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State of the art computer algebra packages allow treatment of
mathematical concepts beyond those which are traditionally offered or
predefined. This is important for mathematics education since such
concepts are precisely those which were scarcely understood by students
both in secondary and tertiary education. Implementation of these
mathematical concepts will greatly improve the possibilities for
mathematics education at these levels. Examples of such concepts are:
• handling of inequalities;
• limits, continuity, Lipschitz conditions and smoothness;
• growth of functions and the speed with which limit values are
approached;
• quotients of structures;
• spatial geometry and visualisation of objects in up to four
dimensions.
Examples of this methodology | 677.169 | 1 |
GCSE Maths Complete
This handy revision app teaches you everything you need to know for GCSE Maths. It combines the separate apps for Number, Algebra, Geometry, Measures, Statistics and Probability produced by Haslam and Hall Publishing, a leading educational publisher in the UK.
Features:
* Includes Foundation and Higher levels.
* Revise the key facts for GCSE Maths.
* Take Quick Quizzes and try to beat your saved best score.
* OVER 1000 MULTIPLE CHOICE QUESTIONS with full worked solutions.
* No internet connection needed once installed.
* Suitable for all exam boards (AQA, Edexcel, OCR | 677.169 | 1 |
LearningExpress's 20 Minutes a Day guides make challenging subject areas more accessible by tackling one small part of a larger topic and building upon that knowledge with each passing day. Practical Math Success in 20 Minutes a Day features: • A walkthrough of the fundamental concepts of pre-algebra, algebra, and geometry • Hundreds of practice exercises for essential practice • A posttest, which reveals your progress • Access to a free, instantly scored online practice test | 677.169 | 1 |
If you don't have the time to take actual courses, textbooks help a lot—find out relevant textbooks for various classes (this is easily done through google or browsing college course catalogues online), and borrow/buy them for self-study. Math takes a lot of discipline, though—to get anywhere without taking classes you have to constantly review the material and practice, practice, practice. It's all about doing problems, which makes it one of the harder things to pick up especially when you're a busy working adult since it consumes so much time.
Of course, this only works up to a certain level. Elementary calculus, trigonometry and geometry and perhaps some linear algebra can be picked up by studying yourself; after that, for a truly rigorous foundation in higher level math (i.e. analysis, algebra etc.) you'll definitely need to take classes at a college.
Math requires a lot of time spent outside of the classroom. Most of the books you'll find at the local book stores (The Complete Idiot's Guide to Calculus, Calculus for Dummies, etc) are usually pretty thin on the exercises and are meant to supplement a proper calculus book.
Once of the most important things in a Math class is practice. I think they might also sell accompanying exercise books for these, but the standard calculus textbook comes loaded with easily a hundred or more exercises per section. I haven't any experience with the Thompson book, but Stewart's Calculus (this is a college textbook) is pretty good and helped me deal with some pretty awful calculus professors without affecting my GPA.
It's also really farking expensive.
Another option would be to take classes at a community college. They usually have classes or seminars for non-degree-seeking people, meaning you can just take a math class for whatever personal benefit. Even the best book can't make up for personal instruction, so if you're looking for the best learning experience I recommend taking a class.
I didn't have much trouble teaching myself discrete mathematics, linear algebra, or anything below pre-calculus, but there's no way in hell I would have made it through Integral Calculus (Calc II at most colleges) or Multi-variable Calculus (Calc III) without the help of professors and TAs.
Find online courses or go to night school. The community college system where I live has math all the way up to calculus. Math is a subject that could easily be taught online so such programs must exist. Once you have mastered calculus, check out this site.
If you can afford it, find an online or distance ed course through a university. (I'm assuming the work and family constraints mean that you don't have the ability to take night classes at a community college.) If you have self-discipline and the ability to learn from books, a course that is online or other distance ed may be the answer b/c you can work when and where you get the chance. If you need a tutor to help one on one, then sometimes you can find a teacher at the local high school to help you (or a college student in a math major who enjoys teaching). | 677.169 | 1 |
Introduction to Economic Analysis This book presents introductory economics ("principles") material using standard mathematical tools, including calculus. It is designed for a relatively sophisticated undergraduate who has not taken a basic university course in economics. It also contains the standard intermediate microeconomics material. 328 page pdf. Author(s): No creator set
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Mathematics for Computer Science A basic introduction to Calculus and Linear Algebra. The goal is to make students mathematically literate in preparation for studying a scientific/engineering discipline. The first week covers differential calculus: graphing functions, limits, derivatives, and applying differentiation to real-world problems, such as maximization and rates of change. The second week covers integral calculus: sums, integration, areas under curves and computing volumes. This is not meant to be a comprehensive calcu Author(s): No creator set
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Discrete Mathematics This course covered the mathematical topics most directly related to computer science. Topics included: logic, relations, functions, basic set theory, countability and counting arguments, proof techniques, mathematical induction, graph theory, combinatorics, discrete probability, recursion, recurrence relations, and number theory. Emphasis will be placed on providing a context for the application of the mathematics within computer science. The analysis of algorithms requires the ability to count Author(s): No creator set
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Applied Probability Focuses on modeling, quantification, and analysis of uncertainty by teaching random variables, simple random processes and their probability distributions, Markov processes, limit theorems, elements of statistical inference, and decision making under uncertainty. This course extends the discrete probability learned in the discrete math class. It focuses on actual applications, and places little emphasis on proofs. A problem set based on identifying tumors using MRI (Magnetic Resonance Imaging) i Author(s): No creator set
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Algorithms The design of algorithms is studied, according to methodology and application. Methodologies include: divide and conquer, dynamic programming, and greedy strategies. Applications involve: sorting, ordering and searching, graph algorithms, geometric algorithms, mathematical (number theory, algebra and linear algebra) algorithms, and string matching algorithms. Analysis of algorithms is studied - worst case, average case, and amortized - with an emphasis on the close connection between the time co Author(s): No creator set
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Classroom Innovations through Lesson Study Classroom Innovations through Lesson Study is an APEC EDNET Project that aims to improve the quality of education in the area of Mathematics. This project is sponsored by APEC Members Japan and Thailand. The APEC-Tsukuba International Conference III was broadcast live from Tokyo, December 9-10, 2007. The project has produced useful papers describing mathematical thinking, lesson videos of classroom instruction.
This project focuses on Lesson Study with the goal of improving the quality of educat Author(s): Creator not set
Personalisation Services for Self e-Learning Networks This paper describes the personalisation services designed for self e-learning networks in the SeLeNe project. A self e-learning network consists of web-based learning objects that have been made available to the network by its users, along with metadata descriptions of these learning objects and of the network's users. The proposed personalisation facilities include: querying learning object descriptions to return results tailored towards users' individual goals and preferences; the ability to Author(s): Keenoy Kevin,Poulovassilis Alexandra,Christophides7.60 Cell Biology: Structure and Functions of the Nucleus (MIT) The goal of this course is to teach both the fundamentals of nuclear cell biology as well as the methodological and experimental approaches upon which they are based. Lectures and class discussions will cover the background and fundamental findings in a particular area of nuclear cell biology. The assigned readings will provide concrete examples of the experimental approaches and logic used to establish these findings. Some examples of topics include genome and systems biology, transcription, an Author(s): Sharp, Phillip,Young, Richard264 GG So Many Questions Today's topic is how to format questions. You think you already know this, don't you? I wonder if you're right. Author(s): No creator set
Stop 10: Josh Cheuse - Run DMC WHO SHOT ROCK & ROLL:
A Photographic History, 1955 to the Present
February 25, 2011 - May 22, 2011
Who Shot Rock & Roll is the first major exhibition on rock and roll to put photographers in the...
Rockets: Educators Guide Few classroom topics generate as much excitement as rockets. The scientific, technological, engineering and mathematical foundations of rocketry provide exciting classroom opportunities for authentic hands-on, minds-on experimentation. The activities and lesson plans contained in this educator guide emphasize hands-on science, prediction, data collection and interpretation, teamwork, and problem solving. The guide also contains background information about the history of rockets and basic rocket Author(s): No creator set
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Reasonable Basic Algebra Reasonable Basic Algebra is:
* An introduction that appeals to the reader's reason rather than to her/his ability to memorize.
* A complete tool for teaching "developmental" students twice a week for 15 weeks.
* A way for adults to learn some mathematics—more or less in the same spirit as mathematicians do.
* A text, with a story-line, written to be read and reread.
* A presentation that pays pedantic attention to the linguistic difficulties the reader is likely to have in Author(s): No creator set
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A Problem Course in Mathematical Logic A Problem Course in Mathematical Logic is intended to serve as the text for an introduction to mathematical logic for undergraduates with some mathematical sophistication. It supplies definitions, statements of results, and problems, along with some explanations, examples, and hints. The idea is for the students, individually or in groups, to learn the material by solving the problems and proving the results for themselves. The book should do as the text for a course taught using the modified Mo Author(s): No creator set | 677.169 | 1 |
Who Should Enroll
Middle school math teachers (Grades 4-8), math interventionists, and math specialists seeking research-based practices to help students improve math achievement scores, practical ideas for motivating students to appreciate mathematics, and strategies to show students how math applies to real-life situations. Learn to apply different technologies to make your math classroom come alive.
You may enroll in this course to meet your goals for professional development, continuing education, license renewal, or to complete graduate credits and transfer to another university.
This course includes investigation of ratio, proportion, percent, number theory, data analysis, patterns; and connections to algebra and geometry topics in the context of the middle school mathematics curriculum including survey of technologies and educational software to develop mathematical thinking.
You will learn advanced teaching strategies and math interventions to help students meet Common Core math standards, improve test scores, and provide for individual needs.
e-Textbook
An e-textbook will be provided when you login to the course. You may open the e-book to read online from your laptop or desktop. The e-textbook software is compatible with an iPad, Kindle Fire or fully internet-capable device. It is not compatible with a Kindle Reader.
Alignment with Teaching Standards
International Society for Technology in Education, National Educational Technology Standards for Teachers (NETS-T) III, V
No travel to campus required. Because this class is online and open to you 24/7, you may participate from your home or work computer during hours that are flexible and convenient for your work and family schedule and responsibilities.
The class is highly interactive with a significant discussion component. All discussion postings, projects, and assignments will be submitted via the course discussion board and Dropbox. Activities are conducted according to a schedule with specific due dates each week; there are no required "live" chat sessions.
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A Faculty Project Course - Best Professors Teaching the World
Every year, people across the United States predict how the field of 65 teams will play in the Division I NCAA Men's Basketball Tournament by filling out a tournament bracket for the postseason play. Not sure who to pick? Let math help you out!
In this course, you will learn three popular rating methods two of which are also used by the Bowl Championship Series, the organization that determines which college football teams are invited to which bowl games. The first method is simple winning percentage. The other two methods are the Colley Method and the Massey Method, each of which computes a ranking by solving a system of linear equations. We also learn how to adapt the methods to take late season momentum into account. This allows you to create your very own mathematically-produced brackets for March Madness by writing your own code or using the software provided with this course.
From this course, you will learn math driven methods that have led Dr. Chartier and his students to place in the top 97% of 4.6 million brackets submitted to ESPN! See more:
What are the requirements?
The software supplied with the course uses Java applets available on the Internet and Java applications that can be run on one's won computer. Your browser or computer must be set up to run such programs.
What am I going to get from this course?
By the end of the course, you will be able to rank sports teams using 3 popular sports ranking methods and create brackets for March Madness.
In this course, you will learn how to rank using winning percentage, the Colley method, and the Massey method, and how to adapt each ranking method to integrate momentum.
What is the target audience?
This course starts with fractions and moves on into linear systems (linear algebra). If you are new to linear algebra, you may or may not find the "more math" lectures helpful on the Colley and Massey methods.
The activities are designed to deepen everyone's knowledge. The software that is supplied does not rely on any knowledge of linear algebra. Put in your numbers for modeling momentum and you are ready to create your sports ranking!
In this course, we will learn to use sports ranking to create math-generated brackets. Our final ranking will inform us as to who is predicted to beat who. This lecture discusses issues in sports ranking such as ranking the entire list and all Division 1 games for a March Madness bracket – not just ranking how the teams in the tournament played each other.
NOTE: Download the slides from the lecture so you can follow and practice alongside the video.
In this lecture, we discuss how to incorporate a model of momentum into the standard winning percentage calculation. In this way, a team on a winning streak going into the tournament can be rewarded in a ranking.
NOTE: Download the slides from the lecture so you can follow and practice alongside the video.
In this activity, you learn to use software to rank NCAA Division I men's basketball teams from different years. You'll use winning percentage and be able to weight the games to create a ranking based on your math model of momentum.
In this lecture, we learn how to form a linear system according to the Massey method, another of the ranking methods of the Bowl Championship Series. This sports ranking method can also be adapted to basketball to create your March Madness bracket.
In this activity, you learn to use software to rank NCAA Division I men's basketball teams from different years. You'll use a method, called the Massey Method, used by the Bowl Championship Series (BCS) to rank college football teams.
In this lecture, we learn to incorporate a model of momentum into the Colley and Massey methods. Such models can produce more robust rankings and allow you to create your own personalized bracket with techniques utilized but the Bowl Championship Series.
In this final activity, you learn to use software to rank NCAA Division I men's basketball teams from different years. You can use winning percentage, the Colley Method or Massey Method. The ability to weight games will enable you to create your own personal bracket.
Instructor Biography
Tim Chartier is an Associate Professor of Mathematics at Davidson College. He is a recipient of a national teaching award from the Mathematical Association of America. Published by Princeton University Press, Tim coauthored Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms with Anne Greenbaum. As a researcher, Tim has worked with both Lawrence Livermore and Los Alamos National Laboratories on the development and analysis of computational methods targeted to increase efficiency and robustness of numerical simulation on the lab's supercomputers, which are among the fastest in the world. Tim's research with and beyond the labs was recognized with an Alfred P. Sloan Research Fellowship.
Tim serves on the Editorial Board for Math Horizons, a mathematics magazine of the Mathematical Association of America. He also on the Advisory Board of YourMusicOn (YMO), a mobile music startup company and the Advisory Council for the Museum of Mathematics, which will be the first museum of mathematics in the United States and opens in December 2012. Tim has been a resource for a variety of media inquiries which includes fielding mathematical questions for the Sports Science program on ESPN. He also writes for the Science blog of the Huffington Post.
As an artist, Tim has trained at Le Centre du Silence mime school and Dell'Arte School of International Physical Theater. He also studied in master classes with Marcel Marceau. Tim has taught and performed mime throughout the United States and in national and international settings.
In his time apart from academia, Tim enjoys the performing arts, mountain biking, nature walks and hikes, and spending time with his family.
Learn more about Prof. Chartier's teaching, research and presentations with mime and math on his blog.
More from Tim Chartier
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Please confirm that you want to add Math is Everywhere: Applications of Finite Math to your Wishlist. | 677.169 | 1 |
Thursday, May 19, 2016
Traditional Logic I Complete Set, published by Memoria Press, is a formal traditional logic course written for 7th grade and up. It doesn't cover the more commonly taught informal logic (informal fallacies), but instead teaches the system of logic taught and studied by the ancient Greeks and later by medieval Christians in their pursuit of truth.
The course includes four components:
The Student Book is the heart of the program. It includes 14 chapters with teaching material and daily exercises.
The Quizzes and Tests Book provides a quiz for each chapter and a final exam.
This is a pretty tough course. It focuses on vocabulary and abstract concepts. Surprisingly Emily has really enjoyed it and it's often the first subject she completes each day. The introduction and each of the 14 chapters begin with 5-6 pages of text in which the topic for the chapter is taught. The text is followed by exercises for 4 days plus a review exercises. The Quizzes and Test book includes a test for each chapter.
The text requires students to think very abstractly about concepts. For example, in the first chapter, the student learns the difference between sensing a chair, holding the mental image of a chair in his mind, and understanding the concept of a chair, even when one is not physically present. Then he reads about the difference between simple apprehension and judgment (affirming something about the chair).
We really liked that the lessons were short. Emily often did more than one lesson in a day. Once she had read the chapter, the lessons often took only a few minutes to complete. (That's probably one reason she liked this course so well!) Each lesson explains the topic well and provides sufficient examples. Although the concepts are abstract, the student is required to learn the definitions and to apply the knowledge in the daily exercises enough times to ensure that it sticks. There is sufficient review from week to week to make sure the student retains the material from earlier chapters.
The recommended grade level for this course is 7th grade and up, but my personal opinion is that it is better suited for high school students. I think that Emily would have been in over her head if she had attempted it in 7th grade! Now that she's older, she is finding the study of logic quite interesting and is enjoying the challenge.
The only component we didn't enjoy was the DVD. Most of the content from the DVD lessons was the same as that found in the text, down to the same examples, so Emily didn't feel that the video lesson helped her. The teacher/author also discussed and answered a few of the actual lesson questions, giving the viewer a head start on the question sets. While many students benefit from having a teacher or video lesson, Emily prefers to read the text and teach herself. She found the presentation style a bit dull as well. If your child benefits from hearing a lesson explained, the DVD set might be useful for you, but we decided that, for us, the course was just fine without it.
Read more about this program and several other Memoria Press products by visiting the Crew Blog below.
The Teacher's Manual explains the benefits of memorization, which include developing confidence, strengthening the mind (including building new neurological pathways), and improving the ability to learn and memorize from any content area. The Teacher's Manual explains how to implement the program and includes 96 poems and speech to memorize, divided into five levels. It also includes explanatory notes or definitions in the margins of many of the selections, short poet biographies, and optional lesson enhancements. Purchase of the Teacher's Manual includes download links for audio MP3's of seven of Pudewa's talks and the e-book version of the Student Book.
The Student Book includes the same selections of poetry. Each poem is on a separate page, many with illustrations. Each level has a chart for keeping track of progress and practice sessions. The Student Book is available spiral-bound as a separate purchase, or may be downloaded free with the purchase of the teacher's guide. (We were given the spiral bound guide for this review, so it was wonderful not to have to print it out!)
The CD/DVD Set includes 6 discs: 5 CD's with the poems read aloud by Andrew Pudewa and one DVD with a talk on "Nurturing Competent Communicators."
Our Experience
Until this year, Emily had done almost no memorization. She has always been rather uncooperative about doing so and I haven't pushed it. Several months ago, she realized that she could memorize, and could do it very easily and has been learning whole chapters of scripture. I knew that the Linguistic Development Through Poetry Memorization program would be enjoyable for her and take advantage of her current interest in memory work.
First, I watched the included DVD, "Nurturing Competent Communicators," which gave me a lot of motivation to incorporate memory work into our lives. This is a talk given by Andrew Pudewa, that explains the importance of good literature to the development of communication skills, including writing. He explains that memorizing good literature, especially poetry, improves focus, helps with building brain connections, improves writing skills, and has many more connections to other learning areas.
We have listened to the first cd several times to become familiar with the poems from Level 1. Later, when I read them, I can "hear" Pudewa's voice and intonation when I read each poem! The first day, Emily memorized the first two poems, "Ooey Gooey" and "Celery." On subsequent days, she skimmed through the poems she had already memorized and studied a new one for about 3-5 minutes. Then she would recite each of the poems that she has memorized thus far. She has already almost completed Level 1. When she starts Level 2, in addition to reciting the Level 2 poems, she will practice the odd numbered Level 1 poems on odd days and the even numbered Level 1 poems on even days. Through Levels 3, 4, and 5, she will continue to practice the poems from earlier levels occasionally to keep them fresh. Each level includes a chart to direct this practice.
The poems for Level One are all poems that would appeal to young children. They are fairly short, easy to understand, and most are funny and rhyme. They are all older poems, so many are familiar, such as Robert Louis Stevenson's "The Swing," and "My Shadow." Others are new favorites for me, such as "The Yak," by Hilaire Belloc.
As a friend to the children, commend me the Yak;
You will find it exactly the think;
It will carry and fetch, you can ride on its back,
Or lead it about with a string.
The Tartar who dwells on the plains of Tibet
(A desolate region of snow),
Has for centuries made it a nursery pet,
And surely the Tartar should know!
Then tell your papa where the Yak can be got,
And if he is awfully rich,
He will buy you the creature—or else he will not
(I cannot be positive which).
Level 1 is a great warm-up for any age because the poems are simple. As the levels progress, the poems become longer and more difficult and will appeal more to older children. Level 4 includes selections like "The Tiger," by William Blake, "The Quality of Mercy" from The Merchant of Venice, by William Shakespeare, and "Lockinvar," by Sir Walter Scott. I am looking forward to Emily reaching the higher levels and at the rate she is progressing, it won't be long. A younger student would be expected to take several years to complete memorization of all 96 poems and speeches.
We have used Linguistic Development through Poetry Memorization solely for memorization. Because Emily is memorizing the poems so quickly and because we otherwise have a very full schedule, that works well for us. For families who want to spend more time with each poem, the Lesson Enhancements in the Appendix include instruction on literary and poetic devices, additional literature tie-ins (such as Treasure Island to go with Robert Louis Stevenson's poems, or At the Back of the North Wind to go with Rosetti's "Who Has Seen the Wind?" Map, art and science activities are suggested for some poems. I think we'll be likely to use more of this resource when we get to the more difficult poems.
Emily has enjoyed using Linguistic Development through Poetry Memorization and I have seen significant results in only 5-10 minutes a day. Although the program is quite simple (and is easy to just pick up and do), having the sequence of poems laid out for us with a practice chart ensures that poetry memorization actually happens! I wish we had discovered the program years ago.
I'm adding this program to my list of IEW programs that I love! If you'd like to read more reviews, visit the crew blog.
Physics Central is an awesome site dedicated to teaching students about physics. Once a year, they send out kits to teachers (including homeschoolers) that include a comic book with a mystery to be solved and all the equipment needed to do several physics-related experiments to solve the mystery. We've done this several years with a group of homeschoolers and really enjoyed the projects.
The Happy Scientist has some fun science videos for free, and a larger selection with membership.
Exploratorium is sponsored by the San Francisco science museum of the same name. You can find hundreds of experiments and learning opportunities here.
Do you have a student interested in forensics? The ACS ChemClub has links to lots of hands-on projects to explore the topic.
