Optimization Theory is an active area of research with numerous applications; many of the books are designed for engineering classes, and thus have an emphasis on problems from such fields. Covering much of the same material, there is less emphasis on coding and detailed applications as the intended audience is more mathematical. There are still several important problems discussed (especially scheduling problems), but there is more emphasis on theory and less on the nuts and bolts of coding. A constant theme of the text is the "why" and the "how" in the subject. Why are we able to do a calculation efficiently? How should we look at a problem? Extensive effort is made to motivate the mathematics and isolate how one can apply ideas/perspectives to a variety of problems. As many of the key algorithms in the subject require too much time or detail to analyze in a first course (such as the run-time of the Simplex Algorithm), there are numerous comparisons to simpler algorithms which students have either seen or can quickly learn (such as the Euclidean algorithm) to motivate the type of results on run-time savings.

The essential lifesaver for students who want to master probability For students learning probability, its numerous applications, techniques, and methods can seem intimidating and overwhelming. That's where The Probability Lifesaver steps in. Designed to serve as a complete stand-alone introduction to the subject or as a supplement for a course, this accessible and user-friendly study guide helps students comfortably navigate probability's terrain and achieve positive results. The Probability Lifesaver is based on a successful course that Steven Miller has taught at Brown University, Mount Holyoke College, and Williams College. With a relaxed and informal style, Miller presents the math with thorough reviews of prerequisite materials, worked-out problems of varying difficulty, and proofs. He explores a topic first to build intuition, and only after that does he dive into technical details. Coverage of topics is comprehensive, and materials are repeated for reinforcement--both in the guide and on the book's website. An appendix goes over proof techniques, and video lectures of the course are available online. Students using this book should have some familiarity with algebra and precalculus. The Probability Lifesaver not only enables students to survive probability but also to achieve mastery of the subject for use in future courses. * A helpful introduction to probability or a perfect supplement for a course* Numerous worked-out examples* Lectures based on the chapters are available free online* Intuition of problems emphasized first, then technical proofs given* Appendixes review proof techniques* Relaxed, conversational approach

How quickly can you compute the remainder when dividing $109837^{97}$ by 120143? Why would you even want to compute this? And what does this have to do with cryptography? Modern cryptography lies at the intersection of mathematics and computer sciences, involving number theory, algebra, computational complexity, fast algorithms, and even quantum mechanics. Many people think of codes in terms of spies, but in the information age, highly mathematical codes are used every day by almost everyone, whether at the bank ATM, at the grocery checkout, or at the keyboard when you access your email or purchase products online. This book provides a historical and mathematical tour of cryptography, from classical ciphers to quantum cryptography. The authors introduce just enough mathematics to explore modern encryption methods, with nothing more than basic algebra and some elementary number theory being necessary. Complete expositions are given of the classical ciphers and the attacks on them, along with a detailed description of the famous Enigma system. The public-key system RSA is described, including a complete mathematical proof that it works. Numerous related topics are covered, such as efficiencies of algorithms, detecting and correcting errors, primality testing and digital signatures. The topics and exposition are carefully chosen to highlight mathematical thinking and problem solving. Each chapter ends with a collection of problems, ranging from straightforward applications to more challenging problems that introduce advanced topics. Unlike many books in the field, this book is aimed at a general liberal arts student, but without losing mathematical completeness.

Benford's law states that the leading digits of many data sets are not uniformly distributed from one through nine, but rather exhibit a profound bias. This bias is evident in everything from electricity bills and street addresses to stock prices, population numbers, mortality rates, and the lengths of rivers. Here, Steven Miller brings together many of the world's leading experts on Benford's law to demonstrate the many useful techniques that arise from the law, show how truly multidisciplinary it is, and encourage collaboration. Beginning with the general theory, the contributors explain the prevalence of the bias, highlighting explanations for when systems should and should not follow Benford's law and how quickly such behavior sets in. They go on to discuss important applications in disciplines ranging from accounting and economics to psychology and the natural sciences. The contributors describe how Benford's law has been successfully used to expose fraud in elections, medical tests, tax filings, and financial reports. Additionally, numerous problems, background materials, and technical details are available online to help instructors create courses around the book. Emphasizing common challenges and techniques across the disciplines, this accessible book shows how Benford's law can serve as a productive meeting ground for researchers and practitioners in diverse fields.

