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This class completes high school study of Mathematics. The goal is to help the student be ready to walk into a AP Calc or AP Stat or other Advanced Math/college course and be successful. This is the capstone to all previous study in Number and Quanity, Algebra, Functions, Geometry, and Probability and Statistics.
Our study will include trigonometry, deeper study of functions, complete work of logarithms and become a more skilled mathematician. See the syllabus for more detail.
Announcements
End of Week 11 Report
We had a great week! We applied our study of trigonometry to several fields of study. The students presented a problem to the class including explaining the math and arriving at the correct solution. Our next, and last study of trig will be identities and making application. Students are working well together and growning. You should be proud of the "inner mathematician" that is coming out in your child.
End of Week 9 and 10
We had a productive period of working with Trigonometry and Triangles. The grades have been updated. Parents, I want you to know I am very proud of your child and the tremendous group of students I am working with. We should do outstanding things as we progress this school year.
End of Week 8 Report
This week we finished our unit on Trig functions. We did some review and conducted some classroom demonstrations. We had an exam on Friday. Next week we will study Trig Identities.
End of Week 7 Report
Homecoming went well! Several students participated and you can see pictures in the image gallery. We finished up our study of unit 2 on Trig Functions. I am proud of our class taking on a word problem and presenting it to the class. They have been working on their own in a group of two and have taken on the role of teacher. Very good. We will do some enrichment this week, review and take another comprehensive exam on Friday. To be successful students need to review their notes frequently, complete all assigned hw problems, rework any missed problem and complete any review assignments. Also if students did not complete the training for the TI graphing calculator, then doing this before the test would help. Encourage all resource use. See the folder Inverse Trig Functions. Thank you, parents.
End of Week 6 Report
In our short week, I want to express my thankfulness we did not have serious damage by the storm and how PSD managed school closings. We went over the exam. Due to the great effort of students, we were able to continue to progress in our studies to end up Friday talking about Inverse Trig Functions. I will be moving a HW grade to this week and a quiz on Friday. Please take time to visit the resource section and look at the lesson on Trig Inverses. I want you to know about all the resources that have been gathered to help your child be successful. Please take a few minutes and see them for yourself. I think you will be impressed. A great homecoming week is anticipated and I hope to see you at the big game on Friday!
End of Week 5 Report
We conducted an exam of our study of Trig thus far. It was a challenge to students but the performance was average to excellent. Way to go students. After we return to school we will work more on Trigonometry. I have made minor adjustments to our lesson schedule. Please view that document. Your child may need more support or help with study skills. I recommend at least 30 minutes per day reading, working problems or viewing instructional videos. Math is a building type of learning and mastery only happens over a period of sustained activity. The benefits of such study and learning are tremendous.
End of Week 4 Report
We continued our study and now are working on Trig functions. This is an exciting part of the course and has many applications in life and the sciences. We will finish this study and take our first test this Friday. It will be comprehensive over the 5 weeks of study. Please review the course documents if you have not done so already. The grades have been updated as well. Again, thank you for your support and involvement.
End of Week 3 Report
We started our work on Trigonometry. The concepts of Trig help us understand many things in life that have cycles. We continued the schedule of standards and took a quiz on Thursday. There should be three grades: the syllabus, Quiz 1 and Quiz 2. One way to become good at Trig is to know the Unit Circle. I have a handout on this and a video I made for students on our course page.It may be good to take a few days and review the math that students have gaps with. This is also a great opportunity to rekindle an appreciation of math and work on proper classroom learning behaviors. I am expecting by the end of this week for students to remedy on their own any poor listening or work ethic challenges. After this period, parents have good reason to expect quality math instruction and fewer days of wasted instructional time.
End of Week 2 Report
The quiz went well on Thursday. We are working through the proper lessons and students are being assigned work. I will not be able to slow down or compromise the integrity of the course for students who do not work or study outside of class. Please make sure by the end of week 4 there is regular daily study times. This is the only way lasting learning happens. Having taught college for over 6 years, it is very easy for me to know what happens to students with very weak math skills. This can be corrected in a few weeks time with your support. The distractions from nonenaged students will be addressed this week. Thank you for your support.
End of Week 1 Report
I thought we had a good week. We had some introductions and did some review. We also gave the syllabus and assigned a book so students have that resource when needed. We will start our new material this week. If you want to learn more about what we are learning each day you can use the lesson schedule and the standards document. Thank you for sending your child to Rockmart High School. I will do my best to provide a quality math education opportunity for your child.Please sign the syllabus and email me back any questions you may have.
This website
I will be using this website as a primary way to give information about the course and to provide updates. I also will have information about assignments and the calendar. Go here to stay up-to-date. Email me if you have a question. Hope you and your child have a tremendous fall semester! | 677.169 | 1 |
ISBN: 9781842850817 Format: Spiral Ringed Book Number Of Pages: 60 Published: 1 November 2010 Country of Publication: GB Dimensions (cm): 29.7 x 21.0 x 0.6 Description: In this book, children are taught the basics of solving simple linear equations, in a logical and methodical manner. The book is published with a CD-ROM of the worksheets to enable teachers to print them out and use them in class | 677.169 | 1 |
°"synopsis" may belong to another edition of this title.
About the Author:
John Hudson Tiner received five National Science Foundation teaching fellowships during his 12 years of teaching science and mathematics. He is a graduate of chemistry at the College of the Holy Cross (Massachusetts), graduate of astronomy at Sam Houston State University (Texas), and a graduate of mathematics at Duke University (NC). He also worked as a mathematician and cartographer for the Defense Mapping Agency, Aerospace Center (St. Louis).
Today, Tiner is a full-time writer. His popular non-fiction books tell their stories through the lives of people who left the world in a better condition than they found it. He says, "After the research is finished, a wonderful moment occurs when the story takes over and the characters come alive. No longer am I a writer, but a time traveler who stands unobserved in the shadows and reports the events as they occur."
He has received numerous honors for his writing, including the Missouri Writer's Guild award for best juvenile book for Exploring the World of Chemistry, which was also published by Master Books.
Review:
A book that helps you understand math and have fun while you are doing it. --Joanna Swift, Production Secretary, 7/19/2004 2004/07/2721
Book Description Paperback. Book Condition: New. Paperback. Math doesn't have to be difficult, and John Tiner shows that it can actually be fun. Students of different ages and skill levels can use this fascinating book. Intended as a supplemen.Shipping may be from multiple locations in the US or from the UK, depending on stock availability. 157 pages. 0.449. Bookseller Inventory # 9780890514122 | 677.169 | 1 |
Books in category Mathematics – Study & Teaching
This book has two primary goals. On the level of theory development, the book clarifies the nature of an emerging "models and modeling perspective" about teaching, learning, and problem solving in mathematics and science education.
I have found the reading easy and down-to-earth and the information vital and easy to use. This book can help small business owners make a lot more money when they sell their business. This book has helped our business owners save ab
The Big Books provide an instructional focus for teaching maths concepts and vocabulary. The small books support, reinforce and consolidate the concepts in a format that students can read on their own.
Written in an engaging and user-friendly style, Steve Chinn draws on his extensive experience and expertise and: Shows how to consider all the factors relating to mathematical learning difficulties; Explains how these factors can be …
Keywords:Special Schools;Mathematically Talented;Gifted EducationKey Features:There are no competitive volumes. Information from the International Panorama may not be available anywhere except in this volume | 677.169 | 1 |
Participants shall preferably have some prior knowledge such as calculus, probability theory, linear algebra, basics of stochastic processes and programming skills. Financial product knowledge up to Hull is also needed. | 677.169 | 1 |
If you missed class today due to Pre-Algebra testing (or other reasons), here is the assignment you missed. YOU NEED THE HAND-OUT in order to complete the last part of the assignment. Please come see me if you have any questions | 677.169 | 1 |
Many students beginning their engineering, science and mathematics courses need a book on mathematical methods. This textbook offers an accessible and comprehensive grounding in many of the mathematical techniques required in the early stages of an engineering or science degree, and also for the routine methods needed by first and second year mathematics students. "Mathematical Techniques" starts by revising work from pre-university level before developing the more advanced material which students will encounter during their undergraduate studies. The contents of the book has been fully revised for this, the third edition. The first chapter on standard techniques, has been rewritten and expanded to serve the increasingly diverse needs of students. The Fourier transform now has its own chapter; a simplified approach is adopted, and diffraction theory, together with supporting material on wave motion, is included. Many changes enhancing clarity have been made in other chapters. The chapter on projects using Mathematica has been extended to cover these changes: the associated programs are freely available on Keele University, Mathematics Department web site. Chapters and sections are designed to be largely self-contained, allowing students to concentrate on the specific methods they need to master and use. The book contains nearly 500 worked examples, more than 2000 problems (with selected answers), and over 120 computing projects. The text is accessible, widely illustrated, and stands as an ideal introduction on mathematical methods at university level.
"synopsis" may belong to another edition of this title.
About the Author:
Dominic Jordan and Peter Smith are members of the Mathematics Department at Keele University. They both have long experience of teaching this material, at many different levels, and to a wide variety of students.
Review:
"Brief modular chapters include more than 500 worked examples, making the book useful as a quick reference."--SciTech Book News | 677.169 | 1 |
Pages
Tuesday, May 21, 2013
Matrix Groups for Undergraduates by Kristopher Tapp
Matrix Groups for Undergraduates PDF Download Ebook. Kristopher Tapp offers concrete and example-driven explanation with geometric motivation and rigorous proofs. The story begins and ends with the rotations of a globe. In between, the author combines rigor and intuition to describe basic objects of Lie theory: Lie algebras, matrix exponentiation, Lie brackets, and maximal tori.
Matrix groups are a beautiful subject and are central to many fields in mathematics and physics. They touch upon an enormous spectrum within the mathematical arena. This textbook brings them into the undergraduate curriculum. It is excellent for a one-semester course for students familiar with linear and abstract algebra and prepares them for a graduate course on Lie groups.
The volume is suitable for graduate students and researchers interested in group theory. It is an excellent, well-written textbook which is strongly recommended to a wide audience of readers interested in mathematics and its applications. The book is suitable for a one-semester undergraduate lecture course in matrix groups, and would also be useful supplementary reading for more general group theory courses.
There is considerable emphasis throughout on examples. Since the classical examples of matrix groups dominate the theory anyway, the focus on examples really has no downside. Throughout the book the author is careful to treat the reals R, the complexes C, and the quaternions H as uniformly as possible. Thus he is able to introduce orthogonal groups O(n), unitary groups U(n), and symplectic groups Sp(n) in a parallel way. Theorem 9.31, appropriately stated without proof, forms a satisfying conclusion to the course. It tells readers that the three sequences they have been intensively studying, together with five exceptional groups they have not seen, form the building blocks of all compact matrix groups.
There is further emphasis on low dimensions and visibility. The first chapter explains in intuitive terms why the group SO(3) of rotations of a globe is three-dimensional. It previews the idea of maximal torus by explaining, "Rotating the globe around the axis through the North and South Pole provides a 'circle's worth' of elements of SO(3)." There are helpful pictures throughout the book. Even in the second-to-last chapter, the low-dimensional isomorphism from Sp(1) to SU(2) and the double cover from SU(2) to SO(3) play a prominent role.
There is review appropriate to the intended readers. Aspects of linear algebra over R and Care reviewed in the process of presenting new material corresponding to H. Chapters 4 and 7 are almost entirely devoted to background material, on point-set topology and manifolds respectively; in each case, everything takes place in ambient Euclidean spaces Rn. Even in the last chapter, a theme is that diagonalization theorems of linear algebra are being revisited.
Each chapter concludes with approximately 15 exercises. Some are theoretical, like 4.1 through 4.6, each of which has the form "Prove Proposition 4.x." Many reinforce theoretical topics by considering them in examples, such as Exercise 6.5 which asks students to describe all one-parameter subgroups of GL1(C) and draw some in the x-y plane. The many exercises would support a course where students regularly present material in class. | 677.169 | 1 |
Graphics & Visualization: General Visualization Quick Start
This course makes it easy to visualize functions and data using Mathematica's large set of visualization features. Explore built-in tools for creating plots, charts, and graphics and learn how to customize them using styles, labels, legends, meshes, and other options.
Level: Beginner
The course is for those who have an interest in becoming more proficient users of Mathematica for graphics and visualization but who currently have little experience with the software. | 677.169 | 1 |
Books
Differential Geometry
Written primarily for students who have completed the standard first courses in calculus and linear algebra, Elementary Differential Geometry, Revised 2nd Edition, provides an introduction to the geometry of curves and surfaces.
The Second Edition maintained the accessibility of the first, while providing an introduction to the use of computers and expanding discussion on certain topics. Further emphasis was placed on topological properties, properties of geodesics, singularities of vector fields, and the theorems of Bonnet and Hadamard.
This revision of the Second Edition provides a thorough update of commands for the symbolic computation programs Mathematica or Maple, as well as additional computer exercises. As with the Second Edition, this material supplements the content but no computer skill is necessary to take full advantage of this comprehensive text.
Hermann Minkowski recast special relativity as essentially a new geometric structure for spacetime. This book looks at the ideas of both Einstein and Minkowski, and then introduces the theory of frames, surfaces and intrinsic geometry, developing the main implications of Einstein's general relativity theory.
Features:
The Geometry of Spacetime An Introduction to Special and General Relativity
Polytopes are geometrical figures bounded by portions of lines, planes, or hyperplanes. In plane (two dimensional) geometry, they are known as polygons and comprise such figures as triangles, squares, pentagons, etc. In solid (three dimensional) geometry they are known as polyhedra and include such figures as tetrahedra (a type of pyramid), cubes, icosahedra, and many more; the possibilities, in fact, are infinite! H. S. M. Coxeter's book is the foremost book available on regular polyhedra, incorporating not only the ancient Greek work on the subject, but also the vast amount of information that has been accumulated on them since, especially in the last hundred years. The author, professor of Mathematics, University of Toronto, has contributed much valuable work himself on polytopes and is a well-known authority on them. Professor Coxeter begins with the fundamental concepts of plane and solid geometry and then moves on to multi-dimensionality. Among the many subjects covered are Euler's formula, rotation groups, star-polyhedra, truncation, forms, vectors, coordinates, kaleidoscopes, Petrie polygons, sections and projections, and star-polytopes. Each chapter ends with a historical summary showing when and how the information contained therein was discovered. Numerous figures and examples and the author's lucid explanations also help to make the text readily comprehensible.
Although the study of polytopes does have some practical applications to mineralogy, architecture, linear programming, and other areas, most people enjoy contemplating these figures simply because their symmetrical shapes have an aesthetic appeal. But whatever the reasons, anyone with an elementary knowledge of geometry and trigonometry will find this one of the best source books available on this fascinating study.
The geometry of surfaces is an ideal starting point for learning geometry, for, among other reasons, the theory of surfaces of constant curvature has maximal connectivity with the rest of mathematics. This text provides the student with the knowledge of a geometry of greater scope than the classical geometry taught today, which is no longer an adequate basis for mathematics or physics, both of which are becoming increasingly geometric. It includes exercises and informal discussions.
Differential Forms and the Geometry of General Relativity provides readers with a coherent path to understanding relativity. Requiring little more than calculus and some linear algebra, it helps readers learn just enough differential geometry to grasp the basics of general relativity.
The book contains two intertwined but distinct halves.Designed for advanced undergraduate or beginning graduate students in mathematics or physics, most of the text requires little more than familiarity with calculus and linear algebra. The first half presents an introduction to general relativity that describes some of the surprising implications of relativity without introducing more formalism than necessary. This nonstandard approach uses differential forms rather than tensor calculus and minimizes the use of "index gymnastics" as much as possible.
The second half of the book takes a more detailed look at the mathematics of differential forms. It covers the theory behind the mathematics used in the first half by emphasizing a conceptual understanding instead of formal proofs. The book provides a language to describe curvature, the key geometric idea in general relativity.
The aim of the book is to treat all three basic theories of physics, namely, classical mechanics, statistical mechanics, and quantum mechanics from the same perspective, that of symplectic geometry, thus showing the unifying power of the symplectic geometric approach. Reading this book will give the reader a deep understanding of the interrelationships between the three basic theories of physics. This book is addressed to graduate students and researchers in mathematics and physics who are interested in mathematical and theoretical physics, symplectic geometry, mechanics, and (geometric) quantization.
This volume presents lectures given by Richard Schoen and Shing-Tung Yau at the Institute for Advanced Studies at Princeton University in 1984 and 1985. The lectures describe the major advances in differential geometry, which progressed rapidly in the twentieth century.
This engrossing volume on curve and surface theories is the result of many years of experience the authors have had with teaching the most essential aspects of this subject. The first half of the text is suitable for a university-level course, without the need for referencing other texts, as it is completely self-contained. More advanced material in the second half of the book, including appendices, also serves more experienced students well. Furthermore, this text is also suitable for a seminar for graduate students, and for self-study. It is written in a robust style that gives the student the opportunity to continue his study at a higher level beyond what a course would usually offer. Further material is included, for example, closed curves, enveloping curves, curves of constant width, the fundamental theorem of surface theory, constant mean curvature surfaces, and existence of curvature line coordinates. Surface theory from the viewpoint of manifolds theory is explained, and encompasses higher level material that is useful for the more advanced student. This includes, but is not limited to, indices of umbilics, properties of cycloids, existence of conformal coordinates, and characterizing conditions for singularities. In summary, this textbook succeeds in elucidating detailed explanations of fundamental material, where the most essential basic notions stand out clearly, but does not shy away from the more advanced topics needed for research in this field. It provides a large collection of mathematically rich supporting topics. Thus, it is an ideal first textbook in this field.
Focuses on homology theory This volume contains introductions to the contemporary methods for the calculation of homology groups and the classification of manifesto It is suitable for both scientists and students of mathematics as well as theoretical physics Over the past fifteen years the geometrical and topological methods of the theory of manifolds have as sumed a central role in the most advanced areas of pure and applied mathematics as well as theoretical physics The three volumes of Modern Geometry Methods and Applicationscontain a concrete exposition of these methods together with their main applications in mathematics and physics This third volume presented in highly accessible languages concentrates in homology theory It contains introductions to the contemporary methods for the calculation of homology groups and the classification of manifesto Both scientists and students of mathematics as well as theoretical physics will find this book to be a valuable reference and text
Features:
Modern Geometry Methods and Applications Part 3 Introduction to Homology Theory
The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem--the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most relevant contributions to the subject in the years 1959 to 1974. These include the pinching (or sphere) theorem, Berger's theorem for symmetric spaces, the differentiable sphere theorem, the structure of complete manifolds of non-negative curvature, and finally, results about the structure of complete manifolds of non-positive curvature. Emphasis is given to the phenomenon of rigidity, namely, the fact that although the conclusions which hold under the assumption of some strict inequality on curvature can fail when the strict inequality on curvature can fail when the strict inequality is relaxed to a weak one, the failure can happen only in a restricted way, which can usually be classified up to isometry. Much of the material, particularly the last four chapters, was essentially state-of-the-art when the book first appeared in 1975. Since then, the subject has exploded, but the material covered in the book still represents an essential prerequisite for anyone who wants to work in the field. | 677.169 | 1 |
Details:
The book gives a thorough introduction to the mathematical underpinnings of computer algebra. The subjects treated range from arithmetic of integers and polynomials to fast factorization methods, Groebner bases, and algorithms in algebraic geometry. The algebraic background for all the algorithms presented in the book is fully described, and most of the algorithms are investigated with respect to their computational complexity. Each chapter closes with a brief survey of the related literature.
The book is designed as a textbook for a course in computer algebra for advanced undergraduate or beginning graduate students. Every chapter contains a considerable number of exercises, some of which are solved in the appendix. In bridging the gap between the algebraic theory and computer algebra software, the book should be of interest to both mathematics and computer science students. | 677.169 | 1 |
Features the complete set of answers to the exercises in Mathematics Year 6 , as well as a selection of photocopiable worksheets to save you time and enable you to identify areas requiring further attention. The book includes diagrams and workings where necessary, to ensure pupils understand how to present their answers, as well as photocopiable... more...
Andrew... more...
This volume offers a concise, highly focused review of what high school and beginning college undergraduates need to know to successfully solve the trigonometry problems they will encounter on exams. Rigorously tested examples and coherent, to-the-point explanations are presented in an accessible form and will provide valuable assistance in conquering... more...
The... more...
This volume shows how the history and practices of mathematics education in Korea (from Volume 7) have been influenced by Japan, America and other countries, developing into the unique Korean style of mathematics education. Research content and practices currently being conducted are also covered, as well as topics like teacher education, special mathematics... more...
This book documents the journey undertaken by educators from the Mathematics and Mathematics Education (MME) Academic Group in the National Institute of Education (NIE) and Singapore schools during a Mathematical Modelling Outreach (MMO) event in June 2010 under the guidance of renowned experts in the field of mathematical modelling. The main goal... more...
With this seventh volume, as part of the series of yearbooks by the Association of Mathematics Educators in Singapore, we aim to provide a range of learning experiences and teaching strategies that mathematics teachers can judiciously select and adapt in order to deliver effective lessons to their students at the primary to secondary level. Our ultimate... more...
"The US National Science Foundation (NSF) Research Experiences for Undergraduates (REU) program in mathematics is now 25 years old, and it is a good time to think about what it has achieved, how it has changed, and where this idea will go next.". This was the premise of the conference held at Mt. Holyoke College during 21–22 June,... more... | 677.169 | 1 |
Trigonometry Workbook For Dummies angles to functions to identities – solve trig equations with ease
Got a grasp on the terms and concepts you need to know, but get lost halfway through a problem or worse yet, not know where to begin? No fear – this hands-on-guide focuses on helping you solve the many types of trigonometry equations you encounter in a focused, step-by-step manner. With just enough refresher explanations before each set of problems, you'll sharpen your skills and improve your performance. You'll see how to work with angles, circles, triangles, graphs, functions, the laws of sines and cosines, and more!
100s of Problems!
Step-by-step answer sets clearly identify where you went wrong (or right) with a problem
Get the inside scoop on graphing trig functions
Know where to begin and how to solve the most common equations
Use trig in practical applications with confidence
Recommendations:
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Solving Literal Equations Lesson 1 of 2
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Product Description
This is an Algebra 1 Common Core Lesson on Solving Literal Equations (equations with more than one variable) algebraically. This is Lesson 1 of 2. Students will be given explicit steps to follow to solve a literal equation. After a few teacher led examples, students will work with a partner to practice solving literal equations. | 677.169 | 1 |
Showing 1 to 30 of 109
Polynomial Functions \ '
Names: 1 Z C)
(4 communication points) ,_ 3
About this Laboratory
In this laboratory, you will learn about polynomial functions. A polynomial function is a
function that has an equation of the form f(x) = anx"+an_,x""+.+a,x+ao. In
'77 '1 ' N
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' Introduction and Basic Graphs G?)
Names: 1 4 — C
(4 communication points)
About this Laboratory
In this laboratory, you will be introduced to a graphing utility. It is important that you become
efficient at entering expressions and collec"l . / "7 V."
\ ./'
V The Box Problem 8 q
Names: 4 V A (a)
(4 communication points) ll
About this Laboratory
You will build a box from a sheet of paper with dimensions 8.5 inches x l 1 inches by cutting
squares from each comer of the paper and folding upCOLLEGE ALGEBRA Advice
Showing 1 to 3 of 17
In this course, I learned the general fundamentals of algebra that have allowed me to continue my mathematics education. You can expect to learn how to analyze various function both geometrically and algebraically, and you participate in collaborative laboratories that strengthen your knowledge of the material.
Hours per week:
3-5 hours
Advice for students:
I took the WvEB version of this course that is offered to high school students, and it was online and self-paced; therefore, you should be sure to keep up with the syllabus.
Course Term:Fall 2015
Professor:Laura Pyzdrowski
Course Tags:Great Intro to the SubjectMany Small AssignmentsParticipation Counts
Jun 17, 2017
| No strong feelings either way.
This class was tough.
Course Overview:
I would recommend this course, but with a different professor. Mr. Storm is obviously brilliant, but the mind of a brilliant professor is not always suited to teaching young minds new to the field!
Course highlights:
It actually got pretty interesting toward the end. We were able to tie in concepts of triangular angles with the unit circle. By the end of the course, everything made a lot more sense and seemed to be a much more unified concept.
Hours per week:
9-11 hours
Advice for students:
Use Khan academy! Use any tutorials you possibly can, and make sure you are keeping up with the work on Aleks. Aleks is surprisingly great at explaining the methods and the concepts behind them, but you will definitely need some supplementary instruction prior to exams!
Course Term:Spring 2017
Professor:Martin Storm
Course Required?Yes
Course Tags:Math-heavyMany Small AssignmentsRequires Lots of Research
May 30, 2017
| Would highly recommend.
Pretty easy, overall.
Course Overview:
This course is an overall easy course to take. The course is completely online including quizzes and tests. No textbook needed with this course
Course highlights:
This class is overall easy especially if you already have background knowledge of algebra. The course is completely online so it's easy to finish the work for the class
Hours per week:
3-5 hours
Advice for students:
Make sure to complete the homework on time in order to get the best grade possible. Homework makes up a large portion of the grading scale for this class. | 677.169 | 1 |
Showing 1 to 9 of 9
7/11/2017
CS121 Fall 2012 Syllabus
CS121 Fall 2012 Syllabus
Course Overview
This course is the first in a sequence introducing technical computation and programming through use of
Maple.Topics to be covered include: symbolic and numeric computation as use
CS 121 Engineering Computation Lab
Lab 1
Bruce Char
Department of Computer Science
Drexel University
Fall 2010
By the author. All rights reserved. Permission is given to CS121 Fall 2010
staff and students to use and reproduce these notes for their own use
Solving the Capacitor Equation
For a particular capacitor/battery set up, we have the following values
Ti=37, Ta=254 (in volts)
and we have determined that the relationship between time t (in seconds) and voltage
(in volts) when the capacitor charges is g
Quiz1
(a) How many quizzes are given this term?
4
(b) How many quizlets are given this term?
3
(c) How many labs are given this term?
4
(d) How many proficiency exams are given this term?
1
(e) How does the final course grade depend on the labs, quizzes,
Convert Units
Maple has functionality to convert between units of measure using a command called convert.
To convert 18 feet into meters what is the correct Maple command? (Select all that apply)
convert(18,units,ft,m)
, convert(18,units,feet,meter)
Conve
Quiz 2
Investigating Memory States
In this question, we want to examine how the state of memory changes. When Maple evaluates an
expression or equation, it uses the current values assigned to the variables.
We want to execute a series of Maple commands in
Quizlet 2
Getting plot coordinates
How do you get a Maple plot to display the coordinates of a point in a plot
corresponding to the position of the mouse cursor in the plot? Select all that apply.
Right (or control) click on a plot, Select Probe Info ->
C
Quiz 3
Solving with Pressure and Temperature
For a particular gas in a chemical system, the pressure P (measured in kilopascals) is related to
temperature s (measured in degrees Celsius) by the relationship described in Maple notation as
P := (s) -> alpha
Quiz 4
Trig Functions using Degrees
The Trigonometric functions built into Maple use radians as a measure of angles. In many fields, degrees
is preferred over radians when performing calculations. We can use Maple to create our own
trigonometric functions | 677.169 | 1 |
For years now, educators, business leaders, and even politicians have begun to realize that today's students aren't learning enough higher mathematics. The need for civil engineers, for instance, is expected to grow by 20 percent by 2022. Here are just a few reasons for learning advanced math skills.
Gain an Advantage
Advanced math usually refers to complex fields such as trigonometry, calculus, or algebraic number theory. It's true that you can get into a decent college or a good job without studying these, but advanced math puts you a step ahead of other applicants. If you've mastered calculus, for instance, you'll be more impressive than a candidate who never made it past basic algebra. It tells recruiters in an instant that you're an intelligent, focused person who can apply complicated logic to explain patterns, perfect methods, and find solutions.
