In this ambitious study, David Corfield attacks the widely held view that it is the nature of mathematical knowledge which has shaped the way in which mathematics is treated philosophically and claims that contingent factors have brought us to the present thematically limited discipline. Illustrating his discussion with a wealth of examples, he sets out a variety of approaches to new thinking about the philosophy of mathematics, ranging from an exploration of whether computers producing mathematical proofs or conjectures are doing real mathematics, to the use of analogy, the prospects for a Bayesian confirmation theory, the notion of a mathematical research programme and the ways in which new concepts are justified. His inspiring book challenges both philosophers and mathematicians to develop the broadest and richest philosophical resources for work in their disciplines and points clearly to the ways in which this can be done.
Combinatorics is mathematics of enumeration, existence, construction, and optimization questions concerning finite sets. This text focuses on the first three types of questions and covers basic counting and existence principles, distributions, generating functions, recurrence relations, Pólya theory, combinatorial designs, error correcting codes, partially ordered sets, and selected applications to graph theory including the enumeration of trees, the chromatic polynomial, and introductory Ramsey theory. The only prerequisites are single-variable calculus and familiarity with sets and basic proof techniques. The text emphasizes the brands of thinking that are characteristic of combinatorics: bijective and combinatorial proofs, recursive analysis, and counting problem classification. It is flexible enough to be used for undergraduate courses in combinatorics, second courses in discrete mathematics, introductory graduate courses in applied mathematics programs, as well as for independent study or reading courses. What makes this text a guided tour are the approximately 350 reading questions spread throughout its eight chapters. These questions provide checkpoints for learning and prepare the reader for the end-of-section exercises of which there are over 470. Most sections conclude with Travel Notes that add color to the material of the section via anecdotes, open problems, suggestions for further reading, and biographical information about mathematicians involved in the discoveries.
Praise for David Darling The Universal Book of Astronomy "A first-rate resource for readers and students of popular astronomy and general science. . . . Highly recommended." -Library Journal "A comprehensive survey and . . . a rare treat." -Focus The Complete Book of Spaceflight "Darling's content and presentation will have any reader moving from entry to entry." -The Observatory magazine Life Everywhere "This remarkable book exemplifies the best of today's popular science writing: it is lucid, informative, and thoroughly enjoyable." -Science Books & Films "An enthralling introduction to the new science of astrobiology." -Lynn Margulis Equations of Eternity "One of the clearest and most eloquent expositions of the quantum conundrum and its philosophical and metaphysical implications that I have read recently." -The New York Times Deep Time "A wonderful book. The perfect overview of the universe." -Larry Niven
How can you broaden student thinking and help them develop their independence and confidence as problem solvers? Real-life problems are a remarkable tool to stretch student thinking and help them develop a deeper understanding of mathematics and its role in everyday life. Rather than using textbook exercises, the book argues that solving real-world problems promotes flexibility and encourages students to adjust and grow their thinking. It inspires them to consider alternatives and apply math in authentic contexts. You will find practical ways to engage students in critical thinking, develop their independence, and make connections with the world.
Molecular Biology, Third Edition, provides a thoroughly revised, invaluable resource for college and university students in the life sciences, medicine and related fields. This esteemed text continues to meet the needs of students and professors by offering new chapters on RNA, genome defense, and epigenetics, along with expanded coverage of RNAi, CRISPR, and more ensuring topical content for a new class of students. This volume effectively introduces basic concepts that are followed by more specific applications as the text evolves.Moreover, as part of the Academic Cell line of textbooks, this book contains research passages that shine a spotlight on current experimental work reported in Cell Press articles. These articles form the basis of case studies found in the associated online study guide that is designed to tie current topics to the scientific community. - Winner of a 2020 Textbook Excellence Award (College) (Texty) from the Textbook and Academic Authors Association - Contains new chapters on non-coding RNA, genome defense, epigenetics and epigenomics - Features new and expanded coverage of RNAi, CRISPR, genome editing, giant viruses and proteomics - Provides an ancillary package with updated PowerPoint slide images
This up to date book is essential reading for all those teaching or training to teach primary mathematics. Problem solving is a key aspect of teaching and learning mathematics, but also an area where teachers and pupils often struggle. Set within the context of the new primary curriculum and drawing on research and practice, the book identifies the key knowledge and skills required in teaching and learning problem solving in mathematics, and examines how these and can be applied in the classroom. It explores the issues in depth while remaining straightforward and relevant, emphasises the enrichment of maths through problem-solving, and provides opportunities for teachers to reflect on and further develop their classroom practice.
