Mathematics For The Nonmathematician Epub Bud
Niki Wienberg
Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. (PsycINFO Database Record
This is an introduction to probability theory, designed for self-study. It covers the same topics as the one-semester introductory courses which I taught at the University of Minnesota, with some extra discussion for reading on your own. The reasons which underlie the rules of probability are emphasized. Probability theory is certainly useful. But how does it feel to study it? Well, like other areas of mathematics, probability theory contains elegant concepts, and it gives you a chance to exercise your ingenuity, which is often fun. But in addition, randomness and probability are part of our experience in the real world, present everywhere and yet still somewhat mysterious. This gives the subject of probability a special interest.
Mathematical modelling plays an increasingly important role in almost any area of life sciences, and this interactive textbook focuses on the areas of population ecology, infectious diseases, immunology and cell dynamics, gene networks and pharmacokinetics. It is aimed at anyone who is interested in learning about how to model biological systems, including undergraduate and postgraduate mathematics students who have not studied mathematical biology before, life-sciences students with an interest in modelling, and post-16 mathematics students interested in university-level material. Some mathematical knowledge is assumed, and the mathematical models used are all in the form of ordinary differential equations.
It is thus more likely to be a good source from which to generate newer formats, e.g., MathML [namely HTML, or more specifically XML, that handles mathematics correctly -- note that the MathML people plan a LaTeX to MathML translator, but dvi/ps/pdf lack the necessary document structuring concepts]. Possession of the source thus provides many additional options for future document migrations. Using emerging new technology, most of the Postscript generated from the source contains hyperlinks, so that using new versions of PostScript previewers (e.g., the next version of Ghostscript/Ghostview), readers can point-and-click to navigate within the paper, and even over the web itself.
Leaving aside the power and flexibility of LaTeX, the huge existing codebase coupled with the lack of good conversion tools is a currently an insurmountable obstacle to any move away from LaTeX. I teach university mathematics. Like most of my colleagues, I maintain several hundred teaching related LaTeX documents (plus many other research documents). I would dearly love to be able to generate html pages with MathML equations from the LaTeX source seamlessly in a way that:
At present, this is all a dream. Even if good conversion tools existed, the lack of browser support for MathML means few mathematicians would even contemplate publishing anything this way. So we are stuck with publishing materials in pdf format on web sites, with all of the downsides that entails. So in university mathematics and engineering departments, I would say LaTeX is unlikely to yield much ground in the near future. Anyway, I thought that the perspective of a major and influential segment of the LaTeX user base might be of interest.
This volume features a complete set of problems, hints, and solutions based on Stanford University's well-known competitive examination in mathematics. It offers high school and college students an excellent mathematics workbook of rigorous problems that will assist in developing and cultivating their logic and probability skills.These 20 sets of intriguing problems test originality and insight rather than routine competence. They involve theorizing and verifying mathematical facts; examining the results of general statements; discovering that highly plausible conjectures can be incorrect; solving sequences of subproblems to reveal theory construction; and recognizing "red herrings," in which obvious relationships among the data prove irrelevant to solutions. Hints for each problem appear in a separate section, and a final section features solutions that outline the appropriate procedures.Ideal for teachers seeking challenging practice math problems for their gifted students, this book will also help students prepare for mathematics, science, and engineering programs. Mathematics buffs of all ages will also find it a source of captivating challenges.
The study of mathematics is apt to commence in disappointment. The important applications of the science, the theoretical interest of its ideas, and the logical rigor of its methods, all generate the expectation of a speedy introduction to processes of interest. We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it 'Tis here 'tis there, 'tis gone" and what we do see does not suggest the same excuse for illusiveness as sufficed for the ghost, that it is too noble for our gross methods.
The object of the following Chapters is not to teach mathematics, but to enable students from the very beginning of their course to know what the science is about, and why it is necessarily the foundation of exact thought as applied to natural phenomena. All allusion in what follows to detailed deductions in any part of the science will be inserted merely for the purpose of example, and care will be taken to make the general argument comprehensible, even if here and there some technical process or symbol which the reader does not understand is cited for the purpose of illustration.
