Science of Learning Mathematical Proofs, The: An Introductory Course
College students struggle with the switch from thinking of mathematics as a calculation based subject to a problem solving based subject. This book describes how the introduction to proofs course can be taught in a way that gently introduces students to this new way of thinking. This introduction utilizes recent research in neuroscience regarding how the brain learns best. Rather than jumping right into proofs, students are first taught how to change their mindset about learning, how to persevere through difficult problems, how to work successfully in a group, and how to reflect on their learning. With these tools in place, students then learn logic and problem solving as a further foundation.Next various proof techniques such as direct proofs, proof by contraposition, proof by contradiction, and mathematical induction are introduced. These proof techniques are introduced using the context of number theory. The last chapter uses Calculus as a way for students to apply the proof techniques they have learned.
Reliability Analysis and Plans for Successive Testing
Reliability Analysis and Plans for Successive Testing: Start-up Demonstration Tests and Applications discusses all past and recent developments on start-up demonstration tests in the context of current numerical and illustrative examples to clarify available methods for distribution theorists and applied mathematicians dealing with control problems. Throughout the book, the authors focus on the panorama of open problems and issues of further interest. As contemporary manufacturers face tremendous commercial pressures to assemble works of high reliability, defined as 'the probability of the product performing its role under the stated conditions and over a specified period of time', this book helps address testing issues.
Au Bonheur des Maths
Cette m矇thode fait d矇couvrir et utiliser, mentalement ou par 矇crit, les proc矇d矇s de calculs les mieux adapt矇s aux nombres 矇tudi矇s et aux op矇rations ? effectuer, et parmi ces proc矇d矇s figurent les techniques op矇ratoires usuelles. Le but de cet ouvrage est de fournir ? l'矇l癡ve qui est difficult矇 scolaire des outils d'appropriation et de structuration du savoir. L'organisation tr癡s structur矇e de cette m矇thode permet de prendre en compte les difficult矇s des 矇l癡ves en leur proposant des sch矇mas de progressions en rapport avec le socle commun de connaissances de comp矇tences et de culture. Les exercices sont programm矇s par l'enseignant au fur et ? mesure des points abord矇s en classe.
Introduction to Logic
This classic undergraduate treatment examines the deductive method in its first part and explores applications of logic and methodology in constructing mathematical theories in its second part. Exercises appear throughout.Alfred Tarski, one of the greatest logicians of all time, is widely thought of as 'the man who defined truth'. His work on the concepts of truth and logical consequence as defined by mathematical theory are cornerstones of modern logic, influencing developments in mathematics, philosophy, linguistics, and computer science. His teaching on logic and mathematics culminated in the 1941 classic INTRODUCTION TO LOGIC, which uses the method of deduction and explores logic and methodology as it pertains to creating mathematical theories.
The Impact of Scale on Children’s Spatial Thought
In this book, Cathleen Heil addresses the question of how to conceptually understand children's spatial thought in the context of geometry education. She proposes that in order to help children develop their abilities to successfully grasp and manipulate the spatial relations they experience in their everyday lives, spatial thought should not only be addressed in written or tabletop settings at school. Instead, geometry education should also focus on settings involving real space, such as during reasoning with maps.In a first part of this book, she theoretically addresses the construct of spatial thought at different scales of space from a cognitive psychological point of view and shows that maps can be rich sources for spatial thinking. In a second part, she proposes how to measure children's spatial thought in a paper-and-pencil setting and map-based setting in real space. In a third, empirical part, she examines the relations between children's spatialthought in those two settings both at a manifest and latent level.
Recent Investigations of Differential and Fractional Equations and Inclusions
weakly upper semicontinuous; essential maps; homotopy; Riemann-Liouville fractional differential equation; delay; lower and upper solutions; monotone-iterative technique; homoclinic solutions; fourth-order p-Laplacian differential equations; minimization theorem; Clark's theorem; exponential dichotomy; roughness; asymptotically constant matrices; double fuzzy Sumudu transform; partial Volterra fuzzy integro-differential equations; n-th order fuzzy partial H-derivative; m-dissipative operators; limit solutions; integral solutions; one-sided Perron condition; Banach spaces; fixed point; complete metric space; fractional differential equations; optimal feedback control; Voigt model; alpha-model; fractional derivative; Riemann-Liouville fractional differential equations; nonlocal boundary conditions; positive solutions; existence; multiplicity; Caputo derivative; Riemann-Liouville integral; multipoint and sub-strip boundary conditions; existence; fixed point theorem; fractional Navier-Stokes equations; variable delay; modified fractional Halanay inequality; generalized comparison principle; dissipativity; Fourier-Laplace transforms; porous material; eigenvalues method; fractional time derivative
Journal of Applied Logics. The IfCoLog Journal of Logics and their Applications. Volume 8, Issue 2, March 2021. Special issue Assertion and Proof
The Journal of Applied Logics - IfCoLog Journal of Logics and their Applications (FLAP) covers all areas of pure and applied logic, broadly construed. All papers published are open access, and available via the College Publications website. This Journal is open access, and available in both printed and electronic formats. It is published by College Publications, on behalf of IfCoLog (www.ifcolog.net).
Model Theory for Beginners. 15 Lectures
This book presents an introduction to model theory in 15 lectures. It concentrates on several key concepts: first-order definability, classification of complete types, elementary extensions, categoricity, automorphisms, and saturation; all illustrated with examples that require neither advanced alegbra nor set theory. A full proof of the compactness theorem for countable languages and its applications are given, followed by a discussion of the Ehrefeucht-Mostowski technique for constructing models admitting automorphisms. Additional topics include recursive saturation, nonstandard models of arithmetic, Abraham Robinson's model-theoretic proof of Tarski's theorem on undefinability of truth, and the proof of the Infinite Ramsey Theorem using an elementary extension of the standard model of arithmetic.
Conformable Dynamic Equations on Time Scales
This book is devoted to the qualitative theory of conformable dynamic eqs. on time scales and summarizes the most recent contributions in this area, and vastly expands on them to conceive of a comprehensive theory developed exclusively for this book.
A Gentle Introduction to Homological Mirror Symmetry
Homological mirror symmetry has its origins in theoretical physics but is now of great interest in mathematics due to the deep connections it reveals between different areas of geometry and algebra. This book offers a self-contained and accessible introduction to the subject via the representation theory of algebras and quivers. It is suitable for graduate students and others without a great deal of background in homological algebra and modern geometry. Each part offers a different perspective on homological mirror symmetry. Part I introduces the A-infinity formalism and offers a glimpse of mirror symmetry using representations of quivers. Part II discusses various A- and B-models in mirror symmetry and their connections through toric and tropical geometry. Part III deals with mirror symmetry for Riemann surfaces. The main mathematical ideas are illustrated by means of simple examples coming mainly from the theory of surfaces, helping the reader connect theory with intuition.