ACS also includes learning topics and experiments for all ages of students to help them learn about chemistry.
If you own the Burgess Bird Book for Children, this companion site includes links and activities for each chapter.
Handbook of Nature Study is packed with inspiration and ideas for doing nature study with your children. Many ideas are linked to the book, Handbook of Nature Study, by Anna Botsford Comstock. This could be your science curriculum for a full year!
Thursday, May 12, 2016
What do you look for when choosing a laundry detergent? If you are like me, two qualities are important: It gets my clothes clean and it is easy to use. That's why I like 2 in 1 products like Purex plus Clorox. I save both time and money if I can use one product instead of two.
When I received a free bottle of Purex with Clorox detergent to try, I decided to do a stain test. I took two scraps of fabric and stained them with red clay dirt, coffee, and mustard. I then washed one scrap in a load with Purex with Clorox detergent and the other in a load with store brand detergents. They both did fairly well. The mustard and coffee stains were gone. The red clay was harder. Both fabrics had a small amount of stain left, but the Purex plus Clorox did a better job with the stain. The Purex stain was too faint to show up in the photo, but the generic detergent stain is somewhat visible. The fabric washed in Purex also came out whiter. I know which bottle I'll be reaching for when I have tough loads to wash!
Close-up of remaining stain:
Would you like to win 2 coupons for free bottles of any Purex detergent (up to $7 value each)? Enter here!
Monday, May 9, 2016
Zeezok Publishing LLC sells an amazing music appreciation program called: Music Appreciation Book 1: for the Elementary Grades. This program is written primarily for elementary-aged students, but we found that the quality is so good that it is quite beneficial even up to high school age students.
The program includes 7 biographies of musicians: Bach, Handel, Mozart, Beethoven, Paganini, Schubert, and Hayden. (We started our study with Paganini.) The biographies are older books, written in the 30's, 40's, and 50's by Opal Wheeler and Sybil Deucher. I remember reading some of these books when I was a child! They are wonderfully written, interesting stories, based entirely on the lives of these great classical musicians. Even my 15 year old proclaimed that, "These books are addicting!" The books are heavily illustrated with black and white drawings and each includes several easy pieces of music that children who play the piano could actually play as they learn about each musician!
The student activity book is a hefty, 354 page guide that turns the wonderful children's classics into a curriculum. It includes 4 weeks of activities for each musician, including reading comprehension activities, maps, additional information about each composer, character studies, lessons that teach about the instruments, reading music, elements of music, and musical eras, and even a few period recipes and complementary science experiments. A cd with lapbook printables provides even more hands-on activities for these topics.
Finally, a disc set of cd's features music for all of the composers (including the pieces that are printed in the biographies) and additional music that corresponds to various music appreciation activities in the student activity guide. We really enjoyed listening to this quality music during the day. How We Used Music Appreciation: Book 1 for the Elementary Grades:
Emily is in high school, so she's well outside the target age group (K-6) for this program. I knew that she would still gain a lot from it, though. She did most of the work independently, taking 2 weeks to cover each musician instead of the expected 4 weeks. I allowed her to skip a few activities that were particularly easy, but she completed and benefited from most of the assignments. I thought about having her do additional research on the musicians, but decided that after she had read a biography plus additional information in the workbook for each musician, that I didn't need to require more.
We began with Paganini, the only musician in the set with whom I wasn't familiar. In this study, Emily learned about the diligence required to become excellent at anything, even if you begin with great talent. She learned about Italy, and even made spaghetti soup for dinner one night—one of the dishes mentioned in the biography. She learned some Italian words, listened to a variety of music of her choice and made a chart labeling the style of music, sound quality, and song's message. She learned some musical terminology, read about Napoleon, and compared music from different cultures.
Next, we skipped back to the beginning of the course (because Emily wanted to proceed in order instead of studying the musicians in random order) and began our study of Bach. She enjoyed learning about Bach's large family and his faith, the geography of Germany, and older keyboard instruments, such as the clavichord, harpsichord, spinet, and virginal. She was introduced to the Baroque period, learned about different types of songs, such as fugue, minuet, gavotte, cantata, and bourree, reviewed musical note names, and learned that a recording of Bach's Brandenburg Concerto No. 2 was sent into space aboard the Voyager in 1977.
When Emily studied Handel, she learned about melody and harmony, dynamics, rhythm, and tempo and did exercises to learn the musical terms and symbols to describe these. Much of this was a review of what she has learned in her piano studies. She learned what timbre is and described the timbre of various instruments. She learned a little about the city of Venice and listened to pairs of songs and contrasted the musical styles ( march vs. lullaby, classical vs. folk, etc.) She completed a timeline of historical events that occurred during Handel's lifetime and learned more about his composition of his Messiah. She says that Handel has been her favorite musician so far. (And I am very much enjoying listening to his music!)
I was disappointed that there were only two recordings on the cd's for Paganini. We really enjoyed his music and would have liked to hear more. There were many more pieces for the other musicians, though—as many as 35 for some musicians! We have enjoyed listening to the recordings and immersing ourselves in each artist as we study him. Each of the pieces printed in the composer biographies is included on the cd. The cd's also include other pieces for listening and music appreciation in addition to the focus musicians. We compared styles of music, listened to music from different cultures, and Emily even drew pictures and designs to visually represent some pieces.
Emily has a little bit of piano playing experience, but plays at a very basic level. I am picking out some of the easiest songs from each book for her to learn as she studies the composer. That is probably the most difficult part of the study for her, but she is sticking with the challenge to master these new pieces. I think that learning about the composer, listening to his works and then learning to play one or two makes a rich program. I'm so glad I didn't have to hunt for easy piano music to supplement the curriculum! Music Appreciation: Book 1 for the Elementary Grades is a very impressive and comprehensive programs. I've seen other music appreciation programs that don't begin to cover this scope of information and that don't include recordings. The biographies are wonderful all by themselves, but the full curriculum really adds to them. The depth of the program is enough that I feel good about giving high school credit for it. We plan to use this program toward a music appreciation 1/2 credit course for Emily. At the same time, it is easy to use and simple and colorful enough to engage even children of younger elementary ages.
Thursday, May 5, 2016
As you can probably tell from this blog, I'm a bit of a homeschool curriculum "junkie." There are so many wonderful products available and I love to try out new things! To tell the truth, though, I think some of my favorite homeschooling years were ones when we spent very little money. There really are many resources for homeschooling that cost little or nothing.
There is a bit of a trade-off for free homeschool, though. Generally, you will spend more time putting together a curriculum, searching the library catalogs, and even teaching when you go the "free" route. You could end up with a program that perfectly meets your goals and is as rich as anything you could buy, or you could just end up with "cheap" and substandard. That is why it is important to carefully evaluate your goals and choose materials that will meet them.
Here are some possible resources:
1. The Library—my absolute favorite resource! Your children will have a much richer education if they read "real" books instead of textbooks. You can pick a subject to study, visit the library and come home with a stack of books to browse, read, and study—anything from insects to pyramids! For the early grades, I love the Five in a Row curriculum. Many of the required books and supplements are available at most libraries, so all you need is the manual and you are ready to go! You can even put together your own phonics/reading program. Libraries usually have sets of phonetic readers (like the Bob Books) that help you teach your child to decode words in a sequential manner, one phoneme at a time.
2. Notebooking is a great way to solidify learning and to keep records. Just have your children draw or write about the topics in those great books that they borrowed from the library (see above) and keep their pages in a binder. You don't need all those workbooks—notebooking is a fine way to learn and to document your learning. If you need some inspiration, sites like notebookingpages.com offer a variety of free pages.
3. Easy Peasy All-In-One Homeschool has a program laid out for homeschooling preschool through high school, all using free internet resources. Course include "extras" like art, foreign language, and PE in addition to core classes. If you want something that's "open and go" and fully planned, this might be perfect for you.
4. Kahn Academy has full math programs and many resources in other subjects as well. Content in non-math subjects is more geared for middle schoolers and up, but even your little ones could do math here. If you sign up for a teacher account, you can direct your child's learning and monitor their progress.
5. I've found many free Spanish Resources:
Salsa is a series of Spanish videos for younger children featuring puppets.
Destinos is a video series and course for high school students and above. The videos are free online, as are computer-based practice activities. You can make this into a full 2-year course with the addition of the text and workbook, which I found on Amazon for about $3 each. (We're using the cheaper first edition, which works just fine.)
Mi Vida Loca also has videos and teaching activities for Spanish. We haven't tried this one yet, but it looks like a lot of fun!
StudySpanish.com is a great resource for learning basic concepts and grammar. Because it offers direct instruction and grammar charts, it's also helpful as a resource for quickly looking something up, such as how to conjugate a verb in a particular tense.
Duolingo offers free instruction in many different languages. It's also available as an app for mobile devices. I've used this and it's fun!
6. Want to teach geography? These sites have free map games that will have you naming off countries in no time!
7. We've been watching CNN Student news each day and have found this 10 minute show a great way to help teens learn about current events. Since I'm not a regular news watcher myself, it helps me keep abreast of what's happening in the world as well.
This list is really just the tip of the iceberg of free resources, but I hope that you can find some useful resources here and get inspired to search for more!
Monday, May 2, 2016
I've been making and selling mermaid tails for swimming on Etsy for a few years now, but I'm happy to announce that my Mystic Cove Mermaid store now has its own website! My fabric mermaid tails can be used with or without a monofin and are fun for swimming, dress-up, or bathtub play. (Swimming in deep water is recommended for strong swimmers only and with adult supervision.)
Tails can be used with or without a monofin. The bottoms are partially open to allow walking. Please visit my website to learn more!
Enter below to win your choice of a MERMAID TAILAND TOP ($50 value) or an American Girl DOLL MERMAID SET ($20 value).
Don't want to wait for the contest to end? The Mystic Cove Mermaid website isn't currently set up to take coupons, but you can use the coupon code "DEBHSC" on my Etsy shop for a 20% discount on mermaid tails or doll sets.
Wednesday, April 27, 2016
They Say We Are Infidels, by Mindy Belz offers a close-up look at the persecution of Christians in the Middle East and the rise of Isis. Belz has been a foreign correspondent for World magazine for over 25 years, so she has a first hand look at the tensions in the Middle East. This book shares her experiences visiting Iraq and Syria from shortly after 9/11 to the present.
When Belz visited Iraq and Syria, she didn't stay in the safe zones as many reporters do. She traveled from city to city, meeting with and staying with Christians in different areas and learning about their experiences. She describes life under Saddam Hussein, the hope and increased freedom in the midst of the material devastation after the Iraq war, then the increasing persecution and attacks on Christians as radical Islamists pushed their way into power in the new government.
Personally, I have never had a good grasp of Middle East conflict. Mainstream news covers the conflicts, but recently, I've been wondering about the causes of these conflicts, the extent of Muslim hatred toward Christians and the West and whether there are any solutions toward peace in our time. I was surprised by what I learned. Although we don't hear much about Christians who live in the Middle East, this area was the birthplace of Christianity and there are still churches that date back to well before Islam began. Ten years ago, the Iraqi population was 10% Christian, although that number is rapidly approaching zero because of ISIS' goal of creating a pure Islamic state. Many of the Christians who have been forced to leave simply wanted to live in their homeland side by side with their moderate Muslim neighbors. It was heartbreaking to read about the devastation that non-Muslims have faced and about the role the U.S. had in this by removing Saddam Hussein and the Baathist government, but failing to put forth the leadership that might have prevented ISIS and other radical Islamists from filling the vacuum. I can't say that this was a hope-filled book, but it gave me a vivid picture of the situation. Education is the first step in effecting change.
They Say We Are Infidels is a "must-read" for anyone who wants to learn more about Islam, ISIS, and the Middle East. I will definitely be sharing my copy with family and friends.
I received a free copy of these book from Tyndale House Publishers in exchange for my honest review. All opinions are my own.
Tuesday, April 26, 2016
Over the past year or so, I have loved trying out several different products from Koru Naturals, including emu oil, manuka honey propolis soap, skin clear cream, and emu oil shampoo and conditioner. While I enjoyed all of these products, my absolute favorite has been the emu oil. Since my initial review, I have purchased several more bottles, both for myself, and to give away.
While I have no problem with using animal products, many people do, so emu oil would be something they would not want to use. Because of this, Devonian has created a new type of beauty oil called GREEMU that has very similar composition to emu oil, but is made entirely of plant oils. (GREEMU is also distributed by Koru Naturals.)
My GREEMU oil arrived in a 4 oz. green bottle. I expect, from my experience with emu oil, that the bottle will last a long time since I only need a few drops per application!
My primary use for GREEMU oil was as a facial lotion. I spread a few drops over my face every morning and evening. It soaked in quickly and left my face feeling very soft and moisturized. Although it is an oil, it didn't make my face break out or feel oily because it absorbed so nicely. Occasionally, I smoothed a few drops into the ends of my hair as a conditioning treatment. I had to be careful here—a little bit does go a long way! It leaves my skin so soft and works as well as any expensive wrinkle cream I've used.
I compared my Koru Naturals emu oil and the GREEMU by using the emu oil on the back of my left hand and the GREEMU oil on my right. The GREEMU oil was a bit thinner without the slightly creamy texture of the emu oil. It also took just a bit longer to absorb into the skin. Both worked very well for moisturizing, though. I also thought the oil was wonderful for my dry feet-rubbing it in before bed left my feet well moisturized the next day.
A year ago (before I discovered emu oil), I would have been very wary of the concept of putting oil on my face, but I have fallen in love with both these products (emu oil and GREEMU) and their ability to moisturize and soften my skin. I still would give a slight edge to emu oil, but really like both of them.
Monday, April 25, 2016
I've read several articles lately about Finnish schools. The schools in Finland are some of the top performing schools in the world, yet their approach to education is opposite to that of the U.S or Asia. School days are short, children do not even begin formal education until age 7, outdoor play is an important part of the school day, and little or no standardized testing is done. Children are allowed to be children. They are expected to have fun at school and the teachers trust that they will learn when ready. It sounds like they let kids be kids instead of pushing them to do more and more.
Finnish schooling seems similar to the philosophy of many homeschoolers. I've been picking up some additional ideas for our homeschool, though. For example, craft time is an essential part of the school experience. And "craft time" doesn't mean cutting, coloring, and gluing paper! Even in elementary school, children are learning to use sewing machines, knit, crochet, cook, and to use power tools. Not only are they learning practical life skills, but they are using academic skills in real life by measuring and figuring out problems as they create useful items. Teaching Emily some of these skills (or finding people who can teach her) is one of my goals for her last few years of high school. But now I'm thinking that it would have been a great idea to have started teaching life skills much younger!
One trend in Finnish schools is "teaching by topic," or incorporating all of the subjects into one topical theme….sounds like unit studies to me! It's funny that schools are just "discovering" the advantages of something that homeschoolers have been doing for years!
It seems that few children are "left behind" in Finland because any child who struggles, including immigrants and those with learning disabilities, get the attention they need to keep up with the group. On the other end of the spectrum, though, there isn't a lot of support for gifted or advanced students because of the country's focus on equality rather than achievement.
I think a lot of Finland's child-friendly techniques would be wonderful in American schools (that are heading in the opposite direction), but at least we homeschoolers are free to individualize our children's learning, teaching what our children need when they need it and fostering a love to learn. I've linked several articles above in case you want to learn more.
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I am a speech pathologist and homeschooling mom of four. I enjoy writing about my family and homeschooling. I am the author of the Super Star Speech series of books and blog about speech and language topics at
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"Say goodbye to dry presentations, grueling formulas, and abstract theory that would put Einstein to sleep--now there's an easier way to master chemistry, biology, trigonometry, and geometry. McGraw-Hill's Demystified Series teaches complex subjects in a unique, easy-to-absorb manner and is designed for users without formal training, unlimited time, or genius IQs. Organized like self-teaching guides, they come complete with key points, background information, questions at the end of each chapter, and final exams. There's no better way to gain instant expertise! ABOUT GEOMETRY DEMYSTIFIED: * Will help users understand circle and triangle models; inverses of circular functions; graphs of functions; coordinate conversions; angles and distances; waves and phase; complex numbers; vectors; trigonometry in 3-space, and much more " | 677.169 | 1 |
MATLAB
Resources on the 'K:' drive
• Now, you may find some books and notes
about MATLAB for beginners and for experts
on the 'K:' drive under the folder name
"MATLAB E-Books"
4.
Introduction to MATLAB
What is MATLAB ?
MATLAB started as an interactive program for
doing matrix calculations and has now grown
to a high level mathematical language that
can solve integrals and differential equations
numerically and plot a wide variety of two and
three dimensional graphs. MATLAB also
contains a programming language.
5.
Introduction to MATLAB
How to get started?
Command Window
Work Space
Command History
9.
Introduction to MATLAB
The order of operations
• If you are using brackets, that will save you a
lot of effort!
• However, the operators have precedence!
1. "( )" brackets
2. "^" Power
3. "* /" Multiplication and division
4. "+ -" Addition and subtraction
10.
Introduction to MATLAB
Variable names
• Variable may have names that consist of
characters and digits, but they can not start
with a number!
• Matlab distinguishes between lower and
upper cases - so A and a are different objects
• Only the first 19 characters in a variable name
are important.
11.
Introduction to MATLAB
Try this!
• You have just created two vectors, x & y!
• Now try some operations on them! (multiply
by a constant, use sin(x), sqrt(x), exp(x), …
23.
Introduction to MATLAB
Solving Equations!
• Now we may use the tools we have to solve a
system of equations!
• If we have the equations:
• Just transform it into matrix form!
632
892
735
=++
=+−
=−+
zyx
zyx
zyx | 677.169 | 1 |
Izolda Fotiyeva
I thought this book would be light reading, and hopefully I would come across some interesting word problems and clever ways to approach them that I could use in my own classes. Indeed the book is full of a large variety of word problems, over hundred of them are solved in detail, and several of them are quite fun for someone who enjoys a little math with her warm drink of choice. Nonetheless, I confess that when I put the book down, it left an unpleasant aftertaste.
The book is well-organized, (mostly) well-written and doubtlessly intended for an audience that does not include me. So my reaction to it will certainly not be the reaction of the student who picks this book up with the hope to find shortcuts and simple algorithms to attack the diverse word problems that he has to face and solve using algebra. For the student who is looking for the shortcuts and the clear-cut simplistic explanations, the book might be just appropriate and it may even be helpful.
The few Amazon reviews so far have been quite positive, and are indeed truthful: the book is quite successful at providing a structure to the seemingly chaotic zoo of word problems, by classifying them into several categories depending on their main context. Thus a student who has difficulty with problems involving liquid solutions can immediately find where to go, while the students who only care about work problems (those problems that involve a task that can be done by different people at different rates) do not have to wade through much before they find their way to the relevant section. And the book is quite exhaustive; going over standard high school textbooks, I cannot easily come up with a word problem that will not fit into one of these categories.
However the idealist in me cringed a bit every time I turned the page to start a new chapter that addressed a new collection of problems. What troubled me is what the publisher of this book promotes as its main strength: All the problems are nicely classified into these well-defined packages. By dividing and conquering in this manner, the book helps the student to attack a problem by first identifying its type and then using the appropriate tools provided for that type. But in this way the book also allows the student to lose track of the whole, the underlying goal of word problems: to develop the student's ability to extract the information that is given that can be represented best by a mathematical equation or two and actually come up with that representation. A student who reads the book from beginning to the end and who actually thinks along the way may in fact comprehend this beautiful and powerful fact, but my hunch is that that rare student would benefit from just about any other book containing a large collection of word problems. By creating this unnatural classification of the word problems it handles, the book does a disservice to the whole genre. Divide and conquer, sure, but don't take out its soul along the way.
This is most likely not the author's fault. In fact at each juncture you hear her voice, you get the sense that you are conversing with a caring, compassionate and competent teacher who is on your side, who wants you to succeed, who goes out of her way to simplify things for you as much as possible.
"Make things as simple as possible, but no simpler," said Einstein; the author does not always follow him on that latter part. For instance in the part on percentages the reader is told explicitly that "You can't change a fraction to a percent directly. First change a fraction into a decimal and then change the decimal into a percent" (p. 90). Thus the student loses the opportunity to see that problems may be attacked in multiple ways, that there are several different representations of the same ratio, and much more urgently that you can indeed convert certain fractions directly into a percent easily — especially if the denominator is a divisor of 100, this is in fact quite simple.
Dividing up word problems into neat little categories is counterproductive if the end goal is not only that the student pass an exam but also that he gain some understanding of the way numerical data can be embedded in written language and some experience working out the translation between the text and the mathematical representation. I say a lot more on this issue, tying word problems to the more general and urgent issue of quantitative literacy, in a paper of mine, so I will now step down from that soapbox.
All in all, the gist of this review is that the book was slightly disappointing. I think I will go and see if I can find the author's other book, Math with Mom; I have a feeling I will like that one… | 677.169 | 1 |
The new feature, the Euclidean Fountain, allows users to perform an action to both sides of the equation. The fountain will facilitate the problem solving process by users who wish to simplify problems by performing an action to both sides of the equation.
Algebra Touch features:
* Appropriate for learning or reviewing of algebra
* For students of any age
* Drag to rearrange, click to simplify, and draw lines to eliminate identical terms
* Distribute by clicking and sliding, Factor Out by dropping terms on one another
* Easily switch between lessons and randomly generated practice problems
* Users may create their own sets of problems
* Topics include: Simplification, Like Terms, Commutativity, and Order of Operations
* Additional topics: Factorization, Prime Numbers, Elimination, and Isolation
* Advanced topics: Variables, Solving Equations, Distribution, Factoring Out, and Substitution
Other iOS apps by Regular Berry Software include Long Division Touch, an educational app for learning and practicing long division problems. The app can supplement classroom lessons by adding a guided method of practicing and exploring long division principles. By providing instant feedback the app simplifies and reinforces how to solve long division problems.
Regular Berry Software is an educational app software company. Their goal is to reveal to students that math problems are just puzzles, and can be fun if you know the rules. Copyright (C) 2012 Regular Berry Software LLC. All Rights Reserved. Apple, the Apple logo, iPhone, iPod and iPad are registered trademarks of Apple Inc. in the U.S. and/or other countries. | 677.169 | 1 |
Math Refresher
This course is designed for people who are perhaps mathphobic or who have been away from math for a long time and are interested in refreshing their math skills - for college placement tests, both undergraduate and graduate, for GRE and GMAT prep courses and exams, and other professional or educational endeavors.
