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Spreadsheets and Numerical Analysis
Av D. McLaren
250 sidor, 1997, 230 kr (exkl. moms och frakt)
Using spreadsheets as a powerful tool to discover numerical analysis at college and undergraduate level. The text includes examples to illustrate the various methods discussed and includes appropriate sample spreadsheets. Many are structured so that the reader has the exercise of finishing them in order to see the results mentioned in the text. It is intended that readers' curiosity will lead them to explore beyond the given problems.
The book is based on a second year course taught by the author in the La Trobe University School of Mathematics. The mathematical knowledge assumed is that gained from first-year mathematics, namely basic calculus and elementary matrix algebra.
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I've always wanted to learn worksheet + finding the slope , it seems like there's a lot that can be done with it that I can't do otherwise. I've searched the internet for some useful learning resources, and checked the local library for some books, but all the information a lot of money! Anyway, now you can't change it. Now to make sure that you do well in your exams I would recommend trying Algebra Buster. It's a very easy to use software. It can solve the toughest problems for you, and what's even cooler is the fact that it can even explain how it did so! There used to be a time when even I was having difficulty understanding geometry, binomial formula and ratios. But thanks to Algebra Buster, it's all good now.
I am a regular user of Algebra Buster. It not only helps me complete my homework faster, the detailed explanations given makes understanding the concepts easier. I strongly advise using it to help improve problem solving skills.
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Organic Chemistry — A Market Leading, Traditional Approach to Organic Chemistry Throughout all seven editions, Organic Chemistry has been designed to meet the needs of ... > read more
Calculus — Stewart's CALCULUS, Fifth Edition has the mathematical precision, accuracy, clarity of exposition and outstanding examples and problem sets that haveDigital Teaching Aids Make Mathematics Fun(February 24, 2010) — It will come as a surprise to schoolchildren everywhere: Learning the intricacies of algebra, calculus and geometry can be fun. So say a team of European researchers who believes they have cracked ... > read more
Sharing Wisdom, Teacher to Teacher(June 22, 2011) — How do you teach math students to speak and write effectively about what they do? Crucially, how do you teach their teachers -- themselves mathematicians -- how to impart and evaluate these skills? A ... > read more
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BASIC CONCEPTS MIDDLE SCHOOL
Math
Price:$7.99 Available Qty: 8
Qty:
Middle School Geometry: Basic Concepts These lessons provide step-by-step instructions, sample problems, and practice that enable students to work independently and focus on needed skills. Includes assessments in standardized test forms and answer key. 48
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Book Description: Only elementary math skills are needed to follow this instructive manual, which covers many familiar machines and their components, including levers, block and tackle, and the inclined plane and wedge, in addition to hydrostatic and hydraulic machines, internal combustion engines, trains, and more. 204
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Math 130-03, Spring 2001 Information for the Third Test
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The last in-class test in this course takes place in class on Friday, April 20.
It covers Chapter 4, Sections 1,2, 4, and 5; Chapter 5, Section 1; and Labs
first three labs 9, 10, and 11. Of course, you are also responsible for previous
material, especially the derivative formulas that were covered on the previous test.
Here are some of the terms and ideas that you should have mastered for this test:
All the derivative formulas that you learned previously
Inverse functions
Inverse functions as "undo" operations
Domain and range of an inverse function
Finding an inverse function from a formula
Finding an inverse function from a graph
One-to-one function
Horizontal line test
Restricting the domain of a function to get an invertible function
The derivative of an inverse function
Exponential functions
The number e
Logarithmic functions
Logarithmic functions are the inverse functions of exponential functions
The natural logarithm, ln(x)
Properties of exponential functions
Properties of logarithmic functions
Using inverse functions to solve equations
Solving equations involving logs and exponentials
Derivative formulas for logarithmic and exponential functions
Using the chain rule with logarithmic and exponential functions
Inverse trigonometric functions: arcsin, arccos, arctan, arcsec
Derivatives of the inverse trigonometric functions
Related rates
Solving related rate word problems (This is a big one!)
A function that is increasing or decreasing on an interval
Relationship of the first derivative to increasing/decreasing
A function that is concave up or concave down on an interval
Relationship of the second derivative to concavity
Relationship of the first derivative to concavity
Inflection point
Drawing graphs of functions, using derivatives, concavity, etc.
Reading properties such as increasing/decreasing or concavity from a graph
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Are calculus and real analysis the same thing? They are written in greek. I was wrong , the total pages are 2800 (2 theory and some problems and examples and 2 other only problems.) It uses literature from apostol,ayoub,birkhoff,comtet,ciang and lots of other[80 total].But they are extreemly hard to read. Even the most difficult textbook for calculus is easy compared to them.And they are given at engineering school
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study was performed using a convenience sample of 90 students at a northeastern community college to determine gender differences of math anxiety and its effect on math avoidance. Four sections of an introductory English class were given aDuring the last decade, new technologies created a deluge of potential drug targets. Sifting through thousands of potential drug targets is a major industry bottleneck. Pharmaceutical companies can save billions of dollars by identifying most...
Each year thousands of students are tracked into mathematics classes. In these particular classes, students may struggle or find their mathematics skills less academically able than their classmates and give up on the tasks that are introduced to
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This is the first in a sequence of courses designed to prepare students to take Advanced Placement Calculus. It incudles aglebraic expressions, linear equations, and inequalities and their graphs, functions, and function notation, exponential relationships and models of exponential functions, transformations in the corrdinate plane, interpreting, comparing and summarizing data fitting, constructions, similar and congruent triangles, right triangle trig, circles, area and volume. (Prerequisite course: 8th grade math)
Last Test over the semester Tuesday May 14th! Then will will begin exam review.
This is the third in a sequence of 4 math courses designed to prepare students to enter college at the calculus level.It includes exponential and logarithmic functions, matrices, polynomial functions or higher degree, conic sections, and normal distributions.(Prerequisite Course: successful completion of Math 2)
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Our reviewers—top-flight teachers and other outstanding science educators—have determined that this resource is among the best available supplements for science teaching.
[Read the full review]
Description
This Title Also Available as Part of a Set:
Set: Stop Faking It! Series, Set of 9 Books
Intimidated by inertia? Exasperated by electricity? Panicked over the periodic table? The best-selling Stop Faking It! series comes to your rescue. Author Bill Robertson has been helping teachers develop a deeper understanding of scientific principles for years. He uses fun examples, easy-to-understand language, and accurate explanations to teach in a stress-free way. This 9-book set includes all the books in the series.
Member Price: $161.56
Nonmember Price: $201.90
Book Series
View other books in the Stop Faking It! Finally Understanding Science So You Can Teach It Series.
Think critically and logically to make the relationships between evidence and explanations.
Use mathematics in all aspects of scientific inquiry.
Published Reviews
"A rich resource that will help teachers develop a deeper understanding of the concepts they teach. Robertson also includes inquiry-based activities, supported by written and illustrated descriptions, that can be easily adapted across grade levels. With humor and insight, the author encourages teachers and students to go beyond memorization to understanding."
Curriculum Connections, School Library Journal, Spring 2007
"Science educator and writer Robertson has in mind teachers and parents as he presents the basics of mathematics at a very accessible level. He uses everyday examples and common sense…. Robertson is sensitive to the needs of the learner and refreshingly free from anything that might make the reader feel like a complete idiot."
Reference & Research Book News, August 2006
Customer Reviews
Great Re-Fresher!
Reviewed by: Emily Kelly (, ) on June 23, 2009
An excellent, easy to read book for anyone; from students to teachers! The book is very easy to understand and provides great clarification on all aspects provided. If all math books were this easy to read and clear cut, math wouldn't be so dreaded and challanging. This is an excellent book to help you gain a better understanding behind the math operations and rules. This book answers all of your math questions you or your students may have, from basic to more indepth! Stop Faking It has clear explanations, it's easy to follow, and has great illustrations.
Quick Refresher
Reviewed by: Robert Gilmore (Milford, MA) on July 15, 2008
When I finished reading this book I found myself wishing there was even more... If only standard math books could be read as easily and math concepts shared as effectively. I've enjoyed all of my Stop Faking It! books.
Stop Faking It! Math
Reviewed by: Whitney (Carlisle, PA) on May 2, 2008
Stop Faking It! is the ideal resource for teachers, parents, or for anyone who wants to get a better understanding of both some very fundamental and more advanced math concepts. The book is meant to give educators and others a deeper understanding of why we have certain math "rules" and procedures. Most of us, especially educators who do not have a subject-specific certification, have learned "rules" for many math procedures. We know what the rule is and that it works for a particular situation, but in many cases we don't actually know where the rule came from or why it works. This book attempts to address the where, and why of math "rules", particularly those that apply to:
• adding/subtracting/dividing/multiplying in base 10, base 5 and base 2
• finding equivalent fractions
• using common denominators when adding/subtracting fractions
• solving word problems
• using variables
• and much more!
The book is most beneficial if the reader follows the suggestions of the author and reads the entire chapter pertaining to a specific concept. In each chapter there is a short preview where the author suggests some activities that help to get the reader thinking about the concept. For example, when preparing to introduce the base 10, 5, and 2 number systems, the author "assigns" activities that have the reader separating blocks into groups of ten. Next comes the explanation, where the author introduces the concept and explains it, referencing the activities the reader has just completed. Most of us have experience with base 10, and so the author builds on our prior knowledge and then guides us to transfer that understanding to the procedure for using base 5 and base 2. The combination of carefully chosen pre-explanation activities and clear, concise explanations helps the reader to "get" the reason behind the "rule" or procedure. Following the explanations, the author gives a summary and suggestions for practice.
Stop Faking It! is not a large book, which makes it seem readable. The explanations are thorough, but not too wordy. There are many pictures and diagrams which help guide the reader very well. In this particular book, the author has included "guideposts". Guideposts are reminders for the specific skill or concept being addressed. Their purpose is to help the reader stay focused on the task at hand. They are also helpful because they allow the reader to get a "preview" of what they are going to learn should they decide to purchase and read the book.
Judging by what I have learned about concepts I thought I understood, I can only imagine the benefit of reading about topics I know I don't understand. Again, the idea is that the reader gains a deeper understanding so that they are able to better teach the concepts to their students or children.
Stop Faking It! Math is just one of 7 books in the series. The other six cover Science topics such as sound, force & motion, chemistry basics, electricity and magnetism, energy, and light. The series, put out by the NSTA (National Science Teachers Association) Press, has won many awards for its success in helping educators and parents in their quest to help their students and better understand concepts themselves.
Resource for the Math Impaired
Reviewed by: Rosalind Charlesworth (Ogden, UT) on November 2, 2007
I recommended it as a possible text to colleagues who are developing a course in math for early childhood teachers. The objective of the course is to build math understanding for prek-3 preservice teachers prior to taking their math methods course. These students tend to be victims of poor math instruction and need to gain confidence. I think this book's hands-on method would be excellent for these students.
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Peer Review
Ratings
Overall Rating:
This site is an interactive learning object that utilizes the GeoGebra tool (see to investigate lines and their equations. It contains three interactive windows where the student can move points and pieces of a line construction to see the effect on the line and its equation.
Learning Goals:
To understand the relationship between the graph of a line and its equation.
Target Student Population:
Beginning algebra students.
Prerequisite Knowledge or Skills:
Knowledge of the coordinate plane and equations and their coefficients.
Type of Material:
Simulation
Recommended Uses:
An instructor can use this to present lines and equations or can assign activities for students to work on.
Technical Requirements:
JAVA enabled browser
Evaluation and Observation
Content Quality
Rating:
Strengths:
This learning object contains every aspect of a line and its equation. As a student moves a point or other piece of a line, the equation dynamically changes. For the first window, the slope and y-intercept is shown both in the equation as the coefficients and alone. The student has the ability to change the window, the fixed point, the slope and the y-intercept. For the second window, with a given fixed point, the student can change the slope and watch the effect of everything else. For the third window, with the slope fixed the y-intercept can be changed or with the y-intercept fixed, the slope can be changed. There is sound use of color coding throughout.
Concerns:
There is too much information given on each screen. A beginning algebra student will get lost in the details and will lose the main point.
The explanation of the first window does not match what the first window is all about. Two links in the bottom of the page point to non-existing locations.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
For the tactile learner, this can be and effective exploration tool. An instructor can create a set of questions that guide the student through the tool and through learning how the equation of a line is related to the graph of the line.
Concerns:
The beginning algebra student is likely to get turned of due to the number of technical displays that are given. For example there is use of delta x over delta y for the slope, which is notation that this population has not seen before. Also the equation:
LPtLsp(x) = m(x – P1) + P2
is not something beginning algebra students can comprehend.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
The second and third activities are accompanied with explanations that will let the student know what can be done. The slider is simple to use and the dragging the point is also easy.
Concerns:
Since the explanation of the first activity does not match the activity, a student will get very confused about what to do.
The applet windows do not work in Slimbrowser. Two dead links in the bottom of the page create navigation problems.
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Click on the Google Preview image above to read some pages of this book!
Emphasizes a Problem Solving Approach A first course in combinatorics
Completely revised, How to Count: An Introduction to Combinatorics, Second Edition shows how to solve numerous classic and other interesting combinatorial problems. The authors take an easily accessible approach that introduces problems before leading into the theory involved. Although the authors present most of the topics through concrete problems, they also emphasize the importance of proofs in mathematics.
New to the Second Edition This second edition incorporates 50 percent more material. It includes seven new chapters that cover occupancy problems, Stirling and Catalan numbers, graph theory, trees, Dirichlet's pigeonhole principle, Ramsey theory, and rook polynomials. This edition also contains more than 450 exercises.
Ideal for both classroom teaching and self-study, this text requires only a modest amount of mathematical background. In an engaging way, it covers many combinatorial tools, such as the inclusion-exclusion principle, generating functions, recurrence relations, and Pólya's counting theorem.
The current edition is about 60% longer and represents an extensively updated collaboration coauthored with R.B.J.T. Allenby. Both authors have decades of experience teaching related material at the University of Leeds. ... The book is beautifully structured to facilitate both instruction in a classroom as well as self-instruction. ... Every section of the book has a number of [paired] exercises which are designed to solidify and build understanding of the topics in the section. ... This is exactly the kind of exercise regimen serious readers, instructors, and students need and are so rarely provided. ... Another pedagogical asset of the text is the extensive incorporation of historical anecdotes about the discoverers of the results. ... it fosters an admiration of the developers of the field, an attitude which is key to transforming students of mathematics into professional mathematicians. ... The authors have created an interesting, instructive, and remarkably usable text. The book clearly benefits instructors who need a solid, readable text for a course on discrete mathematics and counting. In fact, for any professional who wants an understandable text from which they can acquire a broad and mathematically solid view of many of the classic problems and results in counting theory, including their origin, proof, and application to other problems in combinatorics, this book is recommended. -James A. McHugh, SIAM Review, 54 (1), 2012 ... thoughtfully written, contain[s] plenty of material and exercises ... very readable and useful ... -MAA Reviews, February 2011 The reasons I adopted this book are simple: it's the best one-volume book on combinatorics for undergraduates. It begins slowly and gently, but does not avoid subtleties or difficulties. It includes the right mixture of topics without bloat, and always with an eye to good mathematical taste and coherence. Enumerative combinatorics is developed rather fully, through Stirling and Catalan numbers, for example, before generating functions are introduced. Thus this tool is very much appreciated and its 'naturalness' is easier to comprehend. Likewise, partitions are introduced in the absence of generating functions, and then later generating functions are applied to them: again, a wise pedagogical move. The ordering of chapters is nicely set up for two different single-semester courses: one that uses more algebra, culminating in Polya's counting theorem; the other concentrating on graph theory, ending with a variety of Ramsey theory topics. ... I was very much impressed with the first edition when I encountered it in 1994. I like the second edition even more. ... -Paul Zeitz, University of San Francisco, California, USA Completely revised, the book shows how to solve numerous classic and other interesting combinatorial problems. ... The reading list at the end of the book gives direction to exploring more complicated counting problems as well as other areas of combinatorics. -Zentralblatt MATH 1197
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An Introduction to the Mathematical Skills Needed to Understand
Finance and Make Better Financial Decisions
Mathematical Finance enables readers to develop the mathematical skills
needed to better understand and solve financial problems that arise in
business, from small entrepreneurial operations to large corporations,
and to also make better personal financial decisions. Despite the
availability of automated tools to perform financial calculations, the
author demonstrates that a basic grasp of the underlying mathematical
formulas and tables is essential to truly understand finance.
The book begins with an introduction to the most fundamental
mathematical concepts, including numbers, exponents, and logarithms;
mathematical progressions; and statistical measures. Next, the author
explores the mathematics of the time value of money through a discussion
of simple interest, bank discount, compound interest, and annuities.
Subsequent chapters explore the mathematical aspects of various
financial scenarios, including:
- Return and risk, along with a discussion of the Capital Asset Pricing
Model (CAPM)
- Life annuities as well as life, property, and casualty insurance
Throughout the book, numerous examples and exercises present realistic
financial scenarios that aid readers in applying their newfound
mathematical skills to devise solutions. The author does not promote the
use of financial calculators and computers, but rather guides readers
through problem solving using formulas and tables with little emphasis
on derivations and proofs.
Extensively class-tested to ensure an easy-to-follow presentation,
Mathematical Finance is an excellent book for courses in business,
economics, and mathematics of finance at the upper-undergraduate and
graduate levels. The book is also appropriate for consumers and
entrepreneurs who need to build their mathematical skills in order to
better understand financial problems and make better financial choices
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Advance... read more
A First Look at Perturbation Theory by James G. Simmonds, James E. Mann, Jr. This introductory text explains methods for obtaining approximate solutions to mathematical problems by exploiting the presence of small, dimensionless parameters. For engineering and physical science undergraduatesCalculus: A Short Course by Michael C. Gemignani Geared toward undergraduate business and social science students, this text focuses on sets, functions, and graphs; limits and continuity; special functions; the derivative; the definite integral; and functions of several variables. 1972 edition. Includes 142 figuresAn Introduction to the Calculus of Variations by L.A. Pars Clear, rigorous introductory treatment covers applications to geometry, dynamics, and physics. It focuses upon problems with one independent variable, connecting abstract theory with its use in concrete problems. 1962 edition.
Calculus: A Modern Approach by Karl Menger An outstanding mathematician and educator presents pure and applied calculus in a clarified conceptual frame, offering a thorough understanding of theory as well as applications. 1955Calculus of Variations by Lev D. Elsgolc This text offers an introduction to the fundamentals and standard methods of the calculus of variations, covering fixed and movable boundaries, plus solutions of variational problems. 1961 edition.
The Malliavin Calculus by Denis R. Bell This introductory text presents detailed accounts of the different forms of the theory developed by Stroock and Bismut, discussions of the relationship between these two approaches, and a variety of applications. 1987Tensor Calculus: A Concise Course by Barry Spain Compact exposition of the fundamental results in the theory of tensors; also illustrates the power of the tensor technique by applications to differential geometry, elasticity, and relativity. 1960 edition.
Calculus of Variations by I. M. Gelfand, S. V. Fomin Fresh, lively text serves as a modern introduction to the subject, with applications to the mechanics of systems with a finite number of degrees of freedom. Ideal for math and physics studentsIntroduction to the Calculus of Variations by Hans Sagan Provides a thorough understanding of calculus of variations and prepares readers for the study of modern optimal control theory. Selected variational problems and over 400 exercises. Bibliography. 1969 edition.
Tensor Calculus by J. L. Synge, A. Schild Fundamental introduction of absolute differential calculus and for those interested in applications of tensor calculus to mathematical physics and engineering. Topics include spaces and tensors; basic operations in Riemannian space, curvature of space, more.
Product Description:
Advanced undergraduate/graduate-level. 1984
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"The course was excellent. It has contained everything I needed as a beginner to decision maths, it helped me to understand the contents of the module as well as learning the best way to teach and support my students". January 2012
Many students find the transition from AS level Mathematics to A2 difficult and do not perform to the best of their ability. This course unpicks the best ways to boost achievement of lower ability students through focused teaching, careful monitoring and tailored support. The course will provide teachers with useful materials to use in their day to day lessons, straightforward tools for identifying students who are having difficulty and ideas for helping struggling students.
What are the benefits of attending this course?
Teachers attending this course will feel more confident in:
Identifying those topics which cause less able students the most difficulty
Managing the transition of less able students from AS level to A2 level Mathematics
Tracking students' progress to identify problems as, and when they occur
Providing tailored support for any students struggling with a topic
Teaching the difficult topics to lower ability students
Planning their teaching to support the less able students in a group
Preparing students to obtain the highest grades possible commensurate to their ability
Who should attend?
Any A level Mathematics teacher who wishes to learn how to support their less able students
Resources & Materials
On arrival at this course you will receive a specially prepared file containing detailed notes, teaching materials and resources which will be of immediate practical benefit in the classroom
You will also receive a full set of additional resources electronically
Course Leader: Phil Chaffé
Phil Chaffé is the West Midlands Area Coordinator of the Further Mathematics Support Programme. He has wide experience of A level Mathematics teaching. Phil has organised revision days for AS and A2 mathematics modules at Warwick University and has vast experience in professional development courses for Teachers. He is experienced and knowledgeable about current initiatives in post-16 mathematics and is well placed to discuss their implications for teaching and learning.
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Elementary Algebra - 9th edition
Summary: Ideal for lecture-format courses taught at the post-secondary level, ELEMENTARY ALGEBRA, Ninth Edition, makes algebra accessible and engaging. Author Charles ''Pat'' McKeague's passion for teaching mathematics is apparent on every page. With many years of experience teaching mathematics, he knows how to write in a way that you will understand and appreciate. His attention to detail and exceptionally clear writing style help you to move through each new concept with ease, and real-wor...show moreld applications in every chapter highlight the relevance of what you are learning
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GCSE Maths:Linking sequences, functions and graphs
Algebra Study Unit 9: Linking sequences, functions and graphs is for individual teachers or groups of teachers in secondary schools who are considering their teaching of algebra. It discusses some stimulating activities to help pupils to link sequences, functions and graphs.
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Course Communities
Sequences and Series of Constants Plotter
The applet shows graphically and numerically consecutive terms of a sequence or consecutive partial sums of a series. The user enters a formula for a sequence or a series and the terms are plotted. Many examples and practice problems are given. The applet illustrates many concepts associated with convergence and divergence of sequences and series, including the speed of convergence, subsequences, and Weyl's Theorem on Uniform Distribution. It provides a quick and easy illustration that finding limits of sequences by evaluating a few terms can be misleading.
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Center for Distance and Independent Study 6th Grade Math, Part One
Welcome
We are pleased that you selected this independent study course to fulfill your unique educational needs. You are now a member of a large and diverse student body—a student body that comes from all parts of the United States and many parts of the world.
Although the freedom to choose when and where to study is a privilege, it is also a responsibility that requires motivation and self-discipline. To succeed at independent study, you will need to develop a study plan by setting realistic goals and working toward them.
Course Introduction
This course is designed to instruct you in the skills of basic mathematics at the 6th grade level. Each section of the course builds on previously covered material to lead to complete understanding of topics. These topics include recognition and use of number patterns; graphing and statistics; addition, subtraction, multiplication, and division with decimals; relating decimals and fractions; and mathematical operations involving fractions.
Catalog Description:This course focuses on building number concepts, recognizing and using number patterns and simple algebra, exploring statistics, and performing basic operations using decimals and fractions.
Time Limit for Course Completion: 9 months. All assessments must be submitted and graded within this time.
Textbooks/Materials
Required Textbook and Other Materials
In addition to your textbook, you will also need a notebook and pencil to complete each lesson. Some exercises call for a basic calculator. This can be any type of calculator. You will need only the basic addition, subtraction, multiplication, and division functions.
In some cases, you will need graph paper. Graph paper marked in quarter-inch increments is best for this course. You can access this for free at MathBits.com or at many other Web sites.
Additional supplies are also needed to complete many of the activities suggested in the course. Most of the supplies are things that can easily be found around your home. They are listed here by lesson and more specifically by section at the beginning of each lesson.
Note: Materials for the Additional Practice Exercises are listed in the Parent-Teacher Manual only.
How to Study for This Course
The new material presented in each section of this course is designed to build on material covered in previous sections. Thus, it is a good idea to take the time to review material from previous sections as you progress through the lessons. The following study hints will help you review and learn new material more easily:
Set a work time and stick to it. Decide what time of day you work best, and then work at that time as often as possible; don't allow other interests or activities to interfere with your work time.
Set a work pace. Decide with your parent or instructor the pace at which you will complete the sections. A recommended pace is to complete one section per day. However, you may find that you need more time or can work more quickly.
Reward yourself. Set goals for the amount of work you need to complete to stay on your schedule. Then reward yourself after you have completed your goal for the day. You might have a snack, take time to read a favorite book, etc. Don't forget to take short breaks while you are working as well.
Skim the reading assignment. When you begin a new lesson, briefly look over the entire reading assignment in the textbook for that lesson. The correct chapter and pages for the lesson will be listed under the Reading Assignment banner for each lesson. This will give you an idea of the material you will be studying throughout the lesson.
Check your skills. You may want to work the Getting Started exercises at the beginning of each chapter in your textbook. This will help you know whether there are skills you need to review before beginning the new lesson. You can access the answers to Getting Started exercises by clicking on the link in your given lesson's overview, which appears right after you are prompted to do the exercises.
Read textbook pages first. As you begin a new section of a lesson, carefully read the textbook pages listed next to the section title in the commentary. You should read these pages before reading the commentary, which will refer back to textbook examples and material.