Lectures on Random Lozenge Tilings
Over the past 25 years, there has been an explosion of interest in the area of random tilings. The first book devoted to the topic, this timely text describes the mathematical theory of tilings. It starts from the most basic questions (which planar domains are tileable?), before discussing advanced topics about the local structure of very large random tessellations. The author explains each feature of random tilings of large domains, discussing several different points of view and leading on to open problems in the field. The book is based on upper-division courses taught to a variety of students but it also serves as a self-contained introduction to the subject. Test your understanding with the exercises provided and discover connections to a wide variety of research areas in mathematics, theoretical physics, and computer science, such as conformal invariance, determinantal point processes, Gibbs measures, high-dimensional random sampling, symmetric functions, and variational problems.
The Semantic Conception of Logic
This collection of new essays presents cutting-edge research on the semantic conception of logic, the invariance criteria of logicality, grammaticality, and logical truth. Contributors explore the history of the semantic tradition, starting with Tarski, and its historical applications, while central criticisms of the tradition, and especially the use of invariance criteria to explain logicality, are revisited by the original participants in that debate. Other essays discuss more recent criticism of the approach, and researchers from mathematics and linguistics weigh in on the role of the semantic tradition in their disciplines. This book will be invaluable to philosophers and logicians alike.
A Gentle Introduction to Homological Mirror Symmetry
Homological mirror symmetry has its origins in theoretical physics but is now of great interest in mathematics due to the deep connections it reveals between different areas of geometry and algebra. This book offers a self-contained and accessible introduction to the subject via the representation theory of algebras and quivers. It is suitable for graduate students and others without a great deal of background in homological algebra and modern geometry. Each part offers a different perspective on homological mirror symmetry. Part I introduces the A-infinity formalism and offers a glimpse of mirror symmetry using representations of quivers. Part II discusses various A- and B-models in mirror symmetry and their connections through toric and tropical geometry. Part III deals with mirror symmetry for Riemann surfaces. The main mathematical ideas are illustrated by means of simple examples coming mainly from the theory of surfaces, helping the reader connect theory with intuition.
An Illustrative Guide to Multivariable and Vector Calculus
This textbook focuses on one of the most valuable skills in multivariable and vector calculus: visualization. With over one hundred carefully drawn color images, students who have long struggled picturing, for example, level sets or vector fields will find these abstract concepts rendered with clarity and ingenuity. This illustrative approach to the material covered in standard multivariable and vector calculus textbooks will serve as a much-needed and highly useful companion. Emphasizing portability, this book is an ideal complement to other references in the area. It begins by exploring preliminary ideas such as vector algebra, sets, and coordinate systems, before moving into the core areas of multivariable differentiation and integration, and vector calculus. Sections on the chain rule for second derivatives, implicit functions, PDEs, and the method of least squares offer additional depth; ample illustrations are woven throughout. Mastery Checks engage students in material on the spot, while longer exercise sets at the end of each chapter reinforce techniques. An Illustrative Guide to Multivariable and Vector Calculus will appeal to multivariable and vector calculus students and instructors around the world who seek an accessible, visual approach to this subject. Higher-level students, called upon to apply these concepts across science and engineering, will also find this a valuable and concise resource.
An Introduction to Symbolic Dynamics and Coding
Symbolic dynamics is a mature yet rapidly developing area of dynamical systems. It has established strong connections with many areas, including linear algebra, graph theory, probability, group theory, and the theory of computation, as well as data storage, statistical mechanics, and $C^*$-algebras. This Second Edition maintains the introductory character of the original 1995 edition as a general textbook on symbolic dynamics and its applications to coding. It is written at an elementary level and aimed at students, well-established researchers, and experts in mathematics, electrical engineering, and computer science. Topics are carefully developed and motivated with many illustrative examples. There are more than 500 exercises to test the reader's understanding. In addition to a chapter in the First Edition on advanced topics and a comprehensive bibliography, the Second Edition includes a detailed Addendum, with companion bibliography, describing major developments and new research directions since publication of the First Edition.
A Mathematician’s Apology
A Mathematician's Apology is the famous essay by British mathematician G. H. Hardy. It concerns the aesthetics of mathematics with some personal content, and gives the layman an insight into the mind of a working mathematician. Indeed, this book is often considered one of the best insights into the mind of a working mathematician written for the layman.A Mathematician's Apology is the famous essay by British mathematician G. H. Hardy. It concerns the aesthetics of mathematics with some personal content, and gives the layman an insight into the mind of a working mathematician. Indeed, this book is often considered one of the best insights into the mind of a working mathematician written for the layman.
Kundalini Awakening
Kundalini Awakening will give you all of the insight you need to awaken your Kundalini energy, balance it, and explore life post-awakening. In this comprehensive guide, you'll discover important insight on the background of Kundalini energy, including where it began and what it's referencing. You'll also receive valuable advice from Kundalini Gurus and Masters, tips on how you can awaken Kundalini further, and practices you should use to invoke your awakening...This book is designed to support you in your entire Kundalini lifestyle change. If you're ready to come home to your true nature and experience life in its entirety, this book will provide you with all of the information and support you need to get there...In this book you'll learn: Spiritual AwakeningThe science of the Third EyeAstral ProjectionVibrational EnergiesMastering Our MindsAchieving Peace of MindUnderstanding of KundaliniReiki HealingCleansing of the Auric FieldPositive and Negative Effects of Our EnvironmentsThe Meaning of ChiThe Power of KundaliniThe Ability to Achieve Inner PeaceGrounding Our Vibrational WavesImportance of Human TrialKnowledge of Various MudraThe Healing Power of MantrasHistory of the Sikh GurusLevels of the Astral PlaneAnimal Teachings and HealingThe Power of Healing PlantsResidual EnergiesAll Spiritual Planes and DimensionsCommunication with Spiritual GuidesFocusing on Our Vibrational EnergiesAnd So Much More!This book will change your life and free yourself from negative energies. NOW is the time to make a change and live a happier life!Grab your copy of Kundalini Awakening now!
Kundalini Awakening
Kundalini Awakening is the complete comprehensive guide that will teach you how to unleash your psychic abilities, intuition, clairvoyance, and awaken your Kundalini. If you've been searching for the right guide that can enrich your spirituality and psychic senses, then this book is for you. This book unveils the secrets that will allow you to create positive changes in your life...In this book you'll learn: What Kundalini isHow to awaken your KundaliniThe effects of Kundalini activationPrana and how to control itChakra awakening and Chakra healingHow to sense energyThe 4 elementsEnhance your psychic abilitiesAstral travelMeet your spirit guideHow to see aurasHow to raise your vibrationBest practicesA step-by-step guide to masteryDifferent terminologies and their meaningsAnd so much more!What's discussed in each chapter: - Chapter 1 discusses what the Kundalini is, as well as how you can tap and awaken its incredible power.- Chapter 2 teaches the nature of prana, which is the energy that pervades everything.- Chapter 3 explains the different main chakras of the body.- Chapter 4 talks about meditation and lays down guidelines on how to do meditation properly.- Chapter 5 teaches how to direct or control prana or energy.- Chapter 6 talks about the intuition, as well as how you can develop it.- Chapter 7 is a discussion on the 4 elements.- Chapter 8 teaches the ways on how you can heal your chakras.- Chapter 9 is about the different psychic abilities.- Chapter 10 teaches how you can develop your psychic abilities.- Chapter 11 talks about psychic games that you can play to help develop your psychic powers.- Chapter 12 is a discussion about the aura, as well as how you can see auras.- Chapter 13 is about vibration, as well as how you can raise your vibration.- Chapter 14 shares 5-minute meditation sessions that you can do to relax, relieve stress, and awaken your psychic senses.- Chapter 15 teaches 30-minute meditation sessions that can take you to deeper levels of consciousness and places of power.- Chapter 16 talks about the incredible power of the mind.- Chapter 17 is a discussion on enlightenment.- Chapter 18 lays down the best practices for success in your spiritual journey.- Chapter 19 is an actual step-by-step guide from beginner to mastery. - Chapter 20 defines the different terminologies related to the awakening of the Kundalini, psychic powers, enlightenment, and spirituality.This book will change your life and free yourself from negative energies. NOW is the time to make a change and live a happier life!Grab your copy of Kundalini Awakening now!
Kundalini Awakening
Kundalini Awakening is the ultimate guide that will teach you how to unlock your hidden powers and live a more meaningful life. For years, this ancient knowledge has been kept a secret. It is now time to unveil the techniques and practices that will unleash your true power...In this book you'll learn: The basics of Kundalini AwakeningThe 7 main Chakras of the bodyPrana and how to control itThe 4 mighty elements and their qualitiesThe AkashaMeditation guidelinesHow to develop your IntuitionChakra HealingSecret Meditation techniquesEnhance your mind powerAstral travelFastingHow to raise your vibrationHow to see the AuraEnlightenmentBest practicesRoad to masteryAnd So Much More!What's discussed in each chapter: - Chapter 1 is about the basics of Kundalini Awakening. Find out more about this ancient mystery and how you can tap its amazing power.- Chapter 2 talks about the different Chakras of the body. Chakras are energy centers that have many functions and attributes.- Chapter 3 is about prana. Everything in the universe is made of prana. Without prana, life cannot exist. Learn more about this amazing energy.- Chapter 4 discusses the world of the elements and about their attributes and fine qualities, as well as how you can use them to your advantage.- Chapter 5 talks about the akasha. Akasha is that mysterious force from which all the elements come from.- Chapter 6 is about how to practice meditation to enhance your Kundalini experience.- Chapter 7 teaches the secrets of the intuition. Learn how you can use and develop your intuition and connect to a higher power.- Chapter 8 is about chakra healing. Learn how you can heal your chakras naturally and through meditation.- Chapter 9 discusses the different psychic abilities and the proper training that you can do to develop these abilities. - Chapter 10 is about astral travel. Learn how you can separate your spiritual body from your physical body and travel the whole universe.- Chapter 11 teaches how you can connect to your higher-self, also known as the god-self.- Chapter 12 gives 5-minute meditation sessions that are excellent for beginners.- Chapter 13 teaches 30-minute meditation sessions. These are good for those who already have experience in the practice of meditation.- Chapter 14 talks about the aura. Learn how to sense and see auras. - Chapter 15 is about vibration. Learn how you can raise your vibration and be protected from psychic vampires.- Chapter 16 explores the power of the mind. Learn more about your mind and the infinite power that you possess.- Chapter 17 discusses the meaning of true enlightenment and how you can achieve it in your life.- Chapter 18 is about the practice and importance of fasting.- Chapter 19 teaches the best practices to help you succeed in life.- Chapter 20 teaches the road to mastery from a beginner to adept.This book will change your life and free yourself from negative energies. NOW is the time to make a change and live a happier life!Grab your copy of Kundalini Awakening now!
Observations Regarding Non-Prime Odd Numbers
For centuries, mathematicians have been captivated by the mystery of prime numbers. Their effort to decipher that mystery has focused on the most abstract mathematics concepts and techniques known. Yet still they have no answers. Others, frustrated by the nature of earlier attempts, have suggested the primes can be counted by a much simpler method using calculations that involve the numbers that are not prime-identifying and removing them until only prime numbers remain.In Observations Regarding Non-Prime Odd Numbers, New York Times bestselling author Joe Hilley examines non-prime numbers in an attempt to gain clues about the nature of prime numbers, their propagation, and occurrence. Informative, readable, and entertaining, Joe provides clues you won't find anywhere else and surprising insights sure to generate lively debate.
Kundalini Awakening
Kundalini Awakening will give you all of the insight you need to awaken your Kundalini energy, balance it, and explore life post-awakening. In this comprehensive guide, you'll discover important insight on the background of Kundalini energy, including where it began and what it's referencing. You'll also receive valuable advice from Kundalini Gurus and Masters, tips on how you can awaken Kundalini further, and practices you should use to invoke your awakening...This book is designed to support you in your entire Kundalini lifestyle change. If you're ready to come home to your true nature and experience life in its entirety, this book will provide you with all of the information and support you need to get there...In this book you'll learn: Spiritual AwakeningThe science of the Third EyeAstral ProjectionVibrational EnergiesMastering Our MindsAchieving Peace of MindUnderstanding of KundaliniReiki HealingCleansing of the Auric FieldPositive and Negative Effects of Our EnvironmentsThe Meaning of ChiThe Power of KundaliniThe Ability to Achieve Inner PeaceGrounding Our Vibrational WavesImportance of Human TrialKnowledge of Various MudraThe Healing Power of MantrasHistory of the Sikh GurusLevels of the Astral PlaneAnimal Teachings and HealingThe Power of Healing PlantsResidual EnergiesAll Spiritual Planes and DimensionsCommunication with Spiritual GuidesFocusing on Our Vibrational EnergiesAnd So Much More!This book will change your life and free yourself from negative energies. NOW is the time to make a change and live a happier life!Grab your copy of Kundalini Awakening now!
Kundalini Awakening
Kundalini Awakening will teach you everything you need to know about Kundalini, a well-kept secret for centuries. This book will take you on a journey to discover Kundalini, its origins, how to utilize it, how to unlock your psychic powers, how to use your chakras, how to awaken your full potential, how to broaden your mind, and so much more...In this book you'll learn: The basics of KundaliniThe origins of Kundalini YogaThe benefits of practicing KundaliniThe differences between Kundalini and PranaThe relationship between Kundalini and ChiHow Kundalini helps you stay healthyExercises and meditations for KundaliniKundalini Yoga positions for clearing your chakrasThe famous Kundalini gurusThe effects of activating KundaliniHow awakening your Kundalini feels likeHow to develop your psychic senses and learn how to move and manipulate energyAnd So Much More!This book is an uplifting blend of Kundalini practices and meditation, geared towards both the spiritual and physical aspects of this sacred practice. It features mantras and dynamic breathing techniques to help you clear blockages and cleanse your chakras towards your growth in Kundalini...This book also explores the foundations and history of Kundalini in order to provide you with a better understanding of this ancient practice, the Gurus who brought Kundalini to the world as well as some fundamental information on the what, how, and why of Kundalini. As you go on reading this book, you will also find concluding meditations at the end of selected chapters. These meditations help you engage and immerse yourself with the readings you have done for each chapter. Last but not least, this book explores an important aspect of meditation: mindfulness. The chapters dedicated to mindfulness are towards the end to help you practice better meditation skills, employing traditional poses with Kundalini and the importance of mindfulness in meditation...This book will change your life and free yourself from negative energies. NOW is the time to make a change and live a happier life!Grab your copy of Kundalini Awakening now!
Kundalini Awakening
Kundalini Awakening is the #1 guide that will help you unleash your potential and unlock your full power through guided meditation techniques. What was once a guarded secret is now revealed in this book. Now, you too can use these secret techniques!Learn about Kundalini, Chakras, Prana, and more and how to use them to realize your higher capabilities. If your goals are to enrich your spirituality and enhance your mind and psychic abilities -- maybe even gain enlightenment -- then this book will guide you toward them...Kundalini Awakening will help you connect with your Divine Purpose within and spark the uncoiling of Kundalini. These things will all be taught by going back to the very basics to when and how Kundalini Yoga & Meditation was originally created, which is one of the main goals of Kundalini Awakening. It is my hope that the knowledge within this book will help you begin this grand move forward in harnessing your psychic abilities and achieving a better peace of mind...In this book you'll learn: Spiritual AwakeningThe science of the Third EyeAstral ProjectionVibrational EnergiesMastering Your MindAchieving Peace of MindUnderstanding of KundaliniKnowledge of Various MudraThe Healing Power of MantrasHistory of the Sikh GurusLevels of the Astral PlaneThe Power of Healing PlantsResidual Energies All Spiritual Planes and DimensionsCommunication with Spiritual GuidesFocusing on Vibrational EnergiesReiki HealingCleansing of the Auric FieldPositive and Negative Effects of Our EnvironmentThe Meaning of ChiThe Power of KundaliniThe Ability to Achieve Inner PeaceGrounding Our Vibrational WavesImportance of Human TrialAnd So Much More!This book will change your life and free yourself from negative energies. NOW is the time to make a change and live a happier life!Grab your copy of Kundalini Awakening now!
Kundalini Awakening
Kundalini Awakening will teach you everything you need to know about Kundalini, a well-kept secret for centuries. This book will take you on a journey to discover Kundalini, its origins, how to utilize it, how to unlock your psychic powers, how to use your chakras, how to awaken your full potential, how to broaden your mind, and so much more...In this book you'll learn: The basics of KundaliniThe origins of Kundalini YogaThe benefits of practicing KundaliniThe differences between Kundalini and PranaThe relationship between Kundalini and ChiHow Kundalini helps you stay healthyExercises and meditations for KundaliniKundalini Yoga positions for clearing your chakrasThe famous Kundalini gurusThe effects of activating KundaliniHow awakening your Kundalini feels likeHow to develop your psychic senses and learn how to move and manipulate energyAnd So Much More!This book is an uplifting blend of Kundalini practices and meditation, geared towards both the spiritual and physical aspects of this sacred practice. It features mantras and dynamic breathing techniques to help you clear blockages and cleanse your chakras towards your growth in Kundalini...This book also explores the foundations and history of Kundalini in order to provide you with a better understanding of this ancient practice, the Gurus who brought Kundalini to the world as well as some fundamental information on the what, how, and why of Kundalini. As you go on reading this book, you will also find concluding meditations at the end of selected chapters. These meditations help you engage and immerse yourself with the readings you have done for each chapter. Last but not least, this book explores an important aspect of meditation: mindfulness. The chapters dedicated to mindfulness are towards the end to help you practice better meditation skills, employing traditional poses with Kundalini and the importance of mindfulness in meditation...This book will change your life and free yourself from negative energies. NOW is the time to make a change and live a happier life!Grab your copy of Kundalini Awakening now!
Kundalini Awakening
Kundalini Awakening is the #1 guide that will help you unleash your potential and unlock your full power through guided meditation techniques. What was once a guarded secret is now revealed in this book. Now, you too can use these secret techniques!Learn about Kundalini, Chakras, Prana, and more and how to use them to realize your higher capabilities. If your goals are to enrich your spirituality and enhance your mind and psychic abilities -- maybe even gain enlightenment -- then this book will guide you toward them...Kundalini Awakening will help you connect with your Divine Purpose within and spark the uncoiling of Kundalini. These things will all be taught by going back to the very basics to when and how Kundalini Yoga & Meditation was originally created, which is one of the main goals of Kundalini Awakening. It is my hope that the knowledge within this book will help you begin this grand move forward in harnessing your psychic abilities and achieving a better peace of mind...In this book you'll learn: Spiritual AwakeningThe science of the Third EyeAstral ProjectionVibrational EnergiesMastering Your MindAchieving Peace of MindUnderstanding of KundaliniKnowledge of Various MudraThe Healing Power of MantrasHistory of the Sikh GurusLevels of the Astral PlaneThe Power of Healing PlantsResidual Energies All Spiritual Planes and DimensionsCommunication with Spiritual GuidesFocusing on Vibrational EnergiesReiki HealingCleansing of the Auric FieldPositive and Negative Effects of Our EnvironmentThe Meaning of ChiThe Power of KundaliniThe Ability to Achieve Inner PeaceGrounding Our Vibrational WavesImportance of Human TrialAnd So Much More!This book will change your life and free yourself from negative energies. NOW is the time to make a change and live a happier life!Grab your copy of Kundalini Awakening now!
Kundalini Awakening
Kundalini Awakening is the complete comprehensive guide that will teach you how to unleash your psychic abilities, intuition, clairvoyance, and awaken your Kundalini. If you've been searching for the right guide that can enrich your spirituality and psychic senses, then this book is for you. This book unveils the secrets that will allow you to create positive changes in your life...In this book you'll learn: What Kundalini isHow to awaken your KundaliniThe effects of Kundalini activationPrana and how to control itChakra awakening and Chakra healingHow to sense energyThe 4 elementsEnhance your psychic abilitiesAstral travelMeet your spirit guideHow to see aurasHow to raise your vibrationBest practicesA step-by-step guide to masteryDifferent terminologies and their meaningsAnd so much more!What's discussed in each chapter: - Chapter 1 discusses what the Kundalini is, as well as how you can tap and awaken its incredible power.- Chapter 2 teaches the nature of prana, which is the energy that pervades everything.- Chapter 3 explains the different main chakras of the body.- Chapter 4 talks about meditation and lays down guidelines on how to do meditation properly.- Chapter 5 teaches how to direct or control prana or energy.- Chapter 6 talks about the intuition, as well as how you can develop it.- Chapter 7 is a discussion on the 4 elements.- Chapter 8 teaches the ways on how you can heal your chakras.- Chapter 9 is about the different psychic abilities.- Chapter 10 teaches how you can develop your psychic abilities.- Chapter 11 talks about psychic games that you can play to help develop your psychic powers.- Chapter 12 is a discussion about the aura, as well as how you can see auras.- Chapter 13 is about vibration, as well as how you can raise your vibration.- Chapter 14 shares 5-minute meditation sessions that you can do to relax, relieve stress, and awaken your psychic senses.- Chapter 15 teaches 30-minute meditation sessions that can take you to deeper levels of consciousness and places of power.- Chapter 16 talks about the incredible power of the mind.- Chapter 17 is a discussion on enlightenment.- Chapter 18 lays down the best practices for success in your spiritual journey.- Chapter 19 is an actual step-by-step guide from beginner to mastery. - Chapter 20 defines the different terminologies related to the awakening of the Kundalini, psychic powers, enlightenment, and spirituality.This book will change your life and free yourself from negative energies. NOW is the time to make a change and live a happier life!Grab your copy of Kundalini Awakening now!
Kundalini Awakening
Kundalini Awakening is the ultimate guide that will teach you how to unlock your hidden powers and live a more meaningful life. For years, this ancient knowledge has been kept a secret. It is now time to unveil the techniques and practices that will unleash your true power...In this book you'll learn: The basics of Kundalini AwakeningThe 7 main Chakras of the bodyPrana and how to control itThe 4 mighty elements and their qualitiesThe AkashaMeditation guidelinesHow to develop your IntuitionChakra HealingSecret Meditation techniquesEnhance your mind powerAstral travelFastingHow to raise your vibrationHow to see the AuraEnlightenmentBest practicesRoad to masteryAnd So Much More!What's discussed in each chapter: - Chapter 1 is about the basics of Kundalini Awakening. Find out more about this ancient mystery and how you can tap its amazing power.- Chapter 2 talks about the different Chakras of the body. Chakras are energy centers that have many functions and attributes.- Chapter 3 is about prana. Everything in the universe is made of prana. Without prana, life cannot exist. Learn more about this amazing energy.- Chapter 4 discusses the world of the elements and about their attributes and fine qualities, as well as how you can use them to your advantage.- Chapter 5 talks about the akasha. Akasha is that mysterious force from which all the elements come from.- Chapter 6 is about how to practice meditation to enhance your Kundalini experience.- Chapter 7 teaches the secrets of the intuition. Learn how you can use and develop your intuition and connect to a higher power.- Chapter 8 is about chakra healing. Learn how you can heal your chakras naturally and through meditation.- Chapter 9 discusses the different psychic abilities and the proper training that you can do to develop these abilities. - Chapter 10 is about astral travel. Learn how you can separate your spiritual body from your physical body and travel the whole universe.- Chapter 11 teaches how you can connect to your higher-self, also known as the god-self.- Chapter 12 gives 5-minute meditation sessions that are excellent for beginners.- Chapter 13 teaches 30-minute meditation sessions. These are good for those who already have experience in the practice of meditation.- Chapter 14 talks about the aura. Learn how to sense and see auras. - Chapter 15 is about vibration. Learn how you can raise your vibration and be protected from psychic vampires.- Chapter 16 explores the power of the mind. Learn more about your mind and the infinite power that you possess.- Chapter 17 discusses the meaning of true enlightenment and how you can achieve it in your life.- Chapter 18 is about the practice and importance of fasting.- Chapter 19 teaches the best practices to help you succeed in life.- Chapter 20 teaches the road to mastery from a beginner to adept.This book will change your life and free yourself from negative energies. NOW is the time to make a change and live a happier life!Grab your copy of Kundalini Awakening now!
Kundalini Awakening
Kundalini Awakening is the number one ultimate guide that will teach you everything that you need to know about unlocking your hidden powers and living a more meaningful life. For years, this body of ancient and secret knowledge has been kept a closely guarded secret revealed only to a few chosen individuals. Now is the time to unveil the techniques and practices that can unleash your true power...Learn about Kundalini, Chakras, Prana, and more and how to use them to realize your higher capabilities. If your goals are to enrich your spirituality and enhance your mind and psychic abilities--maybe even gain enlightenment--then this book will guide you toward them...This book will give you the keys to power so that you can create positive changes and live a more spiritual and meaningful life -- the life that you deserve...This five-in-one series includes the following 5 books: 1. KUNDALINI AWAKENING: Guided Meditation to Heal Your Body, Gain Enlightenment, Expand Mind Power, Intuition, Clairvoyance, Psychic Awareness, Enhance Psychic Abilities (Book 1)2. KUNDALINI AWAKENING: Achieve Higher Consciousness, Awaken Your Energetic Potential, Expand Mind Power, Enhance Psychic Abilities, Activate and Decalcify Pineal Gland (Book 2)3. KUNDALINI AWAKENING: Guided Meditation Techniques to Increase Energy, Achieve Higher Consciousness, Heal Our Body, Gain Enlightenment, Expand Mind Power, Enhance Psychic Abilities, Clairvoyance, Intuition (Book 3)4. KUNDALINI AWAKENING: Heal Your Body Through Guided Self-Realization, Divine Energy, Expand Mind Power, Clairvoyance, Astral Travel, Intuition, Achieve Higher Consciousness, Awaken Your Energetic Potential (Book 4)5. KUNDALINI AWAKENING: Ultimate Guide to Gain Enlightenment, Awaken Your Energetic Potential, Achieve Higher Consciousness, Activate and Decalcify Pineal Gland, Expand Mind Power, Intuition, Enhance Psychic Abilities, Divine Energy, Self-Realization (Book 5)In this book you'll learn: The basics and understanding of KundaliniThird Eye AwakeningThe 7 main Chakras of the bodyPrana and how to control itThe 4 mighty elements and their qualitiesThe AkashaReiki HealingMeditation GuidelinesHow to develop your IntuitionChakra HealingSecret Meditation TechniquesGrounding your Vibrational WavesHow to increase your vibrationEnhance your Mind PowerAstral TravelFastingHow to see the AuraCommunication with Spiritual GuidesEnlightenmentBest practicesRoad to masteryAnd So Much More!This book will help you discover things about yourself that you never knew. You'll start seeing things in a different light, and your quality of life will grow in the best way possible!Grab your copy of Kundalini Awakening now!
Differential Geometry, Differential Equations, and Mathematical Physics
Poisson and Symplectic Structures, Hamiltonian Action, Momentum, and Reduction.- Notes on Tractor Calculi.- Symmetries and Integrals.- Finite Dimensional Dynamics of Evolutionary Equations with Maple.- Critical Phenomena in Darcy and Euler Flows of Real Gases.- Differential Invariants for Flows of Fluids and Gases.
Anisotropy Across Fields and Scales
This open access book focuses on processing, modeling, and visualization of anisotropy information, which are often addressed by employing sophisticated mathematical constructs such as tensors and other higher-order descriptors. It also discusses adaptations of such constructs to problems encountered in seemingly dissimilar areas of medical imaging, physical sciences, and engineering. Featuring original research contributions as well as insightful reviews for scientists interested in handling anisotropy information, it covers topics such as pertinent geometric and algebraic properties of tensors and tensor fields, challenges faced in processing and visualizing different types of data, statistical techniques for data processing, and specific applications like mapping white-matter fiber tracts in the brain.The book helps readers grasp the current challenges in the field and provides information on the techniques devised to address them. Further, it facilitates the transfer of knowledge between different disciplines in order to advance the research frontiers in these areas.This multidisciplinary book presents, in part, the outcomes of the seventh in a series of Dagstuhl seminars devoted to visualization and processing of tensor fields and higher-order descriptors, which was held in Dagstuhl, Germany, on October 28-November 2, 2018.
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 24th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 28 regular papers presented in this volume were carefully reviewed and selected from 88 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems.
Kundalini Awakening
Kundalini Awakening is the number one ultimate guide that will teach you everything that you need to know about unlocking your hidden powers and living a more meaningful life. For years, this body of ancient and secret knowledge has been kept a closely guarded secret revealed only to a few chosen individuals. Now is the time to unveil the techniques and practices that can unleash your true power...Learn about Kundalini, Chakras, Prana, and more and how to use them to realize your higher capabilities. If your goals are to enrich your spirituality and enhance your mind and psychic abilities--maybe even gain enlightenment--then this book will guide you toward them...This book will give you the keys to power so that you can create positive changes and live a more spiritual and meaningful life -- the life that you deserve...This five-in-one series includes the following 5 books: 1. KUNDALINI AWAKENING: Guided Meditation to Heal Your Body, Gain Enlightenment, Expand Mind Power, Intuition, Clairvoyance, Psychic Awareness, Enhance Psychic Abilities (Book 1)2. KUNDALINI AWAKENING: Achieve Higher Consciousness, Awaken Your Energetic Potential, Expand Mind Power, Enhance Psychic Abilities, Activate and Decalcify Pineal Gland (Book 2)3. KUNDALINI AWAKENING: Guided Meditation Techniques to Increase Energy, Achieve Higher Consciousness, Heal Our Body, Gain Enlightenment, Expand Mind Power, Enhance Psychic Abilities, Clairvoyance, Intuition (Book 3)4. KUNDALINI AWAKENING: Heal Your Body Through Guided Self-Realization, Divine Energy, Expand Mind Power, Clairvoyance, Astral Travel, Intuition, Achieve Higher Consciousness, Awaken Your Energetic Potential (Book 4)5. KUNDALINI AWAKENING: Ultimate Guide to Gain Enlightenment, Awaken Your Energetic Potential, Achieve Higher Consciousness, Activate and Decalcify Pineal Gland, Expand Mind Power, Intuition, Enhance Psychic Abilities, Divine Energy, Self-Realization (Book 5)In this book you'll learn: The basics and understanding of KundaliniThird Eye AwakeningThe 7 main Chakras of the bodyPrana and how to control itThe 4 mighty elements and their qualitiesThe AkashaReiki HealingMeditation GuidelinesHow to develop your IntuitionChakra HealingSecret Meditation TechniquesGrounding your Vibrational WavesHow to increase your vibrationEnhance your Mind PowerAstral TravelFastingHow to see the AuraCommunication with Spiritual GuidesEnlightenmentBest practicesRoad to masteryAnd So Much More!This book will help you discover things about yourself that you never knew. You'll start seeing things in a different light, and your quality of life will grow in the best way possible!Grab your copy of Kundalini Awakening now!
Selbstwirksamkeit, Leistung Und Calibration in Mathematik
Die vorliegende Arbeit widmet sich dem Problem der Selbsteinsch瓣tzung, insbesondere ?bersch瓣tzung, in Mathematik bei Studienanf瓣ngerinnen. Die quantitative Studie untersucht den Einfluss von Aufgabenmerkmalen und Feedback auf die mathematische Leistung, Selbstwirksamkeitserwartung und Calibration bei Studienanf瓣nger/innen wirtschaftswissenschaftlicher Studieng瓣nge. Die Untersuchungen zeigen, dass vor allem Aufgabenmerkmale wie die curriculare Wissensstufe und der Bearbeitungsumfang die Selbstwirksamkeitserwartung und die tats瓣chlich erbrachte Leistung auf unterschiedliche Weise beeinflussen. Innerhalb des ersten Studiensemesters ver瓣ndern sich bei der untersuchten Kohorte Selbstwirksamkeitserwartung und Leistung, wodurch eine deutliche Reduzierung der Selbst羹bersch瓣tzung erreicht wurde. Inwieweit das Feedback dazu beigetragen hat, kann methodisch bedingt nicht eindeutig festgestellt werden. Die Autorin Angela Laging ist Lehrerin f羹r Mathematik und Kunst an einem Gymnasium.
A Brief Journey in Discrete Mathematics
The goal of this book is to showcase the beauty of mathematics as revealed in nine topics of discrete mathematics. In each chapter, properties are explored through a series of straightforward questions that terminate with results that lie at the doorstep of a field of study. Each step along the way is elementary and requires only algebraic manipulation. This frames the wonder of mathematics and highlights the complex world that lies behind a series of simple, mathematical, deductions. Topics addressed include combinatorics, unifying properties of symmetric functions, the Golden ratio as it leads to k-bonacci numbers, non-intuitive and surprising results found in a simple coin tossing game, the playful, trick question aspect of modular systems, exploration of basic properties of prime numbers and derivations of bewildering results that arise from approximating irrational numbers as continued fraction expansions. The Appendix contains the basic tools of mathematics that are used in the text along with a numerous list of identities that are derived in the body of the book. The mathematics in the book is derived from first principles. On only one occasion does it rely on a result not derived within the text. Since the book does not require calculus or advanced techniques, it should be accessible to advanced high school students and undergraduates in math or computer science. Senior mathematicians might be unfamiliar with some of the topics addressed in its pages or find interest in the book's unified approach to discrete math.
The Zeroth Book of Graph Theory
Marking 94 years since its first appearance, this book provides an annotated translation of Sainte-Lagu禱's seminal monograph Les r矇seaux (ou graphes), drawing attention to its fundamental principles and ideas. Sainte-Lagu禱's 1926 monograph appeared only in French, but in the 1990s H. Gropp published a number of English papers describing several aspects of the book. He expressed his hope that an English translation might sometime be available to the mathematics community. In the 10 years following the appearance of Les r矇seaux (ou graphes), the development of graph theory continued, culminating in the publication of the first full book on the theory of finite and infinite graphs in 1936 by D矇nes K繹nig. This remained the only well-known text until Claude Berge's 1958 book on the theory and applications of graphs. By 1960, graph theory had emerged as a significant mathematical discipline of its own. This book will be of interest to graph theoristsand mathematical historians.
Convex Optimization with Computational Errors
The book is devoted to the study of approximate solutions of optimization problems in the presence of computational errors. It contains a number of results on the convergence behavior of algorithms in a Hilbert space, which are known as important tools for solving optimization problems. The research presented in the book is the continuation and the further development of the author's (c) 2016 book Numerical Optimization with Computational Errors, Springer 2016. Both books study the algorithms taking into account computational errors which are always present in practice. The main goal is, for a known computational error, to find out what an approximate solution can be obtained and how many iterates one needs for this. The main difference between this new book and the 2016 book is that in this present book the discussion takes into consideration the fact that for every algorithm, its iteration consists of several steps and that computational errors for different steps are generally, different. This fact, which was not taken into account in the previous book, is indeed important in practice. For example, the subgradient projection algorithm consists of two steps. The first step is a calculation of a subgradient of the objective function while in the second one we calculate a projection on the feasible set. In each of these two steps there is a computational error and these two computational errors are different in general. It may happen that the feasible set is simple and the objective function is complicated. As a result, the computational error, made when one calculates the projection, is essentially smaller than the computational error of the calculation of the subgradient. Clearly, an opposite case is possible too. Another feature of this book is a study of a number of important algorithms which appeared recently in the literature and which are not discussed in the previous book. This monograph contains 12 chapters. Chapter 1 is an introduction. In Chapter 2 we study the subgradient projection algorithm for minimization of convex and nonsmooth functions. We generalize the results of [NOCE] and establish results which has no prototype in [NOCE]. In Chapter 3 we analyze the mirror descent algorithm for minimization of convex and nonsmooth functions, under the presence of computational errors. For this algorithm each iteration consists of two steps. The first step is a calculation of a subgradient of the objective function while in the second one we solve an auxiliary minimization problem on the set of feasible points. In each of these two steps there is a computational error. We generalize the results of [NOCE] and establish results which has no prototype in [NOCE]. In Chapter 4 we analyze the projected gradient algorithm with a smooth objective function under the presence of computational errors. In Chapter 5 we consider an algorithm, which is an extension of the projection gradient algorithm used for solving linear inverse problems arising in signal/image processing. In Chapter 6 we study continuous subgradient method and continuous subgradient projection algorithm for minimization of convex nonsmooth functions and for computing the saddle points of convex-concave functions, under the presence of computational errors. All the results of this chapter has no prototype in [NOCE]. In Chapters 7-12 we analyze several algorithms under the presence of computational errors which were not considered in [NOCE]. Again, each step of an iteration has a computational errors and we take into account that these errors are, in general, different. An optimization problems with a composite objective function is studied in Chapter 7. A zero-sum game with two-players is considered in Chapter 8. A predicted decrease approximation-based method is used in Chapter 9 for constrained convex optimization. Chapter 10 is devoted tominimization of quasiconvex functions. Minimization of sharp weakly convex functions is discussed in Chapter 11. C
Activity Book for Adults & Seniors
This Hard Logic Puzzles book is packed with the following features: - 48 Sudoku Puzzles, 36 Fillomino Puzzles, 48 Kakuro Puzzles, 32 Futoshiki Puzzles, 48 Hitori Puzzles, 36 Slitherlink Puzzles, 48 Killer Sudoku Puzzles, 40 Calcudoku Puzzles, 48 Jigsaw Sudoku Puzzles, 36 Skyscrapers Puzzles, 48 Shikaku Puzzles and 32 Numbrix Puzzles.- Answers to every puzzle are provided.- Each puzzle is guaranteed to have only one solution.Includes free bonus puzzles you can download book (Tons of Sudoku Puzzles for Adults & Seniors) Includes free bonus puzzles you can download book (Word Search With Hidden Message: 102 Puzzles for Adults and Seniors)
Activity Book for Adults & Seniors
This Medium Logic Puzzles book is packed with the following features: - 48 Sudoku Puzzles, 36 Fillomino Puzzles, 48 Kakuro Puzzles, 32 Futoshiki Puzzles, 48 Hitori Puzzles, 36 Slitherlink Puzzles, 48 Killer Sudoku Puzzles, 40 Calcudoku Puzzles, 48 Jigsaw Sudoku Puzzles, 36 Skyscrapers Puzzles, 48 Shikaku Puzzles and 32 Numbrix Puzzles.- Answers to every puzzle are provided.- Each puzzle is guaranteed to have only one solution.Includes free bonus puzzles you can download book (Tons of Sudoku Puzzles for Adults & Seniors) Includes free bonus puzzles you can download book (Word Search With Hidden Message: 102 Puzzles for Adults and Seniors)
The Giant Book of Kakuro
✓ Great gift for family, friends or work colleaguesThis Logic Puzzles book is packed with the following features: ① 1000 Hard Kakuro (10x10) Puzzles.② Each puzzle is guaranteed to have only one solution.③ Includes free bonus puzzles you can download book (Logic Puzzles & Brain Games for Adults) ④ Answers to every puzzle are provided at the back of the book.⚠ Six puzzles per page (8.5 x 11 inches).✓ Includes Tables of Kakuro Combinations & Kakuro Magic Squares.★★★★★ The Giant Book of Kakuro offers hours of entertainment for adults of all ages, from young adults to seniors ★★★★★We hope this will be an entertaining and uplifting mental workout, enjoy The Giant Book of Kakuro.
