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.

A Concise Introduction to Logic is an introduction to formal logic suitable for undergraduates taking a general education course in logic or critical thinking, and is accessible and useful to any interested in gaining a basic understanding of logic. This text takes the unique approach of teaching logic through intellectual history; the author uses examples from important and celebrated arguments in philosophy to illustrate logical principles. The text also includes a basic introduction to findings of advanced logic. As indicators of where the student could go next with logic, the book closes with an overview of advanced topics, such as the axiomatic method, set theory, Peano arithmetic, and modal logic. Throughout, the text uses brief, concise chapters that readers will find easy to read and to review.

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.

Derek Turner, Professor of Philosophy, has written an introductory logic textbook that students at Connecticut College, or anywhere, can access for free. The book differs from other standard logic textbooks in its reliance on fun, low-stakes examples involving dinosaurs, a dog and his friends, etc.

This work is published in 2020 under a Creative Commons AttributionNonCommercial-NoDerivatives 4.0 International License. You may share this text in any format or medium. You may not use it for commercial purposes. If you share it, you must give appropriate credit. If you remix, transform, add to, or modify the text in any way, you may not then redistribute the modified text.

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.

This lesson focuses on the biggest problem faced by any young programmer - i.e. the LOGIC BUILDING required while solving a particular problem. With programming, the solution to a particular problem lies in the head, but one is unable to convert it into a computer program. This is because the thought processes of a human are much faster than the sense of observation. If this thought process could be slowed down, logic to solve a programming problem could be found very easily. This lesson focuses on converting this psychological thought process in a step-by -step logic fashion that a computer program can understand. This lesson is recorded in a kitchen where the basic programming concepts are taught by giving examples from the process of making a mango milk shake. This lesson teaches the 4 following techniques: 1) Swapping two variables by swapping a glass of milk with a glass of crushed ice; 2) Finding max from an array by finding the biggest mango; 3) Sorting an array by arranging the jars; and 4) Understanding the concept of a function, parameters and return type by comparing it with the blender/juicer. The lesson targets those students who know the syntax of programming in any language (C or GWBASIC preferred), but are unable to build the logic for a program. It can be taught in a class of 45 to 50 minutes.

This lesson is also available in Mandarin Chinese.

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.

Inferring and Explaining is a book in practical epistemology. It examines the notion of evidence and assumes that good evidence is the essence of rational thinking. Evidence is the cornerstone of the natural, social, and behavioral sciences. But it is equally central to almost all academic pursuits and, perhaps most importantly, to the basic need to live an intelligent and reflective life.

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.

Student groups are challenged to program robots with light sensors to follow a black line. Learning both the logic and skills behind programming robots for this challenge helps students improve their understanding of how robots "think" and widens their appreciation for the complexity involved in programming LEGO® MINDSTORMS® NXT robots to do what appears to be a simple task. They test their ideas for approaches to solve the problem and ultimately learn a (provided) working programming solution. They think of real-world applications for line-follower robots that use sensor input. A PowerPoint® presentation and pre/post quizzes are provided.

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 resource may be used as a primary source for a general education/quantitative reasoning (QR) math course delivered in the inquiry based learning style. It may also be used to supplement a QR course with occasional in-class active learning activities.

As the first engineering design challenge of the unit, students are introduced to the logic for solving a maze. First they observe a blindfolded student volunteer being guided through a classroom maze by the simple verbal instructions of another student. In this demonstration, the blindfolded student represents a robot and the guiding student represents programming commands. Then student groups apply that logic to program LEGO MINDSTORMS(TM) NXT robots to navigate through a maze, first with no sensors, and then with sensors. A PowerPoint® presentation, pre/post quizzes and a worksheet are provided.

Students expand upon their understanding of simple machines with an introduction to compound machines. A compound machine a combination of two or more simple machines can affect work more than its individual components. Engineers who design compound machines aim to benefit society by lessening the amount of work that people exert for even common household tasks. This lesson encourages students to critically think about machine inventions and their role in our lives.

The Open Logic Text is an open textbook on mathematical logic aimed at a non-mathematical audience, intended for advanced logic courses as taught in many philosophy departments. It is open-source: you can download the LaTeX code. It is open: you’re free to change it whichever way you like, and share your changes. It is collaborative: a team of people is working on it, using the GitHub platform, and we welcome contributions and feedback. And it is written with configurability in mind.