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Math for Deep Learning: What You Need to Know to Understand Neural Networks
by Ronald T. KneuselMath for Deep Learning provides the essential math you need to understand deep learning discussions, explore more complex implementations, and better use the deep learning toolkits.With Math for Deep Learning, you'll learn the essential mathematics used by and as a background for deep learning. You&’ll work through Python examples to learn key deep learning related topics in probability, statistics, linear algebra, differential calculus, and matrix calculus as well as how to implement data flow in a neural network, backpropagation, and gradient descent. You&’ll also use Python to work through the mathematics that underlies those algorithms and even build a fully-functional neural network.In addition you&’ll find coverage of gradient descent including variations commonly used by the deep learning community: SGD, Adam, RMSprop, and Adagrad/Adadelta.
Math for Programmers: 3D graphics, machine learning, and simulations with Python
by Paul OrlandIn Math for Programmers you&’ll explore important mathematical concepts through hands-on coding. Filled with graphics and more than 300 exercises and mini-projects, this book unlocks the door to interesting–and lucrative!–careers in some of today&’s hottest fields. As you tackle the basics of linear algebra, calculus, and machine learning, you&’ll master the key Python libraries used to turn them into real-world software applications.Summary To score a job in data science, machine learning, computer graphics, and cryptography, you need to bring strong math skills to the party. Math for Programmers teaches the math you need for these hot careers, concentrating on what you need to know as a developer. Filled with lots of helpful graphics and more than 200 exercises and mini-projects, this book unlocks the door to interesting–and lucrative!–careers in some of today&’s hottest programming fields. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the technology Skip the mathematical jargon: This one-of-a-kind book uses Python to teach the math you need to build games, simulations, 3D graphics, and machine learning algorithms. Discover how algebra and calculus come alive when you see them in code! About the book In Math for Programmers you&’ll explore important mathematical concepts through hands-on coding. Filled with graphics and more than 300 exercises and mini-projects, this book unlocks the door to interesting–and lucrative!–careers in some of today&’s hottest fields. As you tackle the basics of linear algebra, calculus, and machine learning, you&’ll master the key Python libraries used to turn them into real-world software applications. What's inside Vector geometry for computer graphics Matrices and linear transformations Core concepts from calculus Simulation and optimization Image and audio processing Machine learning algorithms for regression and classification About the reader For programmers with basic skills in algebra. About the author Paul Orland is a programmer, software entrepreneur, and math enthusiast. He is co-founder of Tachyus, a start-up building predictive analytics software for the energy industry. You can find him online at www.paulor.land. Table of Contents 1 Learning math with code PART I - VECTORS AND GRAPHICS 2 Drawing with 2D vectors 3 Ascending to the 3D world 4 Transforming vectors and graphics 5 Computing transformations with matrices 6 Generalizing to higher dimensions 7 Solving systems of linear equations PART 2 - CALCULUS AND PHYSICAL SIMULATION 8 Understanding rates of change 9 Simulating moving objects 10 Working with symbolic expressions 11 Simulating force fields 12 Optimizing a physical system 13 Analyzing sound waves with a Fourier series PART 3 - MACHINE LEARNING APPLICATIONS 14 Fitting functions to data 15 Classifying data with logistic regression 16 Training neural networks
Math for Programming
by Ronald T. KneuselA one-stop-shop for all the math you should have learned for your programming career.Every great programming challenge has mathematical principles at its heart. Whether you&’re optimizing search algorithms, building physics engines for games, or training neural networks, success depends on your grasp of core mathematical concepts. In Math for Programming, you&’ll master the essential mathematics that will take you from basic coding to serious software development. You&’ll discover how vectors and matrices give you the power to handle complex data, how calculus drives optimization and machine learning, and how graph theory leads to advanced search algorithms.Through clear explanations and practical examples, you&’ll learn to:Harness linear algebra to manipulate data with unprecedented efficiencyApply calculus concepts to optimize algorithms and drive simulationsUse probability and statistics to model uncertainty and analyze dataMaster the discrete mathematics that powers modern data structuresSolve dynamic problems through differential equationsWhether you&’re seeking to fill gaps in your mathematical foundation or looking to refresh your understanding of core concepts, Math for Programming will turn complex math into a practical tool you&’ll use every day.
