The wide range of examples in the text are meant to augment the "favorite examples" that most instructors have for teaching the topcs in discrete mathematics.

To provide diagnostic help and encouragement, we have included solutions and/or hints to the odd-numbered exercises. These solutions include detailed answers whenever warranted and complete proofs, not just terse outlines of proofs.

Our use of standard terminology and notation makes Applied Discrete Structures a valuable reference book for future courses. Although many advanced books have a short review of elementary topics, they cannot be complete.

The text is divided into lecture-length sections, facilitating the organization of an instructor's presentation.Topics are presented in such a way that students' understanding can be monitored through thought-provoking exercises. The exercises require an understanding of the topics and how they are interrelated, not just a familiarity with the key words.

An Instructor's Guide is available to any instructor who uses the text.

In this learning area, you will learn how to develop an argumentative essay and stronger critical thinking skills. This learning area will help you develop your arguments, understand your audience, evaluate source material, approach arguments rhetorically, and avoid logical fallacies. Here, you’ll also learn about evaluating other arguments and creating digital writing projects related to your argument.

Discrete Mathematics: An Open Introduction is a free, open source textbook appropriate for a first or second year undergraduate course for math majors, especially those who will go on to teach. The textbook has been developed while teaching the Discrete Mathematics course at the University of Northern Colorado. Primitive versions were used as the primary textbook for that course since Spring 2013, and have been used by other instructors as a free additional resource. Since then it has been used as the primary text for this course at UNC, as well as at other institutions.

Foundations of Computation is a free textbook for a one-semester course in theoretical computer science. It has been used for several years in a course at Hobart and William Smith Colleges. The course has no prerequisites other than introductory computer programming. The first half of the course covers material on logic, sets, and functions that would often be taught in a course in discrete mathematics. The second part covers material on automata, formal languages, and grammar that would ordinarily be encountered in an upper level course in theoretical computer science.

Fundamental Methods of Logic is suitable for a one-semester introduction to logic/critical reasoning course. It covers a variety of topics at an introductory level. Chapter One introduces basic notions, such as arguments and explanations, validity and soundness, deductive and inductive reasoning; it also covers basic analytical techniques, such as distinguishing premises from conclusions and diagramming arguments. Chapter Two discusses informal logical fallacies. Chapters Three and Four concern deductive logic, introducing the basics of Aristotelian and Sentential Logic, respectively. Chapter Five deals with analogical and causal reasoning, including a discussion of Mill's Methods. Chapter Six covers basic probability calculations, Bayesian inference, fundamental statistical concepts and techniques, and common statistical fallacies.

This course provides a challenging introduction to some of the central ideas of theoretical computer science. It attempts to present a vision of "computer science beyond computers": that is, CS as a set of mathematical tools for understanding complex systems such as universes and minds. Beginning in antiquity--with Euclid's algorithm and other ancient examples of computational thinking--the course will progress rapidly through propositional logic, Turing machines and computability, finite automata, GĚŚdel's theorems, efficient algorithms and reducibility, NP-completeness, the P versus NP problem, decision trees and other concrete computational models, the power of randomness, cryptography and one-way functions, computational theories of learning, interactive proofs, and quantum computing and the physical limits of computation. Class participation is essential, as the class will include discussion and debate about the implications of many of these ideas.

Examines the development of computing techniques and technology in the nineteenth and twentieth centuries, particularly critical evaluation of how the very idea of "computer" changes and evolves over time. Emphasis is on technical innovation, industrial development, social context, and the role of government. Topics include Babbage, Hollerith, differential analyzers, control systems, ENIAC, radar, operations research, computers as scientific instruments, the rise of "computer science," artificial intelligence, personal computers, and networks. Includes class visits by members of the MIT community who have made important historical contributions. This course focuses on one particular aspect of the history of computing: the use of the computer as a scientific instrument. The electronic digital computer was invented to do science, and its applications range from physics to mathematics to biology to the humanities. What has been the impact of computing on the practice of science? Is the computer different from other scientific instruments? Is computer simulation a valid form of scientific experiment? Can computer models be viewed as surrogate theories? How does the computer change the way scientists approach the notions of proof, expertise, and discovery? No comprehensive history of scientific computing has yet been written. This seminar examines scientific articles, participants' memoirs, and works by historians, sociologists, and anthropologists of science to provide multiple perspectives on the use of computers in diverse fields of physical, biological, and social sciences and the humanities. We explore how the computer transformed scientific practice, and how the culture of computing was influenced, in turn, by scientific applications.

