Machine Learning Algorithms for Problem Solving in Computational Applications

A broad introduction to algorithms for decision making under uncertainty, introducing the underlying mathematical problem formulations and the algorithms for solving them.Automated decision-making systems or decision-support systems―used in applications that range from aircraft collision avoidance to breast cancer screening―must be designed to account for various sources of uncertainty while carefully balancing multiple objectives. This textbook provides a broad introduction to algorithms for decision making under uncertainty, covering the underlying mathematical problem formulations and the algorithms for solving them. The book first addresses the problem of reasoning about uncertainty and objectives in simple decisions at a single point in time, and then turns to sequential decision problems in stochastic environments where the outcomes of our actions are uncertain. It goes on to address model uncertainty, when we do not start with a known model and must learn how to act through inte

A comprehensive update of the leading algorithms text, with new material on matchings in bipartite graphs, online algorithms, machine learning, and other topics. Some books on algorithms are rigorous but incomplete; others cover masses of material but lack rigor. Introduction to Algorithms uniquely combines rigor and comprehensiveness. It covers a broad range of algorithms in depth, yet makes their design and analysis accessible to all levels of readers, with self-contained chapters and algorithms in pseudocode. Since the publication of the first edition, Introduction to Algorithms has become the leading algorithms text in universities worldwide as well as the standard reference for professionals. This fourth edition has been updated throughout. New for the fourth edition New chapters on matchings in bipartite graphs, online algorithms, and machine learningNew material on topics including solving recurrence equations, hash tables, potential functions, and suffix arrays140 new exerc

Fundamental theory and practical algorithms of weakly supervised classification, emphasizing an approach based on empirical risk minimization.Standard machine learning techniques require large amounts of labeled data to work well. When we apply machine learning to problems in the physical world, however, it is extremely difficult to collect such quantities of labeled data. This book presents theory and algorithms for weakly supervised learning, a paradigm of machine learning from weakly labeled data. Emphasizing an approach based on empirical risk minimization and drawing on state-of-the-art research in weakly supervised learning, the book provides both the fundamentals of the field and the advanced mathematical theories underlying them. It can be used as a reference for practitioners and researchers and in the classroom.The book first mathematically formulates classification problems, defines common notations, and reviews various algorithms for supervised binary and multiclass classif

Probabilistic numerical computation formalises the connection between machine learning and applied mathematics. Numerical algorithms approximate intractable quantities from computable ones. They estimate integrals from evaluations of the integrand, or the path of a dynamical system described by differential equations from evaluations of the vector field. In other words, they infer a latent quantity from data. This book shows that it is thus formally possible to think of computational routines as learning machines, and to use the notion of Bayesian inference to build more flexible, efficient, or customised algorithms for computation. The text caters for Masters' and PhD students, as well as postgraduate researchers in artificial intelligence, computer science, statistics, and applied mathematics. Extensive background material is provided along with a wealth of figures, worked examples, and exercises (with solutions) to develop intuition.

This self-contained introduction to machine learning, designed from the start with engineers in mind, will equip students with everything they need to start applying machine learning principles and algorithms to real-world engineering problems. With a consistent emphasis on the connections between estimation, detection, information theory, and optimization, it includes: an accessible overview of the relationships between machine learning and signal processing, providing a solid foundation for further study; clear explanations of the differences between state-of-the-art techniques and more classical methods, equipping students with all the understanding they need to make informed technique choices; demonstration of the links between information-theoretical concepts and their practical engineering relevance; reproducible examples using Matlab, enabling hands-on student experimentation. Assuming only a basic understanding of probability and linear algebra, and accompanied by lecture slide

In recent years the development of new classification and regression algorithms based on deep learning has led to a revolution in the fields of artificial intelligence, machine learning, and data analysis. The development of a theoretical foundation to guarantee the success of these algorithms constitutes one of the most active and exciting research topics in applied mathematics. This book presents the current mathematical understanding of deep learning methods from the point of view of the leading experts in the field. It serves as both a starting point for researchers and graduate students in mathematics trying to get into the field, as well as an invaluable reference for future research.