The course offers an intense, fast paced review of the fundamentals of arithmetic, algebra, and geometry. Included in the course are basic math operations, word problems, graphs, linear and quadratic equations, formula solving and manipulation and the basic concepts of geometry and their applications.
Students will be introduced to the language of math and many shortcuts will be presented. When possible, courses are scheduled in advance of our GMAT and GRE prep course offerings for those students who are taking the exams. However, it must be emphasized that this course is not designed solely for those going on to graduate school and it is not a strategy class.
Register early. Enrollment is limited.
To register online
Click on box to the right of of the course and click on orange button "Continue Registering" at the bottom of page. | 677.169 | 1 |
Undergraduate Program:
Prospective Students
Northwestern offers a variety of ways to study mathematics.
The MENU program (Mathematical Experience for Northwestern Undergraduates)
is a special program for entering freshmen with strong mathematical skills
who are interested in mathematics, either for its own sake or because of
its powerful and broad applications. It offers such students the
opportunity to expand their mathematical knowledge while retaining
flexibility about their ultimate major. People in this program can start
with either the Math 290-1,2,3 or the more theoretical Math 291-1,2,3.
See the MENU webpage for more information. | 677.169 | 1 |
This course covers the study of indefinite integrals, applications of integration, techniques of integration, and an introduction to differential equations. A graphing calculator is required.
Prerequisite
Prerequisite: MATH& 151 with a grade of C or higher.
Additional Course Details
Contact Hours (based on 11 week quarter)
Lecture: 55
Lab: 0
Other: 0
Systems: 0
Clinical: 0
Intent:Distribution Requirement(s) Status:
Academic
Natural Sciences, Quantitative
Equivalencies At Other Institutions
Other Institution Equivalencies Table
Institution
Course #
Remarks
CWU
172.2
OTHER
Meets GUR at 3 BIS
U of W
125 T
WSU
172 T
WWU
125 T
Learning Outcomes
After completing this course, the student will be able to:
Compute definite and indefinite integrals.
Find areas bounded by two curves.
Find volumes of revolution.
Calculate moments, centers of mass and centroids.
Solve problems involving logarithmic functions: growth and decay.
Integrate trigonometric functions.
Use various techniques of integration: partial fractions, substitution, integration by parts, etc.
Use tables of integration.
Use numeric integration.
Find arc length.
Solve applied problems using integration.
Solve separable differential equations.
Apply alternative mathematical techniques, from a historical perspective where appropriate.
Understand how mathematics is used in other fields and occupations.
Understand the use of mathematics cross-culturally.
General Education Learning Values & Outcomes
Revised August 2008 and affects outlines for 2008 year 1 and later.
2. Critical Thinking
Definition:
The ability to think critically about the nature of knowledge within a discipline and about the
ways in which that knowledge is constructed and validated and to be sensitive to the ways these
processes often vary among disciplines. | 677.169 | 1 |
The Humongous Book of SAT Math Problems (PagePerfect NOOK Book)OverviewThe Humongous Book of SAT Math Problems takes a typical SAT study guide of solved math problems and provides easy-to-follow margin notes that add missing steps and simplify the solutions, thereby preparing students to solve all types of problems that appear in both levels of the SAT math exam.
Related Subjects
Meet the Author
W. Michael Kelley is an award-winning former math teacher and author of seven math books, including the very successful Humongous Book series. His method of making intimidating math topics very approachable, even humorous, has helped students and adults alike conquer their fear of numbers. Kelley taught high school mathematics for 7 years before leaving to work at the University of Maryland College Park Education College. After serving as the director of teacher preparation at the American Board for Certification of Teacher Excellence for nearly 10 years, he now works for Laureate Education, developing online coursework for colleges and universities. Author home: Prince Frederick, MD. | 677.169 | 1 |
This module introduces the learner to a particular mathematical approach to analysing real life activity that focuses on making specific decisions in constrained situations. The approach, called linear programming, is presented here with an emphasis on appreciation of the style of thinking and interpretation of mathematical statements generated, rather than on computational competency per se, which is left to appropriate and readily available ICT software package routines.
The module begins with Unit One that consists of 2 main Activities. Activity 1, formulation of a linear programming problem, is on a mathematical description of the problematic situation under consideration, and Activity 2, the geometrical approach considers a visual description of a plausable solution to the problem situation. Unit 1 therefore should move the learner towards an appreciation of real-life activity situations that can be modelled as linear programming problems.
With 3 main activities, Unit 2 considers computational algorithms for finding plausible optimal solutions to the linear programming problem situations of the type formulated in Unit 1. Activity 3 examines conditions for optimality of a solution, which is really about recognising when one is moving towards and arrives at a candidate and best solution. Activity 4 discusses the centre piece of computational algebraic methods of attack, the famed Simplex algorithm. This module focuses on the logic of the algorithm and the useful associated qualitative properties of duality, degeneracy, and efficiency. The final Activity touches on the problem of stability of obtained optimal solutions in relation to variations in specific input or output factors in the constraints and objective functions. This so called post optimality or sensitivity analysis is presented here only at the level of appreciation of the analytic strategies employed.
In addition to downloading the files below, you can also view them directly: | 677.169 | 1 |
9780395888 second-level text in an innovative workbook series, Introductory Algebra: An Integrated Approach is ideal for the first-year developmental arithmetic and pre-algebra instructor seeking to accommodate individual teaching and learning styles. Aufmann and Lockwood present math as a cohesive subject by weaving the themes of number sense, logic, geometry, statistics, and probability throughout the text at increasingly sophisticated levels. These themes are illustrated by applications from more than 100 disciplines. | 677.169 | 1 |
The Prentice Hall Algebra 1 curriculum introduces the basic concepts and properties of algebra along with numerous practice and problem solving exercises. Homeschoolers, please note: the textbook references a number of online elements on a website, including videos, online assignments, interactive activities, vocabulary definitions, and more. Access to this website is not included, or available to homeschoolers. The course can be used without these components. Grade 9/Algebra 1 provides instruction on the foundations of algebra, solving equations, solving inequalities, functions, linear functions, systems of equalities and inequalities, exponents and exponential functions, polynomials and factoring, quadratic functions and equations, radical expressions and equations, rational expressions | 677.169 | 1 |
Syllabus
1. Review: read Chapters 0 and 1; attempt all exercises in them.
2. Exponential and trigonometric Functions: read Chapter 2 and do
exercises.
3. The dot product and matrices. Read Chapter 3 through 3.7 and
do exercises.
4. The determinant and the cross product. Assignment tba.
5. Vectors and geometry.
6. Review and take home quiz.
31. Numerical integration of ordinary integrals and line integrals.
32. Stokes and divergence theorem.
33. Reducing area and surface integrals to multiple integrals and the Jacobian.
34. Doing area surface and volume integrals.
35. Series.
36. Review and take home examination. | 677.169 | 1 |
Forum for Science, Industry and Business
The Aftermath of Calculator Use in College Classrooms
13.11.2012
Students may rely on calculators to bypass a more holistic understanding of mathematics, says Pitt researcher
Math instructors promoting calculator usage in college classrooms may want to rethink their teaching strategies, says Samuel King, postdoctoral student in the University of Pittsburgh's Learning Research & Development Center.
King has proposed the need for further research regarding calculators' role in the classroom after conducting a limited study with undergraduate engineering students published in the British Journal of Educational Technology.
"We really can't assume that calculators are helping students," said King. "The goal is to understand the core concepts during the lecture. What we found is that use of calculators isn't necessarily helping in that regard."
Together with Carol Robinson, coauthor and director of the Mathematics Education Centre at Loughborough University in England, King examined whether the inherent characteristics of the mathematics questions presented to students facilitated a deep or surface approach to learning. Using a limited sample size, they interviewed 10 second-year undergraduate students enrolled in a competitive engineering program. The students were given a number of mathematical questions related to sine waves—a mathematical function that describes a smooth repetitive oscillation—and were allowed to use calculators to answer them. More than half of the students adopted the option of using the calculators to solve the problem.
"Instead of being able to accurately represent or visualize a sine wave, these students adopted a trial-and-error method by entering values into a calculator to determine which of the four answers provided was correct," said King. "It was apparent that the students who adopted this approach had limited understanding of the concept, as none of them attempted to sketch the sine wave after they worked out one or two values."
After completing the problems, the students were interviewed about their process. A student who had used a calculator noted that she struggled with the answer because she couldn't remember the "rules" regarding sine and it was "easier" to use a calculator. In contrast, a student who did not use a calculator was asked why someone might have a problem answering this question. The student said he didn't see a reason for a problem. However, he noted that one may have trouble visualizing a sine wave if he/she is told not to use a calculator.
"The limited evidence we collected about the largely procedural use of calculators as a substitute for the mathematical thinking presented indicates that there might be a need to rethink how and when calculators may be used in classes—especially at the undergraduate level," said King. "Are these tools really helping to prepare students or are the students using the tools as a way to bypass information that is difficult to understand? Our evidence suggests the latter, and we encourage more research be done in this area."
King also suggests that relevant research should be done investigating the correlation between how and why students use calculators to evaluate the types of learning approaches that students adopt toward problem solving in mathematics | 677.169 | 1 |
Teaching with Maple
by Reid M. Pinchback
Academic Computing Services, MIT
onsider
the following situation:
Take a room and draw a line down the middle of it. Fill the room with
mathematics instructors. Open up the discussion with "should we use
computer algebra systems (CAS) for teaching freshman math classes?".
What do you get? Division.
This is a scenario that has begun to replay itself in schools not just
all over the country, but literally all over the world. Some view the
development of CAS as a great opportunity, claiming it will remove the
drudgery of educationally contentless algebraic manipulation, and thus
provide the chance to explore mathematical issues that were infeasible
to address in the classroom before. Others see a great danger that
students will become mathematically illiterate, will treat these
software tools as though they are perfectly implemented black boxes,
and will end up with little or no understanding of the mathematics that
those black boxes purport to implement.
Which side of the debate is correct? As with all difficult social
questions, the answer is both and neither. The optimistic viewpoint
lets us see what we have to gain by the journey, and the pessimist
viewpoint shows us the pit-falls that we must either avoid or bridge
across if we are to come through the endevour safely. In other words,
we need to find a position between the extremes were we get the most
of the good and the least of the bad. For now we will defer
discussion of the wonderful possibilities and instead examine some of
the dangers in order to better understand and hopefully avoid them.
One of the most frequent issues that comes up in these discussions
are concerns over the fabled "black boxes". Black boxes are bad,
black boxes are evil, we cannot have black boxes or students won't
learn anything... or will they? Let us take a closer look at this
concept of a black box.
By a box we roughly mean a process that has inputs given to it and which
then outputs some results or a behaviour of some sort. We call a box
black when it is opaque and we can't see what is going on inside. We
hope that the right thing is happening, but often we don't know for sure.
Programmers deal with black boxes all the time by using subroutines,
libraries, and programs written by other people. As long those tools
work properly and we know how to use them, we rarely concern ourselves
with the internal workings. This leads to efficiency of work.
This is a good thing.
In mathematics when we have a black box, then there are mathematical
concepts hidden inside. If students can't see the internal workings
then they may not learn those mathematical concepts intrinsic to the
implementation of the black box. Students may work at assignments
efficiently, but since learning the math is the true objective, the
efficiently-performed work could be to little purpose. This is a bad
thing.
Consider, however, an extreme alternative perhaps reflective of the
current state of affairs. If we give students large volumes of the
relatively simple problems suitable for manual algebraic manipulation,
they may learn a few skills thoroughly by brute force repetition, but
never have the time to tackle the more interesting and worthwhile
mathematical issues. How many times have students cried "don't show
me the proof, show me how to do the homework assignment"? Lots of
work is done, some skills might be learned (at least until the final
exam is over and done with), but the level of true mathematical
understanding achieved can be minimal. This is also a bad thing.
Obviously we need some way to move forward. Consider for a moment a
typical two-semester freshman calculus sequence, where students deal
with the usual collection of topics in differentiation, limits,
integration, and series. What gets taught in these classes? Maybe a
little real and complex analysis, some topology, formal logic,
Gödel-Bernays set theory... Hold on a second, those topics aren't
taught in freshman calculus! They aren't taught, but they do
underlay the simpler mathematical concepts that are being taught.
In other words, we treat the more formal and rigorous mathematics as
black boxes, if not explicitly, then by unmentioned assumption. We
use the black boxes to hide confusing complexity from students when
they aren't ready for it. This allows instructors to teach high-level
concepts, just like black-box subroutines allow programmers to write
high-level software code. Thus, black boxes are not inherently bad
things, in fact they are a necessary fact of educational life.
The idea I am putting forward is this: mathematics instruction has
always contained black boxes, and they are not inherently bad things.
In fact, much of the process of designing any kind of course can be
viewed as deciding which black boxes to present and which to ignore
the existence of. If we now accept the idea that black boxes can be
good things, namely when they provide us with useful abstractions and
help us to maintain a focus on the topics that we really want to
teach, when do black boxes become bad things? Here are a few
possibilities:
When students are denied access to the inside of a black box.
Consider the Maple routine int, which provides
symbolic definite and indefinite integration capabilities. This can
be a convenient way of quickly integrating functions, but it is the
ultimate in an undesireable black box with respect to the objective of
teaching freshman calculus. If this were the only functionality
available, then a CAS like Maple would be of no use in teaching such a
subject. What we really need is the ability to rip the cover off of
int and let students see the pieces of it in action.
With Maple we have such options: in this case we can use the
student package to perform smaller steps in problem
solving, for example by using the intparts routine for doing
integration by parts. For other situations instructors are exploring
the Maple worksheet interface as a mechanism for presenting the steps
in an algorithm, instead of just providing pre-written subroutines as
a fait accompli. Students modify portions of the worksheet for a
given problem and step their way through the algorithm, and are thus
more involved with the CAS-based presentation of the material.
When students don't understand how the black box works even when
it is opened.
This is perhaps one of the most important things that educators and
administrators must realize when considering the use of a CAS for
teaching. Just because you have a piece of software, even a really
good piece of software with lots of online help available, students
still need a teacher to help them understand a subject. The teacher
knows from experience which black boxes are important to open, how to
explain what the internal contents are, and explain why those contents
were put there in the first place. A teacher provides context,
relevance, and detailed as-need explanations. A piece of software
just does whatever it is told to do. This may seem an obvious
statement, but was been a source of problems in attempts to use the
technologies lumped under the label Computer Aided Education. To put
it in simple terms, if you expect your students to use Maple and learn
something, then you need to be sure that you are prepared to help and
guide them through that process.
When students never have reason to care about the internal workings of
a box containing concepts critical to a subject.
Obviously if we give students simple questions, then they will use the
most convenient Maple routines to quickly generate simple answers.
Instructors will have the chance to become more creative in their
design of assignments, replacing simple problems:
"integrate the following function"
with more challenging ones:
"integrate the following function both by parts and by partial fractions,
showing the steps used and intermediate results. Discuss which method was
more effective and why. If the results aren't the same fix the mistake or
explain the difference."
While it will take effort to rethink the design of assignments in this
way, the potential exists for giving fewer or at least less repetitive
assignments that will require students to really think about what they
are doing. If students aren't expected to spend their time in mechanical
algebraic manipulations, they can shift their efforts towards learning
more interesting content than ever was possible before.
This is a good thing.
Originally published in the Athena Insider, Volume 5 Issue 3
Copyright 1994 Massachusetts Institute of Technology
Last modified: 94/10/26
(reidmp@mit.edu) | 677.169 | 1 |
Out of PrintWith examples of all 450 functions in action plus tutorial text on the mathematics, this book is the definitive guide to Experimenting with Combinatorica, a widely used software package for teaching and research in discrete mathematics. Three interesting classes of exercises are provided--theorem/proof, programming exercises, and experimental explorations--ensuring great flexibility in teaching and learning the material. The Combinatorica user community ranges from students to engineers, researchers in mathematics, computer science, physics, economics, and the humanities. Recipient of the EDUCOM Higher Education Software Award, Combinatorica is included with every copy of the popular computer algebra system Mathematica.
The definitive guide to the latest version of the Combinatorica software, included with every copy of Mathematica, with new functionality, significantly improved performance, and advanced graphics
Reviews & endorsements
"This book is the definitive reference guide to Combinatorica -- an extension of the popular computer software, Mathematica -- with examples of the 450 combinatorics functions. The authors developed the newest version of this software that has dramatic improvements in graphical processing performance, representation, visualization, and many brand new functions...This book is highly recommended. It is a well organized and readable textbook for beginners and intermediate students."
Leonardo
Look Inside
Authors
Sriram Pemmaraju, Indian Institute of Technology, Bombay, and University of Iowa
Steven Skiena, State University of New York, Stony Brook Steven Skiena is Distinguished Teaching Professor of Computer Science at Stony Brook University. His research interests include the design of graph, string, and geometric algorithms, and their applications (particularly to biology). He is the author of five books, including The Algorithm Design Manual and Calculated Bets: Computers, Gambling, and Mathematical Modeling to Win. He is co-founder and Chief Scientist at General Sentiment ( a media measurement company based on his Lydia text/sentiment analysis system. Skiena received his PhD in Computer Science from the University of Illinois in 1988, and is the author of over 130 technical papers. He is a former Fulbright scholar, and a recipient of the ONR Young Investigator Award and the IEEE Computer Science and Engineer Teaching Award | 677.169 | 1 |
4/23Numerical Methods
Student Solutions Manual for Faires/Burden's Numerical Methods, 4th
Student Solutions Manual for Faires/Burdenís Numerical Methods, 3rd
Summary
NUMERICAL METHODS, Fourth Edition emphasizes the intelligent application of approximation techniques to the type of problems that commonly occur in engineering and the physical sciences. Readers learn why the numerical methods work, what kinds of errors to expect, and when an application might lead to difficulties. The authors also provide information about the availability of high-quality software for numerical approximation routines. The techniques are the same as those covered in the authors' top-selling Numerical Analysis text, but this text provides an overview for students who need to know the methods without having to perform the analysis. This concise approach still includes mathematical justifications, but only when they are necessary to understand the methods. The emphasis is placed on describing each technique from an implementation standpoint, and on convincing the reader that the method is reasonable both mathematically and computationally. | 677.169 | 1 |
Math Course Takes 'Real Life' Approach to Algebra
Educational courseware publisher American Education Corp. is taking a new approach to answering the age-old question, "What does algebra have to do with real life?" The company has announced the release of a new course for its A+nyWhere Learning System program. Algebra I: A Function Approach Part 1 is the first semester segment of a full-year algebra course geared to grades 9 and 10, and, in addition to the fundamental concepts and tools of algebra, the course aims to relate the material to "real life."
Taking the fundamentals and applying them to real-world situations using exercises in relevant scenarios allows students to realize the practical uses of linear and quadratic equations, graphs and coordinates, functions, and other algebraic concepts.
The A+nyWhere program is computer based, so students taking courses like Algebra I can use a number of tools incorporated into the software to aid in their assignments and overall comprehension of the material. These tools include onscreen standard and scientific calculators, pictures and diagrams, video tutorials, exercises, practice exams, and, for upper-level courses, interactive feedback | 677.169 | 1 |
Back toschoolnight
3.
Connecting to the Real World● Algebra is about finding the unknown. It is about putting real life problems into equations and solving them.I will help your students connect Algebra to thereal world.
5.
Why We Love Algebra● Algebra encourages students to use both inductive and deductive reasoning.● Algebra encourages the student to recognize patterns.● Algebra creates critical thinkers for the 21st century.
7.
Word Problem of the WeekAnalyze Effectively.Synthesize and Make Connections.Solve different kinds of non-familiar problems inboth conventional and innovative ways.Identify and ask significant questions.
8.
Project - Create a Math ComputerGameNear the end of the year, students will create amath computer game using algebraic concepts.It will be a group project that will involveworking creatively with others.They will receive feedback from lower grades toimprove and maximize their creative efforts.
9.
Remember"The essence of mathematics is not to makesimple things complicated, but to makecomplicated things simple." S. Gudder | 677.169 | 1 |
Algebra is an abstract language. Success with algebra involves understanding the symbols and grammar of algebra, as well as the concepts of algebra. But students have different learning styles. Some students may need a concrete, hands-on approach. Some do well even with an abstract approach, provided it is presented clearly and logically | 677.169 | 1 |
Jerry:
Bill is right. Need to look at more of the test to make a good judgment and answer your question.
However: YES, math is different than arithmetic. Most arithmetic is used in math and therefore a necessary basic.
Joe Bo | 677.169 | 1 |
Details about Intermediate Algebra:
For use in secondary schools this text includes graphing and functions early to make a clear distinction between intermediate and beginning algebra. It emphasizes real-world mathematics applications throughout.
Back to top
Rent Intermediate Algebra 4th edition today, or search our site for other textbooks by K. Elayn Martin-Gay. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Pearson.
Need help ASAP? We have you covered with 24/7 instant online tutoring. Connect with one of our Algebra tutors now. | 677.169 | 1 |
WIRIS cas
WIRIS cas is an online platform for mathematical calculations designed for education. You can access a powerful calculation toolbar through an HTML page that includes integrals and limits calculation, function graphing in 2D or 3D and symbolic matrices manipulation, among others.
WIRIS cas covers all mathematical topics from primary school to university level (Calculus, Algebra, Geometry, Differential Equations...). | 677.169 | 1 |
This booklet includes 19 problems that explore the topic of radiation and human exposure to its different forms. The problems span math abilities from basic multiplication and unit conversions, to algebra and calculus. For example, students learn about the various natural radiation dosages to which they are exposed daily, work quantitatively with authentic radiation dosage units to estimate the total annual dosages resulting from different lifestyles, and determine probabilities of occurrence for flares and other radiation events in space. Math skills include graph analysis, Venn diagramming, probability and statistics, evaluating equations in more than one variable, extrapolation and forecasting, scientific notation, integral calculus. (8.5 x11, 28 pages, 11 color images, PDF file) | 677.169 | 1 |
Student Resources
Course Information
Course Information Mathematics and Statistics
The Department of Mathematics and Statistics offers a variety of courses to:
prepare students to enter graduate school,
teach at the elementary and secondary level,
understand and use mathematics in other fields of knowledge with basic mathematical skills for everyday living, and
be employed and to act in a consulting capacity on matters concerning mathematics.