Combining the study of animal minds, artificial minds, and human evolution, this book examine the advances made by comparative psychologists in explaining the intelligent behaviour of primates, the design of artificial autonomous systems and the cognitive products of language evolution.
Risk Analysis concerns itself with the quantification of risk, the modeling of identified risks and how to make decisions from those models. Quantitative risk analysis (QRA) using Monte Carlo simulation offers a powerful and precise method for dealing with the uncertainty and variability of a problem. By providing the building blocks the author guides the reader through the necessary steps to produce an accurate risk analysis model and offers general and specific techniques to cope with most modeling problems. A wide range of solved problems is used to illustrate these techniques and how they can be used together to solve otherwise complex problems.
This book is an introduction to the modern theory of Markov chains, whose goal is to determine the rate of convergence to the stationary distribution, as a function of state space size and geometry. This topic has important connections to combinatorics, statistical physics, and theoretical computer science. Many of the techniques presented originate in these disciplines. The central tools for estimating convergence times, including coupling, strong stationary times, and spectral methods, are developed. The authors discuss many examples, including card shuffling and the Ising model, from statistical mechanics, and present the connection of random walks to electrical networks and apply it to estimate hitting and cover times. The first edition has been used in courses in mathematics and computer science departments of numerous universities. The second edition features three new chapters (on monotone chains, the exclusion process, and stationary times) and also includes smaller additions and corrections throughout. Updated notes at the end of each chapter inform the reader of recent research developments.
This unified account of various aspects of a powerful classical method, easy to understand in its simplest forms, is illustrated by applications in several areas of number theory. As well as including diophantine approximation and transcendence, which were mainly responsible for its invention, the author places the method in a broader context by exploring its application in other areas, such as exponential sums and counting problems in both finite fields and the field of rationals. Throughout the book, the method is explained in a 'molecular' fashion, where key ideas are introduced independently. Each application is the most elementary significant example of its kind and appears with detailed references to subsequent developments, making it accessible to advanced undergraduates as well as postgraduate students in number theory or related areas. It provides over 700 exercises both guiding and challenging, while the broad array of applications should interest professionals in fields from number theory to algebraic geometry.
Maths is everywhere, in everything. It’s in the finest margins of modern sport. It’s in the electrical pulses of our hearts and the flight of every bird. It is our key to secret messages, lost languages and perhaps even the shape of the universe of itself. David Darling and Agnijo Banerjee reveal the mathematics at the farthest reaches of our world – from its role in the plots of novels to how animals employ numerical skills to survive. Along the way they explore what makes a genius, why a seemingly simple problem can confound the best and brightest for decades, and what might be the great discovery of the twenty-first century. As Bertrand Russell once said, ‘mathematics, rightly viewed, possesses not only truth, but supreme beauty’. Banerjee and Darling make sure we see it right again.
This graduate-level text presents mathematical theory and problem-solving techniques associated with enumeration problems. Subjects include the combinatorics of the ordinary generating function and the exponential generating function, the combinatorics of sequences, and the combinatorics of paths. The text is complemented by approximately 350 exercises with full solutions. 1983 edition. Foreword by Gian-Carlo Rota. References. Index.
A fascinating journey into the mind-bending world of prime numbers Cicadas of the genus Magicicada appear once every 7, 13, or 17 years. Is it just a coincidence that these are all prime numbers? How do twin primes differ from cousin primes, and what on earth (or in the mind of a mathematician) could be sexy about prime numbers? What did Albert Wilansky find so fascinating about his brother-in-law's phone number? Mathematicians have been asking questions about prime numbers for more than twenty-five centuries, and every answer seems to generate a new rash of questions. In Prime Numbers: The Most Mysterious Figures in Math, you'll meet the world's most gifted mathematicians, from Pythagoras and Euclid to Fermat, Gauss, and Erd?o?s, and you'll discover a host of unique insights and inventive conjectures that have both enlarged our understanding and deepened the mystique of prime numbers. This comprehensive, A-to-Z guide covers everything you ever wanted to know--and much more that you never suspected--about prime numbers, including: * The unproven Riemann hypothesis and the power of the zeta function * The "Primes is in P" algorithm * The sieve of Eratosthenes of Cyrene * Fermat and Fibonacci numbers * The Great Internet Mersenne Prime Search * And much, much more
Book 6 in the Princeton Mathematical Series. Originally published in 1941. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
This "alternative textbook" integrates pedagogy and content exploration in ways that are unique in mathematics education, provoking new ideas for making mathematics education meaningful to teachers at all levels as well as their students.