This is an introductory textbook in logic and critical thinking. The goal of the textbook is to provide the reader with a set of tools and skills that will enable them to identify and evaluate arguments. The book is intended for an introductory course that covers both formal and informal logic. As such, it is not a formal logic textbook, but is closer to what one would find marketed as a critical thinking textbook. Downloadable as a pdf file.

This is an introductory course to Philosophy, which is the study of general and fundamental problems such as those connected with existence, knowledge, values, reason, mind, and language. Students will be introduced to the primary branches of Philosophy - ethics, logic, metaphysics, and epistemology. The course considers philosophers and works of Western Philosophy, including Plato, Hebrew scripture, Schopenhauer, Swedenborg, Buber, Kant, Hume, Locke and Berkeley.

In this course we will cover central aspects of modern formal logic, beginning with an explanation of what constitutes good reasoning. Topics will include validity and soundness of arguments, formal derivations, truth-functions, translations to and from a formal language, and truth-tables. We will thoroughly cover sentential calculus and predicate logic, including soundness and completeness results.

This course begins with an introduction to the theory of computability, then proceeds to a detailed study of its most illustrious result: Kurt GĚŚdel's theorem that, for any system of true arithmetical statements we might propose as an axiomatic basis for proving truths of arithmetic, there will be some arithmetical statements that we can recognize as true even though they don't follow from the system of axioms. In my opinion, which is widely shared, this is the most important single result in the entire history of logic, important not only on its own right but for the many applications of the technique by which it's proved. We'll discuss some of these applications, among them: Church's theorem that there is no algorithm for deciding when a formula is valid in the predicate calculus; Tarski's theorem that the set of true sentence of a language isn't definable within that language; and GĚŚdel's second incompleteness theorem, which says that no consistent system of axioms can prove its own consistency.

" This course develops logical, empirically based arguments using statistical techniques and analytic methods. Elementary statistics, probability, and other types of quantitative reasoning useful for description, estimation, comparison, and explanation are covered. Emphasis is on the use and limitations of analytical techniques in planning practice."

This subject exposes students to a variety of visualization techniques so that they learn to understand the work involved in producing them and to critically assess the power and limits of each. Students concentrate on areas where visualizations are crucial for meaning making and data production. Drawing on scholarship in science and technology studies on visualization, critical art theory, and core discussions in science and engineering, students work through a series of case studies in order to become better readers and producers of visualizations.

Introductory Writing Course developed through the Ohio Department of Higher Education OER Innovation Grant. The course is part of the Ohio Transfer Module and is also named TME002. This work was completed and the course was posted in September 2018. For more information about credit transfer between Ohio colleges and universities, please visit: www.ohiohighered.org/transfer.Team LeadRachel Brooks-Pannell                       Columbus State Community CollegeContent ContributorsCatherine Braun                                  Ohio State UniversityMartin Brick                                         Ohio Dominican UniversityPeter Landino                                      Terra State Community CollegeBrian Leingang                                    Edison State Community CollegeBonnie Proudfoot                                Hocking CollegeJason Reynolds                                  Southern State Community CollegeMarie Stokes                                       Stark State CollegeLibrarianKatie Foran-Mulcahy                           University of Cincinnati Clermont CollegeReview TeamAnna Bogen                                        Marion Technical CollegeSteven Mohr                                       Terra State Community CollegeKelsey Squire                                      Ohio Dominican University