To satisfy the core requirements for graduation, students have the option to take one of two courses. Please visit the link for more information on our core mathematics courses.
Core Mathematics Courses Some students are required to begin in our Pre-Core Mathematics course. (Beginning in Fall 2012, we will no longer offer two separate developmental courses Elementary Algebra and Intermediate Algebra.) Please view the link for more information on our pre-core mathematics course.
Pre-Core Mathematics Courses For a complete listing of our courses, please view the link for our entire list of undergraduate courses in mathematics and statistics. | 677.169 | 1 |
The Pre-Algebra Problems are designed for those students who are consolidating and practicing their knowledge of basic mathematics skills and who are beginning to prepare for algebra. The problems cover approximately the same materials as the NCTM Standards for Grades 6-8.
Math Fundamentals, difficulty level 2. Sophie tells the truth only on Monday, Tuesday, Wednesday, and Thursday. Her sister tells the truth only on Monday, Friday, Saturday, and Sunday. If they both confess to their mom that "Yesterday I lied," what day is it today?
... more>> | 677.169 | 1 |
Find a Gainesville, GA Algebra 1
...This algebra deals mostly with linear functions. Algebra 2 is a more advanced, more complex version of algebra 1. Here we get more involved with non-linear functions as well as imaginary and complex numbers. | 677.169 | 1 |
MatheAss means Mathematical Assistant and that's exactly what this program is designed to be. It's for secondary level or high school students and teachers and anybody else who has anything to do with mathematics.
This software allows working with times tables and mental calculation on a 3D race. During the race, signposts and direction signs show operations to solve. The racer has to solve them to continue the race
A two players mode allows to have more fun!
Rt-Plot is a tool to generate Cartesian X/Y-plots from scientific data. You can enter and calculate tabular data. View the changing graphs, including linear and non linear regression, interpolation, differentiation and integration, during entering. | 677.169 | 1 |
Product Description
A comprehensive teacher resource for middle level math that includes hands-on activities which promote an investigative approach, helping students arrive at a deeper understanding of geometric concepts. Includes teacher's notes, solutions, and glossary. 48 pages. Grades 6-10.
Prices listed are U.S. Domestic prices only and apply to orders shipped within the United States.
Orders from outside the United States may be charged additional distributor, customs, and shipping charges. | 677.169 | 1 |
Details about Geometry:
This second edition effectively prepares education students, elementary or secondary school teachers, or college instructors to teach geometry. It can also serve as a useful reference for anyone in these fields. This book can also serve as a textbook in an elementary plane geometry course having an investigative emphasis. The text explores geometric concepts inductively first and then presents deductive proof. Students are encouraged to explore geometric ideas using constructions, laboratory materials, and various other investigative techniques. The text promotes student interaction by emphasizing small group investigation. This edition helps teachers implement the latest NCTM standards by addressing the development of critical thinking, the use of technology to explore geometric relationships, the use of geometry as a medium for problem solving, and the importance of applications in geometry.
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Rent Geometry 2nd edition today, or search our site for other textbooks by Phares G. O'Daffer. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Pearson. | 677.169 | 1 |
Master Algebra Lite
This is for students in High School/College learning algebra. If you are a beginner in algebra you might be thinking X+Y=XY, Is not it? But it's not.
The beauty of algebra is, it deals with variables, expressions & equations. You will come to know various formulas.
For example if you know (a+b)^3= a^3+b^3+3a^2b+3ab^2.
You can calculate any number to the powers 2,3,4…in a fraction of seconds.
In the above equation a ,b are variables. So you can calculate (1.034)^3 also using that formula. Just feed a=1& b=.034
IMathPractice Algebra's 3 steps method of teaching has sections like Tutorial, Practice Skills, Practice Test & Algebra Challenge. Under tutorial it teaches you.
Numbers
Types of Number like real number, integer, negative number, complex number
Addition, Subtraction, Multiplication & Division of Real Number
Addition, Subtraction, Multiplication & Division of Negative Number
Addition, Subtraction, Multiplication & Division of Complex Number
Properties of Number | 677.169 | 1 |
Matrices (the plural of matrix) are a convenient way of organizing linear functions and systems of equations. Before you can move on to the higher-math applications of matrices, you have to master the basic methods of solving matrices. Your first introduction to solving matrices will probably be using them to solve systems of equations, using basic algebraic operations"Reduced row form" means that any numbers may be in the rightmost column, but the rest of the entries in any given row consist of a single "1" entry accompanied by as many zeroes as necessary to fill the rest of the spaces.
In reduced row form, order the rows so that the "1" entries like up in a rightward, downward diagonal line. So the first line of the matrix might be "1 0 0 24," the second line "0 1 0 46," and the third line "0 0 1 5."
2
Switch any 2 rows in the matrix to make performing the other operations easier, or to arrange the "1" entries properly in reduced row form. This doesn't affect the overall value of the matrix.
You must swap the 2 lines completely, with no intermingling of the numbers for each row. So for example if you had a matrix with entries "3 12 2" in the first row and "4 6 3" in the second row, you could swap "4 6 3" to be the first row and "3 12 2" to be the second row. But you couldn't swap just 1 or 2 of the elements from each row.
Method 1
Row Addition and Subtraction
1
Combine the elements of any 2 matrix rows by adding and subtracting them. This creates a third row (the result), which you then substitute for 1 of the original 2 rows.
Add and subtract each element individually, working your way across the row. So if you were to add the rows "3 12 2" and "4 6 3," the resulting new row would be "7 18 5."
The results row must replace 1 of the rows you just used to create it; you cannot arbitrarily add a new row to the matrix and keep the other rows unchanged.
Method 2
Scalar Matrix Multiplication
1
Multiply every element of a given row by the same scalar.
As long as you multiply each element in the row by the same scalar, you don't actually change the value of the matrix. But scalar multiplication can make performing the other matrix row operations easier. For example, if you have the rows "2 5 3" and "-1 2 9," multiplying the second row by 2 is the perfect setup for then adding the resulting rows together. The scalar multiplication gives you "-2 4 18," which when added to the first row yields "0 9 21." If you then scalar multiply the resulting row by 9, you have "0 1 (21/9)", and this row is prepared for reduced row form. | 677.169 | 1 |
(4)
Relationship between equations and functions. Equations arise as a way of
asking and answering questions involving functional relationships. Students
work in many situations to set up equations and use a variety of methods to
solve these equations.
(5) Tools
for algebraic thinking. Techniques for working with functions and equations are
essential in understanding underlying relationships. Students use a variety of
representations (concrete, numerical, algorithmic, graphical), tools, and technology, including,
but not limited to, powerful and accessible hand-held calculators and computers
with graphing capabilities and model mathematical situations to solve
meaningful problems.
(d)
Quadratic and other nonlinear functions: knowledge and skills and performance
descriptions.
3) The
student understands there are situations modeled by functions that are neither
linear nor quadratic and models the situations. Following are performance
descriptions.
(A) The
student uses patterns to generate the laws of exponents and applies them in
problem-solving situations.
So, which salary would you take right now, Miranda's or the rookie's?† Why?
Thinking a million dollars is
going to be way more than double the amount from year to year, they choose Miranda's.†
††††††††††††††††††††††††††††††††††††††††††††††† †††
Explore:
Handout the problem and divide the students into groups.
Walks around, monitoring the
progress of the groups.
Shows them how to make a
graph using Excel.†
†††††
Describe the graphs in your group.†
Students break into groups
and get into Excel.
Enter the data into Excel
giving titles where needed.†
See and compare the graphs.
††††
Explain:
As a class, we come together and answer the questions.
What
is Miranda's salary in year 15?† What is the rookie's?
In
which year does the rookie's salary overtake Miranda's?
At
the end of 25 years, who received the most money?
What
is Miranda's salary in year n?† What is the rookie's?†† What is Miranda's
total at n years?†† Rookie's?
Read and explain their
answers.
15, 000,000
16,384
In year 21.
The rookie
M=1,000,000
R=2^n
m=1,000,000n
r=∑ i=1n 2n† (they would be able to write this but they
should be able to explain it comparing to how they got Miranda's
total)
†††††††††††††††††††††††††††††††††††††††††††††††
Extend / Elaborate:
Teacher asks other questions not on
paper.
††††††
So, now whose salary would
you pick? What if you only planned to play 10 years?† 20 years?†
30 years?† Why?†††
What kind of function does
Miranda's salary represent?† The rookie's?
What is a general
statement that you can make about exponential and constant functions?†
The Rookie's.
Miranda's.
Miranda's.
The Rookie's?
Constant.
Exponential.
†††
† Evaluate:
Give other problems using that same
kind of scenario.† Have the groups do each of their assigned problems and then present and explain them.
†
Students
work on the problems and present to the class.
Percent
effort each team member contributed to this lesson plan:
___%___†††††† ____Name of group
member_____________________
___%___†††††† ____Name of group
member_____________________†††††††††††
Name_________________________
Miranda and the Rookie
Miracle Miranda plays for the
California Hoops basketball team. After the Hoops won the WNBA championship,
the manager offered her a million dollars a year for the next 25 years,
whereas a new rookie for the same team was given $1 the first year, $2 the
second year, $4 the third year, and so on, for the next 25 years. | 677.169 | 1 |
applied approach to calculas
1.
CHAPTER 0 Review *This chapter consists of review material. It may be used as the first part of the course or later as ajust-in-time review when the content is required. Specific references to this chapter occur throughoutthe book to assist in the review process.
2.
0.1 Real NumbersPREPARING FOR THIS SECTION Before getting started, review the following:OBJECTIVES 1 Classify numbers 2 Evaluate numerical expressions 3 Work with properties of real numbersSetsWhen we want to treat a collection of similar but distinct objects as a whole, we use the idea of a set. Forexample, the set of digits consists of the collection of numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. If we use thesymbol D to denote the set of digits, then we can writeIn this notation, the braces { } are used to enclose the objects, or elements, in the set. This method ofdenoting a set is called the roster method . A second way to denote a set is to use set-builder notation,where the set D of digits is written asread as "D is the set of all x such that x is a digit." EXAMPLE 1 Using Set-Builder Notation and the Roster Method (a) E = { x | x is an even digit} = {0, 2, 4, 6, 8} (b) O = { x | x is an odd digit} = {1, 3, 5, 7, 9}In listing the elements of a set, we do not list an element more than once because the elements of a set aredistinct. Also, the order in which the elements are listed is not relevant. For example, {2, 3} and {3, 2}both represent the same set.If every element of a set A is also an element of a set B, then we say that A is a subset of B. If two sets Aand B have the same elements, then we say that A equals B. For example, {1, 2, 3} is a subset of {1, 2, 3,4, 5}, and {1, 2, 3} equals {2, 3, 1}.Finally, if a set has no elements, it is called the empty set , or the null set , and is denoted by the symbolØ.
3.
Classification of NumbersIt is helpful to classify the various kinds of numbers that we deal with as sets. The counting numbers, ornatural numbers, are the numbers in the set {1, 2, 3, 4, …}. (The three dots, called an ellipsis , indicatethat the pattern continues indefinitely.) As their name implies, these numbers are often used to countthings. For example, there are 26 letters in our alphabet; there are 100 cents in a dollar. The wholenumbers are the numbers in the set {0, 1, 2, 3, …}, that is, the counting numbers together with 0. The integers are the numbers in the set {…, −3, −2, −1,0,1,2,3, …}.These numbers are useful in many situations. For example, if your checking account has $10 in it and youwrite a check for $15, you can represent the current balance as −$5.Notice that the set of counting numbers is a subset of the set of whole numbers. Each time we expand anumber system, such as from the whole numbers to the integers, we do so in order to be able to handlenew, and usually more complicated, problems. The integers allow us to solve problems requiring bothpositive and negative counting numbers, such as profit/loss, height above/below sea level, temperatureabove/below 0°F, and so on.But integers alone are not sufficient for all problems. For example, they do not answer the question"What part of a dollar is 38 cents?" To answer such a question, we enlarge our number system to includerational numbers. For example, answers the question "What part of a dollar is 38 cents?" A rational number is a number that can be expressed as a quotient of two integers. The integer a is called the numerator , and the integer b, which cannot be 0, is called the denominator . The rational numbers are the numbers in the set { where a and b, b ≠ 0, are integers}.Examples of rational numbers are , , , , and . Since for any integer a, it follows that theset of integers is a subset of the set of rational numbers.Rational numbers may be represented as decimals. For example, the rational numbers , , , andmay be represented as decimals by merely carrying out the indicated division:Notice that the decimal representations of and terminate, or end. The decimal representations ofand do not terminate, but they do exhibit a pattern of repetition. For , the 6 repeats indefinitely;for , the block 06 repeats indefinitely. It can be shown that every rational number may be representedby a decimal that either terminates or is nonterminating with a repeating block of digits, and vice versa.
4.
On the other hand, there are decimals that do not fit into either of these categories. Such decimalsrepresent irrational numbers. Every irrational number may be represented by a decimal that neitherrepeats nor terminates. In other words, irrational numbers cannot be written in the form , where a and b,b ≠ 0, are integers.Irrational numbers occur naturally. For example, consider the isosceles right triangle whose legs are eachof length 1. See Figure 1. The length of the hypotenuse is , an irrational number. FIGURE 1Also, the number that equals the ratio of the circumference C to the diameter d of any circle, denoted bythe symbol π (the Greek letter pi), is an irrational number. See Figure 2. FIGURE 2 Together, the rational numbers and irrational numbers form the set of real numbers.Figure 3 shows the relationship of various types of numbers. FIGURE 3
6.
SOLUTION (a) 10 is the only natural number. (b) −3 and 10 are integers. (c) and 10 are rational numbers. (d) and π are irrational numbers. (e) All the numbers listed are real numbers. NOW WORK PROBLEM 3.ApproximationsEvery decimal may be represented by a real number (either rational or irrational), and every real numbermay be represented by a decimal.The irrational numbers and π have decimal representations that begin as follows:In practice, decimals are generally represented by approximations. For example, using the symbol ≈ (readas "approximately equal to"), we can writeIn approximating decimals, we either round off or truncate to a given number of decimal places. Thenumber of places establishes the location of the final digit in the decimal approximation. Truncation: Drop all the digits that follow the specified final digit in the decimal. Rounding: Identify the specified final digit in the decimal. If the next digit is 5 or more, add 1 to the final digit; if the next digit is 4 or less, leave the final digit as it is. Now truncate following the final digit.
7.
EXAMPLE 3 Approximating a Decimal to Two PlacesApproximate 20.98752 to two decimal places by (a) Truncating (b) RoundingSOLUTIONFor 20.98752, the final digit is 8, since it is two decimal places from the decimal point. (a) To truncate, we remove all digits following the final digit 8. The truncation of 20.98752 to two decimal places is 20.98. (b) To round, we examine the digit following the final digit 8, which is 7. Since 7 is 5 or more, we add 1 to the final digit 8 and truncate. The rounded form of 20.98752 to two decimal places is 20.99. EXAMPLE 4 Approximating a Decimal to Two and Four Places Rounded to Rounded to Truncated to Truncated to Two Decimal Four Decimal Two Decimal Four Decimal Number Places Places Places Places (a) 3.14159 3.14 3.1416 3.14 3.1415 (b) 0.056128 0.06 0.0561 0.05 0.0561 (c) 893.46125 893.46 893.4613 893.46 893.4612
8.
NOW WORK PROBLEM 7.CalculatorsCalculators are finite machines. As a result, they are incapable of displaying decimals that contain a largenumber of digits. For example, some calculators are capable of displaying only eight digits. When anumber requires more than eight digits, the calculator either truncates or rounds. To see how yourcalculator handles decimals, divide 2 by 3. How many digits do you see? Is the last digit a 6 or a 7? If it isa 6, your calculator truncates; if it is a 7, your calculator rounds.There are different kinds of calculators. An arithmetic calculator can only add, subtract, multiply, anddivide numbers; therefore, this type is not adequate for this course. Scientific calculators have all thecapabilities of arithmetic calculators and also contain function keys labelled ln, log, sin, cos, tan, x y , inv,and so on. Graphing calculators have all the capabilities of scientific calculators and contain a screen onwhich graphs can be displayed.For those who have access to a graphing calculator, we have included comments, examples, and exercisesmarked with a , indicating that a graphing calculator is required. We have also included an Appendixthat explains some of the capabilities of a graphing calculator. The comments, examples, andexercises may be omitted without loss of continuity, if so desired.OperationsIn algebra, we use letters such as x, y, a, b, and c to represent numbers. The symbols used in algebra forthe operations of addition, subtraction, multiplication, and division are +, −, ·, and /. The words used todescribe the results of these operations are sum, difference, product, and quotient. Table 1 summarizesthese ideas. TABLE 1 Operation Symbol Words Addition a+b Sum: a plus b Subtraction a−b Difference: a minus b Multiplication a· b, (a)· b, a·(b), (a)·(b), ab, (a)b, a(b), (a)(b) Product: a times b Division a/b or Quotient:a divided by bWe generally avoid using the multiplication sign × and the division sign ÷ so familiar in arithmetic. Noticealso that when two expressions are placed next to each other without an operation symbol, as in ab, or inparentheses, as in (a)(b), it is understood that the expressions, called factors , are to be multiplied.We also prefer not to use mixed numbers.When mixed numbers are used, addition is understood; forexample, means . The use of a mixed number may be confusing because the absence of an
9.
operation symbol between two terms is generally taken to mean multiplication. The expression istherefore written instead as 2.75 or as .The symbol =, called an equal sign and read as "equals" or "is," is used to express the idea that thenumber or expression on the left of the equal sign is equivalent to the number or expression on the right. EXAMPLE 5 Writing Statements Using Symbols (a) The sum of 2 and 7 equals 9. In symbols, this statement is written as 2 + 7 = 9. (b) The product of 3 and 5 is 15. In symbols, this statement is written as 3 · 5 = 15. NOW WORK PROBLEM 19.Order of Operations2 Evalute numerical expressionsConsider the expression 2 + 3 · 6. It is not clear whether we should add 2 and 3 to get 5, and then multiplyby 6 to get 30; or first multiply 3 and 6 to get 18, and then add 2 to get 20. To avoid this ambiguity, wehave the following agreement. We agree that whenever the two operations of addition and multiplication separate three numbers, the multiplication operation will be performed first, followed by the addition operation.For example, we find 2 + 3 · 6 as follows: EXAMPLE 6 Finding the Value of an ExpressionEvaluate each expression. (a) 3 + 4 · 5 (b) 8 · 2 + 1
11.
Rules for the Order of Operations 1. Begin with the innermost parentheses and work outward. Remember that in dividing two expressions the numerator and denominator are treated as if they were enclosed in parentheses. 2. Perform multiplications and divisions, working from left to right. 3. Perform additions and subtractions, working from left to right. EXAMPLE 8 Finding the Value of an ExpressionEvaluate each expression. (a) 8 · 2 + 3 (b) 5 · (3 + 4) + 2 (c) (d) 2 + [4 + 2 · (10 + 6)]SOLUTION (a) (b)
12.
(c) (d) NOW WORK PROBLEMS 37 AND 45.Properties of Real NumbersWork with properties of real numbersWe have used the equal sign to mean that one expression is equivalent to another. Four importantproperties of equality are listed next. In this list, a, b, and c represent numbers. 1. The reflexive property states that a number always equals itself; that is, a = a. 2. The symmetric property states that if a = b then b = a. 3. The transitive property states that if a = b and b = c then a = c. 4. The principle of substitution states that if a = b then we may substitute b for a in any expression containing a.Now, let's consider some other properties of real numbers.We begin with an example. EXAMPLE 9 Commutative Properties (a)
13.
(b)This example illustrates the commutative property of real numbers, which states that the order in whichaddition or multiplication takes place will not affect the final result. Commutative Properties (1a) (1b)Here, and in the properties listed next and on pages 10–13, a, b, and c represent real numbers. EXAMPLE 10 Associative Properties (a) (b)The way we add or multiply three real numbers will not affect the final result. So, expressions such as2 + 3 + 4 and 3 · 4 · 5 present no ambiguity, even though addition and multiplication are performed on onepair of numbers at a time. This property is called the associative property . Associative Properties (2a) (2b)
14.
The next property is perhaps the most important. Distributive Property (3a)The distributive property may be used in two different ways. EXAMPLE 11 Distributive Property NOW WORK PROBLEM 63.The real numbers 0 and 1 have unique properties. EXAMPLE 12 Identity Properties (a) 4 + 0 = 0 + 4 = 4 (b) 3 · 1 = 1 · 3 = 3The properties of 0 and 1 illustrated in Example 12 are called the identity properties . Identity Properties (4a) (4b)We call 0 the additive identity and 1 the multiplicative identity.For each real number a, there is a real number − a, called the additive inverse of a, having the followingproperty:
15.
Additive Inverse Property (5a) EXAMPLE 13 Finding an Additive Inverse (a) The additive inverse of 6 is −6, because 6 + (−6) = 0. (b) The additive inverse of −8 is −(−8) = 8, because −8 + 8 = 0.The additive inverse of a, that is, − a, is often called the negative of a or the opposite of a. The use ofsuch terms can be dangerous, because they suggest that the additive inverse is a negative number, which itmay not be. For example, the additive inverse of −3, namely −(−3), equals 3, a positive number.For each nonzero real number a, there is a real number , called the multiplicative inverse of a, havingthe following property: Multiplicative Inverse Property (5b)The multiplicative inverse of a nonzero real number a is also referred to as the reciprocal of a. EXAMPLE 14 Finding a Reciprocal (a) The reciprocal of 6 is , because . (b) The reciprocal of −3 is −3, because . (c) The reciprocal of is , because .
16.
