Thư viện số
Giáo trình, tài liệu tham khảo và tài nguyên học tập mở.
Nguồn ngoài
Elementary Algebra
John Redden · Saylor Foundation · 2011
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! A few other differences are highlighted below: Equivalent mathematical notation using standard text found on a keyboard A variety of applications and word problems included in most exercise sets Clearly enumerated steps found in context within carefully chosen examples Alternative methods and notation, modularly integrated, where appropriate Video examples available, in context, within the online version of the textbook Robust and diverse exercise sets with di
Nguồn ngoài
College Algebra
Carl Stitz; Jeff Zeager · Stitz Zeager Open Source Mathematics · 2013
College Algebra is an introductory text for a college algebra survey course. The material is presented at a level intended to prepare students for Calculus while also giving them relevant mathematical skills that can be used in other classes. The authors describe their approach as "Functions First," believing introducing functions first will help students understand new concepts more completely. Each section includes homework exercises, and the answers to most computational questions are included in the text (discussion questions are open-ended). Graphing calculators are used sparingly and only as a tool to enhance the Mathematics, not to replace it. The authors also offer a Precalculus version of this text, which has two extra chapters covering Trigonometry.
Nguồn ngoài
Calculus
Gilbert Strang · Wellesley-Cambridge Press · 1991
Published in 1991 by Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. Prof. Strang has also developed a related series of videos, Highlights of Calculus, on the basic ideas of calculus.
Nguồn ngoài
Book of Proof
Richard Hammack · Richard Hammack · 2018
This is a book about how to prove theorems. Until this point in your education, you may have regarded mathematics primarily as a computational discipline. You have learned to solve equations, compute derivatives and integrals, multiply matrices and find determinants; and you have seen how these things can answer practical questions about the real world. In this setting, your primary goal in using mathematics has been to compute answers. But there is another approach to mathematics that is more theoretical than computational. In this approach, the primary goal is to understand mathematical structures, to prove mathematical statements, and even to invent or discover new mathematical theorems and theories. The mathematical techniques and procedures that you have learned and used up until now have their origins in this theoretical side of mathematics. For example, in computing the area under a curve, you use the fundamental theorem of calculus. It is because this theorem is true that your answer is correct. However, in your calculus class you were probably far more concerned with how that theorem could be applied than in understanding why it is true. But how do we know it is true? How can we convince ourselves or others of its validity? Questions of this nature belong to the theoretical realm of mathematics. This book is an introduction to that realm. This book will initiate you into an esoteric world. You will learn and apply the methods of thought that mathematicians use to verify theorems,explore mathematical truth and create new mathematical theories. This will prepare you for advanced mathematics courses, for you will be better able to understand proofs, write your own proofs and think critically and inquisitively about mathematics. This text has been used in classes at: Virginia Commonwealth University, Lebanon Valley College, University of California - San Diego, Colorado State University, Westminster College, South Dakota State University, PTEK College - Brunei,
Nguồn ngoài
A First Course in Linear Algebra
Robert Beezer · Robert Beezer · 2015
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.
Nguồn ngoài
Introduction to Criminal Law
University of Minnesota Libraries Publishing · 2015
Criminal Law uses a two-step process to augment learning, called the applied approach. First, after building a strong foundation from scratch, Criminal Law introduces you to crimes and defenses that have been broken down into separate components. It is so much easier to memorize and comprehend the subject matter when it is simplified this way. However, becoming proficient in the law takes more than just memorization. You must be trained to take the laws you have studied and apply them to various fact patterns. Most students are expected to do this automatically, but application must be seen, experienced, and practiced before it comes naturally. Thus the second step of the applied approach is reviewing examples of the application of law to facts after dissecting and analyzing each legal concept. Some of the examples come from cases, and some are purely fictional. All the examples are memorable, even quirky, so they will stick in your mind and be available when you need them the most (like during an exam). After a few chapters, you will notice that you no longer obsess over an explanation that doesn't completely make sense the first time you read it—you will just skip to the example. The examples clarify the principles for you, lightening the workload significantly.