Migrate from pandas and scikit-Learn to PySpark to handle vast amounts of data and achieve faster data processing time. This book will show you how to make this transition by adapting your skills and leveraging the similarities in syntax, functionality, and interoperability between these tools. Distributed Machine Learning with PySpark offers a roadmap to data scientists considering transitioning from small data libraries (pandas/scikit-learn) to big data processing and machine learning with PySpark. You will learn to translate Python code from pandas/scikit-learn to PySpark to preprocess large volumes of data and build, train, test, and evaluate popular machine learning algorithms such as linear and logistic regression, decision trees, random forests, support vector machines, Na鴳e Bayes, and neural networks. After completing this book, you will understand the foundational concepts of data preparation and machine learning and will have the skills necessary to apply these methods using

A guide to computational thinking education, with a focus on artificial intelligence literacy and the integration of computing and physical objects. Computing has become an essential part of today’s primary and secondary school curricula. In recent years, K–12 computer education has shifted from computer science itself to the broader perspective of computational thinking (CT), which is less about technology than a way of thinking and solving problems―“a fundamental skill for everyone, not just computer scientists,” in the words of Jeanette Wing, author of a foundational article on CT. This volume introduces a variety of approaches to CT in K–12 education, offering a wide range of international perspectives that focus on artificial intelligence (AI) literacy and the integration of computing and physical objects. The book first offers an overview of CT and its importance in K–12 education, covering such topics as the rationale for teaching CT; programming as a general problem-solving

Recovering the phase of the Fourier transform is a ubiquitous problem in imaging applications from astronomy to nanoscale X-ray diffraction imaging. Despite the efforts of a multitude of scientists, from astronomers to mathematicians, there is, as yet, no satisfactory theoretical or algorithmic solution to this class of problems. Written for mathematicians, physicists and engineers working in image analysis and reconstruction, this book introduces a conceptual, geometric framework for the analysis of these problems, leading to a deeper understanding of the essential, algorithmically independent, difficulty of their solutions. Using this framework, the book studies standard algorithms and a range of theoretical issues in phase retrieval and provides several new algorithms and approaches to this problem with the potential to improve the reconstructed images. The book is lavishly illustrated with the results of numerous numerical experiments that motivate the theoretical development and p

A detailed and up-to-date introduction to machine learning, presented through the unifying lens of probabilistic modeling and Bayesian decision theory.This book offers a detailed and up-to-date introduction to machine learning (including deep learning) through the unifying lens of probabilistic modeling and Bayesian decision theory. The book covers mathematical background (including linear algebra and optimization), basic supervised learning (including linear and logistic regression and deep neural networks), as well as more advanced topics (including transfer learning and unsupervised learning). End-of-chapter exercises allow students to apply what they have learned, and an appendix covers notation. Probabilistic Machine Learning grew out of the author’s 2012 book, Machine Learning: A Probabilistic Perspective. More than just a simple update, this is a completely new book that reflects the dramatic developments in the field since 2012, most notably deep learning. In addition, the ne

New edition of a graduate-level textbook on that focuses on online convex optimization, a machine learning framework that views optimization as a process.In many practical applications, the environment is so complex that it is not feasible to lay out a comprehensive theoretical model and use classical algorithmic theory and/or mathematical optimization. Introduction to Online Convex Optimization presents a robust machine learning approach that contains elements of mathematical optimization, game theory, and learning theory: an optimization method that learns from experience as more aspects of the problem are observed. This view of optimization as a process has led to some spectacular successes in modeling and systems that have become part of our daily lives. Based on the “Theoretical Machine Learning” course taught by the author at Princeton University, the second edition of this widely used graduate level text features:Thoroughly updated material throughoutNew chapters on boosting, ad

A new paradigm for scientific discovery through computational tools now permeates every aspect of astronomical research. Computational astrophysics combines modern computational methods, novel hardware designs, advanced algorithms, original software implementations, and associated technologies to discover new phenomena and to make predictions in astronomy. The proceedings of IAU Symposium 362 summarizes ongoing developments in computational astrophysics through astronomers in diverse fields sharing their knowledge and approaches. It focuses on computational methods applied to speed up and broaden the scope of scientific studies, such as finding trends in observational data, high performance computing, automated search algorithms, and model predictability. Experts discuss a palette of challenging informational and technical developments, with the goal of coordinating their efforts and the improvement of techniques in pursuit of a wide range of astronomical studies, including fluid dynam