Look for textbook notes and boxes. When you read the textbook pages, pay careful attention to the notes in the margins. These notes will tell you things like "What You'll Learn," "New Vocabulary" for the section, "Real-Life Math" situations, and "Study Tips." Also look for "Key Concept" and "Concept Summary" boxes throughout the sections. These will highlight important information you need to know.
Keep note cards with important concepts and tricky vocabulary. As you learn new concepts or challenging words, write them on note cards and keep them in a folder or file box. Then you can quickly refer back to the note cards as needed. Important vocabulary words are shown in bold in the lesson commentaries.
Work your assignments in a notebook. If you keep your work together in the same place, you can more quickly refer back to it to refresh your memory as you progress.
Use Internet resources. Throughout the course, Web sites will be listed in the commentaries and elsewhere. If you have Internet access, be sure to check them out for helpful hints, interactive practice, or further explanation of material. Also be sure to make use of your textbook publisher's Online Study Tools. The site has lots of extra examples, self-checking quizzes, study guides, and vocabulary review activities. Information is provided for each section in the textbook.
Take advantage of the additional Practice Exercises provided in the Parent-Teacher Manual. You probably won't need to work all of these, but you will want to work many of them. They are there to help you review, expand ideas, and have fun. Don't miss out on the chance to challenge yourself!
Additional Study Hints
Submit your first progress evaluation early. However, don't rush the course. The minimum completion time for all credit courses at this level is four weeks, and you have up to nine months to complete the course.
Be able to do all lesson objectives. Learning is active, and courses at any level are often designed with objectives or actions that can be done as evidence that you have learned something. One advantage of independent study is that learning objectives are clearly written for each lesson.
Review the hints for independent study.This is an independent study course and is likely different from other courses you have taken. Begin by reviewing these hints, which will help you adjust your computing and study habits so you will have the best chance of earning the grade you want.
Download an "Independent Study Planning Sheet" (pdf) to track your progress. The number of lessons, progress evaluations, and exams will directly affect how long it takes to complete any given CDIS course. As you work through this course, check your schedule often to make sure you're on track. Keep in mind that all progress evaluations must be submitted and graded within the course time limit.
About the Course Developer
Welcome to Sixth Grade Mathematics, Part One! I am excited to have the opportunity to help you explore new math concepts and develop new skills this semester. My name is Emily Hall, and I live with my family in St. Charles, Missouri. I received a Bachelor of Science degree in education from the University of Missouri in 1998. I am certified to teach grades 1–6. Before leaving to stay home with my daughter, I taught for several years in the Fort Zumwalt School District, in O'Fallon, Missouri. While there, I served as curriculum and grade-level coordinator. I now enjoy writing and tutoring students, especially in all levels of math!
Technical Specifications
To complete this course, you will need access to a computer with a modern Web browser (see recommended browsers below), a working Internet connection (56k dial-up or broadband), word processing software, and disk space to save your work.
Recommended Web Browsers
Windows: Internet Explorer (version 7 or 8) or Firefox 3.5.
Mac OS: Safari 4 or Firefox 3.5.
Your browser should support graphics at a screen resolution of 800 x 600 or higher, run JavaScript (the browsers above do by default), and accept cookies, which are used solely to verify your login. This course has been designed to be accessible to all students, including those using assistive technologies.
Portions of this course may require Adobe Flash Player.
Word Processing Software
You online. We do not provide or support any word processing software; however, OpenOffice is available free-of-charge at the above link.
or You may need to view PDF documents as part of this course.
Virus Protection
It is suggested that you have virus protection software on your system. Virus protection software will help to protect your system (and ours) against computer viruses. Students can visit the anti-virus software page from the Division of IT for more information.
Additional Technical Specifications
In order to view the interactive exercises in this course, your computer must have the most recent version of Flash player, which you can download for free from the Adobe Flash Player Web site by clicking on the link below.
Begin Coursework
Starting with the first lesson, study the lesson's purpose, objectives, and commentary. Then complete the reading assignment and any recommended study activities. Take notes and make sure you understand all the material presented in the readings. Follow this procedure for each lesson. Complete progress evaluations in the order they are presented in this course.
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Advanced Maths Calculator
Description
Advanced Maths is a command line tool for calculating advanced maths functions, it diplays every step it calculates and provides you with as full an answer as it can. To download the pre-compiled binary packages go to the project homepage.
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Discrete Mathematics With Application - 4th edition
Summary: Susanna Epp's DISCRETE MATHEMATICS WITH APPLICATIONS, FOURTH EDITION provides a clear introduction to discrete mathematics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision. This book presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such conce...show morepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography, and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to the science and technology of the computer age. Overall, Epp's emphasis on reasoning provides students with a strong foundation for computer science and upper-level mathematics courses. ...show less
0495391328 Brand New. Exact book as advertised. Delivery in 4-14 business days (not calendar days). We are not able to expedite delivery.
$184.97
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Course Outcome Summary for Intermediate Algebra
G.
Perform ope rations onexponents and polynomials
Linked Core Abilities
Critical thinking Mathematics
Competence will be demonstrated:
G.1. by a satisfactory score on all tests, quizzes, or graded assignments
incorporating
this competency Criteria - Performance will be satisfactory when:
G.1. you apply product , quotient, and power rules to integer exponents
G.2. you identify the degree of a polynomial
G.3. you add polynomials
G.4. you subtract polynomials
G.5. you multiply polynomials
G.6. you divide polynomials
G.7. you illustrate the difference between factoring, the verb, and factor, the
noun
G.8. you factor out the greatest common factors
G.9. you factor trinomials
G.10. you factor by substitution
G.11. you factor the difference of two squares
G.12. you factor the difference of two cubes
G.13. you factor the difference of the sum of two cubes
G.14. you identify when to use the zero factor property
G.15. you solve quadratic equations by factoring
G.16. you factor by grouping
G.17. you solve cubic equations by factoring
J. Graphing quadratic functions and solving quadratic equations
Linked Core Abilities
Critical thinking
Mathematics Competence will be demonstrated:
J.1. by a satisfactory score on all tests, quizzes, or graded assignments
incorporating
this competency Criteria - Performance will be satisfactory when:
J.1. you use the square root property to solve a quadratic equation
J.2. you use the factoring to solve a quadratic equation
J.3. you use the completing the square formula to solve a quadratic equation
J.4. you use quadratic formula to solve a quadratic equation
J.5. you distinguish which of the above four techniques should be used to most
efficiently solve a quadratic equation
J.6. you solve application problems which involve quadratics
J.7. you use the Pythagorean Theorem to solve problems involving right triangles
J.8. you graph quadratic functions
J.9. you identify quadratic functions and its x-and y-intercepts
J.10. you identify quadratic functions and its domain
J.11. you identify quadratic functions and its range
J.12. you identify quadratic functions and its vertex
J.13. you identify quadratic functions and its axis of symmetry
J.14. you identify quadratic functions and its concavity
J.15. you identify quadratic functions and where the function increases
J.16. you identify quadratic functions and where the function decreases
J.17. you sketch the corresponding quadratic function for a given quadratic
application
problem
J.18. you solve quadratic inequalities
J.19. you solve rational inequalities
J.20. you use distance formula to determine the basic equation of a circle
J.21. you graph equations of a circle
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is designed to help people who will not from maths background and easily understand the maths concepts and formulas totally free. We understand how difficult maths is. That's why we have sure that all the lessons or topics of Algebra, Geometry, Trigonometry, Graph Theory Descrete Mathematics with a clear explainations, practice sessions, quizzes, question and answers etc.
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Read the whole thing. Algebra is hard for many American students, so make it non-mandatory to learn? What about Geometry? Physics?
Al And the more advanced math subjects are not for everyone. No amount of cramming kids into an algebra class is going to make them actually understand and appreciate algebra. You can get history and lit and social studies if you have basic reading comprehension skills. You don't automatically get algebra and higher maths if you have even solid basic math skills. Frankly, I think we'd be much better off requiring a course in basic finance at the high school level instead of algebra. And this is coming from a guy who truly appreciates the value of math in and of itself as a way of expanding the intellect, like philosophy or theology. But it's not for everyone, at least beyond what you can do on a cheap calculator. Better that kids understand interest rates and statistics than quadratic equations.
Is any subject necessary? Why not just close the schools and have all the kids go apprentice somewhere? That way we can make sure they never have to learn anything that is not absolutely necessary for their profession. We will have a greater abundance of self esteem than we could ever wish for.
I understand what you're saying, but I think algebra has a value above and beyond just the ability to repeat the quadratic formula.
Proper algebra instruction teaches systematic problem solving. The application of a few simple rules -- one can always add or subtract 0, multiply or divide by 1, order of operations -- can take all kinds of mathematical expression and turn them into something valuable.
Now, I'll be the first to acknowledge that students aren't taught to treat the rules of algebra as tools to solve problems, nor are they taught any kind of formal logic that might make algebraic problem solving less of a foreign language. But to abandon algebra is to abandon the one subject wherein logic is still required and can't be written out of the curriculum.
I am math challenged but I still think at least a few courses in Algebra (and especially geometry) are a good thing. I have had to pull out my old math book over the many years since and figure something out. However my big (huge) mistake was taking the 3 quarter math course for my college major instead of the computer course. They were at the end of cards then (isn't that funny?), but how much more useful this knowledge would have been on many different levels, and what the heck is calculus anyway. I'm actually still a little angry they didn't tell me this and steer me in that direction. If your kids aren't getting an education in computers (use and how they work) you should try to remedy the situation.
Dropping algebra is a step in the wrong direction. Too many Americans are innumerate as it is. The need for the kind of skills required to master algebra, a relatively low-level mathematical skill, are just the kinds that are needed for an increasing proportion of jobs, not to mention life itself.
Years ago, Fran Lebowitz could quip, "In real life, I assure you, there is no such thing as algebra." Today, that sounds absurd. Get math or get left behind. It's that simple.
This complaint reminds me of the following (non-CoC compliant) web page. Don't click on it if you are averse to strong language. Here's an excerpt to give you the flavor:
Math is exactly like cooking: just follow the recipe. Symbols look confusing? Can't figure out how to solve a problem? All I hear is, "Waaah! Boo-hoo! I didn't read the introduction to the chapter that tells me exactly how to solve this generic category of problems!"
Math isn't some voodoo that only smart people understand. It's something that people understand on their path to enlightenment, and it's about as straightforward as thinking gets.
douglas, algebra isn't THAT hard. it's part of basic math and helps you with logical thinking.
Douglas: Al
Douglas: But it's not for everyone, at least beyond what you can do on a cheap calculator. Better that kids understand interest rates and statistics than quadratic equations.
1. Don't confuse mathematics with 'what you can do on a cheap calculator.' Memorizing and regurgitating addition and multiplication tables is not mathematics.
2. You can't learn statistics without algebra. In fact, you can't learn almost any mathematics without a solid mastery of algebra. Many students who struggle in other math classes (like stats) have trouble precisely because they didn't learn algebra.
John Marzan: I think the real goal here is to level the playing field and narrow the achievement gap by removing math. · 11 minutes ago
This is a plausible hypothesis. Sadly, efforts to reduce the gap have been unsuccessful so far. I guess if you can't do it legitimately, other ideas will occur to you.
The Left has tried to explain away the gap in a number of disingenuous and unhelpful ways in the past, blaming everyone except the most likely culprits. This only prolongs the agony and condemns victims of a poor educational system to flipping burgers or unemployment.
The first step in solving a problem is acknowledging it. Eliminating algebra from the curriculum does the opposite. Instead of acknowledging the problem of bad schools, it blames algebra for being too hard. NYT, hop on the clue train. It's pulling out of the station. Most kids, with solid work will at best be competent, and that's it. And that's the nature of the world, the way of things. We can no more change that than we can make the sun rise in the West. There are natural levels of abilities in human beings, and nothing we do is going to make most kids understand advanced math better. Its pearls before swine here.
But Douglas, I don't think anyone is talking about turning every child into a prodigy. We just want every child to have basic competency in simple algebra. In algebra, you learn how to read a graph. You learn orders of magnitude, and the difference between arithmetic and geometric (exponential) growth and decay. You learn how to distinguish known and unknown quantities, and that there are sometimes dependencies between knowns and unknowns that allow you, through the proper manipulation, to figure out the unknowns. You learn to recognize patterns and fill in the missing values or extrapolate.
These are basic skills for any responsible citizen in a democracy. They give the citizen the ability to question their elders and the "experts". When the average citizen can't tell the difference between simple mathematics and magic, we'll be in serious trouble
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Have you seen this film? It is fairly closely based on historical events. The kids in the story were ordinary kids, but with some disadvantages. And yet they managed to learn calculus. The key difference was theteacher. And by the way, learning calculus does not equate to being a concert pianist. There are a lot more successful high school calculus students (a few hundred thousand per year) than there are concert pianists (a handful). That's 14% of graduating seniors.
Can any kid learn calculus? Maybe, maybe not. But we're talking algebra here, not calculus. The subtext of the NYT piece is, most kids are too dumb to learn math. If so, we're in trouble. I think educating them is worth a try
The students taught by Edward James Olmos's character (Jaime Escalante) weren't "prodigies" but ordinary students who were either failing or had the potential to dropout of high school.
I teach HS chemistry. Our students have abyssmal math scores. I have students enter my class who cannot divide by 1 without a calculator, or manipulate simple equations (like the density formula D = M/V). Students are so reliant upon calculators and computers that they lack the basic math knowlege to recognize even glaring errors. Even using calculators and computers, you have to know some basic math facts to know if the electronic answer makes some sense.
Part of the problem is letting all students use calculators for elementary math. Another (related) issue is that for a long time we moved away from memorization of basic math tables under the delusion that students would be able to do critical thinking without being able to recall basic facts.
At third problem is our culture tolerates innumeracy. No one admits being illiterate without some shame, but I have seen teachers tell students - with a smile- that they can't do math.
Lastly, while true you don't NEED "advanced" math to make it in the real world (I haven't since college), the more math you learn the better you get at the basic stuff you DO need.
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047141770X
9780471417705
Modern Advanced Mathematics for Engineers: A convenient single source for vital mathematical concepts, written by engineers and for engineers.Builds a strong foundation in modern applied mathematics for engineering students, and offers them a concise and comprehensive treatment that summarizes and unifies their mathematical knowledge using a system focused on basic concepts rather than exhaustive theorems and proofs.The authors provide several levels of explanation and exercises involving increasing degrees of mathematical difficulty to recall and develop basic topics such as calculus, determinants, Gaussian elimination, differential equations, and functions of a complex variable. They include an assortment of examples ranging from simple illustrations to highly involved problems as well as a number of applications that demonstrate the concepts and methods discussed throughout the book. This broad treatment also offers:* Key mathematical tools needed by engineers working in communications, semiconductor device simulation, and control theory * Concise coverage of fundamental concepts such as sets, mappings, and linearity * Thorough discussion of topics such as distance, inner product, and orthogonality * Essentials of operator equations, theory of approximations, transform methods, and partial differential equationsIt makes an excellent companion to less general engineering texts and a useful reference for practitioners. «Show less
Modern Advanced Mathematics for Engineers: A convenient single source for vital mathematical concepts, written by engineers and for engineers.Builds a strong foundation in modern applied mathematics for engineering students, and offers them a concise and comprehensive treatment that... Show more»
Rent Modern Advanced Mathematics for Engineers 1st Edition today, or search our site for other Polis Electrical
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Oswaal CBSE CCE Question bank is the best guide with complete solutions for Class 10 Term II Mathematics that provide questions related to the topics to prepare for the exams. It is necessary for the students to revise their syllabus before their exams, and the best way is to practice according to the question banks.
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and is self-contained. It is suitable both as a text and as a reference.
* A wide ranging all encompasing overview of mathematical programming from its origins to recent developments * A result of over thirty years of teaching experience in this feild * A self-contained guide suitable both as a text and as a reference less
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MATHCOUNTS® Prep
Course Description
Description
This course is intended to prepare students for future MATHCOUNTS® training and competition by strengthening their analytical and problem-solving skills. It is designed to challenge and motivate students who have had no previous MATHCOUNTS® experience. The web-based whiteboard provides interactive and team-building experiences for students.
Topics include:
averages
estimation
fractions
decimals and percents
exponential expressions
scientific notation
probability
statistics
area and volume
geometry
number theory
patterns
logic
Materials Needed
There are no required materials for this course.
List of Topics
The following topics will be covered in this course:
Integers
Fractions and Decimals
Variables, Functions & Expressions
Exponents and Radicals
Number Sense and Patterns
Algebra
Plane Geometry and Solid Geometry
Coordinate System
Probability and Statistics
Graphs and Diagrams
Transformations and Similarity
Whiteboard Session Times
The instructor will hold whiteboard sessions each week at the following times:
Wednesday from 6:45 PM ET to 7:45 PM ET
Wednesday from 8:00 PM ET to 9:00 PM ET
Whiteboard Demo
System Requirements
All CTYOnline courses require a properly-maintained computer with Internet access and a recent-version web browser (such as Firefox, Safari, or Internet Explorer) with the Adobe Flash plugin. Students are expected to be familiar with standard computer operations (e.g. login, cut & paste, email attachments, etc).
This course uses an online mathematical whiteboard for individual or group discussions with the instructor. The whiteboard web site requires cookies, popup windows, and the Java Runtime Environment.(Note: iOS & Android devices cannot run Java applets.)
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Appropriate for an elementary or advanced undergraduate first course of varying lengths. Also appropriate for beginning graduate students. Its in-depth elementary presentation is intended primarily for students in science, engineering, and applied mathematics. Emphasizing the physical interpret...
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To log in and use all the features of Khan Academy, please enable JavaScript in your browser.
Algebra II
Sal works through 80 questions taken from the California Standards Test for Algebra II ( If you struggle with these you can get more help by viewing the "algebra" topic and completing its exercises.
Sal works through 80 questions taken from the California Standards Test for Algebra II ( If you struggle with these you can get more help by viewing the "algebra" topic and completing its exercises.
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Who are the Math Tutors?
We are primarily students like yourself with a little more experience in math. Some of us started with Math 054 or 055 and slowly made our way to calculus, so we know what you are going through. If you prefer working with an "expert," we have Educational Technicians who have already acquired their degrees in math or sciences.
Why go to the LC for math help?
If you are having trouble understanding what is going on in your math class or cannot finish your homework, you can come for help. Helping students in distress is indeed one of our main functions, yet it would be wrong to think that having "trouble" is the only reason to come see us. Students come for everything from a little moral support to sharing insights to discussing the nature of mathematics.
What are the Tutors likely to do for you?
We will try to make the math you are doing more comprehensible. This might include working on problems with you, explaining a concept, or simply letting you know you are on the right track. A simple statement of our philosophy might be that we help you help yourself. Yes, we know how trite that sounds, but it does underscore the idea that we are a resource to aid in your understanding, not a substitute for understanding.
Will I pass my math class if I come to the Learning Center?
Coming to the Learning Center will almost certainly increase your understanding of math, which is directly related to passing the course. But that alone will not get you through--attending lectures, doing your homework, and passing exams are important too. The more you do to try and better understand the mathematics you are learning, the better you will do in your math courses.
What other services do you provide?
A grant from the Alaska State Library provides Alaskan students with free access to live one-on-one online help with assignments, papers and exam preparation in math, science, social studies and writing. Visit tutor.com via the Statewide Library Electronic Doorway on the web any day of the week from 1 pm until 12 am.
There are periodic workshops offered during the semester that range from course specific problem solving sessions to how to effectively use your calculator. During these workshops you can review course material in a group setting, moderated and assisted by a tutor. We also have a collection of math exams for review online, which will help you prepare for your tests. Textbooks and calculators are available for use at the Learning Center, and some textbooks can be checked out.
If there is a service you wish we offered, come tell us about it or call us at 796-6348. We are always open to suggestions.
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Introduction to Digital Signal Processing, CourseSmart eTextbook
Description
Designed for the undergraduate discrete-time signal processing course
¿
Discrete-Time Signal Processing covers the information that the undergraduate electrical computing and engineering student needs to know about DSP. Core material, with necessary theory and applications, is presented in Chapters 1-7. Four unique chapters that focus on advanced applications follow the core material. MATLAB® is heavily emphasized throughout the book. Most applications have an accompanying lab or sequence of homework problems that have a lab component.
Table of Contents
1.1 What is a digital filter?
The analog circuit analysis
A digital filter replacement
1.2 Overview of Analysis and Design
The Analysis Process
The Design Process
CHAPTER 2 Discrete-Time Signals
2.0 Introduction
2.1 Discrete-Time Signals and Systems
Unit Impulse and Unit Step Functions
Related operations
2.2 Transformations of Discrete-Time Signals
Time Transformations
Amplitude Transformations
2.3 Characteristics of Discrete-Time Signals
Even and Odd Signals
Signals Periodic in n
Signals Periodic in &
2.4 Common Discrete-Time Signals
2.5 Discrete-Time Systems
2.6 Convolution for Discrete-Time Systems
Impulse representation of discrete-time signals
Convolution
Properties of convolution
Power gain
Chapter Summary
CHAPTER 3 Frequency Domain Concepts
3.0 Introduction
3.1 Orthogonal Functions and Fourier Series
The Exponential Fourier Series
Discrete Fourier Series
3.2 The Fourier Transform
Definition of the Fourier Transform
Properties of the Fourier Transform
Fourier Transforms of Periodic Functions
3.3 The Discrete-Time Fourier Transform
The Discrete-Time Fourier Transform (DTFT)
Properties of the Discrete-Time Fourier Transform
Discrete-Time Fourier Transforms of Periodic Sequences
3.4 Discrete Fourier Transform
Shorthand Notation for the DFT
Frequency resolution of the DFT
3.5 Fast Fourier Transform
Decomposition-in-Time Fast Fourier Transform Algorithm
Applications of the Discrete / Fast Fourier Transform
Calculation of Fourier Transforms
Convolution Calculations with the DFT/FFT
Linear Convolution with the DFT
Computational Efficiency
3.6 The Laplace Transform
Properties of the Laplace transform
Transfer functions
Frequency response of continuous-time LTI systems
3.7 The z-Transform
Definitions of z-Transforms
z-Transforms
Regions of Convergence
Inverse z-Transforms
z-Transform Properties
LTI System Applications
Transfer Functions
Causality
Stability
Invertibility
Discrete-Time Fourier Transform–z-transform Relationship
Frequency Response Calculation
Chapter Summary
Chapter 4 Sampling and Reconstruction
4.1 Sampling Continuous-Time Signals
Impulse Sampling
Shannon's sampling theorem
Practical sampling
4.2 Anti-aliasing Filters
Low pass analog Butterworth filters
A low pass Butterworth analog filter has a transfer function given by Switched-capacitor filters
Oversampling
4.3 The Sampling Process
Errors in the sampling process
4.4 Analog to Digital Conversion
Conversion techniques
Successive Approximation Converter
Flash Converter
Sigma-Delta Conversion
Error in A/D conversion process
Dither
4.5 Digital to Analog Conversion
D/A conversion techniques
4.6 Anti-Imaging Filters
Chapter 5 FIR Filter Design and Analysis
5.1 Filter Specifications
5.2 Fundamentals of FIR Filter Design
Linear phase and FIR filters
Conditions for linear phase in FIR filters
Restrictions Imposed by Symmetry
Window Functions and FIR Filters
High pass, band pass, and band stop filters
5.3 Advanced Window Functions
Kaiser Window
Dolph-Chebyshev window
5.4 Frequency Sampling FIR filters
5.5 The Parks-McClellan Design Technique for FIR filters
5.6 Minimum Phase FIR filters
5.7 Applications
Moving Average FIR Filter
Comb Filters
Differentiators
Hilbert Transformers
5.8 Summary of FIR Characteristics
Chapter 6 Analysis and Design of IIR Filters
6.1 Fundamental IIR design Using the Bilinear Transform
Example 6.1
6.2 Stability of IIR Filters
6.3 Frequency transformations
6.4 Classic IIR filters
The Butterworth Filter
Chebyshev Filters
Inverse Chebyshev filter
Elliptic Filters
Summary of Classic IIR Filters
Invariant Impulse Response
6.5 Poles and Zeros in the z-Plane for IIR Filters
Summary of pole and zero locations for IIR filters
6.6 Direct Design of IIR Filters
Design by pole/zero placement
Design of resonators and notch filters of second order
Numerical Direct Design — Pade method
Numerical Direct Design — Prony's method
Numerical Direct Design — Yule-Walker method
6.7 Applications of IIR Filters
All Pass Filters
IIR Moving Average Filters
IIR Comb Filters
Inverse Filters
Chapter Summary
Chapter 7 Sample Rate Conversion
7.1 Integer Decimation
Frequency spectrum of the down sampled signal
Cascaded Decimation
7.2 Integer Interpolation
Cascaded Interpolators
7.3 Conversion by a Rational Factor
7.4 FIR Implementation
Decimation filters
Interpolation filters
7.5 Narrow Band Filters
7.6 Conversion by an Arbitrary Factor
Hold interpolation
Linear Interpolation
7.7 Bandpass Sampling
7.8 Oversampling in Audio Applications
Chapter Summary
Chapter 8 Realization and Implementation of Digital Filters
8.1 Implementation Issues
8.2 Number Representation
Two's Complement
Sign/Magnitude
Floating point representation
8.3 Realization Structures
FIR Structures
IIR Structures
State Space Representation
8.4 Coefficient Quantization Error
8.5 Output Error due to Input Quantization
8.6 Product Quantization
8.7 Quantization and Dithering
8.8 Overflow and Scaling
8.9 Limit Cycles
8.10 DSP on Microcontrollers
Microcontroller Characteristics for DSP
Implementation in C
FIR Implementation in C
IIR Implementation in C
Speed optimization
Chapter 9 Digital Audio Signals
9.1 The Nature of Audio Signals
9.2 Audio File Coding
Pulse Code Modulation
Differential Pulse Code Modulation
9.3 Audio File Formats
Lossless file format examples
Lossless compressed format examples
Lossy compressed format examples
9.4 Audio Effects
Oscillators and signal generation
Delay
Flanging
Chorus
Tremolo and Vibrato
Reverberation
The Doppler Effect
Equalizers
Chapter Summary
Chapter 10 Introduction to Two-Dimensional Digital Signal Processing
10.1 Representation of Two-Dimensional Signals
Properties of Two-Dimensional Difference Equations
10.2 Two-Dimensional Transforms
The Z-Transform in Two Dimensions
The two-dimensional Discrete Fourier Transform
Properties of the 2D DFT
The Two Dimensional DFT and Convolution
The Two-Dimensional DFT and Optics
The Discrete Cosine Transform in Two Dimensions
10.3 Two-Dimensional FIR Filters
Window method
Frequency Sampling in Two-Dimensions
Transform methods
Applying FIR Filters to Images
Chapter Summary
Chapter 11 Introduction to Wavelets
11.1 Overview
11.2 The Short Term Fourier Transform
11.3 Wavelets and the Continuous Wavelet Transform
The HAAR Wavelet
The Daubechies Wavelet
Other Wavelet Families
11.4 Interpretation of the Wavelet Transform Data
11.5 The Undecimated Discrete Wavelet Transform
11.6 The Discrete Wavelet Transform
Chapter Summary
APPENDIX A Analog Filter Design
A.1 Analog Butterworth Filters
A.2 Analog Chebyschev Filters
A.3 Analog Inverse Chebyschev Filters
A.4 Analog Elliptic Filters
A.5 Summary of analog filter characteristics
APPENDIX B Bibliography
APPENDIX C Background Mathematics
C.1. Summation Formulas for Geometric Series
C.2. Euler's Relation
C.3. Inverse Bilateral Z-Transforms by Partial Fraction Expansion
C.4. Matrix Algebra
C.5 State Variable Equations
APPENDIX D MATLAB® User Functions and Commands
D.1. MATLAB User Functions
D.2. MATLAB
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From the minds of educators.
