Shrinkage for Stabilizing the Detection of Changepoints in Covariances for High-Dimensional Data
Diploma Thesis from the year 2012 in the subject Mathematics, grade: 1,0, University of Kaiserslautern (Fakult瓣t f羹r Mathematik), language: English, abstract: In mathematical statistics, detecting changes in parameters of real-life data series, known as change-point problems, is crucial. Originating in quality control during the 1950s, these problems have widespread applications today, spanning fields like economics, finance, medicine, and geology. In finance, fluctuations in asset returns can violate assumptions of constant variance, leading to inaccurate forecasts. Chapter 2 briefly discusses the univariate case, focusing on detecting changes in mean and variance parameters over time. The Cumulative Sums (CUSUM) test statistics, derived from likelihood ratios, serve as change-point estimators. However, their asymptotic distribution complexity and slow convergence limit applicability to small sample sizes. Nevertheless, asymptotic quantiles help determine if changes have occurred. Chapter 3 extends this analysis to the multivariate case, specifically addressing changes in covariance matrices. Estimating the covariance matrix, particularly in scenarios with many variables and few observations, poses challenges. Shrinkage estimators, like the Ledoit-Wolf (LW) estimator, offer improvements over sample covariance matrices, especially in small sample sizes. The Rao-Blackwell theorem leads to the development of the Rao-Blackwellized Ledoit-Wolf (RBLW) estimator, enhancing performance under Gaussian assumptions. A simulation study in Chapter 5 demonstrates the effectiveness of using these shrinkage estimators in detecting change-points, resulting in improved test power and accuracy. However, due to the absence of an asymptotic distribution for the test statistics, quantiles must be obtained through simulation.
General Combination Theorem and Selected Combinations
Document from the year 2024 in the subject Mathematics - Algebra, language: English, abstract: So for combinations are discussed with different theorems in algebra. In this chapter I apply assembly analysis to get the theorems easy and memorable. After assembly analysis applied there becomes a lot of new theorems and all the theorems get a new face by summation methods. We have a full idea about combination. It indicates the outcome of arandom experiment. That is combination is the selection of M different components taken V at a time what is called usually a random experiment where order is not taken into account and repetitions are not allowed.
General Permutation Theorem and Selected Permutations
Document in the subject Mathematics - Algebra, language: English, abstract: We have permutations are discussed with different theorems in algebra. In this chapter I apply B system analysis to get the theorems easy and memorable. After B system analysis applied there becomes a lot of new theorems and all the theorems get a new face by summation methods. One usual theorem described with summation method and face new looks.
Math Mammoth Place Value 2
Math Mammoth Place Value 2 is a short worktext dealing with place value and three-digit numbers.The first lessons present three-digit numbers using a visual model of the base-ten blocks (hundred-flats, ten-pillars, and one-cubes) and number lines. To reinforce the important concept of place value, children practice separating three-digit numbers into their different "parts" (hundreds, tens, and ones), and making numbers from these parts.Next, we study skip-counting by tens, by twos, and fives. Then students compare and order three-digit numbers, including comparing simple number expressions.After this, we study rounding three-digit numbers to the nearest ten and to the nearest hundred. Lastly, the book includes a lesson on reading bar graphs and pictographs, which provide a nice real-life application for using three-digit numbers.
Actuarial Loss Models
This book covers part of the learning outcomes of the Fundamentals of Actuarial Mathematics (FAM) exam and the Advanced Short-Term Actuarial Mathematics (ASTAM) exam administered by the Society of Actuaries. It can be used by students and practitioners who prepare for actuarial exams.
Math Mammoth Place Value 1
Math Mammoth Place Value 1 focuses on place value and two-digit numbers and is primarily meant for first grade level math.When children count, they basically just learn numbers as some kind of continuum that goes on without end. With simple counting, your child might not catch on to the inherent structure of the number system. Our number system is based on the idea that if you have lots and lots of objects, the efficient way to count and denote them is with groups of tens, hundreds, and thousands - not individually.The crucial point in understanding the concept of place value is therefore that a certain position represents a certain size group. The digit in each position tells us how many groups of that size there are. For example, in the number 2,381, an adult already knows that the 8 represents eight tens, and not just "8" and that the 3 represents three hundreds, and not just "3". The place of the digit tells us the size of the group, and the digit itself tells how many of that group.The initial lessons of the book that introduce tens and ones use a 100-bead abacus extensively. This 100-bead abacus or school abacus simply contains ten beads on ten rods, for a total of 100 beads. It is not the special abacus used by the Chinese or the Japanese. Each bead simply represents one. The 100-bead abacus lets children both "see" the numbers and use their touch while making them.You will need to purchase this school abacus separately, such as on Amazon, or make your own.The abacus is used in the first lessons, but it is not the only model used in the book. We also use base-ten blocks as a visual representation of two-digit numbers. If you own a set of base-ten blocks (manipulatives), you can use them along with the visual exercises, if desired.Moreover, we also use number lines and the 100-chart. Number lines help to visualize how numbers continue indefinitely and also relate to the concept of measuring. The 100-chart helps the child to be familiar with the numbers below 100 and find patterns in the number system.While most of the lessons in the book focus on place value, students also practice adding and subtracting multiples of ten, and rounding numbers to the nearest ten. The two lessons near the end of the book about tally marks and graphs are real-life applications of two-digit numbers. The last lesson about regrouping can be challenging, thus is optional.
