Mathematics

Optimization of Advanced Manufacturing Processes

Sandip Kunar, Prasenjit Chatterjee, M. Sreenivas Reddy

Optimization for advanced manufacturing processes in fabrication is becoming increasingly important around the world across a range of industries because of its improved productivity, capabilities, efficacy, and sustainability characteristics. This new book explains how to optimize various industrial systems and processes utilizing new significant statistical and evolutionary methodologies. Statistical, multi-criteria decision-making, and evolutionary strategies for single- and multi-objective optimization are covered here, with relevant theoretical details, salient characteristics, implementation processes, effectiveness studies, and results in manufacturing. The chapters present a variety of advanced manufacturing processes and optimization techniques. Processes are described with basic explanations, characteristics, and applications in various technological and biomedical domains. The chapters address the processes prediction of mechanical properties, design and development of tools, impact of power supply, increasing machining precision and efficiency, genetic algorithm optimization, additive manufacturing, and much more. Providing a comprehensive study of advanced manufacturing processes, this volume is a valuable reference for engineers and R&D researchers involved in optimization for advanced manufacturing processes as well as for academics and postgraduate-level students in mechanical engineering, manufacturing engineering, and machining processes.

Math Hacks for Scratch: Unlock the Power of Math with Scratch Programming

Michael Mays

Push Scratch programming to the limits as you explore primes, Fibonacci numbers, Pascal’s triangle, and other mathematical curiosities through hands-on coding projects. If you’re a student looking for project ideas to practice your math and coding skills, or a Scratch enthusiast just looking for something different, this is the book for you! Scratch is mainly used to learn programming and design computer games, but it has plenty of other useful applications—like solving math problems. This book reveals the block-based coding system’s mathematical superpowers, guiding you through over 20 hands-on projects that investigate a variety of interesting numerical puzzles. You’ll quickly find that core math concepts, like number representations, divisibility, and cryptography, are fun to code using Scratch. In addition to learning how to hack Scratch to get it to work with numbers in unusual ways, you’ll discover efficient algorithms for making time-consuming computations a snap. Along the way, you'll see how the right mathematical or programming trick can simplify a seemingly complex task, as you think through bonus coding challenges that further promote independent experimentation while improving both your math and programming skills.

Robust Control Algorithms for Flexible Manipulators

Kshetrimayum Lochan, Binoy Krishna Roy, Bidyadhar Subudhi, Santhakumar Mohan

Various modelling and control of two-link flexible manipulators are presented in this book. The lumped parameter modelling method and the assumed modes method modelling are comprehensively reviewed. The book also reviews the trajectory tracking problem and tip trajectory tracking problem along with the suppression of tip deflection of the links. An exponential time varying signal and a chaotic signal are considered as the desired trajectories. The identical/ non-identical slave manipulator is synchronised with the controlled master manipulator so that the slave manipulator indirectly follows the desired manipulator.

Mathematical Methods of Physics

Igor V. Kolokolov, Evgeny A. Kuznetsov, Alexander I. Milstein, Evgeny V. Podivilov, Alexander I. Chernykh, David A. Shapiro, Elena G. Shapiro

This book, translated from Russian, is a comprehensive guide to mathematical methods in physics, offering theoretical insights and problem-solving techniques. Authored by experienced physicists, it is suitable for self-study and has been effectively used in fields such as theoretical physics, plasma physics, and hydrodynamics. The English edition aims to equip readers with the skills to master modern mathematical methods applicable to different physical problems.