The TI-34 MultiView scientific calculator was designed with educators in mind. It's ideal for use in these middle grades math and science classes: Middle School Math, Pre-Algebra, Algebra I & II, Trigonometry, General Science, Geometry and Biology. View multiple calculations on a four-line display and easily scroll through entries. See math expressions and symbols, including stacked fractions, exactly as they appear in textbooks.
In Classic mode the TI-34 MultiView can be used in the same classrooms as the TI-34 II Explorer Plus
Enter multiple calculations to compare results and explore patterns, all on the same
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"QL advocates need
to be very clear about what all students need to know and be able to do."
Janice Summers
02/19/12
Quantitative
Literacy/Reasoning Textbooks
These college textbooks focus
on Quantitative Reasoning (QR) or Quantitative Literacy (QL).
Also shown are
college textbooks that focus on Modern Mathematics or Mathematics for
the Liberal Arts. [This page is not produced, reviewed or approved by
the MAA or by any of the authors or publishers]
Hard Copy (pdf) of this page (w/o
pictures)
The need for
quantitative reasoning courses has never been stronger: Citing a recent
study funded by the Pew Charitable Trusts, the Associated Press reported
in 2006 that more than half of the nation's students at four-year
colleges and universities "lack the literacy to handle complex,
real-life tasks" such as understanding credit card offers, balancing
checkbooks, and computing restaurant tips.
Quantitative Reasoning: Tools for Today's Informed Citizen helps
students connect mathematics in the classroom with applications in the
real world. Through a series of hands-on activities and explorations,
the text empowers students by teaching them to apply quantitative
reasoning skills to make informed decisions in their daily lives.
Authors Alicia Sevilla and Kay Somers developed this engaging,
activity-based text for students enrolled in an introductory-level,
problem-based general education quantitative reasoning course, often
called Quantitative Reasoning, Quantitative Literacy, Statistical
Reasoning, Statistical Literacy, (Mathematical) Problem Solving, or
Liberal Arts Mathematics. At many colleges and universities, this course
satisfies a general education requirement in quantitative reasoning
Book
Description: The Heart of
Mathematics addresses the big ideas of mathematics (many of which are
cutting edge research topics) in a non-computational style intended to
be both read and enjoyed by students and instructors, as well as by
motivated general readers. It features an engaging, lively, humorous
style full of surprises, games, mind-benders, and all without either
sacrificing good mathematical thought or relying on mathematical
computation or symbols.
The authors
are award-winning authors, holding awards such as: Distinguished
Teaching Award (Burger, from the Mathematical Association of America);
Chauvenet Prize (the best expository mathematics writer in the world,
Burger, from the MAA) and many others.
Fun and Games (An Introduction
to Rigorous Thought).
1.1 Silly Stories Each with a Moral (Conundrums that evoke
Techniques of Effective Thinking), 1. 2 Nudges (Leading
Questions and and Hints for Resolving the Stories), 1.3 The
Punch Lines (Solutions and Further Commentary), 1.4 From
Play to Power (Discovering Effective Strategies of Thought for
Life).
Number Contemplation.
2.1 Counting (How the Pigeonhole Principle Leads to Precision
Thought Estimation), 2.2 Numerical Patterns in Nature
(Discovering the Beauty of the Fibonacci Numbers), 2.3 Prime
Cuts of Numbers (How the Prime Numbers are the Building Blocks of
All Numbers), 2.4 Crazy Clocks and Checking Out Bars (Cyclical
Clock Arithmetic and Bar Codes), 2.5 Public Secret Codes and
How to Become a Spy (Encrypting Information Using Modular Arithmetic
and Primes), 2.6 The Irrational Side of Numbers (Are There
Numbers Beyond Fractions), 2.7 Get Real (The Point of Decimals
and Pinpointing Numbers on the Real Line).
Infinity. 3.1 Beyond
Numbers (What Does Infinity Mean?), 3.2 Comparing the Infinite
(Pairing Up Collections Via a One-to-One Correspondence), 3.3
The Missing Member (George Canton Answers: Are Some Infinities
Larger Than Others?), 3.4 Travels Toward the Stratosphere of
Infinities (The Power Set and the Question of the Infinite Galaxy of
Infinities), 3.5 Straightening Up the Circle (Exploring
the Infinite Within Geometric Objects).
Geometric Gems. 4.1
Pythagoras and his Hypotenuse (How a Puzzle Leads to a Proof of One
of the Gems of Mathematics), 4.2 A View of an Art Gallery
(Using Computational Geometry to Place Security Cameras in Museums),
4.3 The Sexiest Rectangle (Finding Aesthetics in Life, Art and Math
Through the Golden Rectangle), 4.4 Smoothing Symmetry
and Spinning Pinwheels (Can a Floor Be Tiled Without Any Repeating
Pattern?), 4.5 The Platonic Solids Turn Amorous (Discovering
the Symmetry and the Interconnections Among the Platonic Solids),
4.6 The Shape of Reality? (How Straight Lines Can Bend in
Non-Euclidean Geometries), 4.7 The Fourth Dimension (Can You
See It?).
Contortions of Space.
5.1 Rubber Sheet Geometry (Discovering the Topological Idea of
Equivalence by Distortion), 5.2 The Band that Wouldn't
Stop Playing (Experimenting with the Mŏbius band and Klein Bottle),
5.3 Feeling Edgy? (Exploring Relationships Among Vertices, Edges and
Faces), 5.4 Knots and Links (Untangling Ropes and Rings),
5.5 Fixed Points, Hot Loops and Rainy Days (How the Certainty of
Fixed Points Implies Certain Weather Phenomena).
Chaos and Fractals.
6.1 Images (Viewing a Gallery of Fractals), 6.2 The Dynamics
of Change (Can Change be Modeled by Repeated Applications of Simple
Processes?), 6.3 The Infinitely Detailed Beauty of Fractals
(How to Create Works of Infinite Intricacy Though Repeated
Processes), 6.4 The Mysterious Art of Imaginary Fractals
(Creating Julia and Mandelbrot Sets by Stepping Out in the Complex
Plane), 6.5 Predetermined Chaos (How Repeated Simple Processes
Result in Utter Chaos), 6.6 Between Dimensions (Can the
Dimensions of Fractals Fall between the Cracks?).
Taming Uncertainty.
7.1 Chance Surprises (Some Scenarios Involving Chance that Confound
Our Intuition), 7.2 Predicting the Future in an Uncertain
World (How to Measure Uncertainty Using the Idea of Probability),
7.3 Random Thoughts (Are Coincidences as Truly Amazing as They First
Appear?), 7.4 Down for the Count (Systematically Counting All
Possible Outcomes), 7.5 Collecting Data Rather than Dust (The
Power and Pitfalls of Statistics), 7.6 What the Average
American Has (Different Means of Describing Data), 7.7
Parenting Peas, Twins and Hypotheses (Making Inferences from Data).
Deciding Wisely (Applications
of Rigorous Thinking). 8.1 Great Expectations (Deciding
How to Weigh the Unknown Future), 8.2 Risk (Deciding Personal
and Public Policy), 8.3 Money Matters (Deciding between
Faring Well and Welfare), 8.4 Peril at the Polls (Deciding Who
Actually Wins an Election), 8.5 Cutting Cake for Greedy People
(Deciding How to Allocate Scarce Resources).
"The Heart of Mathematics is easily the best liberal-arts math textbook
ever written. The authors really understand which math is really
beautiful and interesting. .. They are pioneers in writing
engagingly about mathematics." Professor David Kennedy, Granville
State College.
Book
Description:
Environmental Mathematics seeks to marry the most pressing challenge of
our time with the most powerful technology of our time - mathematics.
This book does this at an elementary level and demonstrates a wide
variety of significant environmental applications that can be explored
without resorting to calculus. Environmental Mathematics in the
Classroom includes several chapters accessible enough to be a text in a
general education course, or to enrich an elementary algebra course.
Ground-level ozone, pollution and water use, preservation of whales,
mathematical economics, the movement of clouds over a mountain range, at
least one population model and a smorgasbord of 'newspaper mathematics'
can be studied at this level and would form a stimulating course. It
would prepare future teachers not only to learn basic mathematics, but
to understand how they can integrate it into other topics that will
intrigue students.
About the
Authors:
Ben Fusaro received his PhD from the University of Maryland. He went on
to be a Professor Mathematics at the University of South Florida. Queens
College (NC) and Salisbury State University. He introduced
"Environmental Mathematics," a liberal arts course, at Salisbury in
1984, and created the Mathematical Modeling Course in 1985. He has been
actively involved in organizing workshops, and increasing awareness in
the area of environmental mathematics.
Pat
Kenschaft's' many former books include "Mathematics for Human Survival,"
a text for quantitative literacy for college students with all its
exercises and examples using numbers from environmental health, and
peace issues, and "Winning Women into Mathematics," published by the
MAA. She received her PhD in functional analysis from the University of
Pennsylvania, and is currently Professor of Mathematics at Montclair
State University.
Measurement and Geometric Models
4.1 The Metric System
4.2 The U.S. Customary System
4.3 Basic Concepts of Euclidean Geometry
4.4 Perimeter and Area of Plane Figures
4.5 Properties of Triangles
4.6 Volume and Surface Area
4.7 Introduction to Trigonometry
by Jeffrey O. Bennett,
William L. Briggs (3rd ed. 2004).
From Book News, Inc. "Aimed at students majoring in nonmathematical
fields--particularly those who feel some anxiety about math--this
textbook focuses on the practical applications of mathematics in
college, career, and life. Although not remedial in nature, the text
is suitable for students with a wide range of mathematical
backgrounds. The use of critical thinking skills is emphasized
throughout. Topics include, for example, income taxes, statistical
reasoning, mathematics and music, voting theory, and exponential
population growth. Table of Contents (by Chapter)
Principles of Reasoning. 1A The Forces of Persuasion, An Overview of
Common Fallacies, 1B Propositions: The Building Blocks of
Arguments, 1C Arguments: Deductive and Inductive, 1D Analyzing Real Arguments.
by Bennett and Briggs (1st ed. 2002). "This premiere text serves the newly emerging
Quantitative Reasoning/Literacy Course, as well as an alternative
approach for Liberal Arts/Survey Math. It provides a legitimate
alternative for non-quantitative majors, helping to reduce math
anxiety and emphasizing practicality. It's the mathematics you
need for college, career, and life. Essentials of Using and
Understanding Mathematics is a condensed version of the full
book [see above]. It is designed for those who see only the "core"
material for their courses."
For All Practical Purposes: Mathematical Literacy in Today's Worldby COMAP (1988, 6th ed. 2002) "COMAP -- the
Consortium of Mathematics and Its Applications -- is a group of
mathematicians and educators dedicated to the improvement in the teaching of
math by demonstrating to students how math is a crucial part of the world
around us. They believe that students must cultivate an understanding
of math -- develop mathematical literacy -- if they are to succeed in a
society that is increasingly process-driven and where problem-solving skills
are increasingly important."
Chapter 1:
Measurement and Units. Mercury and the Inuit of
Greenland, Measuring, Accuracy and Precision of Measurement,
Estimation and Approximation, Units of Measurement, Unit Conversion,
Compound Units, Units in Equations and Formulas, Unit Prefixes,
Scientific Notation and Order of Magnitude, Powers of 10 and
Logarithms, Logarithmic Scales
Chapter 2:
Ratios and Percentages. Ratios, Normalization, Percentage as
a Type of Ratio, Parts per Thousand, Parts per Million and Parts per
Billion, Percentage as a Measure of Change, Percentage Difference
and Percentage Error, Proportions, Probability, Recurrence Interval.
Chapter
11: Fundamentals of Statistics. Measures of Center and Other
Descriptive Statistics, Weighted Means, Quartiles and the 5 Number
Summary, Boxplots, Using Technology: Finding Descriptive Statistics,
Shape of a Data Set, Using Technology: Histograms, A Skew Formula,
Comparing the Mean and Median, Sampling.
An
introductory quantitative math book with an environmental theme. The
emphasis of this text is on analyzing real environmental information and
problems, using mathematics accessible to students with an intermediate
algebra background. Students using this text will develop mathematical
(and environmental) literacy as they model natural processes using
algebraic, graphical and numerical methods, and analyze data
quantitatively to assist in objective decision making.
The textbook
is comprised of 4 principal sections: (1) basic numeracy; (2) function
modeling; (3) difference equation modeling, and; (4) elementary
statistics. Furthermore, this textbook combines both a reform and
traditional approach. Traditional in that each chapter presents
introductory material, worked examples, multiple student problems, and
solutions to odd exercises. It is reform in that it investigates
material through a synthesis of algebraic, graphical, numerical and
verbal approaches.
Chapter 8:
Quadratics, Polynomials and Beyond. 8.1) An
Introduction to Quadratic Functions, 8.2) Finding the Vertex:
Transformations of Y = X2,
8.3) Finding the Horizontal Intercepts, 8.4) The Average
Rate of Change of a Quadratic Function, 8.5), An introduction
to Polynomial Functions, 8.6) New Functions from Old. An
Extended Exploration: The Scientific Method, The Free-Fall
Experiment, Collecting and Analyzing Data from a Free-Fall
Experiment.
Book Description
Explorations
in College Algebra, 3/e and its accompanying ancillaries are designed to
make algebra interesting and relevant to the student. The text adopts a
problem-solving approach that motivates students to grasp abstract ideas
by solving real-world problems. The problems lie on a continuum from
basic algebraic drills to open-ended, non-routine questions. The focus
is shifted from learning a set of discrete mathematical rules to
exploring how algebra is used in the social, physical, and life
sciences. The goal of Explorations in College Algebra, 3/e is to prepare
students for future advanced mathematics or other quantitatively based
courses, while encouraging them to appreciate and use the power of
algebra in answering questions about the world around us.
Explorations
in College Algebra was developed by the College Algebra Consortium based
at the University of Massachusetts, Boston and funded by a grant from
the National Science Foundation. The materials were developed in the
spirit of the reform movement and reflect the guidelines issued by the
various professional mathematics societies (including AMATYC, MAA, and
NCTM).
To Students:
"This is not a math course in the familiar sense." The purpose of this
course is "to show why mathematics is necessarily the language of
science. The math topics we cover are fairly elementary, but our
use of them is not. In order to understand how scientists think, you
have to learn to think for yourself using the tools that mathematics
provides. This course aims to show how one can take real world
problems, translate them into mathematics, and solve them." "Quantitative
Reasoning explores the mathematical tools you will need to
understand why mathematics became the language of science."
To Instructors: These materials "address the issue of promoting
quantitative literacy among the vast majority of college students who do
not intend to major in mathematics of the sciences. They were also
designed to be a vehicle for enhancing math and science backgrounds of
the non-specialist K-12 teachers in training."
Measuring Things in the
Real World. What is Mathematics? Real World
Measurements: Dealing With Units, The Art of Making Estimates.
How Big is the Sun, How Far
are the Stars? Scaling Transformations, Size & Form,
Angles & Size of the Earth, Measuring the Inaccessible:
Triangulation, Angular Diameter and the Resolving Power of the Eye,
Next Steps in the Cosmic Distance Ladder, Method of Std. Candles.
Estimation, Approximation and Judging the
Reasonableness of Answers. 4.1
Review of the algebraic solution of polynomial equations and systems
of linear equations, 4.2 Inequalities - Maxima and Minima, 4.3 The
Function Concept and the Average Rate of Change,
4.4 Sequential Thinking and the Formulation of Algorithms, 4.5 Error
Analysis.
This text is
intended for a general education mathematics course. The authors focus
on the topics that they believe students will likely encounter after
college. These topics fall into the two main themes of functions
and statistics. After the concept of a function is introduced and
various representations are explored, specific types of functions
(linear, exponential, logarithmic, periodic, power, and multivariable)
are investigated. These functions are explored symbolically,
graphically, and numerically and are used to describe real world
phenomena. On the theme of statistics, the authors focus on different
types of statistical graphs and simple descriptive statistics. Linear
regression, as well as exponential and power regression, is also
introduced. Simple types of probability problems as well as the idea of
sampling and confidence intervals are the last topics covered in the
text.
The text is
written in a conversational tone. Each section begins by setting the
mathematics within a context and ends with an application. The questions
at the end of each section are called Reading Questions because students
are expected to be able to answer most of these after carefully reading
the text. Activities and Class Exercises are also found at the end of
each section. These activities are taken from public sources such as
newspapers, magazines, and the World Wide Web. Doing these activities
demonstrates to students that they can use mathematics as a tool in
interpreting quantitative information they encounter outside of the
academy. The course is designed to allow students to spend most of
their time in class working in groups on the activities. Rather than
having students passively listen, this approach requires students to
read, discuss, and apply mathematics. The text assumes that students
will have access to some type of technology such as a graphing
calculator.
Book Description: "This collection of "excursions" into
modern mathematics is written in an informal, very readable style, with
features that make the material interesting, clear, and easy-to-learn.
It centers on an assortment of real-world examples and applications,
demonstrating attractive, useful, and modern coverage of liberal arts
mathematics. The book consists of four independent parts, each
consisting of four chapters—1) Social Choice, 2) Management Science, 3)
Growth and Symmetry, and 4) Statistics. For the study of mathematics."
Preface of 1998 edition, "We have made an concerted
effort to introduce the reader to a view of mathematics that is entirely
different from the traditional algebra-geometry-trigonometry-finite math
curriculum that so many people have learned to dread, fear and
occasionally abhor. The notion that general education mathematics
must be dull, unrelated to the real world, highly technical and deal
mostly with concepts that are historically ancient is totally unfounded.
Applicability: The connection between the mathematics presented
here and down-to-earth, concrete real-life problems is direct and
immediate." Accessibility: We have found Intermediate Algebra to
be an appropriate and sufficient prerequisite. Aesthetics: A
fundamental objective of this book is to develop an appreciation for the
aesthetic elements of mathematics."
Mathematics: One of the Liberal Artsby Thomas
J. Miles, Douglas W. Nance (1st ed., 1997) Book Description: "This text
includes a history of math and covers logic, computing, finance, and
geometry. The numerous exercise and problem sets, including writing
exercises, provide non-majors with a thorough foundation of
mathematics."
|
Eighth Edition of this highly dependable book retains its best features-accuracy, precision, depth, and abundant exercise sets-while substantially updating its content and pedagogy. Striving to teach mathematics as a way of life, Sullivan provides understandable, realistic applications that are consistent with the abilities of most readers. Chapter topics include Graphs; Polynomial and Rational Functions; Conics; Systems of Equations and Inequalities; Exponential and Logarithmic Functions; Counting and Probability; and more. For individuals... MORE with an interest in learning algebra as it applies to their everyday lives. This latest edition of the successful Contemporary Sullivan Series features more modeling and real world data throughout the text. The usage of the Graphing Calculator remains optional, as do the new Internet Chapter Openings. Newly expanded website is more usable than ever.
|
The Parent and Student Study Guide Workbook is designed to help parents support, monitor, and improve their child's math performance. These worksheets are written so that parents do not have to be mathematicians to help their child.
Pre-Algebra, Spanish Parent and Student Study Guide Workbook
Editorial review
The Parent and Student Study Guide Workbook is designed to help parents support, monitor, and improve their child's math performance. These worksheets are written so that parents do not have to be mathematicians to help their child.
This book does not have any instructional information on how to do the exercises, it's for students that have already studied these types of problems and know what to do and it does not include an answer key, which is a disapointment! You
Pre-Algebra, Practice Workbook
Editorial review
The Practice Workbook mimics the computational and verbal problems in each lesson at an average level providing more challenging problems for students who are moving at a regular or faster pace
|
Calculus 2: Multivariable and Differential Equations
BUEM001S5 (30 credits)
Aims
This module aims to develop the ideas and techniques of calculus introduced in Calculus 1: Single Variable to functions of more than one variable. It also covers exact and numerical solutions of ordinary differential equations, as well as modelling problems using differential equationsHyperbolic and Special Functions Hyperbolic functions, sinh, cosh and tanh, gamma functions, beta functions, properties of hyperbolic and special functions, application of hyperbolic and special functions to evaluate certain integrals.
Ordinary Differential Equations First order differential equations, variable separable, exact differential equations, integrating factors, homogeneous differential equations, some special families of first order differential equations, second order differential equations, homogeneous and non homogeneous differential equations with constant coefficients, some special families of second order differential equations numerical methods for finding approximate solutions of a differential equation.
Learning Outcomes
On successful completion of this module a student will be expected to be able to:
Knowledge and understanding of, and the ability to use, mathematical and/or statistical techniques. In particular:
Techniques of calculus of more than one variable;
Methods of solution of ordinary differential equations.
Knowledge and understanding of a range of results in mathematics.
Appreciation of the need for proof in mathematics, and the ability to follow and construct mathematical arguments. In particular:
Knowledge of the theory underpinning the techniques of calculus;
Ability to produce proofs of some results in calculus
Awareness of the use of mathematics and/or statistics to model problems in the natural and social sciences, and the ability to formulate such problems using appropriate notation. In particular:
Modelling oscillating systems;
Modelling problems in biology;
Modelling problems in finance and economics.
Knowledge and understanding of the processes and limitations of mathematical approximation and computational mathematics. In particular:
Approximating functions using Taylor series;
Finding numerical solutions to differential equations;
Estimating the error in numerical solutions to differential equations.
Knowledge and understanding of a range of modelling techniques, their conditions and limitations, and the need to validate and revise models. In particular:
Modelling problems using differential equations.
A deeper knowledge of some particular areas of mathematics.
Ability to use a modern mathematical and/or statistical computer package with a programming facility, together with knowledge of other suitable packages
|
How to solve problems from algebra Three basic problems from university algebra and how to solve them, including: equations on lines in 3-dimensional space; the span of a set of vectors; and solving systems of equations.
The methods involve basic algebraic techniques such as matrix methods and Gaussian elimination.
Such ideas are seen in 1st-year university or college algebra courses, Author(s): No creator set
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Greg Cronin_at Massachusetts_1_29_11.MP4 Northeastern men's hockey coach Greg Cronin address the media after a 2-2 at Massachusetts on Saturday, Jan. 29, 2011 at the Mullins Center in Amherst, Mass. Author(s): No creator set
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Greg Cronin_at Massachusetts_1_29_11.MP4 Northeastern University men's hockey coach Greg Cronin address the media after a 2-2 tie at the Mullins Center against the University of Massachusetts on Saturday, Jan. 29, 2011. Author(s): No creator setWilson Bentley - The Snowflake Man Step back in time to learn about the man who taught us that no two snowflakes are alike. The picture quality is not great, but the information is useful. There are actual moving images of Bentley in this video. He was ahead of his time--some of his theories were not proven until fifty years after his death. (03:20) Author(s): No creator set
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The Snowflake Man-- A Short Film About Wilson Bentley A short documentary by Chuck Smith about Wilson A. Bentley (1865-1931), the first man to ever photograph a snowflake. There are still and moving images of Wilson Bentley in this video. There are also images of his still photographs of snowflakes. (08:33License information
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HIGHGATE CEMETERY, Hampstead, London. Graves in the fog of the West Cemetery. Photographed by John Gay in 1992.