Exploring Unique Expressions of Positive Integers through Partitions and Theorems
Research Paper (postgraduate) from the year 2024 in the subject Mathematics - Algebra, language: English, abstract: This paper delves into the realm of natural numbers and their expression as sums of other natural numbers, a concept known as partitions. Focusing on partitions originating from a positive integer and comprising positive integers, a systematic analysis is presented. Essential terms are defined to lay the groundwork, followed by the introduction of three key theorems and a consequential corollary. These theorems elucidate the uniqueness of expressions formed through arithmetic addition operations on such partitions, offering valuable insights into the structure and properties of positive integers. This exploration not only contributes to the theory of numbers but also holds implications for various mathematical and computational applications.
Analyzing Repartition Numbers of Parent Partitions. Theorems and their Implications
Research Paper (postgraduate) from the year 2024 in the subject Mathematics - Algebra, language: English, abstract: This paper delves into the intricate realm of partition theory, specifically focusing on the repartition numbers of parent partitions. Through a systematic development of six theorems, insights into the distribution of repartitions, delineating distinct patterns for two separate parent partitions, are unveiled. Theorems are structured to elucidate the occurrences of repartitions based on the number of components involved, providing a comprehensive understanding of the repartition phenomena. The findings contribute to a deeper comprehension of partition theory and its implications across various domains.
Math Mammoth Add & Subtract 2-B
Math Mammoth Add & Subtract 2-B is a continuation to the book Math Mammoth Add & Subtract 2-A. The goal of this book is to study addition and subtraction within 0-100, both mentally and in columns, especially concentrating on regrouping in addition (carrying) and in subtraction (borrowing).Mental math is important because it builds number sense. This book includes many lessons that practice mental math. For example, the child practices adding and subtracting two-digit numbers when one of the numbers is a whole ten (such as 30 + 14 or 66 - 20).The students also learn to solve sums such as 36 + 8 or 45 + 9 with mental math (there is a regrouping), comparing them to the sums 6 + 8 and 5 + 9. Since 6 + 8 fills the first ten and is four more than the next ten, the sum 36 + 8 fills the next whole ten (40), and is four more than that, or 44.At the same time, students also learn to add two-digit numbers with regrouping. This is explained in detail with the help of visual models (base-ten blocks). You are welcome to use actual physical manipulatives, if you prefer. The main concept to understand is that 10 ones are regrouped to form a new ten, and this new ten is written using a little "1" in the tens column.After addition, the lessons focus on column subtraction, initially without regrouping and then with regrouping.The lesson Regrouping practices breaking down a ten into 10 ones. It is crucial that the child understands what happens here. Otherwise, they might end up only memorizing the procedure, and will probably at some point misremember how it was done. If you notice that the child does not understand the concept of regrouping, provide more practice with concrete manipulatives or visual exercises before proceeding.After learning regrouping, students practice mental subtraction in two separate lessons. One of them expounds on several methods for mental subtracting. The other is about Euclid's game-a fun game that also practices subtraction of two-digit numbers.
Math Mammoth Add & Subtract 2-A
Math Mammoth Add & Subtract 2-A deals with two main themes: strategies for adding and subtracting within 0-20; such as adding just one more, a trick with nine and eight, and subtracting using addition;memorizing the basic addition and subtraction facts of single-digit numbers with an answer between 10 and 18.While focusing on addition and subtraction techniques, the lessons also include many word problems.The goal is to memorize the facts, or at least become so fluent with them that an outsider cannot tell if the child remembers the answer or uses some mental math strategy to get the answer.Some children will accomplish this quicker and need less practice, whereas others will take longer. Thus, don't assign all the exercises in the book by default. Use your judgment, and try to match the amount of exercises to your child's need. The ones that don't get assigned can be used later for review. You can also use games to reinforce the facts, and in place of some of the exercises in the book (a list of games is provided in the book).Learning addition and subtraction facts is quite important for later study. For example, regrouping in addition and subtraction (carrying/borrowing) requires the ability to recall the basic facts efficiently and fluently.We will start the book with a few mental math strategies (Add Using "Just One More" and A Trick with Nine and Eight). The lesson Adding within 20 reviews those strategies and gives more practice. These initial lessons don't yet involve actual memorization techniques.The lesson Subtract to Ten explains another basic strategy, and has to do with subtracting in parts. For example, to do 13 - 5, one can subtract 5 in two parts: first do 13 - 3, which equals 10, and then subtract the rest, or 2 more. Memorizing the subtraction facts will be more efficient, but I want children to understand this strategy, because it is useful in many other situations also.Then we review how to complete the next whole ten, which is an important concept. An example of this concept is the question: What number do you add to 23 to get 30? As an equation, we write: 23 + __ = 30.In the next lesson, we study sums that go over ten, doing these sums in two parts. For example, in the sum 9 + 7, the child first completes 10 by adding 9 + 1. Then, the child adds the rest, or 6, to 10. Learning this prepares the child for addition facts where the sum is more than 10.The next lessons, Adding with 9, Adding with 8, Adding with 7, and Adding with 6, provide lots of practice for learning and memorizing the basic addition facts. There are 20 such facts: 9 + 2 till 9 + 9: 8 facts8 + 3 till 8 + 8: 6 facts7 + 4 till 7 + 7: 4 facts6 + 5 till 6 + 6: 2 factsThe last part of the book includes various lessons titled Number Rainbows and Fact Families with.... These give lots of practice and reinforcement for the basic addition and subtraction facts, emphasizing the connection between addition and subtraction as a strategy for subtraction facts.The follow-up to this book, Add & Subtract 2-B, practices adding and subtracting two-digit numbers mentally and in columns (regrouping).