Motivating Mathematics demonstrates that pupils can be motivated by being given the Big Picture, including a clearer picture of the nature of maths, and by linking topics to the sciences, rather than teaching each topic in isolation. The author emphasises the many virtues of problem-solving, strongly emphasised in secondary education specifications, especially the role of perception, and the ability of pupils to create their own proofs and to appreciate 'cool' ideas and arguments.David Wells draws on his extensive experience of teaching primary and secondary pupils and his understanding not just of how students think about mathematics, but of how they feel about a subject which so often seems merely a collection of facts and rules to be mastered. This book will be of immediate practical use to teachers and students at all levels.Anyone involved in mathematics education will benefit from reading this inspiring book, whether classroom teacher, trainer, teacher in training or professional development, or even parent. The book will also be of interest to policy makers and others with an investment in the future of mathematics education.
Thoroughly revised, this edition summarizes the field of fungal physiology from a dynamic, experimental perspective. Integrates molecular genetics with biochemistry and development of fungi. Reorganized into 14 chapters it describes the latest contemporary experimental approaches to fungal research as well as future developments.
The foundational textbook on the study of virology Basic Virology, 4th Edition cements this series’ position as the leading introductory virology textbook in the world. It’s easily read style, outstanding figures, and comprehensive coverage of fundamental topics in virology all account for its immense popularity. This undergraduate-accessible book covers all the foundational topics in virology, including: The basics of virology Virological techniques Molecular biology Pathogenesis of human viral disease The 4th edition includes new information on the SARS, MERS and COVID-19 coronaviruses, hepatitis C virus, influenza virus, as well as HIV and Ebola. New virological techniques including bioinformatics and advances in viral therapies for human disease are also explored in-depth. The book also includes entirely new sections on metapneumoviruses, dengue virus, and the chikungunya virus.
Allowing students to focus on real-life applications of mathematics. Selected examples feature traditional algebraic as well as optional graphing calculator solutions. We have taken great care to only use this format in examples where the graphing calculator can naturally be used to support and/or enhance the algebraic solution. For those interested in Mathematics.
Gene Control offers a current description of how gene expression is controlled in eukaryotes, reviewing and summarizing the extensive primary literature into an easily accessible format. Gene Control is a comprehensively restructured and expanded edition of Latchmans Gene Regulation: A Eukaryotic Perspective, Fifth Edition. The first part of the book deals with the fundamental processes of gene control at the levels of chromatin structure, transcription, and post-transcriptional processes. Three pairs of chapters deal with each of these aspects, first describing the basic process itself, followed by the manner in which it is involved in controlling gene expression. The second part of the book deals with the role of gene control in specific biological processes. Certain chapters deal with the importance of gene control in cellular signaling processes and for normal development of the embryo. Another chapter discusses the key roles played by gene-regulatory processes in the specification of differentiated cell types such as muscle cells and neurons. The final chapters discuss the consequences of errors in gene control; the relationship between gene misregulation and human diseases, especially cancer; and potential therapies designed specifically to target particular levels of gene control. Gene Control will be of value to students in biological sciences, as well as to scientists and clinicians interested in how genes are regulated in health and disease.
This first book on the market covers the many new and important RNA species discovered over the past five years, explaining current methods for the enrichment, separation and purification of these novel RNAs. Building up from general principles of RNA biochemistry and biophysics, this book addresses the practical aspects relevant to the laboratory researcher throughout, while discussing the performance and potential problems of the methods discussed. An appendix contains a glossary with the important terms and techniques used in RNA analysis. By explaining the basic and working principles of the methods, the book allows biochemists and molecular biologists to gain much more expertise than by simply repeating a pre-formulated protocol, enabling them to select the procedure and materials best suited to the RNA analysis task at hand. As a result, they will be able to develop new protocols where needed and optimize and fine-tune the general purpose standard protocols that come with the purification equipment and instrumentation.