Statistical Prediction and Machine Learning

John Tuhao Chen, Clement Lee, Lincy Y. Chen

Written by an experienced statistics educator and two data scientists, this book unifies conventional statistical thinking and contemporary machine learning framework into a single overarching umbrella over data science. The book is designed to bridge the knowledge gap between conventional statistics and machine learning. It provides an accessible approach for readers with a basic statistics background to develop a mastery of machine learning. The book starts with elucidating examples in Chapter 1 and fundamentals on refined optimization in Chapter 2, which are followed by common supervised learning methods such as regressions, classification, support vector machines, tree algorithms, and range regressions. After a discussion on unsupervised learning methods, it includes a chapter on unsupervised learning and a chapter on statistical learning with data sequentially or simultaneously from multiple resources. One of the distinct features of this book is the comprehensive coverage of the topics in statistical learning and medical applications. It summarizes the authors’ teaching, research, and consulting experience in which they use data analytics. The illustrating examples and accompanying materials heavily emphasize understanding on data analysis, producing accurate interpretations, and discovering hidden assumptions associated with various methods. Key Unifies conventional model-based framework and contemporary data-driven methods into a single overarching umbrella over data science. Includes real-life medical applications in hypertension, stroke, diabetes, thrombolysis, aspirin efficacy. Integrates statistical theory with machine learning algorithms. Includes potential methodological developments in data science.

Problems in Quantum Mechanics and Field Theory with Mathematical Modelling

Aleksander V. Chichurin, Elena M. Ovsiyuk, Viktor M. Red’kov

In Problems in Quantum Mechanics and Field Theory with Mathematical Modelling, a number of exactly solvable problems in electrodynamics and in quantum-mechanics of particles with different spins are presented. The main topics covered the Cox scalar particle with intrinsic structure in presence of the magnetic field in the spaces of constant curvature, Euclid, Riemann, and Lobachevsky; Cox particle in the Coulomb field; tunneling effect through Schwarzschild barrier for a spin 1/2 particle; electromagnetic field in Schwarzschild space-time, the Majorana - Oppenheimer approach in electrodynamics; scalar particle with polarizability in the Coulomb field; Dirac particle in the Coulomb field on the background of hyperbolic Lobachevsky and spherical Riemann models; particle with spin 1 in the Coulomb field; geometrical modeling of the media in Maxwell electrodynamics; P-asymmetric equation for a spin 1/2 particle; fermion with two mass parameters in the Coulomb field; helicity operator for a spin 2 particle in presence of the magnetic field. The book will be of interest to researchers, and is accessible enough to serve as a self-study resources for courses at undergraduate and graduate levels.

Quantitative Literacy Through Games and Gambling

Mark Hunacek

This book was developed to address a need. Quantitative Literacy courses have been established in the mathematics curriculum for decades now. The students in these courses typically dislike and fear mathematics, and the result is often a class populated by many students that are unmotivated and uninterested in the material. This book is a text for such a course; however, it is focused on a single idea that most students seem to already have some intrinsic interest in and is written at an accessible level. It covers the basic ideas of discrete probability and shows how these ideas can be applied to familiar games (roulette, poker, blackjack, etc.) The gambling material is interweaved through the book, introduced as soon as the necessary mathematics has been developed. Throughout, mathematical formalism and symbolism have been avoided, and numerous examples are provided. The book starts with a simple definition of probability, goes through some basic concepts like combining events and expected value, and then discusses some elementary mathematical aspects of various games. Roulette is introduced very early on, as is the game of craps, which requires some knowledge of conditional probability. Other games like poker, blackjack and lotteries, whose study requires some rudimentary combinatorics come shortly thereafter. The book ends with a brief introduction to zero-sum games, with some attention paid to the use of these ideas in studying bluffing. In addition to discussion of these traditional games, the author motivates probability by talking about a few applications in legal proceedings which illustrate how mathematics has been misused in the courtroom. There is also a discussion of the Monty Hall problem, a non-intuitive result in probability that has an interesting and colorful history. Hopefully, students studying from this text will find mathematics is not as horrible as he or she has always thought and offers some interesting applications in the real world. This should perhaps be the goal of any quantitative literacy course.