The Eternal Life
Applied Math to Life ResearchUsing the objectiveness of the Mathematical Language to analyze, study and conclude on the spiritual eternal life, the successive lifetimes, life, death and related subjects.A "must not miss" book, quite deep on its subjects but joyfully presented on a youngish style.
Holy Trinity & Inverted Holy Trinity
The Trinities are all over the place!There is the positive Holy Trinity turned upwords... and there is the negative or Inverted Holy Trinity, turned upside down. From a Mathematical perspective. Applied Math to Life, Research. Bridge/Fusion between Mathematical Science & Spirituality.
Math Mammoth Subtraction 1
Math Mammoth Subtraction 1 is a worktext that covers the concept of subtraction, the relationship between addition and subtraction, and the various meanings of subtraction.In the first lesson, Subtraction Is Taking Away, the child learns the basic meaning of subtraction as taking away objects, and learns to write subtractions from an illustration where some objects are crossed out.In the next lesson, the child counts down to subtract, which ties in subtraction with the number line. This is a transitional strategy to solve subtraction problems, because later students will learn more efficient ways to subtract, but it is important conceptually.The following lesson, Subtraction and Addition in the Same Picture, begins the study of the relationship between addition and subtraction. This concept will span several lessons. This first lesson presents two sets of objects, such as blue and white balls, and the student writes both an addition sentence and a subtraction sentence from this illustration.The lesson When Can You Subtract? concentrates on the idea that some subtractions, such as 4 - 5, are meaningless when you think of taking away. The child also makes subtraction patterns in this lesson.Then we continue studying the connection between addition and subtraction in the lesson Two Subtractions from One Addition. As an example, the child writes both 8 - 3 = 5 and 8 - 5 = 3 from the addition 3 + 5 = 8. This idea ties in with fact families, a concept that is coming up soon.In the lesson Two Parts - One Total, we study word problems that do not involve the idea of taking away but have two parts making up a total. For example, if there are 10 flowers of which some are white and some are red, and seven of them are white, how many are red?Then we study fact families, which means writing two additions and two subtractions using the same three numbers.In the lesson How Many More? students find how many more or how many fewer objects one person has than the other by drawing the objects. This lesson can easily be done with manipulatives if desired.In the very next lesson, "How Many More" Problems and Differences, we continue the theme, this time writing a missing addend addition for problems that ask "how many more." For example, Veronica has 4 marbles and Ann has 6. We write the missing addend sentence 4 + ___ = 6 to find how many more Ann has. In the next lesson the child then learns to write subtraction sentences for such problems.
Reliability
This text provides an elementary introduction to the probabilistic models and statistical methods used by reliability engineers that are applied to a system of components. Probability models include the exponential distribution, Weibull distribution, competing risks, mixtures, accelerated life model, proportional hazards model, and repairable systems models. Statistical methods emphasize determining point and interval estimates for parameters from censored data sets. Applications are drawn from a variety of disciplines. Over 600 exercises make this text appropriate for a class on reliability.
The 2018-2024 Canadian Twin Prime Conjecture Solo Expedition
... one of - if not the most famous proof in all of mathematics - admired for its elegance - simplicity and profundity is Euclid's Proof of Infinite Primes - mathematical rigor currently enjoys an unprecedented historical resurgence over its long history - yet to this author - it seems the strength of the deep-learned analysis and logical arguments used in ancient Greek proof somehow remains missing in contemporary mathematics - to address this - the author does not follow conventional research protocol and abandons research into all prior knowledge on the elusive proof of the long-standing Twin Prime Conjecture - rather - a rare summit attempt is made from first principals alone - equipped with little more than the definition of a twin prime - this Canadian mathematician begins a six year mathematical solo research expedition into unravelling the chaos that is the twin primes - always in search of patterns - the nature of the of twin primes has led several mathematicians to conclude that the exhibited random pattern is chaotic - no discernible pattern exists - under such conditions we cannot predict anything about how twin primes behave nor attempt to count them over increasingly large - infinite domains - lacking a proof akin to Euclid's - that outcome places twin primes outside the harmonious mathematics of the ancient Greeks - a world that we mathematicians have always sought to retain - such incongruity and disharmony is jarring and harsh for any mathematician to accept - after undergoing my transformation into a mathematical alpinist - the expedition strategy was to focus not on the (twin) primes but rather their theoretical complement - the odd composites - it was conjectured by the author that a deeper understanding of these simplistic mathematical entities would indirectly reveal how twin primes are constructed - to summit one of the highest unclimbed mathematical peaks - required new innovative techniques - bold daring thoughts and inexhaustible patience and persistence - if you continue to climb and gain altitude you must - eventually - reach the summit - one painful step at a time - lastly - having reached the summit - by far the most daunting task was to collate and present the argument in such a manner that others would not only understand it but be convinced of the result in the same manner that those who read Euclid's proof are - with elegance - simplicity and profundity ...... this long-awaited Proof of the Twin Prime Conjecture rescues the harmonious nature of mathematics out of chaos ... it was an exhilarating unforgettable intellectual mathematical alpine expedition ... more than once I felt at the brink of physical and mental exhaustion and had to take a brief walk away simply to recover from the task - too often any discussion of the hard intellectual struggles are omitted from the discourse and too often the final result alone is presented as if it was the initial effort and attempt - when the truth involved so much more ...