With these properties for adding and multiplying real numbers, we can now define the operations ofsubtraction and division as follows: The difference a − b, also read " a less b" or " a minus b," is defined as (6)To subtract b from a, add the opposite of b to a. If b is a nonzero real number, the quotient , also read as " a divided by b" or "the ratio of a to b," is defined as (7) EXAMPLE 15 Working with Differences and Quotients (a) 8 − 5 = 8 + (−5) = 3 (b) 4 − 9 = 4 + (−9) =−5 (c)For any number a, the product of a times 0 is always 0. Multiplication by Zero (8)For a nonzero number a, we have the following division properties.
18.
(11) EXAMPLE 17 Using the Cancellation Properties (a) If 2x = 6, then (b)NOTE: We follow the common practice of using slash marks to indicate cancellations. Zero-Product Property (12) EXAMPLE 18 Using the Zero-Product PropertyIf 2x = 0, then either 2 = 0 or x = 0. Since 2 ≠ 0, it follows that x = 0. Arithmetic of Quotients (13) (14)
19.
(15) EXAMPLE 19 Adding, Subtracting, Multiplying, and Dividing Quotients (a) (b) (c) NOTE: Slanting the cancellation marks in different directions for different factors, as shown here, is a good practice to follow, since it will help in checking for errors. (d)NOTE: In writing quotients, we shall follow the usual convention and write the quotient in lowest terms;that is, we write it so that any common factors of the numerator and the denominator have been removedusing the cancellation properties, Equation 11. For example,
20.
NOW WORK PROBLEMS 47, 51, AND 61.Sometimes it is easier to add two fractions using least common multiples (LCM). The LCM of twonumbers is the smallest number that each has as a common multiple. EXAMPLE 20 Finding the Least Common Multiple of Two NumbersFind the least common multiple of 15 and 12.To find the LCM of 15 and 12, we look at multiples of 15 and 12.SOLUTION 15, 30, 45, 60, 75, 90, 105, 120, … 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, …The common multiples are in blue. The least common multiple is 60. EXAMPLE 21 Using the Least Common Multiple to Add Two FractionsFind:SOLUTIONWe use the LCM of the denominators of the fractions and rewrite each fraction using the LCM as acommon denominator. The LCM of the denominators (12 and 15) is 60. Rewrite each fraction using 60 asthe denominator. NOW WORK PROBLEM 55.
22.
11. 0.0629112. 0.0538813. 9.998514. 1.000615.16.17.18.In Problems 19–28, write each statement using symbols.19. The sum of 3 and 2 equals 5.20. The product of 5 and 2 equals 10.21. The sum of x and 2 is the product of 3 and 4.22. The sum of 3 and y is the sum of 2 and 2.23. 3 times y is 1 plus 2.
27.
77. Explain why 2(3 · 4) is not equal to (2 · 3) · (2 · 4).78. Explain why is not equal to .79. Is subtraction commutative? Support your conclusion with an example.80. Is subtraction associative? Support your conclusion with an example.81. Is division commutative? Support your conclusion with an example.82. Is division associative? Support your conclusion with an example.83. If 2 = x, why does x = 2?84. If x = 5, why does x2 + x = 30?85. Are there any real numbers that are both rational and irrational? Are there any real numbers that are neither? Explain your reasoning.86. Explain why the sum of a rational number and an irrational number must he irrational.87. What rational number does the repeating decimal 0.999 | 677.169 | 1 |
Electronic edition of a major revision of the popular Beginner's Guide to Mathematica Version 2. An ideal first book for anyone getting started with Mathematica, or interested in finding out about it. Contains advanced chapters on the new features in Version 3, including complete listings of front end programming functions. The electronic edition allows you to see all graphics in full color, see animations move, and listen to sounds. If the reader has Mathematica, every example in the book can be changed so that extensive experimentation is possible without the hassle of copying complicated functions. In all there are 70 chapters. A traditional paper version of this book will be published by Cambridge University Press in October 1997. | 677.169 | 1 |
willThis course offers an introduction to the polynomial method as applied to solving problems in combinatorics in the last...
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This course offers an introduction to the polynomial method as applied to solving problems in combinatorics in the last decade. The course also explores the connections between the polynomial method as used in these problems to the polynomial method in other fields, including computer science, number theory, and The Polynomial Method | Mathematics to your Bookmark Collection or Course ePortfolio
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This course offers an introduction to the finite sample analysis of high- dimensional statistical methods. The goal is to...
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This course offers an introduction to the finite sample analysis of high- dimensional statistical methods. The goal is to present various proof techniques for state-of-the-art methods in regression, matrix estimation and principal component analysis (PCA) as well as optimality guarantees. The course ends with research questions that are currently open. You can read more about Prof. Rigollet's work and courses on his website High-Dimensional Statistics | Mathematics to your Bookmark Collection or Course ePortfolio
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The goal of this class is to prove that category theory is a powerful language for understanding and formalizing common...
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The goal of this class is to prove that category theory is a powerful language for understanding and formalizing common scientific models. The power of the language will be tested by its ability to penetrate into taken-for-granted ideas, either by exposing existing weaknesses or flaws in our understanding, or by highlighting hidden commonalities across scientific fields996 Category Theory for Scientists | Mathematics to your Bookmark Collection or Course ePortfolio
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The subject of enumerative combinatorics deals with counting the number of elements of a finite set. For instance, the number...
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The subject of enumerative combinatorics deals with counting the number of elements of a finite set. For instance, the number of ways to write a positive integer n as a sum of positive integers, taking order into account, is 2n-1. We will be concerned primarily with bijective proofs, i.e., showing that two sets have the same number of elements by exhibiting a bijection (one-to-one correspondence) between them. This is a subject which requires little mathematical background to reach the frontiers of current research. Students will therefore have the opportunity to do original research. It might be necessary to limit enrollment66 The Art of Counting | Mathematics to your Bookmark Collection or Course ePortfolio
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This course, which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for...
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This course, which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates34 Problem Solving Seminar | Mathematics to your Bookmark Collection or Course ePortfolio
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The purpose of the class is to expose undergraduate and graduate students to the mathematical concepts and techniques used in...
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The purpose of the class is to expose undergraduate and graduate students to the mathematical concepts and techniques used in the financial industry. Mathematics lectures are mixed with lectures illustrating the corresponding application in the financial industry. MIT mathematicians teach the mathematics part while industry professionals give the lectures on applications in finance with Applications in Finance | Mathematics to your Bookmark Collection or Course ePortfolio
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This is a mostly self-contained research-oriented course designed for undergraduate students (but also extremely welcoming to...
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This is a mostly self-contained research-oriented course designed for undergraduate students (but also extremely welcoming to graduate students) with an interest in doing research in theoretical aspects of algorithms that aim to extract information from data. These often lie in overlaps of two or more of the following: Mathematics, Applied Mathematics, Computer Science, Electrical Engineering, Statistics, and / or Operations Research of Data Science | Mathematics to your Bookmark Collection or Course ePortfolio
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Find a PhoenixThis material usually is the real difference between more computational/numerical problems to a more sophisticated understanding of mathematics. I have covered basic mathematics, algebra, and trigonometry for many years. Also, the application of algebra to higher mathematics is a really important skill to have. | 677.169 | 1 |
Current Media Coverage
Online education will be the focal point of the Maple T.A. User Summit in Amsterdam. Discussions at the Summit will revolve around trends and evolutions in e-learning, and how technical courses such as science and math can benefit from online tools.
The latest version of Maple T.A. brings full functionality to tablets, new question types for technical assessment, updates to the connectivity features to allow a seamless integration into course management systems, as well as a number of other features.
Incorporating customer feedback from students, instructors, and administrators, Maple T.A. 10 improves upon Maplesoft's powerful online testing and assessment system designed especially for STEM courses. Increased scope, usability, and flexibility for testing and assessment online are just a few of the enhancements made to Maple T.A. 10.
The rise of technology brings good news to instructors responsible for assessing student performance: their burden is getting lighter. Computers offer features that a paper-and-pencil test cannot, such as multi-part answers or interacting with graphs. Paul DeMarco, director of development at Maplesoft, discusses how Maple T.A. can be used to ease the load of the instructor.
Computers are able to now simulate problems in science and engineering at much more rapid rate and with a higher degree of accuracy than "exact methods" could ever hope for. Most problems are so complex today, that they are not amenable to anything other than a numerical solution. In this 20th anniversary edition of Scientific Computing World, Jim Cooper discusses the role of mathematics in both traditional and non-traditional sectors of industry.
This blog post serves as a sound overview of Clickable Calculus as discussed by Dr. Robert Lopez in a recent webinar. Clickable Calculus allows students to explore the finer points of mathematics using computer algebra software such as Maple, without having to invest time to learn commands.
Mathematics is at the core of all the technical disciplines, no matter the size or complexity of the problems they solve. A wide range of organizations are using mathematics to solve problems critical to their business. As engineers, scientists, and mathematicians look to the future, they are seeking solutions and tools that help them find better and more efficient ways to work. The CEO of Maplesoft, Jim Cooper, discuss how mathematics have played an integral part in technological advances over the last 20 years.
Machine-to-machine, or M2M, is a type of design that often eliminates human interaction. Such devices are becoming increasingly used in tasks that require them to operate more autonomously and in conjunction with other devices. Simulation has become the starting point to design and implement these embedded networks. MapleSim and Maple allow engineers and system designers to create communications designs.
The Maplesoft Engineering Solutions group recently announced that revenue has now exceeded $10 Million. Past projects have included a robotic arm for drilling mines, a motion platform for driving simulators, a torsional vibration analysis tool for marine drivelines, batteries for hybrid-electric vehicles, and dialysis machines.
Maplesoft has sponsored the 2014 SEE Math Camp, which takes place at Texas A&M University for two weeks in July. Sixth, seventh and eighth graders are taking part in this summer educational enrichment program for students gifted in mathematics and science. Students are learning to write and crack code with Maple, as well as design computer animations. The students who have created the top animations at the end of the two weeks will win copies of Maple 18.
Maplesoft recently announced that the consulting services offered by the Maplesoft Engineering Solutions group has exceeded $10 million. The Maplesoft Engineering Solutions team provides assistance where it is most needed, whether they offer consulting during one or more phases of a project, provide a complete turn-key solution, or equip engineers with software tools to meet their daily challenges. | 677.169 | 1 |
Introduction to Abstract Algebra, 4th Edition
Books
". . . an expository masterpiece of the highest didactic
value that has gained additional attractivity through the various
improvements . . ."—Zentralblatt MATH
The Fourth Edition of Introduction to Abstract Algebra
continues to provide an accessible approach to the basic structures
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and permutations before the abstract structures are defined.
Readers can immediately begin to perform computations using
abstract concepts that are developed in greater detail later in the
text.
The Fourth Edition features important concepts as well as
specialized topics, including:
The treatment of nilpotent groups, including the Frattini and
Fitting subgroups
Symmetric polynomials
The proof of the fundamental theorem of algebra using symmetric
polynomials
The proof of Wedderburn's theorem on finite division rings
The proof of the Wedderburn-Artin theorem
Throughout the book, worked examples and real-world problems
illustrate concepts and their applications, facilitating a complete
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notes and biographies of mathematicians provide context for and
illuminate the discussion of key topics. A solutions manual is also
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Introduction to Abstract Algebra, Fourth Edition is an
excellent book for courses on the topic at the upper-undergraduate
and beginning-graduate levels. The book also serves as a valuable
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engineering, computer science, and applied mathematics | 677.169 | 1 |
Algebra 2
Algebra 2 makes you learn the basics of Equations, Inequalities, Linear equations, Matrices, Determinants, Quadratic equations and factoring equations. This is one of the important phase of study to get more acquainted with the subject knowledge. | 677.169 | 1 |
Details about Basic College Mathematics:
Aimed at students in a developmental mathematics program, this textbook covers basics such as whole numbers, fractions, decimals, ratio and proportion, percent, and measurement. It also provides an introduction to basic algebra and geometry and touches on statistics. The volume begins with a diagnos
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Rent Basic College Mathematics 6th edition today, or search our site for other textbooks by Margaret L. Lial. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Addison-Wesley Longman, Incorporated. | 677.169 | 1 |
Fourier Analysis - Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to Fourier analysis, which studies approximations and decompositions of functions using trigonometric
polynomials. Of incalculable value in many applications of analysis, this field has grown to include many specific and powerful results, including convergence criteria, estimates and inequalities, and existence and uniqueness results. Extensions include the theory of singular integrals, Fourier transforms, and the study of the appropriate function spaces. Also approximations by other orthogonal families of functions, including orthogonal polynomials and wavelets. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus.
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An Introduction to Wavelets - Amara Graps; Institute of Electrical and Electronics Engineers, Inc.
A paper giving an overview of wavelets: mathematical functions that cut up data into different frequency components, and then study each component with a resolution matched to its scale. Wavelets have advantages over traditional Fourier methods in analyzing physical situations where the signal contains discontinuities and sharp spikes. This paper include information about signal processing algorithms, Orthogonal Basis Functions, and wavelet applications.
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Wavelet Digest: wavelet.org - Wim Sweldens
A free monthly newsletter with all kinds of information concerning wavelets; announcement of conferences, preprints, software, questions, etc. The latest issue and searchable copies of back issues (beginning in 1992) are available; links to other wavelet sites are provided.
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97800631829 Dictionary of Mathematics
`This dictionary is one of the best I have come across' - Mathematics Teaching
This dictionary gives a useful account of basic concepts in mathematics (such as number, sum and point); provides brief explanation of standard topics likely to appear in syllabuses (Taylor series, uniform convergence) and is also an informative reference to concepts or ideas likely to be met by students in general reading even if unlikely to be in the required textbooks (Tucker circle, Godell number, verging methods).
Prepared in consultation with a panel of advisers and readers (including students) whose experience between them covered the range of use, it gives definitions of about 2,500 terms with about 500 diag | 677.169 | 1 |
Mathematics (National Curriculum)
Description: The National Curriculum handbooks are the official National Curriculum documents for secondary and primary schools. They are the revised blue-print for what every child will be required to learn in school from September 2000 National Curriculum handbooks are the official National Curriculum documents for secondary and primary schools. They are the revised blue-print for what every child will be required to learn in school from September 2000 | 677.169 | 1 |
Modern Engineering Mathematics
Description
A rigorous, applications-focused introduction to the field of Engineering Mathematics. Suitable for a first year course in the subject area, the book presents the key mathematical concepts that engineers will be expected to know. The applications focus allows the student to see the mathematics in action and helps to contextualise what they are actually learning. As such, it is also well suited to maths courses within the physical sciences and applied mathematics. Incorporates many exercises throughout the chapters so students can reinforce their learning. This edition will be accompanied by online bridging chapters refresher units in core subjects to bring students up to speed with what they'll need to know before taking the engineering mathematics course. | 677.169 | 1 |
is a unique and integrated account of the history of North American vegetation and paleoenvironments over the past 70 million years. It includes discussions of the modern plant communities, causal factors for environmental change, biotic response, and methodologies. The history reveals a North American vegetation that is vast, immensely... more...
The paleoecological history of the Americas is as complex as the region is broad: stretching from the Arctic Circle to Tierra del Fuego, the New World features some of the most extraordinary vegetation on the planet. But until now it has lacked a complete natural history. Alan Graham remedies that with A Natural History of the New World . With plants... more...
Six mathematical forces are at the heart of shaping your personality. Dr Alan Graham explains their importance, their history, how they impact your life, and how you can make them work for you. more...
Statistics: A Complete Introduction is the most comprehensive yet easy-to-use introduction to using Statistics. Written by a leading expert, this book will help you if you are studying for an important exam or essay, or if you simply want to improve your knowledge. The book covers all the key areas of Statistics including graphs, data interpretation,... more...
The book covers all the basic areas of mathematics including calculating, fractions, decimals, percentages, measuring, graphs and formulae. Everything you will need is here in this one book. Each chapter includes not only an explanation of the knowledge and skills you need, but also worked examples and test questions. At the end of the book a series... more...
This guide combines theory on teaching methodology with advice on good teaching practice in order to help teachers face the challenge of larger numbers of students in their classrooms. It includes a number of case studies which explore innovative teaching methods. more... | 677.169 | 1 |
Algebra 1: Linearity, Slope, & Direct Variation
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Relationship between the Constant of Variation and Slope | 677.169 | 1 |
Looking closely at algebra, its historical development, and its many useful applications, Algebra examines in detail the question of why this type of math is so important that it arose in different cultures at different times. The book also discusses the relationship between algebra and geometry, shows the progress of thought throughout the centuries,... more...
Covering the many aspects of geometry, this volume of the History of Mathematics series presents a compelling look at mathematical theories alongside historical occurrences. The engaging and informative text, complemented by photographs and illustrations, introduces students to the fascinating story of how geometry has developed. Biographical information... more...
Examining the pioneering ideas, works, and applications that have made math the language of science, Mathematics and the Laws of Nature looks at the many ways in which so-called ''pure'' math has been used in the applied sciences. For example, the volume explores how mathematical theories contributed to the development of Kepler's laws of planetary... more...
Numbers deals with the development of numbers from fractions to algebraic numbers to transcendental numbers to complex numbers and their uses. The book also examines in detail the number pi, the evolution of the idea of infinity, and the representation of numbers in computers. The metric and American systems of measurement as well as the applications... more...
Probability and Statistics provides a detailed look at the many aspects of this branch of mathematical investigation. Covering everything from ancient games of chance played around the world and the theories of Fermat and Pascal to phrenology, the specious use of statistics, and statistical methods to stop epidemics, this book offers a comprehensive... more...
Of all the problems associated with energy production, none is more complex than those associated with the production of biofuels, including plant matter, animal wastes, and municipal wastes. This book describes the ways that biofuels are used and the technical, social, policy, and environmental consequences of large-scale consumption. more...
Coal and oil are two of the world's most important sources of primary energy. A multi-trillion dollar infrastructure has been created to locate, produce, transport, process, and burn coal and oil. This title describes the history of these sources of energy. It focuses on global dependence on these resources. more...
Whether solid, liquid, or gaseous, the phase of a fuel has important implications for how it can be used. In US approximately 20 per cent of the nation's electricity is obtained from natural gas-fired power plants. This book describes the technology and scale of the infrastructure that has evolved to produce, transport, and consume natural gas. more...
Commercial nuclear power has long been one of the most controversial of all power-generating technologies, but the debate has not always been particularly informed. This book discusses the physics and technology of energy production, reactor design, nuclear safety, and attempts made by the US to resolve the problem of nuclear waste disposal. more...
Solar energy and geothermal energy have a good deal in common. They are abundant and widely, if unevenly, distributed. Describing the nature of solar and geothermal energy and the processes by which these sources of energy can be harnessed, this book details how they are used in practice to supply electricity to the power markets. more... | 677.169 | 1 |
Algebra and Trigonometry With Analytic Geometry latest edition in the highly respected Swokowski/Cole precalculus series retains the elements that have made it so popular with instructors and students alike: its exposition is clear, the time-tested exercise sets feature a variety of applications, its uncluttered layout is appealing, and the difficulty level of problems is appropriate and consistent. The goal of this text is to prepare students for further courses in mathematics. Mathematically sound, ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY (CLASSIC EDITION), Eleventh Edition, effectively prepares students for further courses in mathematics through its excellent, time-tested problem sets.
Preface
vii
Fundamental Concepts of Algebra
1
(52)
Real Numbers
2
(14)
Exponents and Radicals
16
(11)
Algebraic Expressions
27
(13)
Fractional Expressions
40
(13)
Review Exercises
50
(2)
Discussion Exercises
52
(1)
Equations and Inequalities
53
(72)
Equations
54
(8)
Applied Problems
62
(12)
Quadratic Equations
74
(14)
Complex Numbers
88
(6)
Other Types of Equations
94
(9)
Inequalities
103
(9)
More on Inequalities
112
(13)
Review Exercises
120
(3)
Discussion Exercises
123
(2)
Functions and Graphs
125
(106)
Rectangular Coordinate Systems
126
(6)
Graphs of Equations
132
(10)
Lines
142
(15)
Definition of Function
157
(16)
Graphs of Functions
173
(12)
Quadratic Functions
185
(11)
Operations on Functions
196
(9)
Inverse Functions
205
(11)
Variation
216
(15)
Review Exercises
222
(6)
Discussion Exercises
228
(3)
Polynomial and Rational functions
231
(54)
Polynomial Functions of Degree Greater Than 2
232
(8)
Properties of Division
240
(8)
Zeros of Polynomials
248
(10)
Complex and Rational Zeros of Polynomials
258
(7)
Rational Functions
265
(20)
Review Exercises
282
(2)
Discussion Exercises
284
(1)
Exponential and Logarithmic functions
285
(60)
Exponential Functions
286
(10)
The Natural Exponential Function
296
(8)
Logarithmic Functions
304
(16)
Properties of Logarithms
320
(8)
Exponential and Logarithmic Equations
328
(17)
Review Exercises
340
(3)
Discussion Exercises
343
(2)
The Trigonometric functions
345
(94)
Angles
346
(10)
Trigonometric Functions of Angles
356
(17)
Trigonometric Functions of Real Numbers
373
(18)
Values of the Trigonometric Functions
391
(8)
Trigonometric Graphs
399
(12)
Additional Trigonometric Graphs
411
(8)
Applied Problems
419
(20)
Review Exercises
431
(7)
Discussion Exercises
438
(1)
Analytic Trigonometry
439
(64)
Verifying Trigonometric Identities
440
(5)
Trigonometric Equations
445
(12)
The Addition and Subtraction Formulas
457
(11)
Multiple-Angle Formulas
468
(10)
Product-to-Sum and Sum-to-Product Formulas
478
(5)
The Inverse Trigonometric Functions
483
(20)
Review Exercises
498
(3)
Discussion Exercises
501
(2)
Applications of Trigonometry
503
(60)
The Law of Sines
504
(10)
The Law of Cosines
514
(9)
Vectors
523
(14)
The Dot Product
537
(10)
Trigonometric Form for Complex Numbers
547
(6)
De Moivre's Theorem and nth Roots of Complex Numbers
553
(10)
Review Exercises
558
(4)
Discussion Exercises
562
(1)
Systems of Equations and Inequalities
563
(90)
Systems of Equations
564
(9)
Systems of Linear Equations in Two Variables
573
(9)
Systems of Inequalities
582
(8)
Linear Programming
590
(9)
Systems of Linear Equations in More Than Two Variables
599
(14)
The Algebra of Matrices
613
(9)
The Inverse of a Matrix
622
(6)
Determinants
628
(6)
Properties of Determinants
634
(8)
Partial Fractions
642
(11)
Review Exercises
648
(3)
Discussion Exercises
651
(2)
Sequences, Series, and Probability
653
(78)
Infinite Sequences and Summation Notation
654
(10)
Arithmetic Sequences
664
(7)
Geometric Sequences
671
(9)
Mathematical Induction
680
(7)
The Binomial Theorem
687
(9)
Permutations
696
(7)
Distinguishable Permutations and Combinations
703
(9)
Probability
712
(19)
Review Exercises
725
(3)
Discussion Exercises
728
(3)
Topics from Analytic Geometry
731
(70)
Parabolas
732
(9)
Ellipses
741
(13)
Hyperbolas
754
(12)
Plane Curves and Parametric Equations
766
(11)
Polar Coordinates
777
(13)
Polar Equations of Conics
790
(11)
Review Exercises
796
(2)
Discussion Exercises
798
(3)
Appendixes
801
(1)
I Common Graphs and Their Equations
802
(2)
II A Summary of Graph Transformations
804
(2)
III Graphs of Trigonometric Functions and Their Inverses
806
(2)
IV Values of the Trigonometric Functions of Special Angles on a Unit Circle | 677.169 | 1 |
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Show More information here in one source. Coverage includes everything from sine, cosine and tangent to resultant prism and resolving prism to polarized filters - and much more!Features a user-friendly format that facilitates the review process, with practical examples throughout.Provides a convenient review of optical formulas and basic math problems.Begins each chapter with a brief discussion of the topic, then proceeds with exercises and examples; answers are provided at the end of the book.New work-text design allows the reader to complete practice exercises within the book and section being studied.More complex formulas include "how to use the calculator" boxes, and multiple choice review sections have been added to the sections.Advanced exercises such as non-formula exercises are now included throughout | 677.169 | 1 |
Tensor algebra and tensor analysis were developed by Riemann, Christo?el, Ricci, Levi-Civita and others in the nineteenth century. The special theory of relativity, as propounded by Einstein in 1905, was elegantly expressed by Minkowski in terms of tensor ?elds in a ?at space-time. In 1915, Einstein formulated the general theory of relativity, in which... more...