Math for Security: From Graphs and Geometry to Spatial Analysis
by Daniel ReillyUse applied math to map fire stations, develop facial recognition software, solve the art gallery problem and more in this hands-on, real-world infosec book.Explore the intersection of mathematics and computer security with this engaging and accessible guide.Math for Security will equip you with essential tools to tackle complex security problems head on. All you need are some basic programming skills. Once you&’ve set up your development environment and reviewed the necessary Python syntax and math notation in the early chapters, you&’ll dive deep into practical applications, leveraging the power of math to analyze networks, optimize resource distribution, and much more. In the book&’s final chapters, you&’ll take your projects from proof of concepts to viable applications and explore options for delivering them to end users.As you work through various security scenarios, you&’ll:Employ packet analysis and graph theory to detect data exfiltration attempts in a networkPredict potential targets and find weaknesses in social networks with Monte Carlo simulationsUse basic geometry and OpenCell data to triangulate a phone&’s location without GPSApply computational geometry to Voronoi diagrams for use in emergency service planningTrain a facial recognition system with machine learning for real-time identity verificationUse spatial analysis to distribute physical security features effectively in an art galleryWhether you&’re an aspiring security professional, a social network analyst, or an innovator seeking to create cutting-edge security solutions, this book will empower you to solve complex problems with precision and confidence. Embrace the intricate world of math as your secret weapon in computer security!Covers Python 3.x
Mathematica Cookbook: Building Blocks for Science, Engineering, Finance, Music, and More
by Sal ManganoMathematica Cookbook helps you master the application's core principles by walking you through real-world problems. Ideal for browsing, this book includes recipes for working with numerics, data structures, algebraic equations, calculus, and statistics. You'll also venture into exotic territory with recipes for data visualization using 2D and 3D graphic tools, image processing, and music.Although Mathematica 7 is a highly advanced computational platform, the recipes in this book make it accessible to everyone -- whether you're working on high school algebra, simple graphs, PhD-level computation, financial analysis, or advanced engineering models.Learn how to use Mathematica at a higher level with functional programming and pattern matchingDelve into the rich library of functions for string and structured text manipulationLearn how to apply the tools to physics and engineering problemsDraw on Mathematica's access to physics, chemistry, and biology dataGet techniques for solving equations in computational financeLearn how to use Mathematica for sophisticated image processingProcess music and audio as musical notes, analog waveforms, or digital sound samples
Mathematica Data Visualization
by Nazmus SaquibIf you are planning to create data analysis and visualization tools in the context of science, engineering, economics, or social science, then this book is for you. With this book, you will become a visualization expert, in a short time, using Mathematica.
Mathematica for Bioinformatics: A Wolfram Language Approach To Omics
by George MiasThis book offers a comprehensive introduction to using Mathematica and the Wolfram Language for Bioinformatics. The chapters build gradually from basic concepts and the introduction of the Wolfram Language and coding paradigms in Mathematica, to detailed worked examples derived from typical research applications using Wolfram Language code. The coding examples range from basic sequence analysis, accessing genomic databases, differential gene expression, and machine learning implementations to time series analysis of longitudinal omics experiments, multi-omics integration and building dynamic interactive bioinformatics tools using the Wolfram Language. The topics address the daily bioinformatics needs of a broad audience: experimental users looking to understand and visualize their data, beginner bioinformaticians acquiring coding expertise in providing biological research solutions, and practicing expert bioinformaticians working on omics who wish to expand their toolset to include the Wolfram Language.
Mathematical Adventures in Performance Analysis
by Eitan Bachmat This book describes problems in the field of performance analysis, primarily the study of storage systems and the diverse mathematical techniques that are required for solving them. Topics covered include best practices for scheduling I/O requests to a disk drive, how this problem is related to airplane boarding, and how both problems can be modeled using space-time geometry. Also provided is an explanation of how Riemann's proof of the analytic continuation and functional equation of the Riemann zeta function can be used to analyze express line queues in a minimarket. Overall, the book displays the surprising relevance of abstract mathematics that is not usually associated with applied mathematics topics. Advanced undergraduate students or graduate students with an interest in the applications of mathematics will find this book to be a useful resource. It will also be of interest to professional mathematicians who want exposure to the surprising ways that theoretical mathematics may be applied to engineering problems. To encourage further study, each chapter ends with notes pointing to various related topics that the reader may want pursue. This mathematically rigorous work was noted in the news section of the journal Nature, and in popular media such as New Scientist, The Wall Street Journal, The Guardian, and USA Today.