Ring Theory - Proceedings of the Biennial Ohio State-Denison Conference 1992
Math Mammoth Fractions 2
Math Mammoth Fractions 2 continues the study of fraction topics after Math Mammoth Fractions 1. (I sincerely recommend that the student study the Fractions 1 book prior to studying this book, if he has not already done so.)This book is meant for fifth grade, and deals in-depth with the following topics: simplifying; including simplifying before multiplyingmultiplication of fractions (and of mixed numbers)division of fractionsWe start out by simplifying fractions. Since this process is the opposite of making equivalent fractions, studied in Math Mammoth Fractions 1, it should be relatively simple for students to understand. We also use the same visual model, just backwards: This time the pie pieces are joined together instead of split apart.Next comes multiplying a fraction by a whole number. Since this can be solved by repeated addition, it is not a difficult concept at all.Multiplying a fraction by a fraction is first explained as taking a certain part of a fraction, in order to teach the concept. After that, students are shown the usual shortcut for the multiplication of fractions.Then, we find the area of a rectangle with fractional side lengths, and show that the area is the same as it would be found by multiplying the side lengths. Students multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.Simplifying before multiplying is a process that is not absolutely necessary for fifth graders. I have included it here because it prepares students for the same process in future algebra studies and because it makes fraction multiplication easier.Students also multiply mixed numbers, and study how multiplication can be seen as resizing or scaling. This means, for example, that the multiplication (2/3) ? 18 km can be thought of as finding two-thirds of 18 km.Next, we study the division of fractions. The first lesson on the topic shows how fractions can be seen as divisions; in other words, for example, 5/3 is the same as 5 繩 3. This of course gives us a means of dividing whole numbers and getting fractional answers (for example, 20 繩 6 = 3 2/6).The next lesson on the topic explores the thought of solving division problems by multiplying, and then introduces reciprocal numbers and the common shortcut for fraction division.The following two lessons focus on two ways to think about division: equal sharing, and fitting the divisor (measurement division), and how they apply to fraction division. Here is an example of equal sharing: If two people equally share 4/5 of a pizza, how much will each person get? This is represented by the division (4/5) 繩 2 = 2/5.
Math Mammoth Addition 1
Math Mammoth Addition 1 is a worktext (includes both teaching and exercises), dealing with the concept of addition and addition facts within 0-10 (in few occasions numbers between 10 and 20 are used). The book is most suitable for first grade.The book starts out with very easy addition problems within 0-5, using pictures. If the student does not yet know the symbols + and =, you can introduce them first orally. In other words, use blocks or rocks and make addition problems where you use both kinds of wordings: "Three blocks and four blocks makes seven blocks. Three blocks PLUS four blocks EQUALS seven blocks." Play like that until the child can use the words PLUS and EQUALS in his/her own speech. This will make it easier for him/her to use the written symbols.Soon the lessons start including "missing addend" problems. We first use pictures, and gradually get to the abstract 1 + __ = 5 with symbols only. Keep in mind that children may confuse this problem with1 + 5 = __. You can word these problems like this: "1 and how many more makes 5?" You can MODEL them by drawing: First draw 1 ball. Tell the child that we need to have a total of 5 balls. He is to draw more until there are five balls. In the missing addend problem, however many balls the child has to draw is the number that goes on the empty line. So, first there is one ball, then we need to add (draw) some more to make 5. But how many more were drawn?After that, the book contains many lessons called Sums with... whose goal is to help the child memorize addition facts.My approach to memorization is many-fold: Structured drill, such as you see in the lessons Sums with 5, Sums with 6, and so on. This is not random drill, because you will start it by showing the pattern or the structure in the facts. This will help the student to tie the addition facts in with a context and help him understand the facts more on a conceptual level, instead of merely memorizing them at random. In sums with 5, the child learns the number combinations that add up to 5: 0 & 5, 1 & 4, and 2 & 3. This understanding is the basis for the drills.Using addition facts in games, in math problems, everyday life, or anywhere else. Games are especially useful because they help children like mathematics.Random drilling may also be used as a tool among others.Memory helps such as silly mnemonics or writing math facts on a poster and hanging it on the wall. These are not needful for all children.However, keep in mind that children will need LOTS of opportunities to add numbers to actually memorize the facts, so the memorization may not totally occur as your child works through this book. These same addition facts are further studied and used in the Math Mammoth Subtraction 1 book, and in all later math work since they are constantly used. At the latest, your child should memorize addition facts during second grade.