Since the turn of the century, the idea that intellectual capacity is fixed has been generally accepted. But increasingly, psychologists, educators, and others have come to challenge this premise. Outsmarting IQ reveals how earlier discoveries about IQ, together with recent research, show that intelligence is not genetically fixed. Intelligence can be taught. David Perkins, renowned for his research on thinking, learning, and education, identifies three distinct kinds of intelligence: the fixed neurological intelligence linked to IQ tests; the specialized knowledge and experience that individuals acquire over time; and reflective intelligence, the ability to become aware of one's mental habits and transcend limited patterns of thinking. Although all of these forms of intelligence function simultaneously, it is reflective intelligence, Perkins shows, that affords the best opportunity to amplify human intellect. This is the kind of intelligence that helps us to make wise personal decisions, solve challenging technical problems, find creative ideas, and learn complex topics in mathematics, the sciences, management, and other areas. It is the kind of intelligence most needed in an increasingly competitive and complicated world. Using his own pathbreaking research at Harvard and a rich array of other sources, Perkins paints a compelling picture of the skills and attitudes underlying learnable intelligence. He identifies typical pitfalls in multiple perspectives, and neglecting evidence. He reveals the underlying mechanisms of intelligent behavior. And he explores new frontiers in the development of intelligence in education, business, and other settings. This book will be of interest to people who have a personal or professional stake in increasing their intellectual skills, to those who look toward better education and a more thoughtful society, and not least to those who follow today's heated debates about the nature of intelligence.
New in Paperback! Make learning more meaningful by teaching the "whole game" David Perkins, a noted authority on teaching and learning and co-director of Harvard's Project Zero, introduces a practical and research-based framework for teaching. He describes how teaching any subject at any level can be made more effective if students are introduced to the "whole game," rather than isolated pieces of a discipline. Perkins explains how learning academic subjects should be approached like learning baseball or any game, and he demonstrates this with seven principles for making learning whole: from making the game worth playing (emphasizing the importance of motivation to sustained learning), to working on the hard parts (the importance of thoughtful practice), to learning how to learn (developing self-managed learners). Vividly explains how to organize learning in ways that allow people to do important things with what they know Offers guidelines for transforming education to prepare our youth for success in a rapidly changing world Filled with real-world, illustrative examples of the seven principles At the end of each chapter, Perkins includes "Wonders of Learning," a summary of the key ideas.
The appeal of games and puzzles is timeless and universal. In this unique book, David Wells explores the fascinating connections between games and mathematics, proving that mathematics is not just about tedious calculation but imagination, insight and intuition. The first part of the book introduces games, puzzles and mathematical recreations, including knight tours on a chessboard. The second part explains how thinking about playing games can mirror the thinking of a mathematician, using scientific investigation, tactics and strategy, and sharp observation. Finally the author considers game-like features found in a wide range of human behaviours, illuminating the role of mathematics and helping to explain why it exists at all. This thought-provoking book is perfect for anyone with a thirst for mathematics and its hidden beauty; a good high school grounding in mathematics is all the background that is required, and the puzzles and games will suit pupils from 14 years.
This revised and updated second edition maintains the content and spirit of the first edition and includes a new chapter, "Recent Experiences", that provides examples of experimental mathematics that have come to light since the publication of the first edition in 2003. For more examples and insights, Experimentation in Mathematics: Computational P
Research on teaching and learning proof and proving has expanded in recent decades. This reflects the growth of mathematics education research in general, but also an increased emphasis on proof in mathematics education.
Stochastic point processes are sets of randomly located points in time, on the plane or in some general space. This book provides a general introduction to the theory, starting with simple examples and an historical overview, and proceeding to the general theory. It thoroughly covers recent work in a broad historical perspective in an attempt to provide a wider audience with insights into recent theoretical developments. It contains numerous examples and exercises. This book aims to bridge the gap between informal treatments concerned with applications and highly abstract theoretical treatments.
