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A Computational Introduction to Number Theory and Algebra
No full textAll 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.https://mds.marshall.edu/oa-textbooks/1142/thumbnail.jp
Linear Algebra
No full textWe believe the entire book can be taught in twenty five 50-minute lectures to a sophomore audience that has been exposed to a one year calculus course. Vector calculus is useful/ but not necessary preparation for this book/ which attempts to be self-contained. Key concepts are presented multiple times/ throughout the book/ often first in a more intuitive setting/ and then again in a definition/ theorem/ proof style later on. We do not aim for students to become agile mathematical proof writers/ but we do expect them to be able to show and explain why key results hold. We also often use the review exercises to let students discover key results for themselves; before they are presented again in detail later in the book. The book has been written such that instructors can reorder the chapters (using the La- TeX source) in any (reasonable) order and still have a consistent text. We hammer the notions of abstract vectors and linear transformations hard and early/ while at the same time giving students the basic matrix skills necessary to perform computations. Gaussian elimination is followed directly by an “exploration chapter” on the simplex algorithm to open students minds to problems beyond standard linear systems ones. Vectors in Rn and general vector spaces are presented back to back so that students are not stranded with the idea that vectors are just ordered lists of numbers. To this end/ we also labor the notion of all functions from a set to the real numbers. In the same vein linear transformations and matrices are presented hand in hand. Once students see that a linear map is specified by its action on a limited set of inputs/ they can already understand what a basis is. All the while students are studying linear systems and their solution sets/ so after matrices determinants are introduced. This material can proceed rapidly since elementary matrices were already introduced with Gaussian elimination. Only then is a careful discussion of spans/ linear independence and dimension given to ready students for a thorough treatment of eigenvectors and diagonalization. The dimension formula therefore appears quite late/ since we prefer not to elevate rote computations of column and row spaces to a pedestal. The book ends with applications–least squares and singular values. These are a fun way to end any lecture course. It would also be quite easy to spend any extra time on systems of differential equations and simple Fourier transform problems.https://mds.marshall.edu/oa-textbooks/1143/thumbnail.jp
Psychology
No full textPsychologyis designed to meet the scope and sequence for the single-semester introduction to psychology course. For many students/ this may be their only college-level psychology course. As such/ this textbook provides an important opportunity for students to learn the core concepts of psychology and understand how those concepts apply to their lives. The authors strive to make psychology/ as a discipline/ interesting and accessible to students. A comprehensive coverage of core concepts is grounded in both classic studies and current and emerging research/ including coverage of the DSM-5 in discussions of psychological disorders. The text incorporates discussions that reflect the diversity within the discipline/ as well as the diversity of cultures and communities across the globe. OpenStax College has compiled many resources for faculty and students/ from faculty-only content to interactive homework and study guides.https://mds.marshall.edu/oa-textbooks/1161/thumbnail.jp
Discover Psychology 2.0: A Brief Introductory Text
No full textThis textbook presents core concepts common to introductory courses. The 15 units cover the traditional areas of intro-to-psychology; ranging from biological aspects of psychology to psychological disorders to social psychology. This book can be modified: feel free to add or remove modules to better suit your specific needs. Each module in this book is accompanied by instructor\u27s manual/ PowerPoint presentation/ test items/ adaptive student quiz/ and reading anticipation guide. Please note that the publisher requires you to login to access and download the textbooks.https://mds.marshall.edu/oa-textbooks/1177/thumbnail.jp
Digital Circuit Projects: An Overview of Digital Circuits Through Implementing Integrated Circuits
No full textDigital circuits/ often called Integrated Circuits or ICs/ are the central building blocks of a Central Processing Unit (CPU). To understand how a computer works/ it is essential to understand the digital circuits which make up the CPU. This text introduces the most important of these digital circuits; adders/ decoders/ multiplexers/ D flip-flops/ and simple state machines. What makes this textbook unique is that it puts the ability to understand these circuits into the hands of anyone/ from hobbyists to students studying Computer Science. This text is designed to teach digital circuits using simple projects the reader can implement. But unlike most lab manuals used in classes in Digital Circuits or Computer Organization classes/ this textbook is designed to remove the barrier of a laboratory infrastructure needed in a face-to-face environment at a college or university. This textbook is designed to be used by the reader to create the circuits in their own homes. The textbook is free. The cost of the kits needed to do the labs is reasonable. And the projects are well documented and can be implemented by even novices to electronic projects. This text allows professors to add laboratory projects in digital circuits to students in online classes in Computer Organization. This enhances these classes with interesting and fun exercises that reinforce the classroom topics. This text can also be used by a hobbyist who wants to learn more about digital circuits and how computers work. The material is presented at a level that someone with no experience in digital circuits and electronics can successfully complete the projects/ and gain an understanding of the circuits which go into making up a computer.https://mds.marshall.edu/oa-textbooks/1181/thumbnail.jp
Spiral Workbook for Discrete Mathematics