Nguồn ngoài
Open Logic Project
Richard Zach; Andrew Arana; Jeremy Avigad; Walter Dean · Open Logic Text · 2016
The Open Logic Text is an open-source, collaborative textbook of formal meta-logic and formal methods, starting at an intermediate level (i.e., after an introductory formal logic course). Though aimed at a non-mathematical audience (in particular, students of philosophy and computer science), it is rigorous. The Open Logic Text is a collaborative project and is under active development. Coverage of some topics currently included may not yet be complete, and many sections still require substantial revision. We plan to expand the text to cover more topics in the future. We also plan to add features to the text, such as a glossary, a list of further reading, historical notes, pictures, better explanations, sections explaining the relevance of results to philosophy, computer science, and mathematics, and more problems and examples. If you find an error, or have a suggestion, please let the project team know. The project operates in the spirit of open source. Not only is the text freely available, we provide the LaTeX source under the Creative Commons Attribution license, which gives anyone the right to download, use, modify, re-arrange, convert, and re-distribute our work, as long as they give appropriate credit.
Nguồn ngoài
Notes on Diffy Qs: Differential Equations for Engineers
Jirí Lebl · Jirí Lebl · 2014
A one semester first course on differential equations, aimed at engineering students. Prerequisite for the course is the basic calculus sequence. This free online book (e-book in webspeak) should be usable as a stand-alone textbook or as a companion to a course using another book such as Edwards and Penney, Differential Equations and Boundary Value Problems: Computing and Modeling or Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems (section correspondence to these two is given). I developed and used these notes to teach Math 286/285 at the University of Illinois at Urbana-Champaign Sample Dirichlet problem solution (one is a 4-day-a-week, the other a 3-day-a-week semester-long course). I have also taught Math 20D at University of California, San Diego with these notes (a 3-day-a-week quarter-long course). There is enough material to run a 2-quarter course, and even perhaps a two semester course depending on lecturer speed.
Nguồn ngoài
Elementary Differential Equations with Boundary Value Problems
William Trench · A.T. Still University · 2013
Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student's place, and have chosen to err on the side of too much detail rather than not enough. An elementary text can't be better than its exercises. This text includes 1695 numbered exercises, many with several parts. They range in difficulty from routine to very challenging. An elementary text should be written in an informal but mathematically accurate way, illustrated by appropriate graphics. I have tried to formulate mathematical concepts succinctly in language that students can understand. I have minimized the number of explicitly stated theorems and definitions, preferring to deal with concepts in a more conversational way, copiously illustrated by 250 completely worked out examples. Where appropriate, concepts and results are depicted in 144 figures. Although I believe that the computer is an immensely valuable tool for learning, doing, and writing mathematics, the selection and treatment of topics in this text reflects my pedagogical orientation along traditional lines. However, I have incorporated what I believe to be the best use of modern technology, so you can select the level of technology that you want to include in your course. The text includes 336 exercises – identified by the symbols C and C/G – that call for graphics or computation and graphics. There are also 73 laboratory exercises – identified by L – that require extensive use of technology. In addition, several sections include informal advice on the use of technology. If you prefer not to emphasize technology, simply ignore these exercises and the advice.
Nguồn ngoài
Basics of Fluid Mechanics
Genick Bar-Meir · Potto Project · 2025
The topic of fluid mechanics is common to several disciplines: mechanical engineering, aerospace engineering, chemical engineering, and civil engineering. In fact, it is also related to disciplines like industrial engineering, and electrical engineering. While the emphasis is somewhat different in this book, the common material is presented and hopefully can be used by all. One can only admire the wonderful advances done by the previous geniuses who work in this field. In this book it is hoped to insert, what and when a certain model is suitable than other models. One of the difference in this book is the insertion of the introduction to multiphase flow. Clearly, multiphase is an advance topic. However, some minimal familiarity can be helpful for many engineers who have to deal with non pure single phase fluid. This book is the third book in the series of POTTO project books. POTTO project books are open content textbooks so everyone are welcome to joint in. The topic of fluid mechanics was chosen just to fill the introduction chapter to compressible flow. During the writing it became apparent that it should be a book in its own right. In writing the chapter on fluid statics, there was a realization that it is the best chapter written on this topic. It is hoped that the other chapters will be as good this one. This book is written in the spirit of my adviser and mentor E.R.G. Eckert. Eckert, aside from his research activity, wrote the book that brought a revolution in the education of the heat transfer. Up to Egret's book, the study of heat transfer was without any dimensional analysis. He wrote his book because he realized that the dimensional analysis utilized by him and his adviser (for the post doc), Ernst Schmidt, and their colleagues, must be taught in engineering classes. His book met strong criticism in which some called to "burn" his book. Today, however, there is no known place in world that does not teach according to Eckert's doctrine. It is assumed that
Nguồn ngoài
Yet Another Introductory Number Theory Textbook (Cryptology Emphasis Version)
Jonathan Poritz · Jonathan Poritz · 2014
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.
