his book is an introduction to combinatorial mathematics, also known as combinatorics. …
his book is an introduction to combinatorial mathematics, also known as combinatorics. The book focuses especially but not exclusively on the part of combinatorics that mathematicians refer to as “counting.” The book consists almost entirely of problems. Some of the problems are designed to lead you to think about a concept, others are designed to help you figure out a concept and state a theorem about it, while still others ask you to prove the theorem. Other problems give you a chance to use a theorem you have proved. From time to time there is a discussion that pulls together some of the things you have learned or introduces a new idea for you to work with. Many of the problems are designed to build up your intuition for how combinatorial mathematics works. There are problems that some people will solve quickly, and there are problems that will take days of thought for everyone. Probably the best way to use this book is to work on a problem until you feel you are not making progress and then go on to the next one. Think about the problem you couldn’t get as you do other things. The next chance you get, discuss the problem you are stymied on with other members of the class. Often you will all feel you’ve hit dead ends, but when you begin comparing notes and listening carefully to each other, you will see more than one approach to the problem and be able to make some progress. In fact, after comparing notes you may realize that there is more than one way to interpret the problem. In this case your first step should be to think together about what the problem is actually asking you to do. You may have learned in school that for every problem you are given, there is a method that has already been taught to you, and you are supposed to figure out which method applies and apply it. That is not the case here. Based on some simplified examples, you will discover the method for yourself. Later on, you may recognize a pattern that suggests you should try to use this method again.
Table of Contents 1 What is Combinatorics? 2 Applications of Induction and Recursion in Combinatorics and Graph Theory 3 Distribution Problems 4 Generating Functions 5 The Principle of Inclusion and Exclusion 6 Groups Acting on Sets
Access also available here: https://math.dartmouth.edu/news-resources/electronic/kpbogart/
his book is an introduction to combinatorial mathematics, also known as combinatorics. …
his book is an introduction to combinatorial mathematics, also known as combinatorics. The book focuses especially but not exclusively on the part of combinatorics that mathematicians refer to as “counting.” The book consists almost entirely of problems. Some of the problems are designed to lead you to think about a concept, others are designed to help you figure out a concept and state a theorem about it, while still others ask you to prove the theorem. Other problems give you a chance to use a theorem you have proved. From time to time there is a discussion that pulls together some of the things you have learned or introduces a new idea for you to work with. Many of the problems are designed to build up your intuition for how combinatorial mathematics works. There are problems that some people will solve quickly, and there are problems that will take days of thought for everyone. Probably the best way to use this book is to work on a problem until you feel you are not making progress and then go on to the next one. Think about the problem you couldn’t get as you do other things. The next chance you get, discuss the problem you are stymied on with other members of the class. Often you will all feel you’ve hit dead ends, but when you begin comparing notes and listening carefully to each other, you will see more than one approach to the problem and be able to make some progress. In fact, after comparing notes you may realize that there is more than one way to interpret the problem. In this case your first step should be to think together about what the problem is actually asking you to do. You may have learned in school that for every problem you are given, there is a method that has already been taught to you, and you are supposed to figure out which method applies and apply it. That is not the case here. Based on some simplified examples, you will discover the method for yourself. Later on, you may recognize a pattern that suggests you should try to use this method again.
Communication in the Real World: An Introduction to Communication Studies overviews the …
Communication in the Real World: An Introduction to Communication Studies overviews the time-tested conceptual foundations of the field, while incorporating the latest research and cutting-edge applications of these basics. Each chapter will include timely, concrete, and real-life examples of communication concepts in action. A key feature of this book is the integration of content regarding diversity and organizational communication in each chapter through examples and/or discrete sub-sections. Discussions of diversity are not relegated to feature boxes. Also integrated into the content are examples that are inclusive in terms of race, gender, sexuality, ability, age, marital status, religion, and other diverse identity characteristics.
This course provides knowledge and skills in supporting English Language Development and …
This course provides knowledge and skills in supporting English Language Development and Inclusive Learningthroughout Out-of-School (OST) environments. Educators learn learn to welcome, support, and enhance language and literacy skill development for all children and youth and respond appropriately to the individualized ELD needs of non-native speakers of English.
In Australia and internationally much still needs to occur to promote inclusive …
In Australia and internationally much still needs to occur to promote inclusive practices in education and society with many educators not feeling equipped to recognise or appreciate diversity or cater effectively for inclusion (Hardy & Woodcock, 2015). It is into this space that a University of Southern Queensland team of researchers, practitioners, and academics intends to contribute an open textbook “Opening Eyes onto Inclusion and Diversity”. With embedded audio–visual components, the Open Textbook is designed to enhance the quality of the reader’s experience with each chapter posing key understandings underpinning inclusion and diversity. Readers are encouraged to answer questions on culture, special learning needs, varied educational contexts, gender diversity and more. The key expected outcome of this open textbook is to engage readers in making meaning of inclusion and diversity and applying their learning to their own individual contexts.
This course explores how social theories of urban life can be related …
This course explores how social theories of urban life can be related to the city's architecture and spaces. It is grounded in classic or foundational writings about the city addressing such topics as the public realm and public space, impersonality, crowds and density, surveillance and civility, imprinting time on space, spatial justice, and the segregation of difference. The aim of the course is to generate new ideas about the city by connecting the social and the physical, using Boston as a visual laboratory. Students are required to present a term paper mediating what is read with what has been observed.
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