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|
Ashley,
I do believe that one should have a reader when dealing with math. It is a
very difficult concept to learn if you cannot physically see the graphs and
charts. I used a reader and believe it is the best way to approach any sort
of math course. I took basic math lab, elementary algebra, intermediate
algebra, and contemporary math and look forward to a statistics class in the
future. A reader was my saving grace in all of those courses, because I
don't know nemmeth code and didn't have the time to learn it when I needed
to. I learned enough to get by, but not enough to actually read a textbook
and be able to completely workout a problem in Braille. I am sure that APH
has materials to make tactile graphics and with a little bit of creativity
they can be made with materials you can get at a hobby shop like pipe
cleaners and such. I wish anyone taking a math class luck, as it is a very
cumbersome subject for me personally.
Alicia
-----Original Message-----
From: nabs-bounces at acb.org [mailto:nabs-bounces at acb.org] On Behalf Of
bookwormahb at earthlink.net
Sent: Monday, August 01, 2011 4:51 PM
To: Discussion list for NABS, National Alliance of Blind Students.
Subject: Re: [nabs] Fw: Accessibility Questions for MML+
Alicia,
It seems to me many in ACB think technology can solve all our issues, and
that isn't the case. Unless you have
tactile graphics or a tiger embosser to produce tactile graphics, math is
not accessible via a computer.
Math books have diagrams, charts and graphs. How would you make a pie chart
accessible or a scatter plot or a function graph accessible on a computer?
Um, to my knowledge, there is no way. Remember Birkir just told us that
rendering math books in electronic
format via Word is not accessible. Yes online math software like MML would
be more accessible with HTML.
But that doesn't solve the accessibility of the graphs and the textbook.
All blind students I know have had to use a reader; some have used RFB but
they still had to copy down the problems. Math is something where you have
to work the problems out; teachers do not care as much about the answer;
they want to see the five, six or seven steps you took to solve the problem.
So a blind student would work the problems in braille if they know it, and
then for a test they dictate the work to a scribe.
Some math can be done on the computer; it depends on what class.
I believe braille will be very valuable in this case for homework.
I think APH has materials to make tactile graphs. I have tunnel vision and
used it to see the graphs and charts; with numbers and word problems, I used
a reader. I also had my first math class in college, preparing for college
math, in audio from RFB.
I had to copy down the stuff from the book the reader was reading. Math is
a weak skill for me too, and I just barely got through it.
Ashley
-----Original Message-----
From: Starner, Alicia M.
Sent: Monday, August 01, 2011 9:59 AM
To: 'Discussion list for NABS,National Alliance of Blind Students.'
Subject: Re: [nabs] Fw: Accessibility Questions for MML+
Amen! I agree with you 100%. There is no reason why in this day and age with
the technological advances that are available to us that classes should be
unaccessible. For me as a totally blind person, math concepts were extremely
difficult and took a lot of time to comprehend, but that should not be
compounded by textbooks that are not accessible and supplemental programs
such as MML that are largely unusable. Good luck with your math course and
hope it goes well.
Alicia
-----Original Message-----
From: nabs-bounces at acb.org [mailto:nabs-bounces at acb.org] On Behalf Of Birkir
R. Gunnarsson
Sent: Monday, August 01, 2011 8:19 AM
To: nabs at acb.org
Subject: Re: [nabs] Fw: Accessibility Questions for MML+
Hi
You can take the class but also file the appropriate complaints. And
if you are refused accessible textbook material and a reader, and you
have no money to pay one, there's no way you can do the class anyway.
Math is not accessible in a Word file unless it is extremely simple
math or if it is created using MathType plug in. Publishers havenot,
thus far, botherred to do that, it is quite a bit of work.
But you can do the course but also file the complaint. If we do not do
that and we find work arounds, sometimes at our own expense, our
problems will never become a priority for anyone, and a long term
solution will never be found.
Unemployment rate amongst blind kids is staggering, I believe over
70%, it's not because we're stupid or unambitiou, or because social
security is so high it's better than working, it's in large part
because the world works visually and there's to little attention paid
to people who can't use that medium, espcially true with books and
text books. As we move into eBooks and online platforms there is 0
reason this should not be different. All that designers and content
authors have to do is to follow guidelines and standards that usually
result in better experience for everyone (remember our problems are
similar to those of people using cell phones to access online sites).
That's why we must speak up at every opportunity, rather than fail
courses, or barely pass, may be at our own expense.
And ther's no reason one couldn't do both, try to take the course, but
also draw attention to the fact the school needs to find a different
platform that is accessible to all, or that the platform provider has
to take steps to include everyone.
Of course it's ultimately up to Netta to decide what she wants to do,
but it's important to know she has every right to demand accessible
education, at whatever cost to the school, and that accessibility to
math can be achieved quite easily with the willingness and the right
tools.
Cheers and good luck
-B
|
Journal of Applied & Computational Mathematics under the Open Access category allows free, faster and unconstrained access to the scientific research and their results. JACM encourages and also depends upon data interpretation, efforts and analysis of mathematical data. The contents of the journal are freely accessible through internet and promptly available to share the innovations of researchers and scholars for the progress of Applied and Computational Mathematics.
Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Computational mathematics involves mathematical research in areas of science where computing plays a central and essential role in emphasizing algorithms, numerical methods and symbolic methods.
|
Jeremy Ross
Copyright 2008 by Sharp Electronics Corporation. All rights reserved. This publication may not be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise without written permission. Sharp is a registered trademark of Sharp Corporation.
Table of Contents
Calculator Layout Special Functions Examples Using the Sharp EL-W535B Calculator TEACHING ACTIVITIES FOR THE CLASSROOM BASIC ARITHMETIC Calculator Activity Practice Activity FRACTIONS Calculator Activity Practice Activity POWERS AND ROOTS Calculator Activity Practice Activity PARENTHESES AND EDITING Calculator Activity Practice Activity ANGLE CONVERSIONS Calculator Activity Practice Activity TRIGONOMETRIC FUNCTIONS Calculator Activity Practice Activity INVERSE TRIGONOMETRIC FUNCTIONS Calculator Activity Practice Activity COORDINATE CONVERSIONS Calculator Activity Practice Activity LOGARITHMS Calculator Activity Practice Activity INVERSE LOGARITHMS Calculator Activity Practice Activity BASE CONVERSIONS Practice Activity Practice Activity RANDOM NUMBERS, DIE, COINS, AND INTEGERS Calculator Activity Practice Activity PROBABILITY Calculator Activity Practice Activity 34
1 VARIABLE STATISTICS Calculator Activity Practice Activity 2 VARIABLE STATISTICS & LINEAR REGRESSION Calculator Activity Practice Activity ANSWERS
Special Functions of the Sharp EL-W535B Calculator
Modes. This calculator has three modes. NORMAL, STAT, and DRILL mode. To access these modes press STAT, and for DRILL. followed by for NORMAL, for
Degrees. The EL-W535B can be set to degrees, radians, or grads. Press and enter and for grads. for DRG. Then press for degrees, for radians,
Display. There are five display notation systems. To set the number of decimals places press for FSE. For fixed decimal type and then choose your TAB or decimal setting. To set the calculator for scientific notation press. Now enter the number of significant figures. To set the calculator for engineering notation press and then enter the desired TAB setting. To set
the floating-point number system in scientific notation press either or to choose NORM1 or NORM2. To choose WriteView, which displays formulas and equations just like textbooks, press. For Line Editor press followed by. Then press. If in and then
followed by
. Then press
Line Editor you can choose an entry mode by pressing for insert and for overwrite. and the function key,. ,
Hyperbolic Functions. Press Enter the angle. Then press
Trigonometric Functions. Press the trigonometric function key,. Enter the angle. Then press Inverse Hyperbolic Functions. Press trigonometric function key. , ,. followed by
. Then press.
. Enter the number. Then press. Enter the number. Then press
Base Logarithms. If in WriteView mode press press and enter the number. Then press. Enter the base. Then press. Higher roots. Enter the index. Press radicand. Then press Cube roots. Press. followed by
. Enter the base. Then. If in Line Editor press. Enter the number. Then Press
. Enter the
. Enter the radicand. Then press followed by
Reciprocals. Enter the number. Press. Antilogarithms. Press Exponentials. Press.
. Enter the exponent. Then press followed by
. Enter the exponent. Then press
Cubes. Enter the number to be cubed. Press
Scientific Notation. Enter the number. Press press.
. Enter the.
Memory. The calculator has 9 memories. Memory calculations can be performed in NORMAL and STAT modes. Enter the value to be stored. Press. Press the location you wish to store the value A-F, M, X, or Y. Recall Memory. Press or Y. Press the location you wish to access A-F, M, X,
Last Answer Recall. Perform a calculation. Press the operation key. The last answer will be recalled. Enter the number. Then press.
Definable Memories. You can store functions or operations in definable memories (D1-D4). Press function , , ,. Press the location you wish to store your. Press the operation you want to store.
Change. You can change your answer from decimals to mixed numbers to fractions by pressing. Also, you can change your answer from decimals or fractions to answer containing the pi symbol or square root symbol by pressing. Random. You can generate random numbers, dice, coin flips, or integers. Press. Press for random numbers between 0 and 1. Press for random coin flips where 0 is
for random dice rolls from 1 to 6. Press heads and 1 is tails. Press
for random integers between 0 and 99.
P<->R Conversion. To convert to polar coordinates enter your x-coordinate first. Then press. Then enter the y-coordinate. Press. To convert
to rectangular coordinates enter your r-value. Press theta. Press. followed by
. Enter
. Enter the number. Enter the expression. Press.
Binary. To convert from one of the supported base systems into binary enter the number. Then press.
Hexadecimal. To convert from one of the supported base systems into hexadecimal enter the number. Then press.
Octadecimal. To convert from one of the supported base systems into octadecimal enter the number. Then press.
Decimal. To convert from one of the supported base systems into decimal enter the number. Then press.
Pentadecimal. To convert from one of the supported base systems into pentadecimal enter the number. Then press.
Examples:
Please refer to the following examples and the keystrokes required to enter each problem. From these simple examples more complicated expressions can be easily entered.
153 33%
log10 ln e
sin 30
cos 1 0
tanh 78
3! 10C 5 6P1
Using the Sharp EL-W535B Calculator GETTING STARTED
The National Council of Teachers of Mathematics and many other organizations with a commitment to the mathematics education of our youth have all given their support to the ongoing and appropriate use of calculators. In this document, convincing arguments for the ongoing use of calculators to enhance the mathematical capabilities of students at all grade levels are presented as well as a description of the features expected to be available on calculators. The EL-W535B uses WriteView technology and allows students to enter equations as they are seen in their textbooks.
ACTIVITY AND PRACTICE SHEETS
The fifteen calculator activities and practice sheets found in this book have been designed to be used with the Sharp EL-W535B calculator. The activities have been written and developed for students in grades nine through twelve. Some of the activities will be more appropriate for students in a particular grade, while others could be used at any grade level. Of course, the classroom teacher can and should make the decision as the appropriateness of each activity. Each activity page has an objective statement and some practice key strokes. The activity page does not attempt to teach mathematics. It only identifies the mathematics being used and demonstrates the calculator key strokes necessary to conduct a calculation. The practice page provides activities for the students to practice using the key strokes presented on the activity page. Answers to the activity and practice sheets are provided at the end of this booklet.
TEACHING ACTIVITIES FOR THE CLASSROOM
The Sharp EL-W535B was designed with you and your students in mind. The following activities have been written to provide the practice students need to succeed in mathematics, as they become familiar with the wonderful features of this exciting and powerful mathematical tool.
Calculator Activity BASIC ARITHMETIC
OBJECTIVE: To perform basic operations by developing a sequence of numbers. Performing a specified operation repeatedly can generate a sequence of numbers. For example, if you start with the number 4 and add 2 repeatedly you will generate the sequence 4,6,8,10
1. Add 13 to 54 twice: STEP 1: Enter 13 by pressing STEP 2: Add by pressing STEP 3: Enter 54 by pressing STEP 4: Find the first sum by pressing STEP 5: Add 13 again by pressing.
2. Subtract 9 from 32 once. STEP 1: Enter 32 by pressing STEP 2: Subtract by pressing STEP 3: Enter 9 by pressing.
STEP 4: Find the difference by pressing
3. Multiply -2 by 5 three times. STEP 1: Enter 2 by pressing STEP 2: Multiply by pressing STEP 3: Enter 5 by pressing. followed by.
STEP 4: Find the first product by pressing STEP 5: Multiply by 5 again by pressing STEP 6: Multiply by 5 a third time by pressing
NAME ___________________________________________ DATE________________
BASIC ARITHMETIC
Use your EL-W535B to develop a series of sequences. 1. Find the first seven numbers of the sequence starting with 3 where each additional term is found by adding 4. -3, ___, ___, ___, ___, ___, ___, 2. Find the first four numbers of the sequence starting with 2 where each additional term is found by adding 1. 2, ___, ___, ___, 3. Find the first five numbers of the sequence starting with 6 where each additional term is by adding 3. 6, ___, ___, ___, ___, 4. Find the first three numbers of the sequence starting with 144 where each additional term is found by dividing by 2. 144, ___, ___, 5. Find the first six terms of the sequence starting with 729 where each additional term is found by dividing by 3. 729, ___, ___, ___, ___, ___, 6. Find the first three terms of the sequence starting with 1 where each additional term is found by multiplying by 45. 1, ___, ___, 7. Find the first five terms of the sequence starting with 100 where each additional term is found by subtracting 10. 100, ___, ___, ___, ___, 8. Find the first four terms of the sequence starting with 1 where each additional term is found by adding 20. 1, ___, ___, ___,
4. Simplify 2 3
5. Simplify
Calculator Activity PARENTHESES AND EDITING
OBJECTIVE: To perform basic operations with parentheses by finding the volume of a sphere, by recalling the expressions, and editing them to perform a new calculation.
The volume of a sphere is defined to be Volume radius of the sphere.
r , where r is the 3
1. Given the radius is
2 find the volume of the sphere.
. and then.
2 by pressing
2 to the third power by pressing
STEP 5: Calculate the answer by pressing
2. Edit the previous equation and solve the volume of the sphere given the radius is 1. Then convert the answer to a decimal STEP 1: Recall the previous equation by pressing or. STEP 2: Move the cursor so it is to the immediate right of the third power. STEP 3: Delete the power, the parenthesis, the 2, and the square root by pressing five times. followed by.
STEP 4: Enter the number 1 by pressing STEP 5: Raise 1 to the third power by pressing STEP 6: Calculate the answer by pressing
STEP 7: Press to convert it to an improper fraction. Press one more time to convert it to a decimal.
PARENTHESES AND EDITING
Use your EL-W535B and the formula to find the volume of a sphere. Recall and edit previous equation to prevent typing the whole expression over and over again.
Volume
1. Find the volume of the sphere whose radius is 6. ____________________________ 2. Find the volume of the sphere whose radius is 5. ____________________________ 3. Find the volume of the sphere whose radius is 9. ____________________________ 4. Find the volume of the sphere whose radius is 10. ____________________________ 5. Find the volume of the sphere whose diameter is 10. ____________________________ 6. Find the volume of a sphere whose diameter is 12. ____________________________
Calculator Activity ANGLE CONVERSIONS
OBJECTIVE: To make angle conversions by finding the missing angle of a polygon. Angles can be expressed in degrees, radians and grads. Degrees can be expressed in either decimal degrees or degrees-minutes-seconds. Remember 180 = radians = 200 grads. The formula for the sum of the angles of an n-side polygon in degrees is 180(n-2). Before inputting an angle for conversion, press angular units. and then choose the appropriate
1. Convert 45 to radians and grads. STEP 1: Set the angular units to degrees by pressing STEP 2: Enter 45 by pressing STEP 3: Convert to radians by pressing STEP 4: Convert to grads by pressing.
ANGLE CONVERSIONS
The sum of the angles in degrees of an n-side polygon is 180(n-2). Remember 180 radians 200 grads. Before inputting an angle for conversion press and then choose the corresponding angular units. Use your EL-W535B to find the missing angle in the specified units. 1. A triangle has two angles, which are 45 and 60. Find the missing angle and express your answer in radians. _____________________ 2. A pentagon has four angles, which are 30, 30 , 60, and 100. Find the missing angle and express your answer in grads. _____________________
3. A triangle has two angles, which are 100 grads and 20 grads. Find the missing angle and express your answer in radians. _____________________
4. A hexagon has five angles, which are 1.5 radians,.3 radians,.4 radians,.5 radians, and radians. Find the missing angle and express your answer in degrees. _____________________
5. A four-sided figure has three angles, which are 16.3, 22.1, and 45. Find the missing angle and express your answer in degrees-minutesseconds. _____________________
Calculator Activity TRIGONOMETRIC FUNCTIONS
OBJECTIVE: To find the distance between points by using trigonometric functions. The law of sines and the law of cosines can help determine the sides and
a b c . sin sin sin The law of cosines is as follows c 2 a 2 b 2 2ab cos .
angles of triangles. The law of sines is as follows
1. Using the law of sines find the length of side a given 37, 53, b 4. STEP 1: Set the angular units to degrees by pressing STEP 2: Multiply 4 by sin(37) by pressing. STEP 3: Divide by sin(53) by pressing.
2. Using the law of cosines fine the length of c given
a 5, b 12,
radians. 2
STEP 1: Set the angular units to radians by pressing STEP 2: Add and by pressing
STEP 3: Subtract 12 cos( ) by pressing 2
. STEP 4: Take the square root by pressing.
Note: Tangent can be used in a similar manner as sine as cosine
TRIGONOMETRIC FUNCTIONS
Use your EL-W535B together with the law of sines and the law of cosines to find the distance of the missing side
The law of sines is
a b c . sin sin sin
The law of cosines is c 2 a 2 b 2 2ab cos .
1. Given 30, 63, a 11 determine the length of side c. ___________________
2. Given 16 grads, 69 grads, b 123 find the length of side a. ___________________
3. Given a 30, b 40, 1.5 radians find the length of side c.
___________________
4. Given a 15, c 30, 45 find the length of side b.
5. Given b 13, c 23, 100 grads find the length of side a using the law of sines.
Calculator Activity INVERSE TRIGONOMETRIC FUNCTIONS
OBJECTIVE: To perform operations with inverse trigonometric functions.
1. Find in degrees when tan 1 STEP 1: Set the angular units to degrees by pressing STEP 2: Enter tan 1 (1) by pressing STEP 3: Calculate the answer by pressing.
2. Find in degrees when cos 0 STEP 1: Set the angular units to degrees by pressing STEP 2: Enter cos 1 (1) by pressing STEP 3: Calculate the answer by pressing.
3. Find in radians when sin
STEP 1: Set the angular units to radians by pressing STEP 2: Enter sin 1 (
2 ) by pressing 2
INVERSE TRIGONMETRIC FUNCTIONS
Use your EL-W535B and the law of sines and the law of cosines to find the missing angle.
1. Given a 2, b 7, 23 find in grads. ___________________
2. Given a 34, c 21, 94 grads, find in radians. ___________________
3. Given a 3, b 4, c 5 find in degrees. ___________________
4. Given a 40, b 24, c 17 find in radians ___________________
5. Given a 5, b 12, c 13 find in degrees. ___________________
Calculator Activity COORDINATE CONVERSIONS
OBJECTIVE: To convert from polar coordinates to rectangular coordinates and vice versa. A point on a circle can be described with rectangular coordinates ( x, y ) or polar coordinates ( r , ) , where r is the radius of the circle and is the angle counterclockwise from the positive x-axis.
( r , )
1. While in degrees convert the rectangular coordinates (1,1) to polar coordinates.
STEP 1: Set the angular units to degrees by pressing STEP 2: Enter 1,1 by pressing.
STEP 3: Convert to polar coordinates by pressing
2. While in radians convert the polar coordinates of ( ,60) to rectangular coordinates. STEP 1: Set the angular units to radians by pressing STEP 2: Enter ,60 by pressing. STEP 3: Convert to rectangular coordinates by pressing.
COORDINATE CONVERSIONS
A point on a circle can be described with rectangular coordinates ( x, y ) or polar coordinates ( r , ) , where r is the radius of the circle and is the angle counterclockwise for the positive x-axis.
Before converting, press and then choose degrees, radians, or grads. Use your EL-W535B to find the corresponding point on the circle. 1. While in degrees convert the rectangular coordinates (2,2) to polar coordinates ( r , ).
6. Solve for z. z e 23
followed by either
1. Convert the binary number 10011001 to decimal. STEP 1: Set the calculator to binary by pressing STEP 2: Enter 10011001 by pressing. STEP 3: Convert to decimal by pressing.
2. Convert the hexadecimal number 16841601 to octadecimal. STEP 1: Set the calculator to hexadecimal by pressing STEP 2: Enter 16841601 by pressing. STEP 3: Convert to octadecimal by pressing.
3. Convert the decimal number 144169 to pentadecimal. STEP 1: Set the calculator to decimal by pressing STEP 2: Enter the number 144169 by pressing. STEP 3: Convert to pentadecimal by pressing.
BASE CONVERSIONS
Use your EL-W535B to convert to and from binary, decimal, hexadecimal, octadecimal, and pentadecimal base systems. Before converting make sure you are in the right base system by pressing followed by either , , , ,.
1. Convert the octadecimal number 161033 to pentadecimal. ____________________________
2. Convert the hexadecimal number 123 to binary.
3. Perform the indicated operations in hexadecimal and then convert your answer to octadecimal. (12)
4. Perform the indicated operations in decimal and then convert your answer to binary.
5. Convert the binary number 10101010 to decimal, octadecimal, and pentadecimal.
2. How many different ways can you choose 1 from a group of 6? STEP 1: Enter the larger number, 6, by pressing STEP 2: Enter the combination symbol by pressing STEP 3: Enter the smaller number, 1, by pressing STEP 4: Calculate the answer by pressing.
3. Find the number of permutations of 4 things taken 2 at a time. STEP 1: Enter the larger number, 4, by pressing STEP 2: Enter the permutation symbol by pressing STEP 3: Enter the smaller number, 2, by pressing STEP 4: Calculate the answer by pressing.
PROBABILITY
Use your EL-W535B to find the following number of combinations and permutations and to evaluate factorials. 1. How many groups or 4 can be formed from a class of 10 where order does not matter? ____________________________ 2. How many groups of 4 can be formed from a class of 10 where order does matter? ____________________________ 3. How many sets of 3 officers can be formed from a group of 15 where order does not mater? ____________________________ 4. How many sets of 3 officers can be formed from a group of 15 where order does matter? ____________________________ 5. Evaluate 5! ____________________________ 6. What is 0! ? What is 1! ? Explain why the answer is so. ____________________________________________________ ____________________________________________________ ____________________________________________________
Calculator Activity 1 VARIABLE STATISTICS
OBJECTIVE: To perform 1 variable statistics.
15 1. Analyze the set ,25,35,35, 50using 1 variable statistics.
STEP 1: Set the calculator to single variable statistics by pressing. STEP 2: Enter 15 by pressing STEP 3: Enter 25 by pressing STEP 4: Enter 35 two times by pressing STEP 5: Enter 50 by pressing.
STEP 6: To determine the mean of the sample press
STEP 7: To determine the sample mean standard deviation press. STEP 8: To determine the population standard deviation press. STEP 9: To determine the number of samples press STEP 10: To determine the sum of the samples press STEP 11: To determine the sum of squares of samples press.
1 VARIABLE STATISTICS
Use your EL-W535B to analyze the following sets using 1 variable statistics. 1. Analyze the set {1,1,2,2,2,3,3,3,3}
STEP 1: Set the calculator to 2 variable statistics by pressing STEP 2: Enter 1,2 two times by pressing STEP 3: Enter 2,4 by pressing STEP 4: Enter 3,7 by pressing STEP 5: Enter 10,10 by pressing.
STEP 6: To determine the mean of the sample press. STEP 7: To determine the sample mean standard deviation for x press. STEP 8: To determine the population standard deviation for x press STEP 9: To determine the number of samples for x press STEP 10: To determine the sum of the samples for x press STEP 11: To determine the sum of squares of samples for x press STEP 12: To determine the mean of the samples for y press. STEP 13: To determine the sample mean standard deviation for y press STEP 14: To determine the population standard deviation for y press. STEP 15: To determine the sum of the samples for y press STEP 16: To determine the sum of squares of samples for y press STEP 17: To determine a press STEP 18: To determine b press.
NOTE: Other regressions can be done in a similar manner by just setting your EL-W535B to the proper STATS Mode.
2 VARIABLE STATISTICS & LINEAR REGRESSION
Use your EL-W535B to analyze the following sets using 2 variable statistics and to perform a linear regression. 1. Analyze the set and run a linear regression. X Y 4 8
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Math 129-002
General Resources for Students
Trigonometry
The following are lessons and worksheets that constitute a quick course in
trigonometry ideal for students reviewing before taking a calculus course.
Read the lesson, try the worksheet, and check your solutions. These files could
also be used by a student studying trigonometry for the first time.
Geometry
The files found by clicking the following link constitute a quick review of major
geometry topics taught at the high school level. They are ideal for a student reviewing
for a placement exam or a course that uses geometry.
