Many in the mathematics community in the U.S. are involved in mathematics education in various capacities. This book highlights the breadth of the work in K-16 mathematics education done by members of US departments of mathematical sciences. It contains contributions by mathematicians and mathematics educators who do work in areas such as teacher education, quantitative literacy, informal education, writing and communication, social justice, outreach and mentoring, tactile learning, art and mathematics, ethnomathematics, scholarship of teaching and learning, and mathematics education research. Contributors describe their work, its impact, and how it is perceived and valued. In addition, there is a chapter, co-authored by two mathematicians who have become administrators, on the challenges of supporting, evaluating, and rewarding work in mathematics education in departments of mathematical sciences. This book is intended to inform the readership of the breadth of the work and to encourage discussion of its value in the mathematical community. The writing is expository, not technical, and should be accessible and informative to a diverse audience. The primary readership includes all those in departments of mathematical sciences in two or four year colleges and universities, and their administrators, as well as graduate students. Researchers in education may also find topics of interest. Other potential readers include those doing work in mathematics education in schools of education, and teachers of secondary or middle school mathematics as well as those involved in their professional development.

This book presents important works by the Scottish mathematician Colin MacLaurin (1698-1746), translated in English for the first time. It includes three of the mathematician 's less known and often hard to obtain works. A general introduction puts the works in context and gives an outline of MacLaurin's career. Each translation is also accompanied by an introduction and analyzed both in modern terms and from a historical point of view.

The first instance of pre-computer fractals was noted by the French mathematician Gaston Julia. He wondered what a complex polynomial function would look like, such as the ones named after him (in the form of z2 + c, where c is a complex constant with real and imaginary parts). The idea behind this formula is that one takes the x and y coordinates of a point z, and plug them into z in the form of x + i*y, where i is the square root of -1, square this number, and then add c, a constant. Then plug the resulting pair of real and imaginary numbers back into z, run the operation again, and keep doing that until the result is greater than some number. The number of times you have to run the equations to get out of an 'orbit' not specified here can be assigned a colour and then the pixel (x,y) gets turned that colour, unless those coordinates can't get out of their orbit, in which case they are made black. Later it was Benoit Mandelbrot who used computers to produce fractals. A basic property of fractals is that they contain a large degree of self similarity, i.e., they usually contain little copies within the original, and these copies also have infinite detail. That means the more you zoom in on a fractal, the more detail you get, and this keeps going on forever and ever. The well-written book 'Getting acquainted with fractals' by Gilbert Helmberg provides a mathematically oriented introduction to fractals, with a focus upon three types of fractals: fractals of curves, attractors for iterative function systems in the plane, and Julia sets. The presentation is on an undergraduate level, with an ample presentation of the corresponding mathematical background, e.g., linear algebra, calculus, algebra, geometry, topology, measure theory and complex analysis. The book contains over 170 color illustrations.

This new edition of Luke Robinson's popular textbook 'Pure Mathematics for CCEA AS Level' has been comprehensively updated to meet the requirements of the CCEA specification and fully covers unit AS1: Pure Mathematics. Following teacher feedback, it has been re-designed with a new two-colour style for ease of use. Each section of the book contains theory and examples with key words and definitions throughout. It also provides a large number of exercises, with answers included at the back of the book. Contents: Indices and Surds Quadratics Simultaneous Equations and Inequalities Algebraic Manipulation Graph Manipulation Graphs and Transformations Straight Lines Circles Binomial Expansion Trigonometry Exponentials and Logs Differentiation Integration Vectors Problem Solving

Budgeting can be stressful and overwhelming to the average American. You can learn how to cut corners from grocery shopping, to going on that much wanted vacation to saving money on entertainment that it hard to afford on the budget you have yet to make. Don't feel drained at the end of the month; read Life on A budget to begin feeling more energized by your "desire" and "motivation."