Math Mammoth Introduction to Fractions
Math Mammoth Introduction to Fractions contains lessons for fraction arithmetic for grades 1-4. This material does not include division or multiplication of fractions, nor adding unlike fractions, which are topics for 5th and 6th grades. Also, most of the material here is for 3rd and 4th grades, and only a few lessons are meant for grades 1-2.The topics covered are on a simple level, constantly illustrated with visual models, and with small denominators. The presentation avoids spelling out specific rules for manipulating fractions, but instead relies on the usage of pictures on a very concrete level. Children easily confuse the various rules for fraction arithmetic, because there are so many. There is a place for the rules, as shortcuts for ideas that are already understood, but we do not start with them. The goal is to let the big ideas sink in conceptually first, followed by some shortcuts.The topics covered areone half and one fourthconcept of a fractionconcept of a mixed numbercomparing fractionsequivalent fractionsadding and subtracting like fractionsadding and subtracting mixed numbers with like fractional partsadding one fraction that has tenths and another that has hundredths (such as 3/10 + 7/100)multiplying a fraction by a whole numberThe lessons are organized by topic, not by increasing difficulty. For reference, 1st grade students study only the concept of one half and one fourth. In 2nd grade, they study the concept of a fraction and optionally the easiest (first) lesson on comparing fractions. In 3rd grade, students study the concept of a fraction, fractions on a number line, comparing fractions, and equivalent fractions. Then in 4th, they study mixed numbers, comparing fractions, equivalent fractions, adding and subtracting fractions and mixed numbers, and multiplying fractions by whole numbers.The answers are appended.
Once Upon a Prime
A New York Times Book Review Editors' Choice "Wide-ranging and thoroughly winning." --Jordan Ellenberg, The New York Times Book Review "An absolute joy to read!" --Steven Levitt, New York Times bestselling author of Freakonomics For fans of Seven Brief Lessons in Physics, an exploration of the many ways mathematics can transform our understanding of literature and vice versa, by the first woman to hold England's oldest mathematical chair. We often think of mathematics and literature as polar opposites. But what if, instead, they were fundamentally linked? In her clear, insightful, laugh-out-loud funny debut, Once Upon a Prime, Professor Sarah Hart shows us the myriad connections between math and literature, and how understanding those connections can enhance our enjoyment of both. Did you know, for instance, that Moby-Dick is full of sophisticated geometry? That James Joyce's stream-of-consciousness novels are deliberately checkered with mathematical references? That George Eliot was obsessed with statistics? That Jurassic Park is undergirded by fractal patterns? That Sir Arthur Conan Doyle and Chimamanda Ngozi Adichie wrote mathematician characters? From sonnets to fairytales to experimental French literature, Professor Hart shows how math and literature are complementary parts of the same quest, to understand human life and our place in the universe. As the first woman to hold England's oldest mathematical chair, Professor Hart is the ideal tour guide, taking us on an unforgettable journey through the books we thought we knew, revealing new layers of beauty and wonder. As she promises, you're going to need a bigger bookcase.
Math Mammoth Grade 8 Review Workbook
Math Mammoth Review Workbook, Grade 8 is intended to give students a thorough review of eighth grade math, following the topics listed in the Common Core Standards.The book has both topical as well as mixed (spiral) review worksheets, and includes both topical tests and a comprehensive end-of-year test. The tests can also be used as review worksheets, instead of tests.Please note: The content for this workbook is taken from Math Mammoth Grade 8 Complete Curriculum (Light Blue Series), so this book is redundant if you already own Math Mammoth grade 8.You can use this workbook for various purposes: for summer math practice, to keep a student from forgetting math skills during other break times, or to prepare students who are going into algebra 1.The topics reviewed in this workbook are: exponentsscientific notationgeometric transformationsvolumeangle relationshipslinear equationsintroduction to functionsgraphing linear equationssystems of linear equationssquare roots and the Pythagorean Theorembivariate dataPlease note this book does not contain lessons or instruction for the topics. It is not intended for initial teaching. It also will not work if the student needs to completely re-study these topics (the student has not learned the topics at all). For that purpose, please consider Math Mammoth Grade 8 Complete Curriculum, which has all the necessary instruction and lessons.
Math Mammoth Fractions 1
Math Mammoth Fractions 1 is the first book of two that cover all aspects of fraction arithmetic. This book covers the concepts of fraction and mixed number, equivalent fractions, adding and subtracting like and unlike fractions, adding and subtracting mixed numbers, comparing fractions, and measuring in inches. The book Math Mammoth Fractions 2 covers the rest of fraction arithmetic: simplifying fractions and multiplication and division of fractions.Studying fractions involves lots of rules, and many students learn them only mechanically, not really understanding the underlying concepts and principles. Students then end up making lots of mistakes because they confuse the different rules, and either apply the wrong one or apply the right rule but don't remember it quite right. All this can make students even fear fractions.To avoid that, we use the visual model of a pie divided into slices all the way through the book. It is a natural model because a circle can be divided into any number of circle sectors (slices). When students work with this model from lesson to lesson, they will eventually start seeing these pies in their mind. This, in turn, gives them the ability to do many of the easier fraction calculations mentally. It also enables students to really UNDERSTAND these concepts, and not just learn mechanical rules.You are welcome to use manipulatives along with the book; however the visual pie model is probably sufficient for most students in the fifth grade level. I have also included (in the appendix) printable cut-outs for fractions from halves to twelfths.This workbook is most suitable for 5th grade. However, it is not tied to any grade level and does not mention anything about grade levels (except in the introduction), and so it can be used in various settings. It is also very good for remedial teaching or for students with learning challenges because of its heavy usage of visual models.The answers are appended.
