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| advanced algebra with financial applications: Financial Algebra Robert Gerver, Richard J. Sgroi, 2017-02-15 By combining algebraic and graphical approaches with practical business and personal finance applications, Financial Algebra offers an applications based learning approach incorporating Algebra I, Algebra II, and Geometry topics. Explanations and exercises encourage students to be actively involved in applying mathematical ideas to their everyday lives -- credit, banking insurance, the stock market, independent living and more. |
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| advanced algebra with financial applications: College Algebra Jay Abramson, 2018-01-07 College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they've learned. Coverage and Scope In determining the concepts, skills, and topics to cover, we engaged dozens of highly experienced instructors with a range of student audiences. The resulting scope and sequence proceeds logically while allowing for a significant amount of flexibility in instruction. Chapters 1 and 2 provide both a review and foundation for study of Functions that begins in Chapter 3. The authors recognize that while some institutions may find this material a prerequisite, other institutions have told us that they have a cohort that need the prerequisite skills built into the course. Chapter 1: Prerequisites Chapter 2: Equations and Inequalities Chapters 3-6: The Algebraic Functions Chapter 3: Functions Chapter 4: Linear Functions Chapter 5: Polynomial and Rational Functions Chapter 6: Exponential and Logarithm Functions Chapters 7-9: Further Study in College Algebra Chapter 7: Systems of Equations and Inequalities Chapter 8: Analytic Geometry Chapter 9: Sequences, Probability and Counting Theory |
| advanced algebra with financial applications: An Introduction to Mathematical Finance with Applications Arlie O. Petters, Xiaoying Dong, 2016-06-17 This textbook aims to fill the gap between those that offer a theoretical treatment without many applications and those that present and apply formulas without appropriately deriving them. The balance achieved will give readers a fundamental understanding of key financial ideas and tools that form the basis for building realistic models, including those that may become proprietary. Numerous carefully chosen examples and exercises reinforce the student’s conceptual understanding and facility with applications. The exercises are divided into conceptual, application-based, and theoretical problems, which probe the material deeper. The book is aimed toward advanced undergraduates and first-year graduate students who are new to finance or want a more rigorous treatment of the mathematical models used within. While no background in finance is assumed, prerequisite math courses include multivariable calculus, probability, and linear algebra. The authors introduce additional mathematical tools as needed. The entire textbook is appropriate for a single year-long course on introductory mathematical finance. The self-contained design of the text allows for instructor flexibility in topics courses and those focusing on financial derivatives. Moreover, the text is useful for mathematicians, physicists, and engineers who want to learn finance via an approach that builds their financial intuition and is explicit about model building, as well as business school students who want a treatment of finance that is deeper but not overly theoretical. |
| advanced algebra with financial applications: Quantitative Equity Portfolio Management Edward E. Qian, Ronald H. Hua, Eric H. Sorensen, 2007-05-11 Quantitative equity portfolio management combines theories and advanced techniques from several disciplines, including financial economics, accounting, mathematics, and operational research. While many texts are devoted to these disciplines, few deal with quantitative equity investing in a systematic and mathematical framework that is suitable for |
| advanced algebra with financial applications: Regression Modeling with Actuarial and Financial Applications Edward W. Frees, 2010 This book teaches multiple regression and time series and how to use these to analyze real data in risk management and finance. |
| advanced algebra with financial applications: Advanced Algebra Anthony W. Knapp, 2007-10-11 Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Advanced Algebra includes chapters on modern algebra which treat various topics in commutative and noncommutative algebra and provide introductions to the theory of associative algebras, homological algebras, algebraic number theory, and algebraic geometry. Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems. Together the two books give the reader a global view of algebra and its role in mathematics as a whole. |
| advanced algebra with financial applications: Python for Finance Yves J. Hilpisch, 2018-12-05 The financial industry has recently adopted Python at a tremendous rate, with some of the largest investment banks and hedge funds using it to build core trading and risk management systems. Updated for Python 3, the second edition of this hands-on book helps you get started with the language, guiding developers and quantitative analysts through Python libraries and tools for building financial applications and interactive financial analytics. Using practical examples throughout the book, author Yves Hilpisch also shows you how to develop a full-fledged framework for Monte Carlo simulation-based derivatives and risk analytics, based on a large, realistic case study. Much of the book uses interactive IPython Notebooks. |