This contributed volume is an exciting product of the 22nd MAVI conference, which presents cutting-edge research on affective issues in teaching and learning math. The teaching and learning of mathematics is highly dependent on students' and teachers' values, attitudes, feelings, beliefs and motivations towards mathematics and mathematics education. These peer-reviewed contributions provide critical insights through their theoretically and methodologically diverse analyses of relevant issues related to affective factors in teaching and learning math and offer new tools and strategies by which to evaluate affective factors in students' and teachers' mathematical activities in the classroom. Among the topics discussed: The relationship between proxies for learning and mathematically related beliefs. Teaching for entrepreneurial and mathematical competences. Prospective teachers' conceptions of the concepts mean, median, and mode. Prospective teachers' approach to reasoning and proof The impact of assessment on students' experiences of mathematics. Through its thematic connections to teacher education, professional development, assessment, entrepreneurial competences, and reasoning and proof, Students' and Teachers' Values, Attitudes, Feelings and Beliefs in Mathematics Classrooms proves to be a valuable resource for educators, practitioners, and students for applications at primary, secondary, and university levels.

In the 5th century the Indian mathematician Aryabhata (476-499) wrote a small but famous work on astronomy, the Aryabhatiya. This treatise, written in 118 verses, gives in its second chapter a summary of Hindu mathematics up to that time. Two hundred years later, an Indian astronomer called Bhaskara glossed this mathematial chapter of the Aryabhatiya.

An english translation of Bhaskara s commentary and a mathematical supplement are presented in two volumes.

Subjects treated in Bhaskara s commentary range from computing the volume of an equilateral tetrahedron to the interest on a loaned capital, from computations on series to an elaborate process to solve a Diophantine equation.

This volume contains an introduction and the literal translation.

The introduction aims at providing a general background for the translation and is divided in three sections: the first locates Bhaskara s text, the second looks at its mathematical contents and the third section analyzes the relations of the commentary and the treatise."

The area of analysis and control of mechanical systems using differential geometry is flourishing.

This book collects many results over the last decade and provides a comprehensive introduction to the area.

This monograph, divided into four parts, presents a comprehensive treatment and systematic examination of cycle spaces of flag domains. Assuming only a basic familiarity with the concepts of Lie theory and geometry, this work presents a complete structure theory for these cycle spaces, as well as their applications to harmonic analysis and algebraic geometry.

Key features:

* Accessible to readers from a wide range of fields, with all the necessary background material provided for the nonspecialist

* Many new results presented for the first time

* Driven by numerous examples

* The exposition is presented from the complex geometric viewpoint, but the methods, applications and much of the motivation also come from real and complex algebraic groups and their representations, as well as other areas of geometry

* Comparisons with classical Barlet cycle spaces are given

* Good bibliography and index.

Researchers and graduate students in differential geometry, complex analysis, harmonic analysis, representation theory, transformation groups, algebraic geometry, and areas of global geometric analysis will benefit from this work.

In the 5th century the Indian mathematician Aryabhata (476-499) wrote a small but famous work on astronomy, the Aryabhatiya. This treatise, written in 118 verses, gives in its second chapter a summary of Hindu mathematics up to that time. Two hundred years later, an Indian astronomer called Bhaskara glossed this mathematial chapter of the Aryabhatiya.

An english translation of Bhaskara s commentary and a mathematical supplement are presented in two volumes.

Subjects treated in Bhaskara s commentary range from computing the volume of an equilateral tetrahedron to the interest on a loaned capital, from computations on series to an elaborate process to solve a Diophantine equation.

This volume contains explanations for each verse commentary translated in Volume 1. These supplements discuss the linguistic and mathematical matters exposed by the commentator. Particularly helpful for readers are an appendix on Indian astronomy, elaborate glossaries, and an extensive bibliography.

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This text gives a detailed account of various techniques that are used in the study of dynamics of continuous systems, near as well as far from equilibrium. The analytic methods covered include diagrammatic perturbation theory, various forms of the renormalization group and self-consistent mode coupling. Dynamic critical phenomena near a second order phase transition, phase ordering dynamics, dynamics of surface growth and turbulence form the backbone of the book. Applications to a wide variety of systems (e.g. magnets, ordinary fluids, super fluids) are provided covering diverse transport properties (diffusion, sound).