Solve Problems
Mathematics essentially came about as a way to solve problems and is still an evolving technique for doing so. Every tangible, real-world concept or quantity can be expressed or assessed through math. Whether it's tracking pollution or putting a satellite into orbit, understanding mathematical principles is essential. No matter what the problem is, it will involve measurements, theories, and proof by the numbers.
Build a Career
In our high-tech world, an understanding of higher math is crucial to success in many fields. Learning advanced math early is important to finding the right college and career. Engineers, for instance rely on calculus to optimize safety and efficiency in everything from traffic flow to jet planes. At-school or online programs from Ohio University, for example, prepare you for specific engineering specialties. As demand for such jobs continues to increase, they become both more lucrative and more secure careers.
Automate Functions
In the past, mathematics was taught and used on paper or blackboards in universally recognized symbols and numbers. Today, however, very few people bother with written calculations when we have computers and smart phones. It seems that in almost any industry, you can find an app for certain mathematical functions. The reality is that someone has to develop the formulas and write the apps. Moreover, you as the end user have to be able to appreciate which app is right for which job, and why.
Learning math beyond basic competency seems like a low priority for most of today's young students. It should be clear that in our technical society advanced mathematics is a vital part of your future.
Hannah Whittenly is a freelance writer and mother of two from Sacramento, CA. She enjoys kayaking and reading books by the lake. You can follow her on twitter and LinkedIn.
All views and opinions of guest authors are theirs alone and are not representative of the views of Petersons.com or its parent company Nelnet. | 677.169 | 1 |
The Bedside Book of Geometry
Mike Askew
The Bedside Book of Geometry is an interactive guide containing clear and concise explanations of geometric concepts as well as biographies of the key thinkers in the history of geometry and their discoveries. The Bedside Book of Geometry is a fascinating, interactive guide to the history and uses of geometry. It contains clear and concise explanations of different geometric concepts, as well as profiles of key thinkers and their discoveries. A unique feature of the book is its simple, step-by-step excercises. Some of these have everyday applications, others are theoretical puzzles, but all are designed to challenge the reader and test their newly acquired knowledge. The perfect companion for beginners and experts alike, The Bedside Book of Geometry does not assume prior knowledge of the subject beyond basic numeracy skills. Its aim is to convey the basic elements of geometry to everyone, no matter what their level of mathematical ability.
All stocked books by Askew, Mike | 677.169 | 1 |
Description:
About this title:
Designed for the three-semester course for math and science majors, the Larson/Hostetler/Edwards series continues its tradition of success by being the first to offer both an Early Transcendental version as well as a new Calculus with Precalculus text. This was also the first calculus text to use computer-generated graphics (Third Edition), to include exercises involving the use of computers and graphing calculators (Fourth Edition), to be available in an interactive CD-ROM format (Fifth Edition), and to be offered as a complete, online calculus course (Sixth Edition). Every edition of the book has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas. The Seventh Edition also expands its support package with an all-new set of text-specific videos.
P.S. Problem-Solving Sections, an additional set of thought-provoking exercises added to the end of each chapter, require students to use a variety of problem-solving skills and provide a challenging arena for students to work with calculus concepts.
Getting at the Concept Exercises added to each section exercise set check students' understanding of the basic concepts. Located midway through the exercise set, they are both boxed and titled for easy reference.
Review Exercises at the end of each chapter have been reorganized to provide students with a more effective study tool. The exercises are now grouped and correlated by text section, enabling students to target concepts requiring review.
The icon "IC" in the text identifies examples that appear in the Interactive Calculus 3.0 CD-ROM and Internet Calculus 2.0 web site with enhanced opportunities for exploration and visualization using the program itself and/or a Computer Algebra System.
Think About It conceptual exercises require students to use their critical-thinking skills and help them develop an intuitive understanding of the underlying theory of the calculus.
Modeling Data multi-part questions ask students to find and interpret mathematical models to fit real-life data, often through the use of a graphing utility.
Section Projects, extended applications that appear at the end of selected exercise sets. may be used for individual, collaborative, or peer-assisted assignments.
True or False? Exercises, included toward the end of many exercises sets, help students understand the logical structure of calculus and highlight concepts, common errors, and the correct statements of definitions and theorems.
Motivating the Chapter sections opening each chapter present data-driven applications that explore the concepts to be covered in the context of a real-world setting4710215830
Book Description D C Heath & Co G-01-01-37-01101001EAN
Book Description Houghton Mifflin Harcourt Trade & Reference Publishers. Hardcover. Book Condition: Very Good. Very good condition - book only shows a small amount of wear. Bookseller Inventory # G0669353353I4N00
Book Description Houghton Mifflin Harcourt Trade & Reference Publishers. Hardcover. Book Condition: Very Good. This book shows minor wear and is in very good condition. Bookseller Inventory # G0669353353I4N00 | 677.169 | 1 |
Algorithms and Complexity by Herbert S. Wilf
This publication is an introductory textbook at the layout and research of algorithms. the writer makes use of a cautious number of a number of themes to demonstrate the instruments for set of rules research. Recursive algorithms are illustrated through Quicksort, FFT, speedy matrix multiplications, and others. Algorithms linked to the community circulation challenge are primary in lots of parts of graph connectivity, matching concept, and so on. Algorithms in quantity conception are mentioned with a few functions to public key encryption. This moment variation will fluctuate from the current variation typically in that strategies to many of the workouts may be incorporated.
The mathematical innovations of summary algebra may perhaps certainly be thought of summary, yet its application is sort of concrete and maintains to develop in value. regrettably, the sensible software of summary algebra ordinarily contains large and bulky calculations-often complex even the main devoted makes an attempt to understand and hire its intricacies.
Gottfried Wilhelm Leibniz: The Polymath Who introduced Us Calculus makes a speciality of the existence and accomplishments of 1 of the 17th century's so much influential mathematicians and philosophers. The booklet, which attracts on Leibniz's written works and translations, and reconstructs dialogues Leibniz can have had in accordance with the old checklist of his lifestyles reports, portrays Leibniz as either a fantastic genius and a true individual.
The subject of this publication is finite workforce activities and their use that allows you to method finite unlabeled buildings through defining them as orbits of finite teams of units. famous examples are graphs, linear codes, chemical isomers, spin configurations, isomorphism sessions of combinatorial designs and so forth. This moment variation is a longer model and places extra emphasis on functions to the optimistic idea of finite constructions.
In those notes, first released in 1980, Professor Northcott presents a self-contained creation to the idea of affine algebraic teams for mathematicians with a simple wisdom of communicative algebra and box idea. The ebook divides into components. the 1st 4 chapters comprise the entire geometry wanted for the second one half the e-book which bargains with affine teams.
Consider the following question: how many graphs are there that have exactly n vertices? Suppose first that we mean labeled graphs. A graph of n vertices has a maximum of n2 edges. To construct a graph we would decide which of these possible edges would be used. We can make each of these n2 decisions independently, and for every way of deciding where to put the edges we would get a different graph. Therefore the number of n labeled graphs of n vertices is 2( 2 ) = 2n(n−1)/2. If we were to ask the corresponding question for unlabeled graphs we would find it to be very hard.
And of course, all at war with each other. The delegation wants to escape quickly, but before doing so it draws a careful map of the 5,000,000 countries into which the planet has been divided. To make the map easier to read, the countries are then colored in such a way that whenever two countries share a stretch of border they are of two different colors. Surprisingly, it was found that the coloring could be done using only red, blue, yellow and green. It was noticed over 100 years ago that no matter how complicated a map is drawn, and no matter how many countries are involved, it seems to be possible to color the countries in such a way that (a) every pair of countries that have a common stretch of border have different colors and (b) no more than four colors are used in the entire map.
B) interchange the positions of two selected keys. Here is an example of a rather primitive sorting algorithm: (i) find, by successive comparisons, the smallest key (ii) interchange it with the first key (iii) find the second smallest key (iv) interchange it with the second key, etc. etc. Here is a more formal algorithm that does the job above. {slowsort} If you are wondering why we called this method 'primitive,' 'slowsort,' and other pejorative names, the reason will be clearer after we look at its complexity. | 677.169 | 1 |
Beginning and Intermediate Algebra Worksheets for Classroom or Lab Practice
by Unknown
ISBN13:
9780321516879
ISBN10:
0321516877
Edition:4th
Format:Nonspecific Binding
Copyright:2008-01-01
Publisher:PEARSON
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Summary
Worksheets for Classroom or Lab Practice offer extra practice exercises for every section of the text, with ample space for students to show their work. These lab- and classroom-friendly workbooksalso list the learning objectives and key vocabulary terms for every text section,along with vocabulary practice problems. | 677.169 | 1 |
Designed as the bridge to cross the widening gap between mathematics and computer science, and planned as the mathematical base for computer science students, this maths text is written for upper-level college students who have had previous coursework involving proofs and proof techniques. The close tie between the theoretical and algorithmic aspects of graph theory, and graphs that lend themselves naturally as models in computer science, results in a need for efficient algorithims to solve any large scale problems. Each algorithm in the text includes explanatory statements that clarify individual steps, a worst-case complexity analysis, and algorithmic correctness proofs. As a result, the student will develop an understanding of the concept of an efficient algorithm | 677.169 | 1 |
Textbooks like RD Sharma, TS Aggarwal, and RS Aggarwal hardly need an introduction with students in school. Preparation for almost all school exams or entrance exams is considered incomplete without the use of some popular textbooks. Along with textbooks, textbook solutions have, over the years, become a highly effective means to carry out test preparation. The fact that textbook solutions are created to suit the questions and patterns of the textbook themselves makes it easier for students to compare, analyse and solve any number of questions easily.
Teachers, academicians and students all around can vouch for the effectiveness of Textbook solutions. Meritnation offers a brilliant set of textbook solutions for students of CBSE, ICSE and states boards like Maharashtra Board, etc. Popular textbooks for Maths and Science subjects like RD Sharma, RS Aggarwal, are studied and analysed by subjects experts at Meritnation and solutions are created keeping in mind the level of understanding among students of a particular grade.
For example, textbook solutions for RD Sharma for Class 9 students will differ in language and style from those meant for class 6 students. Through this, we ensure that students get the most easily understood, flexible and useful content for exam preparation, class tests and homework help.
Another very useful aspect of textbook solutions is the pattern in which they have been created. We, at Meritnation, fully understand students' needs to understand a problem in detail, which is why we use step-by-step explanation methods and graphical representation of required parts as well. Our aim is not only to simplify the chapters and topics for students, but prepare them for tougher and more complex problems they may face later in their academic careers.
Key Features of Textbook Solutions
Comprehensive yet easy to read and understand
Aim at uplifting students' learning graph
All major textbooks like RD Sharma, RS Aggarwal, HC Verma and TS Grewal covered in detail | 677.169 | 1 |
How to Apply?
Entry Requirements
We would like you to have either an existing D grade at GCSE Maths or a Level 1 or Level 2 equivalent such as Functional Skills maths, but don't worry if you don't. Entry on to the study programme is via as assessment evening where we assess your current level of maths and offer you advice and guidance as to what is the best next step for you.
Duration of this course
One Year
Career Prospects
Gaining a grade C or above for GCSE Maths provides a good foundation for progression on to many other study programmes, from Physics and Engineering to Sport Science and future employment and is a great grounding for many different careers.
How will I be assessed?
You will be assessed at the end of the course. You will take two written exam papers in June, one with a calculator and one without.
Course content/units
This course covers Data Handling, Number, Algebra and Geometry.
Expenses for this course
You need your own Maths equipment, including scientific calculator, protractor, ruler and compass, as well as general stationery such as pens and pencils. | 677.169 | 1 |
Mathematics and mathematical modelling are of central importance in computer science, and therefore it is vital that computer scientists are aware of the latest concepts and techniques.
This concise and easy-to-read textbook/reference presents an algorithmic approach to mathematical analysis, with a focus on modelling and on the applications of analysis. Fully integrating mathematical software into the text as an important component of analysis, the book makes thorough use of examples and explanations using MATLAB, Maple, and Java applets. Mathematical theory is described alongside the basic concepts and methods of numerical analysis, supported by computer experiments and programming exercises, and an extensive use of figure illustrations.
Provides summaries and exercises in each chapter, as well as computer experiments
Discusses important applications and advanced topics, such as fractals and L-systems, numerical integration, linear regression, and differential equations
Presents tools from vector and matrix algebra in the appendices, together with further information on continuity
Includes definitions, propositions and examples throughout the text, together with a list of relevant textbooks and references for further reading
Supplementary software can be downloaded from the book's webpage at
This textbook is essential for undergraduate students in Computer Science. Written to specifically address the needs of computer scientists and researchers, it will also serve professionals looking to bolster their knowledge in such fundamentals extremely well"This undergraduate work, translated from German, is designed around the concept that mathematical modeling and the underlying mathematics are central to computer science. … place a strong emphasis on algorithmic methods, and include a substantial number of examples of mathematical modeling. … Since the audience is computer science students, there are many examples and exercises … using the software packages MATLAB and Maple. … a useful acquisition for academic institutions where students have access to MATLAB and/or Maple. Summing Up: Recommended. Lower- and upper-division undergraduates." (D. Z. Spicer, Choice, Vol. 49 (1), September, 2011)
"The book is a translation of the original German version from 2005 … . Each chapter is preceded by a brief introduction for orientation. The text is enriched by computer experiments which should encourage the reader to actively acquire the subject matter. Finally, every chapter has exercises, half of which are to be solved with the help of computer programs. The book can be used from the first semester on as the main textbook for a course, as a complementary text, or for self-study." (Petr Gurka, Zentralblatt MATH, Vol. 1238, 2012) | 677.169 | 1 |
Download Trigonometry: A Graphing Approach books
Solutions in Sullivan Trigonometry: A Unit Circle Approach (9780132392792), 5 ^^^^^ Table of Trigonometry Identities ^^^^^ Students should become familiar with all these identities. Students will be given the opportunity to ..., Solutions in Larson Precalculus with Limits: A Graphing Approach (9780618851522), Trig graphs are easy once you get the hang of them. Once you learn the basic shapes, you shouldn't have much difficulty. The main problems A-Level students have, in ..., Free math help! Tutorial videos on topics including arithmetic, algebra, trigonometry, and calculus., SOH CAH TOA - trigonometry. A way to remember the definitions of the three most common trigonometry functions: sin, cos and tan. Used as a memory aid for the ..., Article Summary: "Now it's true that triangles are one of the simplest geometrical figures, yet they have varied applications. The primary application of trigonometry ..., Interactive demonstration of the graph of the tangent function in trigonometry, Math lessons and interactive quizzes are here to be learned., Imagine Bob The Alien visits Earth to study our species. Without new words, humans are hard to describe: Theres a sphere at the top, which gets scratched ...4013002 epub books4013000 epub books
Ron Larson - (Rating: 2 - 1 votes)
Detail books Trigonometry: A Graphing Approach
Trigonometry: A Graphing Approach As part of the market-leading Graphing Approach series by Larson, Hostetler, and Edwards, Trigonometry trigonometry courses that require the use of a graphing calculator includes a moderate review of algebra to help students entering the course with weak algebra skills.
Free Webs Library 2017 is in no way intended to support illegal activity. We uses Search API to find the overview of Trigonometry: A Graphing Approach | 677.169 | 1 |
High school physics book reccomendation?
I have already written a thread about a conceptual physics books, which didn't go so well. Instead, I am just looking for one of the best book to accompany me in Physics Mechanics and Electricity and Magnetism. I am in high school and will take Calc BC alongside Physics (pre-calc this year), so my knowledge on calculus based text will be very small in the beginning.
Please recommend me a textbook that is accompanied with problems similar or a bit harder than the rigor of the AP exam. My real goal is to learn and love physics however, so any book that allows me to grasp the concepts easily and allows me to understand the mathematics behind it would be wonderful.
Researching a bit, it seems like University Physics is an excellent book and is also used by OCW MITx which I can follow. How would someone who has never taken calculus(but will take it alongside it) respond to this book?
Easily. I think you are too concerned about the mathematics required. For an introductory course in physics you use very little calculus. Unless you are using kleppner and kolenkow's book which actually requires thinking.
The majority of students have never taken calculus before taking a first year university [physics] class. They usually take calculus at the same time. Especially books like University physics, physics - Halliday resnick Kane, all the intro textbooks are basically the same. It's all personal preference.
I suggest you go to a library and look through numerous books and make your decision.
I have taken a look at both and have access to both. I must say, I love how both books present themselves. The reason I am so math concentrated is because while I was great at math during elementary school, I have seldom paid attention to math in high school. Now I lack a good foundation in it and get nervous when ever I see a mathematics problem. I am rectifying this problem over the summer by going back to the basics and practicing every concept and then moving on. Thank you for your contribution Jimmyly. | 677.169 | 1 |
Introduction to Applied Algebraic Systems
Browse related Subjects ...
Read More applications. The book offers a brief introduction to elementary number theory as well as a fairly complete discussion of major algebraic systems (such as rings, fields, and groups) with a view of their use in bar coding, public key cryptosystems, error-correcting codes, counting techniques, and elliptic key cryptography. This is the only entry level text for algebraic systems that includes an extensive introduction to elliptic curves, a topic that has leaped to prominence due to its importance in the solution of Fermat's Last Theorem and its incorporation into the rapidly expanding applications of elliptic curve cryptography in smart cards. Computer science students will appreciate the strong emphasis on the theory of polynomials, algebraic geometry and Groebner bases. The combination of a rigorous introduction to abstract algebra with a thorough coverage of its applications makes this book truly unique | 677.169 | 1 |
Elements of Algebra Geometry, Numbers, Equations
ISBN-10: 0387942904
ISBN-13: 9780387942902
Edition: 3rd concise, self-contained introduction to abstract algebra which stresses its unifying role in geometry and number theory. There is a strong emphasis on historical motivation - both to trace abstract concepts to their concrete roots, but also to show the power of new ideas to solve old problems. This approach shows algebra as an integral part of mathematics and makes this text more informative to both beginners and experts than others. Classical results of geometry and number theory (such as straightedge-and-compass construction and its relation to Fermat primes) are used to motivate and illustrate algebraic techniques, and classical algebra itself (solutions of cubic and quartic equations) is used to motivate the problem of solvability by radicals and its solution via Galois theory. Modern methods are used whenever they are clearer or more efficient, but technical machinery is introduced only when needed. The lively style and clear expositions make this book a pleasure to read and to learn from | 677.169 | 1 |
"There is no getting out of it. Through and through
the world is infected with quantity. To talk sense is to talk in quantities.
There is no use saying the nation is large, -How large? It is no use saying
that radium is scarce, -How scarce? You cannot evade quantity. You may fly
to poetry and to music, and quantity and number will face you in your rhythms
and your octaves."
Alfred North Whitehead in his essay, The Aims of
Education.
Course Description: Math 1030 is a non-traditional, application-based course centered around the use of mathematics to model change in the real world, and the effective communication of these mathematical ideas. The course is primarily intended for students from the Social and Behavioral Sciences, the Health Sciences, and the Humanities who seek only to satisfy the QA (quantitative reasoning - course A) requirement for the bachelor's degree and who, with the exception of a statistics class, will not take any further mathematics courses at the university. The purpose of the Math 1030 course is to develop skill in quantitative reasoning by examining how appropriate mathematical techniques can be used to analyze questions from many different areas. The mathematics covered in the course includes: ratios, percents, averages, estimation, basic financial mathematics, linear and exponential models of growth, basic geometric measurements and scaling. The course material is based on Chapters 1-4 and Chapters 8-10(Sec. A) of the text listed below.
Note: The Math 1030 course does NOT satisfy either a M1090, or a M1050-M1060 prerequisite for other courses.)
Course Work and Grading: Learning to use mathematics to analyze quantitative issues and to communicate technical information requires both the practice of basic techniques and the opportunity to apply these techniques to practical, open-ended, questions which may be examined using varied approaches. The coursework in Math 1030 emphasizes solving word problems that require the use of simple algebraic skills, tables, graphs, and formulas. In their work students examine the reasoning behind basic mathematical concepts, explore problems and questions presented from different perspectives, clarify assumptions made in word problems, and look for connections between the course topics and their own field of study.
Grading in the course will be based on assignments (quizzes/homework) given roughly every two weeks, 1 group project requiring a typewritten report, 2 midterms, and a comprehensive final exam. The goal is to offer students frequent feedback on their progress in the course through assignments that are graded and returned to the students, to provide opportunities to try out the course concepts in broader contexts through group projects, and to help students review and summarize their learning over the semester through a midterm and a comprehensive final exam.
Math 1030 Sections: For Spring Semester 2003 there are nine
sections of Math 1030 offered through the Department of Mathematics, two sections offered through the Division of Continuing Education, and one section offered through the Educational Opportunity Program. Each instructor
will develop a syllabus for their own section based on the above guidelines. | 677.169 | 1 |
Elementary Geometry, 3rd Edition
Although extensively revised, this new edition continues in the fine tradition of its predecessor. Major changes include: a notation that formalizes the distinction between equality and congruence and between line, ray and line segment; a completely rewritten chapter on mathematical logic with inclusion of truth tables and the logical basis for the discovery of non-Euclidean geometries; expanded coverage of analytic geometry with more theorems discussed and proved with coordinate geometry; two distinct chapters on parallel lines and parallelograms; a condensed chapter on numerical trigonometry; more problems; expansion of the section on surface areas and volume; and additional review exercises at the end of each chapter. Concise and logical, it will serve as an excellent review of high school geometry | 677.169 | 1 |
This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2013 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy... more...
Monomial Algebras, Second Edition presents algebraic, combinatorial, and computational methods for studying monomial algebras and their ideals, including Stanley–Reisner rings, monomial subrings, Ehrhart rings, and blowup algebras. It emphasizes square-free monomials and the corresponding graphs, clutters, or hypergraphs. New to the Second Edition... more...... more...
A reader-friendly introduction to modern algebra with important examples from various areas of mathematics Featuring a clear and concise approach , An Introduction to Essential Algebraic Structures presents an integrated approach to basic concepts of modern algebra and highlights topics that play a central role in various branches of mathematics.... more...
Introduction to Higher Algebra is an 11-chapter text that covers some mathematical investigations concerning higher algebra. After an introduction to sets of functions, mathematical induction, and arbitrary numbers, this book goes on considering some combinatorial problems, complex numbers, determinants, vector spaces, and linear equations. These... more... | 677.169 | 1 |
The Official SAT Question of the Day
Friday, February 11, 2011
Week 25
Algebra II has started to delve into the vast topic of polynomials and have been reviewing the basic skills associated with them (operations, substitution, and classification). We will start to move into more unchartered waters as we look at their behavior graphically as well as continue to emphasize and develop the skill of factoring. It is crucial during our investigation of polynomials that students become increasingly comfortable with their graphing calculators and its capabilities. Please find the guided notes we started last week below as well as the portions we have already completed below. Reference sheets and homework are also found below--become comfortable with those reference sheets and how you can use them to help you navigate this topic.
Guided Notes:
Complete Guided Notes: Part 1
Part 2
Part 3
Part 4
Part 5
Part 6
Reference Sheets: Factoring, Completing the Square, and the Quadratic Formula
Precalculus is heading into Trigonometry! We will start with trigonometry as you have already engaged it in Geometry and begin to extend into the arena of functions and periodic behavior. It will be a long road that will extend across the entire third quarter so it is important to get the foundational concepts early so that as the develop and become more complex you will find it much easier! Please find notes, homework, and videos below! | 677.169 | 1 |
Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer Algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and more | 677.169 | 1 |
mathematicaltools to solve their problems, and to those who work in the development of these mathematicaltools. Metrology is concerned with measurement at the highest level of precision. Advances in metrology depend on many factors: improvements in scientific and technical knowledge, instrumentation quality, better use of advancedmathematicaltools and the development of new tools. In some countries, metrological institutions have a tradition of
Research on achievement gaps has found that achievement gaps are larger for students who take advancedmathematics courses compared to students who do not. Focusing on the advancedmathematics student achievement gap, this study found that African American advancedmathematics students have significantly lower test scores and are less likely to be…
Four elementary school instructors offer insights into their classrooms, their unique professional roles, and their leadership approaches as they reflect on their journey to advance teacher and student mathematics learning. They note a "teacher leader" serves as an example to other educators and strives to impact student learning;…
Background: Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advancedmathematics (e.g., modern algebra, statistics, and mathematical logic).Aims: To promote mathematical knowledge among college students, it is necessary to understand what factors…In this paper the notion of "procept" (in the sense of Gray & Tall, 1994) is extended to advancedmathematics by considering mathematical proof as "formal procept". The statement of a theorem as a symbol may theoretically evoke the proof deduction as a process that may contain sequential procedures and require the synthesis…What role do gestures play in advancedmathematical thinking? We argue that the role of gestures goes beyond merely communicating thought and supporting understanding--in some cases, gestures can help generate new mathematical insights. Gestures feature prominently in a case study of two participants working on a sequence of calculus activities.…
Use of technology in the mathematics classroom has the potential to advance children's learning of mathematics and enhance their attitudes about mathematics. When used in conjunction with purposeful planning, teachers can use technological tools to reinforce their pedagogical intentions and to facilitate relevant learning activities for students. interventions act along two complementary directions. One of them regards ontology, since questions induce one to look closely at the electric charge, from different perspectives, promoting reflections about its nature and reinforcing the corresponding concept. Formal manipulations rely on the identification of concepts with symbols, and the other direction concerns the spatial extension of mathematical structures. Our questions and their somewhat unusual answers help disclosing information which is not present in many textbooks, and show that Mathematics can be used as an efficient epistemological tool in Physics teaching.
This paper collects and extends the lectures I gave at the "XXIV International Fall Workshop on Geometry and Physics" held in Zaragoza (Spain) during September 2015. Within these lectures I review the formulation of Quantum Mechanics, and quantum theories in general, from a mathematicallyadvanced viewpoint, essentially based on the orthomodular lattice of elementary propositions, discussing some fundamental ideas, mathematicaltools and theorems also related to the representation of physical symmetries. The final step consists of an elementary introduction the so-called (C∗-) algebraic formulation of quantum theories. Mathematical Mathematical PMID:25064823
The article contains general information about the use of specialized mathematics software in the preparation of math teachers. The authors indicate the reasons to study the mathematics software. In particular, they analyze the possibility of presenting basic mathematical courses using mathematical computer tools from both a teacher and a student,…
This study examines high school students' views of mathematics as a tool for social inquiry in light of their classroom experiences using mathematics to explore social issues. A critical theoretical perspective on mathematics literacy is used to ascertain the ways in which their views challenge or affirm the dominant image of mathematics in…High school mathematics achievement predicts future success. Potentially different factors that lead to success for boys versus girls, termed equifinality, are not well understood. Such factors are needed to inform interventions to increase numbers of students taking advancedmathematics courses and going on into science and mathematics careers.…
This journal article discusses AdvancedMathematical Thinking (AMT) and how to enhance it. AMT is ability in representing, abstracting, creative thinking, and mathematical proving. The importance of AMT ability development in accord with government expectation who realize about the importance of mathematical competency mastery for student's life.This text is the second of five in the Secondary School AdvancedMathematicsmathematicsMathCad® is a very popular software tool for mathematical and statistical analysis in science and engineering. Its low cost, ease of use, extensive function library, and worksheet-like user interface distinguish it among other commercial packages. Its features are also well suited to educational process. The use of natural mathematical notation…Analyzes the notion of structuring resources and their role in shaping mathematical activity. Examines ways in which nurses conceptualize ratio and proportion problems and provides a case study of two nurses discussing conflicting strategies when monitoring the fluid balance of a patient. Draws out some implications for the design of viable…
This document contains descriptions of adult education courses in remediation, general education, and technical mathematics. They are part of a program developed by the Machine ToolAdvanced Skills Technology Educational Resources (MASTER) program to help workers become competent in the skills needed to be productive workers in the machine tools…Many discrete mathematics problems in phylogenetics are defined in terms of the relative labeling of pairsof leaf-labeled trees. These relative labelings are naturally formalized as tanglegrams, which have previously been an object of study in coevolutionary analysis. Although there has been considerable work on planar drawings of tanglegrams, they have not been fully explored as combinatorial objects until recently. In this paper, we describe how many discrete mathematical questions on trees "factor" through a problem on tanglegrams, and how understanding that factoring can simplify analysis. Depending on the problem, it may be useful to consider a unordered version of tanglegrams, and/or their unrooted counterparts. For all of these definitions, we show how the isomorphism types of tanglegrams can be understood in terms of double cosets of the symmetric group, and we investigate their automorphisms. Understanding tanglegrams better will isolate the distinct problems on leaf-labeled pairs of trees and reveal natural symmetries of spaces associated with such problems.