The Giant Book of Battleships
✓ Great gift for family, friends or work colleaguesThis Logic Puzzles book is packed with the following features: ① 1000 Battleships Puzzles {333 (8x8) puzzles, 334 (9x9) puzzles, 333 (10x10) puzzles}.② Each puzzle is guaranteed to have only one solution.③ Includes free bonus puzzles you can download book (Logic Puzzles & Brain Games for Adults) ④ Answers to every puzzle are provided at the back of the book.⚠ Six puzzles per page (8.5 x 11 inches).Playing Battleships is not just a fun way to pass the time, due to its logical elements it has been found as a proven method of exercising and stimulating portions of your brain, training it even if you will and just like training any other muscle regularly you can expect to see an improvement in cognitive functions. Some studies go as far as indicating regular puzzles can even help reduce the risk of Alzheimer's and other health problems in later life.Completing Battleships regularly helps the brain process both problem solving and improves the logical thought process with the use of deductive reasoning, which can also be applied to approaching real-life challenges in a different manner.★★★★★ The Giant Book of Battleships offers hours of entertainment for adults of all ages, from young adults to seniors ★★★★★We hope this will be an entertaining and uplifting mental workout, enjoy The Giant Book of Battleships.
The Giant Book of Battleships
✓ Great gift for family, friends or work colleaguesThis Logic Puzzles book is packed with the following features: ① 1000 Battleships 10x10 Puzzles from Easy to Hard (333 Easy - 334 Medium - 333 Hard).② Each puzzle is guaranteed to have only one solution.③ Includes free bonus puzzles you can download book (Logic Puzzles & Brain Games for Adults) ④ Answers to every puzzle are provided at the back of the book.⚠ Six puzzles per page (8.5 x 11 inches).Playing Battleships is not just a fun way to pass the time, due to its logical elements it has been found as a proven method of exercising and stimulating portions of your brain, training it even, if you will and just like training any other muscle regularly you can expect to see an improvement in cognitive functions. Some studies go as far as indicating regular puzzles can even help reduce the risk of Alzheimer's and other health problems in later life.Completing Battleships regularly helps the brain process both problem solving and improves logical thought process with the use of deductive reasoning, which can also be applied to approaching real life challenges in a different manner.★★★★★ The Giant Book of Battleships offers hours of entertainment for adults of all ages, from young adults to seniors ★★★★★We hope this will be an entertaining and uplifting mental workout, enjoy Big Book of Battleships.
Division by Zero
"Division by Zero" is not really a book about math. It's about thinking creatively, re-thinking mathematically and the importance of growing personally. It uses math as the basis for discussion and looks to nature as a guide. Afterall, nature teaches us that when things stop growing, they die.
Practical Discrete Mathematics
A practical guide simplifying discrete math for curious minds and demonstrating its application in solving problems related to software development, computer algorithms, and data scienceKey Features: Apply the math of countable objects to practical problems in computer scienceExplore modern Python libraries such as scikit-learn, NumPy, and SciPy for performing mathematicsLearn complex statistical and mathematical concepts with the help of hands-on examples and expert guidanceBook Description: Discrete mathematics deals with studying countable, distinct elements, and its principles are widely used in building algorithms for computer science and data science. The knowledge of discrete math concepts will help you understand the algorithms, binary, and general mathematics that sit at the core of data-driven tasks.Practical Discrete Mathematics is a comprehensive introduction for those who are new to the mathematics of countable objects. This book will help you get up to speed with using discrete math principles to take your computer science skills to a more advanced level.As you learn the language of discrete mathematics, you'll also cover methods crucial to studying and describing computer science and machine learning objects and algorithms. The chapters that follow will guide you through how memory and CPUs work. In addition to this, you'll understand how to analyze data for useful patterns, before finally exploring how to apply math concepts in network routing, web searching, and data science.By the end of this book, you'll have a deeper understanding of discrete math and its applications in computer science, and be ready to work on real-world algorithm development and machine learning.What You Will Learn: Understand the terminology and methods in discrete math and their usage in algorithms and data problemsUse Boolean algebra in formal logic and elementary control structuresImplement combinatorics to measure computational complexity and manage memory allocationUse random variables, calculate descriptive statistics, and find average-case computational complexitySolve graph problems involved in routing, pathfinding, and graph searches, such as depth-first searchPerform ML tasks such as data visualization, regression, and dimensionality reductionWho this book is for: This book is for computer scientists looking to expand their knowledge of discrete math, the core topic of their field. University students looking to get hands-on with computer science, mathematics, statistics, engineering, or related disciplines will also find this book useful. Basic Python programming skills and knowledge of elementary real-number algebra are required to get started with this book.
Boundary Value Problems for Fractional Differential Equations and Systems
This book is devoted to the study of existence of solutions or positive solutions for various classes of Riemann-Liouville and Caputo fractional differential equations, and systems of fractional differential equations subject to nonlocal boundary conditions. The monograph draws together many of the authors' results, that have been obtained and highly cited in the literature in the last four years.In each chapter, various examples are presented which support the main results. The methods used in the proof of these theorems include results from the fixed point theory and fixed point index theory. This volume can serve as a good resource for mathematical and scientific researchers, and for graduate students in mathematics and science interested in the existence of solutions for fractional differential equations and systems.