The House in the Pines

Ana Reyes

Armed with only hazy memories, a woman who long ago witnessed her friend's sudden, mysterious death, and has since spent her life trying to forget, sets out to track down answers. What she uncovers, deep in the woods, is hardly to be believed.... Maya was a high school senior when her best friend, Aubrey, mysteriously dropped dead in front of the enigmatic man named Frank whom they'd been spending time with all summer. Seven years later, Maya lives in Boston with a loving boyfriend and is kicking the secret addiction that has allowed her to cope with what happened years ago, the gaps in her memories, and the lost time that she can't account for. But her past comes rushing back when she comes across a recent YouTube video in which a young woman suddenly keels over and dies in a diner while sitting across from none other than Frank. Plunged into the trauma that has defined her life, Maya heads to her Berkshires hometown to relive that fateful summer--the influence Frank once had on her and the obsessive jealousy that nearly destroyed her friendship with Aubrey. At her mother's house, she excavates fragments of her past and notices hidden messages in her deceased Guatemalan father's book that didn't stand out to her earlier. To save herself, she must understand a story written before she was born, but time keeps running out, and soon, all roads are leading back to Frank's cabin.... Utterly unique and captivating, The House in the Pines keeps you guessing about whether we can ever fully confront the past and return home.

How to Solve It: A New Aspect of Mathematical Method

G. Pólya, John H. Conway

A perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out―from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft―indeed, brilliant―instructions on stripping away irrelevancies and going straight to the heart of the problem.

God Created The Integers: The Mathematical Breakthroughs that Changed History

Stephen Hawking

In this collection of landmark mathematical works, editor Stephen Hawking has assembled the greatest feats humans have ever accomplished using just numbers and their brains.

Fermat's Last Theorem

Simon Singh

The extraordinary story of the solving of a puzzle that has confounded mathematicians since the 17th century. The solution of Fermat’s Last Theorem is the most important mathematical development of the 20th century. In 1963 a schoolboy browsing in his local library stumbled across the world’s greatest mathematical problem: Fermat’s Last Theorem, a puzzle that every child can understand but which has baffled mathematicians for over 300 years. Aged just ten, Andrew Wiles dreamed that he would crack it. Wiles’s lifelong obsession with a seemingly simple challenge set by a long-dead Frenchman is an emotional tale of sacrifice and extraordinary determination. In the end, Wiles was forced to work in secrecy and isolation for seven years, harnessing all the power of modern maths to achieve his childhood dream. Many before him had tried and failed, including a 18-century philanderer who was killed in a duel. An 18-century Frenchwoman made a major breakthrough in solving the riddle, but she had to attend maths lectures at the Ecole Polytechnique disguised as a man since women were forbidden entry to the school. A remarkable story of human endeavour and intellectual brilliance over three centuries, Fermat ‘s Last Theorem will fascinate both specialist and general readers.

Solve It Science and Mathematics

George Pólya

A perennial bestseller by eminent mathematician G. Polya, "How to Solve It" will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem. In this best-selling classic, George Polya revealed how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft instructions on stripping away irrelevancies and going straight to the heart of a problem. "How to Solve It" popularized heuristics, the art and science of discovery and invention. It has been in print continuously since 1945 and has been translated into twenty-three different languages. Polya was one of the most influential mathematicians of the twentieth century. He made important contributions to a great variety of mathematical research: from complex analysis to mathematical physics, number theory, probability, geometry, astronomy, and combinatorics. He was also an extraordinary teacher--he taught until he was ninety--and maintained a strong interest in pedagogical matters throughout his long career. In addition to "How to Solve It," he published a two-volume work on the topic of problem solving, "Mathematics of Plausible Reasoning," also with Princeton. Polya is one of the most frequently quoted mathematicians, and the following statements from "How to Solve It" make clear why: "My method to overcome a difficulty is to go around it." "Geometry is the science of correct reasoning on incorrect figures." "In order to solve this differential equation you look at it till a solution occurs to you."

The Golden Ratio: The Story of Phi, the World's Most Astonishing Number

Mario Livio

Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that phi , or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper , and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market! The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist.

What Is Mathematics? An Elementary Approach to Ideas and Methods

Richard Courant, Ian Stewart, Herbert Robbins

For more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant's and Herbert Robbins's classic work seeks to address this problem. Its goal is to put the meaning back into mathematics. Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics? Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced discussions, readers can easily pick and choose areas of particular interest without impairing their understanding of subsequent parts. Brought up to date with a new chapter by Ian Stewart, What is Mathematics? Second Edition offers new insights into recent mathematical developments and describes proofs of the Four-Color Theorem and Fermat's Last Theorem, problems that were still open when Courant and Robbins wrote this masterpiece, but ones that have since been solved. Formal mathematics is like spelling and grammar - a matter of the correct application of local rules. Meaningful mathematics is like journalism - it tells an interesting story. But unlike some journalism, the story has to be true. The best mathematics is like literature - it brings a story to life before your eyes and involves you in it, intellectually and emotionally. What is Mathematics is like a fine piece of literature - it opens a window onto the world of mathematics for anyone interested to view.

Principles of Mathematical Analysis

Walter Rudin

The third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first-year graduate students. The text begins with a discussion of the real number system as a complete ordered field. (Dedekind's construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included. This text is part of the Walter Rudin Student Series in Advanced Mathematics.

Essential Mathematics for Economics

Alexis Akira Toda

Essential Mathematics for Economics covers mathematical topics that are essential for economic analysis in a concise but rigorous fashion. The book covers selected topics such as linear algebra, real analysis, convex analysis, constrained optimization, dynamic programming, and numerical analysis in a single volume. The book is entirely self-contained, and almost all propositions are proved. Features Replete with exercises and illuminating examples Suitable as a primary text for an advanced undergraduate or postgraduate course on mathematics for economics Basic linear algebra and real analysis are the only prerequisites. Supplementary materials such as Matlab codes, teaching slides etc. are posted on the book website

Mathematical Modeling and Simulation: Introduction for Scientists and Engineers

Kai Velten, Katrin Kahlen, Dominik M. Schmidt

This concise and clear introduction to the topic requires only basic knowledge of calculus and linear algebra—all other concepts and ideas are developed in the course of the book. Lucidly written so as to appeal to undergraduates and practitioners alike, it enables readers to set up simple mathematical models on their own and to interpret their results and those of others critically. To achieve this, many examples have been chosen from various fields, such as biology, ecology, economics, medicine, agricultural, chemical, electrical, mechanical and process engineering, which are subsequently discussed in detail. Based on the author's modeling and simulation experience in science and engineering and as a consultant, the book answers such basic questions What is a mathematical model? What types of models do exist? Which model is appropriate for a particular problem? What are simulation, parameter estimation, and validation? The book relies exclusively upon open-source software which is available to everybody free of charge. The entire book software—including 3D CFD and structural mechanics simulation software—can be used based on a free CAELinux-Live-DVD that is available in the Internet (works on most machines and operating systems).

System Dynamics: Modeling, Simulation, and Response

Osama Gad

System Dynamics covers linearity-based modeling techniques before delving into nonlinear systems. It compares the Bond Graph technique against traditional techniques (Newton's law, Kirchhoff's law, the law of the conservation of energy, and the heat transfer law). Presenting transient response analyses of first- and second-order systems subjected to various inputs, the book provides a thorough discussion of computational analyses of transient responses using MATLAB®/Simulink and 20-sim software. It introduces the Lagrangian method and its application in handling mechanical and electrical systems. The book reviews the classical method for solving differential equations and includes Laplace Transforms. The book is intended for upper-level undergraduate mechanical and aerospace engineering students taking System Dynamics courses. Instructors will be able to utilize a Solutions Manual and Figure Slides for their course.

Einstein's Entanglement: Bell Inequalities, Relativity, and the Qubit

Prof W. M. Stuckey, Prof Michael Silberstein, Dr Timothy McDevitt

Non-Equilibrium Statistical Mechanics

James H. Luscombe

Statistical mechanics provides a framework for relating the properties of macroscopic systems (large collections of atoms, such as in a solid) to the microscopic properties of its parts. However, what happens when macroscopic systems are not in thermal equilibrium, where time is not only a relevant variable, but also essential? That is the province of nonequilibrium statistical mechanics – there are many ways for systems to be out of equilibrium! The subject is governed by fewer general principles than equilibrium statistical mechanics and consists of a number of different approaches for describing nonequilibrium systems. Financial markets are analyzed using methods of nonequilibrium statistical physics, such as the Fokker-Planck equation. Any system of sufficient complexity can be analyzed using the methods of nonequilibrium statistical mechanics. The Boltzmann equation is used frequently in the analysis of systems out of thermal equilibrium, from electron transport in semiconductors to modeling the early Universe following the Big Bang. This book provides an accessible yet very thorough introduction to nonequilibrium statistical mechanics, building on the author's years of teaching experience. Covering a broad range of advanced, extension topics, it can be used to support advanced courses on statistical mechanics, or as a supplementary text for core courses in this field. Key · Features a clear, accessible writing style which enables the author to take a sophisticated approach to the subject, but in a way that is suitable for advanced undergraduate students and above. · Presents foundations of probability theory and stochastic processes and treats principles and basic methods of kinetic theory and time correlation functions. · Accompanied by separate volumes on thermodynamics and equilibrium statistical mechanics, which can be used in conjunction with this book James H. Luscombe received the PhD in Physics from the University of Chicago in 1983. After post-doctoral positions at the University of Toronto and Iowa State University, he joined the Research Laboratory of Texas Instruments, where he worked on the development of nanoelectronic devices. In 1994, he joined the Naval Postgraduate School in Monterey, CA, where he is Professor of Physics. He was Chair of the Department of Physics from 2003 – 2009. He teaches a wide variety of topics, including general relativity, statistical mechanics, mathematical methods, and quantum computation. He has published more than 60 research articles, and has given more than 100 conference presentations; he holds 2 patents.

Applied Mathematics

Joao Luis De Miranda

Applied A Computational Approach aims to provide a basic and self-contained introduction to Applied Mathematics within a computational environment. The book is aimed at practitioners and researchers interested in modeling real-world applications and verifying the results — guiding readers from the mathematical principles involved through to the completion of the practical, computational task. Features Provides a step-by-step guide to the basics of Applied Mathematics with complementary computational tools Suitable for applied researchers from a wide range of STEM fields Minimal pre-requisites beyond a strong grasp of calculus.

Statistical Methods Using SPSS

Gabriel Otieno Okello

Statistical Methods Using SPSS provides a practical approach for better understanding of the advanced statistical concepts that are applied in business, economics, epidemiology, public health, agriculture, and other areas of data analytics. Advanced statistical methods or advanced statistical techniques for analysing data arise because of the complex nature of data sets that cannot be analysed using the basic or the usual and common analytical techniques. This book describes more advanced statistical methods, offering a modern approach by introducing the advanced statistical concepts, before showing the application of these concepts in real-world examples with the application of SPSS statistical software. This book is useful in explaining advanced statistical analysis techniques to postgraduate students, doctoral students, and researchers. It is also a useful reference for students and researchers who require further guidance in advanced data analysis, and is designed for those with basic statistical knowledge. Exercises and solution manuals are also included to aid in the understanding of the statistical analysis techniques explained in the book. Key includes many topics advanced statistical techniques; provides manual computations of statistical concepts; includes a step-by-step guide for the different statistical analysis techniques being done using SPSS; has a variety of data set examples to help explain the different statistical concepts; and includes practical applications of the statistical concepts in SPSS.