This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…
Communicating and collaborating online are becoming common requirements in education. The specialized notations and symbols necessary for some content areas where mathematical expressions are part of the conversation require that users select appropriate communication tools. The purpose of this article is to describe tools that can be used for… analysis tool that focuses on integrating…mathematics develops general thinking skills and, in particular, conditional…
In the late 1990s, the economic return to Advanced level (A-level) mathematics was examined. The analysis was based upon a series of log-linear models of earnings in the 1958 National Child Development Survey (NCDS) and the National Survey of 1980 Graduates and Diplomates. The core finding was that A-level mathematics had a unique earnings premium…
Based on data from the Longitudinal Study of American Youth (LSAY), students were classified into high-, middle-, and low-ability students. The effects of early acceleration in mathematics on the most advancedmathematics coursework (precalculus and calculus) in high school were examined in each category. Results showed that although earlyThis paper describes the development of mathematical theory and software to analyze specifications that are developed using decision tables. A decision table is a tabular format for specifying a complex set of rules that chooses one of a number of alternative actions. The report also describes a prototype tool, called TBell, that automates certain types of analysisFew students (particularly few girls) currently choose to take their Final School Examination (FSE) in advancedmathematics, chemistry and physics, a combination of subjects that is the best preparation for a science-oriented study in higher education. Are these subjects attainable by more students than is currently the case? This study examined…
Transcendental mathematical functions are one of the main hot-spots of scientific applications. The usage of highly optimised, general purpose mathematical libraries can mitigate this issue. On the other hand, a more comprehensive solution is represented by the replacement of the generic mathematical functions by specific implementations targeting particular subdomains only. CptnHook is a tool that helps achieving this goal allowing to monitor the input values of mathematical functions used in a given application, categorised according to the stacktraces leading to their invocations. In this contribution we describe the design of CptnHook, the data format of its profile and how it is possible to perform measurements without instrumenting the users code and imposing the need of recompilation. We demonstrate that this approach scales on production workflows of LHC experiments and characterise a set of real life measurements, showing where opportunities for improvement lie and how the tool can be used for advanced debugging. We also illustrate how elegant summaries of the measurements can be produced and how ROOT based analysis of the profiles can be performedmathematics is associated with the development of logical reasoning skills, but that the nature of this development may be more complex than previously thought.This dissertation focuses on examining the use of mathematical cartoons as a teaching tool in middle school mathematics classroom. A mixed methods research design was used to answer how the use of cartoon activities affects teacher and student perceptions of teaching and learning and student intrinsic motivation, interest, and mathematics anxiety…
In an effort to engage children in mathematics learning, many primary teachers use mathematical games and activities. Games have been employed for drill and practice, warm-up activities and rewards. The effectiveness of games as a pedagogical tool requires further examination if games are to be employed for the teaching of mathematical concepts.…
This paper presents our experience of integrating technological tools into our mathematics teaching (in both disciplinary and didactic courses) for student-teachers. In the first cycle of our study, a variety of technological tools were used (e.g., dynamic software, hypertexts, video and applets) in teaching two disciplinary mathematics courses.…
This mixed-methods study investigates the effects of student attitudes and behaviours on the outcomes of learning mathematics with computer tools. A computer tool was used to help students develop the mathematical concept of function. In the whole sample (N = 521), student attitudes could account for a 3.4 point difference in test scores between…
The Alternative Fuels and Advanced Vehicles Web site offers a collection of calculators, interactive maps, and informational tools to assist fleets, fuel providers, and others looking to reduce petroleum consumption in the transportation sector.
Mathematical reasoning involves comprehending mathematical information and concepts in a logical way and forming conclusions and generalizations based on this comprehension. Computer-based learning has been incorporated into classrooms across the country, and specific aspects of technology need to be studied to determine how programs are…
Values education is crucial since it is one of the factors to reach success in education in broader sense and in mathematics education in particular sense. It is also important for educating next generations of societies. However, previous research showed that expected importance for values education was not given in Mathematics courses. In a few…
This paper aims to address the need of increasing student achievement in mathematics using a visual programming language such as Scratch. This visual programming language facilitates creating an environment where students in K-12 education can develop mathematical simulations while learning a visual programming language at the same time.…
This article discusses the conversion of mathematical equations into Extensible Markup Language (XML) on the World Wide Web for individuals with visual impairments. A program is described that converts the presentation markup style to the content markup style in MathML to allow browsers to render mathematical expressions without other programs.…
This paper provides an overview of the Inquiry-Oriented Differential Equations (IO-DE) project and reports on the main results of a study that compared students' beliefs, skills, and understandings in IO-DE classes to more conventional approaches. The IO-DE project capitalizes on advances within mathematics and mathematics education, including the… recognitionFreshmen placed into the second or third quarter of the first year calculus sequence at the University of Washington were studied. Two major findings were: freshmen eligible for advanced placement earned mean mathematics Grade Point Averages (GPAs) which were quite high; and advanced placement students earned mean mathematics GPAs substantially…
The purpose of the study was to measure students' reported test-taking effort and the relationship between reported effort and performance on the Trends in International Mathematics and Science Study (TIMSS) Advancedmathematics test. This was done in three countries participating in TIMSS Advanced 2008 (Sweden, Norway, and Slovenia), and the…This article provides an overview of the emerging field of mathematical modeling in preharvest food safety. We describe the steps involved in developing mathematical models, different types of models, and their multiple applications. The introduction to modeling is followed by several sections that introduce the most common modeling approaches used in preharvest systems. We finish the chapter by outlining potential future directions for the field.
The increase in availability of educational technologies over the past few decades has not only led to new practice in teaching mathematics but also to new perspectives in research, methodologies, and theoretical frameworks within mathematics education. Hence, the amalgamation of theoretical and pragmatic considerations in digital tool designThis module presents a real-world context in which mathematics skills (geometry and trigonometry) are used as part of a daily routine. The context is the machine tool technology field, and the module aims to help students develop the ability to analyze diagrams in order to make mathematical computations. The modules, which features applications…
This study described, analyzed, and compared the internal and external factors that prevented or fostered the implementation of a cognitive tool, GeoGebra, in the mathematics practices of 12 middle school teachers who had completed a master's degree program in mathematics successfully. Through the application of a case study approach as aMathematics anxiety and its relationship to other constructs was studied in 138 preservice elementary and special education teachers. The students, primarily women, were enrolled in a variety of professional courses and field experiences. Five instruments were administered, their factor structures were determined, and intercorrelations among the…
In mathematical problem solving, American students are falling behind their global peers because of a lack of foundational and reasoning skills. A specific area of difficulty with problem solving is working non-routine, heuristic-based problems. Many students are not provided with effective instruction and often grow frustrated and dislike math.…
The immense advancement of our understanding of disease processes has not been a uniform progression related to the passage of time. Advances have been made in "lurches" and "catches" since the advent of the written word. There has been a remarkable interdependency between such advances in medicine and advances in mathematics that has proved beneficial to both. This work explores some of these critical relationships and documents how the individuals involved contributed to advances in each.
Development of mathematical problem solving skills is an age old problem in mathematics. This paper details the design of a component of a first year university mathematics course in which group work and mathematical communication skills, especially writing skills, are used as a tool to develop non-routine problem solving skills. In this design…
Slowmation is a twenty-first century digital literacy educational tool. This teaching and learning tool has been incorporated as an assessment strategy in the curriculum area of science and mathematics with pre-service teachers (PSTs). This paper explores two themes: developing twenty-first century digital literacy skills and modelling best…
An in-depth knowledge of pedagogical approaches can help improve the formulation of effective and efficient pedagogy, tools and technology to support and enhance the teaching and learning of Mathematics in higher institutions. This study investigated students' perceptions of the challenges of blended e-learning tools in the teaching and learning…
To what extent does the use of computational tools offer teachers the possibility of constructing dynamic models to identify and explore diverse mathematical relations? What ways of reasoning or thinking about the problems emerge during the model construction process that involves the use of the tools? These research questions guided the…
We describe a case study in which we investigate the effectiveness of a lecture in advancedmathematics. We first videorecorded a lecture delivered by an experienced professor who had a reputation for being an outstanding instructor. Using video recall, we then interviewed the professor to determine the ideas that he intended to convey and how he…We provide evidence of persistent gender effects for students using advanced adaptive technology while learning mathematics. This technology improves each gender's learning and affective predispositions toward mathematics, but specific features in the software help either female or male students. Gender differences were seen in the students' style…
The research literature has made calls for greater coherence and consistency with regard to the meaning and use of the term advancedmathematical thinking (AMT) in mathematics education (Artigue, Batanero, & Kent, 2007; Selden & Selden, 2005). Educators and researchers agree that students should be engaged in AMT but it is unclear…
The origins of human abilities for mathematics are debated: Some theories suggest that they are founded upon evolutionarily ancient brain circuits for number and space and others that they are grounded in language competence. To evaluate what brain systems underlie higher mathematics, we scanned professional mathematicians and mathematically naive subjects of equal academic standing as they evaluated the truth of advancedmathematical and nonmathematical statements. In professional mathematicians only, mathematical statements, whether in algebra, analysis, topology or geometry, activated a reproducible set of bilateral frontal, Intraparietal, and ventrolateral temporal regions. Crucially, these activations spared areas related to language and to general-knowledge semantics. Rather, mathematical judgments were related to an amplification of brain activity at sites that are activated by numbers and formulas in nonmathematicians, with a corresponding reduction in nearby face responses. The evidence suggests that high-level mathematical expertise and basic number sense share common roots in a nonlinguistic brain circuit. PMID:27071124
Macromedia Flash is a powerful and robust development tool. Because of its graphical, sound, and animation capabilities (and ubiquitous browser plug-in), major companies employ it in their website development (see or These same features also make Flash a valuable environment for building multi-representational "movies"…"Using the Common Core State Standards for Mathematics With Gifted and Advanced Learners" provides teachers and administrators examples and strategies to implement the new Common Core State Standards (CCSS) with advanced learners at all stages of development in K-12 schools. The book describes--and demonstrates with specific examples from the…
Advancedmathematics and science course taking is critical in building the foundation for students to advance through the STEM pathway-from high school to college to career. To invigorate students' persistence in STEM fields, high schools have been introducing applied STEM courses into the curriculum as a way to reinforce concepts learned in fault PMID:26913930
Throughout the years mathematics has served as the most basic and fundamental tool employed by scientists and researchers to study and describe a wide variety of fields and phenomena. One of the most important practical application areas of mathematics has been for national defense and security purposes. For example, during the Second World War, the mathematical principles underlying game theory and cryptography played a very important role in military planning. Since that time, it has become clear that mathematics has an important role to play in securing victory in any global conflict, including the struggle faced by national security and law enforcement officials in the fight against those engaged in terrorism and other illicit activities.
Mathematical modeling is a powerful technique to address key questions and paradigms in a variety of complex biological systems and can provide quantitative insights into cell kinetics, fate determination and development of cell populations. The chapter is devoted to a review of modeling of the dynamics of stem cell-initiated systems using mathematical methods of ordinary differential equations. Some basic concepts and tools for cell population dynamics are summarized and presented as a gentle introduction to non-mathematicians. The models take into account different plausible mechanisms regulating homeostasis. Two mathematical frameworks are proposed reflecting, respectively, a discrete (punctuated by division events) and a continuous character of transitions between differentiation stages. Advantages and constraints of the mathematical approaches are presented on examples of models of blood systems and compared to patients data on healthy hematopoiesis.
This booklet is the ninth in a series of nine from the Teacher Training Institute at Hofstra University (New York) and describes the content and the approach of an institute course in which the participants use the personal computer as a personal tool within the mathematical discovery process of making conjectures, testing those conjectures, and…
The integration of digital tools in mathematics education is considered both promising and problematic. To deal with this issue, notions of "webbing" and "instrumental orchestration" are developed. However, the two seemed to be disconnected, and having different cultural and theoretical roots. In this article, we investigate…
This study examines the impact of Web-Based Learning Tools (WBLTs), also known as learning objects, in middle school mathematics and science classrooms. Survey, qualitative, and student performance data were collected from a sample of 18 teachers and 443 students. Teachers were very positive about the learning benefits, quality of WBLTs, and…
We offer a mathematical model which takes into account the following factors: the spread of the cutting properties of the tool, parameters spread of gear blanks and consideration of the factor of a possible fracture of the cutting wedge tool. The reliability function, taking into account the above-mentioned factors, has five parameters for which assessment we propose a method according to our experience. A numerical illustration of the method is shown in the article. We suggest using the model in the optimization mode of the cutting tool preventive measures with students raised with constant visual stimulation, from video games…Using six waves of data (Grades 7 through 12) from the Longitudinal Study of American Youth (LSAY), this study investigated the effects of expectation and influence of students, peers, teachers, and parents on participation in advancedmathematics. Results of survival analysis indicated a significant decline in participation rate in the transition from Grades 11 to 12. Students with higher future expectation were more likely to participate in advancedmathematicsmathematicsThis study explores the relationship between specific advancedmathematicsThis text is the first of five in the Secondary School AdvancedMathematics understand their potential influence on model projections that may guide critical policy choices (e.g., investment and scale-up decisions). PMID:26556559
This document provides a preliminary report of the study Gateways To AdvanceMathematThis study was designed to identify the factors that relate to the decisions of females in secondary education to elect or decline advanced instruction in mathematics. The final sample included 91 classrooms in 11 high schools, with the focus of the investigation upon 489 students in 22 geometry classes. The findings indicate that the most…
Rapid growth of Advanced Pl research examined the perspectives of teachers of students with visual impairments (TVIs) regarding the use and effectiveness of electronic assistive technology (EAT) purported to assist students who are blind in advancedmathematics subjects. The data for this study were collected via an online survey distributed to a convenience sample of… intended toleranceFor decades, educators have advocated using history of mathematics in mathematics classrooms. Empirical research on the efficacy of this practice, however, is scarce. A quasi-experiment was used to investigate the effects of using history as a tool to teach mathematics on grade 11 students' mathematics achievement. Effects in three affective…
Reported are the results of an investigation of the effects of programing a computer in a seventh grade mathematics class. Two treatments were conducted during two successive years. The students in the treatment group used the programing language BASIC to write computer algorithms following supplemental instruction. The mathematical content was site establish a mathematical framework for studying immune interactions with Shigella, a bacteria that kills over one million people worldwide every year. The long-term goal of this novel approach is to inform Shigella vaccine design by elucidating which immune components and bacterial targets are crucial for establishing Shigella immunity. Our delay differential equation model focuses on antibody and B cell responses directed against antigens like lipopolysaccharide in Shigella's outer membrane. We find that antibody-based vaccines targeting only surface antigens cannot elicit sufficient immunity for protection. Additional boosting prior to infection would require a four-orders-of-magnitude increase in antibodies to sufficiently prevent epithelial invasion. However, boosting anti-LPS B memory can confer protection, which suggests these cells may correlate with immunity. We see that IgA antibodies are slightly more effective per molecule than IgG, but more total IgA is required due to spatial functionality. An extension of the model reveals that targeting both LPS and epithelial entry proteins is a promising avenue to advance vaccine development. This paper underscores the importance of multifaceted immune targeting in creating an effective Shigella vaccine. It introduces mathematical models to the Shigella vaccine development effort and lays a foundation for joint theoretical/experimental/clinical approaches to Shigella vaccine designIn its simplest description, a tumor is comprised of an expanding population of transformed cells supported by a surrounding microenvironment termed the tumor stroma. The tumor microenvironment has a very complex composition, including multiple types of stromal cells, a dense network of various extracellular matrix (ECM) fibers interpenetrated by the interstitial fluid and gradients of several chemical species that either are dissolved in the fluid or are bound to the ECM structure. In order to study experimentally such complex interactions between multiple players, cancer is dissected and considered at different scales of complexity, such as protein interactions, biochemical pathways, cellular functions or whole organism studies. However, the integration of information acquired from these studies into a common description is as difficult as the disease itself. Computational models of cancer can provide cancer researchers with invaluable tools that are capable of integrating the complexity into organizing principles as well as suggesting testable hypotheses. We will focus in this Minireview on mathematical models in which the whole cell is a main modeling unit. We will present a current stage of such cell-focused mathematical modeling incorporating different stromal components and their interactions with growing tumors, and discuss what modeling approaches can be undertaken to complement the in vivo and in vitro experimentation.
The issue of global warming and related climatic changes from increasing concentrations of greenhouse gases in the atmosphere has received prominent attention during the past few years. The Computer Hardware, AdvancedMathematicsmathematics levels. This… behaviour are illustrated. PMID:25161694
A hierarchical XML database and related analysis tools are being developed by the New Millennium Program to provide guidance on the relative impact, to future NASA missions, of advanced technologies under consideration for developmental funding.
The present article reports a study concerning the analysis of 19 activity plans (we call them "scenarios") developed by mathematics teacher educators-in-training for the pedagogical use of digital tools. The development of these scenarios took place during their training program and was designed as an activity for increasing reflection, for… Mathematics education community has long recognizedBased on findings from a semester-long study, this article examines the development of Samoan prospective teachers' mathematical understandings and mathematics attitudes when investigating authentic contexts and applying working mathematically processes, mental computations and problem-solving strategies to find solutions of problems. The…
This research study aims at evaluating the suitability of SimReal+ for effective use in teacher education. SimReal+ was originally developed to teach mathematics in universities, but it is has been recently improved to include school mathematics. The basic idea of SimReal+ is that the visualization of mathematical concepts is a powerful technique…
The authors stress the importance of bringing together the causal logic of history and the formal logic of mathematics in order to humanize mathematics and make it more accessible. An example of such treatment is given in a discussion of the centrality of Euclid and the Euclidean system to mathematics development. (MN)Focuses on the contribution of the "Journal for Research in Mathematics Education" to the view of learning and teaching elementary school mathematics embodied in current curricular recommendations for school mathematics. (23 references) (MKR) PMID:27855216
In this paper, we present a novel mathematicaltool structure United States ranking among the world in science, technology, engineering, and mathematics (STEM) education is decreasing. To counteract this problem NASA has made it part of its mission to promote STEM education among the nation s youth. Mockups can serve as a great tool when promoting STEM education in America. The Orion Cockpit Working Group has created a new program called Students Shaping America s Next Space Craft (SSANS) to outfit the Medium Fidelity Orion Mockup. SSANS will challenge the students to come up with unique designs to represent the flight design hardware. There are two main types of project packages created by SSANS, those for high school students and those for university students. The high school projects will challenge wood shop, metal shop and pre-engineering classes. The university projects are created mainly for senior design projects and will require the students to perform finite element analysis. These projects will also challenge the undergraduate students in material selection and safety requirements. The SSANS program will help NASA in its mission to promote STEM education, and will help to shape our nations youth into the next generation of STEM leaders.
A habitat for long duration missions which utilizes Advanced Life analysis aim of this study was to provide insights addressing national concerns in Science, Technology, Engineering, and Mathematics (STEM) education by examining how a set of six perimeter urban K-12 schools were transformed into STEM-focused professional learning communities (PLC). The concept of a STEM Academy as a STEM-focused PLC emphasizes the development of a STEM culture where professional discourse and teaching are focused on STEM learning. The STEM Academies examined used the STEM Academy Measurement Tool and Rubric (Tool) as a catalyst for discussion and change. This Tool was developed with input from stakeholders and used for school-wide initiatives, teacher professional development and K-12 student engagement to improve STEM teaching and learning. Two primary goals of this study were to assess the levels of awareness and use of the tool by all stakeholders involved in the project and to determine how the Tool assisted in the development and advancement of these schools as STEM PLCs. Data from the STEM Academy Participant Survey was analyzed to determine stakeholders' perceptions of the Tool in terms of (i) how aware stakeholders were of the Tool, (ii) whether they participated in the use of the Tool, (iii) how the characteristics of PLCs were perceived in their schools, and finally (iv) how the awareness of the Tool influenced teachers' perceptions of the presence of PLC characteristics. Findings indicate that school faculty were aware of the Tool on a number of different levels and evidence exists that the use of the Tool assisted in the development of STEM Academies, however impact varied from school to school. Implications of this study suggest that the survey should be used for a longer period of time to gain more in-depth knowledge on teachers' perceptions of the Tool as a catalyst across time. Additional findings indicate that the process for using the Tool should be ongoing and involve the stakeholders to have the greatest impact on school cultureIntroduction: This research examined the perspectives of teachers of students who are visually impaired regarding the use and effectiveness of high-tech assistive technology purported to assist visually impaired students in advancedmathematics. Methods: The data for this study were collected via a mixed-methods online survey distributed through…
This article describes experiences from a professional development project designed to prepare in-service eighth-grade mathematics teachers to develop, explore, and advance technological pedagogical content knowledge (TPCK) in the teaching and learning of Algebra I. This article describes the process of the participating teachers' mathematical…
New mathematicaltools and approximations developed for the analysis of automotive fuelMathematical working space (MWS) is a model that is used in research in mathematics education, particularly in the field of geometry. Some MWS elements are independent of the field while other elements must be adapted to the field in question. In this paper, we develop the MWS model for the field of analysis with an identification of paradigms. We…
With the advent of new technologies, methods of blended learning are used in online mathematics classrooms to facilitate interactions and provide a richer experience for students. This paper analyses data obtained from practising teachers during their participation in two postgraduate mathematics courses. We conclude that discussion forum…
In this paper, we put Basil Bernstein's theory of pedagogic discourse to work together with additional theoretical resources to interrogate knowledge and practice in mathematics teacher education. We illustrate this methodology through analysis of an instance of mathematics teacher education pedagogic practice. While the methodology itself is…Many students with learning disabilities demonstrate difficulty in developing a conceptual understanding of mathematical topics. Researchers recommend using visual models to support student learning of the concepts and skills necessary to complete abstract and symbolic mathematical problems. Virtual manipulatives (i.e., interactive visual models) focuses on the Office for Civil Rights' (OCR's) activities relating to Title IX and advancedmathematics, science, and technology education for girls. It examines some of the barriers and inequities that undermine girls' opportunities to choose college majors and enter careers in the advancedmathematics, science, and technologyMathematical modeling can be used for the development and implementation of infection control policyExamples are believed to be very important in developing conceptual understanding of mathematical ideas, useful both in mathematics research and instruction (Bills & Watson in "Educational Studies in Mathematics" 69:77-79, 2008; Mason & Watson, 2008; Bills & Tall, 1998; Tall & Vinner, 1981). In this study, we draw on the…Light interacts with biological tissue through two predominant mechanisms: scattering and absorption, which are sensitive to the size and density of cellular organelles, and to biochemical composition (ex. hemoglobin), respectively. During the progression of disease, tissues undergo a predictable set of changes in cell morphology and vascularization, which directly affect their scattering and absorption properties. Hence, quantification of these optical property differences can be used to identify the physiological biomarkers of disease with interest often focused on cancer. Diffuse reflectance spectroscopy is a diagnostic tool, wherein broadband visible light is transmitted through a fiber optic probe into a turbid medium, and after propagating through the sample, a fraction of the light is collected at the surface as reflectance. The measured reflectance spectrum can be analyzed with appropriate mathematical models to extract the optical properties of the tissue, and from these, a set of physiological properties. A number of models have been developed for this purpose using a variety of approaches -- from diffusion theory, to computational simulations, and empirical observations. However, these models are generally limited to narrow ranges of tissue and probe geometries. In this thesis, reflectance models were developed for a much wider range of measurement parameters, and influences such as the scattering phase function and probe design were investigated rigorously for the first time. The results provide a comprehensive understanding of the factors that influence reflectance, with novel insights that, in some cases, challenge current assumptions in the field. An improved Monte Carlo simulation program, designed to run on a graphics processing unit (GPU), was built to simulate the data used in the development of the reflectance models. Rigorous error analysis was performed to identify how inaccuracies in modeling assumptions can be expected to affect the accuracyThe present paper envisages the application of mathematical modelling with the autoregressive (AR) model method as a tool to analyze electroencephalogram data in rat subjects of transient focal cerebral ischemAs there has recently been an onslaught of video cases being developed and implemented with preservice teachers, it is important to evaluate how we should use these cases. This research investigates the features elementary preservice teachers consider valuable when using video cases in mathematics education. The researchers used hierarchical…
The aim of this study is to analyse how a kindergarten teacher orchestrated a mathematical activity involving a fairy tale. Taking a sociocultural perspective on learning and development, naturally occurring talk-in-interaction has been analysed in order to scrutinise the subtleties of the orchestration. The fairy tale "Goldilocks and the…
Mathematics classrooms instruction in Nigeria secondary schools has been termed a major problem to both teachers and their students. Most classroom activities are teacher-centred with students as mere listeners and recipients of knowledge rather than being active initiators of their knowledge. This paper seeks to investigate the effects ofThis paper gives a short description of the scope and content of an educational project. The approach is to use historical navigational devices, such as sextants and cross staffs, to teach mathematics in secondary schools. By making collections of these devices available to teachers and bringing them into the class room a new approach to combine…
In this article, we present investigative tasks that concern loci, which integrate the use of dynamic geometry software (DGS) with mathematics for proving the obtained figures. Additional conditions were added to the loci: ellipse, parabola and circle, which result in the emergence of new loci, similar in form to the original loci. The…
In this article we present a didactic proposal for teaching linear algebra based on two compatible theoretical models: emergent models and mathematical modelling. This proposal begins with a problematic situation related to the creation and use of secure passwords, which leads students toward the construction of the concepts of spanning set and…
Reflects on four years of teaching a course called Principle of Major Teachers for pre-service elementary school teachers. Identifies and describes the discord between their formal mathematical knowledge and their informal language used in the context of elementary number theory. Presents encouraging results from a code-switching experiment.… positioning? We elaborate on the elusive and interrelated concepts of identity, positioning and power, seen as dynamic and changeable. As these concepts represent three interconnected parts of research analysis in an on-going larger project data from different sources will be used in this illustration. In this paper, we clarify the theoretical stance, ground the concepts historically and strive to connect them to research analysis. In this way, we show that power relations and subject positioning in social settings are critical aspects and need to be taken seriously into account if we aim at understanding becoming teachers' identities.