Probability and Statistics
Probability and Statistics: Theory and Exercises is a textbook focused on practical examples of probability theory and statistics, with the goal of giving readers a thorough understanding of mathematical relationships in these subjects. The book is designed for basic courses in probability and statistics, and is aimed primarily at non-specialists and beginner level students. The book is divided into 2 sections, respectively. Probability: Includes a primer on set theory, basic probability theory definitions and calculations, combinatorial analysis, random variables and distribution laws Statistics: Covers basic concepts of descriptive statistics Key features - Simple, clear language for easy comprehension of key concepts - Carefully chosen exercises with solutions for self-learning - Over 40 Illustrations for clear explanations - References for further reading and tutorials
Complex Analysis
This book is an in-depth and modern presentation of important classical results in complex analysis and is suitable for a first course on the topic, as taught by the authors at several universities. The level of difficulty of the material increases gradually from chapter to chapter, and each chapter contains many exercises with solutions and applications of the results, with the particular goal of showcasing a variety of solution techniques.
Sudoku for beginners - 50 puzzles from Mio - think for yourself
The playing field is a 9x9 square, divided into smaller squares with a side length of 3 fields. The main goal of the game is to fill the empty cells with numbers from 1 to 9 so that each number appears only once in each row, column and 3x3 square. Can you fill in all the cells correctly?
Single Variable Calculus
The book is a comprehensive yet compressed entry-level introduction on single variable calculus, focusing on the concepts and applications of limits, continuity, derivative, defi nite integral, series, sequences and approximations. Chapters are arranged to outline the essence of each topic and to address learning diffi culties, making it suitable for students and lecturers in mathematics, physics and engineering. ContentsPrerequisites for calculusLimits and continuityThe derivativeApplications of the derivativeThe definite integralTechniques for integration and improper integralsApplications of the definite integralInfinite series, sequences, and approximations
Philosophy of Mathematics
The present book is an introduction to the philosophy of mathematics. It asks philosophical questions concerning fundamental concepts, constructions and methods - this is done from the standpoint of mathematical research and teaching. It looks for answers both in mathematics and in the philosophy of mathematics from their beginnings till today. The reference point of the considerations is the introducing of the reals in the 19th century that marked an epochal turn in the foundations of mathematics. In the book problems connected with the concept of a number, with the infinity, the continuum and the infinitely small, with the applicability of mathematics as well as with sets, logic, provability and truth and with the axiomatic approach to mathematics are considered. In Chapter 6 the meaning of infinitesimals to mathematics and to the elements of analysis is presented. The authors of the present book are mathematicians. Their aim is to introduce mathematicians and teachers of mathematics as well as students into the philosophy of mathematics. The book is suitable also for professional philosophers as well as for students of philosophy, just because it approaches philosophy from the side of mathematics. The knowledge of mathematics needed to understand the text is elementary. Reports on historical conceptions. Thinking about today's mathematical doing and thinking. Recent developments. Based on the third, revised German edition. For mathematicians - students, teachers, researchers and lecturers - and readersinterested in mathematics and philosophy. Contents On the way to the reals On the history of the philosophy of mathematics On fundamental questions of the philosophy of mathematics Sets and set theories Axiomatic approach and logic Thinking and calculating infinitesimally - First nonstandard steps Retrospection
Functional Analysis with Applications
This book on functional analysis covers all the basics of the subject (normed, Banach and Hilbert spaces, Lebesgue integration and spaces, linear operators and functionals, compact and self-adjoint operators, small parameters, fixed point theory) with a strong focus on examples, exercises and practical problems, thus making it ideal as course material but also as a reference for self-study.
Tensor Analysis
Tensor calculus is a prerequisite for many tasks in physics and engineering. This book introduces the symbolic and the index notation side by side and offers easy access to techniques in the field by focusing on algorithms in index notation. It explains the required algebraic tools and contains numerous exercises with answers, making it suitable for self study for students and researchers in areas such as solid mechanics, fluid mechanics, and electrodynamics. ContentsAlgebraic ToolsTensor Analysis in Symbolic Notation and in Cartesian CoordinatesAlgebra of Second Order TensorsTensor Analysis in Curvilinear CoordinatesRepresentation of Tensor FunctionsAppendices: Solutions to the Problems; Cylindrical Coordinates and Spherical Coordinates
Single Variable Calculus
A computer algebra system such as Mathematica(R) is able to do much more than just numerics: This text shows how to tackle real mathematical problems from basic analysis. The reader learns how Mathematica(R) represents domains, qualifiers and limits to implement actual proofs - a requirement to unlock the huge potential of Mathematica(R) for a variety of applications.
Foundations of Information and Knowledge Systems
This LNCS conference volume constitutes the proceedings of the 13th International Symposium, FoIKS 2024, in Sheffield, UK, in April 2024. The 18 full papers together with 3 short papers included in this volume were carefully reviewed and selected from 42 submissions.The Symposium focuses on fundamental aspect of information and knowledge systems, including submissions that apply ideas, theories, or methods from specific disciplines to information and knowledge systems. Examples of such disciplines are discrete mathematics, logic and algebra, model theory, databases, information theory, complexity theory, algorithmics and computation, statistics, and optimization.
Martingale Methods in Statistics
This gives a comprehensive introduction to the (standard) statistical analysis based on the theory of martingales and develops entropy methods in order to treat dependent data in the framework of martingales. The author starts a summary of the martingale theory, and then proceeds to give full proofs of the martingale central limit theorems.