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| advanced algebra with financial applications: Statistics and Data Analysis for Financial Engineering David Ruppert, David S. Matteson, 2015-04-21 The new edition of this influential textbook, geared towards graduate or advanced undergraduate students, teaches the statistics necessary for financial engineering. In doing so, it illustrates concepts using financial markets and economic data, R Labs with real-data exercises, and graphical and analytic methods for modeling and diagnosing modeling errors. These methods are critical because financial engineers now have access to enormous quantities of data. To make use of this data, the powerful methods in this book for working with quantitative information, particularly about volatility and risks, are essential. Strengths of this fully-revised edition include major additions to the R code and the advanced topics covered. Individual chapters cover, among other topics, multivariate distributions, copulas, Bayesian computations, risk management, and cointegration. Suggested prerequisites are basic knowledge of statistics and probability, matrices and linear algebra, and calculus. There is an appendix on probability, statistics and linear algebra. Practicing financial engineers will also find this book of interest. |
| advanced algebra with financial applications: Advances in Financial Machine Learning Marcos Lopez de Prado, 2018-01-23 Learn to understand and implement the latest machine learning innovations to improve your investment performance Machine learning (ML) is changing virtually every aspect of our lives. Today, ML algorithms accomplish tasks that – until recently – only expert humans could perform. And finance is ripe for disruptive innovations that will transform how the following generations understand money and invest. In the book, readers will learn how to: Structure big data in a way that is amenable to ML algorithms Conduct research with ML algorithms on big data Use supercomputing methods and back test their discoveries while avoiding false positives Advances in Financial Machine Learning addresses real life problems faced by practitioners every day, and explains scientifically sound solutions using math, supported by code and examples. Readers become active users who can test the proposed solutions in their individual setting. Written by a recognized expert and portfolio manager, this book will equip investment professionals with the groundbreaking tools needed to succeed in modern finance. |
| advanced algebra with financial applications: Solutions Manual - a Linear Algebra Primer for Financial Engineering Dan Stefanica, 2016-08-22 |
| advanced algebra with financial applications: Advanced Linear Algebra Steven Roman, 2007-12-31 Covers a notably broad range of topics, including some topics not generally found in linear algebra books Contains a discussion of the basics of linear algebra |
| advanced algebra with financial applications: Essentials of Time Series for Financial Applications Massimo Guidolin, Manuela Pedio, 2018-05-29 Essentials of Time Series for Financial Applications serves as an agile reference for upper level students and practitioners who desire a formal, easy-to-follow introduction to the most important time series methods applied in financial applications (pricing, asset management, quant strategies, and risk management). Real-life data and examples developed with EViews illustrate the links between the formal apparatus and the applications. The examples either directly exploit the tools that EViews makes available or use programs that by employing EViews implement specific topics or techniques. The book balances a formal framework with as few proofs as possible against many examples that support its central ideas. Boxes are used throughout to remind readers of technical aspects and definitions and to present examples in a compact fashion, with full details (workout files) available in an on-line appendix. The more advanced chapters provide discussion sections that refer to more advanced textbooks or detailed proofs. - Provides practical, hands-on examples in time-series econometrics - Presents a more application-oriented, less technical book on financial econometrics - Offers rigorous coverage, including technical aspects and references for the proofs, despite being an introduction - Features examples worked out in EViews (9 or higher) |
| advanced algebra with financial applications: Mathematics for the International Student Michael Haese, Robert C. Haese, David C. Martin, 2013 |
| advanced algebra with financial applications: The CahnHilliard Equation: Recent Advances and Applications Alain Miranville, 2019-09-09 This is the first book to present a detailed discussion of both classical and recent results on the popular CahnHilliard equation and some of its variants. The focus is on mathematical analysis of CahnHilliard models, with an emphasis on thermodynamically relevant logarithmic nonlinear terms, for which several questions are still open. Initially proposed in view of applications to materials science, the CahnHilliard equation is now applied in many other areas, including image processing, biology, ecology, astronomy, and chemistry. In particular, the author addresses applications to image inpainting and tumor growth. Many chapters include open problems and directions for future research. The Cahn-Hilliard Equation: Recent Advances and Applications is intended for graduate students and researchers in applied mathematics, especially those interested in phase separation models and their generalizations and applications to other fields. Materials scientists also will find this text of interest. |