The second edition of a rigorous and example-driven introduction to topics in economic dynamics that emphasizes techniques for modeling dynamic systems.This text provides an introduction to the modern theory of economic dynamics, with emphasis on mathematical and computational techniques for modeling dynamic systems. Written to be both rigorous and engaging, the book shows how sound understanding of the underlying theory leads to effective algorithms for solving real-world problems. The material makes extensive use of programming examples to illustrate ideas, bringing to life the abstract concepts in the text. Key topics include algorithms and scientific computing, simulation, Markov models, and dynamic programming. Part I introduces fundamentals and part II covers more advanced material. This second edition has been thoroughly updated, drawing on recent research in the field.New for the second edition:“Programming-language agnostic” presentation using pseudocode.New chapter 1 covering

Encourage students to develop collaborative problem-solving skills with STEAM Project-Based Learning! The engaging STEAM tasks provide meaningful learning opportunities for students as they work together to study current real-world problems and strategize solutions to help create a better world. These complete units include in-depth activities that provide important context for students as they learn about each topic before they develop solutions. Each robust unit includes a hands-on STEAM task that provides students with a problem to solve using the design process of Problem and Task, Research, Brainstorm and Design, Make It and Explain It. Additional resources in each unit include: - Teacher Page with a unit overview and implementation suggestions - Real-World Connection that introduces the topic with a fictional story - What Is the Problem? page to help students brainstorm solutions to the issue - Learn About the Problem page that provides detailed information about the problem in t

Every day we interact with machine learning systems offering individualized predictions for our entertainment, social connections, purchases, or health. These involve several modalities of data, from sequences of clicks to text, images, and social interactions. This book introduces common principles and methods that underpin the design of personalized predictive models for a variety of settings and modalities. The book begins by revising 'traditional' machine learning models, focusing on adapting them to settings involving user data, then presents techniques based on advanced principles such as matrix factorization, deep learning, and generative modeling, and concludes with a detailed study of the consequences and risks of deploying personalized predictive systems. A series of case studies in domains ranging from e-commerce to health plus hands-on projects and code examples will give readers understanding and experience with large-scale real-world datasets and the ability to design mod

Artificial Intelligence-Aided Materials Design: AI-Algorithms and Case Studies on Alloys and Metallurgical Processes describes the application of artificial intelligence (AI)/machine learning (ML) concepts to develop predictive models that can be used to design alloy materials, including magnetic alloys, nickel-base superalloys, titanium-base alloys, and aluminum-base alloys. Readers new to AI/ML algorithms can use this book as a starting point and use the included MATLAB and Python implementation of AI/ML algorithms through included case studies. Experienced AI/ML researchers who want to try new algorithms can use this book and study the case studies for reference. Offers advantages and limitations of several AI concepts and their proper implementation in various data types generated through experiments and computer simulations and from industries in different file formats Helps readers develop predictive models through AI/ML algorithms by writing their own computer code or usin

The book elucidates the revolutionary and riveting research in the ultramodern domain of drone technologies, drone-enabled IoT applications, and artificial intelligence-based smart surveillance. The book explains the most recent developments in the field, challenges, and future scope of drone technologies. Beyond that, it discusses the importance of a wide range of design applications, drone/UAV development, and drone-enabled smart healthcare systems for smart cities. It describes pioneering work on mitigating cyber security threats by employing intelligent machine learning models in the designing of IoT-aided drones. The book also has a fascinating chapter on application intrusion detection by drones using recurrent neural networks. Other chapters address interdisciplinary fields like artificial intelligence, deep learning, the role of drones in healthcare in smart cities, and the importance of drone technology in agriculture.

With Iterative Learning Control Algorithms and Experimental Benchmarking the authors discuss the main methods of iterative learning control (ILC) and its interactions, as well as comparator performanc

Prepare your child for a brilliant future with Barron's Early Achiever Workbooks. Each workbook provides a hands-on learning experience tailored to grade-level skills. Barron's Early Achiever: Grade 3 Math Workbook is an ideal resource to supplement learning in the classroom, at home, for learning pods, or for homeschooling. Inside you'll find: Fun, interactive activities for comprehension and practiceHelpful tips, math vocabulary, easy-to-understand examples, and instructive illustrations to support learningMultiple, step-by-step problem-solving exercises that aid in children's critical thinking and reasoning skills

Offering a new perspective, this textbook demystifies the operation of electric machines by providing an integrated understanding of electromagnetic fields, electric circuits, numerical analysis, and computer programming. It presents fundamental concepts in a rigorous manner, emphasising underlying physical modelling assumptions and limitations, and provides detailed explanations of how to implement the finite element method to explore these concepts using Python. It includes explanations of the conversion of concepts into algorithms, and algorithms into code, and examples building in complexity, from simple linear-motion electromagnets to rotating machines. Over 100 theoretical and computational end-of-chapter exercises test understanding, with solutions for instructors and downloadable Python code available online. Ideal for graduates and senior undergraduates studying electric machines, electric machine design and control, and power electronic converters and power systems engineerin