Analysis of Distributional Data
In a time when increasingly larger and complex data collections are being produced, it is clear that new and adaptive forms of data representation and analysis have to be conceived and implemented. Distributional data, i.e., data where a distribution rather than a single value is recorded for each descriptor, on each unit, come into this framework. Distributional data may result from the aggregation of large amounts of open/collected/generated data, or it may be directly available in a structured or unstructured form, describing the variability of some features. This book provides models and methods for the representation, analysis, interpretation, and organization of distributional data, taking into account its specific nature, and not relying on a reduction to single values, to be conform to classical paradigms. Conceived as an edited book, gathering contributions from multiple authors, the book presents alternative representations and analysis' methods for distributional data of different types, and in particular, -Uni- and bi-variate descriptive statistics for distributional data-Clustering and classification methodologies-Methods for the representation in low-dimensional spaces-Regression models and forecasting approaches for distribution-valued variablesFurthermore, the different chapters -Feature applications to show how the proposed methods work in practice, and how results are to be interpreted, -Often provide information about available software.The methodologies presented in this book constitute cutting-edge developments for stakeholders from all domains who produce and analyse large amounts of complex data, to be analysed in the form of distributions. The book is hence of interest for companies operating not only in the area of data analytics, but also on logistics, energy and finance. It also concerns national statistical institutes and other institutions at European and international level, where microdata is aggregated to preserve confidentiality and allow for analysis at the appropriate regional level. Academics will find in the analysis of distributional data a challenging up-to-date field of research.
Origins and Varieties of Logicism
This book offers a plurality of perspectives on the historical origins of logicism and on contemporary developments of logicist insights in philosophy of mathematics. It uniquely provides up-to-date research and novel interpretations on a variety of intertwined themes and historical figures related to different versions of logicism.
Analysis of Longitudinal Data with Examples
Development in methodology on longitudinal data is fast. Currently, there are a lack of intermediate /advanced level textbooks which introduce students and practicing statisticians to the updated methods on correlated data inference. This book will present a discussion of the modern approaches to inference, including the links between the theories of estimators and various types of efficient statistical models including likelihood-based approaches. The theory will be supported with practical examples of R-codes and R-packages applied to interesting case-studies from a number of different areas.Key Features: -Includes the most up-to-date methods-Use simple examples to demonstrate complex methods-Uses real data from a number of areas-Examples utilize R code
The Land Between
The Land Between is the first concise history of Slovenia and Slovenes written in English by leading scholars from the country. The authors base their arguments on Slovenian, former Yugoslav, and Western sources to provide a comprehensive account of Slovenes' political, social, economic and cultural history, from early Slav settlements to the present day. The authors focus on Slovenian history but, to their credit, manage to place it in a wider context of empires and states to which Slovenian lands had belonged throughout history. The book will be of use to students of Slovenia and East-Central Europe, to diplomats, journalists, tourists, and anyone interested in this part of the world. It represents a welcome addition to the historiography of Slovenia and former Yugoslavia as well as a unique insight into the state of scholarship in post-1991 Slovenia. Dejan Djokic, historian, National University of Ireland, Maynooth A study which makes the reader feel and understand that since the end of the Cold War there is a new lease of life for Central Europe. The former borderlands between East and West construct their new identities. Slovenia is one of the most successful new democratic societies in the middle of Europe. This book is an excellent history of Slovenia which maps the narrative of a small European people without falling into the traps of national mythmaking. Writing about a small European country with two million inhabitants which crave for Central European, Mediterranean and Balkan traditions at the same time is no simple task. The book makes fine reading for everybody interested in understanding the fascinating and creative complexities in the heart of Europe. Highly recommendable for history lovers and historians alike! Emil Brix, historian and ambassador, Director of the Diplomatische Akademie Wien - Vienna School of International Studies The book presents a concise and intelligible history of the Slovenes. The authors take into due consideration the history of the territory between the Eastern Alps and the Pannonian Plain, starting with the period that began long before the first Slavic settlements. Thus, they wish to emphasize that the Slovenes' ancestors did not settle an empty territory, but rather coexisted with other peoples and cultures ever since their arrival in the Eastern Alps. This has enabled them to build a community shaped by countless influences stemming from a long period of living alongside German, Romance, and South Slav neighbors in a melting pot of languages, cultures, and landscapes. The same reasons have most probably also contributed to the perception of their land as a "land in between." Constituting a link between Eastern and Western Europe, Slovenia has recently also been increasingly perceived as the meeting point of Central Europe and the Balkans. Today, history still occupies the central position in the life of the Slovenes. The heroic period of emancipation has been completed and the Slovenes will be bracing themselves for a no less turbulent period of challenging "essentialist" notions of identity in order to create a thoroughly open society.
Mathematics of Information
Ausgehend vom Shannon-Wiener-Zugang zur mathematischen Informationstheorie beginnt das Buch mit einer Abgrenzung der Begriffe Nachricht und Information und der axiomatischen Zuordnung einer Informationsmenge zu einer Wahrscheinlichkeit. Im zweiten Teil werden abz瓣hlbare Wahrscheinlichkeitsr瓣ume untersucht, deren mittlere Informationsmenge zur Definition der Shannon-Entropie f羹hrt; dabei werden drei klassische Anwendungen der Shannon-Entropie in der statistischen Physik, der mathematischen Statistik und der Nachrichtentechnik vorgestellt, und es wird ein erster Einblick in den Bereich Quanteninformation gegeben. Der dritte Teil behandelt die informationstheoretische Analyse dynamischer Systeme.Das Buch baut auf Bachelor-Wissen auf und legt gro?en Wert auf exakte Beweisf羹hrung.
