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.
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.
This course includes materials on AI programming, logic, search, game playing, machine learning, natural language understanding, and robotics, which will introduce the student to AI methods, tools, and techniques, their application to computational problems, and their contribution to understanding intelligence. The material is introductory; the readings cite many resources outside those assigned in this course, and students are encouraged to explore these resources to pursue topics of interest. Upon successful completion of this course, the student will be able to: Describe the major applications, topics, and research areas of artificial intelligence (AI), including search, machine learning, knowledge representation and inference, natural language processing, vision, and robotics; Apply basic techniques of AI in computational solutions to problems; Discuss the role of AI research areas in growing the understanding of human intelligence; Identify the boundaries of the capabilities of current AI systems. (Computer Science 405)
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.
The rationale of teaching Basic mathematics is that it plays the role of filling up gaps that the student teacher could be having from secondary school mathematics. For instance, a lack of a proper grasp of the real number system and elementary functions etc. It also serves as the launching pad to University Mathematics by introducing the learner to the science of reasoning called logic and other related topics.
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.
This lesson is designed to meet the following learning objectives:
1. Formulate an argument
2. Learn how to anticipate and respond to objections
Explores concepts and applications of logic rules, basic probability and statistics as well as personal finance models. Investigates problem solving techniques (algebraic and nonalgebraic) as well as some nontraditional mathematics topics such as social choice or discrete mathematics. Integrates technology where appropriate.
Intended Outcomes for the course
Upon completion of the course students should be able to:
Use formulas and perform relevant calculations pertaining to personal finance in order to make informed financial decisions
Make and interpret calculations and graphical displays of numerical data in order to perceive and infer patterns within data sets
Calculate and interpret theoretical and empirical probabilities in support of making predictions and decisions in the presence of uncertainty
Use logical reasoning to describe and critique arguments and recognize common logical fallacies
Support conclusions using logical thought, reflection, explanation and justification
Use appropriate representations to effectively communicate, orally and in writing, quantitative results and mathematical processes
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.
This course covered the mathematical topics most directly related to computer science. Topics included: logic, relations, functions, basic set theory, countability and counting arguments, proof techniques, mathematical induction, graph theory, combinatorics, discrete probability, recursion, recurrence relations, and number theory. Emphasis will be placed on providing a context for the application of the mathematics within computer science. The analysis of algorithms requires the ability to count the number of operations in an algorithm. Recursive algorithms in particular depend on the solution to a recurrence equation, and a proof of correctness by mathematical induction. The design of a digital circuit requires the knowledge of Boolean algebra. Software engineering uses sets, graphs, trees and other data structures. Number theory is at the heart of secure messaging systems and cryptography. Logic is used in AI research in theorem proving and in database query systems. Proofs by induction and the more general notions of mathematical proof are ubiquitous in theory of computation, compiler design and formal grammars. Probabilistic notions crop up in architectural trade-offs in hardware design.
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.
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.
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.
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.
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.
At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary’s user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition’s treatment of languages, structures, and deductions, leading to rigorous proofs of Gödel’s First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises.