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Introduction to Number Theory (Textbooks in Mathematics)
by Mark HunacekIntroduction to Number Theory covers the essential content of an introductory number theory course including divisibility and prime factorization, congruences, and quadratic reciprocity. The instructor may also choose from a collection of additional topics. Aligning with the trend toward smaller, essential texts in mathematics, the author strives for clarity of exposition. Proof techniques and proofs are presented slowly and clearly. The book employs a versatile approach to the use of algebraic ideas. Instructors who wish to put this material into a broader context may do so, though the author introduces these concepts in a non-essential way. A final chapter discusses algebraic systems (like the Gaussian integers) presuming no previous exposure to abstract algebra. Studying general systems helps students to realize unique factorization into primes is a more subtle idea than may at first appear; students will find this chapter interesting, fun and quite accessible. Applications of number theory include several sections on cryptography and other applications to further interest instructors and students alike.
Introduction to Number Theory
by Anthony Vazzana David GarthIntroduction to Number Theory is a classroom-tested, student-friendly text that covers a diverse array of number theory topics, from the ancient Euclidean algorithm for finding the greatest common divisor of two integers to recent developments such as cryptography, the theory of elliptic curves, and the negative solution of Hilbert's tenth problem.
An Introduction to Number Theory with Cryptography (Textbooks in Mathematics)
by James Kraft Lawrence Washington<p>Building on the success of the first edition, An Introduction to Number Theory with Cryptography, Second Edition, increases coverage of the popular and important topic of cryptography, integrating it with traditional topics in number theory. <p>The authors have written the text in an engaging style to reflect number theory's increasing popularity. The book is designed to be used by sophomore, junior, and senior undergraduates, but it is also accessible to advanced high school students and is appropriate for independent study. It includes a few more advanced topics for students who wish to explore beyond the traditional curriculum.</p>
Introduction to Numerical Analysis: Second Edition
by F. B. HildebrandThe ultimate aim of the field of numerical analysis is to provide convenient methods for obtaining useful solutions to mathematical problems and for extracting useful information from available solutions which are not expressed in tractable forms. This well-known, highly respected volume provides an introduction to the fundamental processes of numerical analysis, including substantial grounding in the basic operations of computation, approximation, interpolation, numerical differentiation and integration, and the numerical solution of equations, as well as in applications to such processes as the smoothing of data, the numerical summation of series, and the numerical solution of ordinary differential equations.Chapter headings include:l. Introduction2. Interpolation with Divided Differences3. Lagrangian Methods4. Finite-Difference Interpolation5. Operations with Finite Differences6. Numerical Solution of Differential Equations7. Least-Squares Polynomial ApproximationIn this revised and updated second edition, Professor Hildebrand (Emeritus, Mathematics, MIT) made a special effort to include more recent significant developments in the field, increasing the focus on concepts and procedures associated with computers. This new material includes discussions of machine errors and recursive calculation, increased emphasis on the midpoint rule and the consideration of Romberg integration and the classical Filon integration; a modified treatment of prediction-correction methods and the addition of Hamming's method, and numerous other important topics.In addition, reference lists have been expanded and updated, and more than 150 new problems have been added. Widely considered the classic book in the field, Hildebrand's Introduction to Numerical Analysis is aimed at advanced undergraduate and graduate students, or the general reader in search of a strong, clear introduction to the theory and analysis of numbers.
An Introduction to Numerical Analysis
by Endre Süli David F. MayersNumerical analysis provides the theoretical foundation for the numerical algorithms we rely on to solve a multitude of computational problems in science. Based on a successful course at Oxford University, this book covers a wide range of such problems ranging from the approximation of functions and integrals to the approximate solution of algebraic, transcendental, differential and integral equations. Throughout the book, particular attention is paid to the essential qualities of a numerical algorithm - stability, accuracy, reliability and efficiency. The authors go further than simply providing recipes for solving computational problems. They carefully analyse the reasons why methods might fail to give accurate answers, or why one method might return an answer in seconds while another would take billions of years. This book is ideal as a text for students in the second year of a university mathematics course. It combines practicality regarding applications with consistently high standards of rigour.
Introduction to Numerical Analysis and Scientific Computing
by Nabil Nassif Dolly Khuwayri FayyadDesigned for a one-semester course, Introduction to Numerical Analysis and Scientific Computing presents fundamental concepts of numerical mathematics and explains how to implement and program numerical methods. The classroom-tested text helps students understand floating point number representations, particularly those pertaining to IEEE simple an
Introduction to Numerical and Analytical Methods with MATLAB for Engineers and Scientists
by William BoberThis textbook teaches students how to write computer programs on the MATLAB platform and to use many of MATLAB's built-in functions to solve engineering-type problems. To students, MATLAB's built-in functions are black boxes. By combining a textbook on MATLAB with basic numerical and analytical analysis, the mystery of what the black boxes contain is somewhat alleviated. Within each chapter there are exercises related to the topics just covered. The text contains many examples from mechanical, civil, aeronautical, and electrical engineering.
An Introduction to Numerical Methods: A MATLAB Approach (Fourth Edition)
by Abdelwahab Kharab Ronald GuentherPrevious editions of this popular textbook offered an accessible and practical introduction to numerical analysis. An Introduction to Numerical Methods: A MATLAB Approach, Fourth Edition continues to present a wide range of useful and important algorithms for scientific and engineering applications. The authors use MATLAB to illustrate each numerical method, providing full details of the computed results so that the main steps are easily visualized and interpreted. This edition also includes a new chapter on Dynamical Systems and Chaos.
An Introduction to Numerical Methods: A MATLAB® Approach (Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series)
by Abdelwahab Kharab Ronald GuentherAn Introduction to Numerical Methods: A MATLAB® Approach, Fifth Edition continues to offer readers an accessible and practical introduction to numerical analysis. It presents a wide range of useful and important algorithms for scientific and engineering applications, using MATLAB to illustrate each numerical method with full details of the computed results so that the main steps are easily visualized and interpreted. This edition also includes new chapters on Approximation of Continuous Functions and Dealing with Large Sets of Data. Features: Covers the most common numerical methods encountered in science and engineering Illustrates the methods using MATLAB Ideal as an undergraduate textbook for numerical analysis Presents numerous examples and exercises, with selected answers provided at the back of the book Accompanied by downloadable MATLAB code hosted at https/www.routledge.com/ 9781032406824
An Introduction to Numerical Methods and Analysis
by James F. EppersonThe new edition of the popular introductory textbook on numerical approximation methods and mathematical analysis, with a unique emphasis on real-world application An Introduction to Numerical Methods and Analysis helps students gain a solid understanding of a wide range of numerical approximation methods for solving problems of mathematical analysis. Designed for entry-level courses on the subject, this popular textbook maximizes teaching flexibility by first covering basic topics before gradually moving to more advanced material in each chapter and section. Throughout the text, students are provided clear and accessible guidance on a wide range of numerical methods and analysis techniques, including root-finding, numerical integration, interpolation, solution of systems of equations, and many others. This fully revised third edition contains new sections on higher-order difference methods, the bisection and inertia method for computing eigenvalues of a symmetric matrix, a completely re-written section on different methods for Poisson equations, and spectral methods for higher-dimensional problems. New problem sets—ranging in difficulty from simple computations to challenging derivations and proofs—are complemented by computer programming exercises, illustrative examples, and sample code. This acclaimed textbook: Explains how to both construct and evaluate approximations for accuracy and performance Covers both elementary concepts and tools and higher-level methods and solutions Features new and updated material reflecting new trends and applications in the field Contains an introduction to key concepts, a calculus review, an updated primer on computer arithmetic, a brief history of scientific computing, a survey of computer languages and software, and a revised literature review Includes an appendix of proofs of selected theorems and a companion website with additional exercises, application models, and supplemental resources An Introduction to Numerical Methods and Analysis, Third Edition is the perfect textbook for upper-level undergraduate students in mathematics, science, and engineering courses, as well as for courses in the social sciences, medicine, and business with numerical methods and analysis components.
An Introduction to Numerical Methods and Analysis
by James F. EppersonPraise for the First Edition ". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises. "--Zentralblatt MATH ". . . carefully structured with many detailed worked examples. "--The Mathematical Gazette The Second Edition of the highly regarded An Introduction to Numerical Methods and Analysis provides a fully revised guide to numerical approximation. The book continues to be accessible and expertly guides readers through the many available techniques of numerical methods and analysis. An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, spectral collocation, finite element ideas, and Clenshaw-Curtis quadrature, are presented from an introductory perspective, and the Second Edition also features: Chapters and sections that begin with basic, elementary material followed by gradual coverage of more advanced material Exercises ranging from simple hand computations to challenging derivations and minor proofs to programming exercises Widespread exposure and utilization of MATLAB An appendix that contains proofs of various theorems and other material The book is an ideal textbook for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis.
Introduction to Numerical Methods for Time Dependent Differential Equations
by Heinz-Otto Kreiss Omar Eduardo OrtizIntroduces both the fundamentals of time dependent differential equations and their numerical solutionsIntroduction to Numerical Methods for Time Dependent Differential Equations delves into the underlying mathematical theory needed to solve time dependent differential equations numerically. Written as a self-contained introduction, the book is divided into two parts to emphasize both ordinary differential equations (ODEs) and partial differential equations (PDEs).Beginning with ODEs and their approximations, the authors provide a crucial presentation of fundamental notions, such as the theory of scalar equations, finite difference approximations, and the Explicit Euler method. Next, a discussion on higher order approximations, implicit methods, multistep methods, Fourier interpolation, PDEs in one space dimension as well as their related systems is provided.Introduction to Numerical Methods for Time Dependent Differential Equations features:A step-by-step discussion of the procedures needed to prove the stability of difference approximationsMultiple exercises throughout with select answers, providing readers with a practical guide to understanding the approximations of differential equationsA simplified approach in a one space dimensionAnalytical theory for difference approximations that is particularly useful to clarify proceduresIntroduction to Numerical Methods for Time Dependent Differential Equations is an excellent textbook for upper-undergraduate courses in applied mathematics, engineering, and physics as well as a useful reference for physical scientists, engineers, numerical analysts, and mathematical modelers who use numerical experiments to test designs or predict and investigate phenomena from many disciplines.
Introduction to Numerical Methods for Variational Problems (Texts in Computational Science and Engineering #21)
by Hans Petter Langtangen Kent-Andre MardalThis textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.
An Introduction to Numerical Weather Prediction Techniques
by T. N. Krishnamurti Lahouari BounouaAn Introduction to Numerical Weather Prediction Techniques is unique in the meteorological field as it presents for the first time theories and software of complex dynamical and physical processes required for numerical modeling. It was first prepared as a manual for the training of the World Meteorological Organization's programs at a similar level. This new book updates these exercises and also includes the latest data sets. This book covers important aspects of numerical weather prediction techniques required at an introductory level. These techniques, ranging from simple one-dimensional space derivative to complex numerical models, are first described in theory and for most cases supported by fully tested computational software. The text discusses the fundamental physical parameterizations needed in numerical weather models, such as cumulus convection, radiative transfers, and surface energy fluxes calculations. The book gives the user all the necessary elements to build a numerical model. An Introduction to Numerical Weather Prediction Techniques is rich in illustrations, especially tables showing outputs from each individual algorithm presented. Selected figures using actual meteorological data are also used.This book is primarily intended for senior-level undergraduates and first-year graduate students in meteorology. It is also excellent for individual scientists who wish to use the book for self-study. Scientists dealing with geophysical data analysis or predictive models will find this book filled with useful techniques and data-processing algorithms.
Introduction to Octave
by Sandeep NagarFamiliarize yourself with Octave using this concise, practical tutorial that is focused on writing code to learn concepts. Starting from the basics, this book covers array-based computing, plotting, and working with files in Octave, which can run MATLAB files without modification. Introduction to Octave is useful for industry engineers, researchers, and students who are looking for open-source solutions for numerical computation. In this book you will learn by doing, avoiding technical jargon, which makes the concepts easy to learn. First you'll see how to run basic calculations, absorbing technical complexities incrementally as you progress toward advanced topics. Throughout, the language is kept simple to ensure that readers at all levels can grasp the concepts. What You'll Learn Apply sample code to your engineering or science problems Work with Octave arrays, functions, and loops Use Octave's plotting functions for data visualization Solve numerical computing and computational engineering problems with Octave Who This Book Is For Engineers, scientists, researchers, and students who are new to Octave. Some prior programming experience would be helpful but not required.
Introduction to Online Convex Optimization, second edition (Adaptive Computation and Machine Learning series)
by Elad HazanNew 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, adaptive regret, and approachability and expanded exposition on optimizationExamples of applications, including prediction from expert advice, portfolio selection, matrix completion and recommendation systems, SVM training, offered throughout Exercises that guide students in completing parts of proofs
An Introduction to Operator Algebras (Studies in Advanced Mathematics #9)
by Kehe ZhuAn Introduction to Operator Algebras is a concise text/reference that focuses on the fundamental results in operator algebras. Results discussed include Gelfand's representation of commutative C*-algebras, the GNS construction, the spectral theorem, polar decomposition, von Neumann's double commutant theorem, Kaplansky's density theorem, the (continuous, Borel, and L8) functional calculus for normal operators, and type decomposition for von Neumann algebras. Exercises are provided after each chapter.
An Introduction to Optimal Control of FBSDE with Incomplete Information (SpringerBriefs in Mathematics)
by Jie Xiong Zhen Wu Guangchen WangThis book focuses on maximum principle and verification theorem for incomplete information forward-backward stochastic differential equations (FBSDEs) and their applications in linear-quadratic optimal controls and mathematical finance. Lots of interesting phenomena arising from the area of mathematical finance can be described by FBSDEs. Optimal control problems of FBSDEs are theoretically important and practically relevant. A standard assumption in the literature is that the stochastic noises in the model are completely observed. However, this is rarely the case in real world situations. The optimal control problems under complete information are studied extensively. Nevertheless, very little is known about these problems when the information is not complete. The aim of this book is to fill this gap. This book is written in a style suitable for graduate students and researchers in mathematics and engineering with basic knowledge of stochastic process, optimal control and mathematical finance.
An Introduction to Optimal Control Problems in Life Sciences and Economics: From Mathematical Models to Numerical Simulation with MATLAB® (Modeling and Simulation in Science, Engineering and Technology)
by Viorel Arnăutu Sebastian Aniţa Vincenzo CapassoCombining control theory and modeling, this textbook introduces and builds on methods for simulating and tackling concrete problems in a variety of applied sciences. Emphasizing "learning by doing," the authors focus on examples and applications to real-world problems. An elementary presentation of advanced concepts, proofs to introduce new ideas, and carefully presented MATLAB® programs help foster an understanding of the basics, but also lead the way to new, independent research. With minimal prerequisites and exercises in each chapter, this work serves as an excellent textbook and reference for graduate and advanced undergraduate students, researchers, and practitioners in mathematics, physics, engineering, computer science, as well as biology, biotechnology, economics, and finance.
An Introduction to Optimal Control Theory: The Dynamic Programming Approach (Texts in Applied Mathematics #76)
by Onésimo Hernández-Lerma Saul Mendoza-Palacios David González-Sánchez Leonardo R. Laura-GuarachiThis book introduces optimal control problems for large families of deterministic and stochastic systems with discrete or continuous time parameter. These families include most of the systems studied in many disciplines, including Economics, Engineering, Operations Research, and Management Science, among many others. The main objective is to give a concise, systematic, and reasonably self contained presentation of some key topics in optimal control theory. To this end, most of the analyses are based on the dynamic programming (DP) technique. This technique is applicable to almost all control problems that appear in theory and applications. They include, for instance, finite and infinite horizon control problems in which the underlying dynamic system follows either a deterministic or stochastic difference or differential equation. In the infinite horizon case, it also uses DP to study undiscounted problems, such as the ergodic or long-run average cost. After a general introduction to control problems, the book covers the topic dividing into four parts with different dynamical systems: control of discrete-time deterministic systems, discrete-time stochastic systems, ordinary differential equations, and finally a general continuous-time MCP with applications for stochastic differential equations. The first and second part should be accessible to undergraduate students with some knowledge of elementary calculus, linear algebra, and some concepts from probability theory (random variables, expectations, and so forth). Whereas the third and fourth part would be appropriate for advanced undergraduates or graduate students who have a working knowledge of mathematical analysis (derivatives, integrals, ...) and stochastic processes.
An Introduction to Optimization: With Applications to Machine Learning (Wiley Series In Discrete Mathematics And Optimization Ser. #77)
by Edwin K. Chong Wu-Sheng Lu Stanislaw H. ŻakAn Introduction to Optimization Accessible introductory textbook on optimization theory and methods, with an emphasis on engineering design, featuring MATLAB® exercises and worked examples Fully updated to reflect modern developments in the field, the Fifth Edition of An Introduction to Optimization fills the need for an accessible, yet rigorous, introduction to optimization theory and methods, featuring innovative coverage and a straightforward approach. The book begins with a review of basic definitions and notations while also providing the related fundamental background of linear algebra, geometry, and calculus. With this foundation, the authors explore the essential topics of unconstrained optimization problems, linear programming problems, and nonlinear constrained optimization. In addition, the book includes an introduction to artificial neural networks, convex optimization, multi-objective optimization, and applications of optimization in machine learning. Numerous diagrams and figures found throughout the book complement the written presentation of key concepts, and each chapter is followed by MATLAB® exercises and practice problems that reinforce the discussed theory and algorithms. The Fifth Edition features a new chapter on Lagrangian (nonlinear) duality, expanded coverage on matrix games, projected gradient algorithms, machine learning, and numerous new exercises at the end of each chapter. An Introduction to Optimization includes information on: The mathematical definitions, notations, and relations from linear algebra, geometry, and calculus used in optimization Optimization algorithms, covering one-dimensional search, randomized search, and gradient, Newton, conjugate direction, and quasi-Newton methods Linear programming methods, covering the simplex algorithm, interior point methods, and duality Nonlinear constrained optimization, covering theory and algorithms, convex optimization, and Lagrangian duality Applications of optimization in machine learning, including neural network training, classification, stochastic gradient descent, linear regression, logistic regression, support vector machines, and clustering. An Introduction to Optimization is an ideal textbook for a one- or two-semester senior undergraduate or beginning graduate course in optimization theory and methods. The text is also of value for researchers and professionals in mathematics, operations research, electrical engineering, economics, statistics, and business.
An Introduction to Optimization (Wiley Series in Discrete Mathematics and Optimization #72)
by Edwin K. Chong Stanislaw H. ZakPraise from the Second Edition "...an excellent introduction to optimization theory..." (Journal of Mathematical Psychology, 2002) "A textbook for a one-semester course on optimization theory and methods at the senior undergraduate or beginning graduate level." (SciTech Book News, Vol. 26, No. 2, June 2002) Explore the latest applications of optimization theory and methods Optimization is central to any problem involving decision making in many disciplines, such as engineering, mathematics, statistics, economics, and computer science. Now, more than ever, it is increasingly vital to have a firm grasp of the topic due to the rapid progress in computer technology, including the development and availability of user-friendly software, high-speed and parallel processors, and networks. Fully updated to reflect modern developments in the field, An Introduction to Optimization, Third Edition fills the need for an accessible, yet rigorous, introduction to optimization theory and methods. The book begins with a review of basic definitions and notations and also provides the related fundamental background of linear algebra, geometry, and calculus. With this foundation, the authors explore the essential topics of unconstrained optimization problems, linear programming problems, and nonlinear constrained optimization. An optimization perspective on global search methods is featured and includes discussions on genetic algorithms, particle swarm optimization, and the simulated annealing algorithm. In addition, the book includes an elementary introduction to artificial neural networks, convex optimization, and multi-objective optimization, all of which are of tremendous interest to students, researchers, and practitioners. Additional features of the Third Edition include: New discussions of semidefinite programming and Lagrangian algorithms A new chapter on global search methods A new chapter on multipleobjective optimization New and modified examples and exercises in each chapter as well as an updated bibliography containing new references An updated Instructor's Manual with fully worked-out solutions to the exercises Numerous diagrams and figures found throughout the text complement the written presentation of key concepts, and each chapter is followed by MATLAB exercises and drill problems that reinforce the discussed theory and algorithms. With innovative coverage and a straightforward approach, An Introduction to Optimization, Third Edition is an excellent book for courses in optimization theory and methods at the upper-undergraduate and graduate levels. It also serves as a useful, self-contained reference for researchers and professionals in a wide array of fields.
An Introduction to Optimization
by Edwin K. Chong Stanislaw H. ZakPraise from the Second Edition"...an excellent introduction to optimization theory..." (Journal of Mathematical Psychology, 2002)"A textbook for a one-semester course on optimization theory and methods at the senior undergraduate or beginning graduate level." (SciTech Book News, Vol. 26, No. 2, June 2002)Explore the latest applications of optimization theory and methodsOptimization is central to any problem involving decision making in many disciplines, such as engineering, mathematics, statistics, economics, and computer science. Now, more than ever, it is increasingly vital to have a firm grasp of the topic due to the rapid progress in computer technology, including the development and availability of user-friendly software, high-speed and parallel processors, and networks. Fully updated to reflect modern developments in the field, An Introduction to Optimization, Third Edition fills the need for an accessible, yet rigorous, introduction to optimization theory and methods.The book begins with a review of basic definitions and notations and also provides the related fundamental background of linear algebra, geometry, and calculus. With this foundation, the authors explore the essential topics of unconstrained optimization problems, linear programming problems, and nonlinear constrained optimization. An optimization perspective on global search methods is featured and includes discussions on genetic algorithms, particle swarm optimization, and the simulated annealing algorithm. In addition, the book includes an elementary introduction to artificial neural networks, convex optimization, and multi-objective optimization, all of which are of tremendous interest to students, researchers, and practitioners.Additional features of the Third Edition include:New discussions of semidefinite programming and Lagrangian algorithmsA new chapter on global search methodsA new chapter on multipleobjective optimizationNew and modified examples and exercises in each chapter as well as an updated bibliography containing new referencesAn updated Instructor's Manual with fully worked-out solutions to the exercisesNumerous diagrams and figures found throughout the text complement the written presentation of key concepts, and each chapter is followed by MATLAB exercises and drill problems that reinforce the discussed theory and algorithms. With innovative coverage and a straightforward approach, An Introduction to Optimization, Third Edition is an excellent book for courses in optimization theory and methods at the upper-undergraduate and graduate levels. It also serves as a useful, self-contained reference for researchers and professionals in a wide array of fields.
Introduction to Optimization Analysis in Hydrosystem Engineering
by Ehsan Goodarzi Mina Ziaei Edward Zia HosseinipourThis book presents the basics of linear and nonlinear optimization analysis for both single and multi-objective problems in hydrosystem engineering. The book includes several examples with various levels of complexity in different fields of water resources engineering. The examples are solved step by step to assist the reader and to make it easier to understand the concepts. In addition, the latest tools and methods are presented to help students, researchers, engineers and water managers to properly conceptualize and formulate resource allocation problems, and to deal with the complexity of constraints in water demand and available supplies in an appropriate way.
An Introduction to Optimization Techniques
by Vikrant Sharma Vinod Kumar Jain Atul KumarAn Introduction to Optimization Techniques introduces the basic ideas and techniques of optimization. Optimization is a precise procedure using design constraints and criteria to enable the planner to find the optimal solution. Optimization techniques have been applied in numerous fields to deal with different practical problems. This book is designed to give the reader a sense of the challenge of analyzing a given situation and formulating a model for it while explaining the assumptions and inner structure of the methods discussed as fully as possible. It includes real-world examples and applications making the book accessible to a broader readership. Features Each chapter begins with the Learning Outcomes (LO) section, which highlights the critical points of that chapter. All learning outcomes, solved examples and questions are mapped to six Bloom Taxonomy levels (BT Level). Book offers fundamental concepts of optimization without becoming too complicated. A wide range of solved examples are presented in each section after the theoretical discussion to clarify the concept of that section. A separate chapter on the application of spreadsheets to solve different optimization techniques. At the end of each chapter, a summary reinforces key ideas and helps readers recall the concepts discussed. The wide and emerging uses of optimization techniques make it essential for students and professionals. Optimization techniques have been applied in numerous fields to deal with different practical problems. This book serves as a textbook for UG and PG students of science, engineering, and management programs. It will be equally useful for Professionals, Consultants, and Managers.