| advanced algebra with financial applications: Introductory Functional Analysis with Applications Erwin Kreyszig, 1991-01-16 KREYSZIG The Wiley Classics Library consists of selected books originally published by John Wiley & Sons that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: Emil Artin Geometnc Algebra R. W. Carter Simple Groups Of Lie Type Richard Courant Differential and Integrai Calculus. Volume I Richard Courant Differential and Integral Calculus. Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics. Volume II Harold M. S. Coxeter Introduction to Modern Geometry. Second Edition Charles W. Curtis, Irving Reiner Representation Theory of Finite Groups and Associative Algebras Nelson Dunford, Jacob T. Schwartz unear Operators. Part One. General Theory Nelson Dunford. Jacob T. Schwartz Linear Operators, Part Two. Spectral Theory—Self Adjant Operators in Hilbert Space Nelson Dunford, Jacob T. Schwartz Linear Operators. Part Three. Spectral Operators Peter Henrici Applied and Computational Complex Analysis. Volume I—Power Senes-lntegrauon-Contormal Mapping-Locatvon of Zeros Peter Hilton, Yet-Chiang Wu A Course in Modern Algebra Harry Hochstadt Integral Equations Erwin Kreyszig Introductory Functional Analysis with Applications P. M. Prenter Splines and Variational Methods C. L. Siegel Topics in Complex Function Theory. Volume I —Elliptic Functions and Uniformizatton Theory C. L. Siegel Topics in Complex Function Theory. Volume II —Automorphic and Abelian Integrals C. L. Siegel Topics In Complex Function Theory. Volume III —Abelian Functions & Modular Functions of Several Variables J. J. Stoker Differential Geometry |
| advanced algebra with financial applications: Matrix Algebra James E. Gentle, 2007-07-27 Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. |
| advanced algebra with financial applications: Multivariate Time Series Analysis Ruey S. Tsay, 2013-11-11 An accessible guide to the multivariate time series tools used in numerous real-world applications Multivariate Time Series Analysis: With R and Financial Applications is the much anticipated sequel coming from one of the most influential and prominent experts on the topic of time series. Through a fundamental balance of theory and methodology, the book supplies readers with a comprehensible approach to financial econometric models and their applications to real-world empirical research. Differing from the traditional approach to multivariate time series, the book focuses on reader comprehension by emphasizing structural specification, which results in simplified parsimonious VAR MA modeling. Multivariate Time Series Analysis: With R and Financial Applications utilizes the freely available R software package to explore complex data and illustrate related computation and analyses. Featuring the techniques and methodology of multivariate linear time series, stationary VAR models, VAR MA time series and models, unitroot process, factor models, and factor-augmented VAR models, the book includes: • Over 300 examples and exercises to reinforce the presented content • User-friendly R subroutines and research presented throughout to demonstrate modern applications • Numerous datasets and subroutines to provide readers with a deeper understanding of the material Multivariate Time Series Analysis is an ideal textbook for graduate-level courses on time series and quantitative finance and upper-undergraduate level statistics courses in time series. The book is also an indispensable reference for researchers and practitioners in business, finance, and econometrics. |
| advanced algebra with financial applications: Advanced and Optimization Based Sliding Mode Control: Theory and Applications Antonella Ferrara, Gian Paolo Incremona, Michele Cucuzella, 2019-07-01 A compendium of the authors recently published results, this book discusses sliding mode control of uncertain nonlinear systems, with a particular emphasis on advanced and optimization based algorithms. The authors survey classical sliding mode control theory and introduce four new methods of advanced sliding mode control. They analyze classical theory and advanced algorithms, with numerical results complementing the theoretical treatment. Case studies examine applications of the algorithms to complex robotics and power grid problems. Advanced and Optimization Based Sliding Mode Control: Theory and Applications is the first book to systematize the theory of optimization based higher order sliding mode control and illustrate advanced algorithms and their applications to real problems. It presents systematic treatment of event-triggered and model based event-triggered sliding mode control schemes, including schemes in combination with model predictive control, and presents adaptive algorithms as well as algorithms capable of dealing with state and input constraints. Additionally, the book includes simulations and experimental results obtained by applying the presented control strategies to real complex systems. This book is suitable for students and researchers interested in control theory. It will also be attractive to practitioners interested in implementing the illustrated strategies. It is accessible to anyone with a basic knowledge of control engineering, process physics, and applied mathematics. |