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signed numbers to story problems — calculate equations with ease
Practice is the key to improving your algebra skills, and that's what this workbook is all about. This hands-on guide focuses on helping you solve the many types of algebra problems you'll encounter in a focused, step-by-step manner. With just enough refresher explanations before each set of problems, this workbook shows you how to work with fractions, exponents, factoring, linear and quadratic equations, inequalities, graphs, and more!
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M115A-MidtermOneAdvice
Course: MATH 172a, Fall 2012 School: UCLA Rating:
Word Count: 405
Document Preview solve a problem if you do not have the proper tools.
3. You should understand all of the proofs given in class and be able to recreate them on the midterm.
This does not mean you should go out and memorize all of the proofs. You should go and understand
the main idea, trick, and technique of each proof. Most techniques can be repeated or are useful in
other problems.
4. If you are asked to prove something from lecture, you should try to give the proof done in lecture and
cannot use material after the proof given in lecture. If you are asked to prove something new, anything
from class is fair game.
5. Manage your time during the test. When proving result a on the midterm, you should include as much
detail as you deem necessary. If you are unsure whether to go into more detail, leave it and come back
to the problem if you have time.
6. You should try to have an intuition about how to approach problems. This is the most dicult thing
to do in this course and, if you can do this, you should most denitely succeed. When trying to solve
a problem, you should think about what you are given and what the givens imply, think about what
you are trying to do and how you could do it, think about what techniques we have and which might
be useful, and think about which tools (i.e. results and theorems) you have and how they might be
applied.
7. Do not give up on a problem. Most problems in this course do not involve an absurdly dicult trick
and can be solved by reasoning using the denitions and results done in class.
8. Get a good night sleep the night before the midterm. If you are too tired to think because you crammed
all night, the cramming with not be eective and you will not be able to think criticallyCommon Notation and Symbols in Linear AlgebraPaul SkoufranisSeptember 20, 2011The following is an incomplete list of mathematical notation and symbols that may be used MATH 115A.Shorthand Notation:for allthere existstherefores.t.such that=impli
MATH 115A - Practice Final ExamPaul SkoufranisNovember 19, 2011Instructions:This is a practice exam for the nal examination of MATH 115A that would be similar to the nalexamination I would give if I were teaching the course. This test may or may not
MATH 115A - Practice Midterm OnePaul SkoufranisOctober 9, 2011Instructions:This is a practice exam for the rst midterm of MATH 115A that would be similar to a midterm I wouldgive if I were teaching the course. This test may or may not be an accurate
MATH 115A - MATH 33A Review QuestionsPaul SkoufranisSeptember 13, 2011Instructions:This documents contains a series of questions designed to remind students of the material discussed inMATH 33A. It is recommended that students work through these ques
University of California, Los AngelesMidterm Examination 2November 9, 2011Mathematics 115A Section 5SOLUTIONS1. (6 points) Each part is worth 3 points. For each of the following statements, prove or nd a counterexample.(a) Let V and W be nite dimens
Problem Set 1Math 115A/5 Fall 2011Due: Friday, September 30Please note a typo was corrected in problem 3.Read Chapter 2 of the supplemental material in the text.Problem 1Consider the set Mnn (R) of all n n matrices with real entries with the operati
Problem Set 6Math 115A/5 Fall 2011Due: Friday, November 18Problem 1 (4.4.6)Prove that if M Mnn (F ) can be written in the formM=AB0C,where A and C are square matrices, then det(M ) = det(A) det(C ).Problem 2 (5.1.3)For each of the following mat
Problem Set 7Math 115A/5 Fall 2011Due: Monday, November 28Please note a typo was corrected in problem 2.Problem 1 (5.2.3)For each of the following linear operators T on a vector space V , test T for diagonalizability,and if T is diagonalizable, nd a
Problem Set 8Math 115A/5 Fall 2011Due: Friday, December 2Problem 1 (6.2.2)In each part, apply the Gram-Schmidt process to the given subset S of the inner productspace V to obtain an orthogonal basis for span(S ). Then normalize the vectors in the bas
Section 1.3, exercise 12Prove that the upper triangular matrices form a subspace of Mmn (F).Proof. Let W be the set of upper triangular matrices in the vector space Mmn (F). SinceMmn (F) is a vector space, it contains a zero vector and this vector is t
Life Science 15: Concepts and IssuesLecture 2: Intro to Life Science/Science as a Religion1/12/12I. Age of ScienceII. Who am I?III. Scientific ThinkingScientific MethodOrganizedEmpiricalMethodicalStructured way of finding info about observable e
Life Science 15: Concepts and IssuesLecture 3: Scientific thinking and decision making1/17/12I.II.III.IV.Scientific thinking- an efficient way to learn about and understand the worldHypotheses must be tested with critical experimentsControlling v
Life Science 15: Concepts and IssuesLecture 4: Darwins dangerous idea1/19/12I.II.III.The evolution of starvation resistanceWhat is evolution?What is natural selection?Q: How long can a fly live without food? Can we increase the average time to st
Life Science 15: Concepts and IssuesLecture 5: Nurturing nature: the power of culture1/24/12I.II.III.The four ways that evolution can occurSexual selection: NS can create sex differencesThe norm of reaction illustrates the relationship between nat
Life Science 15: Concepts and IssuesLecture 6: What did Mendel discover?1/26/12I.II.III.IV.Who was Mendel?Physical structure of the genomeWhat did Mendel discover?Sex DeterminationMendel:- why do offspring look like their parents?- 1859: Orig
Life Science 15: Concepts and IssuesLecture 8: Friend and foe are fluid categories2/2/12I.II.III.IV.evidence of kin selectioncooperation is rare in the animal worldcertain conditions are conducive to altruism among non-kinreciprocal altruism in
Life Science 15: Concepts and IssuesLecture 9: Unexpected conflict, unexpected cooperation2/7/12I.II.III.inbreeding and unexpected cooperationmothers love and unexpected conflictreciprocity instills us with a sense of fairnessReduce the perceived
Life Science 15: Concepts and IssuesLecture 12: Proteins, carbs, and fats: nutrition and health2/16/12Macromolecule 1: LipidsFeatures:o not water solubleo major storehouses of energyo good insulatorsMajor Types:o fats/triglycerideso phospholipid
Life Science 15: Concepts and IssuesLecture 13: The trouble with testosterone: hormones and sexdifferences2/21/12Hormones: Chemical signals, secreted into body fluids May reach many cells, but only target cells respond Elicit specific responses in
Life Science 15: Concepts and IssuesLecture 14: Reproduction: eggs are big, sperm are small, and menare dogs2/23/12I.II.III.Were built differently1. Early nurturing is necessarily female, 2. Males have greater reproductivecapacity but no paternit
Life Science 15: Concepts and IssuesLecture 15: Reproduction and mating systems2/28/12I.II.III.IV.What is a mating system?How does an embryo become male or female?Symmetry, heterozygosity, and beautyAnother mysterious motivator: the waist-to-hip
Life Science 15: Concepts and IssuesLecture 18: Why are drugs so good? Caffeine and alcohol: casestudies3/8/12I.II.III.The synapseDo-it-again centers in the brainDrugs can hijack pleasure pathwaysAction potential comes down axon in pre-synaptic
Life Science 15: Concepts and IssuesLecture 19: Flourishing in our alien, industrial environment3/13/12I.II.III.Industrial societies: life in an alien environmentWhat is culture?Culture breaks down the fundamental reproductive equationQ: Why is o
Life Science Final Review:1. Happiness: why is rate/direction of change more important than absolutelevel? How does this relate to material acquisitions? The emotion of happiness is a tool our genes use to cause u to behavein ways that will benefit th
Modern Art: Lecture 1 (1/10/12)To be modern is to know what is not possible anymore. Roland Barthes Typical idea of modernism: revolution, liberation, new possibilities Modern = to be self aware of limitationsQuickTime and adecompressorare needed to
Modern Art: Lecture 3 (1/17/12)Gustave Courbet Burial at Omans, 1850Political reactionHistorical painting- an event from his hometownGenre painting- everyday life, subject turns to the peopleEqualizing of attention across canvasQuickTime and adecom
Modern Art: Lecture 4 (2/19/2012)Manet Nymph Surprised, 1861Allusion to bibles Susanna: surprised while bathing by eldersManet takes out the elders, so the audience = the perpetratorsRole of vision in paintingGaze looks back at the viewer- breaks sto
Modern Art: Lecture 5 (1/24/2012)Opposition to culture of the time and monumental works1874- young painters showed work in opposition to any juried public Salon:Impressionists Exhibition.Called themselves anonymous society/corporationQuickTime and a
Modern Art: Lecture 7 (1/31/2012)QuickTime and adecompressorare needed to see this picture.Georges Seurat Bathers Asnires 1883-84Neo-Impressionists subgroup- rejected by Academy/Salon Salon of the IndependentsMovement toward landscape in Impressioni
Modern Art: Lecture 8 (2/2/2012)QuickTime and adecompressorare needed to see this picture.Paul Gauguin Spirit of the Dead Watching, 1892Liberated, arbitrary color not based upon copying the realLeaves France Tahiti (S. Pacific)MythologizeSearching
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Manet Review no clear narrative- fragmentation, citation of old masters concept of looking recognizable at one instant scenes from everyday life urbanism and its effects- some scenes of bourgeois leisure no event, no pregnant moment idea of uncerta
QuickTime and adecompressorare needed to see this picture.Gustav Klimt The Kiss, 1907-08Unification, love, reconciliationQuickTime and adecompressorare needed to see this picture.Gustav Klimt Expectation, 1905-09Excessive focus on lineStart from
Modern Art: Final Review SessionMatisse, Music: Use of color, pure planes Distortions of body, folding in on itself Has Fauvist concernsDistinction between modernism and avant-garde: Crow* Modernism: class of everything weve seen Avant-garde: at t
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Management and Organization TheoryEnvironment and Competitive AdvantageWhy Do Good Companies Go Bad? 2005 Robert H. Smith School of BusinessUniversity of MarylandHow Good Companies Emerge inthe First Place Good companies successfully emerge in the
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Lessons Business Graduates Apply to theReal World May Include Cheating Business students cheat more than students from any otheracademic discipline. Students have become more cavalier about cheating overthe years. They say theyre only acquiring skill
Ethics/Corporate SocialResponsibilityBMGT364Management and OrganizationalTheory 2005 Robert H. Smith School of BusinessUniversity of MarylandPublic recognitionThe banana giant that found its gentle side Financial Times (UK), December 2002Chiquit
Strategic ManagementDoes Strategy Matter? 2005 Robert H. Smith School of BusinessUniversity of MarylandDifferences in Industry ProfitabilityThe average return on invested capital varies markedly fromindustry to industry.Between 1992 and 2006, for e
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Sci-Plus 300 talking scientific calculator
Product features
Perform complex mathematical calculations with ease with the Sci-plus 300 talking scientific calculator. This large screened calculator announces when each button is pressed in a clear US English female voice, enabling you to perform scientific, statistical and trigonometric calculations easily. It also displays on screen numbers in 90 point font.
Product details
Silver casing with large, high contrast 8 digit LCD display
number buttons have white text on a black background in 53 point font
function buttons have white and yellow text on a black or blue background in 22 point font
long life internal lithium battery lasts approx. 80 hours on a full charge
can be used with or without speech function (if using speech, headphones must be used)
supplied with a UK power adaptor, ear phones and large print instructions (other formats available in request)
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This course unit introduces the main notions of modern differential geometry, such as connection and curvature. It builds on the course unit MATH31061/MATH41061 Differentiable Manifolds. A natural language for describing various 'fields' in geometry and its applications such as physics is that of fiber bundles. These are manifolds (or topological spaces) that locally look like the product of a piece of one space called the base with another space called the fiber. The whole space is the union of copies of the fiber parametrized by points of the base. A good example is the Möbius band which locally looks like the product of a piece of a circle S1 with an interval I, but globally involves a "twist", making it different from the cylinder S1× I. A 'field' (or a section) associates to each point in the base a point in the fiber attached to this point. In order to differentiate sections we need an extra structure known as a connection or covariant derivative. It often comes naturally in examples such as surfaces in Euclidean space. In this case a covariant derivative of tangent vectors can be defined as the usual derivative in the Euclidean space followed by the orthogonal projection onto the tangent plane. The curvature of a connection in a fiber bundle is a new phenomenon which does not exist for the derivative of ordinary functions. It generalizes the 'internal' curvature of a surface (which is responsible for the fact that it is impossible to map a region of a sphere onto a flat surface preserving distances). Analysis of curvature on vector bundles directly leads to their topological invariants such as characteristic classes. A prototype of such a relation for the tangent bundle of a surface is given by the classical Gauss-Bonnet theorem.
Textbooks:
No single textbook is followed. It is important to keep the lecture notes.
There are many good sources on differential geometry on various
levels and concerned with various parts of the subject.
Below is a list of books that may be useful. More
sources can be found by browsing library shelves.
Prerequisites, co-requisites, and dependent courses:
Prerequisite: Differentiable Manifolds. Introduction to Topology may
be a plus.
Dependent courses: formally none; however, differential geometry is one of the pillars of modern mathematics; its methods are used in many applications outside mathematics, including physics and engineering.
11. Characteristic classes and topological invariants.
Curvature and parallel transport. Parallel transport over a closed contour. Rotation of a vector under the parallel transport on a surface. Excess of a geodesic triangle. Gauß-Bonnet theorem for triangulated surfaces.
Lecture notes.
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Trigonometry Books
Trigonometry Books
trigonometry books. Are you looking for books for trigonometry students to better understand trigonometry topics?
Your child may need some help with his or her trigonometry class. Or you may be looking for trigonometry math resources for your students. TuLyn is the right place. Learning trigonometry is now easier.
We have hundreds of books for trigonometry students to practice. This page lists books on trigonometry. You can navigate through these pages to locate our trigonometry books.
Trigonometry For Dummies
A plain-English guide to the basics of trig From sines and cosines to logarithms, conic sections, and polynomials, this friendly guide takes the torture out of trigonometry, explaining basic concepts in plain English, offering lots of easy-to-grasp example problems, and adding a dash of humor and fun. It also explains the "why" of trigonometry, using real-world examples that illustrate the value of trigonometry in a variety of careers. Mary Jane Sterling (Peoria, IL) has taught mathematics at Bradley University in Peoria for more than 20 years. She is also the author of the highly successful Algebra For Dummies (0-7645-5325-9).
Math Subjects: Trigonometry
List Price: $19.99 Low Price: $8.81
trigonometry book
Master Math: Trigonometry (Master Math Series)
style and format facilitate an understanding of what can be intimidating and tricky skills. Perfect for both students who need some extra help or rusty professionals who want to brush up, Master Math: Trigonometry will help you master everything from identities and circular functions to solving triangles and trigonometric equations.
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Algebra Knuth) Blanton)
This project is developing Core Math Tools, a suite of Java-based software including a computer algebra system (CAS), interactive geometry, statistics, and simulation tools together with custom apps for exploring specific mathematical or statistical topics. Core Math Tools is freely available to all learners, teachers, and teacher educators through a dedicated portal at the National Council of Teachers of Mathematics (NCTM) web site.
Core Math Tools is a project from Western Michigan University that meets the urgent need of providing mathematical tools that students can use as they explore and learn mathematical concepts that are aligned with the Common Core State Standards in Mathematics (CCSSM). The developers have repurposed and modified tools originally designed for an NSF-funded curriculum project (e.g., Core-Plus Mathematics), creating a suite of tools that supports student learning of mathematics regardless of the curricula choice. Core math Tools is Java-based software that includes a computer algebra system(CAS, interactive geometry, statistics, and simulation tools together with custom apps for exploring specific mathematical and statistical topics. The designers provide exemplary lessons illustrating how the software can be used in the spirit of the new CCSSM. The goal of the project is to provide equitable and easy access to mathematical software both in school and outside of school. The tools are available to all learners and teachers through the web site of the National Council of Teachers of Mathematics (NCTM). The web site includes feedback loops for teachers to provide information about the tools. By using the NCTM website, the tools can be downloaded for use by teachers and students. The dedicated portal on the NCTM website allows supervisors to use the tools in professional development, teachers to use the tools as an integral part of instruction, and students to use the tools for exploring, conjecturing, and problem solving.
This project is designing digital games for middle school students that will help them prepare for success in Algebra. The games are intended to help students gain a deep understanding of measurement and fraction concepts that are critical as they begin to learn algebra. The project studies students' development of fraction concepts, their engagement in the tasks, and the use of hand-held devices as a useful platform for games.
The Gateways to Algebraic Motivation, Engagement and Success (GAMES) project is designing digital games for middle school students that will help them prepare for success in Algebra. The games are intended to help students gain a deep understanding of measurement and fraction concepts that are critical as they begin to learn algebra. The design of the games is based on research on learning fractions and research on engagement. The researchers at Virginia Polytechnic Institute and State University are studying students' development of fraction concepts, their engagement in the tasks, and the use of hand-held devices as a useful platform for games. They are providing valuable information on how students develop fraction concepts and contributing to the development of a learning trajectory that will guide the teaching of measurement and fraction concepts.
The design of the games is based on engagement states that are known to facilitate learning, with specific attention to cognitive, behavioral, and affective domains. The mathematical framework driving the games is based on how students learn fraction concepts. Most grade 6 students think of fractions from a part-whole conception, but this is not an adequate base for developing algebraic concepts. The games help students develop splitting concepts by moving through activities that focus on sequencing, partitioning, and iterating. The games are designed for iOS platforms that provide ease of engagement and data collection flexibility.
The project offers a variety of products ranging from theories to games. The research is building a conceptual framework that identifies features of engagement that lead to learning, and contributing to the development of a learning trajectory related to fraction concepts. The work will produce a scalable model for developing and using digital games to increase engagement and learning of middle school students. In addition, three games and associated tasks are being developed for use with current curricula to enhance students' understanding of fractions and prepare them for learning algebra.
This project is studying how young children in grades K-2 understand mathematical concepts that are foundational for developing algebraic thinking. Researchers are contributing to an ongoing effort to develop a learning trajectory that describes how algebraic concepts are developed. The project uses teaching experiments, with researchers talking directly to students as they explore algebraic ideas. They explore how students think about and develop concepts related to covariation, representations of functions, relationships among variable, and generalization.
The researchers in the Children's Understanding of Functions project are studying how young children in grades K-2 understand mathematical concepts that are foundational for developing algebraic thinking. Researchers at University of Massachusetts at Dartmouth and Tufts University are contributing to an ongoing effort to develop a learning trajectory that describes how algebraic concepts are developed. Most research has focused on student development at the upper elementary and middle school levels, but this project will add information about early elementary learners.
The project's research methodology uses teaching experiments which allow researchers to talk directly to students as they explore algebraic ideas. They explore how students think about and develop concepts related to covariation, representations of functions, relationships among variable, and generalization. Researchers have designed tasks that help students explain their thinking and solve problems where some quantities vary and others are constant. They are analyzing videos and students' written work as they build case studies about the development of algebraic thinking. External evaluation of this exploratory project is one of the responsibilities of its advisory board.
This project is connecting the algebraic thinking of younger children to what has been documented for older children. This process enables them to build an evidence-based learning trajectory about students' development of algebraic thinking. The products of this research can be used to build curricula and lessons that are aligned with what students know and can learn at various points in their development. Project findings, tasks and videos are being disseminated not only to researchers, but also to practitioners through professional publications and the DRK-12 Resource Network.
This exploratory project is working in collaboration with teachers to increase their knowledge of mathematics for teaching in middle school. In addition to geometry and algebra, the research component of the project is providing insights into how teachers use their mathematical knowledge to increase argumentation in the classroom and to help students build skills in mathematical argumentation.
Mathematical Argumentation in the Middle School is an exploratory project that is working in collaboration with teachers to increase their knowledge of mathematics for teaching in middle school. In addition to geometry and algebra, the professional development is focusing on the role of mathematical argumentation in the middle school and strategies for increasing argumentation. The research component of the project is providing insights into how teachers use their mathematical knowledge to increase argumentation in the classroom and to help students build skills in mathematical argumentation. In addition, the project is studying student outcomes such as reasoning, communication skills, and mathematical knowledge.
The project researchers are using both qualitative and quantitative methodologies to ensure that they have high quality data and analysis that will provide insights into the following research questions: 1) How do teachers use what they learn from the professional development (PD) experiences when they teach in the classroom? 2) To what extent does teachers? use of the project materials and what they learn in the PD result in mathematical argumentation in their classroom discourse? 3) Do students gain conceptual understanding of the mathematics as a result of their participation in argumentation in the classroom? Based on previous research, there is adequate evidence to believe that argumentation in the classroom does increase for participants in the workshop, but the researchers are seeking a better understanding of how teachers use their knowledge and the project materials to enact such an important change in mathematics lessons and in student learning. The professional development uses the dynamic software Geometers' Sketchpad, a carefully-designed, geometry curricular unit, and student materials to help teachers see how to set up a classroom environment that supports mathematical conjectures, arguments, and discussion. The research is done in the classroom and assesses the various components of the professional development in promoting argumentation.
The project is providing insights into how teachers use their mathematical knowledge to implement changes in the classroom. The project is creating effective professional development strategies, a middle school curriculum unit on geometry that emphasizes argumentation, and associated materials. The research is explaining how teachers use their knowledge and the materials and providing information on how students' conceptual knowledge develops through argumentation.
Description:
Mathematical Argumentation in Middle School: Bridging from Professional Development to Classroom Practice
This will be educative for teachers, and the teacher materials and professional development methods will work at scale and distance.
Research in biology has become increasingly mathematical, but high school courses in biology use little mathematics. To address this concern, this build on existing work on the use of model eliciting activities and focus science and technology instruction on high-stakes weaknesses in mathematics and science. They address the scaling issue as part of the core design work by developing small units of curriculum that can be applied by early adopters in each context. The materials will undergo many rounds of testing and revision in the early design process with at least ten teachers each time. The materials will be educative for teachers, and the teacher materials and professional development methods will work at scale and distance.
Learning of science content will be measured through the use of existing instruments in wide use. Existing scales of task values, achievement goals and interest are used to measure student motivation. The work performed is guided by a content team; a scaling materials team; a scaling research team; the PI team of a cognitive scientist, a robotics educator, and a mathematics educator specializing in educational reform at scale; and the summative evaluation team lead by an external evaluator.
There is great interest in understanding whether integrated STEM education can interest more students in STEM disciplines. The focus on mathematics integrated with engineering in the context of a science topic is interesting and novel and could contribute to our understanding of integrating mathematics, engineering and science. The development team includes a cognitive scientist, a mathematics educator, teachers and scientists. The issues and challenges of interdisciplinary instruction will be investigated project is
This is an exploratory project that endeavors to initiate an innovative approach to preK students' development of quantitative reasoning through measurement. This quantitative approach builds on measurement concepts and algebraic design of the pre-numeric stage of instruction found in the successful Elkonin-Davydov (E-D) elementary mathematics curriculum from Russia. The PreKEA project will adapt and refocus the conceptual framework of the E-D pre-numeric stage with respect to early algebra in the context of teaching experiments with preK and kindergarten students. A primary goal of the project is to obtain a proof-of-concept and lay down a conceptual and empirical foundation for a subsequent full research and development DR K-12 proposal.
The importance of early algebra (EA) in mathematics education has been acknowledged by the publication of a separate chapter solely devoted to early algebra and algebraic reasoning in the second Handbook of Research on Mathematics Teaching and Learning (Lester, 2007). Given that "much prior research highlights the difficulties that middle and high school students have with algebra," the proponents of EA argue that "the weaving of algebra throughout the K-12 curriculum could lend coherence, depth, and power to school mathematics, and replace late, abrupt, isolated, and superficial high school algebra courses" (Carraher & Schliemann, 2007, pp. 670-671). At the same time, "quantitative thinking is unavoidable in EA" as it "does not seem realistic to first introduce youngsters to the algebra of number and then proceed to problems steeped in quantities as 'applications' of algebra" (ibid., p. 671). While the E-D curriculum with its proven track record focuses on the development of quantitative and measurement reasoning among elementary-aged children in grades 1–6, it is feasible that much younger children, even four-year-olds, can access the pre-numeric ideas. This is supported by research by Baillargeon (2001) and Wynn (1997) who showed that infants as young as two-months old demonstrate the development of number and measurement concepts. The PreKEA project will identify key concepts of the E-D pre-numeric stage relevant to four-year-olds and develop and explore lesson units which can be integrated into US preK settings. The project team combines the international expertise of PI Berkaliev who served as project coordinator and international liaison for an NSF-funded international project US-Russian Working Forum on Elementary Mathematics: Is the Elkonin-Davydov Curriculum a Model for the US? and who also brings the perspective of a mathematician, with the theoretical, methodological, and empirical expertise of co-PI Dougherty who has been one of the leading figures in working with, adapting, and studying the implementations of the E-D curriculum in the US, as well as a group of five leading Russian experts who developed, implemented, and studied the original E-D curriculum. The project resources include the E-D curriculum materials and articles only available in Russian.
The PreKEA (PreK Early Algebra through Quantitative Reasoning) project has the potential to make contributions beyond the preK early algebra curriculum that it will develop and implement. The PreKEA project can benefit disadvantaged students by using an innovative approach to EA instruction that has the potential to broaden access and at an early stage change the situation when disproportionately many disadvantaged students are not prepared adequately for learning quantitative reasoning and algebra. With research in preK narrowly focused on particular topics, the results of this project have the potential to inform a broader field including mathematics education and early childhood education with evidence that young children can access and interact with more complex mathematics, extending beyond counting.
