A+ Click is an interactive collection of more than 3700 math problems and answers for K-1 K-12 school program. It defines the personal level of math knowledge. You move up into the next level if you give 5 correct answers in a row. Practice makes perfect.

Some of the topics that this book addresses are: Vector spaces; finite-dimensional vector spaces; differential calculus; compactness and completeness; scalar product space; differential equations; multilenear functionals; integration; differentiable manifolds; integral calculus on manifolds; exterior calculus.

Note: this is a 57 MB PDF Document.

This course is the second of the three parts of our graduate introduction to semantics. The others are 24.970 Introduction to Semantics and 24.954 Pragmatics in Linguistic Theory. Like the other courses, this one is not meant as an overview of the field and its current developments. Our aim is to help you to develop the ability for semantic analysis, and we think that exploring a few topics in detail together with hands-on practical work is more effective than offering a bird's-eye view of everything. Once you have gained some experience in doing semantic analysis, reading around in the many recent handbooks and in current issues of major journals and attending our seminars and colloquia will give you all you need to prosper. Because we want to focus, we need to make difficult choices as to which topics to cover.
This year, we will focus on topics having to do with modality, conditionals, tense, and aspect.

"Air Safety Investigation – The Journey" is an introductory book that explores the world of air safety investigation. Unlike a how-to manual for investigating aviation accidents, this book focuses on the essential knowledge and mindset required to conduct a safety investigation. It covers the various phases of an investigation, from gathering facts to formulating safety recommendations, with each chapter addressing a different relevant aspect. With the increasing complexity of investigations, critical thinking, logic, and speculation are essential skills for investigators to possess. This book delves into these topics, offering thought-provoking examples and questions to address the challenges of drawing conclusions and obtaining positive investigative outcomes. Its aim is to help students and readers interested in air safety develop the necessary mindset and knowledge to conduct an investigation. By the end of the book, readers will gain a deeper understanding of the complexities involved in an air safety investigation.

6.374 examines the device and circuit level optimization of digital building blocks. Topics covered include: MOS device models including Deep Sub-Micron effects; circuit design styles for logic, arithmetic and sequential blocks; estimation and minimization of energy consumption; interconnect models and parasitics; device sizing and logical effort; timing issues (clock skew and jitter) and active clock distribution techniques; memory architectures, circuits (sense amplifiers) and devices; testing of integrated circuits. The course employs extensive use of circuit layout and SPICE in design projects and software labs.

This book is designed for use in an introductory course on digital logic design, typically offered in computer engineering, electrical engineering, computer science, and other related programs. Such a course is usually offered at the sophomore level. This book makes extensive use of animation to illustrate the flow of data within a digital system and to step through some of the procedures used to design and optimize digital circuits.

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.

Best open source book in Discrete Math. Covers all the subjects in a standard Discrete Math class for mathematics or computer science students and contains sage cells for all subjects. Set Theory, Combinatorics, Logic, Relations, Recursion, Graph Theory, Trees, Algebraic Structures, Boolean Algebras, Automata, etc. Originally published commercially, its original text was peer-reviewed and was adopted for use at several universities throughout the country. Now in its open source version, has the same quality but it is free.

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 teaching guide for teachers to instruct students in the gaming rules and procedures for Basic Wff'n Proof. This game teaches symbolic logic and problem solving. The content is an overview of the game of Wff'n Proof for interested coaches.

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.

This lesson is designed to meet the following learning objectives:
1. Formulate an argument
2. Learn how to anticipate and respond to objections

What is thinking? It may seem strange to begin a logic textbook with this question. ‘Thinking’ is perhaps the most intimate and personal thing that people do. Yet the more you ‘think’ about thinking, the more mysterious it can appear. It is the sort of thing that one intuitively or naturally understands, and yet cannot describe to others without great difficulty. Many people believe that logic is very abstract, dispassionate, complicated, and even cold. But in fact the study of logic is nothing more intimidating or obscure than this: the study of good thinking.

This laboratory manual is required for first year Electrical Engineering Technology students that are enrolled in ET181 Digital Electronics 1 at Mohawk Valley Community College.

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.

The 11th grade learning experience consists of 7 mostly month-long units aligned to the Common Core State Standards, with available course material for teachers and students easily accessible online. Over the course of the year there is a steady progression in text complexity levels, sophistication of writing tasks, speaking and listening activities, and increased opportunities for independent and collaborative work. Rubrics and student models accompany many writing assignments.Throughout the 11th grade year, in addition to the Common Read texts that the whole class reads together, students each select an Independent Reading book and engage with peers in group Book Talks. Students move from learning the class rituals and routines and genre features of argument writing in Unit 11.1 to learning about narrative and informational genres in Unit 11.2: The American Short Story. Teacher resources provide additional materials to support each unit.

In this unit, students will produce two major pieces of work.  The first piece is an argument essay that grapples with one of the core questions of the unit: who are we, and who have we become because of the ways we connect? Students will read, annotate, and discuss several texts together as they consider the issues surrounding this question, and they will also research and annotate independently as they search for more evidence and perspectives to help deepen their ideas.  They will also create a museum exhibit as part of a team.  The exhibit project will help students identify what's worth preserving about their unique place in history.

PROJECT UNITS

This project unit continues to meet the English Language Arts standards as it also utilizes the learning principles established by the Partnership for 21st Century Skills. It is designed to support deep content knowledge and perseverance through long-term project planning and implementation. In addition, it will help students to recognize, develop, and apply the planning, teamwork, communication, and presentation skills they will use while presenting a final product to their class and/or the greater community. This real-world project-based activity will give students an opportunity to apply the skills they have been learning all year and will guide them to develop the motivation, knowledge, and skills they need in order to be college and career ready.

ACCOMPLISHMENTS

Students write an argument paper where they develop a claim about current culture as it has been influenced by digital connectivity.
Students participate in a group project to create a museum exhibit that captures a unique place, time, and relationship to technology. Students acknowledge the differing perspectives of each group member and use those perspectives to synthesize one cohesive visual argument together.

GUIDING QUESTIONS

These questions are a guide to stimulate thinking, discussion, and writing on the themes and ideas in the unit. For complete and thoughtful answers and for meaningful discussions, students must use evidence based on careful reading of the texts.

What does it mean to be digitally connected?
What are the implications of living in a world where everyone is digitally connected?
How does the availability of instant connectivity shape our relationships?
What does our Internet use reveal about people's needs as humans?

BENCHMARK ASSESSMENT: Cold Read

During this unit, on a day of your choosing, we recommend you administer a Cold Read to assess students’ reading comprehension. For this assessment, students read a text they have never seen before and then respond to multiple-choice and constructed-response questions. The assessment is not included in this course materials.

In this lesson, you will read and explore an allegory of modern life on the Internet. You will have a chance to create your own allegory to develop your thoughts about how constant digital connections have shaped our world.In this lesson, students will read and explore an allegory of modern life on the Internet. They will have a chance to create their own allegory to develop their thoughts about how constant digital connections have shaped our world.

This purpose of this exercise is to help students to identify common errors in logic--or "logical fallacies"--in a variety of contexts.  The exercise will serve as a review of reading and lecture on the fallacies and will require that students work together to understand the concepts.

This purpose of this exercise is to help students to identify common errors in logic--or "logical fallacies"--in a variety of contexts.  The exercise will serve as a review of fallacies that have been taught and read in previous lessons. The students will contribute to one "wiki page" that is created on Canvas.