Mathematical Analysis II: ICRAPAM 2018, New Delhi, India, October 23–25 (Springer Proceedings in Mathematics & Statistics #307)
by Vijay Gupta P. N. Agrawal Ana Maria Acu Naokant DeoThis book collects original research papers and survey articles presented at the International Conference on Recent Advances in Pure and Applied Mathematics (ICRAPAM), held at Delhi Technological University, India, on 23–25 October 2018. Divided into two volumes, it discusses major topics in mathematical analysis and its applications, and demonstrates the versatility and inherent beauty of analysis. It also shows the use of analytical techniques to solve problems and, wherever possible, derive their numerical solutions. This volume addresses major topics, such as multi-objective optimization problems, impulsive differential equations, mathematical modelling, fuzzy mathematics, graph theory, and coding theory. It is a valuable resource to students as well as researchers in mathematical sciences.
Mathematical Analysis and Numerical Methods: IACMC 2023, Zarqa, Jordan, May 10–12 (Springer Proceedings in Mathematics & Statistics #466)
by Kai Diethelm Dia Zeidan Aliaa Burqan Juan C. Cortés Ahmad Qazza Rania Saadeh Osama Yusuf AbabnehThis book presents a thoughtful compilation of chapters derived from the proceedings of the 8th International Arab Conference on Mathematics and Computations (IACMC 2023), held at Zarqa University in Zarqa, Jordan, from 10–12 May 2023. Encompassing a broad spectrum of themes crucial to contemporary research and development, the book delved into subjects ranging from partial and differential equations to fractional calculus, from probability and statistics to graph theory, and from approximation theory to nonlinear dynamics. Moreover, it explores pivotal areas such as numerical analysis and methods, as well as fostering interdisciplinary mathematical research initiatives. Building upon the legacy of its predecessors, IACMC 2023 served as a premier platform for scholars, researchers and industry professionals to converge and exchange insights on a myriad of cutting-edge advancements and practical applications within the realm of mathematical sciences. This volume encapsulates the essence of IACMC 2023, offering readers a comprehensive overview of the latest breakthroughs and trends in mathematical sciences while serving as a testament to the collaborative spirit and intellectual vigor that define this esteemed conference series.
Mathematical Analysis of Continuum Mechanics and Industrial Applications III: Proceedings of the International Conference CoMFoS18 (Mathematics for Industry #34)
by Masato Kimura Hiromichi Itou Shiro Hirano Victor A. Kovtunenko Alexandr M. KhludnevThis book focuses on mathematical theory and numerical simulation related to various areas of continuum mechanics, such as fracture mechanics, (visco)elasticity, optimal shape design, modelling of earthquakes and Tsunami waves, material structure, interface dynamics and complex systems. Written by leading researchers from the fields of applied mathematics, physics, seismology, engineering, and industry with an extensive knowledge of mathematical analysis, it helps readers understand how mathematical theory can be applied to various phenomena, and conversely, how to formulate actual phenomena as mathematical problems. This book is the sequel to the proceedings of the International Conference of Continuum Mechanics Focusing on Singularities (CoMFoS) 15 and CoMFoS16.
Mathematical Approaches to Polymer Sequence Analysis and Related Problems
by Renato BruniAn edited volume describing the latest developments in approaching the problem of polymer sequence analysis, with special emphasis on the most relevant biopolymers (peptides and DNA) but not limited to them. The chapters will include peptide sequence analysis, DNA sequence analysis, analysis of biopolymers and nonpolymers, sequence alignment problems, and more.