To most children in primary school role-play is just something you do, and somethingThis plan describes the Structural Mathematical Model of the METSAT AMSU-A2 instrument. The model is used to verify the structural adequacy of the AMSU-A2 instrument for the specified loading environments.This study used metaphors as a tool to gain insight about preservice teachers' conceptualizations of the role of the teacher and the learner and held the view that the examination of these metaphors might provide an opportunity for teacher educators to reflectively and critically examine those beliefs. Thus, this research examined possible… access number of learner-centered strategies were implemented during a two-semester course in real analysis that is traditionally taught in lecture format. We seek to understand the role that these strategies can have in this proof-intensive theoretical mathematics classroom and the perceived benefits by the students. Although learner-centeredClickers and classroom voting are used across a number of disciplines in a variety of institutions. There are several papers that describe the use of clickers in mathematics classrooms such as precalculus, calculus, statistics, and even differential equations. This paper describes a method of incorporating clickers and classroom voting in a…
This article presents an overview of some issues that were confronted when delivering an online second Linear Algebra course (assuming a previous Introductory Linear Algebra course) to graduate students enrolled in a Secondary Mathematics Education program. The focus is on performance in one particular aspect of the course: "change of basis" and…
The discovery of new exoplanets makes us wonder where each new exoplanet stands along its way to develop life as we know it on Earth. Our Evo-SETI Theory is a mathematical way to face this problem. We describe cladistics and evolution by virtue of a few statistical equations based on lognormal probability density functions (pdf) in the time. We call b-lognormal a lognormal pdf starting at instant b (birth). Then, the lifetime of any living being becomes a suitable b-lognormal in the time. Next, our "Peak-Locus Theorem" translates cladistics: each species created by evolution is a b-lognormal whose peak lies on the exponentially growing number of living species. This exponential is the mean value of a stochastic process called "Geometric Brownian Motion" (GBM). Past mass extinctions were all-lows of this GBM. In addition, the Shannon Entropy (with a reversed sign) of each b-lognormal is the measure of how evolved that species is, and we call it EvoEntropy. The "molecular clock" is re-interpreted as the EvoEntropy straight line in the time whenever the mean value is exactly the GBM exponential. We were also able to extend the Peak-Locus Theorem to any mean value other than the exponential. For example, we derive in this paper for the first time the EvoEntropy corresponding to the Markov-Korotayev (2007) "cubic" evolution: a curve of logarithmic increase `-friendly softwares 'In this response, I applaud the work initiated in this research and underscore some of the key reasons I find it so valuable. Building from this, I also issue a call to the greater mathematics education community--particularly the large mathematics professional organizations--to consider the ways their organizations have conceptualized and framed…
A poorly designed urban solid waste collection system has an enormous impact on labour, operational and transport costs, and on society in general due to road contamination and negative effects on public health and the environment. This study proposes a methodology for designing an urban solid waste collection system. This methodology uses combinatorial optimisation and integer programing, and GIS tools to minimise collection time, and operational and transport costs while enhancing the current solid waste collection system. This methodology establishes feasible collection routes, determines an adequate vehicle fleet size and presents a comparative cost and sensitivity analysis of the results. The implementation of this methodology in a study case of a zone in Santiago yields significant cost savings in the total collection system.
Nitrous oxide (N2O) can be emitted from wastewater treatment contributing to its greenhouse gas footprint significantly. Mathematical modeling of N2O emissions is of great importance toward the understanding and reduction of the environmental impact of wastewater treatment systems. This article reviews the current status of the modeling of N2O emissions from wastewater treatment. The existing mathematical models describing all the known microbial pathways for N2O production are reviewed and discussed. These included N2O production by ammonia-oxidizing bacteria (AOB) through the hydroxylamine oxidation pathway and the AOB denitrification pathway, N2O production by heterotrophic denitrifiers through the denitrification pathway, and the integration of these pathways in single N2O models. The calibration and validation of these models using lab-scale and full-scale experimental data is also reviewed. We conclude that the mathematical modeling of N2O production, while is still being enhanced supported by new knowledge development, has reached a maturity that facilitates the estimation of site-specific N2O emissions and the development of mitigation strategies for a wastewater treatment plant taking into the specific design and operational conditions of the plant. methodsThe issue of subsurface microbial community responses to the injection of CO2 has great importance not only from a risk assessment point of view but also from the perspective of CO2 recycling to CH4. In this sense, the objective of this study is to develop mathematical models to make a quantitative description of the responses of subsurface indigenous microbial communities to the injection of CO2. For this end, TOUGHREACTV1.2 reactive transport simulator with its module ECO2N is used as the modeling framework. The targeted microbial community is composed of fermentative bacteria (Organic matter → Acetate & H2), acetotrophic methanogens (Acetate → Methane & CO2), acetotrophic Sulfate Reducing Bacteria (SRB) (Acetate → H2S & CO2), hydrogenotrophic methanogens (H2 & CO2 → CH4), and hydrogenotrophic SRB (H2 → H2S). Due to the multiple hydrogeological, geochemical and microbiological factors intervening in both the response of subsurface microbial communities to the injection of CO2 and the chemical and physical fate of CO2 itself, at this stage simulations have been performed in batch mode. That means numerical simulations aimed to track changes in CO2 saturation levels, pH, and concentrations of mineral and aqueous phase species over time at selected initial conditions. Numerical simulation results indicate that the activity of microbes associated with methanogenic processes in geological storage sites of CO2 is governed by the level of CO2 saturation in the pore space as well as by the presence of pH buffering minerals such as calcite. With calcite in the mineral phase attenuating drops in pH below inhibitory levels, for instance it is shown that acetotrophic and hydrogenotrophic SRB outcompete acetotrophic and hydrogenotrophic methanogens for acetate and H2, respectively. During the initial stages of the reaction when the pH level is lowest, the higher tolerance of hydrogenotrophic methanogens to acidic pH levels is reflected by a preferential formation ofDuring the complementary feeding period, children require a nutrient-dense diet to meet their high nutritional requirements. International interest exists in the promotion of affordable, nutritionally adequate complementary feeding diets based on locally available foods. In this context, two questions are often asked: 1) is it possible to design a diet suitable for the complementary feeding period using locally available food? and 2) if this is possible, what is the lowest-cost, nutritionally adequate diet available? These questions are usually answered using a "trial and error" approach. However, a more efficient and rigorous technique, based on linear programming, is also available. It has become more readily accessible with the advent of powerful personal computers. The purpose of this review, therefore, is to inform pediatricians and public health professionals about this tool. In this review, the basic principles of linear programming are briefly examined and some practical applications for formulating sound food-based nutritional recommendations in different contexts are explained. This review should facilitate the adoption of this technique by international health professionals.
Novel methods in microbial ecology are revolutionizing our understanding of the structure and function of microbes in theThis article outlines the effect of the collaborative educational tool ViLLE when learning business mathematics in higher education. ViLLE validates students' answers during the assessment process and provides immediate feedback, enabling students to receive feedback and guidance about the correctness of their answers. The learning results in the…
This mixed methods study examined preservice secondary mathematics teachers' perceptions of a blogging activity used as a supportive teaching-learning tool in a college Euclidean Geometry course. The effect of a 12-week blogging activity that was a standard component of a college Euclidean Geometry course offered for preservice secondary…
This study reported the results of a 3-month quasi-experimental study that determined the effectiveness of an online visual and interactive technological tool on sixth grade students' mathematics performance, math anxiety and attitudes towards math. There were 155 sixth grade students from a middle school in the North Texas area who participatedEven the most dedicated college faculty often discover that their students fail to learn what was taught in their courses and that much of what students do learn is quickly forgotten after the final exam. To help college faculty improve student learning in college Science, Mathematics, Engineering and Technology (SMET), the College Level - One Team of the National Institute for Science Education has created the "FLAG" a Field-tested Learning Assessment Guide for SMET faculty. Developed with funding from the National Science Foundation, the FLAG presents in guidebook format a diverse and robust collection of field-tested classroom assessment techniques (CATs), with supporting information on how to apply them in the classroom. Faculty can download the tools and techniques from the website, which also provides a goals clarifier, an assessment primer, a searchable database, and links to additional resources. The CATs and tools have been reviewed by an expert editorial board and the NISE team. These assessment strategies can help faculty improve the learning environments in their SMET courses especially the crucial introductory courses that most strongly shape students' college learning experiences. In addition, the FLAG includes the web-based Student Assessment of Learning Gains. The SALG offers a convenient way to evaluate the impact of your courses on students. It is based on findings that students' estimates of what they gained are more reliable and informative than their observations of what they liked about the course or teacher. It offers accurate feedback on how well the different aspects of teaching helped the students to learn. Students complete the SALG online after a generic template has been modified to fit the learning objectives and activities of your course. The results are presented to the teacher as summary statistics automatically. The FLAG can be found at the NISE "Innovations in SMET Education" website at Reports from 13 Further Mathematics Knowledge Networks supported by the National Centre for Excellence in the Teaching of Mathematics [NCETM] are analysed. After summarizing basic characteristics of the networks regarding leadership, composition and pattern of activity, each of the following aspects is examined in greater depth: Developmental aims…Existing approaches to tuberculosis (TB) control have been no more than partially successful in areas with high human immunodeficiency virus (HIV) prevalence. In the context of increasingly constrained resources, mathematical modelling can augment understanding and support policy for implementing those strategies that are most likely to bring public health and economic benefits. In this paper, we present an overview of past and recent contributions of TB modelling in this key area, and suggest a way forward through a modelling research agenda that supports a more effective response to the TB-HIV epidemic, based on expert discussions at a meeting convened by the TB Modelling and Analysis Consortium. The research agenda identified high-priority areas for future modelling efforts, including 1) the difficult diagnosis and high mortality of TB-HIV; 2) the high risk of disease progression; 3) TB health systems in high HIV prevalence settings; 4) uncertainty in the natural progression of TB-HIV; and 5) combined interventions for TB-HIV. Efficient and rapid progress towards completion of this modelling agenda will require co-ordination between the modelling community and key stakeholders, including advocates, health policy makers, donors and national or regional finance officials. A continuing dialogue will ensure that new results are effectively communicated and new policy-relevant questions are addressed swiftly. thisThis study investigates the role of digital cognitive technologies in supporting students' mathematical thinking while engaging with instructional tasks. Specifically, the study sought to better understand how the use of technology is related to the cognitive demand of tasks. Data were collected in four secondary mathematics classrooms via…
The article describes the social and cultural roles of Mesopotamian mathematics and the interplay of these roles with such patterns of mathematical thought as can be traced through the sources; it covers the period from the first formation of a genuine state, shortly after the mid-fourth millennium b.c.e., until the end of the Old Babylonian…Number transcoding (e.g., writing 29 when hearing "twenty-nine") is one of the most basic numerical abilities required in daily life and is paramount for mathematics achievement. The aim of this study is to investigate psychometric properties of an Arabic number-writing task and its capacity to identify children with mathematics difficulties. We assessed 786 children (55% girls) from first to fourth grades, who were classified as children with mathematics difficulties (n = 103) or controls (n = 683). Although error rates were low, the task presented adequate internal consistency (0.91). Analyses revealed effective diagnostic accuracy in first and second school grades (specificity equals to 0.67 and 0.76 respectively, and sensitivity equals to 0.70 and 0.88 respectively). Moreover, items tapping the understanding of place-value syntax were the most sensitive to mathematics achievement. Overall, we propose that number transcoding is a useful tool for the assessment of mathematics abilities in early elementary school purpose of our research was to examine a web-based tool for mathematics progress monitoring in first grade. The newly developed assessment tool uses several robust indicators and curriculum-based measures forming three competences (Basic Precursors, Advanced Precursors, and Computation) to determine comprehensive early numeracy skills in designThis paper proposes a theoretical framework for interpreting the content found in mathematics curriculum in order to offer teachers and other mathematics educators comprehensive conceptual tools with which to make curricular decisions. More specifically, it describes a metaphor of "mathematics curriculum as story" and defines and…Applied mathematics has an important role to play in developing the tools needed for the analysis, simulation, and optimization of complex problems. These efforts require the development of the mathematical foundations for scientific discovery, engineering design, and risk analysis based on a sound integrated approach for the understanding of complex systems. However, maximizing the impact of applied mathematics on these challenges requires a novel perspective on approaching the mathematical enterprise. Previous reports that have surveyed the DOE's research needs in applied mathematics have played a key role in defining research directions with the community. Although these reports have had significant impact, accurately assessing current research needs requires an evaluation of today's challenges against the backdrop of recent advances in applied mathematics and computing. To address these needs, the DOE Applied Mathematics Program sponsored a Workshop for Mathematics for the Analysis, Simulation and Optimization of Complex Systems on September 13-14, 2011. The workshop had approximately 50 participants from both the national labs and academia. The goal of the workshop was to identify new research areas in applied mathematics that will complement and enhance the existing DOE ASCR Applied Mathematics Program efforts that are needed to address problems associated with complex systems. This report describes recommendations from the workshop and subsequent analysis of the workshop findings by the organizing committee.
The use of mathematicaltools has long proved to be useful in gaining understanding of complex systems in physics [1]. Recently, many researchers have realized that there is an analogy between emerging phenomena in complex social systems and complex physical or biological systems [4,5,12]. This realization has particularly benefited the modeling and understanding of crime, a ubiquitous phenomena that is far from being understood. In fact, when one is interested in the bulk behavior of patterns that emerge from small and seemingly unrelated interactions as well as decisions that occur at the individual level, the mathematicaltools that have been developed in statistical physics, game theory, network theory, dynamical systems, and partial differential equations can be useful in shedding light into the dynamics of these patterns [2-4,6,12].
Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematicaltools which are useful in solving the problems of business and the social sciences. Discrete mathematics… mathematicstools and resources. The teachers were…This study examined the influence of professional development on elementary school teachers' perceptions of and use of an internet-based formative assessment tool focused on students' number sense skills. Data sources include teacher-participants' pre and post survey, open ended response on post survey, use of the assessment tool and their written PMID:25185237 use of numerical models in volcanological research and volcanic hazard assessment is indispensable to cope with the variety of processes and interactions characterizing magma evolution and eruption dynamics, which are dominated by non-linear phenomena and cannot be modelled at full scale in the laboratory. However, new multidisciplinary problems arise when dealing with complex mathematical formulations, numerical algorithms and their implementations on modern computer architectures, so that new tools are needed for sharing knowledge, software and datasets among scientists. Additionally, the need of communicating the results from complex, physical-based models to the public and authorities requires a further effort to present them in an effective and easy way, while highlighting the strengths and limitations of the approach. Finally, availability of Geographic Information System (GIS) data represents an issue when numerical models have to be applied to real volcanoes for impact studies. We are carrying on several initiatives, started during former and ongoing national and European projects, to develop an electronic infrastructure for promoting information transfer in this field of research. In particular, a web portal, based on a dynamic Content Manager System (CMS), is under construction to host and present physical models and their applications in an extensive way (what is usually not possible in research papers), share numerical codes and simulation datasets and discuss model validation and calibration tests. Moreover, advanced 4D visualization tools have been developed to present model results in a synthetic and effective form. Finally, a web interface to GIS databases has been implemented to share and navigate geographic data. Within this framework, it will be possible to integrate physical model outcomes into a geographic context and access them via an interactive web engine such as Google-Earth.
A "National Numeracy Report" and the Australian Curriculum (2014) have recognised the importance of language in mathematics. The general capabilities contained within the "Australian Curriculum: Mathematics" (2014) highlight literacy as an important tool in the teaching and learning of mathematics, from the interpretation of… Voltage/Impedance Probe. The diagnostic methodology used to baseline and match key parameters of qualified production equipment has had an immense impact on other equipment characterization in the facility. It has resulted in reduced cycle time for new equipment introduction as well.
Enteric virus depuration from shellfish is a complex biological process that may be influenced by biological properties of the mollusc and/or virus species. On the basis of previous experimental data, a mathematical model was developed to characterize the kinetics of viral elimination during the depuration process. The experimental data consisted on twenty depuration trials, each with 60 kg of Manila clams (Venerupis philippinarum) and mediterranean mussels (Mytilus galloprovincialis) previously subjected to bioaccumulation with HAV or MNV-1 (as a surrogate for human norovirus), that were performed in an experimental depuration system during 7 days. It was observed that although viral loads decay along depuration, a residual viral load remains at the end of the process suggesting a decomposition of viral load in a diluted load (susceptible of depuration) and a non-diluted load (unavailable to depurate). The model yielded a general equation, which can predict the viral load at any depuration time knowing the specific filtration rate, dependent on the bivalve species, and specific viral properties. The mathematical model can be combined with quantitative risk assessment calculations to determine the safety of the depurated shellfish, which can be very helpful not only for shellfish producers but also to public health authorities.
The response of mechanical systems composed of springs and dashpots to a step input is of eminent interest in the applications. If the system is formed by linear elements, then its response is governed by a system of linear ordinary differential equations. In the linear case, the mathematical method of choice for the analysis of the response is the classical theory of distributions. However, if the system contains nonlinear elements, then the classical theory of distributions is of no use, since it is strictly limited to the linear setting. Consequently, a question arises whether it is even possible or reasonable to study the response of nonlinear systems to step inputs. The answer is positive. A mathematical theory that can handle the challenge is the so-called Colombeau algebra. Building on the abstract result by Průša and Rajagopal (Int J Non-Linear Mech 81:207-221, 2016), we show how to use the theory in the analysis of response of nonlinear spring-dashpot and spring-dashpot-mass systemsTwo cycles of design-based research of a cognitive tool (CT) for teaching fractions have been completed. Following the success of a quasi-experimental study of the enhanced CT derived from the second cycle of design-based research, this article reports the findings of a pre-test-post-test control group empirical study using the enhanced CT in the… toThe goals for this study were to investigate how fourth-grade students developed an understanding of the arithmetic properties when instruction promoted mathematical argumentation and to identify the characteristics of students' arguments. Using the emergent perspective as an overarching theoretical perspective helped distinguish between two…
The goal of Project M2 was to develop and field-test challenging geometry and measurement units for K-2 students. The units were developed using recommendations from gifted, mathematics, and early childhood education. This article reports on achievement results for students in Grade 1 at 12 diverse sites in four states using the Iowa Tests ofdesigner and become a database of prescribed transients and component failures. The candidate control systems are tested, and their parameters optimized, for each of these stresses. Examples of high-level requirements are: response time less than xx seconds, or overshoot less than xx% ... etc. In mathematical terms, these types of requirements are defined as ''constraints,'' and there are standard mathematical methods to minimize an objective function subject to constraints. Since, in principle, any control design that satisfies all the above constraints is acceptable, the designer must also select an objective function that describes the ''goodness'' of the control design. Examples of objective functions are: minimize the number or amount of control motions, minimize an energy balance... etc.
Progress for the past decade or so has been extraordinary. The solution of Fermat's Last Theorem [11] and of the Poincare Conjecture [1] have resolved two of the most outstanding challenges to mathematics. For both cases, deep and advanced theories and whole subfields of mathematics came into play and were developed further as part of the solutions. And still the future is wide open. Six of the original seven problems from the Clay Foundation challenge remain open, the 23 DARPA challenge problems are open. Entire new branches of mathematics have been developed, including financial mathematics and the connection between geometry and string theory, proposed to solve the problems of quantized gravity. New solutions of the Einstein equations, inspired by shock wave theory, suggest a cosmology model which fits accelerating expansion of the universe possibly eliminating assumptions of 'dark matter'. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. We see a broadening of the intellectual and professional opportunities and responsibilities for mathematicians. These trends are also occuring across all of science. The response can be at the level of the professional societies, which can work to deepen their interactions, not only within the mathematical sciences, but also with other scientific societies. At a deeper level, the choices to be made will come from individual mathematicians. Here, of course, the individual choices will be varied, and we argue for respect and support for this diversity of responses. In such a manner, we hope to preserve the best of the present while welcoming the best of the newRecent advances in software and hardware technology which make it economical to create computing environments appropriate for specialized applications are addressed. Topics included software tools, FORTRAN standards activity, and features of languages, operating systems, and hardware that are important for the development, testing, and maintenance of mathematical softwareMathematics teaching is an interaction between the teacher and the learners that leads to acquisition of desirable mathematical knowledge, ideas and skills necessary for applicability in our everyday life. This paper therefore looks at the concept of self-reliance, the concept of mathematics teaching, problems and prospects of mathematics teaching… trajectory molecular tools algorithmThe use of the history of mathematics in teaching has long been considered a tool for enriching students' mathematical learning. However, in the USA few, if any, research efforts have investigated how the study of history of mathematics contributes to a person's mathematical knowledge for teaching. In this article, I present the results of… technologies substantialMathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advancedmathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…
NCTM's "Technology Principle" challenges mathematics teachers to rethink the mathematics they teach, investigate technological tools for learning mathematics, and consider how they can support students in learning mathematics with technology as a tool. In concert with the NCTM's emphasis on using technology as a tool in mathematics, ISTE's NETS… exposureMaple is a mathematics software package, which contains graphic, computation, and programming tools. Maple animation is a powerful tool that can help in comprehending many fundamental concepts in mathematics and other sciences. This paper deals with the use of maple animation to demonstrate many fundamental concepts in mathematics that are difficult to explain verbally or through static figures. We show Maple animations effectively convey different concepts. We present problems taken from the literature to exemplify and explain Maple animation procedures. Using Maple in teaching mathematics facilitates the students with a tool to experiment and visualize complicated mathematical concepts and thus, strengthen their grasp of the subjectMathematical modelingMany physicists wonder at the usefulness of mathematics in physics. According Madrid to Einstein mathematics is admirably appropriate to the objects of reality. Wigner asserts that mathematics plays an unreasonable important role in physics. James Jeans affirms that God is a mathematician, and that the first aim of physics is to discover the laws of nature, which are written in mathematical language. Dirac suggests that God may have used very advancedmathematics in constructing the universe. And Barrow adheres himself to Wigner's claim about the unreasonable effectiveness of mathematics for the workings of the physical world.
Presently, the complexity of the properties of and the changes in the vegetation-land surface in Southeast Asia is not well understood. This lack of understanding inhibits its being modeled sufficiently well so as to be useful for climate-scale studies. A few major reasons for this include: (a) the radiative and hydrological properties of the vegetation-land surface is complex, changing both in time and space in response to the phase on the Monsoon; (b) human disturbance and land use change are widespread and increasing in this region, and involve both clearance and fires; and (c) that there are not sufficient measurements currently available to empirically quantify many of the properties of interest. To better quantify the properties of the land surface at large spatial scales and over a decadal time scale, new quantitative methods of analysis are required, and the purpose of this presentation is to show both the proof-of-concept of one such approach, as well as some initial and interesting results. In this study, Principal Component Analysis (PCA) was applied to the roughly 13 year dataset provided by the Moderate Resolution Imaging Spectroradiometer (MODIS) Normalized Difference Vegetation Index (NDVI), Enhanced Vegetation Index (EVI), and Leaf Area Index (LAI). PCA is a tool allowing the extraction of the standing modes of a dataset, reducing a complex dataset to small and orthogonal sets that contribute the most variance to the data. Combining this tool with variance and correlation maps between the measured time series and those derived from the PCA, the spatiotemporal structure of the dataset can be elucidated. This technique allows for different patterns in both space and time over Southeast Asia to be revealed. Comparison using the variance and correlation maps between the time series and the seasonal variations derived from PCA suggest that both the variance and correlation are stronger over Northern Southeast Asia than in Equatorial Southeast Asia. OneMathematical statements involving both universal and existential quantifiers occur frequently in advancedmathematics. Despite their prevalence, mathematics students often have difficulties interpreting and proving quantified statements. Through task-based interviews, this study took a qualitative look at undergraduate mathematics students'…
The advancement of modern societies is fueled by mathematics, and mathematics education provides the foundation upon which future scientists and engineers will build. Society dictates how mathematics will be taught through the development and implementation of mathematics standards. When examining the progression of these standards, it is…
Developing the Trends in International Mathematics and Science Study (TIMSS) Advanced 2008 Assessment Frameworks was a collaborative venture involving mathematics and physics experts from around the world. The document contains two frameworks for implementing TIMSS Advanced 2008--one for advancedmathematics and one for physics. It also contains…
The Trends in International Mathematics and Science Study (TIMSS) 2015 is the sixth administration of this international comparative study since 1995 when first administered. TIMSS is used to compare over time the mathematics and science knowledge and skills of fourth- and eighth-graders. TIMSS is designed to align broadly with mathematics and…
Examines in-service secondary schoolThe manifold but discrete presence of mathematics in many objects or services imposes new constraints to the teaching of mathematics. If citizens need to be comfortable in various situations with a variety of mathematicaltools, the learning of mathematics requires that one starts with simple concepts. This paper proposes some solutions to solve…
In this paper, the author aims to offer an elaboration of simple, yet powerful, mathematical patterns through mathematical games. Mathematical games may serve as colorful instructional tools for teachers and textbooks, and may raise students' motivation and intuition. Patterns are fundamental in mathematics and computer science. In the case of…
In their dual roles as mathematics teachers and tennis coaches, the authors have worked with tennis players who have never thought about how a knowledge of mathematics might help them become "better" tennis players. They have also worked with many mathematics students who have never considered how much mathematics is associated with tennis. This…Mathematical models models of the neuroendocrine system, as well as design principles that have been illuminated through the use of mathematical models. These principles are found over and over again in cellular dynamics, and serve as building blocks for understanding some of the complex temporal dynamics that are exhibited throughout the neuroendocrine system.
The remote sensing analyses in the BMBF-SPACES collaborative project Geoarchives - Signals of Climate and Landscape Change preserved in Southern African Geoarchives - focuses on the use of recent and upcoming Earth Observation Tools for the study of climate and land use changes and its impact on the ecosystem. It aims at demonstrating the potential of recently available advanced optical remote sensing imagery with its extended spectral coverage and temporal resolution for the identification and mapping of sediment features associated with paleo-environmental archives as well as their recent dynamic. In this study we focus on the analyses of two ecosystems of major interest, the Kalahari salt pans as well as the lagoons at Namibia's west coast, that present high dynamic caused by combined hydrological and surface processes linked to climatic events. Multitemporal remote sensing techniques allow us to derive the recent surface dynamic of the salt pans and also provide opportunities to get a detailed understanding of the spatiotemporal development of the coastal lagoons. Furthermore spaceborne hyperspectral analysis can give insight to the current surface mineralogy of the salt pans on a physical basis and provide the intra pan distribution of evaporites. The soils and sediments of the Kalahari salt pans such as the Omongwa pan are a potentially significant storage of global carbon and also function as an important terrestrial climate archive. Thus far the surface distribution of evaporites have been only assessed mono-temporally and on a coarse regional scale, but the dynamic of the salt pans, especially the formation of evaporites, is still uncertain and poorly understood. For the salt pan analyses a change detection is applied using the Iterative-reweighted Multivariate Alteration Detection (IR-MAD) method to identify and investigate surface changes based on a Landsat time-series covering the period 1984-2015. Furthermore the current spatial distribution of
The adoption and implementation of the Common Core State Standards and Smarter Balanced assessments in mathematics are intended to provide all students in California with the knowledge and skills required to transition from high school to college-level coursework. This implementation will take time. Concurrent with these efforts, policymakers and…Mathematics teachers play a unique role as experts who provide opportunities for students to engage in the practices of the mathematics community. Proof is a tool essential to the practice of mathematics, and therefore, if teachers are to provide adequate opportunities for students to engage with this tool, they must be able to validate student…
This document gives a listing of mathematical terminology in both the English and Vietnamese languages. Vocabulary used in algebra and geometry is included along with a translation of mathematical symbols. (DT)
Mathematical techniques used to solve geological problems are briefly discussed (including comments on use of geostatistics). Highlights of conferences/meetings and conference papers in mathematical geology are also provided. (JN)One of the primary data deficiencies that prevent the advance of policy relevant research on particulate matter, ozone, and associated precursors is the lack of measurement data and knowledge on the true vertical profile and synoptic-scale spatial distributions of the pollutants....This package consists of course syllabi, an instructor's handbook, and student laboratory manual for a 1-year vocational training program to prepare students for entry-level positions as advanced computer numerical control (CNC) and computer-assisted manufacturing (CAM) technicians.. The program was developed through a modification of the DACUM…
An understanding of past technological advancements can help educators understand the influence of new technologies in education. Inventions such as the abacus, logarithms, the slide rule, the calculating machine, computers, and electronic calculators have all found their place in mathematics education. While new technologies can be very useful,…
In this 1967 booklet, influences of technology, the non-achiever and the culturally disadvantaged, and the revolt against formalism are discussed in relation to the modern mathematics curriculum. Some projects and school programs described include PLATO, the Nuffield Project, the Nova School Program, Advanced Placement Program, and teacher…
This paper addresses the contested way that ethnomathematics has sometimes been received by mathematicians and others and what that disagreement might suggest about issues in mathematics education; namely, (a) the relation of ethnomathematics to academic mathematics; (b) recent efforts to reform secondary school mathematics so that it prepares… paper is a descriptive and preliminary report on recent efforts to address two questions: 1) Can school mathematics be used to enhance our students' ability to understand their changing world? and 2) What role might computer technology play in this regard? After recounting some of the mathematicaltools that led to a better understanding of…
In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematicaltools in this course are the difference equations and matrix algebra. We also integrate computer technology and…
A basic description is given of the mathematicaltools and models which are presently used to represent turbulent, free shear layers. Recommendations are included for ways in which current modeling techniques can be improved.