How to Use This GuideThis document is intended to highlight resources that can be used to address the topic of Critical Thinking in a Second-Year Writing Course. All resources are Open Access and can be downloaded or added to a Course Management System via hyperlink.IntroductionCritical Thinking is one of the five main learning outcomes for the Ohio Transfer Module’s Ohio guidelines for second-year writing. The Department of Higher Education recognizes that second-year writing builds on the skills of first-year writing and adds the following skills to what a student should be able to do by the end of the courseFind and evaluate appropriate material from electronic and other sources.Locate, evaluate, organize, and use primary and secondary research material. Secondary research material should be collected from various sources, including journal articles and other scholarly texts found in library databases, other official databases (e.g., federal government databases), and informal electronic networks and internet sources.Analyze and critique sources in their writing.Juxtapose and integrate ideas and arguments from sources.Develop a clear line of argument that incorporates ideas and evidence from sources.Use strategies—such as interpretation, synthesis, response, critique, and design/redesign—to compose texts that integrate the writer’s ideas with those from appropriate sources.The materials below range from introductory lessons to more in-depth and detailed explanations for the various processes in critical thinking that build on the material from first-year writing. Many of the second-year material overlaps with other chapters on Reading and Writing in Academia, Understanding Rhetorical Situations, and Conducting Research. The materials are available as single lessons that can be used to supplement other course material and readings, or as standalone sections that can provide weeks of information and activities that can align with other writing assignments.Learning ObjectivesThis module is designed to address the following learning objectives:Find and evaluate appropriate material from electronic and other sourcesUse library resources to locate academic sourcesIdentify appropriate and credible websites and online articles Analyze and critique sources in their writingApply the rhetorical situationExamine the logicJuxtapose and integrate ideas and arguments from sources throughSummaryParaphraseQuotationSynthesisDevelop a clear line of argument that incorporates ideas and evidence from sourcesProvide appropriate support and evidence for claimsIncorporate opposing viewpointsProvide counterarguments

Critical Thinking is one of the five main learning outcomes for the Ohio Transfer Module’s Ohio guidelines for second-year writing. The Department of Higher Education recognizes that second-year writing builds on the skills of first-year writing and adds the following skills to what a student should be able to do by the end of the course:Find and evaluate appropriate material from electronic and other sources.Locate, evaluate, organize, and use primary and secondary research material. Secondary research material should be collected from various sources, including journal articles and other scholarly texts found in library databases, other official databases (e.g., federal government databases), and informal electronic networks and internet sources.Analyze and critique sources in their writing.Juxtapose and integrate ideas and arguments from sources.Develop a clear line of argument that incorporates ideas and evidence from sources.Use strategies—such as interpretation, synthesis, response, critique, and design/redesign—to compose texts that integrate the writer’s ideas with those from appropriate sources.

Textbook for Calgary's Logic II course based on the Open Logic Project. Covers naive set theory, first-order logic, sequent calculus and natural deduction, the completeness, compactness, and Löwenheim-Skolem theorems, Turing machines, and the undecidability of the halting problem and of first-order logic.

This course is an introduction to the theory that tries to explain how minds are made from collections of simpler processes. It treats such aspects of thinking as vision, language, learning, reasoning, memory, consciousness, ideals, emotions, and personality. It incorporates ideas from psychology, artificial intelligence, and computer science to resolve theoretical issues such as wholes vs. parts, structural vs. functional descriptions, declarative vs. procedural representations, symbolic vs. connectionist models, and logical vs. common-sense theories of learning.

This course provides an introduction to symbolic logic with an emphasis on formal logical languages and natural deduction systems of logical proof. Students learn how to translate reasoning into a symbolic logical language and how to prove arguments valid with the precision of mathematics using formal systems of proof.

This course is an introduction to epistemology: the theory of knowledge. We will focus on skepticism—that is, the thesis that we know nothing at all—and we will survey a range of skeptical arguments and responses to skepticism.