Developers and researchers at the Illinois Institute of Technology and Iowa State University are The adaptation is being done in collaboration with experts in Russia who were involved in the original E-D development. A primary goal of the project is to obtain a proof-of-concept and lay down a conceptual and empirical foundation for a subsequent research and development.
The research progresses using teaching experiments involving six students. Each student is engaged in 15 minute one-on-one sessions twice each week. Sessions are videotaped and transcribed for further analysis. The analysis of the data is conducted by the project team in collaboration with Russian consultants.
The research findings and methodology will provide grounds for supporting more complex and sophisticated mathematical ideas that will inform curriculum development for pre-K students and teachers. Results will be published and reported widely.
This project uses items and data from the Program for International Student Assessment (PISA) to develop two kinds of resources for preparation and professional development of secondary mathematics teachers: one in the form of prototype professional learning materials and a second in the form of PISA-based, research-grounded articles written for mathematics teachers and teacher educators. Work on both resources will focus on algebra and quantitative literacy and on factors influencing educational equity.
The UPDATE project seeks to enable significant advances in K-12 teacher and student learning of mathematics by using of items and data from the Program for International Student Assessment (PISA) in ways that enhance the work of mathematics teachers and teacher educators. We hypothesize that PISA can be useful to the field in much the same way as the National Assessment of Educational Progress (NAEP), which has long served as a key source of information for the mathematics education community. In contrast to NAEP and TIMSS, the Program for International Student Assessment (PISA) in the area of mathematics has received little or no attention within the U.S. mathematics education community, beyond noting that the performance of U.S. students is mediocre compared to that of students in many other countries in Asia and Europe. A consequence of the lack of attention to PISA in the U.S. is that we have underutilized a potentially valuable source of information for improvement of mathematics education.
In this project we use PISA as a base to develop resources for mathematics educators to use in teacher education settings The materials will be designed to engage teachers in individual and collaborative inquiry aimed at developing their specialized content knowledge and their pedagogical content knowledge. Materials will be field tested in preservice and inservice teacher professional education settings and also shared at regional and national meetings. A second type of resource comes in the form of PISA-based, research-grounded articles written specifically for mathematics teachers and teacher educators and published in journals that reach these audiences. The articles will be informed not only by our experiences in developing and using the prototype materials, but also by the findings of selected secondary analyses of data collected in the 2003 PISA assessment.
Our work is organized around three distinct focus areas: (1) Algebra – a traditional content topic familiar to mathematics teachers that can be approached in a novel way through PISA tasks; (2) Quantitative Literacy – a nontraditional content topic less familiar to mathematics teachers that can be accessed directly through PISA tasks, and (3) Equity – an issue of import to mathematics educators that can be examined carefully using PISA data. In each component our work blends research inquiry and development, integrating the analysis of tasks and data from the PISA mathematics assessment with the creation of prototype teacher education materials and the preparation of PISA-based, research-grounded articles for teachers and teacher educators.
The results of this exploratory study will be disseminated broadly, and they are likely to generate new activity in research and development related to PISA. Mirroring the tradition of the interpretive reports of NAEP results, we will produce PISA-based resources that can have a significant impact on the mathematics education community as teachers, teacher educators, and graduate students examine the materials and reports we produce and use them to improve the quality of teacher and student learning of mathematics.
This exploratory project led by faculty from the University of Michigan uses items and data from the Program for International Student Assessment (PISA) to develop two kinds of resources for preparation and professional development of secondary mathematics teachers A second type of resource comes in the form of PISA-based, research-grounded articles written specifically for mathematics teachers and teacher educators. Work on both resources will focus on the critical content areas of algebra and quantitative literacy and on factors influencing educational equity.
The project is driven by the hypothesis that PISA assessment instruments and findings can be useful to teachers in much the way that prior analyses of NAEP frameworks, items, and data have been. To address the first project objective, the research team will use selected PISA items and student responses to those items to design, develop, and test a collection of professional learning tasks that engage mathematics teachers in individual and collaborative inquiry aimed at enhancing their specialized content knowledge and their pedagogical content knowledge. To address the second project objective, the research team will prepare articles for practitioner journals that will be informed by experiences in developing and using the prototype materials, but also by the findings of selected secondary analyses of data collected in the 2003 PISA assessment.
The results of this work will be a collection of resources for use in various teacher preparation and professional development settings to stimulate thinking of secondary mathematics teachers about issues of curriculum content, student learning, teaching, and assessment.
Description:
Using PISA to Develop Activities for Teacher Education (UPDATE
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To introduce students
to a sophisticated mathematical subject where elements of different
branches of mathematics are brought together for the purpose of solving an
important classical problem.
Intended Learning Outcomes:
On successful
completion of the course students will:
Have deepened their knowledge about
fields
Have acquired sound understanding of the
Galois correspondence between intermediate fields and subgroups of the
Galois group
Be able to compute the Galois correspondence
in a number of simple examples
Appreciate the insolubility of polynomial
equations by radicals.
Pre-requisites:
212,252,312 (ex-UMIST) MT2262, UM3121 (ex-VUM)
Dependent Courses:
None
Course
Description:
Galois theory is one of
the most spectacular mathematical theories. It gives a beautiful
connection of the theory of polynomial equations and group theory. In
fact, many fundamental notions of group theory originated in the work of
Galois. For example, why some groups are called "soluble" ? Because they
correspond to the equations which can be solved ! (Meaning by a solution
some formula based on the coefficients and involving algebraic operations
and extracting roots of various degrees.) Galois theory explains why we
can solve quadratic, cubic and quartic equations, but no similar formulae
exist for equations of degree greater than 4. It also gives complete
answer to ancient questions such as divising of a circle into n equal arcs
using ruler and compasses. In modern exposition, Galois theory deals with
"field extensions", and the central topic is the "Galois correspondence"
between extensions and groups. Galois theory is a role model for
mathematical theories dealing with "solubility" of a wide range of
problems.
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GeoGebra is a dynamic mathematics software that
joins geometry, algebra, and calculus. Two views
are characteristic of GeoGebra: an expression in
the algebra window corresponds to an object in the
geometry window and vice versa
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MATH 549: Introduction to Number Theory
Course ID
Mathematics 549
Course Title
MATH 549: Introduction to Number Theory
Credits
3
Course Description
Number theory is a branch of mathematics that involves the study of integer properties. Topics covered include factorization, prime numbers, continued fractions and congruences as well as more sophisticated tools, such as quadratic reciprocity, Diophantine equations and number theoretic functions. However, many results and open questions in number theory can be understood by those without an extensive background in mathematics. Additional topics might include Fermat's Last Theorem, twin primes, Fibonacci numbers and perfect numbers. 349/549
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Home Page
GEOMETRY AND ALGEBRA II
CLASS RULES AND PROCEDURES
Attendance:
Mathematics is a challenging subject. One topic builds on another. Daily participation is a must. Do not get behind in your course work. Attendance is mandatory. The school has accepted rules and procedures for dealing with unexcused absences.
Grades and Homework:
Grades are determined by chapter tests, quizzes, and homework. Chapter tests count twice, quizzes count once, and you will receive two homework grades, one for the in-term as well as the term. For example: if there were 9 homework assignments in the first half of the term and 8 in the second half of the term, and you did 8 in the 1st half and 8 in the 2nd half, then you would receive an 8/9 or 89% on the in-term grade and an additional 8/8 or 100% on the term grade.
Geometry and Algebra II are demanding college preparatory math courses and require at least 30 minutes of homework each night. If you find you have made an error, rework the problem until you get the correct answer. By doing so, you will discover errors before they become bad habits. Homework is the place for you to learn from your mistakes. There is no partial credit for homework. All or none!
If a quiz or a test is missed because of an excused absence, it is your responsibility to see me and set a date for a make-up test within one week of your return to class. If the test is not made up during that time, you will receive a failing grade for that test or quiz.
Classroom Materials:
You must have a textbook, notebook, and a graphing calculator. Divide the notebook into two sections: Notes and Homework. Each entrance into your notebook should be dated and titled by both topic and textbook page number. All classes are to bring their textbook, notebook, graphic calculator and a pencil to class every day unless told otherwise. All homework, quizzes, and tests must be done in pencil.
Classroom Management:
You are not to enter the classroom unless I or another faculty member is in the classroom. If you enter the room without an adult present you will receive a detention. As soon as you are seated, open your textbook and take out your homework unless told otherwise.
While other students or I are speaking during class, I expect you to show total respect.
Extra Help:
I am available before and after school for extra help, by appointment, in room 218. Also, during your resource period there will be a math teacher on duty in room 111 to answer any of your math questions.
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Wednesday, January 12, 2011
Virtual Nerd Review
As part of my job as a reviewer for The Old Schoolhouse Review Crew, I recently reviewed Virtual Nerd, which is a website designed to help students in Pre-Algebra, Algebra I, Algebra II, and Physics. Virtual Nerd offers a tutoring option to students who need help in those subjects other than a private tutor.
According to Virtual Nerd:
Virtual Nerd offers online tutoring in math and science to grades 7-12. Our service is both affordable and convenient, providing help whenever and as much as needed. Using our patent pending Dynamic Whiteboard, each student has a very interactive and personalized learning experience. While watching our pre-recorded videos, they can drill-down for more information and access FAQ's terms and definitions to assist in their learning process. Service is available on a subscription plan basis, a month subscription is $49 - multi-month plans are also available.
Before going any further with my review, I would encourage you to check Virtual Nerd out for yourself. You can try all Virtual Nerd has to offer free of charge for 2 hours. As well, you can try Virtual Nerd for just one day (one time only) for $5.00 or for a week (one time only) for $19.00. As you can see, Virtual Nerd offers several inexpensive options with which you can explore the website and see if it would work for your family.
For the purposes of this review, my daughter and I used the site to access some of the video tutorials for Algebra I as this is the math course she is taking right now. From the Algebra I Search page, one can search by:
Keyword
Topic
Textbook Search (Virtual Nerd currently corresponds with Prentice Hall Algebra 1, 2004; Holt Algebra 1, 2007; Glencoe Algebra 1, 2004; and McDougal Littell Algebra 1, 2007). Right now, only Algebra has the option of the textbook search in which specific tutorials are linked to chapter and lesson in the textbook.
Major topics included in the Algebra 1 section include:
getting ready for algebra
foundations for algebra
solving linear equations
relations and functions
analyzing linear equations
solving and graphing linear inequalities
systems of equations and inequalities
exponents and exponential functions
polynomials and factoring
quadratic equations and functions
radical expressions and equations
rational expressions and functions
probability and data analysis.
My daughter and I found the video tutorials very clear and easy to follow. The video tutorials consisted of a real person talking very clearly and writing on a white board. At the end of the video, other videos on the same topic are suggested so that the student can easily link to other, related tutorials that will be helpful. As well, the student can watch the same tutorial again very easily.
The only problem I had with Virtual Nerd was that, when we were first using the site, the tutorials would not load for viewing on our computer. After updating our internet browser, though, I no longer had any problems with the site. The amazingly quick customer service I received in response to my problem was very much appreciated. Even though I e-mailed my question late in the evening, I received a response within 30 minutes!
While Virtual Nerd currently offers over a thousand different tutorials, they plan to expand their tutorials to cover even more Physics, Chemistry, Pre-Calculus, and Calculus in the 2011-2012 school year. If you have a child struggling in Pre-Algebra, Algebra I, Algebra II, or Physics, Virtual Nerd offers the supplemental teaching help that may be a perfect fit for your family.
I received a temporary subscription to Virual Nerd in exchange for this review. No other compensation, monetary or otherwise, was given in exchange for this review.
2 comments:
I thought you would like to know that because Virtual Nerd ( has received such positive feedback and significant interest following your review of their online tutoring service, they are offering a special discount to homeschool parents. Homeschool parents can receive 50% off the 1 and 3 month subscription plans. Just enter the discount code: homeschooldeal when you sign up for service. That is a huge discount, and hurry - the offer is valid until March 31, 2011
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Mathematics classes that will help with physics (list included)
Mathematics classes that will help with physics (list included)
I was wondering if anybody could give me some suggestions on which mathematics courses will be of the most use for theoretical physics. I am a sophomore at Wayne State university and am taking intro to quantum mechanics and a first course in optics this semester.
And I was just wondering if somebody could help me with finding out which classes would be most helpful to pursue studies in theoretical physics. I am dual majoring in mathematics, but I am mainly concerned not with getting a degree, as with getting knowledge
So I have to confine myself to an area and theorize there? The undergrad stuff at my school is this.. I have left (in semester order)
Thermodynamics/stat mechanics, mechanics 1
quantum physics 1, mechanics 2
Quantum physics 2, electromagnetism 1
Electromagnetism 2, modern physics lab
4 semesters. But over the summers they do not offer these classes, so I want to take a lot of math classes over the summers to be the best I can be, I really like quantum mechanics a lot, I want to take a lot of quantum mechanics classes as a grad student, if that helps isolate classes.
I was told elementary analysis (which is the class required to get into all those upper level classes on that list) is good, as well as partial differential equations and complex analysis, but then I heard algebra was good, probability theory, basically every teacher I ask tells me something different so I don't know what to do.
It is quite hard to say since little of math (at least at the level you are considering taking) is useless for physics... following your own interests towards math can help too!
But anyway definitely take an analysis class, and definitely an abstract algebra class (for QM). Taking classes like complex analysis, probability theory, more abstract algebra, more analysis etc can all definitely be useful, but understand that whenever math is necessary in a physics class, you usually learns that math within the physics class, just much more quick and dirty and bare-boned than in a full math class, but it's not like you'll ever get stuck if you don't take them. That being said two very important mathematics topics that usually get taught quite shabbily within a physics context (although it is definitely very useful to know them properly) are: representation theory (very important for QM) and differential geometry (very important for GR). (The problem is that they might be grad courses in your math department.)
If you are really planning on going to the mathematical physics sides of things, i.e. you know you will be studying a lot of math in the future, then take as much analysis, algebra and topology classes to ensure a firm foundation for self-study down the road! is a class called elementary analysis which is the prereq for all the higher math courses. I'm not great at math, I mean, I get A's, but I don't really feel like I understand it, so I want to focus on the things that I can apply towards physics. Unfortunately the elementary analysis is not offered this summer so I will have to take it next year so next summer I can take some algebra and perhaps something else. They do offer a lot of topology and things like that. I should just become a monk and go to school for the rest of my lifeNot at the undergrad level I think. I think for someone who sees himself as a future theorist, it makes sense to study (at least) linear algebra, real analysis, differential geometry, and maybe differential equations, representation theory, complex analysis, linear/harmonic analysis (i.e. Fourier series and stuff), and abstract algebra. Representation theory is super important, but some of it is taught in QM courses. So I can't say that it's essential to take a course on it, but I would definitely recommend it. A similar comment can be made about several of the other topics, in particular differential equations and stuff about Fourier series and integrals. You need some abstract algebra, but I'm not sure you need to take a course. It may be enough to read the early chapters in some book.
If you want to go into mathematical physics, you also need topology, measure and integration theory, and functional analysis.
Quote by Levi Tate was a course like that at my university. I thought it was pretty useless to be honest. In my humble opinion, it's better to take "real" math courses.
Quote by Levi Tate
There is a class called elementary analysis which is the prereq for all the higher math courses.
You will probably need this just to be able to read books on more advanced topics.
Thanks a lot. I suppose I will just reference this thread and reopen the conversation as I get a bit closer. There is so much, it is a bit boggling. I suppose for right now I will content myself to focusing on understanding my classes now.
And thank you everybody else as well. This gave me a lot to think about and I plan to revisit this question as I, and you, progressAs for linear algebra: I assumed one class treated both of those aspects, but if not yes I agree.
As for abstract algebra: actually I agree that the material itself in an abstract algebra is not that important for QM (as in, all the theorems) but what seems immensely valuable to me from such a class is the reasoning skills you obtain when thinking about algebra (and it is a kind of mathematical maturity that is the distinct from the maturity you get from an analysis class, at least in my own experience). My opinion is that once you get the basics down ice-cold, it is much more possible to add to that the specific relevant physics-related pieces that you can self-study (e.g. representation theory), whereas to get the basics down can easily take the length of a proper math course on analysis and abstract algebra respectively.
The weird thing about your classes is that the Advanced Linear Algebra class requires two previous Abstract Algebra Courses. I don't really understand that. I'm not saying that Abstract Algebra isn't useful to understand before Linear Algebra, but I wouldn't put it as prereq.
The weird thing about your classes is that the Advanced Linear Algebra class requires two previous Abstract Algebra Courses. I don't really understand that. I'm not saying that Abstract Algebra isn't useful to understand before Linear Algebra, but I wouldn't put it as prereqHis course doesn't cover modules. And you really don't need group theory to be able to understand quotient spaces and the isomorphism theorems. In fact, I might even say that it's better to first see quotient spaces in the setting of linear algebra than in group theory.
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which provides free online homework for several open math textbooks.
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Copyright is usually used to restrict the rights of the consumer.
Open textbooks are textbooks for which the author has granted a set of permissive rights.
While slight variations exist on what people consider "open", they often include:
The right to use (read) the book without cost, typically through free online viewing
The right to share the book with others
The right to modify, adapt, or remix the book to fit your needs
The right to print the book for your own use
In most cases, the license does require that the original author receive atribution for
the work. Some licenses add additional restrictions. OpenTextBookStore only lists books for
which the original license allows for
commercial use, or for which the author has listed their open textbook on one of our
print partners.
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Topics include the real number system, operations of real numbers, simplification of algebraic expressions, solving equations and inequalities. Topics also include graphing of linear equations, slopes, equations of lines, and graphing inequalities in two variables, systems of linear equations, applications and problem solving. Additional topics are exponents, scientific notation, and operations with polynomials. A grade of C- or better is required. PREREQUISITES: ARTH-073, ARTH-078 or math placement of ALGB-081. This is a developmental course. Credit for this course will not be counted toward fulfilling graduation requirements at STCC.
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Descriptions and Ratings (1)
Date
Contributor
Description
Rating
19 Jun 2009
MathWorks Classroom Resources Team
The objective of this course is to introduce students to the mathematics and modeling tools necessary to analyze and simulate natural and engineered systems. The course includes three broad areas of modeling and analysis: that of stationary processes, linear dynamic systems and neural networks. Topics include modeling time series with ARIMA models, applications of artificial neural networks, building state space models for dynamic systems, and performing sensitivity and stability analyses.
Course material created by Professor Judith Cardell.
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It depends what course youre doing, economics at research level has high maths requirements. Finance is also quite high, although slightly less so unless you are doing something like asset pricing. Other b-school degrees shouldnt have especially high requirements.
(Original post by career)
Well, it is hard to say if that knowledge is really required or if it will be reviewed anyway. That being said, in my experience, lectures are much more enjoyable when you already have some knowledge of what is being taught so that you can understand not only after you fill in the gaps but also during the actual lectures. I assumed the "reading list" is given to achieve this goal.
Thanks for the replies guys. Also not sure how how many textbooks to buy, they recommend 3 per module but I was wondering if I could get away with buying 1 and use the library for the bits of the course my books won't cover.
(Original post by Ghost6)This is wrong for two reasons. First, those are introductory (graduate level) lecture notes so they arent going to be too advanced, theoretical economics at research level obviously requires a deeper grasp of mathematics (here are two papers from the last issue of Econometrica for instance: 12, scroll down to the Appendices). The amount of math in non-theoretical and empirical papers is of course a lot lower, so this is very subfield dependent. Second, as in physics, the point of the courses isnt the math as such, but learning how its used. The focus of those courses is economic modelling, and they assume that you are somewhat familiar with the math used. If you are not comfortable enough with the mathematical background, and need to learn it as you go along, then it will be harder to learn about the economic part since you are basically learning two things at once.
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Practice Makes Perfect Algebra II
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About Practice Makes Perfect Algebra II
A no-nonsense, practical guide to help you improve your algebra II skills with solid instruction and plenty of practice, practice, practice
"Practice Makes Perfect: Algebra II" presents thorough coverage of skills, such as handling decimals and fractions, functions, and linear and quadratic equations, as well as an introducing you to probability and trigonometry. Inside you will find the help you need for boosting your skills, preparing for an exam or re-introducing yourself to the subject. More than 500 exercises and answers covering all aspects of algebra will get you on your way to mastering algebra
About Practice Makes Perfect Algebra II
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This course is an introduction to calculus with elementary functions and includes the topics that are part of the Advanced Placement AB syllabus for differential and integral calculus. Though not mandatory, the course is taught as if each student will be taking the AP examination in the spring. College equivalent work is expected from all students. We will be working together as a group to achieve a passing grade on the AP test. We are also focusing on preparing all students to succeed at the collegiate level. We will explore calculus through the interpretation of graphs and tables as well as analytical methods. The use of technology is integrated to provide a balanced approach to learning that involves: algebraic, numerical, graphical, verbal, and written methods. We encourage students to be inquisitive, to ask challenging questions and
explore. We will all work together to enjoy the discoveries of calculus. Students are required to have a graphing calculator for this course (TI-84 preferred). 19
Algebra I
Grade: 9-10 2 Sem. 1 Credit Prereq: Pre-Algebra
This course will reinforce skills for solving multi-step equations and inequalities. Students will learn to solve and apply proportions to real-life situations. Linear equations and their graphs will be studied in great depth. Students will learn to solve systems of equations and inequalities. They will also learn all of the properties of exponents. Finally the students will be introduced to polynomials and radicals. Students are encouraged to have a scientific calculator (TI-34 II or similar) for this class.
Techniques for solving equations, including quadratic equations, systems of equations, and higher degree equations are developed in depth. These are used in solving problems stated verbally and translated to algebraic symbolism. Polynomial functions and matrices are studied in detail. Exponential and logarithmic notations are introduced, as well as basic analytic geometry. Students are encour-aged to have a graphing calculator for this class (TI-84 / TI-84 Plus or similar). Graphing calculators are used to expand understand-ing.
Geometry
Grade: 9-12 2 Sem. 1 Credit Prereq: Algebra I
This is a standard sophomore course in two and three-dimensional geometry. Some major topics covered are: transformations, parallel and perpendicular lines, polygons, similar and congruent triangles, the Pythagorean theorem, circles, prisms, constructions, perimeters, areas, and volumes. Students must have a compass, and protractor for this class. Students are also encouraged to have a scientific calculator (TI-34 II or similar).
Informal Algebra
Grade: 10 2 Sem. 1 Credit Prereq: Pre-Algebra
This course will begin with the review of pre-algebra skills before moving into algebraic concepts. Some of the concepts to be cov-ered will include solving multi-step equations, graphing, and problem solving. Reading, algebra skills, and real-life problem solving are emphasized. Students are encouraged to have a scientific calculator (TI-34 II or similar) for this class. This course does not meet college requirements in mathematics.
Informal Geometry
Grade: 10-11 2 Sem. 1 Credit Prereq: Informal Algebra or Algebra I
This is a sophomore course intended for those students who had difficulty in Informal Algebra or Algebra I. The course emphasizes applications of such geometric concepts as perimeter, area, volume, parallel and perpendicular lines and polygons. Students must have a compass and protractor for this class. Students are also encouraged to have a scientific calculator (TI-34 II or similar). This course does not meet college requirements in mathematics, including JJC.
This course is designed for students who have experienced difficulty in mathematics. The course emphasizes the basic concepts of graphing and functions, problem solving techniques, real-life and real-data applications, data interpretation, appropriate use of technol-ogy, mental mathematics, number sense, critical thinking, and decision making skills. In addition, time will be spent throughout the school year working with WorkKeys problems from the Prairie State Achievement Exam. Calculators will be used to expand under-standing, therefore, students are encouraged to have a scientific calculator (TI-34 II or similar) for this class. This course will meet state and local requirements for graduation, however, this course may not meet college entrance requirements.
Trigonometry/Analytic Geometry
Grade: 11-12 2 Sem. 1 Credit Prereq: Geometry, Algebra II
Trigonometry is the study of angles, triangles and the trigonometric functions and their inverses. Equation solving is essential and applications are emphasized, especially in finding sides and angles in triangles when solving problems from the sciences and engi-neering. Vector quantities are studied by using problems pertaining to navigation and mechanics (physics). Analytic Geometry is an integration of Algebra and Geometry dealing with relationships between equations and their graphs, notably the conic sections. Con-siderations include the use of reference systems and alterations in them to simplify communication of information. If time permits, calculus is introduced and is primarily concerned with the nature of the derivative and its significance in relation to equations and graphs. Students are encouraged to have a graphing calculator
for this class (TI-84 / TI-84 Plus or similar). Graphing calculators are used to expand understanding.
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One of the most important things you can learn from algebra is problem solving. While you will probably not face day to day situations as a child or an adult that will require you to solve equations for "x" and "y" variables, there will definitely be times when what you learned in algebra will come in handy. For high school students who plan to go onto college, algebra is a subject that they will have to take before getting accepted into their major of choice.
Gaining a foundational understanding of college algebra allows students to understand the math classes that they will need to take to get their college degree. Of course, you can say that you will just major in something that is not related to math, but you should know that many bachelor programs will require that you take at least one or two college level math classes beyond the foundational college algebra. It should also be said that while you are not majoring in math, many other majors will be very closely related to mathematics.
Even if you are not going to college to become a scientist or a doctor, many who want to try their luck as a tradesmen will soon find out that they need algebra to help them do their job correctly. Some careers require testing that involves algebra to be licensed. If you are a parent to a child who does not understand that they need to work hard in their algebra class in order to be successful in life, try talking with them about what they think they might like to be when they grow up. Then try to show how algebra will be valuable in that job setting.