Mathematical Aspects of Computer and Information Sciences: 8th International Conference, MACIS 2019, Gebze, Turkey, November 13–15, 2019, Revised Selected Papers (Lecture Notes in Computer Science #11989)
by Daniel Slamanig Elias Tsigaridas Zafeirakis ZafeirakopoulosThis book constitutes the refereed proceedings of the 8th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2019, held in Gebze, Turkey, in November 2019. The 22 revised papers and 14 short papers presented were carefully reviewed and selected from 66 submissions. The papers are organized in the following topical sections: algorithms and foundation; security and cryptography; combinatorics, codes, designs and graphs; data modeling and machine learning; tools and software track.
Mathematical Aspects of Logic Programming Semantics
by Pascal Hitzler Anthony SedaCovering the authors' own state-of-the-art research results, this book presents a rigorous, modern account of the mathematical methods and tools required for the semantic analysis of logic programs. It significantly extends the tools and methods from traditional order theory to include nonconventional methods from mathematical analysis that depend on topology, domain theory, generalized distance functions, and associated fixed-point theory. The authors closely examine the interrelationships between various semantics as well as the integration of logic programming and connectionist systems/neural networks.
Mathematical Aspects of Network Routing Optimization
by Panos M. Pardalos Carlos A.S. OliveiraBefore the appearance of broadband links and wireless systems, networks have been used to connect people in new ways. Now, the modern world is connected through large-scale, computational networked systems such as the Internet. Because of the ever-advancing technology of networking, efficient algorithms have become increasingly necessary to solve some of the problems developing in this area. "Mathematical Aspects of Network Routing Optimization" focuses on computational issues arising from the process of optimizing network routes, such as quality of the resulting links and their reliability. Algorithms are a cornerstone for the understanding of the protocols underlying multicast routing. The main objective in the text is to derive efficient algorithms, with or without guarantee of approximation. Notes have been provided for basic topics such as graph theory and linear programming to assist those who are not fully acquainted with the mathematical topics presented throughout the book. "Mathematical Aspects of Network Routing Optimization" provides a thorough introduction to the subject of algorithms for network routing, and focuses especially on multicast and wireless ad hoc systems. This book is designed for graduate students, researchers, and professionals interested in understanding the algorithmic and mathematical ideas behind routing in computer networks. It is suitable for advanced undergraduate students, graduate students, and researchers in the area of network algorithms.
Mathematical Control and Numerical Applications: JANO13, Khouribga, Morocco, February 22–24, 2021 (Springer Proceedings in Mathematics & Statistics #372)
by Abdeljalil Nachaoui Abdelilah Hakim Amine LaghribThis book presents some sufficient mathematical content with expressive result. The aim of JANO13 is to bring together scientists to discuss their research in all the aspects of mathematics and their applications to different scientific discipline. The main topics of the conference is partial differential equations, mathematical control, numerical analysis and computer science. The conference is interested in recent developments on numerical analysis and real applications in computer science. The latter is viewed as a dynamic branch on the interface of mathematics and informatics that has been growing rapidly over the past several decades. However, its mathematical modelling and interpretation are still not well-explained and need much more clarifications. The main contributions of this book are to give some sufficient mathematical content with expressive results. As a growing field, it is gaining a lot of attention both in media and in the industry world, which will attract the interest of readers from different scientist disciplines.
Mathematical Entity Linking Methods and Applications
by Philipp ScharpfThis research book explores the adaptation of traditional Entity Linking techniques to Mathematical Entity Linking (MathEL) for STEM disciplines, addressing the limitations of current Information Retrieval methods in handling mathematical expressions. By developing and evaluating novel MathEL approaches using AI, Machine Learning, and the Wikidata Knowledge Graph, significant progress is achieved in areas such as Formula Concept recognition, semantic formula search, mathematical question answering, physics exam question generation, and STEM document classification. The study also introduces a suite of open-source Wikimedia MathEL tools, including AnnoMathTeX, MathQA, and PhysWikiQuiz, designed to advance Mathematical Information Retrieval and support innovative applications in academic and educational contexts.