Up-to-date edition of Computational Geomechanics, broadening the focus of the first edition to include more applications This extended second edition of the highly successful book Computational Geomec

Data assimilation is a hugely important mathematical technique, relevant in fields as diverse as geophysics, data science, and neuroscience. This modern book provides an authoritative treatment of the field as it relates to several scientific disciplines, with a particular emphasis on recent developments from machine learning and its role in the optimisation of data assimilation. Underlying theory from statistical physics, such as path integrals and Monte Carlo methods, are developed in the text as a basis for data assimilation, and the author then explores examples from current multidisciplinary research such as the modelling of shallow water systems, ocean dynamics, and neuronal dynamics in the avian brain. The theory of data assimilation and machine learning is introduced in an accessible and unified manner, and the book is suitable for undergraduate and graduate students from science and engineering without specialized experience of statistical physics.

An introduction to computational modeling for cognitive neuroscientists, covering both foundational work and recent developments. Cognitive neuroscientists need sophisticated conceptual tools to make sense of their field’s proliferation of novel theories, methods, and data. Computational modeling is such a tool, enabling researchers to turn theories into precise formulations. This book offers a mathematically gentle and theoretically unified introduction to modeling cognitive processes. Theoretical exercises of varying degrees of difficulty throughout help readers develop their modeling skills. After a general introduction to cognitive modeling and optimization, the book covers models of decision making; supervised learning algorithms, including Hebbian learning, delta rule, and backpropagation; the statistical model analysis methods of model parameter estimation and model evaluation; the three recent cognitive modeling approaches of reinforcement learning, unsupervised learning, and

What happens to risk as the economic horizon goes to zero and risk is seen as an exposure to a change in state that may occur instantaneously at any time? All activities that have been undertaken statically at a fixed finite horizon can now be reconsidered dynamically at a zero time horizon, with arrival rates at the core of the modeling. This book, aimed at practitioners and researchers in financial risk, delivers the theoretical framework and various applications of the newly established dynamic conic finance theory. The result is a nonlinear non-Gaussian valuation framework for risk management in finance. Risk-free assets disappear and low risk portfolios must pay for their risk reduction with negative expected returns. Hedges may be constructed to enhance value by exploiting risk interactions. Dynamic trading mechanisms are synthesized by machine learning algorithms. Optimal exposures are designed for option positioning simultaneously across all strikes and maturities.

This book describes how computer programs can generate narratives and how studies of computational narrative can illuminate how humans tell stories. Combining an introduction to relevant concepts related to automatic storytelling with accessible descriptions of well-known computer programs that illustrate how such concepts are employed, the book is aimed at an interdisciplinary audience and assumes little or no background in computer science. The book introduces the most relevant techniques employed over the last 60 years for the development of computer models for narrative generation, including narrative templates, problem-solving, planning, author engagement and reflection, and statistical methods such as deep neural networks, ending with an examination of the societal implications of the development of automatic narrative generator systems.

This new volume addresses the growing interest in and use of big data analytics in many industries and in many research fields around the globe; it is a comprehensive resource on the core concepts of big data analytics and the tools, techniques, and methodologies. The book gives the why and the how of big data analytics in an organized and straightforward manner, using both theoretical and practical approaches.The book's authors have organized the contents in a systematic manner, starting with an introduction and overview of big data analytics and then delving into pre-processing methods, feature selection methods and algorithms, big data streams, and big data classification. Such terms and methods as swarm intelligence, data mining, the bat algorithm and genetic algorithms, big data streams, and many more are discussed. The authors explain how deep learning and machine learning along with other methods and tools are applied in big data analytics. The last section of the book presents

An original comprehensive guide on computational nanomechanics discussing basic concepts and implications in areas such as computational physics, materials, mechanics and engineering as well as several other interdisciplinary avenues. This book makes the underlying theory accessible to readers without specialised training or extensive background in quantum physics, statistical mechanics, or theoretical chemistry. It combines a careful treatment of theoretical concepts with a detailed tutorial on computer software and computing implementation, including multiscale simulation and computational statistical theory. Multidisciplinary perspectives are provided, yielding a true insight on the applications of computational nanomechanics across diverse engineering fields. The book can serve as a practical guide with step-by-step discussion of coding, example problems and case studies. This book will be essential reading for students new to the subject, as well as an excellent reference for gra