For instance, if your teenage son hopes to become a general contractor and build houses, he will need some basic math skills that are acquired by taking algebra. Any kind of building or construction job is basically one big math problem, so you have to understand the concepts whether or not you go to college.
Students are not the only ones who need to take steps to make sure they pass their algebra classes. Parents also play an important role by the example they set. If you shrug off algebra homework and act uninterested, your kid will assume it isn't important or relevant to the adult world. By showing interest or attempting to help (or watch!) during homework assignments, you are sending an unspoken message that math is important.
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Reading Assignments
Assignments:
For Friday January 6 lecture: Answer the following Introduction questions in a blog entry.
What is your year in school and major?
Which post-calculus math courses have you taken? (Use names or BYU course numbers.)
Why are you taking this class? (Be specific.)
Tell me about the math professor or teacher you have had who was the most and/or least effective. What did s/he do that worked so well/poorly?
Write something interesting or unique about yourself.
If you are unable to come to my scheduled office hours or the TA's scheduled office hours, what times would work for you?
For Friday January 6 lecture: Read and blog about Sections 1.1-1.3.
For Monday January 9 lecture: Read and blog about Section 2.1.
For Wednesday January 11 lecture: Read and blog about Section 2.2.
For Friday January 13 lecture: Read and blog about Section 2.3.
For Wednesday January 18 lecture: Read and blog about Section 3.1 through the middle of page 48.
For Friday January 20 lecture: Read and blog about the rest of Section 3.1.
For Monday January 23 lecture: Read and blog about Section 3.2.
For Wednesday January 25 lecture: Read and blog about section 3.3.
For Friday January 27 lecture: Write responses to some or all of the following questions.
How long have you spent on the homework assignments? Did lecture and the reading prepare you for them?
What has contributed most to your learning in this class thus far?
What do you think would help you learn more effectively or make the class better for you? (This can be feedback for me, or goals for yourself.)
For Monday January 30 lecture: Read and blog about Section 4.1.
For Wednesday February 1 lecture: Read and blog about Section 4.2.
For Friday February 3 lecture: Read and blog about Section 4.3.
For Monday February 6: Read and blog about Section 4.4.
For Wednesday February 8 lecture: Read and blog about sections 4.5 and 4.6..
Thinking about the answers to these questions can help guide your study. Remember also that the mathematics department's learning outcomes for Math 371 state that students
should know all relevant definitions, correct statements of the major theorems (including their hypotheses and limitations), and examples and non-examples of the various concepts. The students should be able to demonstrate their mastery by solving non-trivial problems related to these concepts, and by proving simple (but non-trivial) theorems about the concepts, related to, but not identical to, statements proven by the text or instructor.
For Friday February 10 lecture: Read and blog about Section 5.1.
For Monday February 13 lecture: Read and blog about Section 5.2.
For Wednesday February 15 lecture: Read and blog about Section 5.3.
For Friday February 17 lecture: Read and blog about Section 6.1 through the middle of page 138.
For Tuesday February 21 lecture: Read and blog about the rest of section 6.1 and Section 6.2 up through the middle of page 147.
For Wednesday February 22 lecture: Read and blog about the rest of Section 6.2.
For Friday February 24 lecture: Read and blog about Section 6.3.
For Monday February 27 lecture: Read and blog about Section 7.1 up through the first full example on page 164.
For Wednesday February 29 lecture: Read and blog about the rest of Section 7.1.
For Friday March 2 lecture: Read and blog about Section 7.2.
For Monday March 5 lecture: Read and blog about Section 7.3.
For Wednesday March 7 lecture: in class on Wednesday.
For Friday March 9 lecture: Read and blog about Section 7.4.
For Monday March 12 lecture: Read and blog about Section 7.5 up through Corollary 7.27. Remember that you can make up a reading assignment by going to Ed Burger's Focus On Math talk at 4 PM on Tuesday March 13 in TMCB 1170 and blogging about it. More information about the talk is available here.
For Wednesday March 14 lecture: Read and blog about the rest of Section 7.5.
For Friday March 16 lecture: Read and blog about Section 7.6 through page 211.
For Monday March 19 lecture: Read and blog about the rest of Section 7.6.
For Wednesday March 21 lecture: Read and blog about Section 7.7.
For Friday March 23 lecture: Read and blog about Section 7.8.
For Monday March 26 lecture: Read and blog about Section 7.9.
For Wednesday March 28 lecture: Read and blog about Section 7.10.
For Friday March 30 lecture: Read and blog about Section 8.1.
For Monday April 2 lecture: Read and blog about Section 8.2.
For Wednesday April 4 lecture: Read and blog about Section 8.3.
For Friday April 6 lecture: Read and blog about Sections 8.4 and 8.5.
For Monday April 9 lecture: Read and blog about Section 9.4.
For Wednesday April 11 lecture: Complete your student ratings for this course. As you study for the final exam (note that there is a study guide available here, and the proof of Cauchy's theorem from class is available here), write responses to the following questions.
Which topics and theorems do you think are important out of those we have studied?
What do you need to work on understanding better before the exam? Come up with a mathematical question you would like to see answered or a problem you would like to see worked out in class.
How do you think the things you learned in this course might be useful to you in the future?
If for whatever reason you are uncomfortable doing a certain assignment on your blog (for instance, if you'd rather not have your answers to specific questions out there on the Internet), you may send me that particular assignment by email.
Instructions:
Set up a blog for this class and do the first two assignments by 11:59 PM on January 5.
Complete each reading assignment (listed above) before lecture.
Write
a blog entry for each reading assignment.
The title of the blog entry should be (Section Number), due on (Date)
so, for example, your first blog entry will be titled Introduction, due on January 6
and the second entry will be titled 1.1-1.3, due on January 6.
A blog entry should have two parts:
1.(Difficult)Answer the question "What was the
most difficult part of the material for you?"Note that "nothing" is not an
acceptable answer. If nothing challenges you, then you should think about
the material at a deeper level and generate some honest questions.
2.(Reflective)Write something reflective about the
reading. This could be the answer to the question "What was the most
interesting part of the material?" or "How does this material
connect to something else you have learned in mathematics?" or
"How is this material useful/relevant to your intellectual or career
interests?" or something else.
The blog posting is due by 11:59 PM on the day before lecture (for example, you should post about the reading for Wednesday's lecture before midnight Tuesday night).
Blog posts will be graded according to the following scheme:
0 points: No blog submission on time.
1 point: Submission of both parts (Difficult and Reflective) on time, but first part (Difficult) is irrelevant or does not sufficiently show that reading has been done.
2 points: Submission of both parts (Difficult and Reflective) on time, demonstrating that you have done the reading and thought about it.
You may make up a missed blog entry by attending a mathematics department colloquium, Focus On Math, or Careers In Math talk and writing about it on your blog. Answer the same two questions about the talk that you would normally answer for a reading assignment.
Setting up a blog:
Note: these instructions should only be followed once. Once you've created a blog, just add new posts to it for each reading assignment.
Click on the orange box with "Get started". If you already have a blog, please create a new one for this class; I'll be dumping all entries into a feed reader, and would like to see only entries related to the course.
Once you have made your first blog post, send me an email with the URL for the main page of your blog. Include your full name in the email message, especially if your name does not appear on your blog.
Make sure to do all of this and to do Assignment 2 (Sections 1.1-1.3) by 11:59 PM on Thursday January 5.
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Math Resources for
Calculus-Based Physics
Math Handouts (pdf). Calculus is a co-requisite (rather than a prerequisite) for the calculus-based
physics course that I teach
at Saint Anselm College. The math handouts address calculus topics that students encounter
in the physics course before they see them in their mathematics course.
Average with Error
Spreadsheet A spreadsheet set up to determine
the mean and standard deviation of a column of values entered by the
user and to display the distribution as a bar graph along with a
scaled gaussian curve determined from the mean and standard
deviation. The curve aids the user in judging whether the data
is part of a gaussian distribution.
Gaussian Error
Propagation Spreadsheet
A spreadsheet set up to determine the distribution (mean and standard
deviation plus a histogram) for the case of a function of one to
six variables when each of the variables is characterized by
a guassian distribution of known mean and standard
deviation.
Math Skills Video The pdf file contains an outline of the topics
covered on the math skills video and the mov file is a QuickTime
movie in which the pre-calculus math skills needed for either an
algebra-based or a calculus-based physics course are reviewed. To
play the video, click on PlayMathSkillsVideo. To download it, RIGHT
click on MathSkillsVideo.mov and click "Save Target
As."
Math Problems Video The
pdf file is a set of 22 pre-calculus mathematics problems. The
mov file is a QuickTime movie in which the solutions to the
mathamatics problems are presented. To play the video, click
on PlayMathProbsVideo. To download it, RIGHT click on
MathSkillsVideo.mov and click "Save Target As."
Calculus
ScreenCams A set of six short Lotus ScreenCam movies in
the form of executable (.exe) files compressed into one zip
file. You need to be running Windows to play these.
The movie titles are: Derivatives, The Chain
Rule for the Function of a Function, Taking the Derivative
of a Power Function, The Chain Rule for the Product of Two
Functions, and Finding the Extrema of a
Function
.
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SIMMS IM LEVEL I - Research Project Help - T. DeBuff
High School freshman-level integrated mathematics research projects, to be used with the Systemic Initiative for Montana Mathematics and Science Integrated Math (SIMMS IM), curriculum Level I. View project descriptions and find links to sites that will
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Society of Actuaries
Actuaries are professionals trained in mathematics, statistics, and economic techniques that allow them to put a financial value on future events. This skill is of great value to insurance companies, investment firms, employee benefits consulting firms,
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Softmath - Neven Jurkovic
Developers of Algebrator, an automated tutor based on Maxima CAS that provides step-by-step solutions to algebra, trigonometry, and statistics problems, and exports answers to MathML. Demo and purchase Algebrator; use Softmath's free online software to
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Software for mathematics education - Piet van Blokland
Software for mathematical education that draws on David Tall's philosophy of teaching: use Graphic Calculus to visualize, explore, and conceptualize the graph of a linear function; analyze the data and simulations included with VUStat to learn statistics
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So Much Data - William D. May
Based on the book So Much Data, So Little Math, tools for learning to do simple data analysis on data sets. Features the online calculation tools "Easy Correlation Calculations" and "Easy Trend Prediction," with explanations, as well as an example of
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Songs for Teaching - S. Ruth Harris, LLC
Lyrics to music that teaches or reinforces math facts and concepts, including addition, subtraction, multiplication, division, algebra, and geometry. Some songs have links to sound files as well.
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The SPSS Decision Maker - Maurits Kaptein
This is a website that guides you through a number of steps to select a statistical technique. Developed for those who do know the basic concepts of research statistics and experimental design but need help determining the final test.
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Standard Deviation, Part 1 - Barbara Christopher
Can the standard deviation pick the most consistent set of numbers? or Which city's temperatures vary the least, San Diego or San Francisco? An interactive project in which students use the Internet to find statistical data for the mean, standard deviation,
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Standard Deviation, Part 2 - Barbara Christopher
Do cities closer to the ocean have more consistent temperatures? A followup to Standard Deviation, Part 1. Students use the Internet to gather temperature data from 3 cities; calculate the standard deviation and percentage error of the gathered temperatures;
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StatApplet - Marcus Kazmierczak
A simple statistics program and a short outline of the underlying mathematics. The statistics applet calculates the sample mean and sample standard deviation, and constructs a 95 percent confidence interval for data values entered.
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Statbag - Worth Swearingen
A blog repository for statistics educators: "... each teacher should have a bag of tricks. Teachers spend years developing their own favorites. While acknowledging that experience is the best teacher, one purpose of this site is to help teachers develop
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Statistical Assessment Service (STATS)
STATS is a non-profit, non-partisan resource on the use and abuse of science and statistics in the media. Its goals are to correct scientific misinformation in the media and in public policy resulting from bad science, politics, or a simple lack of information
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Statistical Consultants Ltd - Dion Walker
Data analytics and other consulting services. See, in particular, the New Zealand company's blog, which dates back to 2010 with posts such as "Battle of Britain Casualty Data," "Gretl: A free alternative to EViews," "Life expectancy at birth versus GDP
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Statistical Rules of Thumb - Gerald van Belle
This companion website to Statistical Rules of Thumb, published by John Wiley & Sons, Inc., offers free PDFs of chapter two ("Sample Size") and more than a dozen "monthly rules of thumb," such as "Use Text for a Few Numbers, Tables for Many Numbers,
...more>>
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I'm a theoretical physics student going into second year, so we took 2/3 of the maths modules. (Didn't do stats, computation I or group theory)
You don't really need to do any work before going into it. Especially if you got A's in matha and applied. They'll assume that you know how to do basic algebra, how to differentiate and integrate, a bit about complex numbers perhaps, but never too much that you'll needed to have studied before covering anything. All of the modules start from scratch, and as long as you keep up with everything being done in the lectures you won't be behind at all, in fact if you keep up with everything during the year you'll find studying toward the end of the year not that difficult at all.
The library is good enough for the books that you'll need. I bought two of the books for the year and didn't really need them. Some lecturers such as Pete (Dr. Paschalis Karageorgis) give such comprehensive lectures that you might not even need to use a book at all for that module. Although you still need to go the lectures... A laptop is handy to have, but by no means necessary, as anything which you might need to do on a computer can be done with the the college's of which there's quite a lot around. I only really used my laptop to access exam papers, and that was just before exams.
Unfortunately as I'd no choice myself I wouldn't really know about which modules are best to pick. If you're at all interested in physics though, I believe not picking mechanics can be very limiting in what modules you can do in 3rd and 4th year.
Ok, I got A's in Maths and Applied Maths and 580pts so I think I've done enough to get into the Maths course
3 questions.
1) Should I be doing anything to prepare for the course? I haven't looked at anything since finishing the l.c and don't want to be slow when the course starts.
2) Are there many books needed for the course or are laptops/eReaders in use?
3) Anyone got any tips for which modules are best to take?
Thanks for any replies
CB
1) Not really, no.
2) Not many books, you shouldn't need to buy any, lecturers generally have notes, or you are expected to take them.
3) You take all courses initially, unless it's changed. So you can decide for yourself reallyUnlikely. They don't assume any knowledge, and having spoken to Donal about it a while back, they won't next year, either. Don't be frightening the first years.
Unlikely. They don't assume any knowledge, and having spoken to Donal about it a while back, they won't next year, either. Don't be frightening the first years.
Either way it's worrying...
Have you seen how little they do in Project Maths? They don't even cover integral calculus...assuming what you say is correct then either:
a) They will dumb-down the course so that incoming PM'ers will find it subjectively as difficult as we did, but the course will cover less.
or
b) They will require extra ramp up material, like integral calculus, to bring incoming PM'ers up to the same level as previous LC students, in addition to the same material we already cover. This will make the course subjectively harder for new students, leading to a higher rate of failures and pressure to dumb-down the course.
Obviously either of these things are bad.
If what you say is not correct (not to accuse of lying, but just to show that either way it's a lose/lose situation), then:
c) The course will be the exact same as before. This will make the course subjectively harder for new students, leading to a higher rate of failures and pressure to dumb-down the course.
I think we're ok for this year as we only did project maths for paper 2, we did the old paper 1 - calculus, algebra, induction etc (the important stuff!).
However the pilot schools would have done the new paper 1 and everyone will be doing it next year. I think these will face the fate mentioned by Tears in Rain.
Integral calculus is not being removed from the project maths but, like the rest of the course, it has been 'dumbed down', I think they have removed u-subs etc.
Thanks for the replies,
1 more question: Are lockers necessary and how do you get them?And yeah, all your lectures are going to be in the Hamilton
Yeah, you're not supposed to leave items in the locker when you're not using the sports centre but who knows whether you're in the sports centre or not. It's ok.
Most lectures will be in the Hamilton however you may have a few tutorials in surrounding buildings. If you're going to get a locker, get one in the Hamilton and be prepared to get to college quite early on the morning that they become available.
Books aren't needed but can be helpful. Even better, you can find free online copies of (most of) the books online. Saves you going to library. Computers are good for checking exam papers, emails, maths websites and research but with regard to in-class, they're a bit of a pain trying to transcribe maths. Better with a pen and paper.
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I'm just wondering if someone can give me a few pointers here so that I can understand the concepts behind problem solver-maths. I find solving problems really tough. I work in the evening and thus have no time left to take extra classes. Can you guys suggest any online resource that can help me with this subject?
Hey. I imagine I can help. Can you elucidate some more on what your troubles are? What specifically are your troubles with problem solver-maths? Getting a good teacher would have been the greatest thing. But do not worry. I think there is a way out. I have come across a number of math programs. I have tried them out myself. They are pretty smart and good quality. These might just be what you need. They also do not cost a lot. I think what would suit you just fine is Algebra Buster. Why not try this out? It could be just be the answer for your problems.
I have used quite a lot of programs to grapple with my difficulties with trinomials, least common denominator and system of equations. Of them, my experience with Algebra Buster has been the best. All I needed to do was to just key in the problem. Punch the solve key. The answer showed up almost instantaneously with an easy to understand steps indicating how to reach the answer. It was simply too easy. Since then I have depended on this Algebra Buster for my difficulties with Algebra 2, Algebra 2 and Intermediate algebra. I would highly recommend you to try out Algebra Buster.
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Data, Graphing, and Statistics Smarts!
Are you having trouble with graphs? Do you wish someone could explain data, graphing, or statistics to you in a clear, simple way? From ratios and line plots to percentiles and sampling, this book takes a step-by-step approach to teaching data, graphing, and statistics concepts. This book is designed for students to use alone or with a tutor or parent, provides clear lessons with easy-to-learn techniques and plenty of examples.
Whether you are looking to learn this information for the first time, on your own or with a tutor, or you would like to review your skills, this book will be a great choice.
show more show less
Edition:
2012
Publisher:
Enslow Publishers, Incorporated
Binding:
Trade Paper
Pages:
64
Size:
6.50" wide x 9
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Graphing is the useful procedure in mathematics for explaining complex equations, functions and relations
and solving them. Graphing of any equation means its corresponding 2D paper representation of ...
Did you know that drinking tea for high blood pressure regularly can actually help lower the risk of hypertension? Read here to find out more!
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Best graphing calculator for high school is the TI 84 Plus "The new TI-84 Plus is a wonderful calculator. If anybody has had the TI-83 or 83 Plus, they know how easy and reliable it is. The 84 Plus is an all-around imprivement on the older version and even worth the additional $15-$20. I have had it since school started and have noticed than any problem I enter, it is solved immediately upon pressing enter, or solve. The speed is a great improvement over the 83-Plus".Read the rest of this review here The kids of today are not like those of our time. Back in the 1990s the older people had to settle for two dimensional graphs and if one wanted an upper triangular matrix then they had do all the row operations by themselves. Today, kids are using advanced graphing calculators. We recommend the TI84 Plus ( read the Full review here )which is the newer version of the famous TI 83. Although it is not as advanced as the TI89 Titanium it allows you to learn to do calculations yourself. In addition the TI84 Plus is acceptable in standardized tests such as SATs. However the TI84 has all you need in high school. Technical Details Graphing calculator handles calculus, engineering, trigonometric, and financial functions USB on-the-go technology for file sharing with other calculators and connecting to PCs 11 apps preloaded Displays graphs and tables on split screen to trace graph while scrolling through table values Backed by 1-year warranty There is also the TI 84 plus Silver edition which is more powerful than the TI84 Plus and is also easier to use than the TI 89. "This calculator is hands-down the best I have ever had the honor of using. While the TI-84 Plus may not have as much space or as many pre-loaded Apps as the TI-84 Plus Silver Edition, the TI-84 Plus offers everything a high school (possibly some college) math student needs in order to successfully learn and solve mathematics material". Read the rest of this review here Many instructors in high school or even college will not allow the use of Ti 89 Titanium because it solves the problems automatically. Some teachers allow students to use calculators for home work but not for exams. The TI 84 Plus or Silver are therefore the best for high school. In addition they can be easily upgraded when needed. The TI 89 is advanced and your teacher may not even know how to use it or dos some calculations. The learning curve on a TI89 is also much steeper than that of TI84 plus or Silver. Many teachers may also be using the TI 84 Plus/Silver - which will leave those with TI 89 to figure out complicated calculators on their own. My advice is to buy the TI 84 Plus/Silver for high school - as you can use it in exams and in standardized tests. You can then purchase the TI 89 later in college if you feel you need it- or are taking specific majors. The best place to buy the TI84 Plus is at Amazon. You pay much less than in regular stores while still getting all the warranties. They also have free shipping, great customer service and great return policies. You also don't pay state sales tax which adds as much as $12 to a $150 calculator. Tip: One other thing to remember is to put new batteries in the Calculator when going for an exam .Some students have forgotten to do so and ended up doing these exams by hand. Sorting products by Store Name Texas Instruments TI-84 Plus Graphing Calculator $110.99 (Packaging may vary) more...
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ALGEBRA II
INTRODUCTION
California Mathematics Framework
Algebra II expands on the mathematical content of Algebra I and Geometry. There is no single
unifying theme. Instead, it introduces many new concepts and techniques that will be basic to
more advanced courses in mathematics and the sciences as well as useful in the work place. In
general terms, the emphasis is on abstract thinking skills, the function
concept, and the algebraic solution of problems in various content areas.
The study of absolute value and inequalities is now extended to include simultaneous linear
systems; it paves the way for linear programming---the maximization or minimization of linear
functions over regions defined by linear inequalities. The relevant standards are:
1.0. Students solve equations and inequalities involving absolute value.
2.0. Students solve systems of simultaneous linear equations and inequalities (in two or
three variables) by substitution, with graphs, or with matrices.
The concept of Gaussian elimination should be introduced for 2x2 matrices and simple 3x3
ones. The emphasis is on concreteness rather than on generality. Concrete applications of both
simultaneous linear equations and linear programming to problems in daily life should be brought
out, but there is no need to emphasize linear programming at this stage. For the purpose of
graphing regions in connection with linear programming, while it would be inadvisable to
advocate the use of graphing calculators all the time, such calculators are helpful once students
are past the initial stage of learning.
At this point of students' mathematical development, knowledge of complex number is
indispensable:
5.0. Students demonstrate knowledge of how real and complex numbers are related
both arithmetically and graphically. In particular, they can plot complex numbers as
points in the plane.
6.0. Students add, subtract, multiply, and divide complex numbers.
It is important to stress the geometric aspect of complex numbers from the beginning, for
example, the addition of two complex numbers in terms of a parallelogram. Also point out the
key difference: the complex numbers cannot be linearly ordered the same way real numbers are
(the real line).
The next general technique is the formal algebra of polynomials and rational expressions.
3.0. Students are adept at operations on polynomials, including long division.
4.0. Students factor polynomials representing the difference of squares, perfect square
trinomials, and the sum and difference of two cubes.
1
7.0. Students add, subtract, multiply, divide, reduce, and evaluate rational expressions
with monomial and polynomial denominators and simplify complicated rational
expressions including those with negative exponents in the denominator.
The importance of formal algebra is sometimes misunderstood. The argument against it is that it
has insufficient real world relevance and it leads easily to an over-emphasis on mechanical drills.
There seems also to be an argument for placing the exponential function ahead of polynomials in
school mathematics because of the former's appearance in many real world situations
(compound interest, for example). However, there is a need to affirm the primacy of
polynomials in mathematics and the importance of formal algebra. The potential for abuse in
Standard 3.0 is all too obvious, but such abuse would be realized only if the important ideas
implicit in it are not brought out. These ideas all center on the abstraction and hence the
generality of the formal algebraic operations on polynomials. Thus the division algorithm (long
division) leads to the understanding of the roots and factorization of polynomials. The factor
theorem (x-a) divides a polynomial p(x) if and only if p(a)=0) should be proved and students
should know the proof. The rational root theorem could be proved too, but only if there is
enough to explain it carefully; otherwise many students would be misled into thinking that all the
roots of a polynomial with integer coefficients are determined by the divisibility properties of the
first and last coefficients.
It would be natural to first prove the division algorithm and the factor theorem for polynomials
with real coefficients. But it would be vitally important to revisit both and point out that the same
proofs work, verbatim, for polynomials with complex coefficients. This not only provides a
good exercise on complex numbers, but also nicely illustrates the
built-in generality of formal algebra.
Two remarks about Standard 7.0 are relevant: (i) a rational expression should be treated
formally and its function-theoretic aspects (the domain of definition, for example) need not be
emphasized at this juncture, and (ii) fractional exponents of polynomials and rational expressions
should be carefully discussed here.
The first high point of the course is the study of quadratic (polynomial) functions:
8.0. Students solve and graph quadratic equations by factoring, completing the square,
or using the quadratic formula. Students apply these techniques in solving word
problems. They also solve quadratic equations in the complex number system.
9.0. Students demonstrate and explain the effect changing a coefficient has on the graph
of quadratic functions. That is, students can determine how the graph of a parabola
changes as a, b, and c vary in the equation y=a(x-b)2 + c.
10.0 Students graph quadratic functions and determine the maxima, mimima, and zeros of
the function.
What distinguishes Standard 8.0 from the same topic in Algebra I is the newly-acquired
generality of the quadratic formula: it now solves all equations ax2 + bx +c =0 with real a, b, and
2
c regardless of whether b2 - 4ac < 0 or not, and it does so even when a, b and c are complex
numbers. Again it should be stressed that the purely formal derivation of the quadratic formula
makes it valid for any object a, b and c so long as the usual arithmetic operations on numbers
can be applied to them. In particular, it makes no difference whether they are real or complex.