Disruptive Technologies and Optimization Towards Industry 4.0 Logistics
This contributed volume guides researchers and practitioners on resource collaborative management of supply chains and manufacturing enterprises within an industrial internet technological environment. The book comprises 10 chapters that cover two major topics in the subject of logistics 4.0, namely the utilization of both disruptive technologies and optimization techniques in smart logistic management. With global research on the book's topic expanding rapidly across various directions and disciplines, it provides a structured framework for international experts to showcase outstanding work and unique approaches. Researchers and students will find the comprehensive outline on collaborative optimization and management of smart manufacturing and production, warehousing, inventory, logistics, transportation, integrated supply chain, and supply network within the industrial internet platform a beneficial guide to understanding current and future practical problems that arise in manufacturing and supply chain management.
Physical and Physiological Analysis of Soya Seeds from the 2016/2017 Harvest
The use of high quality seeds allows access to genetic advances, with guarantees of quality and adaptation technologies in the various producing regions. The factors that influence seed quality can occur during the production phase in the field, during harvesting, drying, processing, storage, transport and sowing. Quality control must therefore be established, which includes analysing and certifying the seed in order to guarantee the genetic purity of the cultivars, thus assuring the farmer of a pure batch with high vigour, which can establish a uniform stand in the field. The quality of soya bean seed is essential for obtaining an adequate plant stand, because when the seed is placed in the soil to germinate and emerge, it usually encounters adverse conditions of humidity and temperature, among other factors. Considering the importance of seed for agricultural production and aiming to achieve higher levels of profitability, this study will present data on the physical and physiological quality of soya bean seeds from the 2017/2018 harvest in northern Rio Grande do Sul.
Journal of Applied Logics, Volume 11, Number 1, January 2024. Special Issue
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 free open access, and available via the College Publications website. This Journal is open access, puts no limit on the number of pages of any article, puts no limit on the number of papers in an issue and puts no limit on the number of issues per year. We insist only on a very high academic standard, and will publish issues as they come.
Cambridge IGCSE Complete Mathematics Core Student Book 6th E
Paradoxes and Inconsistent Mathematics
Logical paradoxes - like the Liar, Russell's, and the Sorites - are notorious. But in Paradoxes and Inconsistent Mathematics, it is argued that they are only the noisiest of many. Contradictions arise in the everyday, from the smallest points to the widest boundaries. In this book, Zach Weber uses "dialetheic paraconsistency" - a formal framework where some contradictions can be true without absurdity - as the basis for developing this idea rigorously, from mathematical foundations up. In doing so, Weber directly addresses a longstanding open question: how much standard mathematics can paraconsistency capture? The guiding focus is on a more basic question, of why there are paradoxes. Details underscore a simple philosophical claim: that paradoxes are found in the ordinary, and that is what makes them so extraordinary.
The Fourth Coming
In a time of dire need, as climate change, conflict, and economic upheaval imperil our existence and our mental well-being deteriorates from not utilising our minds as God intended, Francis Keith Robins introduces a groundbreaking approach to saving humanity - reshaping our thought processes through mathematics. In his book, The Fourth Coming, Robins provides a detailed, step-by-step guide to unlocking our inherent mathematical potential. His vision is to create a society that is inclusive, equal, and peaceful - one that aligns with God's desire for us. He advocates for a paradigm shift where shared mathematical models and systematic thinking supplant the ineffective classes of governments and institutions currently jeopardizing our planet. This revolutionary approach aims to alter the trajectory of human history in a manner that aligns with divine intentions. Robins' theories, described as a work of mathematical brilliance, offer a refreshingly simple yet profound solution to consciousness - which, as noted by 'New Scientist', remains one of the most elusive and significant mysteries in science and philosophy. Furthermore, he concludes that the introduction of religion by God was a response to humanity's failure to use their brains as He intended.
The Fourth Coming
In a time of dire need, as climate change, conflict, and economic upheaval imperil our existence and our mental well-being deteriorates from not utilising our minds as God intended, Francis Keith Robins introduces a groundbreaking approach to saving humanity - reshaping our thought processes through mathematics. In his book, The Fourth Coming, Robins provides a detailed, step-by-step guide to unlocking our inherent mathematical potential. His vision is to create a society that is inclusive, equal, and peaceful - one that aligns with God's desire for us. He advocates for a paradigm shift where shared mathematical models and systematic thinking supplant the ineffective classes of governments and institutions currently jeopardizing our planet. This revolutionary approach aims to alter the trajectory of human history in a manner that aligns with divine intentions. Robins' theories, described as a work of mathematical brilliance, offer a refreshingly simple yet profound solution to consciousness - which, as noted by 'New Scientist', remains one of the most elusive and significant mysteries in science and philosophy. Furthermore, he concludes that the introduction of religion by God was a response to humanity's failure to use their brains as He intended.
Persistent Homology and Persistent Cohomology
Persistent homology has become an important tool in non-linear data reduction. Its sister theory, Persistent cohomology, has attracted less attention in the past eventhough it has many advantages. We surveyed several literatures and present a summary of the status quo in persistent (co)homology covering the theory, computations, representations in terms of cycles (for persistent homology) and cocycles (for persistent cohomology), lens (quotient) space and their equivalence. Moreover, we computed the persistent homology and persistent cohomology for the 2 - sphere both manually and computationally (Using Ripserer). In both cases, same result was obtained, particularly in the computation of their barcodes much more that persistent cohomology is not only faster in computation than persistent homology, but also uses less memory in a little time.
Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume II, Part II
This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1967.
Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Volume III
This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1972.