A high school student can create deep Q-learning code to control her robot, without any understanding of the meaning of 'deep' or 'Q', or why the code sometimes fails. This book is designed to explain the science behind reinforcement learning and optimal control in a way that is accessible to students with a background in calculus and matrix algebra. A unique focus is algorithm design to obtain the fastest possible speed of convergence for learning algorithms, along with insight into why reinforcement learning sometimes fails. Advanced stochastic process theory is avoided at the start by substituting random exploration with more intuitive deterministic probing for learning. Once these ideas are understood, it is not difficult to master techniques rooted in stochastic control. These topics are covered in the second part of the book, starting with Markov chain theory and ending with a fresh look at actor-critic methods for reinforcement learning.

This text provides deep and comprehensive coverage of the mathematical background for data science, including machine learning, optimal recovery, compressed sensing, optimization, and neural networks. In the past few decades, heuristic methods adopted by big tech companies have complemented existing scientific disciplines to form the new field of Data Science. This text embarks the readers on an engaging itinerary through the theory supporting the field. Altogether, twenty-seven lecture-length chapters with exercises provide all the details necessary for a solid understanding of key topics in data science. While the book covers standard material on machine learning and optimization, it also includes distinctive presentations of topics such as reproducing kernel Hilbert spaces, spectral clustering, optimal recovery, compressed sensing, group testing, and applications of semidefinite programming. Students and data scientists with less mathematical background will appreciate the appendice

A proposal that we think about digital technologies such as machine learning not in terms of artificial intelligence but as artificial communication.Algorithms that work with deep learning and big data are getting so much better at doing so many things that it makes us uncomfortable. How can a device know what our favorite songs are, or what we should write in an email? Have machines become too smart? In Artificial Communication, Elena Esposito argues that drawing this sort of analogy between algorithms and human intelligence is misleading. If machines contribute to social intelligence, it will not be because they have learned how to think like us but because we have learned how to communicate with them. Esposito proposes that we think of “smart” machines not in terms of artificial intelligence but in terms of artificial communication.To do this, we need a concept of communication that can take into account the possibility that a communication partner may be not a human being but an al

Renowned for its interactive focus on conceptual understanding, Halliday and Resnick's Principles of Physics, 12th edition, is an industry-leading resource in physics teaching with expansive, insightful, and accessible treatments of a wide variety of subjects. Focusing on several contemporary areas of research and a wide array of tools that support students' active learning, this book guides students through the process of learning how to effectively read scientific material, identify fundamental concepts, reason through scientific questions, and solve quantitative problems. This International Adaptation of the twelfth edition is built to be a learning center with practice opportunities, simulations, and videos.Numerous practice and assessment questions are available to ensure that students understand the problem-solving processes behind key concepts and understand their mistakes while working through problems.

During the past half-century, exponential families have attained a position at the center of parametric statistical inference. Theoretical advances have been matched, and more than matched, in the world of applications, where logistic regression by itself has become the go-to methodology in medical statistics, computer-based prediction algorithms, and the social sciences. This book is based on a one-semester graduate course for first year Ph.D. and advanced master's students. After presenting the basic structure of univariate and multivariate exponential families, their application to generalized linear models including logistic and Poisson regression is described in detail, emphasizing geometrical ideas, computational practice, and the analogy with ordinary linear regression. Connections are made with a variety of current statistical methodologies: missing data, survival analysis and proportional hazards, false discovery rates, bootstrapping, and empirical Bayes analysis. The book con

During the past half-century, exponential families have attained a position at the center of parametric statistical inference. Theoretical advances have been matched, and more than matched, in the world of applications, where logistic regression by itself has become the go-to methodology in medical statistics, computer-based prediction algorithms, and the social sciences. This book is based on a one-semester graduate course for first year Ph.D. and advanced master's students. After presenting the basic structure of univariate and multivariate exponential families, their application to generalized linear models including logistic and Poisson regression is described in detail, emphasizing geometrical ideas, computational practice, and the analogy with ordinary linear regression. Connections are made with a variety of current statistical methodologies: missing data, survival analysis and proportional hazards, false discovery rates, bootstrapping, and empirical Bayes analysis. The book con

Hana has a humongous collection of hijabs and accessories – and her hijab is always styled superbly. But when her overflowing collection gets a little out of hand, Hana knows something needs to be done . . . and comes up with a clever plan for sharing her talents and possessions with her community! Young makers will chuckle along with this humorous tale of creative problem-solving and learning to help others.