Mathematical Foundations for Side-Channel Analysis of Cryptographic Systems
by Sylvain Guilley Wei Cheng Olivier RioulThis book offers the reader a formalization, characterization and quantification of the real threat level posed by side-channel leaks from devices implementing cryptography. It exploits the best mathematical tools for quantifying information leakage and characterizing leakage-based attacks. The two possible approaches are described in detail. This includes the optimal attack strategy that can be derived (in specific contexts) or generic bounds regarding data complexity that can be computed. The tone of this book is essentially mathematical. It aims to establish formal foundations for techniques that are otherwise used as engineering recipes in industrial laboratories or empirical intuitions for deriving security levels from practical implementations. It is a systematization of knowledge and a compilation of relevant tools relating to the practice of side-channel analysis on embedded systems. This book provides an up-to-date and improved analysis and understanding of embedded devices that conceal secrets that can be extracted by an attacker. Typical attacks involve measuring the device's power consumption or radiated electromagnetic field. As a source of noisy information, this correlates it with secrets and enabling these secrets to be retrieved. The attacker in some cases, can purchase a blank device from the same series and learn about its leakage, particularly how it relates to the secrets. This book also covers how such information can enhance hardware attacks deployed on another device. Researchers and engineers working in the field of side-channel security for embedded systems and related countermeasures as well as hardware and software engineers focused on implementing cryptographic functionalities will want to purchase this book as a reference. Advanced-level students majoring in computer science and electrical engineering will find this book valuable as a secondary textbook.
Mathematical Foundations for Signal Processing, Communications, and Networking
by Erchin Serpedin, Thomas Chen and Dinesh RajanMathematical Foundations for Signal Processing, Communications, and Networking describes mathematical concepts and results important in the design, analysis, and optimization of signal processing algorithms, modern communication systems, and networks. Helping readers master key techniques and comprehend the current research literature, the book offers a comprehensive overview of methods and applications from linear algebra, numerical analysis, statistics, probability, stochastic processes, and optimization. From basic transforms to Monte Carlo simulation to linear programming, the text covers a broad range of mathematical techniques essential to understanding the concepts and results in signal processing, telecommunications, and networking. Along with discussing mathematical theory, each self-contained chapter presents examples that illustrate the use of various mathematical concepts to solve different applications. Each chapter also includes a set of homework exercises and readings for additional study. This text helps readers understand fundamental and advanced results as well as recent research trends in the interrelated fields of signal processing, telecommunications, and networking. It provides all the necessary mathematical background to prepare students for more advanced courses and train specialists working in these areas.
Mathematical Foundations of Big Data Analytics
by David Müller Vladimir ShikhmanIn this textbook, basic mathematical models used in Big Data Analytics are presented and application-oriented references to relevant practical issues are made. Necessary mathematical tools are examined and applied to current problems of data analysis, such as brand loyalty, portfolio selection, credit investigation, quality control, product clustering, asset pricing etc. – mainly in an economic context. In addition, we discuss interdisciplinary applications to biology, linguistics, sociology, electrical engineering, computer science and artificial intelligence. For the models, we make use of a wide range of mathematics – from basic disciplines of numerical linear algebra, statistics and optimization to more specialized game, graph and even complexity theories. By doing so, we cover all relevant techniques commonly used in Big Data Analytics.Each chapter starts with a concrete practical problem whose primary aim is to motivate the study of a particular Big Data Analytics technique. Next, mathematical results follow – including important definitions, auxiliary statements and conclusions arising. Case-studies help to deepen the acquired knowledge by applying it in an interdisciplinary context. Exercises serve to improve understanding of the underlying theory. Complete solutions for exercises can be consulted by the interested reader at the end of the textbook; for some which have to be solved numerically, we provide descriptions of algorithms in Python code as supplementary material.This textbook has been recommended and developed for university courses in Germany, Austria and Switzerland.