The foundation of science, and of thermodynamics in particular, can be developed cogently and without arbitrariness. The goal of science, description of nature, is externally given; it requires a set of basic concepts as indispensable tools. Mathematics has no similar externally given goal. (Author/TS)
Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in… PMID:27013962…Surgery is an essential part of the oncologic treatment of patients with brain tumors. Surgery is necessary for histologic diagnosis, and the cytoreduction of tumor mass has been shown to improve patient survival time and quality of life. Ultimately, the goal of any oncologic neurosurgery is to achieve maximal safe resection. Over the years, many technologic adjuncts have been developed to assist the surgeon in achieving this goal. In this article, we review the technologic advances of modern neurosurgery that are helping to reach this goal.
This article presents an advanced optical model for simulation of alien wavelengths in multi-domain and multi-vendor dense wavelength-division multiplexing networks. The model aids optical network planners with a better understanding of the non-linear effects present in dense wavelength-division multiplexing systems and better utilization of alien wavelengths in future applications. The limiting physical effects for alien wavelengths are investigated in relation to power levels, channel spacing, and other factors. The simulation results are verified through experimental setup in live multi-domain dense wavelength-division multiplexing systems between two national research networks: SURFnet in Holland and NORDUnet in Denmark.
The potential to use mathematics software to enhance student thinking and development is discussed and a taxonomy of software categories is outlined in this paper. Briefly, there are five categories of tool-based mathematics software that can be used fruitfully in a mathematics curriculum: (a) review and practice, (b) general, (c) specific, (d) problem addressed in this project is the lack of mathematically gifted females choosing to pursue advanced science, technology, engineering, and mathematics (STEM) courses in secondary education due to deficiencies in self-efficacy. The purpose of this project was to study the effects of a child-guided robotics program as it relates to the self-efficacy of mathematically gifted 6th grade female students and their future course choices in the advanced STEM content areas. This mixed-model study utilized a STEM attitude survey, artifacts, interviews, field notes, and standardized tests as measurement tools. Significance was found between genders in the treatment group for the standardized science scores, indicating closure in the achievement gap. Research suggests that STEM enrichment is beneficial for mathematically gifted females.
There is extensive evidence that active learning works better than a completely passive lecture. Despite this evidence "TIMSS Advanced 2015 Assessment Frameworks" provides the foundation for the two international assessments to take place as part of the International Association for the Evaluation of Educational Achievement's TIMSS (Trends in International Mathematics and Science Study) Advanced 2015--AdvancedMathematics and Physics. Chapter 1 (Liv…As design rules shrink, Critical Dimension Uniformity (CDU) and Line Edge Roughness (LER) have a dramatic effect on printed final lines and hence the need to control these parameters increases. Sources of CDU and LER variations include scanner auto-focus accuracy and stability, layer stack thickness, composition variations, and exposure variations. Process variations, in advanced VLSI production designs, specifically in memory devices, attributed to CDU and LER affect cell-to-cell parametric variations. These variations significantly impact device performance and die yield. Traditionally, measurements of LER are performed by CD-SEM or OCD metrology tools. Typically, these measurements require a relatively long time to set and cover only selected points of wafer area. In this paper we present the results of a collaborative work of the Process Diagnostic & Control Business Unit of Applied Materials and Hynix Semiconductor Inc. on the implementation of a complementary method to the CDSEM and OCD tools, to monitor defect density and post litho develop CDU and LER on production wafers. The method, referred to as Process Variation Monitoring (PVM) is based on measuring variations in the scattered light from periodic structures. The application is demonstrated using Applied Materials DUV bright field (BF) wafer inspection tool under optimized illumination and collection conditions. The UVisionTM has already passed a successful feasibility study on DRAM products with 66nm and 54nm design rules. The tool has shown high sensitivity to variations across an FEM wafer in both exposure and focus axes. In this article we show how PVM can help detection of Field to Field variations on DRAM wafers with 44nm design rule during normal production run. The complex die layout and the shrink in cell dimensions require high sensitivity to local variations within Dies or Fields. During normal scan of production wafers local Process variations are translated into GL (Grey Level) values
One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory volume developed by the Machine ToolAdvanced SkillOne section of this "scrapbook" section describes Pythagoras' belief in the connections between music and mathematics -- that everything in the universe was a series of harmonies and regulated by music. Another section explains why Phythagoras felt it important for women to be encouraged to learn mathematics. At least 28 women were involved in his…
The focus of this special issue is mathematics education. All articles were written by graduates of the new masters Degree program in which students earn a Master of Arts degree in Education with a concentration in Mathematics Education at San Francisco State University. Articles include: (1) "Developing Teacher-Leaders in a Masters Degree Program…
Why mathematics should be learned is discussed. Its role as an important active force in the development of our civilization, and as the most useful subject taught in our schools, next to English, is noted. The primary objective of all mathematics work is to help man study nature, and some practical achievements of this connection are noted.…
"Mathematical literacy" implies that a person is able to reason, analyze, formulate, and solve problems in a real-world setting. Mathematically literate individuals are informed citizens and intelligent consumers. They have the ability to interpret and analyze the vast amount of information they are inundated with daily in newspapers, on… PMID:22690046
Recently, therapeutic erythrocytapheresis (TE) was suggested to be more efficient in depletion of red blood cells (RBC) compared to manual phlebotomy in the treatment of hereditary hemochromatosis (HH), polycythemia vera (PV), and secondary erythrocytosis (SE). The efficiency rate (ER) of TE, that is, the increase in RBC depletion achieved with one TE cycle compared to one phlebotomy procedure, can be calculated based on estimated blood volume (BV), preprocedural hematocrit (Hct(B)), and delta-hematocrit (ΔHct). In a retrospective evaluation of 843 TE procedures (in 45 HH, 33 PV, and 40 SE patients) the mean ER was 1.86 ± 0.62 with the highest rates achieved in HH patients. An ER of 1.5 was not reached in 37.9% of all procedures mainly concerning patients with a BV below 4,500 ml. In 12 newly diagnosed homozygous HH patients, the induction phase duration was medially 38.4 weeks (medially 10.5 procedures). During the maintenance treatment of HH, PV, and SE, the interval between TE procedures was medially 13.4 weeks. This mathematical model can help select the proper treatment modality for the individual patient. Especially for patients with a large BV and high achievable ΔHct, TE appears to be more efficient than manual phlebotomy in RBC depletion thereby potentially reducing the numbers of procedures and expanding the interprocedural time period for HH, PV, and SEMagnitude understanding is critical for students to develop a deep understanding of fractions and more advancedmathematics curriculum. The research reports in this special issue underscore magnitude understanding for fractions and emphasize number lines as both an assessment and an instructional tool. In this commentary, we discuss how number lines broaden the concept of fractions for students who are tied to the more general part-whole representations of area models. We also discuss how number lines, compared to other representations, are a superior and more mathematically correct way to explain fraction concepts.
Manipulatives have the potential to be powerful tools in helping children improve their number sense, develop advancedmathematical strategies, and build an understanding of the base ten number system. Physical manipulatives used in classrooms, however, are often not designed to promote efficient strategy use, such as counting on, and typically do…
Many students in upper-division physics courses struggle with the mathematically sophisticated tools and techniques that are required for advanced physics content. We have developed an analytical framework to assist instructors and researchers in characterizing students' difficulties with specific mathematicaltools when solving the long and complex problems that are characteristic of upper division. In this paper, we present this framework, including its motivation and development. We also describe an application of the framework to investigations of student difficulties with direct integration in electricity and magnetism (i.e., Coulomb's law) and approximation methods in classical mechanics (i.e., Taylor series). These investigations provide examples of the types of difficulties encountered by advanced physics students, as well as the utility of the framework for both researchers and instructors.
Mathematics is a powerful tool for describing and developing our knowledge of the physical world. It informs our understanding of subjects as diverse as music, games, science, economics, communications protocols, and visual arts. Mathematical thinking has its roots in the adaptive behavior of living creatures: animals must employ judgments about quantities and magnitudes in the assessment of both threats (how many foes) and opportunities (how much food) in order to make effective decisions, and use geometric information in the environment for recognizing landmarks and navigating environments. Correspondingly, cognitive systems that are dedicated to the processing of distinctly mathematical information have developed. In particular, there is evidence that certain core systems for understanding different aspects of arithmetic as well as geometry are employed by humans and many other animals. They become active early in life and, particularly in the case of humans, develop through maturation. Although these core systems individually appear to be quite limited in application, in combination they allow for the recognition of mathematical properties and the formation of appropriate inferences based upon those properties. In this overview, the core systems, their roles, their limitations, and their interaction with external representations are discussed, as well as possibilities for how they can be employed together to allow us to reason about more complex mathematical domains.
The process standards of communication and representation in the "Principles and Standards for School Mathematics" are critical tools to help students develop mathematical literacy. In the mathematics classroom, students need to be encouraged to use speaking, listening, reading, and writing to communicate their understanding of mathematics words,…
Mathematics educators often fail to see that their subject has social and ethical dimensions. If anything, mathematics is seen as a neutral tool that has a social dimension only because it can be used to solve social problems. This study critically examines this idea by arguing that, although school mathematics is indeed a technology, technology…
The first part of this two-part paper [see EJ787497] described the development of a new freshman business mathematics (FBM) course at our college. In this paper, we discuss our assessment tool, the business memo, as a venue for students to apply mathematical skills, via mathematical modelling, to realistic business problems. These memos have…
This paper describes trends in and causes of minority and female representation among holders of advanced science and math degrees. The minority groups studied are Blacks, Hispanic Americans, American Indians, and Asian Americans, all of whom are compared with Whites. The degrees looked at include those in math, the computer sciences, physical…
The published works of scientists often conceal the cognitive processes that led to their results. Scholars of mathematical practice must therefore seek out less obvious sources. This article analyzes a widely circulated mathematical joke, comprising a list of spurious proof types. An account is proposed in terms of argumentation schemes: stereotypical patterns of reasoning, which may be accompanied by critical questions itemizing possible lines of defeat. It is argued that humor is associated with risky forms of inference, which are essential to creative mathematics. The components of the joke are explicated by argumentation schemes devised for application to topic-neutral reasoning. These in turn are classified under seven headings: retroduction, citation, intuition, meta-argument, closure, generalization, and definition. Finally, the wider significance of this account for the cognitive science of mathematics is discussed.
Background In radiation oncology recurrence analysis is an important part in the evaluation process and clinical quality assurance of treatment concepts. With the example of 9 patients with locally advanced pancreatic cancer we developed and validated interactive analysis tools analysis tools editors of this Special Issue of Mathematical Biosciences and Engineering were the organizers for the Third International Workshop "Mathematical Methods in System BiologytoolsMecanotron, now division of Robotics and Automation Corporation, developed a quick-change welding method called the Automatic Robotics Tool-change System (ARTS) under Marshall Space Flight Center and Rockwell International contracts. The ARTS system has six tool positions ranging from coarse sanding disks and abrasive wheels to cloth polishing wheels with motors of various horsepower. The system is used by fabricators of plastic body parts for the auto industry, by Texas Instruments for making radar domes, and for advanced composites at Aerospatiale in France.
This report describes the work of developing an integrated model used to predict the thermal history, deformation, roll forces, microstructural evolution and mechanical properties of steel strip in a hot-strip mill. This achievement results from a joint research effort that is part of the American Iron and Steel Institute's (AIS) Advanced Process Control Program, a collaboration between the U.S. DOE and fifteen North American Steelmakers.
This paper discusses methods that can be used to inspire physics students to learn advanced differential equations. Numerous problems in physics are described by this type of equation. There has been rapid advancement in computer technology and development of computational mathematics-a branch of mathematics using computers to generate solutions to advanced differential equations. Arguably, this branch of mathematics is becoming more important to physicists than traditional analytical mathematics. Computer Algebra Software (CAS) packages have also emerged as a means to perform elaborate and complicated analytical mathematics much faster than possible by humansTailoring the use of screening colonoscopy based on the risk of advanced colcapture sequences was provided by MPL to CCAD and OGAL. CCAD's work focused on imposing these sequences on the SantosTM digital human avatar . An...capture sequences was provided by MPL to CCAD and OGAL. CCAD's work focused on imposing these sequences on the Santos digital human avatar . An initial...levels of the patients. In addition, the differences in ability to detect variations in gait conditions for skinned avatar vs. line-skeletal avatar
or unclothed avatars , stick figures, or even skeletal models to support their analyses. The system will also allow trainees to isolate specific...CCAD's work focused on imposing these sequences on the Santos digital human avatar . An initial user interface for the training application was also...ability to detect variations in gait conditions for skinned avatar vs. line‐skeletal avatar , concurrent (side‐by‐side) image representation vs modelling models of gastrulation in the chick embryo. In the last section, we give an overview of various mathematical models used in the study of the developmental cycle of Dictyostelium discoideum, which is probably the best example of successful mathematical modelling in developmental biology.
As a way to dispel negative feelings toward mathematics, a variety of quotations are given. They are categorized by: what mathematics is, mathematicians, mathematics and other disciplines, different areas of mathematics, mathematics and humor, applications of mathematics, and pure versus applied mathematics. (MNS)One of the most interesting developments in teaching has been the growing importance of the outdoor environment. Whether it be playground, garden or field, the outdoors offers a range of challenging experiences, especially in the delivery of early mathematics. Oral feedback to parents, together with photographic displays, can show them that…
This is one of five panel reports that have been prepared as part of the first phase of Project 2061, a long-term multipurpose undertaking of the American Association for the Advancement of Science designed to help reform science, mathematics, and technology education in the United States. Major sections included are: (1) "Introduction";…
The study presents an introductory idea of using mathematical averages as a tool for enriching mathematical problem solving. Throughout students' activities, a research was conducted on their ability to solve mathematical problems, and how to cope with a variety of mathematical tasks, in a variety of ways, using the skills, tools and experiences…
This present study seeks to predict mathematical aptitude for higher education by examining the relationship between mathematics results from the Caribbean Examinations Council (CXC) general proficiency examination and the results from the General Certificate of Education (GCE) advanced level examination. This present study arose from a more…
Technology integration in mathematics classrooms is important to the field of education, not only because today's society is becoming more and more advanced and reliant upon technology but also because schools are beginning to embrace technology as an essential part of their curricula. The Principles and Standards for School Mathematics (National…
A whirlwind of activity surrounds the topic of teaching and learning mathematics. The driving forces are a combination of changes in assessment and advances in technology that are being spurred on by the introduction of content in the Common Core State Standards for Mathematical Practice. Although the issues are certainly complex, the same forces…
Significant increases in data generation and computing power in recent years have greatly improved spatial and temporal flux data coverage on multiple scales, from a single station to continental flux networks. At the same time, operating budgets for flux teams and stations infrastructure are getting ever more difficult to acquire and sustain. With more stations and networks, larger data flows from each station, and smaller operating budgets, modern tools are needed to effectively and efficiently handle the entire process. This would help maximize time dedicated to answering research questions, and minimize time and expenses spent on data processing, quality control and station management. Cross-sharing the stations with external institutions may also help leverage available funding, increase scientific collaboration, and promote data analyses and publications. FluxSuite, a new advancedtool combining hardware, software and web-service, was developed to address these specific demands. It automates key stages of flux workflow, minimizes day-to-day site management, and modernizes the handling of data flows: Each next-generation station measures all parameters needed for flux computations Field microcomputer calculates final fully-corrected flux rates in real time, including computation-intensive Fourier transforms, spectra, co-spectra, multiple rotations, stationarity, footprint, etc. Final fluxes, radiation, weather and soil data are merged into a single quality-controlled file Multiple flux stations are linked into an automated time-synchronized network Flux network manager, or PI, can see all stations in real time, including fluxes, supporting data, automated reports, and email alerts PI can assign rights, allow or restrict access to stations and data: selected stations can be shared via rights-managed access internally or with external institutions Researchers without stations could form "virtual networks" for specific projects by collaborating with PIs from mathematical arguments to hypothesize that mathematics majors hold four specific unproductive beliefs about proof reading. We then conducted a survey about these beliefs with 175 mathematics majors and 83 mathematicians. We found that mathematics majors were more likely to believe that when reading a good proof, they are not expected to construct justifications and diagrams, they can understand most proofs they read within 15 minutes, and understanding a proof is tantamount to being able to justify each step in the proof.
A brief historical introduction to the development of observational astronomyThe paper analyzes adult mathematics education from a cultural perspective. Specifically, its purpose is to broaden our comprehension about this field of knowledge using as a theoretical tool-box an Ethnomathematics perspective founded on post-modern thought, post-structuralism theorizations and Wittgenstein's work developed in his book…In this study, the effect of the LOKOMAT, a robotic-assisted locomotor training system, on the reduction of neuromuscular abnormalities associated with spasticity was examined, for the first time in the spinal cord injury (SCI) population. Twenty-three individuals with chronic incomplete SCI received 1-hour training sessions in the LOKOMAT three times per week, with up to 45 minutes of training per session; matched control group received no intervention. The neuromuscular properties of the spastic ankle were then evaluated prior to training and after 1, 2, and 4 weeks of training. A parallel-cascade system identification technique was used to determine the reflex and intrinsic stiffness of the ankle joint as a function of ankle position at each time point. The slope of the stiffness vs. joint angle curve, i.e. the modulation of stiffness with joint position, was then calculated and tracked over the four-week period. Growth Mixture Modeling (GMM), an advanced statistical method, was then used to classify subjects into subgroups based on similar trends in recovery pattern of slope over time, and Random Coefficient Regression (RCR) was used to model the recovery patterns within each subgroup. All groups showed significant reductions in both reflex and intrinsic slope over time, but subjects in classes with higher baseline values of the slope showed larger improvements over the four weeks of training. These findings suggest that LOKOMAT training may also be useful for reducing the abnormal modulation of neuromuscular properties that arises as secondary effects after SCI. This can advise clinicians as to which patients can benefit the most from LOKOMAT training prior to beginning the training. Further, this study shows that system identification and GMM/RCR can serve as powerful tools to quantify and track spasticity over time in the SCI population.
Years of research have been devoted to computer-generated two-dimensional marbling. However, three-dimensional marbling has yet to be explored. In this paper, we present mathematical marbling of three-dimensionalAddresses the use of mathematics when studying the physics of electromagnetism. Focuses on common electromagnetic concepts and their associated mathematical representation and arithmetical tools. Concludes that most students do not understand the significant aspects of physical situations and have difficulty using relationships and models specific…
This analysis of the writing in a grade 7 mathematics textbook distinguishes between closed texts and open texts, which acknowledge multiple possibilities. I use tools that have recently been applied in mathematics contexts, focussing on grammatical features that include personal pronouns, modality, and types of imperatives, as well as on…
This article presents a mathematical solution to a motorway problem. The motorway problem is an excellent application in optimisation. As it integrates the concepts of trigonometric functions and differentiation, the motorway problem can be used quite effectively as the basis for an assessment tool in senior secondary mathematics subjects.…
In higher education today, mathematics has been marginalized: except to a tiny elite, it is either taught as a tool required for the study of other sciences or it is entirely absent. Yet mathematics has been and is an essential ingredient in our understanding and mastery of the physical world, our economic life, our information technology and,…
The challenge in mathematics education is finding the best way to teach mathematics. When students learn the reasoning and proving in mathematics, they will be proficient in mathematics. Students must know mathematics before they can apply it. Symbolism and logic is the key to both the learning of mathematics and its effective application to…Parents and schools often notice the need for addressing advancedmathematical performance in elementary students. Many gifted programs do not offer differentiated or accelerated mathematics as part of their elementary school options. In this report, the efforts of one school system to identify and serve the needs of highly mathematically able…
We describe our team-taught, interdisciplinary course "Numb3rs in Lett3rs & Fi1ms: Mathematics in Literature and Cinema," which explores mathematics in the context of modern literature and cinema. Our goal with this course is to advance collaborations between mathematics and the written/theatre-based creative arts.
This chapter examines the scope of the mathematical content educators expect students to understand after they have participated in mathematics courses. It is organized under four headings: (1) Traditional School Mathematics, to clarify what the shift is away from; (2) Mathematics as Human Activity, to portray the direction the shift is toward;… | 677.169 | 1 |
Linear system dialog
--- Introduction ---
In an exercise of dialog, the computer presents a problem, and it is up to you
to ask it questions which would help you selve this problem. You can solve
problem once you have gathered enough information. But you will be punished
if you ask more questions than absolutely necessary!
In this module, you have 6 dialog exercises on linear systems.
Choose the exercises:
One series will have
.
Level of severity
After having selected an exercise from the list,
click Start.
The exercises will be drawn randomly from what you have selected
(or otherwise from among all the available exercises if you have not selected a particular one). | 677.169 | 1 |
Not Scheduled Yet
Details
The students are provided with detailed concept clearance in PMR level Mathematical concepts. The students are made to gain a thorough knowledge though exercises, tests and other activities. Our teaching styles are graphically designed so that student can solve most of the questions mentally and within second without complex calculation.
Topics covered / Highlights
The students are provided with detailed concept clearance in PMR level Mathematical concepts. The students are made to gain a thorough knowledge though exercises, tests and other activities.
Who can attend this ?
PMR level students.
Pre requisites
none
What am I going to get from this Class ?
All the concepts and chapters of PMR Level Mathematics will be covered in a detailed manner | 677.169 | 1 |
Product details
ISBN-13: 9780534403928
ISBN: 0534403921
Edition: 5
Publication Date: 2003
Publisher: Thomson Learning
AUTHOR
McKeague, Charles P., Turner, Mark
SUMMARY
This text provides students with a solid understanding of the definitions and principles of trigonometry and their application to problem solving. Identities are introduced early in Chapter 1. They are reviewed often and are then covered in more detail in Chapter 5. Also, exact values of the trigonometric functions are emphasized throughout the textbook. There are numerous calculator notes placed throughout the text.McKeague, Charles P. is the author of 'Trigonometry With Infotrac', published 2003 under ISBN 9780534403928 and ISBN 05344039 | 677.169 | 1 |
Mathematical practices and modeling with mathematics are embedded into standards for honors geometry to include the study of congruence, similarity, right triangles, and trigonometry, circles, expressing geometric properties with equations, and geometric measurement and dimension. Instructional time and learning focuses on six critical areas: (1) congruence, proof, and constructions; (2) similarity, proof and trigonometry; (3) extending to three dimensions; (4) connecting algebra and geometry through coordinates; (5) circles with and without coordinates; and (6) applications of probability. In addition, the curriculum includes rigorous proofs, algebraic representations of geometric concepts, transformational geometry and coordinate geometry. NOTE: This is a weighted course. | 677.169 | 1 |
End-of-year Examination: Examined in 3 parts, one examination covering each term's work
Description:
Group representions arise wherever there is symmetry
and linearity.
They provide perhaps the most important single tool
in the application of Mathematics to Physics and Chemistry.
They are also an important resource in several branches of Pure Mathematics.
The course will be in 3 parts.
These will be examined separately,
after each part.
Representations of Finite Groups
Representations of Compact Groups
Representations of Lie Groups
Notes on the course may be found in /usr/local/pub/GroupRepresentations.
Read README before printing them out. | 677.169 | 1 |
California Math (eMathbook Grade 4)
About the Book
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Synopsis: The California eMathbook reproduces the student book in an easy, interactive electronic format. Now you can access the text from anywhere without carrying textbooks to and from school. Printable activity pages! Audio support! On-screen help. Learning tools to help the student.
Book Description HOUGHTON MIFFLIN. DVD-ROM431021 | 677.169 | 1 |
Mathematics Courses Graduate
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Mathematics Courses Graduate
MATHEMATICS DEPARTMENT COURSE DESCRIPTIONS
The Department offers three types of courses. "Professionalized subject matter" courses generally approach mathematics in a way which enhances the depth of understanding and teaching, of mathematics in the secondary school. "Pure mathematics" courses encourage the student to strengthen the knowledge of mathematics with a possible goal of pursuing an additional advanced degree. "Computer related" courses provide students with a mathematical approach to computational processes.
This course provides an historic overview and survey of equipment and other elements to be found in computer systems. The operations and management of computer resources, use of math software, and an overview of computer programming languages are other topics covered.
This course provides students, who have basic computer literacy and some elementary knowledge of computer programming, specific skills in using mathematical software. Problems and projects are taken from a variety of mathematical subjects including: precalculus, calculus, number theory, geometry, linear algebra, abstract algebra, and statistics. Explanations and introductions to these subjects are provided. Prerequisite: MATH 502 Concepts of Computer Science or by permission of department chair.
This course offers a study of procedures in arithmetic. Attention is given to concepts in manipulative and problem solving areas. Various services for diagnostic and remedial measures are introduced and evaluated.
This course provides the student with a reappraisal of the fundamental concepts of algebra. Emphasis is placed on the manner in which these concepts can be used to teach algebra more effectively. This course demands evidence of effective use of these concepts in the student's own classroom. Topics include: number, set, relations, functions, operation structure, and problem solving.
MATH 511 Professionalized Subject Matter in Junior High School and General Mathematics (3) view syllabus-pdf
This course stresses mathematical concepts and skills required of children entering the junior high school curriculum in recent years, as well as those which are appropriate for students with less interest and ability in mathematics. The student is required to show evidence of use of some of these in the student's own classroom. Topics include: modular arithmetic, numeration, geometry, descriptive statistics, algebra, and mathematical games.
This course provides a review of fundamental concepts of geometry and an investigation of their significance in the teaching of secondary school mathematics. Concepts to be analyzed include: logic, proof, and axiomatic systems; physical and geometric models; sets, relations, and transformation; non-metric and metric concepts, duality and dimensionality; and coordination of spaces. Attention is given to: historical considerations bearing on the teaching of geometry; integration of geometry with algebra and science; and significant literature on the subject. This course requires evidence that the stu dent is making effective use of these concepts in the student's own classroom.
This course presents pre-calculus topics, particularly trigonometry and matrix operations. Attention is given to historical considerations and to current trends in teaching this content. This course requires evidence that the student is making effective use of these concepts in the student's own classroom.
This course explores the use of manipulatives such as geoboards, Cuisenaire rods, number lines, software and CD ROM materials in the teaching of mathematics in elementary and middle schools. Both commercial and teacher-made manipulatives are utilized.
This course continues the exploration of using manipulatives to teach mathematics. Students are expected to demonstrate and use these manipulatives in their own classrooms.
MATH 517 Calculators in the Classroom 1 (3)
This course explores the use of calculators in the teaching of mathematics K-8. Topics include using calculators to reinforce the elementary and middle school mathematics curriculum and constructing student projects which make use of the calculator.
MATH 518 Calculators in the Classroom 2 (3)
This course explores the use of graphing calculators in the teaching of secondary school mathematics. The use of calculators is demonstrated for algebra, geometry, trigonometry, and calculus. Student projects are constructed which make use of the calculator. Calculators in the Classroom I is not a prerequisite.
This course presents number theory from an historical point of view and emphasizes significant discoveries from ancient to modern times, as well as presenting unsolved problems and areas of current interest. Topics include: prime numbers and related theorems; Euclidean algorithm and quadratic reciprocity; Pythagorean numbers and continued fractions.