| advanced algebra with financial applications: Deep Learning for Coders with fastai and PyTorch Jeremy Howard, Sylvain Gugger, 2020-06-29 Deep learning is often viewed as the exclusive domain of math PhDs and big tech companies. But as this hands-on guide demonstrates, programmers comfortable with Python can achieve impressive results in deep learning with little math background, small amounts of data, and minimal code. How? With fastai, the first library to provide a consistent interface to the most frequently used deep learning applications. Authors Jeremy Howard and Sylvain Gugger, the creators of fastai, show you how to train a model on a wide range of tasks using fastai and PyTorch. You’ll also dive progressively further into deep learning theory to gain a complete understanding of the algorithms behind the scenes. Train models in computer vision, natural language processing, tabular data, and collaborative filtering Learn the latest deep learning techniques that matter most in practice Improve accuracy, speed, and reliability by understanding how deep learning models work Discover how to turn your models into web applications Implement deep learning algorithms from scratch Consider the ethical implications of your work Gain insight from the foreword by PyTorch cofounder, Soumith Chintala |
| advanced algebra with financial applications: Data Assimilation: Methods, Algorithms, and Applications Mark Asch, Marc Bocquet, Maelle Nodet, 2016-12-29 Data assimilation is an approach that combines observations and model output, with the objective of improving the latter. This book places data assimilation into the broader context of inverse problems and the theory, methods, and algorithms that are used for their solution. It provides a framework for, and insight into, the inverse problem nature of data assimilation, emphasizing why and not just how. Methods and diagnostics are emphasized, enabling readers to readily apply them to their own field of study. Readers will find a comprehensive guide that is accessible to nonexperts; numerous examples and diverse applications from a broad range of domains, including geophysics and geophysical flows, environmental acoustics, medical imaging, mechanical and biomedical engineering, economics and finance, and traffic control and urban planning; and the latest methods for advanced data assimilation, combining variational and statistical approaches. |
| advanced algebra with financial applications: Advances in Mathematical Finance Michael C. Fu, Robert A. Jarrow, Ju-Yi Yen, Robert J Elliott, 2007-06-22 This self-contained volume brings together a collection of chapters by some of the most distinguished researchers and practitioners in the field of mathematical finance and financial engineering. Presenting state-of-the-art developments in theory and practice, the book has real-world applications to fixed income models, credit risk models, CDO pricing, tax rebates, tax arbitrage, and tax equilibrium. It is a valuable resource for graduate students, researchers, and practitioners in mathematical finance and financial engineering. |
| advanced algebra with financial applications: Forecasting: principles and practice Rob J Hyndman, George Athanasopoulos, 2018-05-08 Forecasting is required in many situations. Stocking an inventory may require forecasts of demand months in advance. Telecommunication routing requires traffic forecasts a few minutes ahead. Whatever the circumstances or time horizons involved, forecasting is an important aid in effective and efficient planning. This textbook provides a comprehensive introduction to forecasting methods and presents enough information about each method for readers to use them sensibly. |
| advanced algebra with financial applications: The Basics of Financial Econometrics Frank J. Fabozzi, Sergio M. Focardi, Svetlozar T. Rachev, Bala G. Arshanapalli, 2014-03-04 An accessible guide to the growing field of financial econometrics As finance and financial products have become more complex, financial econometrics has emerged as a fast-growing field and necessary foundation for anyone involved in quantitative finance. The techniques of financial econometrics facilitate the development and management of new financial instruments by providing models for pricing and risk assessment. In short, financial econometrics is an indispensable component to modern finance. The Basics of Financial Econometrics covers the commonly used techniques in the field without using unnecessary mathematical/statistical analysis. It focuses on foundational ideas and how they are applied. Topics covered include: regression models, factor analysis, volatility estimations, and time series techniques. Covers the basics of financial econometrics—an important topic in quantitative finance Contains several chapters on topics typically not covered even in basic books on econometrics such as model selection, model risk, and mitigating model risk Geared towards both practitioners and finance students who need to understand this dynamic discipline, but may not have advanced mathematical training, this book is a valuable resource on a topic of growing importance. |
| advanced algebra with financial applications: Principles of Financial Engineering Robert Kosowski, Salih N. Neftci, 2014-11-26 Principles of Financial Engineering, Third Edition, is a highly acclaimed text on the fast-paced and complex subject of financial engineering. This updated edition describes the engineering elements of financial engineering instead of the mathematics underlying it. It shows how to use financial tools to accomplish a goal rather than describing the tools themselves. It lays emphasis on the engineering aspects of derivatives (how to create them) rather than their pricing (how they act) in relation to other instruments, the financial markets, and financial market practices. This volume explains ways to create financial tools and how the tools work together to achieve specific goals. Applications are illustrated using real-world examples. It presents three new chapters on financial engineering in topics ranging