The first acquaintance which most people have with mathematics is through arithmetic. That two and two make four is usually taken as the type of a simple mathematical proposition which everyone will have heard of. Arithmetic, therefore, will be a good subject to consider in order to discover, if possible, the most obvious characteristic of the science. Now, the first noticeable fact about arithmetic is that it applies to everything, to tastes and to sounds, to the ideas of the mind and to the bones of the body. The nature of the things is perfectly indifferent, of all things it is true that two and two make four. Thus we write down as the leading characteristic of mathematics that it deals with properties and ideas which are applicable to things just because they are things, and apart from any particular feelings, or emotions, or sensations, in any way connected with them. This is what is meant by calling mathematics an abstract science.
Take an apple and cut it into five pieces. Would you believe that these five pieces can be reassembled in such a fashion so as to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, author of The Pea and the Sun, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Written in an engaging style, The Pea and the Sun catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox. Wapner makes one of the most interesting problems of advanced mathematics accessible to the non-mathematician.
Today's classrooms are full of routines. Although we often think of routines as being used for organization, routines can also be used to enhance instruction. In this book, the authors present seven easily implemented mathematical routines that may be used effectively at a variety of grade levels and with a variety of mathematical content. The book also includes ideas for infusing mathematics into the nonmathematical routines that take time away from instruction.
Each chapter begins with classroom vignettes that provide a glimpse of how the routine might look as it is implemented in a variety of grade levels. A description of the routine and implementation strategies follow and the authors provide examples of student work from various grade levels for each of the routine, including examples of ways to assess student thinking by using the routines, and suggestions for adapting the routines. The book includes connections to the Common Core practice standards and focuses on creating opportunities for differentiated instruction.
A highly useful book, written by seasoned mathematics educators, this book is a must-have for all elementary and middle school mathematics teachers.
Praise forHigh-Yield Routines
The easily implemented routines suggested in High-Yield Routines will provide teachers withopportunities to enhance the content knowledge and mathematical practices of their students.Classroom vignettes, from a variety of grade levels, illustrate how the routines may be usedeffectively across many grade levels and the student work included provides a picture of whatteachers might expect from students. This book will prove to be a valuable resource for teachers bothnew and experienced.--Terry Goodman, Concordia College
High-Yield Routines is a book that should be owned by all elementary and middle schoolmathematics teachers. It shows a quick and easy way to optimize precious classroom minutes,infusing mathematics into otherwise non-mathematical routines. The connections to the CommonCore practice standards will help teachers address this important content throughout the day in waysthat are unexpected but highly productive.--Rita Barger, University of Missouri-Kansas City
High-Yield Routines describes several mathematical routines that will create opportunities fordifferentiated instruction to take place naturally with students. The routines described in thebook allow each student to participate at his or her own level and to build upon existing knowledgeto develop a deeper understanding of the content. The routines are easy to implement andclassroom teachers at all grade levels will be able to utilize the routines to enhance the mathematicsunderstanding of students.--Jami Smith, Archie Middle School
About the Authors
Ann McCoy is an associate professor of mathematics education at the University of CentralMissouri where she teaches mathematics content and methods courses for prospective elementaryand middle school teachers. Prior to teaching at the university, she taught elementary and middleschool mathematics for twenty-two years. She has been actively involved in numerous professionaldevelopment projects for mathematics teachers.
Joann Barnett is retired from the Ozark, MO, school district where she taught elementary andmiddle school mathematics for nearly thirty years. She is now an adjunct instructor for mathematicsand mathematics education at Missouri State University and Ozarks Technical Community College.Over the past thirteen years, she has been involved with various state and federal grants to provideprofessional development for teachers.
Emily Combs is in her fourteenth year as a middle school mathematics teacher at ClintonMiddle School, Clinton, MO. Over the past ten years she has participated in many professionaldevelopment projects including her role as co-principal investigator of a Mathematics and SciencePartnership Grant. She is interested in using learning trajectories to build accessible, mathematicallyrich lessons to deepen mathematics understanding smoothly across grade levels.