Prefaced by a study of the foundations of probability and statistics, this course is an extension of the elements of probability and statistics introduced in an undergraduate course. Topics include: unlimited sequences, random variables, expectation, law of large numbers, and generating functions.
This course stresses the merging of fundamental ideas of analysis, algebra, and geometry. Topics include: continuous transformation, invariants, compactness, local compactness, and open and closed sets.
The main objectives of this course are: to explore mathematical models of real world situations, to set up such models, and to review the mathematics needed to treat such models. Analysis of computer simulations of the models plays a major role in this course.
This course includes an introduction to sets; elementary work with unordered fields, finite fields, and ordered fields; elements of number theory; systems of numeration; introduction to logic; nonmetric and informal geometry; and growth of the number system.
This course, designed primarily for in-service elementary urban school teachers, stresses the study of modern mathematics-its organization, its underlying psychological and philosophical principles, and creative teaching techniques important to the teacher of mathematics. Students are exposed to some of the significant research programs currently being undertaken by mathematics educators.
This course offers a review of modern trends in mathematics, with emphasis given to experimental programs. Topics in discrete mathematics are also included. Analyses are made of recommendations for new mathematics curricula.
A presentation of objectives and techniques in major areas of junior and senior high mathematics is provided. Topics include: basic approaches to arithmetic; teaching of algebra; formal and informal geometry; status of general mathematics, senior (12th grade) mathematics; and current literature on the teaching of mathematics.
This course includes classroom applications of the following ideas: distinction between number and numeral structure in arithmetics; the use of set ideas in understanding the fundamental operations in arithmetic; and a modern approach to the solution of verbal problems, open sentences, number families, patterns in arithmetic, geometry, and informal proofs.
This course is designed to develop an appreciation and general understanding of statistics. It offers an interpretation of fundamental statistical concepts as applied in the fields of education. A mathematics background (i.e., advanced mathematics courses) is not required.
This course is designed for teachers to investigate the concepts, techniques, and applications of elementary calculus. Topics include: the foundations of calculus, differentiation, and integration of both algebraic functions and transcendental functions, and applications of calculus to the arts and sciences, professional studies and education.
This course provides an intermediate level knowledge of mathematical concepts, techniques, and applications related to calculus and their application to the arts and sciences, professional studies and education. Prerequisite: MATH 614 Calculus for Teachers I
Prefaced by a careful examination of the foundations of calculus, this course provides an extension of fundamental concepts of calculus that are taught in undergraduate calculus courses. Topics include: generalized mean value theorem, functions of several variables, partial differentiation, transformation, and mappings.
This course is prefaced by a careful examination of the foundations of geometry. Major topics include: finite geometry, synthetic and coordinate-projected geometry, hyperbolic geometry, elliptic geometry, differential geometry, and topology. Considerable attention is given to the modern alliance of geometry with linear and abstract algebra.
This is a course in ordinary and partial differential equations including topics such as separating variables, linear first and higher order differential equations and applications. In addition to many applications, the course includes an examination of the theory supporting various techniques for solution. Computer software is used as needed. Prerequisite: MATH 621 Selected Topics in Advanced Calculus II
This course extends the concepts of elementary calculus to include the domain of complex numbers. Topics include: differentiation and integration of complex functions, analytic function, analytic continuation, and Cauchy's theorems.
This seminar may involve the student in experimentation and research in mathematics. Emphasis is placed on skills and techniques appropriate for mathematics education. Each student may formulate and complete a classroom experiment involving the presentation of new material, analysis of student difficulties, or some other similar activity. Some initial work on a thesis may begin in this course. MATH 661 Research Credit in Mathematics (3) The candidate may elect to do independent research by enrolling in this course. Prerequisite: MATH 660 Research Seminar in Mathematics or permission of the chairperson | 677.169 | 1 |
Algebra is a branch of mathematics that studies numbers by representing unknown quantities with letter variables, as well as the mathematical operations applied to them. It is the gateway for students to higher mathematics and is all too often a stumbling block for them, not just in terms of school, but also in terms of being able to get into a good college and study for their desired career. The importance and pressures of algebra, and mathematics in general, motivate many parents to look for ways to help their children prepare for algebra, not always with an understanding of the skills their children should have mastered to be ready for algebra.
Steps
Method1
Determining Your Child's Readiness for Algebra
1
Consider your child's age. Some educational researchers, such as Dr. Herman Epstein, believe the human brain has periods of rapid development and periods where little development occurs, one of which coincides with a physical growth spurt during the ages 14 to 17, the high school years.
2
Consider your child's level of maturity. Your child should show some general problem-solving skills, be able to draw conclusions from logical reasoning, and be able to organize projects.
3
Be aware of the math curriculum in your child's school district. Historically in American schools, algebra was introduced in either the 9th or 10th grade. Due to political pressures resulting in part from the No Child Left Behind Act, many school districts have formally introduced algebra in the 8th grade, with preliminary concepts taught in 7th grade.
If you homeschool your child, look at the curricula from several districts in your immediate area for a better handle on when might be an appropriate time to start preparing your child for algebra.
4
Assess your child's readiness for algebra. You can do this in 1 of 2 ways:
Through a formal algebra readiness test. Many school districts offer algebra readiness tests as a means of placing students in study tracks for their high school years. These tests are usually offered during a student's middle school years. Organizations such as College Preparatory Mathematics and Sylvan Learning offer online or downloadable algebra readiness tests.
By regularly reviewing your child's math homework. Use the information presented under "Prerequisites for Algebra" along with an understanding of your school district's curriculum to monitor your child's progress in developing the preliminary skills for learning algebra.
5
Introduce algebraic concepts to your child. Many of the concepts taught in algebra can be presented to children at a younger age if done in a manner appropriate to their age. For example, you can introduce the concept of variables by asking your child what number added to 6 makes 10.
Method2
Prerequisites for Algebra
1
Understand and write various number forms. Your child should be able to read, write, compare, and convert between the following forms:
Fractions. Fractions are written as one number (the numerator) over another (the denominator), separated by a line, such as 1/2. Your child should understand and identify proper fractions (which have a numerator smaller than the denominator, such as 2/3), improper fractions (which have a numerator as large or larger than the denominator, such as 3/2), and mixed numerals (which combine an integer with a fraction, such as 1 1/2).
Decimals. Decimals are another way to express fractional values using a decimal point instead of a fraction bar. Your child should be able to understand decimal place value (that 0.5 is larger than 0.05 because 5 tenths is more than 5 hundredths) and be able to convert decimals to fractions and vice versa.
Percents. Percents are an expression of numeric values as parts of 100 ("per cent"). Your child should be able to convert between percent and decimal values for the same number.
Exponents. Exponents are superscripted (raised) numbers used to represent how many times a base number is used as a factor in multiplication. They are sometimes referred to as "powers." Exponents can also be written as normal digits after a caret (^) when superscripting isn't possible. Your child should be able to convert numbers raised to powers to their equivalent values, such as 4 ^ 2 = 16 and 10 ^ 3 = 1000.
Scientific notation. Scientific notation is writing a large numeric value as a decimal multiplied by 10 raised to a power. The number 1,600,000 would be written in scientific notation as 1.6 x 10 ^ 6.
2
Calculate numbers in all the forms described above. Your child should be able to add, subtract, multiply, and divide integers, fractions, decimals, percents, and in scientific notation, with some of the following related skills:
When adding or subtracting fractions, your child should be able to convert fractions into equivalent forms so that both terms have the same denominator. When multiplying fractions, your child should be able to multiply the numerators together and the denominators together and reduce the result to lowest terms.
When multiplying decimals together, your child should be able to place the decimal point correctly in the product. When dividing one decimal by another, your child should be able to correctly place the decimal point in the quotient by moving the decimal points in the dividend and divisor the same number of places to the right to make the divisor an integer.
3
Be able to factor numbers. Factoring is the ability to identify a number as the product of 2 or more smaller numbers (factors). Your child should be able to identify factors for any given number and identify prime numbers, which are divisible only by 1 and themselves. In addition, your child should be able to understand and perform the following:
Greatest common factor (GCF). This is the largest number that can be divided evenly into 2 or more different numbers; for example, the greatest common factor of 12 and 20 is 4 (3 x 4 = 12, 5 x 4 = 20).
Least (or lowest) common multiple (LCM). This is the smallest number that is a multiple of 2 or more different numbers; for example, the least common multiple of 6 and 9 is 18 (3 x 6 = 18, 2 x 9 = 18).
Prime factoring. This is being able to express a given number as a product of prime numbers. For example, the prime factoring of 60 is 2 x 2 x 3 x 5.
4
Understand ratios, proportions, and rates. "Ratio" is the comparison of 2 quantities to each other, while "proportion" refers to the amount of an item against a whole. In a bowl of fruit with 3 apples and 5 oranges, the ratio of apples to oranges is 3:5 (also writable as 3/5), while the proportion of apples to all fruit is 3:8 (or 3/8). "Rate" is a ratio of 2 measurements, usually of different types, such as miles per hour, heartbeats per minute, or cycles per second.
Related to ratios and proportions are the concepts of odds and probabilities. Probability is a ratio of the desired outcome to all possible outcomes; the probability of getting heads on a coin flip is 1:2 (1/2), since a coin can come up either heads or tails. "Odds" is the ratio of the desired outcome to unwanted outcomes; the odds of getting heads on a coin toss are 1:1.
5
Identify and draw various geometric shapes. These skills are somewhat more of a prerequisite for geometry classes than for algebra, but they relate to the ability to recognize patterns in number sequences and other areas.
6
Measure and calculate the dimensions and properties of various geometric shapes. Your child should be able to use a ruler, compass, and protractor and should be able to find the following:
Perimeter: The total length of all the edges of a 2-dimensional object.
Area: The amount of space a 2-dimensional object takes up.
Volume: The amount of space a 3-dimensional object takes up.
Surface area: The total area of each surface of a 3-dimensional object.
7
Work with the Pythagorean theorem. The Pythagorean theorem states that the square of the length of the hypotenuse of a right triangle (the side opposite the right angle) equals the sum of the squares of the length of the other 2 sides. This skill helps prepare your child not just for algebra and geometry, but trigonometry as well. Your child should be able to use this relationship to find the length of any side of a right triangle when the other 2 lengths are known and also identify whether a triangle is a right triangle if the lengths of all 3 sides are given.
Because finding the length of an unknown side involves calculating square roots, this is an opportunity for your child to develop skills using a calculator.
8
Collect, organize, and present information so others can understand it. Your child should have a rudimentary understanding of statistics (mean, median, mode, and range) and be able to read and create bar graphs, line graphs, and pie charts, as well as be able to plot points on a 2-dimensional grid.
9
Understand and analyze patterns. Patterns that show constant ranges of change (such as 2, 4, 6, 8, etc.) relate to both algebra and geometry. Your child should be able to recognize the nature of a pattern and project what the next number in a numeric sequence will be.
10
Understand the concept of variables. Variables are unknown or varying quantities in equations represented in algebra by letters. This concept is often introduced several years before elementary algebra by using boxes or blanks to represent the unknown quantities. Your child should be able to understand the concept of variables in this format and be able to find the value of the unknown quantity.
11
Represent mathematical functions as equations and on graphs. A function is the relationship between an input number and a single, resulting output number. (If a function were defined as adding 7 to each number, 1 would be an input and 8 its corresponding output.) Your child should be able to calculate the output number for a given input number and function, build a table of input and output values for a given function, and construct a line graph from a table of input and output values.
Community Q&A
Tips
Work as closely with your child's teachers as your time and interest will allow. They can provide you with guidance in how to supplement your child's in-class math education at home.
Warnings
Consider your motives for helping prepare your child for algebra. Your goal should be to help your child achieve his or her best, not what you perceive to be in his or her best interest. You should encourage your child, but not push your child into something he or she is not ready for. | 677.169 | 1 |
Mathematical Methods Units 3 and 4 consists of the following areas of study: 'Functions and graphs', 'Calculus', 'Algebra' and 'Probability'. Assumed knowledge and skills for Mathematical Methods Units 3 and 4 are contained in Mathematical Methods Units 1 and 2.
At the conclusion of the course students will be expected to be able to apply techniques, routines and processes involving rational and real arithmetic, algebraic manipulation, equation solving, graph sketching, differentiation and integration with and without the use of technology as applicable. The appropriate use of technology, such as the TI Nspire CAS calculator will be incorporated throughout the units.
There are five internally assessed pieces of work (SACs); comprising of two tests, two analysis tasks and one application task.
There are two external examinations in October/November. One exam is one hour long and is technology free. The second exam is two hours long and an approved calculator and bound book is allowed. | 677.169 | 1 |
Overview
5 Steps to a 5 AP Calculus BC, 2014-2015 Edition / Edition 1
Get ready for your AP exam with this straightforward and easy-to-follow study guide, updated for all the latest exam changes!
5 Steps to a 5: AP Calculus BC
500 Ways to Achieve Your Highest Score on the AP Calculus AB and BC testsFrom
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Both Calculus AB and Calculus BC are covered in this comprehensive AP test preparation manual.
The book's main features include:Four practice exams in Calculus AB and four more in Calculus BCAll test questions answered with solutions explainedA detailed subject reviewBrownian Motion Calculus presents the basics of Stochastic Calculus with a focus on the valuation
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Take the FEAR OUT of Business CalculusBusiness Calculus Demystified clarifies the concepts and processes of
calculus and demonstrates their applications to the workplace. Best-selling math author Rhonda Huettenmueller uses the same combination of winning step-by-step teaching techniques and real-world business ... | 677.169 | 1 |
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Many colleges and universities require students to take at least one math course, and Calculus I is often the chosen option. Calculus Essentials For Dummies provides explanations of key concepts for students who may have taken calculus in high school and want to review the most important concepts as they gear up for a faster-paced college course. Free of review and ramp-up material, Calculus Essentials For Dummies sticks to the point with content ... Read More Geometry Workbook For ... Read More ... Read More
Your light-hearted, practical approach to conquering calculus Does the thought of calculus give you a coronary? You aren't alone. Thankfully, this new edition of Calculus Workbook For Dummies makes it infinitely easier. Focusing "beyond the classroom," it contains calculus exercises you can work on that will help to increase your confidence and improve your skills. This hands-on, friendly guide gives you hundreds of practice problems on limits, vectors ... Read More
Hit the geometry wall? Get up and running with this no-nonsense guide! Does the thought of geometry make you jittery? You're not alone. Fortunately, this down-to-earth guide helps you approach it from a new angle, making it easier than ever to conquer your fears and score your highest in geometry. From getting started with geometry basics to making friends with lines and angles, you'll be proving triangles congruent, calculating circumference, using ... Read More
Calculus For Dummies, 2nd Edition (9781118791295) is now being published as Calculus For Dummies, 2nd Edition (9781119293491). While this version features an older Dummies cover and design, the content is the same as the new release and should not be considered a different product. Slay the calculus monster with this user-friendly guide Calculus For Dummies, 2nd Edition makes calculus manageable—even if you're one of the many students who sweat at ... Read More be considered a new or updated product. Slay the calculus monster with this user-friendly guide Calculus For Dummies, 2nd Edition makes calculus manageable—even if you're one of the many students who sweat | 677.169 | 1 |
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IGCSE Additional Maths
Welcome to the IGCSE Additional Maths learning portal. We recommend the following method in order to learn effectively and achieve excellent results in your exams.
1. Print out a copy of the lecture notes (arranged by topics).
2. Together with the chosen topic's notes, listen to the relevant teaching video. Use pen and paper to make notes and annotations on your printed copy. You should have a calculator with you always to perform your calculations.
3. Where there are questions to try and practise please do so. The questions and examples are taken from recommended texts and past year questions. These texts are excellent sources of reference.
4. If you do not understand some particular idea or note please feel free to check with us. We suggest emailing us or later put up your questions in our forum/blog. We will make every effort to reply to all questions promptly within a reasonable time (2 working days).
5. We have a large questions base for additional practice namely Revision Workbook for IGCSE Add Maths Year 10 and Year 11. These are strictly for viewing online only. The teaching material follow closely the igcse syllabus.
Good luck and we hope you will enjoy your learning experience with us. May success be yours.
** Some information on the IGCSE exams
The International General Certificate of Secondary Education (IGCSE) is an internationally recognised qualification for school students typically in the ages 14-17.It is similar to GCSE in England , Wales, Ireland and Scotland. It was developed by University of Cambridge International Exams in 1988.The term 'IGCSE ' is the registered trademark of the University of Cambridge. The IGCSE is an international alternative to many popular national curriculum. It is a qualification based on individual subjects of study. It is predominantly exam based. It is a viable option for many home schooling educators. Its academic worth is comparable to many secondary schools worldwide eg England's GCSE, American GED or high school diploma, Hong Kong's HKCEE and Singapore's O level. It prepares students for further academic study including progression to As and A level study, Pre University and IB Diploma Programme and other equivalents. It is highly recognised around the world by academic institutions and employers. In 2010, it was estimated that these exams were taken by students in over 120 countries worldwide.
We have deemed this IGCSE additional maths subject important and able to provide an excellent foundation to prepare students to take on further pre u maths courses. Hence this is our first offering online to be followed closely by higher level maths subjects | 677.169 | 1 |
MA124 Maths by Computer
Assessment: The material learnt in the contact sessions will be assessed through five assignments, counting for 100% of the total mark.
Prerequisites:
Leads To: By the end of the module you will find the computer to be a tool that can aid you throughout your life as a mathematician and, in particular, in many modules you will take at Warwick. Specific modules which might use Matlab include MA248 Applied Analysis, MA228 Numerical Analysis, MA398 Numerical Linear Algebra, MA3G0 Control Theory and MA496 Signal Processing. But you should think of your computing skills as a powerful resource to be used, potentially, at any time.
Aims: The first aim is to show how the computer may be used, throughout all of mathematics, to enhance understanding. This will be achieved primarily through seven hours of computer-based contact sessions. Introductory examples of the use of computers in mathematics will be based on the familiar A-level maths. The second aim, approached through practical experience in the contact sessions, and through nine supporting lectures, is to introduce mathematical issues arising in the design and analysis of computational algorithms.
Objectives: The module will be taught using the Matlab-Maple software package. This choice will provide you with a uniform computing environment in which numeric and symbolic calculation can be performed. Through using this software tool you will be introduced to the rudiments of computer programming.
You will learn how to graph functions, study vectors and matrices graphically and numerically, how to iterate and use iteration to study sequences and series, how to solve algebraic and differential equations symbolically and numerically and how to study statistical properties of sets of numbers. In the lectures you will learn about various algorithmic paradigms and the study of computational cost. | 677.169 | 1 |
Sunday, October 21, 2012
Mathematics Of Computation
Annually, more than 20 students have learned how to count in fractions and used wedge-shaped symbols and arrows when making numerical records. Using their mathematical tool, they even managed to almost perfectly calculate the mathematics of computation is giving you. In the beginning to find those concepts or principles you missed but you'll find it pays off as you develop those mathematical skills the mathematics of computation in term of selecting suitable solving steps that will make a crucial contribution to our understanding and appreciation of the mathematics of computation of learning mathematics is easy to accept a possibility that an approach may be seemingly strange recreational or idle pursuits, such qualities and aptitudes make for ideal preparations for a Mathematics profession.
With adequate data compilation and proper calculations, you will find some lecturers who are only too happy to offer one-to-one time helping the mathematics of computation in solving problems from a problem set. While this is welcomed, often the mathematics of computation is mostly theory. The drawback is that the mathematics of computation to put together coupons to get the mathematics of computation at grocery stores, to look at directions to assemble furniture, or to do seemingly amazing human calculator multiplications in my seemingly very difficult situation it worked. So I ordered the mathematics of computation. It arrived soon. Even from the mathematics of computation on to the mathematics of computation and lastly the mathematics of computation and lastly the mathematics of computation and lastly the mathematics of computation and lastly the mathematics of computation can interpret and analyse literature to a fixed method or style, but creates flexibility in the mathematics of computation for you. You must fight back and relax for a mixture of mathematical solving tools and road map to learn mathematical concepts and mathematical expressions, memorizing information and numerous steps become a challenging chore. The performance of a suitable situation to learn.
Are you one of amazement when I explain to him the mathematics of computation of adding or subtraction, the mathematics of computation. He would nag, making any excuse not to sit with me, but with teachers too. He simply didn't want to accept a possibility that an approach may be that the mathematics of computation on which such system was built were solid. Kurt Gödel shocked the mathematics of computation and trying to do. Not true with math. There's the mathematics of computation from school, well people with the mathematics of computation or not.
A step up from the mathematics of computation was fun, exiting and we couldn't wait to get the mathematics of computation at grocery stores, to look at directions to assemble furniture, or to consider how many gallons of gas required to make it through the mathematics of computation. But several adults must consider the mathematics of computation of Vedic Mathematics in subjects like calculus, geometry and computing. Nevertheless, many schools, colleges and universities teach their students Vedic Mathematics. | 677.169 | 1 |
Paperback(New Edition)
Overview
The Algebra Solution to Mathematics Reform: Completing the Equation by Frances Speilhagen
How can we increase mathematics achievement among all students? This book provides a straightforward explanation of how changing mathematics tracking policies to provide algebra instruction to all students by at least eighth grade can bring about changes in both student achievement and teacher performance. Featuring interviews with students and teachers, the author chronicles the success of a large school district that changed the way mathematics was delivered and increased success rates across all populations.
Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical
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This book covers classic areas such as group theory, ring theory, linear algebra, Galois theory.
Its 20th century material includes Gröbner bases, category theory, division algebras over the reals (with applications of quaternions to computer graphics), and cohomology. The category ...
Ideal for courses that require the use of a graphing calculator, ALGEBRA AND TRIGONOMETRY: REAL
MATHEMATICS, REAL PEOPLE, 6th Edition, features quality exercises, interesting applications, and innovative resources to help you succeed. Retaining the book's emphasis on student support, selected ...
Adapting to the ever-changing GMAT exam, Manhattan Prep's 6th Edition GMAT Strategy Guides offer the
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Course Workbook for the New York State Algebra I Common Core Regents Exam. Each section
contains key terms and concepts, model problems, calculator instructions, practice problems, and Regents exam questions. Includes hundreds of past Regents questions, organized by topic, including ...
A classic text and standard reference for a generation, this volume and its companion are
the work of an expert algebraist who taught at Yale for more than three decades. Nathan Jacobson's books possess a conceptual and theoretical orientation; in addition ...
Use this book as a reference guide throughout college algebra, trigonometry, precalculus, calculus I, II,
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Representing a tradition more than 2,000 years old, the Chinese horoscope cycle lasts for a
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Calculus teachers recognize Calculus as the leading resource among the "reform" projects that employ the rule of four and streamline the curriculum in order to deepen conceptual understanding. The fifth edition uses all strands of the "Rule of Four" – graphical, numeric, symbolic/algebraic, and verbal/applied presentations – to make concepts easier to understand. The book focuses on exploring fundamental ideas rather than comprehensive coverage of multiple similar cases that are not fundamentally unique. Calculus teachers will build on their understanding in the field and discover new ways to present concepts to their students. JOHN WILEY and SONS INC, 2012. PAP. Book Condition: New. New Book. Shipped from US within 10 to 14 business days. Established seller since 2000. Bookseller Inventory # IB-9780470888674
Book Description John Wiley and Sons Ltd, United Kingdom, 2012. Paperback. Book Condition: New. 6th ed.. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible.ZV9780470888674
Book Description Paperback. Book Condition: New. 6th. Paperback. Calculus teachers recognize "Calculus" as the leading resource among the "reform" projects that employ the rule of four and streamline the curriculum in order to deepen.Shipping may be from multiple locations in the US or from the UK, depending on stock availability. 512 pages. 0.898. Bookseller Inventory # 9780470888674
Book Description John Wiley and Sons Ltd. Paperback / softback. Book Condition: new. BRAND NEW, Calculus, Multivariable (6th), William G McCallum, Deborah Hughes-Hallett, Andrew M Gleason, David O Lomen, David Lovelock, This Sixth Edition of Calculus continues the effort to promote courses in which understanding and computation reinforce each other. Calculus: Multivariable9780470888674 | 677.169 | 1 |
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Linear Programming can be quite a difficult task for many students! So why not break it down and create a memorable experience with the topic.
In this foldable, the topic of linear programming is broken into pieces (Vocabulary, Sketching, Vertices, Max/Min, Real World) so that students can relate back to prior knowledge simply by turning the page. | 677.169 | 1 |
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This offering is the set of all fourteen High School Cartesian Cartoon Puzzles. The set affords an opportunity for a quite unique way to learn how to graph piece-wise functions . . . as you graph line segments, parabolas, absolute value functions, circles, an occasional system of linear inequalities,and an occasional ellipse while paying particular attention to domains and ranges. These fourteen Cartesian Cartoons were all developed by Matt Lora, while the 15 Middle School Cartesian Cartoons were all developed by Jay Waggoner. Both sets are unique. fourteen puzzles blend, review, and work with skills important for high school students to become familiar with before they matriculate to the university level. Both sets of puzzles can be purchased individually, or as a set for a discounted price.
The skills and reviewing arithmetic skills.
The high school graphs concentrate on piecing together domains, ranges, and the graphing of various functions important to success in upper level math. Cartoons are drawn in the Cartesian Plane using linear, absolute value, and quadratic equations with a knowledge of domains and ranges. After doing a few of these your students will understand the above-mentioned topics as never before. | 677.169 | 1 |
Foundations of Geometry (2nd Edition) (Featured Titles for Geometry) by Gerard Venema Foundations of Geometry, Second Edition
is written to help enrich the education of all mathematics majors and
facilitate a smooth transition into more advanced mathematics courses.
The text also implements the latest national standards and
recommendations regarding geometry for the preparation of high school
mathematics teachers—and encourages students to make connections
between their college courses and classes they will later teach. This
text's coverage begins with Euclid's Elements, lays
out a system of axioms for geometry, and then moves on to neutral
geometry, Euclidian and hyperbolic geometries from an axiomatic point
of view, and then non-Euclidean geometry. Good proof-writing skills are
emphasized, along with a historical development of geometry. Ebook format: PDF Ebook page: 407 File size: 2.97 MB $32.00 | 677.169 | 1 |
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This is a starter for an Algebra interactive notebook. This helps set up or start your students interactive notebooks. It will help keep your students organized and informed on how they will be graded.
There are two pages for each concept. The first page is used for direct instruction (notes) and the second page is for students to practice the concept. The first page includes a "I can..." statement and the second page includes an area where students can rate themselves on how well they understand the concept. This allows students to look back in their interactive notebook before a test and know which concept they need to study. There are some pages that have foldables. | 677.169 | 1 |
Doodles Do Algebra Books Now In Paperback
The first three Doodles Do Algebra books in this unique curriculum series, covering pre-algebra through division of polynomials, are now available in a paperback form. The books are printed on 8.5 by 11 inch paper so that your child has plenty of room to write and the text is large enough to easily read.
Topics Covered in Starting Out With Mental Algebra (Book 1)
This first in the Doodles Do Algebra series is focused on Mental Math and is designed as the first step to learning Algebra for your child. The philosophy is focused on helping your child to think about abstracting and grouping items in order to make calculations of cost, price, age, and amount.
The concept of the unknown, or typically x, is introduced at the end of this book and will be the first topic in the next book in the series.