One of the most exciting debut anti-heroes since Lee Child's Jack Reacher Turbo Vlost learned early that life is like a game of cards.... It's not always about winning. Sometimes it's just a matter of making your enemies fold first. Turbo is a man with a past—his childhood was spent in the Soviet Gulag, while half of his adult life was spent in service to the KGB. His painful memories led to the demolition of his marriage, the separation from his only son, and his effective exile from Russia. Turbo now lives in New York City, where he runs a one-man business finding things for people. However, his past comes crashing into the present when he finds out that his new client is married to his ex-wife; his surrogate father, the man who saved him from the Gulag and recruited him into the KGB, has been shot; and he finds himself once again on the wrong side of the surrogate father's natural son, the head of the Russian mob in Brooklyn. As Turbo tries to navigate his way through a labyrinthine maze of deceit, he discovers all of these people have secrets that they are willing to go to any lengths to protect. Turbo didn't survive the camps and the Cold War without becoming one wily operator. He's ready to show them all why he's always the one who's...LAST TO FOLD. "One of the most original protagonists I've ever come across — a cross between Arkady Renko and Philip Marlowe: a Russian-born ex-KGB agent living in New York, a private eye with a strong sense of irony and a Russian sense of fatalism. David Duffy knows his Russia inside and out, but most of all, he knows how to tell a story with flair and elegance. This is really, really good." --Joseph Finder, New York Times best-selling author of Vanished and Buried Secrets
The extraordinary true story of the discovery of one of history's greatest mathematicians in rural India. His life is the subject of the major film The Man Who Knew Infinity 'Excellent ... His Hardy is a superb creation' Sunday Telegraph 'A loving exploration of one of the greatest collaborations of the past century, The Indian Clerk is a novel that brilliantly orchestrates questions of colonialism, sexual identity and the nature of genius' Manil Suri January, 1913, Cambridge. G.H. Hardy - eccentric, charismatic and considered the greatest British mathematician of his age - receives a mysterious envelope covered with Indian stamps. Inside he finds a rambling letter from a self-professed mathematical genius who claims to be on the brink of solving the most important mathematical problem of his time. Hardy determines to learn more about this mysterious Indian clerk, Srinivasa Ramanujan, a decision that will profoundly affect not only his own life, and that of his friends, but the entire history of mathematics. Set against the backdrop of the First World War, and populated with such luminaries as D.H. Lawrence and Bertrand Russell, The Indian Clerk fashions from this fascinating period an utterly compelling story about our need to find order in the world. In 2016 a film, The Man Who Knew Infinity, inspired by the same life on which this book is based, was released, starring Dev Patel and Jeremy Irons.
This book provides a comprehensive, up-to-date look at problem solving research and practice over the last fifteen years. The first chapter describes differences in types of problems, individual differences among problem-solvers, as well as the domain and context within which a problem is being solved. Part one describes six kinds of problems and the methods required to solve them. Part two goes beyond traditional discussions of case design and introduces six different purposes or functions of cases, the building blocks of problem-solving learning environments. It also describes methods for constructing cases to support problem solving. Part three introduces a number of cognitive skills required for studying cases and solving problems. Finally, Part four describes several methods for assessing problem solving. Key features includes: Teaching Focus – The book is not merely a review of research. It also provides specific research-based advice on how to design problem-solving learning environments. Illustrative Cases – A rich array of cases illustrates how to build problem-solving learning environments. Part two introduces six different functions of cases and also describes the parameters of a case. Chapter Integration – Key theories and concepts are addressed across chapters and links to other chapters are made explicit. The idea is to show how different kinds of problems, cases, skills, and assessments are integrated. Author expertise – A prolific researcher and writer, the author has been researching and publishing books and articles on learning to solve problems for the past fifteen years. This book is appropriate for advanced courses in instructional design and technology, science education, applied cognitive psychology, thinking and reasoning, and educational psychology. Instructional designers, especially those involved in designing problem-based learning, as well as curriculum designers who seek new ways of structuring curriculum will find it an invaluable reference tool.
First published in 1986. We all play the roles of teacher or learner many times in life, in school and home, on the job and even at play. How can we strengthen those roles, striving for deep understanding and sound thinking? Knowledge As Design demonstrates the strong but neglected unity between learning and critical and creative thinking. Author David Perkins discloses how the concept of design opens a doorway into a deeper exploration of any topic, academic or every day. Knowledge As Design challenges the concept of knowledge as information. Drawing from current philosophy and cognitive science, the book shows how learners can attain a new level of insight when learning highlights the constructed and constructive character of knowledge. Any individual involved in formal or informal learning or teaching can benefit from the general outlook and specific principles laid out in this book. It offers a uniquely intelligent philosophy and psychology of understanding and critical and creative thinking.