This book describes the methods by which tensors can be practically treated and shows how numerical operations can be performed. Applications include problems from quantum chemistry, approximation of multivariate functions, solution of pde and more. more...
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This book provides a comprehensive exposition of tensor analysis. It presents modern developments in the theory of isotropic and anisotropic tensor functions and includes numerous exercises with solutions. more...
The fun and easy way to learn pre-calculus Getting ready for calculus but still feel a bit confused? Have no fear. Pre-Calculus For Dummies is an un-intimidating, hands-on guide that walks you through all the essential topics, from absolute value and quadratic equations to logarithms and exponential functions to trig identities and matrix operations.... more... | 677.169 | 1 |
In its largest aspect, the calculus functions as a celestial measuring tape, able to order the infinite expanse of the universe. Time and space are given names, points, and limits; seemingly intractable problems of motion, growth, and form are reduced to answerable questions. Calculus was humanity's first attempt to represent the world and perhaps... more...
Features an introduction to advanced calculus and highlights its inherent concepts from linear algebra Advanced Calculus reflects the unifying role of linear algebra in an effort to smooth readers' transition to advanced mathematics. The book fosters the development of complete theorem-proving skills through abundant exercises while also promoting... more...
Advances on Fractional Inequalities use primarily the Caputo fractional derivative, as the most important in applications, and presents the first fractional differentiation inequalities of Opial type which involves the balanced fractional derivatives. The book continues with right and mixed fractional differentiation Ostrowski inequalities in the... more...
An easy-to-understand primer on advanced calculus topics Calculus II is a prerequisite for many popular college majors, including pre-med, engineering, and physics. Calculus II For Dummies offers expert instruction, advice, and tips to help second semester calculus students get a handle on the subject and ace their exams. It covers intermediate... more...
Differential and Integral Calculus, Volume 2 : "Unlike modern mathematicians who pursue their research apart from engineering or physical applications, Richard Courant was adverse to abstract theories and vague theorems. The topics covered in this set will provide the reader with a solid background to understanding the mathematics of heat... more...
"This is the perfect solid-as-they-come, timeless book on the calculus, and most likely it will never be surpassed in this domain." –Amazon Review This book is intended for anyone who, having passed through an ordinary course of school mathematics, wishes to apply himself to the study of mathematics or its applications to science... more...
Pre-Calculus Demystified leads the reader through all the intricacies and requirements of this essential course Whether you need to pass a class, a college requirement, or get a leg up on more advanced topics, this book provides clear explanation with a wealth of questions, answers and practical examples. Packed with practical examples, graphs,... more...
This book is a detailed study of Gottfried Wilhelm Leibniz's creation of calculus from 1673 to the 1680s. We examine and analyze the mathematics in several of his early manuscripts as well as various articles published in the Acta Eruditorum. It studies some of the other lesser known "calculi" Leibniz created such as the Analysis Situs,... more... | 677.169 | 1 |
The course is an undergraduate introduction to differential equations for engineer and science majors. Students learn to solve differential equations, discuss some of the properties of the solutions and, in most cases, compute approximate solutions of differential equations. Mathematica is used interactively through out the course and all the materials are available online on the web.
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Practice solving algebraic equations with this interactive quiz brought to you by Interactivate and the Computational Science Education Reference Desk. The quiz allows you to select the difficulty level, time limit and...
The Annenberg Foundation has been an active part of creating educational and professional development tools and instructional aids for teachers for many years. To reach the broadest audience possible, their Annenberg...
Presented by Professor Jody Harris at Broward Community College, these handouts are an excellent resource to print and give to community and technical college students in the algebra classroom. The subjects of the...
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Basic concepts and properties of algebra are introduced early to prepare students for equation solving. Abundant exercises graded by difficulty level address a wide range of student abilities. The Basic Algebra Planning Guide assures that even the at-risk student can acquire course content.
Multiple representations of concepts
Concepts and skills are introduced algebraically, graphically, numerically, and verbally-often in the same lesson to help students make the connection and to address diverse learning styles.
Focused on developing algebra concepts and skills
Key algebraic concepts are introduced early and opportunities to develop conceptual understanding appear throughout the text, including in Activity Labs. Frequent and varied skill practice ensures student proficiency and success.
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Product Description:
Product Description:
By the time teens are in high school, they have already spent years wrestling with a heavy backpack. It's time to solve this problem—and Pearson can help. Explore Pearson@home math products for home use.
Book Description PRENTICE HALL, 2008. Hardcover. Book Condition: New. MULT. COPIES! This is the NJ edition! Same as the national except for the first few pages with state specific material in the beginning of the book. The national edition begins thereafter - all page#'s match up. Brand new, never used. We ship daily!. Bookseller Inventory # AMAN0005763 | 677.169 | 1 |
Details about Intermediate Algebra:
Intermediate Algebra, Fourth Edition effectively prepares students for their next mathematics course. The text presents all the topics associated with a second course in algebra, providing students with the foundation in the concepts and skills that they need to master in order to succeed in the next course. This book helps students develop the ability to integrate and conceptualize and make the connections between geometric and algebraic solutions. Topics are introduced from a intuitive perspective. This text successfully meets the needs of a varied student population. Students with less mathematical background will appreciate the non-technical writing of the authors' notes in worked examples, and the review of basic algebra. Students with more skill will appreciate the comprehensive coverage of topics and the challenging problems that appear at the end of exercise sets.
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Category theory provides a general conceptual framework that has proved fruitful in subjects as diverse as geometry, topology, theoretical computer science and foundational mathematics. Here is a friendly, easy-to-read textbook that explains the fundamentals at a level suitable for newcomers to the subject. Beginning postgraduate mathematicians will find this book an excellent introduction to all of the basics of category theory. It gives the basic definitions; goes through the various associated gadgetry, such as functors, natural transformations, limits and colimits; and then explains adjunctions. The material is slowly developed using many examples and illustrations to illuminate the concepts explained. Over 200 exercises, with solutions available online, help the reader to access the subject and make the book ideal for self-study. It can also be used as a recommended text for a taught introductory course | 677.169 | 1 |
4. Understand, produce, and critique mathematical models and algorithms appropriate to their fields of specialty, utilizing appropriate software where necessary.
5. Understand, appreciate, and explain the motivation and culture of their field(s) of specialty. This includes the major historical developments of the field, and the connections between the field other areas of mathematics and science.
6. Master the techniques, proofs and applications of differential and integral calculus, and apply the methods of calculus in a variety of situations, such as analyzing numerical methods, ordinary differential equations, partial differential equations, measure theory, complex analysis, applicable analysis, and differential geometry. | 677.169 | 1 |
BITSAT 2011 Syllabus
MATHEMATICS
The BITSAT-2011 test will be conducted on the basis of
NCERT syllabus for 11th and 12th class. The detailed syllabus is given in
the Annexure. Candidates may refer to the NCERT textbooks for the contents.
A sample test demonstrating the features of BITSAT will be made available to
the registered candidates at the BITS website on which he/she can practice
as many times as desired.
IIST ISAT 2011 MATHEMATICS SYLLABUS
SETS, RELATIONS AND FUNCTIONS: Sets and their representation; Union, intersection and complement of sets and their algebraic properties; Power set; Relation, Types of relations, equivalence relations, functions;. one-one, into and onto functions, composition of functions.
COMPLEX NUMBERS AND QUADRATIC EQUATIONS: Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a+ib and their representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a complex number, triangle inequality, Quadratic equations in real and complex number system and their solutions. Relation between roots and co-efficients, nature of roots, formation of quadratic equations with given roots.
PERMUTATIONS AND COMBINATIONS: Fundamental principle of counting, permutation as an arrangement and combination as selection, Meaning of P (n,r) and C (n,r), simple applications.
Matrices as a rectangular array of real numbers, equality of matrices,
addition, multiplication by a scalar and product of matrices, transpose of a
matrix, determinant of a square matrix of order up to three, inverse of a square
matrix of order up to three, properties of these matrix operations, diagonal,
symmetric and skew-symmetric matrices and their properties, solutions of
simultaneous linear equations in two or three variables.
Addition and multiplication rules of probability, conditional probability,
Bayes Theorem, independence of events, computation of probability of events
using permutations and combinations.
GUJCET : Gujarat Common Entrance
Test
Gujarat Common Entrance Test (CET) Engineering
Examination Gujarat Common entrance Test (CET) is conducted by The Education
Department, Govt of Gujarat and it has assigned The Gujarat Secondary and Higher
Secondary Education to hold CET for admission into various medical, engineering
and pharmacy courses in the state of Gujarat. The information booklet and the
application form prepared by the Board is available on the payment of Rs.
250/-via Demand Draft from any nationalized bank payable at Gandhinagar/Ahmedabad
in favour of "Secretary, Gujarat Common Entrance Test (CET) Cell, Gandhinagar"
Exam Pattern
Admission to courses will be based on 40% weightage of GUJCET score and 60%
weightage of 12th Marks. For admission to MBBS, 70% marks in 12th are also
required. Please note that marks of either PCM (without practicals) or PCB
(without practicals) are considered so effective weightage is somewhere between
21-28% for GUJCET Exam.
III. VECTOR ALGEBRA: (a) Algebra of vectors – angle between
two non-zero vectors – linear combination of vectors – vector equation of line
and plane (b) Scalar and vector product of two vectors and their applications
(c) Scalar and vector triple products – Scalar and vector products of four
vectors
Karnataka Common Entrance Test (KCET) | Result and Answer Keys of Exam 2010
Karnataka Examination Authority
Common Entrance Test
Karnataka
Karnataka Common Entrance Test Result 2010 has been announced by Karnataka Examination authority. Answer keys are also published by Karnataka examination authority. There are four subject in Karnataka CET entrance exam - Physics, Chemistry, Biology and Mathematics
MATHEMATICS SYLLABUS
MATRICES AND DETERMINANTS:
Types of matrices, addition and multiplication
of matrices-Properties, computation of inverses,
solution of system of linear equations by matrix
inversion method. Rank of a Matrix – Elementary
transformation on a matrix, consistency of a
system of linear equations, Cramer's rule,
Non-homogeneous equations, homogeneous linear
system, rank method.
THEORY OF EQUATIONS,
SEQUENCE AND SERIES
Quadratic equations – Relation between roots and
coefficients – Nature of roots – Symmetric
functions of roots – Diminishing and Increasing
of roots – Reciprocal equations. Arithmetic,
Geometric and Harmonic Progressions-Relation
between A.M., G. M ., and H.M. Special series:
Binomial, Exponential and Logarithmic series –
Summation of Series. VECTOR ALGEBRA
Scalar Product – Angle between two vectors,
properties of scalar product, applications of
dot products. Vector Product – Right handed and
left handed systems, properties of vector
product, applications of cross product. Product
of three vectors – Scalar triple product,
properties of scalar triple product, vector
triple product, vector product of four vectors,
scalar product of four vectors. Lines – Equation
of a straight line passing through a given point
and parallel to a given vector, passing through
two given points, angle between two lines. Skew
lines – Shortest distance between two lines,
condition for
two lines to intersect, point of intersection,
collinearity of three points. Planes – Equation
of a plane, passing through a given point and
perpendicular to a vector, given the distance
from the origin and unit normal, passing through
a given point and parallel to two given vectors,
passing through two given points and parallel to
a given vector, passing through three given
non-collinear points, passing through the line
of intersection of two given planes, the
distance between a point and a plane, the plane
which contains two given lines, angle between
two given planes, angle between a line and a
plane. Sphere – Equation of the sphere whose
centre and radius are given, equation of a
sphere when the extremities of the diameter are
given.
ISAT Mathematics Sample Questions 2010
Question 2:
Last year there were 80 students enrolled in the eighth-grade class. This year
the
number of students enrolled in the eighth-grade class increased by 10%.
How many students are enrolled in the eighth-grade class this year?
A. 88
B. 8
C. 90
D. 81
Question 3 :
A company packs its coffee into cylindrical containers. The height of each
container is 6
inches, and the radius of the container is 3 inches.
Which is closest to the volume of one of these cylindrical containers?
A. 36 cubic inches
B. 113 cubic inches
C. 54 cubic inches
D. 170 cubic inches
Question 4 :
The student council is making snack bags for a class trip. Each snack bag will
contain:
• 1 type of drink
• 1 type of cookie
• 1 type of fruit
To make each snack bag, they will choose from 2 types of drinks, 4 types of
cookies,
and 2 types of fruit.
How many combinations of 1 type of drink, 1 type of cookie, and 1 type of fruit
are
possible?
A. 48
B. 8
C. 3
D. 16
Question 8 :
Between which two consecutive integers is ?
A. 6 and 7
B. 100 and 101
C. 75 and 76
D. 17 and 18
Question 10 :
Amy has of a yard of string to make bracelets. Each bracelet requires of a yard
of string.
What is the greatest number of bracelets Amy can make with this length of
string?
A. 3
B. 6
C. 4
D. 8
Question 12 :
Which point on the number line below represents the value ?
A. Point Q
B. Point S
C. Point P
D. Point R
Question 14 :
Paula multiplied a number by 16. Her result is a positive number less than 16.
Which of
these did Paula multiply by 16?
A. A number greater than one
B. A number less than zero
C. A number between zero and one
D. Zero
With just a few more days to go for the joint entrance exams for India's
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AlgebraActivities that Reach the Kids and Teach the Standards page 2 of 44 Bill will share three of his favorite activities, Take Your Places Pyramid Math Leou0027s Patterns and ...
Planning Group for the Algebra: Gateway to a Technological Future Conference : Francis (Skip) Fennell, McDaniel College President, National Council of Teachers of ...
203 The wave: In this experiment, x equals the number of students, and y equals the time to complete the wave. Start with a group of five students.
Integrated Algebra 1 is a new text for high school algebra that continues the approach that has made Amsco a leader in presenting mathematical ideas in a contemporary ...
Important notice regarding book materials Texas Instruments makes no warranty, either expressed or implied, including but not limited to any implied warranties of ...
Algebra 2 and Trigonometry is a new text for a course in intermediate algebra and trigonometry that continues the approach that has made Amsco a leader in presenting ... 2/Algebra 2 and Trigonometry.pdf
v To the Teacher Since the early 1970u0027s we have been teaching math to learners of all ages, from young children to adults, who represent many different cultures and ...
DR MATH GETS YOU READY FOR ALGEBRA Grades 4-8 This 192-page question-and-answer book prepares kids for algebra and comes from The Math Forum, an award-winning Web site ...
ii Important notice regarding book materials Texas Instruments makes no warranty, either expressed or implied, including but not limited to any implied warranties of ...
Geometry and Algebra: The Future Flight Equation is available in electronic format through NASA Spacelink - one of NASAu0027s electronic resources specifically developed for the ... | 677.169 | 1 |
Bob Miller's Math for the Accuplacer36
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About the Book
Get a Higher Math Score on the Accuplacer with REA's NEW Bob Miller Test Prep If you're one of the millions of students attending community college this year, REA has the perfect Accuplacer test prep for you - "Bob Miller's Math for the Accuplacer. " Written in a lively and unique format, "Bob Miller's Math for the Accuplacer "is an excellent tool for students who have been recently admitted to college and who want to improve their math skills before taking the Accuplacer exam. The book explains math concepts in a lively, easy-to-grasp style. Each chapter includes numerous step-by-step examples and exercises. Detailed explanations of solutions help students understand and retain the material. Bob's targeted review section covers all the math topics tested on the Accuplacer, including arithmetic (17 questions on the test), elementary algebra (12 questions on the test), and college-level math (20 questions on the test). To help you get the most out of your Accuplacer preparation, Bob has included four practice tests for each section - for a total of 12 exams. Our test-taking advice, study tips, and exam strategies will prepare you for exam day, ease your anxiety, and help you boost your score. Packed with Bob Miller's engaging examples and practical advice, this book is a must for any student preparing for the Accuplacer "What is the Accuplacer? ""The Accuplacer exam is used to determine which math courses are appropriate for newly enrolled college students. It is popular in community colleges and both two- and four-year schools. " | 677.169 | 1 |
ALEX Lesson Plans
Title: Discover the Roots of a Polynomial Function
Description:
InStandard(s): [MA2015] AL2 (9-12) 17: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. [A-APR3]
Subject: Mathematics (9 - 12) Title: Discover the Roots of a Polynomial Function Description: In
Title: "Factoring by Mack"
Description:
ThisStandard(s): [MA2015] AL1 (9-12) 8: Use the structure of an expression to identify ways to rewrite it. [A-SSE2]
Subject: Mathematics (9 - 12) Title: "Factoring by Mack" Description: This
Title: Exponential Growth and Decay
Description:
ThisStandard(s): [MA2015] PRE (9-12) 25: Compare effects of parameter changes on graphs of transcendental functions. (Alabama)
Subject: Mathematics (9 - 12) Title: Exponential Growth and Decay Description: This
Title: You Mean ANYTHING To The Zero Power Is One?
Description:
This lesson is a technology-based project to reinforce concepts related to the Exponential Function. It can be used in conjunction with any textbook practice set. Construction of computer models of several Exponential Functions will promote meaningful learning rather than memorization.
Standard(s):
Subject: Mathematics (9 - 12), or Technology Education (9 - 12) Title: You Mean ANYTHING To The Zero Power Is One? Description: This lesson is a technology-based project to reinforce concepts related to the Exponential Function. It can be used in conjunction with any textbook practice set. Construction of computer models of several Exponential Functions will promote meaningful learning rather than memorization.
Title: Factoring Fanatic
Description:
ThisStandard(s):
Subject: Mathematics (9 - 12) Title: Factoring Fanatic Description: This
Thinkfinity Lesson Plans
Title: Predicting Your Financial Future
Description:
In this Illuminations lesson, students use their knowledge of exponents to compute an investment s worth using a formula and a compound interest simulator. Students also use the simulator to analyze credit card payments and debt Mathematics Title: Predicting Your Financial Future Description: In this Illuminations lesson, students use their knowledge of exponents to compute an investment s worth using a formula and a compound interest simulator. Students also use the simulator to analyze credit card payments and debt. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Thinkfinity Learning Activities
Title: Proof Without Words: Completing the Square
Description:
In this student interactive, from Illuminations, students carry out an interactive, geometric '' proof without words'' for the algebraic technique of completing the square. The page also includes directions and a link to the final solution.
Standard(s): [MA2015] GEO (9-12) 29: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. [G-GPE1]
Subject: Mathematics Title: Proof Without Words: Completing the Square Description: In this student interactive, from Illuminations, students carry out an interactive, geometric '' proof without words'' for the algebraic technique of completing the square. The page also includes directions and a link to the final solution. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 | 677.169 | 1 |
Sample Precalculus Problem: Introduction to Sequences
By: Bumsoo Kim
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. | 677.169 | 1 |
ALEX Lesson Plans
Title: Penny Drop That Thang!
Description:
This lesson is designed to introduce and extend students' knowledge on slope and linear equations. Students will be able to differentiate finding the slope to creating a linear equation.
This is a College- and Career-Ready Standards showcase lesson plan.
Standard(s): [MA2015] AL1 (9-12) 23: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* [A-REI11]
Subject: Mathematics (8 - 12) Title: Penny Drop That Thang! Description: This lesson is designed to introduce and extend students' knowledge on slope and linear equations. Students will be able to differentiate finding the slope to creating a linear equation.
This is a College- and Career-Ready Standards showcase lesson plan.
Title: Systems of Equations: What Method Do You Prefer?
