdult Learning Academy - Pre-Algebra
https://www.merlot.org/merlot/viewMaterial.htm?id=1357749
<p>Adult Learning Academy - Pre-Algebra is a competency-based, contextualized and accelerated basic academic skills course aligned to the competencies in the credit developmental education Pre-Algebra math course. Students develop their basic arithmetic skills, improve their ability to solve problems, and successfully transition toward college coursework in pursuit of an academic credential. Successful completion of Adult Learning Academy - Pre-Algebra is an essential step on a pathway to healthcare, IT, machining, and other STEM-related careers.</p>Tue, 09 Jan 2018 21:36:36 GMTMoWINs St. Louis Community CollegeAdult Learning Academy Pre-Algebra Workbook - Unit 2:Fractions
https://www.merlot.org/merlot/viewMaterial.htm?id=1356545
<p>Unit 2 Fractions instructional resources including learning objectives, review material, contextualized word problems, list of video resources including Khan Academy lessons.</p>
<p>An editable copy can be found at: <a href="http://www.skillscommons.org/bitstream/handle/taaccct/2553/STLCC_Portal_ALA%20Pre-Algebra_Unit%202%20Workbook%20Fractions%28formatted%20for%20printing%29.docx?sequence=2&isAllowed=y">http://www.skillscommons.org/bitstream/handle/taaccct/2553/STLCC_Portal_ALA%20Pre-Algebra_Unit%202%20Workbook%20Fractions%28formatted%20for%20printing%29.docx?sequence=2&isAllowed=y</a></p>
<p>One can also download PowerPoint flashcards: <a href="http://www.skillscommons.org/bitstream/handle/taaccct/2553/STLCC_Portal_ALA_PreAlgebra_Unit2Fractions_ReviewFlashcards.ppt?sequence=3&isAllowed=y">http://www.skillscommons.org/bitstream/handle/taaccct/2553/STLCC_Portal_ALA_PreAlgebra_Unit2Fractions_ReviewFlashcards.ppt?sequence=3&isAllowed=y</a></p>
<p> </p>Fri, 05 Jan 2018 00:19:39 GMTDebbie Char; Lisa Whetstine St. Louis Community College; St. Louis Community CollegeAdvanced Problems in Mathematics: Preparing for University
https://www.merlot.org/merlot/viewMaterial.htm?id=1330065
<p>This book is intended to help students prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Papers). STEP examinations are used by Cambridge colleges as the basis for conditional offers in mathematics and sometimes in other mathematics-related subjects. They are also used by Warwick University, and many other mathematics departments recommend that their applicants practice on past papers to become accustomed to university-style mathematics.</p>
<p>Advanced Problems in Mathematics is recommended as preparation for any undergraduate mathematics course, even for students who do not plan to take the Sixth Term Examination Paper. The questions analysed in this book are all based on recent STEP questions selected to address the syllabus for Papers I and II, which is the A-level core (i.e. C1 to C4) with a few additions. 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.</p>
<p>This book is a must read for any student wishing to apply to scientific subjects at university level and for anybody interested in advanced mathematics.</p>
<p>Please note that in this book the mathematical formulas are encoded in MathML. While reading the HTML version, you can right-click on any of the formulas to display the underlying code.</p>Tue, 12 Sep 2017 17:02:01 GMTAPEX Calculus I
https://www.merlot.org/merlot/viewMaterial.htm?id=908754
<div class="summary">
<p>'This text is Part I of a three–text series on Calculus. This first part covers material taught in many “Calc 1” courses: limits, derivatives, and the basics of integration. The second text covers material often taught in “Calc 2:” integration and its applications, along with an introduction to sequences, series and Taylor Polynomials. The third text covers topics common in “Calc 3” or “multi-variable calc:” parametric equations, polar coordinates, vector–valued functions, and functions of more than one variable. All three are available for free at www.vmi.edu/APEX. These three texts are intended to work together and make one cohesive text, APEX Calculus, which can also be downloaded from the website.'</p>
<p>'A result of this spliƫng is that sometimes a concept is said to be explored in a “later section,” though that section does not actually appear in this particular text. Downloading the .pdf of APEX Calculus will ensure that you have all the content. This spliƫing of the material also results in unfortunate page/chapter numberings. Chapter 5 of this text is Chapter 1 of Calculus II. Apart from these numberings, page–for–page the content of the sections that appear in both Calculus I and Calculus II are idenƟcal.'</p>
</div>Thu, 13 Nov 2014 22:46:29 GMTGregory Hartman; Brian S. Heinhold; Troy Siemers; Dimplekumar Chalishajar Virginia Military Institute; Mount Saint Mary’s University; Virginia Military Institute; Virginia Military InstituteBasic Analysis: Introduction to Real Analysis
https://www.merlot.org/merlot/viewMaterial.htm?id=800937
<p>'<span>This free online textbook (e-book in webspeak) is a one semester course in basic analysis. This book started its life as my lecture notes for Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in the fall semester of 2009, and was later enhanced to teach Math 521 at University of Wisconsin-Madison (UW-Madison). A prerequisite for the course is a basic proof course. It should be possible to use the book for both a basic course for students who do not necessarily wish to go to graduate school, but also as a first semester of a more advanced course that also covers topics such as metric spaces.'</span></p>Mon, 14 Oct 2013 20:26:29 GMTJirí Lebl