Historian David E. Rowe captures the rich tapestry of mathematical creativity in this collection of essays from the “Years Ago” column of The Mathematical Intelligencer. With topics ranging from ancient Greek mathematics to modern relativistic cosmology, this collection conveys the impetus and spirit of Rowe’s various and many-faceted contributions to the history of mathematics. Centered on the Göttingen mathematical tradition, these stories illuminate important facets of mathematical activity often overlooked in other accounts. Six sections place the essays in chronological and thematic order, beginning with new introductions that contextualize each section. The essays that follow recount episodes relating to the section’s overall theme. All of the essays in this collection, with the exception of two, appeared over the course of more than 30 years in The Mathematical Intelligencer. Based largely on archival and primary sources, these vignettes offer unusual insights into behind-the-scenes events. Taken together, they aim to show how Göttingen managed to attract an extraordinary array of talented individuals, several of whom contributed to the development of a new mathematical culture during the first decades of the twentieth century.
Unlike most textbooks on this subject, Biotechnology approaches modern biotechnology from a molecular basis. Using straightforward, less technical jargon, Clark and Pazdernik introduce students to the topics and walk them through the process as it evolves into a more specific detailed principle." "This up-to-date text covers a wide realm of topics that are encountered in current media and movies. One of the chapters covers the burgeoning field of nanobiotechnology, stimulating the student to think about biotechnology from a new and much smaller point of view. Another chapter explains the real biotechnology behind crime scene investigations portrayed so dramatically on the hit show CSI. In addition, students will learn about the biotechnology behind making vaccines, genetically-modified plants, stem-cell research, gene therapy, and aging, among many other topics that are part of mainstream media coverage. Students will also learn the molecular basis for many viral diseases, cancer, and bacterial diseases that are bound to affect them or other family members. Finally, the text includes a very thought-provoking chapter on the bioethics of these new advances and applications of today's world of biotechnology, which stimulates the student to think rather than memorize."--BOOK JACKET.
This title is directed primarily towards health care professionals outside of the United States. THE FLESH AND BONES OF MEDICAL CELL BIOLOGY presents a concise, accessible account of medical cell biology. This title covers all the key concepts med students need with no gaps. It can be used either as an introduction to a topic, or as a revision aid. In Section 1, The Big Picture overview gives a descriptive overview of a subject. In the High Yield section, 50 fundamental principles underlying a subject are set out. These 50 principles are expanded into double-page spreads in the 'Fleshed Out' section where double-page explanations of the key principles clearly convey what medical students need to know. Difficult concepts are depicted by cartoon-strip illustrations, which enable rapid understanding and assimilation of information. Big Picture Section - enables readers to relate detail to the subject as a whole High Return Facts - prevents students from having large gaps in their knowledge. Can be used as a revision tool. Reinforces the major points. Cartoon-strip illustrations - enable students to visualize difficult concepts in a step-by-step format. Allow information to be chunked into student-friendly sizes. Double-page overviews - students can read summary of topic without cross-referencing to other pages. All laid out on one spread.
This book is a completely revised new edition of the definitive reference on disorders of hemoglobin. Authored by world-renowned experts, the book focuses on basic science aspects and clinical features of hemoglobinopathies, covering diagnosis, treatment, and future applications of current research. While the second edition continues to address the important molecular, cellular, and genetic components, coverage of clinical issues has been significantly expanded, and there is more practical emphasis on diagnosis and management throughout. The book opens with a review of the scientific underpinnings. Pathophysiology of common hemoglobin disorders is discussed next in an entirely new section devoted to vascular biology, the erythrocyte membrane, nitric oxide biology, and hemolysis. Four sections deal with α and β thalassemia, sickle cell disease, and related conditions, followed by special topics. The second edition concludes with current and developing approaches to treatment, incorporating new agents for iron chelation, methods to induce fetal hemoglobin production, novel treatment approaches, stem cell transplantation, and progress in gene therapy.
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