Since it was first published, LIS students and professionals everywhere have relied on Miller’s authoritative manual for clear instruction on the real-world practice of metadata design and creation. Now the author has given his text a top-to-bottom overhaul to bring it fully up-to-date, making it even easier for readers to acquire the knowledge and skills they need, whether they use the book on the job or in a classroom. By following this book’s guidance, with its inclusion of numerous practical examples that clarify common application issues and challenges, readers will: learn about the concept of metadata and its functions for digital collections, why it’s essential to approach metadata specifically as data for machine processing, and how metadata can work in the rapidly developing Linked Data environment know how to create high-quality resource descriptions using widely shared metadata standards, vocabularies and elements commonly needed for digital collections become thoroughly familiarized with Dublin Core (DC) through exploration of DCMI Metadata Terms, CONTENTdm best practices, and DC as Linked Data discover what Linked Data is, how it is expressed in the Resource Description Framework (RDF), and how it works in relation to specific semantic models (typically called ‘ontologies’) such as BIBFRAME, comprised of properties and classes with ‘domain’ and ‘range’ specifications get to know the MODS and VRA Core metadata schemes, along with recent developments related to their use in a Linked Data setting understand the nuts and bolts of designing and documenting a metadata scheme and gain knowledge of vital metadata interoperability and quality issues, including how to identify and clean inconsistent, missing, and messy metadata using innovative tools such as OpenRefine. Complete with an updated bibliography pointing readers to essential books, articles and web documents for deeper learning, this second edition will prove itself a must-have reference for practitioners and students alike.

More and more libraries, archives, and museums are creating online collections of digitized resources. Where can those charged with organizing these new collections turn for guidance on the actual practice of metadata design and creation? To Metadata for Digital Collections: A How-To-Do-It Manual. This practical, hands-on volume will make it easy for readers to acquire the knowledge and skills they need, whether they use the book on the job or in a classroom. Author Steven Miller introduces readers to fundamental concepts and practices in a style accessible to beginners and LIS students, as well as experienced practitioners with little metadata training. He also takes account of the widespread use of digital collection management systems such as CONTENTdm. Rather than surveying a large number of metadata schemes, Miller covers only three of the schemes most commonly used in general digital resource description, namely, Dublin Core, MODS, and VRA. By limiting himself, Miller is able to address the chosen schemes in greater depth. He is also able to include numerous practical examples that clarify common application issues and challenges. He provides practical guidance on applying each of the Dublin Core elements, taking special care to clarify those most commonly misunderstood. The book includes a step-by-step guide on how to design and document a metadata scheme for local institutional needs and for specific digital collection projects. The text also serves well as an introduction to broader metadata topics, including XML encoding, mapping between different schemes, metadata interoperability and record sharing, OAI harvesting, and the emerging environment of Linked Data and the Semantic Web, explaining their relevance to current practitioners and students. A companion Web site includes exercises for each chapter, with suggestions for instructors, along with additional practical and reference resources.

In a manner accessible to beginning undergraduates, "An Invitation to Modern Number Theory" introduces many of the central problems, conjectures, results, and techniques of the field, such as the Riemann Hypothesis, Roth's Theorem, the Circle Method, and Random Matrix Theory. Showing how experiments are used to test conjectures and prove theorems, the book allows students to do original work on such problems, often using little more than calculus (though there are numerous remarks for those with deeper backgrounds). It shows students what number theory theorems are used for and what led to them and suggests problems for further research.

Steven Miller and Ramin Takloo-Bighash introduce the problems and the computational skills required to numerically investigate them, providing background material (from probability to statistics to Fourier analysis) whenever necessary. They guide students through a variety of problems, ranging from basic number theory, cryptography, and Goldbach's Problem, to the algebraic structures of numbers and continued fractions, showing connections between these subjects and encouraging students to study them further. In addition, this is the first undergraduate book to explore Random Matrix Theory, which has recently become a powerful tool for predicting answers in number theory.

Providing exercises, references to the background literature, and Web links to previous student research projects, "An Invitation to Modern Number Theory" can be used to teach a research seminar or a lecture class.