Description:
TheStandard(s): [MA2015] ALT (9-12) 22: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [A-CED3]
Subject: Mathematics (8 - 12) Title: Systems of Equations: What Method Do You Prefer? Description: The
Thinkfinity Lesson Plans
Title: Shedding the Light
Description:
In
Standard(s): [MA2015] DM1 (9-12) 3: Use the recursive process and difference equations to create fractals, population growth models, sequences, series, and compound interest models. (Alabama)
Subject: Mathematics,Science Title: Shedding the Light Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 | 677.169 | 1 |
Major Concepts/Content: AP Calculus BC provides a deeper understanding of the fundamental concepts and methods of single-variable calculus developed in AP Calculus AB. There is a continued emphasis on calculus applications and techniques, with the use of multiple representations including graphic, numeric, analytic, algebraic, and verbal and written responses. Topics of study include: functions (including parametric, polar and vector), limits, derivatives, the interpretation and application of integrals, and polynomial approximations and series. Technology is an integral part of the course and includes the use of graphing calculators, computers, and data analysis software. On a regular basis, graphing calculators are used to explore, discover, and reinforce concepts of calculus.
Major Instructional Activities: Though our system has an open enrollment policy, students should understand that this course is designed to be a fourth-year mathematics course and the equivalent of a year-long, college-level course in single variable calculus. The course requires a solid foundation of topics in advanced algebra, geometry, trigonometry, analytic geometry, and elementary functions. The breadth, pace, and depth of material covered exceeds the standard high school mathematics course, as does the college-level textbook, and time and effort required of students. AP Calculus BC is an extension of AP Calculus AB, and provides the equivalent of a second course in a college calculus sequence, while AP Calculus AB provides the equivalent of the first course in a college calculus sequence. Students are expected to take the AP Calculus BC Exam at the end of this course.
Develop an in-depth understanding of major topics of calculus including functions, limits, derivatives, integrals, and polynomial approximations and series.
Incorporate multiple representations of functions using graphic, numeric, analytic, algebraic, and verbal and written responses, and understand the connections among these representations.
Construct an understanding of derivatives as an instantaneous rate of change, applications of derivatives as functions, and use various techniques to solve problems including local linear approximations.
Understand definite integrals as a limit of Riemann sums, and as the net accumulation of sums, and use them to solve a variety of problems.
Develop an understanding of the Fundamental Theorem of Calculus as a relationship between derivatives and definite integrals.
Understand the concept of a series as a sequence of partial sums, and use the Power series and Taylor polynomial approximations and series.
Analyze parametric, polar, and vector functions through the use of parametric equations, polar coordinates, and derivatives and applications of these functions.
Computers: Each student has access to a computer with internet access at their local school during their scheduled class period. Most also have use of a computer at home. The entire course is conducted on-line. Most students also have access to a scanner or digital sender for submitting work, but a fax machine can be used if one is not available.
Software: Students use the Microsoft Office programs for projects and for accessing lectures. QuickTime Video is used to run Flash presentations and activities. Jabber is an instant messaging program that we use for real-time communications with the students. Windows Media is required for watching video presentations and demonstrations. Adobe Connect is used for whiteboard presentations with both video and audio real-time collaboration with students.
Graphing calculators are required by the College Board. Students may use any approved model; most use the TI-83+ or TI-89 | 677.169 | 1 |
What's new in this version (4.0):
- Updated content
- Fixed errors
- Offline Access/SDCard support
Description
** A Hard-copy Best-seller **
Well paying careers demand skills like problem solving, reasoning, decision making, and applying solid strategies etc. and Algebra provides you with a wonderful grounding in those skills - not to mention that it can prepare you for a wide range of opportunities.
This is a COMPLETE Pre-Algebra guide to well over 325 rules, definitions and examples, including number line, integers, rational numbers, scientific notation, median, like terms, equations, Pythagorean theorem and much more!
Our guide will take you step-by-step through the basic building blocks of Algebra giving you a solid foundation for further studies in our easy-to-follow and proven format!
Algebra is a very unique discipline. It is very abstract. The abstractness of algebra causes the brain to think in totally new patterns. That thinking process causes the brain to work, much like a muscle. The more that muscle works out, the better it performs on OTHER tasks. In simple terms, algebra builds a better brain! Believe it or not algebra is much easier to learn than many of us think and this guide helps make it easier!
Like all our 'phoneflips', this lightweight application has NO ads, never needs an internet connection and wont take up much space on your phone!
For hard copy versions of this and other great products, please visit:
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Androlicious.com is a website that shows applications and games from Android Market. You can download and install apps and games directly from Android Market using an Android phone or by using WebConnect mobile application. | 677.169 | 1 |
Experiences in Problem Solving
Edited by:
R.H. Eddy and M.M. Parmenter
This book presents most of the contributions to the problem solving
literature of the late W.J. Blundon, a prominent figure in mathematics
and educational circles in Atlantic Canada for many years, and Head of
Mathematics at Memorial University for over 25 years.
Keenly interested in matematical problems, especially those involving
geometry, number theory, and geometric inequalities, Professor Blundon
was a regular contributor to journals such as Crux
Mathematicorum and the American Mathematical
Monthly.
Including both problems and solutions grouped by subject, this book is a
must for teachers and students at the college/advanced high school level.
Send cheque or purchase order for $25 (plus $5 for shipping and
handling, payable in $US for orders from outside Canada) to:
Dr. Edgar G. Goodaire,
Atlantic Provinces Council on the Sciences (APICS)
Department of Mathematics and Statistics
Memorial University of Newfoundland
St. John's, Newfoundland
Canada A1C 5S7
We are always looking to improve our site.
Please write if you have
comments or suggestions. | 677.169 | 1 |
Study Tips
Procedure For Solving Problems
Draw a diagram, if at all possible, even if it is so
simple-minded as to seem silly. Only when you have worked a given
type of problem so often that you automatically draw a mental diagram
can you stop drawing one on paper.
Read the problem carefully, listing all quantities given and
requested. (Leave room for more quantities you may need later).
Play with the situation either mentally or with models. Try
to understand the behavior of the system qualitatively. Look for
simpler special cases (zero angle, 90 degree angle, a zero length, a
large mass, etc.) where the answer to the problem is obvious.
Decide what kind of problem you are working on (response to a
force, energy conservation, equilibrium, or what have you). Use
examples from your notes and text to help with the decision and with
the general techniques used to solve problems of this type. Then put
the examples aside and work this problem without further help. Write
down all principles and equations which apply to this kind of problem,
whether or not it seems that you will use them here. Write down too
many. It is easier to ignore excess information than to realize that
you need something more. Add to the list of quantities you made in
part 2 any that are normally needed for this kind of problem but which
are not specifically mentioned in the problem statement.
Determine whether or not the data given are adequate. If not,
decide what is missing and how to get it. You may need to look up
some standard constant in a table. Work on the algebra to reduce the
number of unknowns. When you have the same number of relevant,
independent equations as you have unknowns, you probably have enough
equations. Sometimes an unknown drops out, so when you have run out
of ideas do some algebra to determine as many as possible of the
unknowns. Substitute numbers into the variables you can solve for and
see if knowing their sizes helps. Sometimes you discover at this
point that you are not working on the kind of problem you thought you
were. If nothing occurs to you in a reasonable amount of time, get
help.
If necessary, add to your list of quantities any additional
ones which you can compute but which were not asked for. Sometimes
these additional quantities can be used to finish the problem. You
can look for additional in the equations you listed in step 4. Now is
a good time to find any equations you may have overlooked at step 4.
Now is also a time when you may have to change your mind about what
kind of problem you are working on.
When you have an algebraic solution, put in numbers WITH
UNITS. Be sure that all your numbers are in consistent units.
CHECK
P lausibility
Algebra OK, numbers reasonable, signs correct?
U nits
Are all consistent and appropriate?
N otation
Vectors shown?
S pecial cases
Does your solution obey those from step 3? If not, why not?
When everything seems to be correct, write out a complete,
logical solution (except when you are working an exam and your first
version is intelligible). You will need this solution later to
understand what you did. On homework problems, outline the method of
solution in 2-3 lines or practice working through the solution
quickly. If a similar problem occurs on an exam, you may have less
time to think than you would like. | 677.169 | 1 |
Category/Mathematics/symbolic
Category/Mathematics
symbolic (7)
GiNaC is an acronym for GiNaC Is Not A CAS, where CAS stands for Computer Algebra System. It lets the user create integrated systems that embed symbolic manipulations together with more established areas of computers sciences under one roof. It has been specifically developed to become a replacement engine for xloops. However, it is not restricted to high energy physics applications. Its design is revolutionary in that contrary to other CAS it does not try to provide extensive algebraic capabilities and a simple programming language but instead accepts a given language (C++) and extends it by a set of algebraic capabilities.
JACAL is an interactive symbolic math program that can manipulate and simplify equations, scalars, vectors, and matrices of single and multiple valued algebraic expressions containing numbers, variables, radicals, and algebraic differential, and holonomic functions.
This is a text editor for writing math lessons and providing tools for doing all the exercises from elementary school to junior high. The software is especially designed to fulfil the needs of disabled pupils, and pupils suffering from dyspraxia in particular. The program manages the child's documents like a notebook, organized with chapters, and separating lessons, exercises and evaluations, making it very easy to navigate through the documents.
'MathStudio' is a project intended to make typing and resolution of mathematical expressions easier and more comfortable. Many other programs like this force the user to write input data using one row only (everything is typed at the same level, exponents and bases are on the same row) and use a lot of brackets to make the operation order explicit. Since this is very different from the math you do manually, the aim of this project is to reduce this gap providing both cross-platform libraries which can be embedded in other programs and a program, MathStudio, which demonstrates their usage.
'Mathomatic' is a small, portable, general purpose symbolic math program that can solve, simplify, combine, differentiate, and compare algebraic equations. It can do standard, complex number, and polynomial arithmetic, and is designed to be as general as possible, with few options | 677.169 | 1 |
Congruent Thoughts is a book of poetry about life and living. The reflective thoughts of the poetry create a sense of reality about living for the reader. Included are beautiful black and white... More > prints by the author that enhance the vision of the poetry.< Less
Math Mammoth Geometry 2 continues the study of geometry after Math Mammoth Geometry 1, and is suitable for grades 6-7. It concentrates on two broad and important topics: area and volume of all common... More > shapes.
In the first section of the book, which is also the longest, students learn to calculate the area of all common shapes: triangles, parallelograms, other polygons, and circles. They encounter Pi and how it relates to the circumference of a circle. We also briefly study the proof for the formula for the area of a circle. I feel it is important that students encounter justifications for mathematical formulas and procedures and even read some proofs before high school. We don't want students to think that mathematics is only a bag of magic tricks or formulas to memorize that seemingly came out of nowhere. Proofs and logical thinking are foundations to mathematics and school mathematics should not be left without themThe Kepler-Poinsot polyhedra are also known as the regular star polyhedra. Each one of these shapes has faces which are congruent regular convex polygons or star polygons and has the same number of... More > faces meeting at each vertex.
Challenge your students by having them construct two of these 3D models; the great dodecahedron, and the great icosahedron.< Less
In Theory: The Trumpet is a supplementary text, which uniquely parallels a basic elementary music theory curriculum. The method provides trumpet students the opportunity to apply to trumpet many... More > concepts of elementary theory, and is presented in a concise manner congruent to an introductory theory course. Concepts presented in this book may benefit high school and college students currently taking an elementary theory course. Furthermore, this method serves as a valuable resource for educators who wish to provide students with supplemental applied lesson materials.< Less
The most significant book on magick ever offered. This is a "Taxonomy of Relative Magick", a 'how to' book for increasing the propensity for magick, miracles and awe in your life. Includes... More > detailed concepts, entertaining stories and poems, exercises and supporting logic. Spiritual rather than religious, with something for every person touched by awe and wonder. An extensive Glossary and congruent organization allows the reader to 'live' the processes they are embracing. An essential theme is a shift form 'believing' to 'knowing'.< Less
"Churchin' The Acts of the Apostles Workbook" is a 3 volume workbook series designed for group Bible Studies and quarterly classes moderated by a Christian Education Department. It's... More > purpose is for the inspiration and motivation of members for engaging in evangelism and outreach ministry services. Each chapter ends with "Reflection Questions"; and each workbook (of the 3) ends with a corresponding summary in Black Church History congruent to an excerpt from The Acts of the Apostles.< Less
These math words to build a foundation of math understanding. Use whole class and particularly with second language learners or struggling math students. The child friendly games and activities... More > give students meaningful ways to practice word definitions! This Math Game packet includes black line masters to reproduce and use as games and activities. The 15 carefully selected words focus on kid friendly definitions that offer rich information about the concept. Words included are: polígono, figuras congruentes, simetría, ordenación, diámetro, líneas paralelas, líneas perpendiculares, área, ángulos, cilindros, perímetro, rombo, cubo, esfera y cono.< Less
These are great math words to build a foundation of math understanding. Use whole class and particularly with second language learners or struggling math students. The child friendly games and... More > activities give students meaningful ways to practice and comprehend word definitions! This Math Game packet includes black line masters to reproduce and use as games and activities. The 15 carefully selected words focus on kid friendly definitions that offer rich information about the concept. Words included are: polygon, congruent figures, symmetry, array, diameter, parallel lines, perpendicular lines, area, angles, cylinder, perimeter, rhombus, cube, sphere, and cone | 677.169 | 1 |
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Having trouble understanding algebra? Do algebraic concepts, equations, and logic just make your head spin? We have great news: Head First Algebra is designed for you. Full of engaging stories and practical, real-world explanations, this book will help you learn everything from natural numbers and exponents to solving systems of equations and graphing polynomials.
Along the way, you'll go beyond solving hundreds of repetitive problems, and actually use what you learn to make real-life decisions. Does it make sense to buy two years of insurance on a car that depreciates as soon as you drive it off the lot? Can you really afford an XBox 360 and a new iPhone? Learn how to put algebra to work for you, and nail your class exams along the way.
Your time is way too valuable to waste struggling with new concepts. Using the latest research in cognitive science and learning theory to craft a multi-sensory learning experience, Head First Algebra uses a visually rich format specifically designed to take advantage of the way your brain really works.
Have a killer app idea for iPhone and iPad? Head First iPhone and iPad Development will help you get your first application up and running in no time. You'll not only learn how to design for Apple's devices, you'll also master the iPhone SDK tools -- including Interface Builder, Xcode, and Objective-C programming principles -- to create eye-catching, top-selling apps. | 677.169 | 1 |
Related software: 03/28/2015 06:29:16 Intermediate Algebra (Concepts and Graphs) [Charles P. McKeague] on Amazon.com. *FREE* shipping on qualifying offers. This textbook has a unique table of contents ...Illustrated Classics: Buy 2, Get the 3rd Free; See the Official Cover for Harper Lee's Go Set a Watchman "Duck & Goose Colors!": Only $3.99 with Kids' Books PurchaseCOUPON: Rent Intermediate Algebra (Textbooks Available with Cengage Youbook) 9th edition (9780840064202) and save up to 80% on textbook rentals and 90% on used textbooks.Summary: Charles P. McKeague is the author of Intermediate Algebra (Textbooks Available with Cengage Youbook), published 2011 under ISBN 9780840064202 and …Are you looking for affordable algebra textbooks for your course? Click here and get information about the latest algebra textbooks at amazingly low prices.Purchase math textbooks, supplements, and an All-Access Pass for XYZ Textbooks and MathTV.A broad selection of popular textbooks may be integrated with various ALEKS courses. What happens when you choose a textbook for integration with your ALEKS course?Cengage Learning, the content leader in higher education textbooks, and WebAssign, the world's easiest to use homework system, provide you with the definitive ...Book Title Author(s) Publisher Questions; College Algebra with Current Interesting Applications and Facts, 1st edition. Table of Contents. Acosta and KarwowskiA selection of popular textbooks can be easily integrated with various ALEKS course products. When you choose to integrate a textbook with an ALEKS class, a custom ... textbook intermediate algebra mckeague | 677.169 | 1 |
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Robotics is an advance technology, which is widely used across all over the world.In this paper we discuss how the problem in the company can be solved by using this technology. The problem is,to pick up the component from the conveyor and to place it on the bed of the CNC machine worker use the overhanging crane and to hold the component they use V-belt. It is wrong way to handling of component and not safe to worker. At this location in company the automation is required. The solution is... Topics: Robotics, Hydraulic Manipulator, Manipulator Design, Hydraulic Calculations
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The purpose of these demonstrations is to make mathematical analysis of electromagnetism take on physical meaning. Based on relatively simple configurations and arrangements of equipment, they make a direct connection between what has been analytically derived and what is observed. They permit the student to observe physically what has been described symbolically. Often presented with a plot of theoretical predictions that are compared to measured data, these demonstrations give the opportunity... Topics: Electromagnetic Fields, Energy, theory, diagrams, calculations
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Published in 1989 by Prentice-Hall, this book is a useful resource for educators and self-learners alike. The text is aimed at those who have seen Maxwell's equations in integral and differential form and who have been exposed to some integral theorems and differential operators. A hypertext version of this textbook can be found here. An accompanying set of video demonstrations is available below. These video demonstrations convey electromagnetism concepts. The demonstrations are related to... Topics: electromagnetic fields, energy, theory, diagrams, calculations
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"(This is being submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics, June 1959.)" Topics: Relaxation methods (Mathematics), Numerical analysis, Numerical calculations
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This NASA video segment discusses gears and how they work together as a simple machine. A demonstration is used to explain primary and follower gears and how different-sized gears affect rotational speeds. Multiplication and division is used to determine the force produced by meshed gears. Topics: mechanics, simple machine, rotational speed, gears, calculations, meshed, force, axel, speed
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Skills not practiced are lost. I am not sure that most retail associates would be able to calculate the correct change for a $37.63 charge if the customer presented a $100 bill. Retail clerks rely on the cash register to calculate the sales tax and change that should be returned to the customer. Some registers even suggest alternative combinations of bills and coins to hand to the customer so that the proper change is delivered. Topics: digitalis americana, arithmetic, math, academics, calculations, calculator, addition, cash...
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Cyborgraph is a collision between analog and digital, hardware and software, complex and primitive workflows. Ralp uses experimental methods to compose patterns and complex sequences, based on graphic logarithms and pseudo random calculations mixed with lots of distortions techniques. It is basically an exploration of how vintage and modern equipment can interact together. The artwork represents some pseudo random sequences located in the timeline that he implemented to compose some rhythms.... Topics: barcelona, hardware, digital, complex, calculations, peudo, random, distortions, rhythms, modular,... | 677.169 | 1 |
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10 Distance Learning Mathematics (NumeracyE-Learning Shop
This advanced, highly interactive assessment based e-learning tool, has been aligned to the Edexcel Functional Skills for Level 1&2 Mathematics, therefore can be used for study towards certification.
The unique e-learning programme uses visually engaging rich 2D and 3D graphics/animation, audio, video and text, as well as interactive quizzes to
This is the ideal programme for individuals who would like to develop and enhance their mathematical skills. The certificate is broken down into small units (Awards) which will help you to build your confidence and ability in a range of topics areas.
The Basic Mathematical Skills course aims to provide students with the foundations of maths
Open Study College
Most employers now seek a qualification in Basic Maths and this course allows you to do just that - from home! Course Content Unit 1: Whole Numbers Place value (tens, hundredths, thousandths) Multiplication Division Long division Addition Subtraction Traditional methods Box methods Unit 2: Using Numbers and Calculations Square numbers and roots
Course Description
If you want to develop your knowledge of English and Basic Maths for your own purposes or to improve your career prospects, then this is the course for you.
Many employers ask for job applicants to have english and basic maths qualifications but having to study this subject all over again can be a daunting option.
TheUnique audio-visual resource for the QTS Numeracy Skills Test 2013. Over 4 hours of learning with Mike and Dave's professional recording; a thinking process is included with every question. Easy navigation with flipping-page interactive softwe and thumbnails. Audio and visual instruction combine to enhance memory and learning. Ideal for 2014).
This course will provide students with a greater knowledge and understanding of Advanced Mathematics and help to enhance your current skills. Learners can expect to explore a number of areas such as understanding numbers and formulae, using decimals, fractions, percentages and much more!
It is the ideal course for adults or young people who
The Intermediate Mathematics Skills programme is ideal for adults or young person who would like to develop and enhance their skills. This course strives to help learners to work towards Mathematic Functional Skills at Entry Level 1. You can expect to learn more about using calculations, fractions, decimals, percentages and much more!
Key
This is the ideal programme for individuals who would like to develop their maths skills. This course will be a great starting point and a first step towards gaining other maths qualifications.
This course strives to help learners work towards Mathematics Functional Skills at Entry Level 3.
Key Topics
The Mathematical Skills (Basic) | 677.169 | 1 |
What is contemporary math?
A:
Quick Answer
Contemporary math is a math course designed for college freshman that develops critical thinking skills through mathematics with an emphasis on practical applications. Contemporary math provides students with an alternative to more traditional college algebra courses.
Keep Learning
Traditionally, most college freshman meet their mathematics requirement with a college algebra course that extends high school mathematics into advanced algebra concepts. The math concepts taught in college algebra are not typically used in careers outside of the areas of math, science and technology. Contemporary mathematics teaches students skills used in other career areas while developing critical thinking skills that are useful in any career. Topics covered in contemporary math courses include statistics, practical geometry and logic.
Related Questions
In mathematics, adding numbers, items or amounts produces a sum. The word also refers to a group of arithmetic problems given as a classroom assignment. As a verb, to sum is to find the total of added amounts.
In math, "model" can be either a noun or a verb is used to refer to how strict mathematics can be used in real-world applications. Mathematical models often involve both equations and graphical representations of a problem, often a word problem, that would occur in real life. These types of problems are common for students going into engineering or other physics-related industries.
While mathematics is a universal language, superficial differences in notation exist between English and Spanish-speaking cultures. The way numerals are rendered differ slightly, with 7 usually having a crosshatch mark and the number 9 often resembling a lower-case g. | 677.169 | 1 |
״This text provides the students with simple "cookbook" recipes for solving problems they might face in their studies of...
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״This text provides the students with simple "cookbook" recipes for solving problems they might face in their studies of economics. Since the target audience was supposed to have some mathematical background (admittance to the program requires at least BA level mathematics), the main goal was to refresh students' knowledge of mathematics rather than teach them math "from scratch״ Cook-Book Of Mathematics to your Bookmark Collection or Course ePortfolio
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This video was recorded at MIT World Series: The Passion to Action Summit: The MIT Leadership Center Launch. If Woodie...