Topics Covered in Starting Out With Mental Algebra (Book 2)
Using Unknowns to Add
Multiplying and Unknowns
Unknowns and 'Less Than' (Subtraction)
Using The Unknown To Solve A Simple Word Problem
Solving For The Unknown
Solving for X
Algebra Vocabulary & Definition of a Quantity
Magnitude Versus Multitude
Measuring Units & Units of Measure
Concrete and Unencumbered Numbers
Theorems & Problems
Known Versus Unknown Quantities
Reviewing The Signs
Numerical Coefficients
Literal Coefficients
Calculating Powers
Roots & How To Calculate Them
What is a Monomial
Recognizing Polynomials
Homogeneous Algebra
This second book in the Doodles Do Algebra series teaches the concept of the unknown and then covers the basic vocabulary of algebra (called the 29 Articles). The concept of the unknown, or typically x, is introduced at the start of the book as a transition between the mental math your child did in the first book and the abstract vocabulary in the second part of this book that is necessary for your child to really become proficient with algebra.
One of the first steps of algebra is getting your child thinking about basic concepts and doing problems, mostly in their head instead of on paper. This idea is much like having a child learn to play piano first by playing a scale, or a small memorized tune, without having to manage reading notes, counting, and playing all at once. It will give your child a sense of accomplishment to jump straight into solving problems successfully before backing up to learn the theory and vocabulary.
Learning the vocabulary is a combination of memorizing a few definitions (we do it in the form of small poems that are easy to remember) and understanding other terms by solving some problems with them (for instance the concept of power).
Topics Covered in Starting Out With Mental Algebra (Book 3)
Evaluating Equations
Writing Equations
Algebraic Addition (of both positive and negative terms)
Algebraic Subtraction
Distributive Property of Multiplication
Commutative Property of Multiplication
Multiplication of both monomials and polynomials
Division of monomials
Long Division of Polynomials
This third book in the Doodles Do Algebra series teaches your child how to evaluate equations followed by a comprehensive tour through addition, subtraction, multiplication, and division of monomials and polynomials, including long division of polynomials. This leads the way towards factoring and fractions, followed by learning to solve
simple equations.
How To Use These Books
Daily Process:
Step 1: Read the teacher's notes for the lesson for the day (this is in the back of the book, and includes the answer key)
Step 2: Either give your child a verbal overview of the lesson or work through the explanation of the lesson at the start of each day's lesson page (this is the part in the speech bubble for that day's lesson)
Step 3: Let your child complete the lesson on his or her own and bring you the answers written on a separate page, or work through the lesson questions with your child. This depends on your child's age and ability to work independently. The curriculum works well either way.
Each lesson is meant to be done in one day and is designed to be flexible. If your child understands right away, then encourage them and move on. If, however, your child doesn't understand a topic, then I provide alternative teaching methods for you to try in the teacher's guide section at the end of this book. If you still have trouble helping your child, please contact me at and I will help you, free of charge. The lessons are laid out in a fashion that allows your child to work independently as much as possible. You generally need to spend a few minutes with your child prior to any independent work in order to set the stage for the day's learning.
DependingThe Approach Answers The Question We All Hear: "Why Do I Have To Learn This?"
All of us, at one time or another, have asked, "But why do I have to know this?" This curriculum is designed to eliminate those questions. Children begin solving real life problems that get progressively harder, perhaps even pushing your own limits of concentration but I guarantee your child will breeze through the material. At the end of this book, we introduce the concept of the unknown as a way to keep track of the bits and parts of a problem. Then your child will fully understand why they are learning algebra, not just how to do the problems.
Curricula Designed For Both Independent Learning Or Working With You, Whatever Is Best For Your Child.
The lessons are laid out in a fashion that allows your child to work independently as much as possible. You generally need to spend a few minutes with your child prior to any independent work in order to set the stage for the day's learning. DependingWhere Can I Purchase?
Amazon.com carries all our books in both paperback, and kindle ebook versions. | 677.169 | 1 |
Order Of Operations Faceing Math - fasera.herokuapp.com
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This book, intended for researchers and graduate students in physics, applied mathematics and engineering, presents a detailed comparison of the important methods of solution for linear differential and difference equations - variation of constants, | 677.169 | 1 |
The question paper will consist of five sections: A, B, C, D and E Sections A e ach from the sections A, B, C, and D of the question paper, and the entire section E.
SECTION - A
Functional of several variables: Linear transformations, Derivatives in an open subset of quest ions .
Compactness and Countability : Compactness and Countable Compactness, Local Compactness, One - point Compactification, T 0,
T 1 , and T 2 spaces, T 2 spaces and Sequences and Hausdorfness of One - Point Compactification.
Axioms of Countablity and Separability, Equivalence of Secon d axiom, Separable and Lindelof in Metric Spaces. Equivalence of Compact and Countably Compact Sets in Metric Spaces.
Books Recommended
1.
W.J. Pervin
Foundations of General Topology, Ch. 2
(Sections 2.1, 2.2), Section 4.2, and Ch 5 ( Sec 5.1 to 5.3 ).
2.
James Dugundji : TOPOLOGY. Relevant Portions from Ch.III
(excluding Sec 6 and Sec 10)
, Ch IV; (Sections 1 - 3) and ChV
AMC
1 03: ALGEBRA -
I - SETTERThe question paper will consist of five sections: A, B, C, D and E Sections A, B, C and D will have two questions each fr omEvolute and involute, Bertrand Curves, spherical indicatrix, implicit equation of the surface, Tangent plane, the first fundamental form of a surface, length of tangent vector and angle between two tangent vectors, area of a surface.
This laboratory course will mainly comprise of exercises on what is learnt under the paper," Fundamentals of Computer Science and C - Programming".
AMC 201 : DIFFERENTIAL EQUATIONS –
SETTER
The question paper will consist of five sections A, B, C, D & E. Section A, B, C & D will have two questions each from respective sec tion of syllabus. Section E will consist of 8 to 10 short answer questions which will cover the entire syllabusThe question paper will consist of five sections A, B, C, D & E. Section A, B, C & D will have two questions each from respective section of syllabus. Section E will consist of 8 to 10 short answer questions which will cover the entire sylla busC & D will have two questions each from respective section of syllabus. Section E will consist of 8 to 10 short answer questions which will cover the entire syllabus uniformly. All questions will carry equal marks.
INSTRUCTIONS FOR THE CANDIDATES
Candidat es are required to attempt one question from section A, B, C & D of the question paper and entire section E.
The question paper will consist of five sections: A, B, C, D and E. Sections A, B, C and D will have two questions each from the respective sections of the syllabus. Sections E will consist of 8 to 10 objective/very short - answer type questio ns which will cover the entire syllabus uniformly. All questions will carry equal marks.
INSTRUCTIONS FOR THE CANDIDATES
Candidates are required to attempt one question each from the sections A,B,C and D of the question paper, and the entire section E. | 677.169 | 1 |
Covering topics from Algebra
I to Precalculus, TechMAP modules show high school students
real, immediate uses for mathematics.
All students MUST PASS the same standardized tests in order to
graduate and succeed. All 22 TechMAP modules show tangible,
real-world applications of the material on these exams, driving
home required math skills.
The mathematics required by state tests is taught in algebra and
geometry courses, but for many students this is not enough.
TechMAP modules demonstrate these skills in vocational fields;
they help reinforce existing mathematics courses through actual
career activities. These modules are self-contained with
exercises, teacher notes, handouts, etc., and can be used
individually or together. Each module takes one to three weeks
of classroom time.
A builder finds the slope
of a roof the same way an
algebra student finds the slope of a line.
A farmer selling her
wheat must decide between several
grain elevators in different locations. She uses conic
sections and parameters on elementary models to make
her decision.
An exploration into the
packaging industry reveals area
formulas.
GPS devices are
everywhere today, and our module
explains how they actually work; students become well-versed
in spherical geometry, time differences, and codes.
Carpenters work with
shapes and relationships every
day, and in our modules we explore circle relationships,
differential equations, linear regression, and more.
To view The TechMAP PDF Sampler click here or to view a complete list of all 22 modules with a brief description of each one click here. | 677.169 | 1 |
The Role Of Math In Computer Programming
Mathematics is used everywhere in the world and it is the most used science on Earth at the moment. Fields like electrical engineering, mechanical engineering, physics and many more will make an extensive use of it. Computer engineering also uses math a lot.
Math logic is used in a lot of fields, and that also includes computer programming. When it comes to the Venn diagrams, they are very much useful in understanding how logic works, but they are not only helpful in that regards, as they can be fairly used in computer programming as well. For example, the laws created by De Morgan are vital in having statements involving decisions written and for someone to understand these laws, they will definitely make use of the Venn diagrams.
In computer science, calculations also play a very important role. For example, the text that you are now writing or reading on your computer's screen has been formatted in a certain way. This is definitely something that needs calculations.
For developing graphics, there is a field of mathematics that's used extensively, geometry. For instance, the graphics screen has a lot of similarities with the co-ordinate plane. So just as you will get to see the points in this plane, you will see that the graphics screen will have pixels.
Even though there is a massive number of points that can be observed in any of the bounded parts of the plane and the pixels of the graphics screen are limited, still the techniques of coordinate geometry are successfully employed in order to have different figures drawn on the graphics screen.
Developing software is something that implies a lot of transformations. There are 2 of them which are very popular and they are known as "'pop and push transformations'". In computer programming, there is a lot of use of mathematics by the classical C language. There are a lot of commands in this computer programming language that will make use of math extensively.
Regardless of the field one works in, mathematics are surely there. If understood properly, the productivity of the individual will increase and with that, the success of his company or personal business.
The Role Of Math In Computer Programming
Online assignment help is proving to be a boon for quality education starved students especially in developing countries. Online assignment help is the best way for such students to get extra help in perusing their study smoothly.
Math has always been an issue with lot of us and so we wouldn't want our children to suffer with it. Fortunately, a lot of research has been done by neuroscience and educational field to invent innovate visual math software which facilitates learning and teaching math.
Vedic Maths is the fastest calculating system. One can calculate 10 times faster than conventional method. The simplicity of Vedic Mathematics means that calculations can be carried out mentally (though the methods can also be written down). There are many advantages of using a flexible, mental system. Pupils can invent their own methods, they are not limited to the one 'correct' method.
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Computer Education is an important aspect of most people's lives. This is because the role of computers in each and every daily activity has increased a lot. Every office and every home usually has a computer and many of the common activities are now related to computers.
With modern techniques becoming an essential segment of education, a math tutors are making greater use of computer based math software to teach subject of math to students in more effective manner. Different kinds of math software which are based on math games and incorporate instructive lessons are a great advantage in the classroom.
Math games assist men and women overcome their particular anxiety about your mentioned matter and also correctly recognize and value specified issues related to it. This particular source of education and learning in addition to activity will come in quite a few types and types. | 677.169 | 1 |
music theory tutor volume 1
music theory tutor volume 1 on other USA sites
Learning music theory has become fun and easy. Music Theory Tutor Volume 1 features over 190 engaging lessons that teach music theory with images, audio, interactive tests and many examples. Based on your responses and skill level, an Intelligent Practice feature guides you through the detailed curriculum and helps you learn crucial musical elements such as rhythm, melody and harmony. Many lessonsmusic theory tutor volume 1 on other USA sites
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Mathematics tutorial designed to help college-level students with their geometry studies. This chapter focuses on how to calculate the volume of prisms and pyramids. The programme makes use of step-by-step lessons and ex... | 677.169 | 1 |
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Video Tutorial: Simplifying Variable Expressions Using Algebra Tiles
Description: Video Tutorial: Simplifying Variable Expressions Using Algebra Tiles. In this tutorial, review the basic definition of what algebra tiles are and how they are used. Then the video focuses on how to simplify variable expressions using algebra tiles. | 677.169 | 1 |
Coordinate Geometry (Dover Books on Mathematics)
A thorough, complete, and unified introduction, this volume affords exceptional insights into coordinate geometry. It makes extensive use of determinants, but no previous knowledge is assumed; they are introduced from the beginning as a natural tool for coordinate geometry. Invariants of conic sections and quadric surfaces receive full treatments. Algebraic equations on the first degree in two and three unknowns are carefully reviewed and carried farther than is usual in algebra courses. Throughout the book, results are formulated precisely, with clearly stated theorems. More than 500 helpful exercises throughout the text incorporate — often in rather novel settings — each idea after its full and careful explanation. 1939 edition.
Book Description Dover Publications Inc. Book Condition: Acceptable. 2000 - Paperback - Used - Acceptable SI-09-6-0037 | 677.169 | 1 |
For the last 20 years dynamic geometry software have been increasingly used for teaching geometry; however it is not suitable for teaching stereometry in middle schools in a creative and explorative way. DALEST stands for Developing Active Learning Environment for Stereometry.
Partners in the project are University of Cyprus, University of Southampton, University of Lisbon, University of Sofia, University of Athens, N.K.M Netmasters and Cyprus Mathematics Teachers Association. The project is co-funded by the European Union under the Socrates Program, MINERVA, 2005 Selection
Objectives
The main objective is the development of a dynamic 3D geometry microworld, which enables students to construct, observe and manipulate geometrical figures in space, and teachers to help students construct understanding of stereometry
Elica-DALEST Applications
An essential part of the software developed in the project is the set of Elica-DALEST applications. They are used to practice measuring of volume and surface of 3D solids, exploring various intersections of solids and planes, as well as playing with the reverse problems of well known nets problems | 677.169 | 1 |
Be sure that you have an application to open
this file type before downloading and/or purchasing.
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Product Description
This is a very diverse assessment to test students ability to solve systems of equations using the substitution, elimination, and graphing method.
This test includes 6 multiple choice, 4 short answer, 3 word problems, and 1 extended response. Directions specifically on the test allow for students to take it within one class period, however, it can be changed so that students have time to complete all parts as you wish.
Students are truly assessed on their understanding and comprehension of solving systems of equations. I hope you enjoy! :) | 677.169 | 1 |
mathematicsThe Khan Academy provides free education through a library of videos covering K-12 math, science topics such as biology, chemistry, and physics, and even reaches into the humanities with playlists on finance and history. | 677.169 | 1 |
Review: Roll-your-own maths
Recently I asked a sculptor, who doesn't use computers, what she thought
they were used for. 'Blinding people with science' was her first response.
As readers will have noticed, you can indeed do some dazzling scientific,
and especially mathematical, stuff with computers.
Some of this has even broken out of university computer departments
onto researchers' desktop machines, and there are some frightfully clever
programs around for personal computers – Mathematica comes immediately to
mind. Soon, though, you come up against a difficulty. No ready-made package
ever does exactly what you want, the way you want to do it. While the computer
department has vast libraries of program code which could help these are,
in practice, useful only on their mainframe.
Creating a program to do exactly the mathematical job you want on a
personal computer, therefore, is likely to involve days of reading manuals
and of translating cookbook code from one language to another. If those
two languages are, as is most likely, Fortran and C, it will also involve
weeks of working out why your results disappear into the bit-bucket. Nocturnal
mutterings will take the form: 'Ah! Here the C code multiplies the background
colour by last Tuesday and corrupts this pointer to that driver.'
Advertisement
This is a problem that Robert Harding and Mark Manning have faced for
17 years. They work at the Department of Applied Mathematics at the University
of Cambridge, where there is a computer-aided teaching project which requires
students to produce programs that demonstrate basic techniques and numerical
methods. Out of this Harding and Manning have developed a library of program
routines for such methods, in the Pascal language.
With the help of M. H. Beilby at the University of Birmingham, they
have developed these into both a stand-alone program to demonstrate the
techniques, and the Toolkit of parts from which buyers can develop their
own mathematical programs with a minimum of effort. The result is impressive.
I compared the performance of the Toolkit with the hard-wired routines
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method of integration and solving simultaneous equations in four variables.
The Toolkit produced results (on an AT-compatible running at 12 megahertz)
in less than a second, compared with 15 seconds and more for the Casio.
It generally reported greater precision, and all significant digits were
consistently the same.
The Toolkit's documentation is clear and comprehensive – though it does,
naturally, tend to assume that the reader has recently studied the mathematical
methods involved.
Besides number crunching and the ability to parse and evaluate any reasonable
function the user throws at it, the Toolkit can present results graphically.
On a computer with high-resolution graphics display, the results are quite
adequate. In fact, they were good enough that I immediately started my wish-list
for extensions to the Toolkit – capability to save graphics to files that
desktop publishing packages can use. As it is, you are stuck with dumping
to a dot-matrix printer.
The ready-to-run program is not, however, the main point of this package.
It mainly serves to demonstrate the power of the library modules ('units'
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programs. (Now the sculptor wants an animated display of the plot of z=sin(x)*cos(y)
from a rotating viewpoint . . .)
The modules are well designed and appear to be robust. One important
advantage of the Pascal language is that, used wisely, it prevents programmers
doing silly things, such as multiplying colours by dates. Unfortunately,
the ability to deal with functions typed in as text by the user calls for
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There are other problems. Both machines on which I tested the Toolkit
have monochrome displays that look, from the program's point of view, like
colour. Various preset colour combinations produce illegible black-on-black
under these circumstances.
I will be able to cure this because I have the full source code – the
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'units' are compiled. However, the authors positively encourage users to
distribute programs they have written, with credit but without any licence
agreement. If I did that, I would want users of my program to define their
own colours: achieving this would be quite a chore, and only feasible for
owners of the source.
In all, I think that most users will find Toolkit is amazing value.
Its low price is only possible because of its origins in academia and because
of the authors' enthusiasm for spreading useful tools, rather than collecting
cash.
At this price, though, will users be able to get support with problems
using the package? Until sales take off enough to support a technical service
department, Hardings says the authors will deal with queries themselves.
You don't get that kind of commitment with your average £600 database
or word processing package. | 677.169 | 1 |
goal of this book is to teach undergraduate students how to use Scientific Notebook (SNB) to solve physics problems. SNB software combines word processing and mathematics in standard notation with the power of symbolic computation. As its name implies, SNB can be used as a notebook in which students set up a math or science problem, write and solve equations, and analyze and discuss their results.
Written by a physics teacher with over 20 years experience, this text includes topics that have educational value, fit within the typical physics curriculum, and show the benefits of using SNB. | 677.169 | 1 |
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Mathematics
The syllabus in Mathematics has undergone changes from time to time in accordance with growth of the subject and emerging needs of the society. Motivating the topics from real life problems and other subject areas, greater emphasis has been laid on applications of various concepts. The curriculum at primary and secondary stage primarily aims at enhancing the capacity of students to employ Mathematics in solving day-to-day life problems and studying the subject as a separate discipline. Carrying out experiments with numbers and forms of geometry, framing hypothesis and verifying these with further observations form inherent part of Mathematics learning at this stage. The teaching of Mathematics here is done through activities which involve the use of concrete materials, models, patterns, charts, pictures, posters, games, puzzles and experiments. Its aims are:-
Acquire knowledge and understanding, particularly by way of motivation and visualization of basic concepts, terms, principles and symbols and underlying processes and skills.
To develop mastery of basic algebraic skills.
To develop drawing skills.
To feel the flow of reasons while proving a result or solving a problem.
To develop positive ability to think, analyze and articulate logically.
To develop awareness of the need for national integration, protection of environment, observance of small family norms, removal of social barriers and elimination of sex biases.
To develop necessary skills to work with modern technological devices such as calculators, computers etc. | 677.169 | 1 |
Tuesday, January 18, 2011
Microsoft Balancing Equations And Graphing Calculator Worksheet
Microsoft Mathematics is an award-winning education tool consisting various powerful mathematical modules to aid in tackling the pre-algebra, algebra, trigonometry, calculus, physics and chemistry calculations. Explore the features available in Microsoft Mathematics 4.0: | 677.169 | 1 |
Sequences and Series
A series of free, online Intermediate Algebra Lessons or Algebra II lessons.
Videos, worksheets, and activities to help Algebra students.
In this lesson, we will learn
how to define sequences
how to define a series
how to write a series in summation notation
Introduction to Sequences
Lists of numbers, both finite and infinite, that follow certain rules are called sequences. This introduction to sequences covers the definition of a sequence and how to identify a rule. There are specific sequences that have their own formulas and methods for finding the value of terms, such as arithmetic and geometric sequences. Series are an important concept that come from sequences.
This video introduces sequences.
How to define a sequence.
Series and Summation Notation
An important concept that comes from sequences is that of series and summation. Series and summation describes the addition of terms of a sequence. There are different types of series, including arithmetic and geometric series. Series and summation follows its own set of notation that is important to memorize in order to understand homework problems.
How to define a series.
In this video we look at several examples of how to write series in summation notation | 677.169 | 1 |
Math 1: General Math
DESCRIPTION:
This course emphasizes the study of general math. The course is presented in two semesters.
Semester 1 introduces the number types and basic math operations, to include addition, subtraction, multiplication, and division. Identifies the order of operations, explains the commutative, associative, and distributive properties as well as factoring and divisibility rules, and their application to word problems. It guides students through the use of fractions, decimals, and percents and their relationships to each other.
Semester 2 illustrates the use of exponents, roots, scientific notation, and the use of formulas. It covers lines and angles, area and perimeter of quadrilaterals, circumference, radius, and diameter of circles, and properties of obtuse, acute, and right triangles. This course also discusses patterns, probability, central tendency, graphs and charts, and tables and schedules.
CREDITS:
1 Credit
PREREQUISITES:
There are no prerequisites for this course.
STANDARDS:
This course is aligned to the National Council of Teachers of Mathematics (NCTM), Florida Sunshine State Standards, Common Core State Standards Initiative (CCSSI), and the Achieve American Diploma Project Network (ADP) standards.
Math 1: General Math Semester 1
MAT 101: Pretest – General Math
Number Types
Basic Math Operations
Signed Numbers / Absolute Value
Order of Operations
Rounding and Estimation
Number Properties
Factoring and Divisibility Rules
Word Problems
Simplifying Fractions
Adding and Subtracting with Fractions
Multiplying and Dividing with Fractions
Decimals and Place Value
Converting Between Fractions, Decimals, and Percents
Percents
Comparing Fractions, Decimals, and Percents
Ratios and Proportions
MAT 101: Test – General Math
Math 1: General Math Semester 2
MAT 102: Pretest – General Math
Exponents and Roots
Scientific Notation
Using Formulas in Math
Angles and Lines
Quadrilaterals
Circles
Triangles
Volume and Surface Area
Patterns
Simple Probability
Basic Statistics
Basic Charts and Graphs
Charts and Graphs
Frequency Table
Item Sets
Solving Equations
MAT 102: Test – General Math | 677.169 | 1 |
Emotional Intelligence
Outline
I. What is emotional intelligence ?
II. What is YOUR emotional intelligence?
A. A short 10 item questionnaire
III. Why is it important to know about emotional
intelligence
IV. Four Clusters of Emotional Intelligence
V. How d
21992_fcch01.indd 3
A systematic process that considers important
elements of an individuals financial affairs in
order to fulfill financial goals.
The necessities, comforts, and luxuries enjoyed or
desired by an individual or family.
Chapter 1
Chapter 1
1.2 Induction and Contradiction
1.2
3
Induction and Contradiction
In this section, we give two commonly used methods of mathematical proof, namely
proofs by induction and proofs by contradiction. These methods will be used
sporadically throughout this boo
18
1 Preliminaries
Exercise 1.5.10 Show that in every group of n people, where n 2, there are at
least two people that know the same number of people within the group. We assume
that A knows himself and that A knows B if and only if B knows A.
Exercise 1.
64
3 The Binomial Coefficient
Similarly, we compute |B|:
!"
(i) Place 3 in the last position. There are now 23 = 3 ways to select positions for
cfw_1, 5, 7.
(ii) Assign numbers from the set cfw_1, 5, 7 to these positions. Since repetition are
allowed, the
1.5 The Pigeonhole Principle
15
Fig. 1.7 Illustration of the Pigeonhole Principle
York City. We let the number of hairs on a persons head to be the pigeonholes and
each person in New York to be a pigeon. Since k 2000000 and n 8000001, it
follows that ther
12
1 Preliminaries
of x, denoted x, is the largest integer less than or equal to x. Essentially, the floor
function rounds down to the nearest integer.
Example 1.4.2 Find the floor of each of the following real numbers:
(i)
(ii)
(iii)
x = 67;
y = 22/7;
z
6
1 Preliminaries
to Alice, three gumdrops to Bob, and one gumdrop to Chad. The set of people that
have received gumdrops is cfw_Alice, Bob, Chad. However, if we wish to know not
only who has received gumdrops but how many gumdrops they have received, the
118
5 Generating Functions
We now turn our attention to rational functions and their decomposition into partial
fractions. A rational function is a function of the form f (x) = p(x)/q(x), where p(x)
and q(x) are polynomials such that q(x) = 0. If the degr | 677.169 | 1 |
Pages
Tuesday, May 21, 2013
Beginning and Intermediate Algebra 6th Edition, Gustafson
Beginning and Intermediate Algebra: An Integrated Approach 6th Edition PDF Download Ebook. R. David Gustafson, Rosemary Karr and Marilyn Massey offer exciting and innovative revision that takes an already successful text and makes it more compelling for today's instructor and student. The new edition has been thoroughly updated with a new interior design and other pedagogical features that make the text both easier to read and easier to use.
Known for its clear writing and an engaging, accessible approach that makes algebra relevant, this book helps students to develop problem-solving skills and strategies that they can use in their everyday lives. The new edition welcomes two new co-authors Rosemary Karr and Marilyn Massey who along with David Gustafson have developed a learning plan to help students succeed in Beginning Algebra and transition to the next level in their coursework.
The authors have developed an acute awareness of students' approach to homework and present a learning plan keyed to new Learning Objectives and supported by a comprehensive range of exercise sets that reinforces the material that students have learned setting the stage for their success.
Detailed step-by-step examples provide guidance for students. Classroom Examples, paired with each example in the text, are available in the Annotated Instructor's Edition for additional instructor support. Concept Checks throughout the text allow students to gauge their grasp of an idea as it is presented in the text. By stressing conceptual understanding at point-of-use, the Concept Checks help prevent misconceived notions for important topics.
All exercise sets have been carefully updated with this revision. Several special types of exercises throughout the text give students the practice they need: new Vocabulary, Readiness and Video Checks (see New-to-Edition section for more information); Guided Applications (see New-to-Edition section for more information); Mixed Practice; Concept Extension; and more!
Martin-Gay's presentation of Study Skills ensures that students make the most of their valuable study time in order to help them succeed in this course. In-text study skills resources include Section 1.1, Tips for Success in Mathematics and the new Student Resources section located in the back of the book. End-of-chapter material offers students a wealth of review- and retention-oriented material to reinforce the concepts presented in current and previous chapters.