Hana has a humongous collection of hijabs and accessories – and her hijab is always styled superbly. But when her overflowing collection gets a little out of hand, Hana knows something needs to be done . . . and comes up with a clever plan for sharing her talents and possessions with her community! Young makers will chuckle along with this humorous tale of creative problem-solving and learning to help others.

How Hansel and Gretel, Sherlock Holmes, the movie Groundhog Day, Harry Potter, and other familiar stories illustrate the concepts of computing.Picture a computer scientist, staring at a screen and clicking away frantically on a keyboard, hacking into a system, or perhaps developing an app. Now delete that picture. In Once Upon an Algorithm, Martin Erwig explains computation as something that takes place beyond electronic computers, and computer science as the study of systematic problem solving. Erwig points out that many daily activities involve problem solving. Getting up in the morning, for example: You get up, take a shower, get dressed, eat breakfast. This simple daily routine solves a recurring problem through a series of well-defined steps. In computer science, such a routine is called an algorithm. Erwig illustrates a series of concepts in computing with examples from daily life and familiar stories. Hansel and Gretel, for example, execute an algorithm to get home from the fore

Techniques for applying mathematical concepts in the real world: six rarely taught but crucial tools for analysis, research, and problem-solving.Many young graduates leave school with a solid knowledge of mathematical concepts but struggle to apply these concepts in practice. Real scientific and engineering problems are different from those found in textbooks: they are messier, take longer to solve, and standard solution recipes might not apply. This book fills the gap between what is taught in the typical college curriculum and what a practicing engineer or scientist needs to know. It presents six powerful tools for analysis, research, and problem-solving in the real world: dimensional analysis, limiting cases, symmetry, scaling, making order of magnitude estimates, and the method of successive approximations. The book does not focus on formulaic manipulations of equations, but emphasizes analysis and explores connections between the equations and the application. Each chapter introdu

Computational thinking is increasingly gaining importance in modern biology, due to the unprecedented scale at which data is nowadays produced. Bridging the cultural gap between the biological and computational sciences, this book serves as an accessible introduction to computational concepts for students in the life sciences. It focuses on teaching algorithmic and logical thinking, rather than just the use of existing bioinformatics tools or programming. Topics are presented from a biological point of view, to demonstrate how computational approaches can be used to solve problems in biology such as biological image processing, regulatory networks, and sequence analysis. The book contains a range of pedagogical features to aid understanding, including real-world examples, in-text exercises, end-of-chapter problems, colour-coded Python code, and 'code explained' boxes. User-friendly throughout, Computational Thinking for Life Scientists promotes the thinking skills and self-efficacy req

Computational thinking is increasingly gaining importance in modern biology, due to the unprecedented scale at which data is nowadays produced. Bridging the cultural gap between the biological and computational sciences, this book serves as an accessible introduction to computational concepts for students in the life sciences. It focuses on teaching algorithmic and logical thinking, rather than just the use of existing bioinformatics tools or programming. Topics are presented from a biological point of view, to demonstrate how computational approaches can be used to solve problems in biology such as biological image processing, regulatory networks, and sequence analysis. The book contains a range of pedagogical features to aid understanding, including real-world examples, in-text exercises, end-of-chapter problems, colour-coded Python code, and 'code explained' boxes. User-friendly throughout, Computational Thinking for Life Scientists promotes the thinking skills and self-efficacy req

Introduce your little one to the wonders of nature with 100+ outdoor learning activities!Give your child all the benefits of nature with this activity book designed for children ages 2-5. Whether you’re planning an afternoon in a local park, a day in the backyard, or a morning hike in a nature preserve, you and your child will find more than 100 ideas in these pages for observing, exploring, creating, and playing in nature.Nature Activity Book for Little Ones features: 100+ outdoor activities for kids ages 2-5, geared toward their interests and developmental milestones—with little or no preparation requiredBonus activities for additional learning, including numbers, letters, shapes, and colorsSchool prep: the activities teach problem-solving, communication, and responsibility, important skills for school succesLess screen time and more nature time together to fuel your child’s curiosity and creativity and help them build an early connection with natureBest of all, this entertaining boo