The developmentsin the recent yearsof the potential theoryemphasized a classof functions larger than that of excessive functions (i.e. the positive superharmonic functionsfromtheclassicalpotentialtheoryassociatedwiththeLaplaceoperator), namely the strongly supermedian functions. It turns out that a positive Borel function will be strongly supermedian if and only if it is the in?mum of all its excessive majorants. Apparently, these functions have been introduced by J.F. Mertens and then they have been studied mainly by P.A. Meyer, G. Mokobodzki, D. Feyel and recently by P.J. Fitzsimmons and R.K. Getoor. The aimofthis bookisamongothersto developa potential theoryappropriate to this new class of functions. Although our methods are analytical, we present also the probabilistic counterparts from the Markov processes theory. The natural frame in which this theory is settled is given by a sub-Markovian resolvent of kernels on a Radon measurable space. After a possible extension of the space, such a resolvent becomes that one associated with a right process on a Radon topological space, not necessary locally compact and without existing a reference measure. Intimately related to the excessive functions we present certain basic tools of the theory: the Ray topology and compacti?cation, the ?ne carrier and the reduction operation on measurable sets. We examine di?erent types of negligible sets with respect to a ?nite measure ?: the ?-polar, ?-semipolar and ?-mince sets. We take advantage of the cone of potentials structure for both excessive functions and measures

This book is devoted to analytically approximate methods in the nonlinear dynamics of a rigid body with cavities (containers) partly filled by a liquid. The methods are normally based on the Bateman-Luke variational formalism combined with perturbation theory. The derived approximate equations of spatial motions of the body-liquid mechanical system (these equations are called mathematical models in the title) take the form of a finite-dimensional system of nonlinear ordinary differential equations coupling quasi-velocities of the rigid body motions and generalized coordinates responsible for displacements of the natural sloshing modes. Algorithms for computing the hydrodynamic coefficients in the approximate mathematical models are proposed. Numerical values of these coefficients are listed for some tank shapes and liquid fillings. The mathematical models are also derived for the contained liquid characterized by the Newton-type dissipation. Formulas for hydrodynamic force and moment are derived in terms of the solid body quasi-velocities and the sloshing-related generalized coordinates. For prescribed harmonic excitations of upright circular (annular) cylindrical and/or conical tanks, the steady-state sloshing regimes are theoretically classified; the results are compared with known experimental data. The book can be useful for both experienced and early-stage mechanicians, applied mathematicians and engineers interested in (semi-)analytical approaches to the "fluid-structure" interaction problems, their fundamental mathematical background as well as in modeling the dynamics of complex mechanical systems containing a rigid tank partly filled by a liquid.

A practical introduction to fundamentals of computer arithmetic

Computer arithmetic is one of the foundations of computer science and engineering. Designed as both a practical reference for engineers and computer scientists and an introductory text for students of electrical engineering and the computer and mathematical sciences, Arithmetic and Logic in Computer Systems describes the various algorithms and implementations in computer arithmetic and explains the fundamental principles that guide them.

Focusing on promoting an understanding of the concepts, Professor Mi Lu addresses:

• Number representations, including the Conventional Radix and
• Signed-Digit Number Systems as well as Floating Point, Residue, and Logarithmic Number Systems
• Ripple Carry Adders and high-speed adders
• Sequential multiplication, parallel multiplication, sequential division, and fast array dividers
• Floating point operations, Residue Number operations, and operations through logarithms

To assist the reader, alternative methods are examined and thorough explanations of the material are supplied, along with discussions of the reasoning behind the theory. Ample examples and problems help the reader master the concepts.

Dialogue and Learning in Mathematics Education is concerned with communication in mathematics class-rooms. In a series of empirical studies of project work, we follow students' inquiry cooperation as well as students' obstructions to inquiry cooperation. Both are considered important for a theory of learning mathematics.
Special attention is paid to the notions of dialogue' and critique'. A central idea is that dialogue' supports critical learning of mathematics'. The link between dialogue and critique is developed further by including the notions of intention' and reflection'. Thus a theory of learning mathematics is developed which is resonant with critical mathematics education.

This book examines the critical roles and effects of mathematics education. The exposition draws from the author's forty-year mathematics career, integrating his research in the psychology of mathematical thinking into an overview of the true definition of math. The intention for the reader is to undergo a "corrective" experience, obtaining a clear message on how mathematical thinking tools can help all people cope with everyday life. For those who have struggled with math in the past, the book also aims to clarify that math learning difficulties are likely a result of improper pedagogy as opposed to any lack of intelligence on the part of the student. This personal treatise will be of interest to a variety of readers, from mathematics teachers and those who train them to those with an interest in education but who may lack a solid math background.