Mathematical Foundations of Computer Science
by Ashwin LallMathematical Foundations of Computer Science introduces students to the discrete mathematics needed later in their Computer Science coursework with theory of computation topics interleaved throughout. Students learn about mathematical concepts just in time to apply them to theory of computation ideas. For instance, sets motivate the study of finite automata, direct proof is practised using closure properties, induction is used to prove the language of an automaton, and contradiction is used to apply the pumping lemma. The main content of the book starts with primitive data types such as sets and strings and ends with showing the undecidability of the halting problem. There are also appendix chapters on combinatorics, probability, elementary number theory, asymptotic notation, graphs, loop invariants, and recurrences. The content is laid out concisely with a heavy reliance on worked examples, of which there are over 250 in the book. Each chapter has exercises, totalling 550. This class-tested textbook is targeted to intermediate Computer Science majors, and it is primarily intended for a discrete math / proofs course in a Computer Science major. It is also suitable for introductory theory of computation courses.The authors hope this book breeds curiosity into the subject and is designed to satisfy this to some extent by reading this book. The book will prepare readers for deeper study of game theory applications in many fields of study.
Mathematical Foundations of Computer Science
by Bhavanari Satyanarayana T.V. Pradeep Kumar Shak Mohiddin ShawPlease note: Taylor & Francis does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka
Mathematical Foundations of Nature-Inspired Algorithms (SpringerBriefs in Optimization)
by Xin-She Yang Xing-Shi HeThis book presents a systematic approach to analyze nature-inspired algorithms. Beginning with an introduction to optimization methods and algorithms, this book moves on to provide a unified framework of mathematical analysis for convergence and stability. Specific nature-inspired algorithms include: swarm intelligence, ant colony optimization, particle swarm optimization, bee-inspired algorithms, bat algorithm, firefly algorithm, and cuckoo search. Algorithms are analyzed from a wide spectrum of theories and frameworks to offer insight to the main characteristics of algorithms and understand how and why they work for solving optimization problems. In-depth mathematical analyses are carried out for different perspectives, including complexity theory, fixed point theory, dynamical systems, self-organization, Bayesian framework, Markov chain framework, filter theory, statistical learning, and statistical measures. Students and researchers in optimization, operations research, artificial intelligence, data mining, machine learning, computer science, and management sciences will see the pros and cons of a variety of algorithms through detailed examples and a comparison of algorithms.
Mathematical Foundations of Software Engineering: A Practical Guide to Essentials (Texts in Computer Science)
by Gerard O'ReganThis textbook presents an introduction to the mathematical foundations of software engineering. It presents the rich applications of mathematics in areas such as error-correcting codes, cryptography, the safety and security critical fields, the banking and insurance fields, as well as traditional engineering applications. Topics and features: Addresses core mathematics for critical thinking and problem solving Discusses propositional and predicate logic and various proof techniques to demonstrate the correctness of a logical argument. Examines number theory and its applications to cryptography Considers the underlying mathematics of error-correcting codes Discusses graph theory and its applications to modelling networks Reviews tools to support software engineering mathematics, including automated and interactive theorem provers and model checking Discusses financial software engineering, including simple and compound interest, probability and statistics, and operations research Discusses software reliability and dependability and explains formal methods used to derive a program from its specification Discusses calculus, matrices, vectors, complex numbers, and quaternions, as well as applications to graphics and robotics Includes key learning topics, summaries, and review questions in each chapter, together with a useful glossary This practical and easy-to-follow textbook/reference is ideal for computer science students seeking to learn how mathematics can assist them in building high-quality and reliable software on time and on budget. The text also serves as an excellent self-study primer for software engineers, quality professionals, and software managers.
Mathematical Foundations of System Safety Engineering: A Road Map for the Future
by Richard R. ZitoThis graduate-level textbook elucidates low-risk and fail-safe systems in mathematical detail. It addresses, in particular, problems where mission-critical performance is paramount, such as in aircraft, missiles, nuclear reactors and weapons, submarines, and many other types of systems where “failure” can result in overwhelming loss of life and property. The book is divided into four parts: Fundamentals, Electronics, Software, and Dangerous Goods. The first part on Fundamentals addresses general concepts of system safety engineering that are applicable to any type of system. The second part, Electronics, addresses the detection and correction of electronic hazards. In particular, the Bent Pin Problem, Sneak Circuit Problem, and related electrical problems are discussed with mathematical precision. The third part on Software addresses predicting software failure rates as well as detecting and correcting deep software logical flaws (called defects). The fourth part on Dangerous Goods presents solutions to three typical industrial chemical problems faced by the system safety engineer during the design, storage, and disposal phases of a dangerous goods’ life cycle.