No full textThis is a text that covers the standard topics in a sophomore-level course in discrete mathematics: logic/ sets/ proof techniques/ basic number theory/ functions/ relations/ and elementary combinatorics/ with an emphasis on motivation. It explains and clarifies the unwritten conventions in mathematics/ and guides the students through a detailed discussion on how a proof is revised from its draft to a final polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times/ sometimes from a different perspective or at a higher level of complexity. The goal is to slowly develop students\u27 problem-solving and writing skills.Open SUNY Textbooks is an open access textbook publishing initiative established by State University of New York libraries and supported by SUNY Innovative Instruction Technology Grants. This initiative publishes high-quality/ cost-effective course resources by engaging faculty as authors and peer-reviewers/ and libraries as publishing service and infrastructure. The pilot launched in 2012/ providing an editorial framework and service to authors/ students and faculty/ and establishing a community of practice among libraries. Participating libraries in the 2012- 2013 pilot include SUNY Geneseo/ College at Brockport/ College of Environmental Science and Forestry/ SUNY Fredonia/ Upstate Medical University/ and University at Buffalo/ with support from other SUNY libraries and SUNY Press. More information can be found at http://textbooks.opensuny.org.https://mds.marshall.edu/oa-textbooks/1187/thumbnail.jp
Precalculus
No full textThese are notes for a course in precalculus/ as it is taught at New York City College of Technology - CUNY (where it is offered under the course number MAT 1375). Our approach is calculator based. For this/ we will use the currently standard TI-84 calculator/ and in particular/ many of the examples will be explained and solved with it. However/ we want to point out that there are also many other calculators that are suitable for the purpose of this course and many of these alternatives have similar functionalities as the calculator that we have chosen to use. An introduction to the TI-84 calculator together with the most common applications needed for this course is provided in appendix A. In the future we may expand on this by providing introductions to other calculators or computer algebra systems. This course in precalculus has the overarching theme of “functions.” This means that many of the often more algebraic topics studied in the previous courses are revisited under this new function theoretic point of view. However/ in order to keep this text as self contained as possible we always recall all results that are necessary to follow the core of the course even if we assume that the student has familiarity with the formula or topic at hand. After a first introduction to the abstract notion of a function/ we study polynomials/ rational functions/ exponential functions/ logarithmic functions/ and trigonometric functions with the function viewpoint. Throughout/ we will always place particular importance to the corresponding graph of the discussed function which will be analyzed with the help of the TI-84 calculator as mentioned above. These are in fact the topics of the first four (of the five) parts of this precalculus course. In the fifth and last part of the book/ we deviate from the above theme and collect more algebraically oriented topics that will be needed in calculus or other advanced mathematics courses or even other science courses. This part includes a discussion of the algebra of complex numbers (in particular complex numbers in polar form)/ the 2-dimensional real vector space R 2 sequences and series with focus on the arithmetic and geometric series (which are again examples of functions/ though this is not emphasized)/ and finally the generalized binomial theorem.https://mds.marshall.edu/oa-textbooks/1195/thumbnail.jp
Conversa Brasileira
No full textConversa Brasileira is an online open access site that contains a series of 35 video scenarios in which Brazilians talk about their daily activities/ everything from hobbies to shopping/ and from traffic jams to soccer games. These materials are designed to help intermediate- and advanced-level learners of Portuguese to analyze the way that Brazilians really talk and improve in their own proficiency and fluency. This textbook provides a hardcopy of all of the online materials/ including the dialog transcriptions/ English translations/ and lesson notes that link to the original website.https://mds.marshall.edu/oa-textbooks/1201/thumbnail.jp
Law for Entrepreneurs
No full textLaw for Entrepreneurs is an up-to-date textbook that covers the broad spectrum of legal issues that entrepreneurs must understand when starting and running a business. The text is organized to permit instructors to tailor the materials to their particular approach. The authors take special care to engage students by relating law to everyday events with their clear/ concise and readable style. After introductory chapters covering the legal environment of business/ Law for Entrepreneurs provides students with context and essential legal concepts relating to contracts/ product liability/ intellectual property/ insurance/ agency law/ partnerships/ corporations/ and employment law. The text provides the vocabulary and legal savvy that entrepreneurs need to talk in an educated way to customers/ suppliers/ employees/ creditors/ shareholders/ government regulators and other stakeholders — and to their own lawyers.https://mds.marshall.edu/oa-textbooks/1226/thumbnail.jp
Think Complexity: Exploring Complexity Science with Python
No full textThis book is about complexity science/ data structures and algorithms/ intermediate programming in Python/ and the philosophy of science: Data structures and algorithms: A data structure is a collection that contains data elements organized in a way that supports particular operations. For example/ a dictionary organizes key-value pairs in a way that provides fast mapping from keys to values/ but mapping from values to keys is generally slower. An algorithm is a mechanical process for performing a computation. Designing efficient programs often involves the co-evolution of data structures and the algorithms that use them. For example/ the first few chapters are about graphs/ a data structure that is a good implementation of a graph---nested dictionaries---and several graph algorithms that use this data structure. Python programming: This book picks up where Think Python leaves off. I assume that you have read that book or have equivalent knowledge of Python. As always/ I will try to emphasize fundmental ideas that apply to programming in many languages/ but along the way you will learn some useful features that are specific to Python. Computational modeling: A model is a simplified description of a system that is useful for simulation or analysis. Computational models are designed to take advantage of cheap/ fast computation. Philosophy of science: The models and results in this book raise a number of questions relevant to the philosophy of science/ including the nature of scientific laws/ theory choice/ realism and instrumentalism/ holism and reductionism/ and Bayesian epistemology. This book focuses on discrete models/ which include graphs/ cellular automata/ and agent-based models. They are often characterized by structure/ rules and transitions rather than by equations. They tend to be more abstract than continuous models; in some cases there is no direct correspondence between the model and a physical system. Complexity science is an interdisciplinary field---at the intersection of mathematics/ computer science and physics---that focuses on these kinds of models. That\u27s what this book is about.https://mds.marshall.edu/oa-textbooks/1235/thumbnail.jp