From Data to Insights

Gianmarco Alberti

This book offers a clear and accessible guide to cross-tabulation analysis, transforming a complex subject into an accessible topic. It diverges from traditional statistical texts, adopting a conversational tone that addresses common questions and concerns. The author demystifies intricate concepts, with clear explanations and relatable analogies that make the material approachable for readers with varying levels of mathematical expertise. Unique in its approach, the book avoids overwhelming readers with complex formulas and instead focuses on the principles underlying cross-tabulation analysis. This method ensures that the content is applicable regardless of specific statistical software used, making it a versatile resource. Targeted at a diverse audience, the book covers the spectrum from foundational elements to comparatively more advanced topics in cross-tabulation analysis. It includes a comprehensive glossary and an appendix of detailed examples, providing practical insight and aiding understanding of key concepts. This book is an invaluable resource for students, researchers, and educators alike, offering a fresh perspective on cross-tabulation analysis that emphasises clarity and practical application. Key Employs a conversational style, making complex statistical concepts in cross-tabulation analysis accessible and engaging for all readers. Combines minimal use of formulas with practical examples, ensuring easy comprehension and application, even for those with minimal mathematical background. Features a consistent running example for continuity, complemented by diverse real-world scenarios to solidify understanding of key concepts. Independently valuable without reliance on specific statistical software, emphasising fundamental principles for adaptability across various platforms. Progressively guides readers from foundational basics to comparatively more advanced methods, supplemented by a comprehensive glossary and detailed appendix for an enriched learning.

Statistics for Data Science and Analytics

Peter C. Bruce, Peter Gedeck, Janet Dobbins

Introductory statistics textbook with a focus on data science topics such as prediction, correlation, and data exploration Statistics for Data Science and Analytics is a comprehensive guide to statistical analysis using Python, presenting important topics useful for data science such as prediction, correlation, and data exploration. The authors provide an introduction to statistical science and big data, as well as an overview of Python data structures and operations. A range of statistical techniques are presented with their implementation in Python, including hypothesis testing, probability, exploratory data analysis, categorical variables, surveys and sampling, A/B testing, and correlation. The text introduces binary classification, a foundational element of machine learning, validation of statistical models by applying them to holdout data, and probability and inference via the easy-to-understand method of resampling and the bootstrap instead of using a myriad of “kitchen sink” formulas. Regression is taught both as a tool for explanation and for prediction. This book is informed by the authors’ experience designing and teaching both introductory statistics and machine learning at Statistics.com. Each chapter includes practical examples, explanations of the underlying concepts, and Python code snippets to help readers apply the techniques themselves. Statistics for Data Science and Analytics includes information on sample topics such Int, float, and string data types, numerical operations, manipulating strings, converting data types, and advanced data structures like lists, dictionaries, and setsExperiment design via randomizing, blinding, and before-after pairing, as well as proportions and percents when handling binary dataSpecialized Python packages like numpy, scipy, pandas, scikit-learn and statsmodels—the workhorses of data science—and how to get the most value from themStatistical versus practical significance, random number generators, functions for code reuse, and binomial and normal probability distributions Written by and for data science instructors, Statistics for Data Science and Analytics is an excellent learning resource for data science instructors prescribing a required intro stats course for their programs, as well as other students and professionals seeking to transition to the data science field.