Nguồn ngoài
The Joy of Cryptography
Mike Rosulek · Oregon State University · 2017
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). A new web-based only version is available at the Joy of Cryptography website.
Nguồn ngoài
Pharo by Example 5.0
Stéphane Ducasse; Dmitri Zagidulin; Nicolai Hess; Dimitris Chloupis · Stéphane Ducasse · 2016
Pharo is an open-source, elegant and pure object-oriented language that supports truly immersive and life programming experience. Pharo offers excellent tools such as hot-debuggers and on the fly code update that change the programming experience. More at http://www.pharo.org.Pharo is a powerful language and IDE that companies use to deliver complex business-effective applications. More at: http://www.pharo.org/success In Pharo everything is an object, and anything can change at run-time under your fingers. Pharo is written in itself you can explore a complete world. You can feel and talk to objects. But Pharo does not stop there, with Pharo you can improve your object-oriented skills by rediscovering the essence of object-oriented programming. Pharo by Example 50, intended for both students and developers, will guide you gently through the Pharo language and environment by means of a series of examples and exercises. This book is available under the Creative Commons Attribution-ShareAlike 3.0 license.
Nguồn ngoài
Squeak by Example
Andrew Black; Stéphane Ducasse; Oscar Nierstrasz; Damien Pollet · University of Bern · 2009
Squeak is a modern open-source development environment for the classic Smalltalk-80 programming language. Despite being the first purely object-oriented language and environment, Smalltalk is in many ways still far ahead of its successors in promoting a vision of an environment where everything is an object, and anything can change at run-time. Squeak by Example, intended for both students and developers, will guide you gently through the Squeak language and environment by means of a series of examples and exercises. The book helps you get started with A Quick Tour of Squeak and guides you through A First Application. The Smalltalk language is introduced in three chapters on Syntax in a Nutshell, Understanding Message Syntax and The Smalltalk Object Model. Development with Squeak is covered in The Squeak Programming Environment and SUnit. Several of the key classes are presented in chapters on Basic Classes, Collections, Streams and Morphic. The first edition of the book concludes with chapters on Classes and Metaclasses and Frequently Asked Questions.
Nguồn ngoài
Algorithms and Data Structures With Applications to Graphics and Geometry
Jurg Nievergelt; Klaus Hinrichs · Global Text Project · 2011
An introductory coverage of algorithms and data structures with application to graphics and geometry.
Nguồn ngoài
Elementary Algebra
Wade Ellis; Denny Burzynski · OpenStax CNX · 2010
This course takes an interdisciplinary approach to ethics in business and provides modules in Ethical Leadership, Ethical Decision-Making, Social Responsibility, and Corporate Governance. Students will actively study ethical theory by carrying out exercises to help them build theory-based tools for encountering ethical problems in business practice. They will also work with cases in business ethics designed to give them practice in developing skills of ethical leadership, ethical decision-making, and carrying out socio-technical analyses to respond to issues of social responsibility. This course will culminate in an Ethics Bowl competition in which students will practice ethics advocacy in a variety of organizational contexts in business.
Nguồn ngoài
Thermodynamics and Introduction to Quantum Mechanics
Cathrine Southern · DePaul University
Có trong mục lục: 5.03: The Chemical Potentials of a Pure Substance in Two Phases in Equilibrium
Nguồn ngoài
Flavors of the Saucier: Stocks, Sauces, and Soups
Amelie Zeringue and William R. Thibodeaux · Nicholls State University
Có trong mục lục: 1.12: Pureed Thick Soups
Nguồn ngoài
Physical Science for Educators Volume 1
Timothy Evans, Kylee Ford, Kenneth Henry, Yogita Kumari, Claude Mona & Suzanne Wakim · Coalinga College
Có trong mục lục: 4.03: Pure Substances and Mixtures
Nguồn ngoài
Chem 51
LibreTexts
Có trong mục lục: 3.05: Pure Substances and Mixtures