from commodity markets to financial engineering applications in hedge fund strategies, correlation swaps, structural models of default, capital structure arbitrage, contingent convertibles, and how to incorporate counterparty risk into derivatives pricing. Poised midway between intuition, actual events, and financial mathematics, this book can be used to solve problems in risk management, taxation, regulation, and above all, pricing. A solutions manual enhances the text by presenting additional cases and solutions to exercises. This latest edition of Principles of Financial Engineering is ideal for financial engineers, quantitative analysts in banks and investment houses, and other financial industry professionals. It is also highly recommended to graduate students in financial engineering and financial mathematics programs. - The Third Edition presents three new chapters on financial engineering in commodity markets, financial engineering applications in hedge fund strategies, correlation swaps, structural models of default, capital structure arbitrage, contingent convertibles and how to incorporate counterparty risk into derivatives pricing, among other topics - Additions, clarifications, and illustrations throughout the volume show these instruments at work instead of explaining how they should act - The solutions manual enhances the text by presenting additional cases and solutions to exercises |
| advanced algebra with financial applications: Analysis, Geometry, and Modeling in Finance Pierre Henry-Labordere, 2008-09-22 Analysis, Geometry, and Modeling in Finance: Advanced Methods in Option Pricing is the first book that applies advanced analytical and geometrical methods used in physics and mathematics to the financial field. It even obtains new results when only approximate and partial solutions were previously available.Through the problem of option pricing, th |
| advanced algebra with financial applications: Advanced Topics in Linear Algebra Kevin O'Meara, John Clark, Charles Vinsonhaler, 2011-09-16 This book develops the Weyr matrix canonical form, a largely unknown cousin of the Jordan form. It explores novel applications, including include matrix commutativity problems, approximate simultaneous diagonalization, and algebraic geometry. Module theory and algebraic geometry are employed but with self-contained accounts. |
| advanced algebra with financial applications: Math for Financial Literacy Todd Knowlton, Paul Douglas Gray, 2012-05 Math for Financial Literacy prepares your students for the real world. Written specifically for teens, Math for Financial Literacy provides instruction for relevant math concepts that students can easily relate to their daily lives. In Math for Financial Literacy, students learn how to apply basic math concepts to the tasks they will use in the real world, including earning a paycheck, managing a bank account, using credit cards, and creating a budget. Other practical topics are presented to help students become financially capable and responsible. Each chapter is designed to present content in small segments for optimal comprehension. The following features also support students in the 5E instructional model. Reading Prep activities give students an opportunity to apply the Common Core State Standards for English Language Arts. These activities are noted by the College and Career Readiness icon and will help students meet the College and Career Readiness (CCR) anchor standards for reading and writing. For just-in-time practice of relevant skills, Build Your Math Skills features provide a preview of skills needed in the lesson, while Review Your Math Skills features reinforce those skills after the lesson instruction. See It and Check It features set the structure for presenting examples of each concept. See It demonstrates the concept, and Check It gives students a chance to try it for themselves. Skills Lab provided at the beginning of the text helps students become reacquainted with the math skills they will encounter in the book. There are 16 labs ranging from place value/order to bar and circle graphs. The Financial Literacy Simulation: Stages of Life Project provides students with real-life personal and professional scenarios that require the math skills and problem-solving techniques they have learned during the course. This capstone chapter is divided into life stages to support students as they enter into the adult world of working and financial planning. Assessment features at the end of the chapters allow for the review of key terms and concepts, as well as a spiral review of content from previous chapters. Additional features include: Financial $marts features offer information that applies the content to the practical matter of personal finance. Money Matters features equip students with background knowledge about the chapter topic. Apply Your Technology Skills features allow students to use technology to apply the math concepts they learned to real-life situations. Career Discovery features offer students an inside look at the math skill they will need for the career of their choice, based on the 16 Career Clusters(TM). FYI tips provide relevant information about the chapter content and math principles. |
| advanced algebra with financial applications: Discovering Advanced Algebra Jerald Murdock, Ellen Kamischke, 2010 Changes in society and the workplace require a careful analysis of the algebra curriculum that we teach. The curriculum, teaching, and learning of yesterday do not meet the needs of today's students. |
| advanced algebra with financial applications: Advanced Real Analysis Anthony W. Knapp, 2008-07-11 * Presents a comprehensive treatment with a global view of the subject * Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician |
| advanced algebra with financial applications: Advanced Engineering Mathematics Michael Greenberg, 2013-09-20 Appropriate for one- or two-semester Advanced Engineering Mathematics courses in departments of Mathematics and Engineering. This clear, pedagogically rich book develops a strong understanding of the mathematical principles and practices that today's engineers and scientists need to know. Equally effective as either a textbook or reference manual, it approaches mathematical concepts from a practical-use perspective making physical applications more vivid and substantial. Its comprehensive instructional framework supports a conversational, down-to-earth narrative style offering easy accessibility and frequent opportunities for application and reinforcement. |
| advanced algebra with financial applications: Methods and Applications of Interval Analysis Ramon E. Moore, 1979-01-01 This book treats an important set of techniques that provide a mathematically rigorous and complete error analysis for computational results. It shows that interval analysis provides a powerful set of tools with direct applicability to important problems in scientific computing. |
| advanced algebra with financial applications: Business Math Steven J. Wilson, 2012-07-09 eBook Version Purchases will receive 6 month access to this electronic text via email after using the shopping cart above to complete your purchase. |
| advanced algebra with financial applications: Apples Stanley Fredric Schmidt, 2011 Not just drill-and-kill. Fred has a need for math in his life. No more, 'when am I ever going to need this stuff'?''-- Cover verso. |
| advanced algebra with financial applications: Advances in Linear Algebra Research Ivan Kyrchei, 2015 This book presents original studies on the leading edge of linear algebra. Each chapter has been carefully selected in an attempt to present substantial research results across a broad spectrum. The main goal of Chapter One is to define and investigate the restricted generalized inverses corresponding to minimization of constrained quadratic form. As stated in Chapter Two, in systems and control theory, Linear Time Invariant (LTI) descriptor (Differential-Algebraic) systems are intimately related to the matrix pencil theory. A review of the most interesting properties of the Projective Equivalence and the Extended Hermite Equivalence classes is presented in the chapter. New determinantal representations of generalized inverse matrices based on their limit representations are introduced in Chapter Three. Using the obtained analogues of the adjoint matrix, Cramer's rules for the least squares solution with the minimum norm and for the Drazin inverse solution of singular linear systems have been obtained in the chapter. In Chapter Four, a very interesting application of linear algebra of commutative rings to systems theory, is explored. Chapter Five gives a comprehensive investigation to behaviors of a general Hermitian quadratic matrix-valued function by using ranks and inertias of matrices. In Chapter Six, the theory of triangular matrices (tables) is introduced. The main characters of the chapter are special triangular tables (which will be called triangular matrices) and their functions paradeterminants and parapermanents. The aim of Chapter Seven is to present the latest developments in iterative methods for solving linear matrix equations. The problems of existence of common eigenvectors and simultaneous triangularization of a pair of matrices over a principal ideal domain with quadratic minimal polynomials are investigated in Chapter Eight. Two approaches to define a noncommutative determinant (a determinant of a matrix with noncommutative elements) are considered in Chapter Nine. The last, Chapter 10, is an example of how the methods of linear algebra are used in natural sciences, particularly in chemistry. In this chapter, it is shown that in a First Order Chemical Kinetics Mechanisms matrix, all columns add to zero, all the diagonal elements are non-positive and all the other matrix entries are non-negative. As a result of this particular structure, the Gershgorin Circles Theorem can be applied to show that all the eigenvalues are negative or zero. |
| advanced algebra with financial applications: Discovering Advanced Algebra Jerald Murdock, Ellen Kamischke, Eric Kamischke, 2013 |
| advanced algebra with financial applications: Optimization Methods in Finance Gerard Cornuejols, Reha Tütüncü, 2006-12-21 Optimization models play an increasingly important role in financial decisions. This is the first textbook devoted to explaining how recent advances in optimization models, methods and software can be applied to solve problems in computational finance more efficiently and accurately. Chapters discussing the theory and efficient solution methods for all major classes of optimization problems alternate with chapters illustrating their use in modeling problems of mathematical finance. The reader is guided through topics such as volatility estimation, portfolio optimization problems and constructing an index fund, using techniques such as nonlinear optimization models, quadratic programming formulations and integer programming models respectively. The book is based on Master's courses in financial engineering and comes with worked examples, exercises and case studies. It will be welcomed by applied mathematicians, operational researchers and others who work in mathematical and computational finance and who are seeking a text for self-learning or for use with courses. |
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