The study of CR manifolds lie at the intersection of three main mathematical disciplines, partial differential equations, complex analysis in several complex variables, and differential geometry. While the complex analysis and PDEs aspect have been intensly studied in the last fifty years, much effort has been recently made to understand the differential geometric side of the subject.This monograph provides a unified presentation of several differential geometric aspects in the theory of CR manifolds and tangential Cauchy-Riemann equations. It presents topics from the Tanaka-Webster connection, a key contributor to the birth of pseudohermitian geometry, to the major differential geometric acheivements in the theory of CR manifolds, such as Fefferman's metric, pseudo-Einstein structures and the Lee conjecture, CR immersions, subelliptic harmonic maps as a local manifestation of pseudoharmonic maps from a CR manifold, Yang-Mills fields on CR manifolds, to name several. It also aims at explaining how certain results from analysis are employed in CR geometry. results and stimulating unproved statements and comments referring to the most recent aspects of the theory, this monograph is suitable for researchers and graduate students in differential geometry, complex analysis, and PDEs.

This book consists of reviewed original research papers and expository articles in index theory (especially on singular manifolds), topology of manifolds, operator and equivariant K-theory, Hopf cyclic cohomology, geometry of foliations, residue theory, Fredholm pairs and others, and applications in mathematical physics. The wide spectrum of subjects reflects the diverse directions of research for which the starting point was the Atiyah-Singer index theorem.

This book highlights the emergence of a new mathematical rationality and the beginning of the mathematisation of physics in Classical Islam. Exchanges between mathematics, physics, linguistics, arts and music were a factor of creativity and progress in the mathematical, the physical and the social sciences. Goods and ideas travelled on a world-scale, mainly through the trade routes connecting East and Southern Asia with the Near East, allowing the transmission of Greek-Arabic medicine to Yuan Muslim China. The development of science, first centred in the Near East, would gradually move to the Western side of the Mediterranean, as a result of Europe's appropriation of the Arab and Hellenistic heritage. Contributors are Paul Buell, Anas Ghrab, Hossein Masoumi Hamedani, Zeinab Karimian, Giovanna Lelli, Marouane ben Miled, Patricia Radelet-de Grave, and Roshdi Rashed.

Probabilistic Conditional Independence Structures provides the mathematical description of probabilistic conditional independence structures; the author uses non-graphical methods of their description, and takes an algebraic approach.

The monograph presents the methods of structural imsets and supermodular functions, and deals with independence implication and equivalence of structural imsets. Motivation, mathematical foundations and areas of application are included, and a rough overview of graphical methods is also given. In particular, the author has been careful to use suitable terminology, and presents the work so that it will be understood by both statisticians, and by researchers in artificial intelligence. The necessary elementary mathematical notions are recalled in an appendix.

Accosiative rings and algebras are very interesting algebraic structures. In a strict sense, the theory of algebras (in particular, noncommutative algebras) originated fromasingleexample, namelythequaternions, createdbySirWilliamR.Hamilton in1843. Thiswasthe?rstexampleofanoncommutative"numbersystem." During thenextfortyyearsmathematiciansintroducedotherexamplesofnoncommutative algebras, began to bring some order into them and to single out certain types of algebras for special attention. Thus, low-dimensional algebras, division algebras, and commutative algebras, were classi?ed and characterized. The ?rst complete results in the structure theory of associative algebras over the real and complex ?elds were obtained by T.Molien, E.Cartan and G.Frobenius. Modern ring theory began when J.H.Wedderburn proved his celebrated cl- si?cation theorem for ?nite dimensional semisimple algebras over arbitrary ?elds. Twenty years later, E.Artin proved a structure theorem for rings satisfying both the ascending and descending chain condition which generalized Wedderburn structure theorem. The Wedderburn-Artin theorem has since become a corn- stone of noncommutative ring theory. The purpose of this book is to introduce the subject of the structure theory of associative rings. This book is addressed to a reader who wishes to learn this topic from the beginning to research level. We have tried to write a self-contained book which is intended to be a modern textbook on the structure theory of associative rings and related structures and will be accessible for independent study.