The World through the Lens of Mathematics

Natali Hritonenko, Yuri Yatsenko

Following up on their previous book, U.S.A. Through the Lens of Mathematics, the authors offer interesting information about all countries in the world, their history,geography, language, culture, and resources presented in the form of mathematical problems. The problems are combined in sections based on related mathematical concepts, including systems of linear algebraic equations, extremum of afunction,sequencies,logicalproblems,andothers. This fascinating book exposes students to a novel educational strategy that aims to overcome fear of mathematics, reduce mathematical anxiety, and show the applicability of mathematics to everyday life and events. The book offers interesting information about all countries in the world, their history, geography, language, culture, and resources are presented in the form of mathematical problems. The problems are combined in sections based on related mathematical concepts, including systems of linear algebraic equations, extremum of a function, sequencies, logical problems, and others. Each problem starts with a brief narrative to introduce its applied content with intriguing facts. The answer key, followed by very detailed solutions accompanying each problem. This unique book aims to shatter the barrier between students and this mathematics by encouraging students to look at mathematics from a different perspective, build a bridge between their surroundings and mathematics and, at the same time, enriches them with new knowledge of culture, history, customs, and geography.

Differential Geometry: Frenet Equations and Differentiable Maps

Muhittin E. Aydin

Maths in Chemistry: Numerical Methods for Physical and Analytical Chemistry

Prerna Bansal

Mathematical Biology

Christina Alvey, Daniel Alvey

This text serves as an exploration of the beautiful topic of mathematical biology through the lens of discrete and differential equations. Intended for students who have completed differential and integral calculus, Mathematical Discrete and Differential Equations allows students to explore topics such as bifurcation diagrams, nullclines, discrete dynamics, and SIR models for disease spread, which are often reserved for more advanced undergraduate or graduate courses. These exciting topics are sprinkled throughout the book alongside the more typical first- and second-order linear differential equations and systems of linear differential equations. This class-tested text is written in a conversational, welcoming voice, which should help invite students along as they discover the magic of mathematical biology and both discrete and differential equations. A focus is placed on examples with solutions written out step by step, including computational steps, with the goal of being as easy as possible for students to independently follow along. Rich in applications, this book can be used for a semester-long course in either differential equations or mathematical biology. Alternatively, it can serve as a companion text for a two-semester sequence beginning with discrete-time systems, extending through a wide array of topics in differential equations, and culminating in systems, SIR models, and other applications.

Research Topics in Analysis, Volume II: Applications

Shouchuan Hu, Nikolaos S. Papageorgiou

This book, the second of two volumes, presents significant applications for understanding modern analysis. It empowers young researchers with key techniques and applications to explore various subfields of this broad subject and introduces relevant frameworks for immediate deployment. The applications list begins with Degree Theory, a useful tool for studying nonlinear equations. Chapter 2 deals with Fixed Point Theory, and Chapter 3 introduces Critical Point Theory. Chapter 4 presents the main spectral properties of linear, nonlinear, anisotropic, and double-phase differential operators. Chapter 5 covers semilinear and nonlinear elliptic equations with different boundary conditions, while Chapter 6 addresses dynamic systems monitored by ordinary and partial differential equations. Chapter 7 delves into optimal control problems, and Chapter 8 discusses some economic models, providing a brief presentation of Game Theory and Nash equilibrium. By offering a clear and comprehensive overview of modern analysis tools and applications, this work can greatly benefit mature graduate students seeking research topics, as well as experienced researchers interested in this vast and rich field of mathematics.

Four Ways of Thinking: A Journey into Human Complexity

David Sumpter

Acclaimed mathematician David Sumpter shares practical and insightful solutions for navigating the chaos and complexity of our lives What is the best way to think about the world? How often do we consider how our own thinking might impact the way we approach our daily decisions? Could it help or hinder our relationships, our careers, or even our health? As acclaimed mathematician David Sumpter shows, thinking about thinking is something we rarely do, yet it is something science questions all the time. He has spent decades studying what we could all learn from the mindsets of scientists, and Four Ways of Thinking is the result. Here he reveals the four easily applied approaches to our statistical, interactive, chaotic, and complex. Combining engaging personal experience with practical advice and inspiring tales of groundbreaking scientific pioneers (with a tiny bit of number crunching along the way), Sumpter shows how these tried and tested methods can help us with every conundrum, from how to bicker less with our partners to pitching to a tough crowd—and in doing so, change our lives.