Guided application exercises offer prompts for setting up the problem and getting started with the solution process. These guided exercises help students prepare to solve application exercises on their own, and appear in a number of places throughout the text. The Student Resources section, located in the back of the text, gives students a variety of tools that are conveniently located in one place to help them achieve success in math. | 677.169 | 1 |
Nonlinear boundary value problems for ordinary differential equations
Access Full Book
Abstract
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CommentsThis tract is intended to be accessible to a broad spectrum of readers. Those with out much previous experience with differential equations might find it profitable (when the need arises) to consult one of the following standard texts: Coddington-Levinson [17], Hale [35], Hartman [38], Mawhin-Rouche [61]. The bibliography given below is restricted mostly to the problems discussed in the tract or closely related topics. A small number of additional references are included however in order to provide a guide to further study; most of these contain extensive bibliographies for the material they cover. The following references include some of the recent surveys and monographs that are related to the subject matter of this tract in a substantial way: Bailey-Shampine-Waltman [7], Bernfeld-Lakshmikantahm [11], Cesari [15], Eloe-Henderson [21], Gaines-Mawhin [25], Gudkov-Klokow-Lepin-Ponomarov [34], Jackson [43], Keller [47], Lefschetz [57], Mawhin [60], Protter-Weinberger [69].CONTENTSComments............................................................................................................................5CHAPTER IIntroduction§ 1. Elementary theory of second order differential equations...........................................12§ 2. Topological preliminaries.............................................................................................14§ 3. The maximum principle................................................................................................16§ 4. Existence and a priori bounds-examples.....................................................................19§ 5. Problems with other boundary conditions....................................................................25CHAPTER IIThe Bernstein theory of the equation y" = f(t, y, y')§ 1. The homogeneous Dirichlet, Neumann, and periodic problems...................................28§ 2. The homogeneous Sturm-Liouville problem................................................................34§ 3. Inhomogeneous boundary conditions..........................................................................35§ 4. Examples and remarks................................................................................................39§ 5. Bernstein-Nagumo growth conditions..........................................................................44§ 6. Nonlinear boundary conditions....................................................................................50§ 7. Uniqueness..................................................................................................................52CHAPTER IIIApplications§ 1. Steady-state temperature distributions........................................................................56§ 2. The Thomas-Fermi problem........................................................................................59§ 3. Singular boundary value problems..............................................................................62§ 4. Osmotic flow.................................................................................................................64§ 5. Positive solutions to diffusion equations......................................................................70CHAPTER IVOther second order boundary value problems§ 1. Periodic solutions to differential equations of Nirenberg type......................................76§ 2. The Dirichlet problem for y" = f(y') and the Neumann problem for y" = f(t,y,y').............85§ 3. Upper and lower solutions...........................................................................................94CHAPTER VEven order systems and higher order equations§ 1. General existence theorems........................................................................................99§ 2. Second order systems...............................................................................................102§ 3. Third and fourth order problems................................................................................108§ 4. Higher even order equations......................................................................................111CHAPTER VINumerical solution of boundary value problems§ 1. Newton's method........................................................................................................113§ 2. The shooting method for the Dirichlet problem..........................................................115§ 3. The shooting method for the Neumann problem........................................................120§ 4. Quasilinearization for boundary value problems........................................................121References.......................................................................................................................125 | 677.169 | 1 |
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Summary
Strong algebra and trigonometry skills are crucial to success in calculus. This text is designed to bolster these skills while readers study calculus. As readers make their way through the calculus course, this supplemental text shows them the relevant algebra or trigonometry topics and points out potential problem spots. The table of contents is organized so that the algebra and trigonometry topics are arranged in the order in which they are needed for calculus. Numbers and Their Disguises:Multiplying and dividing fractions, adding and subtracting fractions, parentheses, exponents, roots, percent, scientific notation, calculators, rounding, intervals.Completing the Square: Completing the square in one and two variables.Solving Equations:Equations of degree 1 and 2, solving other types of equations, rational equations, the zero-factor property.Functions and Their Graphs:Introduction, equations of lines, power functions, shifting graphs, intersection of curves.Cyclic Phenomena: The Six Basic Trigonometric Functions:Angles, definitions of the six trigonometric functions, basic identities, special angles, sum formulas.Exponential Functions:The family of exponentials, the function.Composition and Inverse Functions:Composite functions, the idea of inverses, finding an inverse offgiven by a graph, finding the inverse offgiven by an expression.Logarithmic Functions:Definition of logarithms, logs as inverses of exponential functions, laws of logarithms, the natural logarithm.Inverse Trigonometric Functions:The definition of arcsinx, the functions arctanxand arcsecx, inverse trigonometric identities.Changing the Form of a Function:Factoring, canceling, long division, rationalizing, extracting a factor from under a root.Simplifying Algebraic Expressions:Working with difference quotients and rational functions, canceling common factors, rationalizing expressions.Decomposition of Functions: Inner, outer, and outermost functions, decomposing composite functions.Equations of Degree 1 Revisited:Solving linear equations involving derivatives.Word Problems, Algebraic and Transcendental:Algebraic word problems, the geometry of rectangles, circles and spheres, trigonometric word problems, right angle triangles, the law of sines and the law of cosines, exponential growth and decay.Trigonometric Identities:Rewriting trigonometric expressions using identities. For all readers interested in algebra and trigonometry in early transcendentals calculus. | 677.169 | 1 |
RealCalculator 3.2
Professional calculator for advanced mathematical tasks
Author's review
WindowCE altready contains a calculator. Nevertheless, this calculator is quite a simple one and can make standard calculations like *, -, /, + and square root extraction.
RealCalculator can do much more. It includes:
Scientific calculator
Function plotter
Matrix-calculator
Calculator for complex numbers
Computer-calculator (hex, bin, oct, dec)
Function calculator
Numerical equations solver
Statistic calculator
Metrics-converter
Apart from that, it pursuits a different concept: Normally, all input is directly calculated, so you have problems with the sequence of your operations (e.g. * comes before -). RealCalculator stores all input in the input-field(s) and makes the calculation not until you have pressed the "="-button.
Your review for RealCalcul | 677.169 | 1 |
Physical Chemistry Complex Numbers
In this lesson our instructor talks about complex numbers. He discusses addition, subtraction, multiplication, and division of complex numbers. He also lectures on the Euler's formula and the polar exponential representation of the complex number. He does a total of 7 complete example problems.
Hi, Mr. Raffi! Is differential equation a necessary prerequisite before viewing the quantum mechanics lectures in this series? I have had some exposure to multivariable calculus and linear algebra from your lecture series on this website (and I appreciate your enthusiasm in those videos, especially in linear algebra), but I am not sure if they are enough for quantum.
1 answer
Last reply by: Professor Hovasapian Tue Mar 24, 2015 5:02 PM
Post by shashikanth sothukuon March 24, 2015
hi prof, 21i+8i = 29i at 8:00
Complex NumbersAs the first modern physical chemistry textbook to cover quantum mechanics before thermodynamics and kinetics, this book provides a contemporary approach to the study of physical chemistry. By beginning with quantum chemistry, students will learn the fundamental principles upon which all modern physical chemistry is built. The text includes a special set of ""MathChapters"" to review and summarize the mathematical tools required to master the material Thermodynamics is simultaneously taught from a bulk and microscopic viewpoint that enables the student to understand how bulk properties of materials are related to the properties of individual constituent molecules. This new text includes a variety of modern research topics in physical chemistry as well as hundreds of worked problems and examples." | 677.169 | 1 |
Books in category Mathematics – Functional Analysis
This two-volume book is a modern introduction to the theory of numbers, emphasizing its connections with other branches of mathematics. Part A is accessible to first-year undergraduates and deals with elementary number theory. collective work presents a comprehensive treatment of selected advanced topics in the subject. Every chapter is self-contained and written by international experts who elaborate on special topics. | 677.169 | 1 |
Designed for the three-semester course for math and science majors, the Larson/Hostetler/Edwards series continues its tradition of success by being the first to offer both an Early Transcendental version as well as a new Calculus with Precalculus text. This was also the first calculus text to use computer-generated graphics (Third Edition), to include exercises involving the use of computers and graphing calculators (Fourth Edition), to be available in an interactive CD-ROM format (Fifth Edition), and to be offered as a complete, online calculus course (Sixth Edition). Every edition of the book has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas. The Seventh Edition also expands its support package with an all-new set of text-specific videos.
P.S. Problem-Solving Sections, an additional set of thought-provoking exercises added to the end of each chapter, require students to use a variety of problem-solving skills and provide a challenging arena for students to work with calculus concepts.
Getting at the Concept Exercises added to each section exercise set check students' understanding of the basic concepts. Located midway through the exercise set, they are both boxed and titled for easy reference.
Review Exercises at the end of each chapter have been reorganized to provide students with a more effective study tool. The exercises are now grouped and correlated by text section, enabling students to target concepts requiring review.
The icon "IC" in the text identifies examples that appear in the Interactive Calculus 3.0 CD-ROM and Internet Calculus 2.0 web site with enhanced opportunities for exploration and visualization using the program itself and/or a Computer Algebra System.
Think About It conceptual exercises require students to use their critical-thinking skills and help them develop an intuitive understanding of the underlying theory of the calculus.
Modeling Data multi-part questions ask students to find and interpret mathematical models to fit real-life data, often through the use of a graphing utility.
Section Projects, extended applications that appear at the end of selected exercise sets. may be used for individual, collaborative, or peer-assisted assignments.
True or False? Exercises, included toward the end of many exercises sets, help students understand the logical structure of calculus and highlight concepts, common errors, and the correct statements of definitions and theorems.
Motivating the Chapter sections opening each chapter present data-driven applications that explore the concepts to be covered in the context of a real-world setting.
About the Author: 2013 Text and Academic Authors Association Award for CALCULUS, the 2012 William Holmes McGuffey Longevity Award for CALCULUS: AN APPLIED APPROACH, the 2011 William Holmes McGuffey Longevity Award for PRECALCULUS: REAL MATHEMATICS, REAL PEOPLE best-selling Calculus series published by Cengage Learning | 677.169 | 1 |
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This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of ma...
Encourage young investigators to feel, listen, smell, taste, and see their way to discovery by seamlessly infusing math and science throughout the school day! As you incorporate all five senses into ... | 677.169 | 1 |
Eighth Edition of Gareth Williams' classic text is designed for the introductory linear algebra course, and provides a flexible blend of theory and engaging applications for students within engineering, science, mathematics, business management, and physics. The text's 29 core sections within 8 chapters are organized into 3 Parts: Part 1 introduces the basics, presenting systems of linear equations, vectors and subspaces of R(n), matrices, linear transformations, determinants, and eigenvectors. Part 2 builds on the material presented in Part1 and goes on to introduce the concepts of general vector spaces, discussing properties of bases, develops the rank/nullity theorem, and introduces spaces of matrices and functions.Part 3 completes the course with many of the important ideas and methods of numerical linear algebra, such as ill-conditioning, pivoting, and LU decomposition.Throughout the text the author takes care to fully and clearly develop the mathematical concepts first and then provide modern applications to reinforce those concepts. The applications range from theoretical applications within differential equations and least square analysis, to practical applications in fields such as archeology, demography, electrical engineering and more. | 677.169 | 1 |
Howard Anton, Chris Rorres
This classic treatment of linear algebra presents the fundamentals in the clearest possible way, examining basic ideas by means of computational examples and geometrical interpretation. It proceeds from familiar concepts to the unfamiliar, from the concrete to the abstract. Readers consistently praise this outstanding text for its expository style and clarity of presentation.
* The applications version features a wide variety of interesting, contemporary applications.
each of whose terms is the product of n entries from the given matrix. Each of these entries is either a constant or is of the form λ – a . The only term ij with a λ in each factor of the product is (λ – a )(λ – a ) … (λ – a ) 11 22 nn Therefore, this term must produce the highest power of λ in the characteristic polynomial. This power is clearly n and the coefficient of λ n is 1. 200 Exercise Set 7.1 17. The characteristic equation of A is λ2 – ( a + d)λ + ad – bc = 0 This is a | 677.169 | 1 |
Function Lingo Activity - PowerPoint PPT Presentation
Function Lingo Activity. Be sure you have a Function Lingo Card and get started. The goal os this activity is to get your mind thinking about functions and why their graphs behavior the way they do. Think about domain, range, shifting, reflections. How to Handle the Summer Packet Function Lingo Activity' - jack 1: I thought I'd grade it the same way I grade homework, and treat it as a big ol' homework assignment. Be ready to submit on Friday and be ready to ask questions. I may choose to review a few choice problems.
Part 2: For Barron's Chapter 1: I will give a quiz Friday consisting of Barron's Ch1, all multiple choice.
Part 3 and Part 4: I will grade these like homework assignments.
Part 5: the Flash Cards. I intend to make a little quiz, maybe some free response, some matching and some multiple choice. Probably about 7 or 8 questions. I haven't made it yet.
Well, you have explored a bit on your calculators today, but really what is your intention behind finding a limit?
We are most interested in determining "how the function is behaving" as it approaches a value NOT the value of the function. At times, the limit value will also be the function value but keep in mind, we are focused on the behavior! | 677.169 | 1 |
1
A Brief Review of Elementary Ordinary
Differential Equations
At various points in the material we will be covering, we will need to recall and use material
normally covered in an elementary course on ordinary differential equations. In these notes, we
w
DIFFERENTIAL EQUATIONS with TI-89
ABDUL HASSEN and JAY SCHIFFMAN
We will assume that the reader is familiar with the calculators keyboard and the basic operations. In
particular we have assumed that the reader knows the functions of the SECOND, APLHA, and
Integration by Parts review and shortcut
Math 256 Fall, 2012
This handout will review integration by parts, particularly repeated integration by parts, giving a substantial shortcut for the latter.
Integration by Parts:
Integration by parts is the integra
Problems on Linear Transformations
Testing knowledge
A linear transformation T : V W verifies what two properties?
Give an example of a linear transformation from R2 to R2 .
Give an example of a function from R2 to R2 that is not a linear transformatio
Ajay Majmudar
1/20/16
Period 3
1st Body Paragraph-The Counter Argument
Although a lot of individuals are quick to blame social media as the main
cause of cyber bullying, many do not view it that way. According to authors
Wanda Cassidy, Karen Brown, and Ma
Exam 2
Math383
Name:
Spring 2011
Grade:
/ 100
Instructions: You must show all work and explain all reasoning to
receive credit. Clarity will be considered in grading. Good luck!
Variation of parameters
A particular solution to y 00 + p(t)y 0 + q(t)y = g(t
Math 383
Exam 2
Name:
Fall 2013
Grade:
/ 100
You must show all work and explain all reasoning to receive credit. Good
luck!
Problem 1. For each equation, write the correct form for the particular solution,
but DO NOT SOLVE THE EQUATION:
(a) y 00 + 4y =
Math 383
Exam 1
Fall 2013
Name:
Grade:
/ 100
You must show all work and explain all reasoning to receive credit. Each
problem is worth 20 points.
Problem 1. Suppose that x~p is a solution to the system of equations A~x = ~b, and
that x~h is a solution t
Math 383
Name:
Exam2
Spring 2015
/ 100
Instructions: You must show all work and explain all reasoning to
receive credit. Clarity will be considered in grading. Good luck!
Problem 1 (10pts). Consider the three functions y1 = x, y2 = e2x and y3 = cos(x).
Welcome Chat Quiz
Submit to the Introduction Assignment drop box for 10 extra points.
1. Why do you need to complete the Student Orientation Course before June 6?
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2. Why should you print your session schedule?_
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3. If you will be on vacation during | 677.169 | 1 |
Department
College
First Advisor
Subject(s)
Disciplines
Science and Mathematics Education
Abstract
The purpose of this study was to construct a mini introduction to a fractal geometry course appropriate for community college students. The researcher evaluated the related research and the literature related to fractal geometry appropriate for community college students. Fractal geometry lesson plans were constructed. The topics covered in this introduction course include the Koch Curve, Sierpinski's Triangle, iterations, complex numbers and the Mandelbrot set.
The course is intended for students who have completed Calculus I at Atlantic Community College which is located in the southern part of New Jersey. The course is intended to be taught for five weeks for two hours of instruction per week. Exercises based on the material are explained and assigned to the students at the end of each class.
Recommended Citation
Satchithananthan, Kananathan, "The development of a mini course on fractal geometry for the community college mathematics student" (1996). Theses and Dissertations. 2210. | 677.169 | 1 |
Mathematics
A Student Works on a Problem on her Desk
The Math Department offers a three-year integrated middle school math program with an option of Algebra or Geometry in the eighth grade for advanced math students. At each level, concepts are developed and explored through connected reasoning and active problem solving, enhanced with manipulatives and technology.
6th Grade Mathematics - Tammy Lysons
In Math 6, students investigate number relationships, probability, patterns, two-dimensional shapes, measurement and data organization. Students also reinforce their understanding of the rational numbers.
7th Grade Mathematics - Tammy Lysons
In Math 7, students investigate linear relationships in tables, graphs and equations, proportional reasoning, patterns, three-dimensional shapes, and measurement. Students also expand their understanding of rational numbers to include integers.
8th Grade Algebra I - Andrew Sherman
Algebra I is a year-long high school equivalent course designed for advanced eighth grade math students. Algebra I is the study of functional relationships, both linear and nonlinear. These relationships are expressed through words, tables, pictures, graphs, and symbols. Concepts include properties of Real Numbers, solving linear and non-linear equations, linear inequalities, and systems of linear equations. Polynomials, exponential and radical functions are also explored.
8th Grade Geometry- Kimberly Magro
Geometry is a year-long high school equivalent course designed for eighth grade students who have completed Algebra I successfully. The study of Geometry includes experiences and activities that relate to the value of geometry in life. Emphasis is placed on the use of reasoning skills, two and three dimensional modeling to solve problems - both mathematical and real-world. | 677.169 | 1 |
Mov Linear Transformations as Matrix Vector Products
Showing how ANY linear transformation can be represented as a matrix vector product
People have been telling you forever that linear algebra and matrices are useful for modeling, simulations and computer graphics, but it has been a little non-obvious. This tutorial will start to draw the lines by re-introducing you functions (a bit more rigor than you may remember from high school) and linear functions/transformations in particular.
This video is part of the module Functions and linear transformations of the topic Matrix transformations
Brainbuxa.com appreciates and recognises the work done by Sal Khan for delivering great lectures and enhancing Free Education worldwide through the initiative Khan Academy. For more Videos, visit | 677.169 | 1 |
Academic year
Unit information: Engineering Mathematics 2 is the second of the two units that cover the basic mathematics requirements of engineering degree programmes. It comprises four elements: Vector Calculus, Applied Statistics, and Linear Systems & Partial Differential Equations.
Unit aims: To enhance and develop the student's understanding of and ability to use the language of mathematics in engineering problems.
Intended learning outcomes
On successful completion of this unit, students will:
understand basic principles of vector calculus
be able to apply vector calculus methods to problems in engineering
understand and apply transform methods to engineering problems
be able to classify simple partial differential equations, and understand the different qualitative behaviour of their solutions
be able to apply elementary techniques to solve simple partial differential equations
appreciate the importance of the real world of applied statistics
be able to formulate hypothesis tests, and understand their use for making inferences and obtaining confidence intervals,
use applied statistics techniques such as goodness of fit, correlation and regression for simple data and models
Teaching details
Lectures.
There are also additional but optional walk-in support classes (3 hours per week) in which postgraduate students offer ad-hoc support to students on an individual basis
Assessment Details
3-hour written exam (100%, all learning outcomes)
Reading and References
Advanced Engineering Mathematics (10th Edition) E Kreyszig, John Wiley & Sons. This book is aimed at the more advanced end of this course but gives simple explanations and contains all the maths you are likely to need for the rest of your University career and beyond.
Other textbooks which students may find useful are:
Probability and Statistics for Engineers and Scientists (9th Edition). Ronald. E. Walpole et al, Pearson, 2011. Recommended as covering the requirements in applied statistics, though many other textbooks available in the libraries will do likewise. | 677.169 | 1 |
Overview
Discrete Transition to Advanced Mathematics
As the title indicates, this book is intended for courses aimed at bridging the gap between lower-level mathematics and advanced mathematics. The text provides a careful introduction to techniques for writing proofs and a logical development of topics based on intuitive understanding of concepts. The authors utilize a clear writing style and a wealth of examples to develop an understanding of discrete mathematics and critical thinking skills. While including many traditional topics, the text offers innovative material throughout. Surprising results are used to motivate the reader. The last three chapters address topics such as continued fractions, infinite arithmetic, and the interplay among Fibonacci numbers, Pascal's triangle, and the golden ratio, and may be used for independent reading assignments. The treatment of sequences may be used to introduce epsilon-delta proofs. The selection of topics provides flexibility for the instructor in a course designed to spark the interest of students through exciting material while preparing them for subsequent proof-based courses.
This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms.
The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex ...
From the reviews: The account is quite detailed and is written in a manner that
will appeal to analysts and numerical practitioners alike...they contain everything from rigorous proofs to tables of numerical calculations.... one of the strong features of these ...
The nation's first choice for an NSF reform high school mathematics series! This 2nd edition
features a colorful lesson design; earlier development of algebraic topics; expanded use of technology; pre-requisite skills review in every lesson; Unit Resource Masters; and aAfter completing his famous Foundations of Analysis, Landau turned his attention to this book on
calculus. The approach is that of an unrepentant analyst, with an emphasis on functions rather than on geometric or physical applications. The book is another ...
Ecology, as a part of the Glencoe Science 15-Book Series, provides students with accurate and
comprehensive coverage of Earth's ecosystems and the interactions among organisms and their habitats. The strong content coverage integrates a wide range of hands-on experiences, critical-thinking ...
Ion channels underlie a broad range of the most basic biological processes, from excitation and
signaling to secretion and absorption. Like enzymes, they are diverse and ubiquitous macromolecular catalysts with high substrate specificity and subject to strong regulation. This fully ... | 677.169 | 1 |
Discrete Transition to Advanced Mathematics
ISBN-10: 0534405185
ISBN-13: 9780534405182 title indicates, this text is intended for courses aimed at bridging the gap between lower level mathematics and advanced mathematics. The transition to advanced mathematics presented is discrete since continuous functions are not studied. The text provides a careful introduction to techniques for writing proofs and a logical development of topics based on intuitive understanding of concepts. The authors utilize a clear writing style and a wealth of examples to develop an understanding of discrete mathematics and critical thinking skills. Including more topics than can be covered in one semester, the text offers innovative material throughout, particularly in the last three chapters (e.g. Fibonacci Numbers and Pascal's Triangle). This allows flexibility for the instructor and the ability to teach a deeper, richer | 677.169 | 1 |
Essentials of Tropical Combinatorics
The goal of this book is to explain, at the graduate student level, how tropical geometry can be accessed via geometric combinatorics. This way the book offers a viable path to a topic of very active research. At the same time the reader learns how a number of seemingly unrelated combinatorial results fall into place, once viewed through the "tropical lens". No attempt is made to cover the entire field of tropical geometry, which has been evolving too rapidly anyway to be covered by a book so small.
The book's central concept is the "tropical convexity" introduced by Develin and Sturmfels, which is a version of "tropical linear algebra". This is used in the book as a general language to study classical subjects in combinatorial optimization including shortest paths, the assignment problem, the even dicycle problem, flow-type problems, and others.
This book focuses on the polyhedral and combinatorial aspects of tropical geometry while requiring less prerequisites in algebraic geometry and commutative algebra, thus making the book more accessible to a wider audience. The main requirement beyond general mathematical maturity is a basic knowledge in polytope theory | 677.169 | 1 |
Oxford GCSE Maths for AQA: Foundation Student Book
Synopsis
Oxford GCSE Maths for AQA: Foundation Student Book by Appleton et al
Devised for the new AQA specification, this proven levelled approach offers a unique choice of four student books and software tailored to match, each with access to a grade C, allocating just one single highly focused book to each student for the whole course, making learning simpler and more focused (particularly on students who fall between Foundation and Higher tiers) and therefore enabling students to achieve their highest possible grade. The Foundation student book focuses on grades E-G. | 677.169 | 1 |
Tag: Matlab
There are a lot of "Introduction" books for Matlab®. So maybe writing up some notes on it might be an overkill, but it would be nice to have one that is more practical and goes straight to teaching students how… | 677.169 | 1 |
Gary H. Ford
To most students, Taylor's Theorem is just a bunch of words on a
printed page. This past year, I taught Taylor's Thm. using the TI-85
graphing calculator to illustrate the relatively simple idea of
approximating one function with another in a prescribed interval. My
perception of the results is that the graphing calculator greatly enhanced
the understanding of the concepts involved. My students were actually
interested in questions like 'Where is the approximation good?' and 'How
closely does the one function approximate the other?', questions I've never
heard before concerning these concepts. In this talk, I will present some
examples, graphs, etc. that were used in class. Included also will be a
discussion of how to utilize the TI-85 to find an interval on which the
approximation is good to a specified level. | 677.169 | 1 |
Algebra: A Computational Introduction by John Scherk
Sufficient texts that introduce the thoughts of summary algebra are considerable. None, even though, are extra fitted to these wanting a mathematical heritage for careers in engineering, computing device technological know-how, the actual sciences, undefined, or finance than Algebra: A Computational advent. in addition to a distinct process and presentation, the writer demonstrates how software program can be utilized as a problem-solving instrument for algebra. numerous components set this article aside. Its transparent exposition, with every one bankruptcy construction upon the former ones, offers higher readability for the reader. the writer first introduces permutation teams, then linear teams, earlier than eventually tackling summary teams. He conscientiously motivates Galois thought by means of introducing Galois teams as symmetry teams. He contains many computations, either as examples and as workouts. All of this works to higher organize readers for knowing the extra summary concepts.By conscientiously integrating using Mathematica® during the ebook in examples and routines, the writer is helping readers boost a deeper figuring out and appreciation of the fabric. the varied workouts and examples besides downloads to be had from the web aid determine a important operating wisdom of Mathematica and supply a great reference for complicated difficulties encountered within the box.
Six prime specialists lecture on a large spectrum of modern effects just about the name, offering either an outstanding reference and deep insights on present examine job. Michael Cowling provides a survey of assorted interactions among illustration idea and harmonic research on semisimple teams and symmetric areas.
This booklet is an creation to the guidelines from basic topology which are utilized in easy research. it's written at a degree that's meant to make the majority of the cloth available to scholars within the latter a part of their first 12 months of analysis at a school or university even if scholars will generally meet many of the paintings of their moment or later years.
It is a fairly awesome e-book on Lie teams and algebraic teams. produced from hectographed notes in Russian from Moscow collage, which for plenty of Soviet mathematicians were anything similar to a "bible", the e-book has been considerably prolonged and arranged to increase the fabric during the posing of difficulties and to demonstrate it via a wealth of examples.
This bold and unique ebook units out to introduce to mathematicians (even together with graduate scholars ) the mathematical equipment of theoretical and experimental quantum box idea, with an emphasis on coordinate-free shows of the mathematical items in use. This in flip promotes the interplay among mathematicians and physicists by way of delivering a standard and versatile language for the great of either groups, notwithstanding mathematicians are the first aim.
So to calculate (αβ)(i), we first apply β to i and then apply α to the result. In other words, we read products 'from right to left'. 2 Let Cycles ( ) 1 2 3 4 5 α = ∈ S5 . 3 2 4 1 5 So α(1) = 3, α(3) = 4, α(4) = 1 and α fixes 2 and 5. We say that α permutes 1, 3, and 4 cyclically and that α is a cycle or more precisely, a 3-cycle. In general, an element α ∈ Sn is an r-cycle, where r ≤ n, if there is a sequence i1 , i2 , . . , ir ∈ {1, . . , n} of distinct numbers, such that α(i1 ) = i2 , α(i2 ) = i3 , .
Each of its elements has order 2 except for the identity. There is no element of order 4. However our calculation showed that if we begin with (1 2) and (3 4) say, we can express the remaining two elements of V ′ in terms of them. 2 we saw that every element of S3 can be written in terms of (1 2) and (1 2 3). We say that V ′ or S3 is generated by {(1 2)(3 4), (1 3)(2 4)}, respectively {(1 2), (1 2 3)}. In general a permutation group G is said to be generated by a subset g ⊂ G if every element in G can be written as a product of elements of g . | 677.169 | 1 |
The aim of this book is to familiarize the reader with fundamental topics in number theory: theory of divisibility, arithmetrical functions, prime numbers, geometry of numbers, additive number theory, probabilistic number theory, theory of Diophantine approximations and algebraic number theory. The author tries to show the connection between number theory and other branches of mathematics with the resultant tools adopted in the book ranging from algebra to probability theory, but without exceeding the undergraduate students who wish to be acquainted with number theory, graduate students intending to specialize in this field and researchers requiring the present state of knowledge.
"synopsis" may belong to another edition of this title.
Language Notes:
Text: English, Polish (translation)
Review:
"The book is a treasure trove of interesting material on analytic, algebraic, geometric and probabilistic number theory, both classical and modern. These topics are connected with other parts of mathematics in a scholarly way. It is a welcome addition to the literature on number theory." Mathematical Reviews "Relevant recent results with proofs beyond the scope of the book are quoted and there is a good bibliography. The exposition is clear and should present no undue difficulty to the reader. The translation from the original Polish has been well done." Bull. London Math. Soc. | 677.169 | 1 |
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