Discovering Patterns

Maths for Fun explores maths through interactive projects, experiments and fun games, raging from the simple to the more challenging. Filled with ideas for making helpful tools, hints and tips and even further concepts to explore, Maths for Fun puts the f

This open-ended assignment offers diverse options for all types of learners to show what they've learned. Written specifically for mathematics teachers, this lesson helps facilitate the understanding and process of writing open-ended task lessons.

You are invited to join a fascinating journey of discovery, as Marcia Birken and Anne C. Coon explore the intersecting patterns of mathematics and poetry -- bringing the two fields together in a new way. Setting the tone with humor and illustrating each chapter with countless examples, Birken and Coon begin with patterns we can see, hear, and feel and then move to more complex patterns. Number systems and nursery rhymes lead to the Golden Mean and sestinas. Simple patterns of shape introduce tessellations and concrete poetry. Fractal geometry makes fractal poetry possible. Ultimately, patterns for the mind lead to questions: How do mathematicians and poets conceive of proof, paradox, and infinity? What role does analogy play in mathematical discovery and poetic expression? The book will be of special interest to readers who enjoy looking for connections across traditional disciplinary boundaries.Discovering Patterns in Mathematics and Poetry features centuries of creative work by mathematicians, poets, and artists, including Fibonacci, Albrecht Dürer, M. C. Escher, David Hilbert, Benoit Mandelbrot, William Shakespeare, Edna St. Vincent Millay, Langston Hughes, E.E. Cummings, and many contemporary experimental poets. Original illustrations include digital photographs, mathematical and poetic models, and fractal imagery.

You are invited to join a fascinating journey of discovery, as Marcia Birken and Anne C. Coon explore the intersecting patterns of mathematics and poetry — bringing the two fields together in a new way. Setting the tone with humor and illustrating each chapter with countless examples, Birken and Coon begin with patterns we can see, hear, and feel and then move to more complex patterns. Number systems and nursery rhymes lead to the Golden Mean and sestinas. Simple patterns of shape introduce tessellations and concrete poetry. Fractal geometry makes fractal poetry possible. Ultimately, patterns for the mind lead to questions: How do mathematicians and poets conceive of proof, paradox, and infinity? What role does analogy play in mathematical discovery and poetic expression? The book will be of special interest to readers who enjoy looking for connections across traditional disciplinary boundaries.Discovering Patterns in Mathematics and Poetry features centuries of creative work by mathematicians, poets, and artists, including Fibonacci, Albrecht Dürer, M. C. Escher, David Hilbert, Benoit Mandelbrot, William Shakespeare, Edna St. Vincent Millay, Langston Hughes, E.E. Cummings, and many contemporary experimental poets. Original illustrations include digital photographs, mathematical and poetic models, and fractal imagery.

1 WorkshopTheme Data mining as a discipline aims to relate the analysis of large amounts of user data to shed light on key business questions. Web usage mining in particular, a relatively young discipline, investigates methodologies and techniques that - dress the unique challenges of discovering insights from Web usage data, aiming toevaluateWebusability,understandtheinterestsandexpectationsofusersand assess the e?ectiveness of content delivery. The maturing and expanding Web presents a key driving force in the rapid growth of electronic commerce and a new channel for content providers. Customized o?ers and content, made possible by discovered knowledge about the customer, are fundamental for the establi- ment of viable e-commerce solutions and sustained and e?ective content delivery in noncommercial domains. Rich Web logs provide companies with data about their online visitors and prospective customers, allowing microsegmentation and personalized interactions. While Web mining as a domain is several years old, the challenges that characterize data analysis in this area continue to be formidable. Though p- processing data routinely takes up a major part of the e?ort in data mining, Web usage data presents further challenges based on the di?culties of assigning data streams to unique users and tracking them over time. New innovations are required to reliably reconstruct sessions, to ascertain similarity and di?erences between sessions, and to be able to segment online users into relevant groups.

The collation of large electronic databases of scienti?c and commercial infor- tion has led to a dramatic growth of interest in methods for discovering struc- res in such databases. These methods often go under the general name of data mining. One important subdiscipline within data mining is concerned with the identi?cation and detection of anomalous, interesting, unusual, or valuable - cords or groups of records, which we call patterns. Familiar examples are the detection of fraud in credit-card transactions, of particular coincident purchases in supermarket transactions, of important nucleotide sequences in gene sequence analysis, and of characteristic traces in EEG records. Tools for the detection of such patterns have been developed within the data mining community, but also within other research communities, typically without an awareness that the - sic problem was common to many disciplines. This is not unreasonable: each of these disciplines has a large literature of its own, and a literature which is growing rapidly. Keeping up with any one of these is di?cult enough, let alone keeping up with others as well, which may in any case be couched in an - familiar technical language. But, of course, this means that opportunities are being lost, discoveries relating to the common problem made in one area are not transferred to the other area, and breakthroughs and problem solutions are being rediscovered, or not discovered for a long time, meaning that e?ort is being wasted and opportunities may be lost.

This book constitutes the refereed proceedings of the 5th Pacific-Asia Conference on Knowledge Discovery and Data Mining, PAKDD 2001, held in Hong Kong, China in April 2001. The 38 revised full papers and 22 short papers presented were carefully reviewed and selected from a total of 152 submissions. The book offers topical sections on Web mining, text mining, applications and tools, concept hierarchies, feature selection, interestingness, sequence mining, spatial and temporal mining, association mining, classification and rule induction, clustering, and advanced topics and new methods.

This book constitutes the proceedings of the 19th International Conference on Conceptual Structures, ICCS 2011, held in Derby, UK, in July 2011. The 18 full papers and 4 short papers presented together with 12 workshop papers were carefully reviewed and selected for inclusion in the book. The volume also contains 3 invited talks. ICCS focuses on the useful representation and analysis of conceptual knowledge with research and business applications. It advances the theory and practice in connecting the user's conceptual approach to problem solving with the formal structures that computer applications need to bring their productivity to bear. Conceptual structures (CS) represent a family of approaches that builds on the successes of artificial intelligence, business intelligence, computational linguistics, conceptual modelling, information and Web technologies, user modelling, and knowledge management. Two of the workshops contained in this volume cover CS and knowledge discovery in under-traversed domains and in task specific information retrieval. The third addresses CD in learning, teaching and assessment.