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This video was recorded at MIT World Series: The Passion to Action Summit: The MIT Leadership Center Launch. flooding; Timothy Heidel, who's documenting and field testing technological solutions for schools and healthcare centers in Ghanaian villages; Anat Binar, who brings together young Israeli and Palestinian students for a combined computer science and business program, to promote a common language and joint goals; and Harel Williams who broadcasts news of events to computer screens around the MIT campus. Woodie Flowers believes MIT must be in the business of producing students with far-reaching goals and the skills to attain them: The 21st century demands the "technologically literate and philosophically grounded," he says. Engineering students who typically ask, "Why don't you just give us something to analyze?" should instead demand, "Show us someone who needs help." Though Flowers boasts of having "nerd pride," he believes MIT must help students acquire the means to solve problems in the real world. But can MIT accomplish this major "cultural shift״? We're not here "to celebrate the MIT Center for Avoiding Change," he says. The very successful FIRST (For Inspiration and Recognition of Science and Technology) competitions provide a great model, according to Flowers, of engaging young minds in teamwork and "gracious professionalism," offering "high tech stretch goals" and "the hardest fun you've ever had." And FIRST alumni are more likely to get involved in public service while at college, says Flowers. Ultimately, he says, "Leadership can be in the water at MIT, but it has to start early and work all the way through Future Leaders to your Bookmark Collection or Course ePortfolio
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This video was recorded at 14th International Conference on Concurrent Enterprising (ICE), Lisbon 2008. This year, we are...
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This video was recorded at 14th International Conference on Concurrent Enterprising (ICE), Lisbon 2008. This year, we are honored to host the 14th ICE Conference in Costa da Caparica, Lisbon's most famous beach area. It is both our pleasure and honor to have you with us for this key event. An impressive line-up of speakers has been brought together and interactive sessions and workshops await your presence and participation. And this is not all as you will have plenty of time for networking and making new friends. In fact that is what Concurrent Enterprising is about! Nevertheless, we hope that our social events make the whole experience even more enjoyable. Don't miss this opportunity to join us and enjoy ICE Different EU initiatives and Projects for SMEs in clusters to target Innovation to your Bookmark Collection or Course ePortfolio
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DOAJ covers free full text, quality controlled scientific and scholarly journals, aiming to cover all subjects and...
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DOAJ covers free full text, quality controlled scientific and scholarly journals, aiming to cover all subjects and languages.There are journal articles in the following areas:Agriculture and Food Sciences Arts and Architecture Biology and Life Sciences Business and Economics Chemistry Earth and Environmental Sciences General Works Health Sciences History and Archaeology Languages and Literatures Law and Political Science Mathematics and Statistics Philosophy and Religion Physics and Astronomy Science General Social Sciences Technology and Engineering For more information about DOAJ Directory of Open Access Journals (DOAJ) to your Bookmark Collection or Course ePortfolio
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This video was recorded at International Workshop on Coping with Crises in Complex Socio-Economic Systems. For most...
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This video was recorded at International Workshop on Coping with Crises in Complex Socio-Economic Systems. For most diseases, it is always better to medically intervene earlier compared to later. This is because treatment at an early stage is generally more effective, and less expensive. The same is probably true for economies and financial markets. In the current global financial crisis, we have seen billions of dollars sunk into relief and stimulus packages, with hardly any positive result to show for the effort. The reason is clear: these intervention measures are too late. To implement more effective, and less costly economic and fiscal policies, it is important to detect the onset of a financial crisis early. At the same time, we do not want excessive reactions, when the market has merely caught a 'cold'. In this talk, I will describe recent work, based on the statistical segmentation and clustering analysis of financial time series data, that points to characteristic early signs prior to financial crises, characteristic early signs prior to a true recovery, and the characteristic time scales involved for both processes. By looking into a period that covers both the current crisis, as well as the most recent past crisis, we also hope to learn lessons on which intervention measures are effective, and which intervention measures are not Early Signs of Financial Crises to your Bookmark Collection or Course ePortfolio
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This is a free, online textbook that is available as a pdf. "This book is intended to serve as the textbook for a rst-year...
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This is a free, online textbook that is available as a pdf. "This book is intended to serve as the textbook for a rst-year graduate course in econometrics. It can be used as a stand-alone text, or be used as a supplement to another text. Students are assumed to have an understanding of multivariate calculus, probability theory, linear algebra, and mathematical statistics. A prior course in undergraduate econometrics would be helpful, but not requiredconometrics to your Bookmark Collection or Course ePortfolio
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Game Theory is a misnomer for Multiperson Decision Theory, the analysis of situations in which payoffs to agents depend on...
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Game Theory is a misnomer for Multiperson Decision Theory, the analysis of situations in which payoffs to agents depend on the behavior of other agents. It involves the analysis of conflict, cooperation, and (tacit) communication. Game theory has applications in several fields, such as economics, politics, law, biology, and computer science. In this course, I will introduce the basic tools of game theoretic analysis. In the process, I will outline some of the many applications of game theory, primarily in economics and political science. Game Theory has emerged as a branch of mathematics and is still quite mathematical. Our emphasis will be on the conceptual analysis, keeping the level of math to a minimum, especially at a level that should be quite acceptable to the average MIT student. Yet bear in mind that this still implies that you should be at ease with basic probability theory and calculus, and more importantly, you should be used to thinking in mathematical terms. Intermediate Microeconomics is also a prerequisite (simultaneous attendance to one of the intermediate courses is also acceptable). In any case, if you are taking this course, you should be prepared to work hard Economic Applications of Game Theory to your Bookmark Collection or Course ePortfolio
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This is a free online textbook offered by BookBoon.״This is a short, focused text, considering a range of methods, issues and...
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This is a free online textbook offered by BookBoon.״This is a short, focused text, considering a range of methods, issues and concepts in management decision making. Written from the perspective of a student/manager unfamiliar and/or uncomfortable with mathematics, the text considers a range of established decision making methods and presents them in the context of a need to develop an inclusive and integrated view of decision analysis in management Effective Management Decision Making - An Introduction to your Bookmark Collection or Course ePortfolio
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Select this link to open drop down to add material Effective Management Decision Making - An IntroductionFrance Universite Numerique (FUN) is France's largest MOOC platform provider for MOOCs in French. Here you will find a...
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France Universite Numerique (FUN) is France's largest MOOC platform provider for MOOCs in French. Here you will find a large selection of MOOCs in business and several fields of study to choose from taught by outstanding business professionals and top university faculty from 17+ French Universities. FUN offers MOOC eLearners the opportunity to earn European Credit Transfer and Accumulation System (ECTS) units on selected MOOCs (fee paid by eLearners for MOOC credits France Universite Numerique (FUN): French Platform for MOOCs to your Bookmark Collection or Course ePortfolio
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Integration programs include Riem (calculates a numerical value for the Riemann sum approximation of the definite integral of a function), Circumscribe (calculates an approximation of the definite integral of a function using circumscribed or inscribed rectangles), and Trap (uses the trapezoidal rule to estimate the area under the graph of a function). Secant calculates the difference quotient for a function at a given point. Root-finding programs include General Iteration Procedure and Newt, which uses Newton's method to approximate the root of a function. Miscellaneous programs include Trig (draws a circle of radius 1 and rotates a radius around, drawing the horizontal and vertical lines to the x and y axes, showing the behavior of sine and cosine), FEVAL (evaluates the function y1 at the given input x), and Ratios (when given a list of numbers, provides a list of adjacent ratios, x_(n+1) / x_n). With notes on downloading directly to the graphing calculator and step-by-step instructions for use. | 677.169 | 1 |
I read this message and the reference "Flying Functions as a supplement lesson
to the graphing calculator" caught my eye. I looked around to find what this
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reference? Thank you | 677.169 | 1 |
Algorithmic Puzzles
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Read More as well as newer examples from job interviews with major corporations to show readers how to apply analytical thinking to solve puzzles requiring well-defined procedures. The book's unique collection of puzzles is supplemented with carefully developed tutorials on algorithm design strategies and analysis techniques intended to walk the reader step-by-step through the various approaches to algorithmic problem solving. Mastery of these strategies--exhaustive search, backtracking, and divide-and-conquer, among others--will aid the reader in solving not only the puzzles contained in this book, but also others encountered in interviews, puzzle collections, and throughout everyday life. Each of the 150 puzzles contains hints and solutions, along with commentary on the puzzle's origins and solution methods. The only book of its kind, Algorithmic Puzzles houses puzzles for all skill levels. Readers with only middle school mathematics will develop their algorithmic problem-solving skills through puzzles at the elementary level, while seasoned puzzle solvers will enjoy the challenge of thinking through more difficult puzzles.
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Study in detail the basic concepts of Quadratic and other equations at jagranjosh.com to achieve brilliant scores in the Algebra chapter of Quantitative Aptitude Section. These concepts will prepare you for the CAT, CMAT, MAT, XAT, IIFT, SNAP etc exams.
Get an edge on the concepts of Inequalities at jagranjosh.com to fetch excellent grades in the Quantitative aptitude section. Learn the basic concepts to prepare well for CAT, CMAT, MAT, XAT, IIFT, SNAP etc exams.
Learn theconcepts of Functions chapter at jagranjosh.com to gain excellent grades in the Algebra chapter of Quantitative Aptitude Section. These concepts will prepare you for the CAT, CMAT, MAT, XAT, IIFT, SNAP etc exams.
Prepare the concepts of Speed, Time and Distance chapter at jagranjosh.com to ace the Quantitative aptitude section. Learn the basic concepts to prepare well for CAT, CMAT, MAT, XAT, IIFT, SNAP etc exams.
Get an edge on the concepts of Profit and Loss at jagranjosh.com to fetch excellent grades in the Quantitative aptitude section. Learn the basic concepts to prepare well for CAT, CMAT, MAT, XAT, IIFT, SNAP etc exams.
Learn and understand the concepts of Ratio and Proportion chapter at jagranjosh.com to ace the Quantitative aptitude section. These basic concepts will prepare you well for CAT, CMAT, MAT, XAT, IIFT, SNAP etc exams.
Get an edge on the concepts of Percentage chapter at jagranjosh.com to fetch excellent grades in the Quantitative aptitude section. Learn the basic concepts to prepare well for CAT, CMAT, MAT, XAT, IIFT, SNAP etc exams.
Prepare for the Quantitative aptitude section at jagranjosh.com. Learn the basic concepts of Simple Interest and Compound Interest chapter that would aid you in your preparation for CAT, CMAT, MAT, XAT, IIFT, SNAP etc.
In order to prepare for the Quantitative aptitude section of MBA entrance, you must learn the basic concepts of Number system chapter at jagranjosh.com. These concepts would aid you in your preparation for CAT, CMAT, MAT, XAT, IIFT, SNAP etc.Ravi Handa is the founder of Handa ka Funda and has been giving coaching to CAT Aspirants for years. He shares his expertise and helps aspirants to prepare themselves for CAT Exam 2015 through this article. | 677.169 | 1 |
97801950427 book provides a systematic account of the main algorithms derived from the simplex method and the means by which they may be organized into effective procedures for solving practical linear programming problems on a computer. The book begins by characterizing the problem and the method used to solve it, going on to deal with the practicalities of the subject, emphasizing concerns of implementation. The final section of the book discusses the basic principles of optimization: duality, decomposition, and homotopy. In conjunction with the simplex method, they each lead to other key algorithms of linear programming. The author's approach is distinguished by his detailed exploration of ideas and issues that center on the need to structure data suitably, and to organize calculations in an efficient and numerically stable manner. Unlike many liner programming texts, the author's overall perspective is grounded in nonlinear programming rather than combinatorics | 677.169 | 1 |
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Providing students who need a solid understanding of algebra with an excellent start, this textbook encourages student understanding of algebra through the use of modelling techniques and real-data applications.
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Providing students who need a solid understanding of algebra with an excellent start, this textbook encourages student understanding of algebra through the use of modelling techniques and real-data applications.
Read Less
New. Book is New, Has the same ISBN # as the Student Edition. This is the Instructor's Annotated Edition. Quantity Available: 1. Category: Mathematics; ISBN: 039597626X. ISBN/EAN: 9780395976265. Inventory No: 1560741456 | 677.169 | 1 |
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Show More do the math, but also where the concepts come from and why they work. KEY TOPICS: Whole Numbers; Integers; Expressions and Polynomials; Equations; Fractions and Rational Expressions; Decimals; Ratios, Proportions, and Measurement; Percents; More with Geometry and Graphs MARKET: For all readers interested in prealgebra.
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This student-friendly textbook for the Statistics 1 Module of A-Level Maths comprehensively covers the Edexcel exam specification. It contains straightforward, accessible notes explaining all the theory, backed up with useful step-by-step examples. There are practice questions throughout the book to test understanding, with recap and exam-style questions at the end of each section (detailed answers to all the questions are included at the back). Finally, there's a CD-ROM containing two complete Statistics 1 practice exam papers - ideal to print out for realistic practice before the final tests | 677.169 | 1 |
Curriculum Guide for Grade 8
Mathematics
Note about mathematics curriculum: Mathematics curriculum at any grade level or for any topic identifies what students should know and be able to do at a particular grade level or course. However, intricately connected to and supporting all mathematics content and curriculum are mathematical processes that are common to all strands and specific expectations. Students at all levels need experiences with and growing proficiency in these practices. Educators and parents keep these in mind and integrate them constantly into mathematics instruction. These processes describe ways that students need to engage with mathematical subject matter increasingly as they progress through the grades.
1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Source: National Council of Teachers of Mathematics process standards, National Research Council's report on helping children learn mathematics, Adding It Up.
Algebra and Functions
Work with radicals and integer exponents, including fractional exponents
Vocabulary
ŸUse relationships between words to better understand each word's meaning
ŸUse references (print and digital) to determine or verify a word's meanings, find pronunciation or its part of speech
Interpret and use figurative language in context
Distinguish literal and nonliteral meanings of words in context
Distinguish shades of meaning among related words
ŸDistinguish among connotations of words with similar denotations
Learn and use grade-level general academic vocabulary
Speaking and Listening
Participate in collaborative discussions on a variety of grade-level topics
Express ideas clearly and respectfully in group discussions
Follow agreed-upon rules and preparation procedures for discussions
Ask questions and respond to others, building on others' ideas
Analyze the purpose and motives of information presented in many media and formats
Identify an argument, claims; evaluate the soundness of reasoning and evidence
Present claims or information in logical sequence supported with relevant facts and details
Use clear pronunciation and appropriate eye contact and volume when speaking
Add multimedia and visual components to clarify ideas in presentations
Show command of formal English language when speaking for a variety of tasks
Science
Note about science curriculum: The Next Generation Science and Engineering Standards (developed in 2013 in a joint collaboration among the American Association for the Advancement of Science, the National Research Council, the National Science Teachers Association, and Achieve) describe scientific practices that scientists use as they investigate the natural world and engineering practices that engineers use as they design and build models and systems. In addition, they present seven crosscutting concepts that apply across all the topics and fields of science. The teaching of science topics and the corresponding standards at all grade levels K-12 are intricately interwoven with these practices and crosscutting concepts. Students need consistent experience and connection with these two dimensions of science education (practices and cross-cutting concepts) as they work with the third dimension (core science content topics).
Existence, diversity, extinction, and change of life forms in Earth's history
Fossils and the fossil record
Similarities and differences between organisms today and organisms in the fossil record
Evolutionary history of life on Earth
Physical Science
Types of forces and force interaction
Force and motion
Energy and motion
Newton's laws of motion
Electric and electromagnetic forces
Gravitational force
Gravitational forces between objects in the solar system
Waves (light, heat, sound), their properties, and transmission
Electromagnetic radiation
Magnetic fields; Earth's magnetic fields
Transmission of digital signals as wave pulses
Earth and Space Science
The universe and its stars
Observation of the universe
Classification of celestial objects
Milky Way and other galaxies
The structure of Earth's solar system
Sun, Earth, and moon relationships
Motions of bodies in the solar system
Patterns of apparent motion of the sun, moon, and stars
The tilt of Earth's axis and its effects
Moon phases
Tides
History of planet Earth
Geologic time scale, interpreted from rock strata and the fossil record
Renewable and nonrenewable energy sources
Environmental concerns and conservation
Social Science - United States History through Reconstruction
Notes about social science curriculum:
1. These ten themes of social studies serve as a background framework for the teaching of the social sciences at all grade levels. They weave through all content and are interrelated with one another. Students need exposure to and development of these themes throughout the grades.
2. In addition, there are social studies practices and habits and literacy skills that should be fostered and integrated with all social studies content. Students at all levels need grade-level appropriate experiences that develop and polish these practices.
1. Gathering, interpreting, and using evidence from various sources 2. Applying critical thinking skills to organize, use, and evaluate information 3. Problem solving and decision making processes 4. Chronological reasoning and understanding of causation 5. Comparing and understanding events and relationships in contex 6. Comparing different ways of looking at an event or problem 7. Understanding how people might be affected by events, changes, settings, or problems 8. Communicating knowledge, research conclusions, and ideas in written, oral, and visual forms 9. Geographic reasoning and use of geographic tools 10. Describing and explaining economics and economic systems 11. Civic understanding and participation | 677.169 | 1 |
Peer Review
Ratings
Overall Numeric Rating:
This is a collection of tools to visualize graphs in two and three dimensions. Included are applications to first, second, and third semester calculus.
Type of Material:
Collection of applets
Recommended Uses:
classroom demo; student exploration
Technical Requirements:
Flash Player Version 8 or higher although some of the applets will run on Flash Player 7
Identify Major Learning Goals:
To visualize concepts from calculus.
Target Student Population:
First, second, and third semester calculus
Prerequisite Knowledge or Skills:
A basic knowledge of calculus.
Evaluation and Observation
Content Quality
Rating:
Strengths:
This is a collection of about 25 activities; some were authored in collaboration with Doug Ensley of Shippensburg University. Most of them allow the student to type in the formula for a curve or surface or series and then the computer will sketch it. The activities include parametric curves and surfaces that can be defined in the main coordinate systems: rectangular, polar, cylindrical and spherical. Several of the activities include a gallery of pre-programmed curves and surfaces. The user has the ability to change the scale and rotate the objects. Some of the activities include an exercise where the student is asked to provide the equation for the displayed object. The author did an excellent job of displaying an extensive list of functions for each activity. The displays of the graphs are easy to see. Included on the site is a link to the code for the activities and a tutorial on how to create such code
Concerns:
none
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
This collection can be used by the student who is working on a project or homework problem that involves graphing. An instructor can also create curriculum where the student is asked to visually explore a curve or surface. Some of the activities are exploratory in nature. For example, one of the activities displays the graph of a function. The student uses a slider to graph the derivative and show a piece of the tangent line at the point.
Concerns:
none
Ease of Use for Both Students and Faculty
Rating:
Strengths:
Although there is a lot going on with each activity, the buttons and text fields are easy to use. For the activities that ask the student to enter a function into a text box, there is a syntax button. When the mouse hovers above this button, a full set of instructions is provided. The instructions include examples of functions that could be inputted. The main page that contains links to the activities also includes brief explanations of what the activity demonstrates. The lessons for faculty on how to create the activities are well written. Anyone with math background and with experience using Flash's Actionscript language will be able to create their own 3D animated graphics.
Concerns:
none | 677.169 | 1 |
An Algebra Primer: What You Need to Know BEFORE You Can Solve for X
Overview you need to familiarize yourself with the special signs, symbols, and terms that make up that language."
Product Details
Meet the Author
Mark Phillips has taught at Northwestern University and has worked as an editor in the publishing field for over 40 years. He is the author of 11 books on various subjects, including history, music, grammar, vocabulary building, and mathematics. | 677.169 | 1 |
Mathematics
Mathematics is the abstract study of pattern and structure. Areas of mathematics include arithmetic, algebra, geometry, calculus, and various other theoretical and applied subjects. Mathematics is the foundation for many fields of study, including biological, physical, computer, behavioral, and social sciences, as well as engineering. Students may take mathematics courses to prepare for a mathematics major, to meet prerequisites in related disciplines, or to fulfill general education requirements.
Career options for mathematics majors include actuary, accountant, mathematician, statistician, teacher, and work in various computer-related fields. | 677.169 | 1 |
practical solution for busy
Math online courses are a very practical solution for busy students. Nearly everyone owns a computer or a similar device that can connect you to the internet. The worldwide web contains an ocean of knowledge, starting from the most basic to the most complex data a textbook can offer. | 677.169 | 1 |
New Signpost Maths Student Book 5
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Motivate your maths class, with New Signpost Maths, a series written by Alan McSeveny and his experienced author team to meet the requirements of the NSW, ACT and WA state curricula.
Each of the New Signpost Maths Student Books provide a full year's work, complete with diagnostic tests, a useful dictionary and answers to all activities. Page spreads are visually attractive with a full-colour layout, with the aid of quirky cartoons to assist in the explanation of concepts. Students are encouraged to engage in concrete mathematics experiences as well as pencil and paper activities. Throughout New Signpost Maths there is emphasis on active hands-on learning, language development, problem-solving strategies and the use of calculators and computers. Units are sequenced in a suggested teaching plan, however the student book has a flexible structure, enabling you to create your own teaching schedule. | 677.169 | 1 |
book is for sophomore-level or junior/senior-level first courses in linear algebra and assumes calculus as a prerequisite. This thorough and accessible text, from one of the leading figures in the use of technology in linear algebra, gives students a challenging and broad understanding of the subject. The author infuses key concepts with their modern practical applications to offer students examples of how mathematics is used in the real world. Each chapter contains integrated worked examples and chapter tests. The book stresses the important roles geometry and visualization play in understanding linear algebra | 677.169 | 1 |
About this Book
Mathematical Methods for Physical and Analytical Chemistry presents mathematical and statistical methods to students of chemistry at the intermediate, post-calculus level. The content includes a review of general calculus; a review of numerical techniques often omitted from calculus courses, such as cubic splines and Newton's method; a detailed treatment of statistical methods for experimental data analysis; complex numbers; extrapolation; linear algebra; and differential equations. With numerous example problems and helpful anecdotes, this text gives chemistry students the mathematical knowledge they need to understand the analytical and physical chemistry professional literature. | 677.169 | 1 |
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