This provides another illustration of the built-in generality of formal algebra. Students need to
know every aspect of the proof of the quadratic formula. They should also be made aware that
(i) with the availability of complex numbers, any quadratic polynomial ax2 + bx +c =0 with real
or complex a, b and c can be factored into a product of two linear polynomials with complex
coefficients, (ii) c is the product of the roots and -b is their sum, and (iii) if a, b and c are real
and the roots are complex, then the roots are a conjugate pair.
Standard 9.0 brings the study of quadratic polynomials to a new level by regarding it as a
function. This leads to the exact location of the maximum, minimum, and zeros of this function by
use of the quadratic formula (or more precisely, by completing the square) without recourse to
calculus. The practical applications of these results are as
important as the theory here.
Another application of completing the square is given in standard 17.0 where students learn,
among other things, how to write the equation of an ellipse or hyperbola when only geometric
data are given, such as focus, major axis, minor axis, etc.
A second high point of Algebra II is the introduction of two of the basic functions in all of
mathematics: ex and log x.
11. Students prove simple laws of logarithms.
11.1. Students understand the inverse relationship between exponential and logarithms
and use this relationship to solve problems involving logarithms and exponents.
11.2. Students judge the validity of an argument according to whether the properties of
real numbers, exponents, and logarithms have been applied correctly at each step.
12.0. Students know the laws of (fractional) exponents, understand exponential functions,
and use these functions in problems involving exponential growth and decay.
15.0. Students determine whether a specific algebraic statement involving rational
expressions, radical expressions, or logarithmic or exponential functions is
sometimes true, always true, or never true.
The theory should be done carefully, and students are responsible for the proofs of the laws of
exponents for am where m is a rational number, and of the basic properties of loga x: loga (x1 x2)
= loga (x1)+ loga (x2), loga (1/x) = - loga x, and loga(xr) = r loga x, where r is a rational number
(Standard 15.0). The functional relationships loga(ax) = x and a log(t) = t where a is the base of
the log function, should be taught without a detailed discussion of inverse functions in general, as
students are probably not ready for it yet. Practical applications of this topic to growth and
decay problems are legion.
A third high point of Algebra II is the study of arithmetic and geometric series:
3
23) Students derive the summation formulas for arithmetic series and for both finite and
infinite geometric series.
The geometric series, finite and infinite, is of great importance in mathematics and the sciences,
physical as well as social. Students should be able to recognize this series under all its guises and
compute its sum with ease. In particular, they should know by heart the basic identity that
underlies the theory of geometric series:
xn – yn = (x-y)(xn-1 + xn-2 y + · · · + xyn-2 + yn-1).
This identity gives another example of the utility of formal algebra, and the identity is used in
many other places as well (the differentiation of monomials, for instance).
It should be mentioned that while it is tempting to discuss the arithmetic and geometric
n
series using the sigma notation ∑, it would be advisable to resist this temptation so as not
I =1
to overburden the students.
Students should learn the binomial theorem and how to use it:
20.0. Students know the binomial theorem and use it to expend binomial expressions that
are raised to positive integer powers.
18.0. Students use the fundamental counting principles to compute combinations and
permutations.
19.0. Students use combinations and permutations to compute probabilities.
In this context, the applications almost come automatically with the theory.
Finally, Standards 16.0 (geometry of conic sections), 24.0 (composition of functions and
inverse functions), and 25.0 can be taken up if time permits.
4
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MapleSim for Educators and Students
The modern approach to modeling and simulation
With MapleSim, educators have an industry-proven tool to help bridge the gap between theory and practice. Built on the world-leading Maple mathematics engine and the open-standard Modelica modeling language, MapleSim gives you the ability to engage your students with complex, real-world examples and prepare them for the challenges they will face in industry.
Multiple domains, one environment. The MapleSim modeling environment combines components from different engineering domains so that students in all engineering streams can build and explore realistic designs and study the system-level interactions.
Model systems, not equations. Systems that would take hours or days to construct from first-principle equations can be created in a fraction of the time using MapleSim, so you can incorporate significantly more complex examples into your courses.
Connect the concepts. With system-level equations available for demonstrating concepts like parameter optimization and sensitivity analysis, and the ability to define new components from first principles using mathematical equations, MapleSim allows you to make the connection between the math and the model behavior
Simulate virtually, validate physically. Simulation allows students to safely investigate a much larger range of conditions than is possible by testing with hardware alone, with no risk of damage to equipment and for much less cost.
Would You Like to Teach with MapleSim?
Engineering institutions from around the world have began to adopt MapleSim in the classroom. Benefits include:
MapleSim illustrates concepts, and helps students learn the connection between theory and physical behaviour
A wide variety of models are available to help you get started right away
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...I have taken a wide variety of courses including mathematics and computer applications. I use these skills everyday in life. For example, computer applications such as Microsoft Word are used to create a variety of documents including brochures
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Intermediate Algebra Concepts and Applications
9780201708486
0201708485
Summary: The Sixth Edition of Intermediate Algebra: Concepts and Applications continues to bring your students a best-selling text that incorporates the five-step problem-solving process, real-world applications, proven pedagogy, and an accessible writing style. The Bittinger/Ellenbogen hardback series has consistently provided teachers and students with the tools needed to succeed in developmental mathematics. With this revi...sion, the authors have maintained all the hallmark features that have made this series so successful, including its five-step problem-solving process, student-oriented writing style, real-data applications, and wide variety of exercises. Among the features added or revised are new Aha! exercises that encourage students to think before jumping in to solve a problem, 20% new and added real-data applications, and 50% more new Skill Maintenance Exercises. This series not only provides students with the tools necessary to learn and understand math, but also provides them with insights into how math works in the world around them.[read more]
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If your work involves math that can't easily be done in a spreadsheet, MathCad 6.0 from MathSoft (617 577-1017) may be the tool for you. Both the Standard ($129) and programmable Plus ($349) versions let you do complicated numerical or symbolic calculations on a sort of computerized scratch pad. Results can then be pasted into other Windows applications. While less sophisticated than computer algebra systems such as Wolfram Research's Mathematica, MathCad is much easier to learn and use.BY STEPHEN H. WILDSTROM
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Math Department
Department Chair: Mrs. Joyce Heller
Our primary goal in teaching mathematics is to help students learn the art of reasoning and problem solving, skills that will aid them throughout their educational and professional careers. The ability to evaluate data, turn it into information, and reach timely and pertinent decisions is crucial in achieving success in any field of endeavor. The Ma'ayanot mathematics program helps students learn how to think logically and creatively, perform mathematical calculations both manually and with the use of graphing calculators, and master mathematical functions and concepts.
COURSE OF STUDY:
Entering students take a placement examination in mathematics regardless of their previous mathematical background in elementary school. A multi-track math program allows Ma'ayanot to serve the individual needs of all students. All students are required to take three years of math in high school and they are strongly encouraged to take a fourth year as an elective. PSAT and SAT preparation is incorporated into the curriculum. All students take Algebra I, Algebra II/Trigonometry, and Geometry. Pre-Calculus and AP Calculus AB or BC are offered in the junior and senior years. Students with strong aptitude and interest in mathematics are encouraged to participate in extracurricular math programs, competitions, and research projects in advanced mathematics.
All math courses in the high school program require students to have a TI-83 graphing calculator to be used as a tool for learning and doing mathematics.
Tracking: All mandatory Math classes are tracked (9th - 11th grade), but all students can choose to take Math electives in the senior year. Math classes are tracked independently of other disciplines.
ALGEBRA I
This course is designed to help student understand the basic concepts of elementary algebra and acquire important manipulative algebraic skills. The syllabus has been developed on a level appropriate to the mathematical maturity and sophistication of all students. Enrichment is provided throughout for those students capable of proceeding at a faster pace.
The basic concepts of this course are carefully developed with the use of simple language and symbolism. Explanations and problems lead to the statement of general principles and procedures. Model problems and solutions are detailed in class, helping students to apply these principles independently. Daily exercises cover almost every type of difficulty and tests cover students' understanding of basic concepts as well as mastery of manipulative skills.
GEOMETRY
The geometry syllabus is written to provide appropriate materials to help both teacher and student achieve the following objectives of a modern geometry course.
To develop an understanding of geometric relationships in a plane and in space.
To develop an understanding of the meaning and nature of proof.
To teach the method of deductive proof in both mathematical and non-mathematical situations.
To develop the ability to think creatively and critically in both mathematical and non-mathematical situations.
To integrate geometry with arithmetic, algebra and numerical trigonometry.
ALGEBRA II/TRIGONOMETRY
The major objective of the Algebra II/Trigonometry syllabus is the integration of intermediate algebra, plane trigonometry and coordinate geometry. To achieve this goal, trigonometric content is presented at an early stage and carried along simultaneously with work in algebra. Such a presentation is more effective than one in which the teaching of trigonometry is deferred until intermediate algebra has been completed.
Proper integration of algebra and trigonometry enables a student to make a smooth transition from working with algebraic expressions and equalities to working with trigonometric expressions and equalities. The comprehensive presentation of coordinate geometry also serves as an effective means of integrating intermediate algebra and plane trigonometry. This is accomplished by emphasizing the fundamental ideas underlying the graphs of linear functions, quadratic functions and trigonometric functions.
PRE-CALCULUS
Pre-calculus can serve as preparation for calculus or as a fourth year to the normal curriculum. Topics covered prepare students not only for calculus but for all future college level mathematics courses. During the year, students cover diverse topics, such as examining relations and functions, mathematical induction, polynomial equations, linear programming, conic sections, complex numbers, polar coordinates, sequences and series. Students make extensive use of the graphing calculator to develop mathematical models for real world applications.
Pre-calculus is a required course for students who entered high school with accelerated mathematics and must complete a third year of high school mathematics at Ma'ayanot. It is a prerequisite for students wishing to take calculus either at Ma'ayanot or in college. It is an elective for seniors who would like to explore mathematical concepts in greater depth or expect to need some mathematics in their college studies.
ADVANCED PLACEMENT CALCULUS
Calculus AB is primarily concerned with developing the students' understanding of the concepts of calculus and providing experience with its methods and applications. The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed geometrically, numerically, analytically, and verbally. The connections among these representations are important.
Technology is used regularly by students and teachers to reinforce the relationships among the multiple representations of functions, to confirm written work, to implement experimentation, and to assist in interpreting results.
Through the use of unifying themes of derivatives, integrals, limits, approximation, and applications and modeling, the course becomes a cohesive whole.
The course represents college level mathematics for which most colleges grant advanced placement credit according to the results of an Advanced Placement Examination. The AB course enables a student to obtain credit for the first semester of college calculus.
Calculus BC represents college level mathematics, for which a student may qualify for two semesters of college credit, based upon the results of the Advanced Placement Examination.
ADVANCED PLACEMENT STATISTICS
The purpose of this course is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes:
Students who successfully complete the course and examination may receive credit and/or advanced placement for a one-semester introductory college statistics course.
REAL WORLD FINANCE
This course was designed for seniors who are interested in a pragmatic finance course. The course explores all aspects of investments, including savings accounts, CDs, stocks, bonds, mutual funds, planning for retirement, alternative investment vehicles, and creating a balanced investment portfolio. Forms of credit such as credit cards, student loans, mortgages, and car loans are studied, in addition to life, health, car, homeowners, and ancillary insurance. Planning a household budget, balancing a checkbook, online banking and bill paying, and income taxes round out the course.
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Use Wolfram|Alpha to Solve Calculus Problems and…...
Use Wolfram|Alpha to Solve Calculus Problems and… Everything Else.
Wolfram|Alpha is like Google on crack. However, it is not technically a search engine; it is a "computational knowledge" engine. They use a huge collection of trustworthy, built-in data to get the user the information or knowledge they are looking for. When you search for an item, Wolfram|Alpha gives you all of the relevant knowledge they have on that specific search query. For example, here is the results for the search "when did the Beatles break up?" Not only do you get the date the Beatles broke up, you also get how long away that date is from today and other noteworthy events that occurred on the same day. Here is another example, for the search "carbon footprint driving 536 miles at 32mpg" that tells you the amount of fuel consumed and the amount of c02 and carbon emitted.
Because Wolfram|Alpha is just retrieving answers from its huge database of information and formulas, you have to be specific and ask non-opinionated questions. For example, the website does not know which Lil Wayne song is the best. However, it does know things that are not opinions, like the nutritional facts of 10,000 big macs and how many planes are currently flying directly over you.
I find Wolfram|Alpha to be better than Google when I am quickly looking for specific answers. I just typed in "Countries that border France" on both Wolfram|Alpha and Google. Wolfram|Alpha quickly showed me a list of the 8 countries and a map with of France with its bordering countries highlighted. Google on the other hand sent me over to Yahoo Answers…
Other than a fun search engine, Wolfram|Alpha can also be used as a highly effective tool for college. Like the title mentions, the knowledge engine can in fact solve any calculus problem. It can easily solve any math problem thrown its way, from a basic algebra problem to whatever this is.
Wolfram|Alpha can also be used for many other college courses such as biology, astronomy, history, etc.
As Wolfram|Alpha can be kind of confusing and hard to get the hang of at first, I suggest going through this short tour and looking at some examples to help give you a better sense of how to use it. Even if you find it a little bit confusing at first, keep trying because Wolfram|Alpha really is a great way to "hack college."
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Math Lab is a class created to facilitate increased understanding and application of math concepts. Math Lab 1 is a year long course that focuses on Algebra 1 concepts and prepares students to take the Algebra 1 EOI test during the Spring testing window. Math Lab 2 is a semester long course the provides an intense review of Algebra or Geometry concepts and prepares students to re-take the EOI test during the Winter or Spring testing windows.
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Mathematics Courses:
Catalog Description:
Examines applications of the definite integral; analysis of the natural logarithmic, exponential, trigonometric, and hyperbolic functions; introduction to differential equations; techniques of integration; L'Hopital's Rule and indeterminate forms; improper integrals; and infinite series. Prerequisite: MAT 141 with a grade of 'C' or higher or by placement.
Lecture: 4 hrs.
Course Student Learning Outcomes (CSLOs):
A student who has successfully completed MAT142 is expected to be able to perform the following in an exam setting, without the use of notes, using a scientific or graphing calculator as appropriate:
1. Evaluate the derivative of any exponential, logarithmic, trigonometric, or inverse trigonometric functions
2. Given any integrable function, the student must recognize and apply the correct technique used to integrate (in exact form) from among the following techniques: fundamental integral formulas, U-substitution, method of parts, trigonometric substitution, method of partial fractions, powers of trig functions, or by use of integral tables*
3. Apply the Fundamental Theorem of Calculus to evaluate a definite integral
4. Using integrals, find the area between the two curves
5. Using integrals, sketch any plane region defined by one or more simple curves, and find the volume of the solid generated by revolving the plane region about the x- or y-axis
6. Apply any of the standard approximation techniques (midpoint, trapezoid, Simpson's) to evaluate a definite integral involving any simple function, accurate to three decimal places.
7. Use L'Hopital's Rule to evaluate any limit involving the indeterminate form 0 / 0 or oo/oo
8. Given an infinite series, determine the convergence or divergence of the series using any of the following tests (as appropriate to the particular series): divergence, ratio, root, comparison, limit comparison, geometric, harmonic, integral, p-series.
9. Given a power series, find the interval of convergence.
10. Given a function of a single variable, find and evaluate a Taylor polynomial or Taylor series for the function at a given point.
* This course objective has been identified as a student learning outcome that must be formally assessed as part of the Comprehensive Assessment Plan of the college. All faculty teaching this course must collect the required data and submit the required analysis and documentation at the conclusion of the semester to the Office of Institutional Research and Assessment.
II. Applications of Integration
a. Area between two curves
b. Volume: The Disc Method
c. Volume: The Shell Method
d. Arc Length and Surface Area
e. Work
f. Additional applications at discretion of instructor
VI. Infinite Series
a. Sequences
b. Series and convergence
c. The Integral Test and p-Series
d. Comparisons of series
e. Alternating series
f. The Ratio and Root Tests
g. Power series
h. Taylor & Maclaurin Series and Associated Applications
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Staffed by professional and peer tutors, the Math Learning Center
(MLC) provides free tutoring and support services for students enrolled in
mathematics
and computer science courses at SUNY College at Old Westbury.
The MLC conducts
laboratory sessions for Introductory Algebra (MA0500), and also houses
a library of textbooks, videotapes and educational technology.
Tutoring: Tutoring is available whenever the Center is
open. No appointment is necessary.
Textbooks and Answers: Answer books and textbooks
for most math courses may be borrowed for use in the Center. A
current Old Westbury ID is required.
Videotapes: Videotapes for many of the basic courses
are available for use in the Center. Some of the videotapes are
available for overnight
use. These tapes are especially good for students who have missed
class or who
wish further review of a topic.
Software: Computer software is available for
many of the basic courses.
Do not expect to learn an entire course in one day. Work on one topic at
a time, and try to master it before moving on to the next. First try the
homework on your own, and then ask for help on the material that you have
trouble with.
Before taking a course make sure you satisfy all course prerequisites. Attend
all classes, and do the assigned readings and homework on time.
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…
This Mathematics Matters case study, from the Institute of Mathematics and its Applications, discusses the importance of statistics and computing to developments in medical research. Sequencing the human genome was a fantastic achievement, but it was only the beginning. Now, statisticians are coming up with new methods to sift through…
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This Mathematics Matters case study, from the Institute of Mathematics and its Applications, looks at how mathematics modelling can aid investigations into the circulatory system. Blood-related diseases can seriously harm patients' quality of life and even lead to death. Many of these diseases are caused by problems with the…
This Mathematics Matters case study looks at how mathematicians are aiding the fight against viruses. Many viruses have a symmetrical structure made from basic building blocks, and biologists have struggled to explain some of the more detailed shapes. Now mathematicians are using complex theories of symmetry to reveal these viral…
These two Economic and Social Research Council (ESRC) pages give statistics and key facts about the British population in 2007 and 2008. These statistics give a picture of the UK's population growth rates and age distribution, percentages of ethnic minorities, where we live and work, our income and spending habits, health, educationThis Nuffield Foundation publication was prepared to help students master the calculations involved in GCSE Science courses. The book is divided up into a series individual topics. Each topic is presented in three parts.
• A summary of the ideas students need to know, including any important formulas.
• Worked examples,
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..
Schaum's Outlines-Problem Solved
..
More than 100,000 sold!
..
This book has been updated to reflect the latest course scope and sequence. Review problems have been added after key chapters as well as more supplementary practice problems. An informal level discussion of limits, continuity, and derivatives has also been added, as well as additional information on the algebra of the dot product, exponential form of complex numbers, and conic sections in polar coordinates-plus business applications such as average rate of change, price/demand and science applications, including projectiles.
Description:
Study faster, learn better, and get top gradesA clear review
of standard college course of Mathematics for Elementary School Teachers, this book will be designed to improve your basic knowledge of math content required for this level, engage you ...
Description:
Remarkable technological advances still elave us basing most major engineering
decisions on economic considerations. So, this clear and concise examination of the principles of engineering economics should benefit all undergraduate students, regardless of their area of interest. Students will ...
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A guide to MATLAB : for beginners and experienced users by Brian R Hunt(
Book
) 21
editions published
between
2001
and
2006
in
English
and held by
746
libraries
worldwide
This book is a short, focused introduction to MATLAB, a comprehensive software system for mathematics and technical computing that should be useful to both beginning and experienced users. It contains concise explanations of essential MATLAB commands, as well as easily understood instructions for using MATLAB's programming features, graphical capabilities, and desktop interface. It also includes an introduction to SIMULINK, a companion to MATLAB for system simulation. Written for MATLAB 6, this book can also be used with earlier (and later) versions of MATLAB. Chapters contain worked-out examples of applications of MATLAB to interesting problems in mathematics, engineering, economics, and physics. In addition, it contains explicit instructions for using MATLAB's Microsoft Word interface to produce polished, integrated, interactive documents for reports, presentations, or on-line publishing.
Algebraic K-theory and its applications by J Rosenberg(
Book
) 5
editions published
between
1994
and
1996
in
English
and held by
438
libraries
worldwide
"Algebraic K-theory plays an important role in many areas of modern mathematics: most notably algebraic topology, number theory, and algebraic geometry, but even including operator theory. The broad range of these topics has tended to give the subject an aura of inapproachability. This book, based on a course at the University of Maryland in the fall of 1990, is intended to enable graduate students or mathematicians working in other areas not only to learn the basics of algebraic K-theory, but also to get a feel for its many applications. The required prerequisites are only the standard one-year graduate algebra course and the standard introductory graduate course on algebraic and geometric topology. Many topics from algebraic topology, homological algebra, and algebraic number theory are developed as needed. The final chapter gives a concise introduction to cyclic homology and its interrelationship with K-theory."--BOOK JACKET.
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Math prerequistes for pharmacist to understand relativity
Math prerequistes for pharmacist to understand relativity
I know someone posted something similar before. However, that person definitely has taken some advanced math classes before.
I am a biology/pharmacy major and I want to teach myself relativity. The most difficult math and physic classes I have taken are calculus 3 and physical chemistry respectively.
I am currently reading "Linear algebra and its applications by David C lay"
Can someone make up a list of books I need to read in order to understand relativity? How long will it take to read and understand all the prerequisites?
As far as understanding Special Relativity goes, you should have the necessary math if you've got Calc 1 and Linear Algebra.
For General Relativity, the mathematical language is that of differential geometry and advanced linear algebra (tensor algebra). But I believe the typical student of GR picks up these topics as he studies the physics.
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Prerequisite: Placement through the assessment process or MATH 075 or MATH 075SP or equivalent
Note: In this computer-assisted self-paced class, students study from the textbook, online, during weekly face-to-face meetings and take a combination of online and in-class exams. The online labs require computer access and may be completed either on or off campus. The face-to-face meetings will be held in the DVC Math Lab (for lab schedule go to for Pleasant Hill or for SRC). Students are encouraged to complete MATH 110SP in one semester, or take up to 2 semesters. MATH 110SP is equivalent to MATH 110; students who have completed MATH 110 will not receive credit for MATH 110SP.
This course is a computer-assisted self-paced equivalent to MATH 110. The topics include linear equations and inequalities, development and use of formulas, algebraic expressions, systems of equations, operations on polynomials, factoring, graphs, and an introduction to quadratic equations.
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About McGraw -Hill's Top 50 Math Skills for GED Success
Written for the millions of students each year who struggle with the math portion of the GED, "McGraw-Hill's Top 50 Math Skills for GED Success "helps learners focus on the 50 key skills crucial for acing the test.
From making an appropriate estimate and solving for volume, to interpreting a bar graph and identifying points on a linear equation, this distinctive workbook from the leader in GED study guides features step-by-step instructions; example questions and an explanatory answer key; short concise lessons presented on double-page spreads; an appealing, fully correlated pretest and computational review of basic skills; application, concept, and procedure problems; and more.
About McGraw -Hill's Top 50 Math Skills for GED
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General Site Search
Mathematics (AQA GCSE Level 2)
Course Overview
The College runs the AQA GCSE Modular Mathematics course. This course gives candidates the opportunity to take exams in three smaller chunks rather than one big exam at the end of the course. GCSE Maths is taken as one of two tiers (levels) enabling learners to achieve grades G to C on Foundation, and D to A* on Higher.
Entry Requirements
We run the GCSE Mathematics course over a year, which means the pace of lessons is quite high. For this reason we have the following requirements for entry onto the course:
Candidates wishing to study the Foundation course will either be asked to take an assessment prior to starting the course, or must have already achieved a D grade in the subject. If you do not meet the entry requirements, but have other relevant qualifications or experience your application will be considered independently.
If you wish to study the Higher course we ask that you are already in possession of a C grade at GCSE. Again, if you have other relevant qualifications or experience your application may still be accepted.
College policy is to recruit with integrity, so if you do not have the entry requirements or you have other relevant qualifications your application will be considered independently. All applicants undertake initial diagnostic tests and a personal interview before being accepted on the course.
Duration
32 Weeks
Course Contents
For both levels of the GCSE Mathematics course, lessons will be taught in a classroom environment with the group then being allowed time to practice what they have learned. All electronic teaching materials will be made available to learners on the internet via the College website.
Assessment
The course is split into 3 units:
Unit 1 - Statistics and Number - This unit is worth 27% of the final grade, and the exam is taken in November
Unit 2 - Number and Algebra - This unit is worth 33% of the final grade, and the exam is taken in March
Unit 3 - Geometry and Algebra - This unit is worth 40% of the final grade, and the exam is taken in June
Progression Route
Completion of the Foundation level GCSE at grade C will enable learners to advance onto the Higher level GCSE the following year, which will allow them to gain a grade up to an A*. Attainment of a grade C at either level is often a requirement for entry onto higher level College or University courses. Job prospects are also greatly improved upon gaining a grade C
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The Chapter 1 Test is postponed, until after I return from my absence. Please make sure that you retain all of the knowledge and understanding you have worked so hard to acquire!
If you have hand held technology device on which you can access our text book, please bring it to class this week!
Tuesday 9/25/2012
No HW
Thursday 9/27/2012
Practice Constructions.
RTN & GP Lesson 2.1
Monday 10/1/2012
Prepare for Unit 1 Test: Sections 1.1 - 1.5 and 2.1
Tuesday 10/2/2012
The take home portion (constructions) of your Test is due on Thursday
RTN & GP Lesson 2.2 and page 86 (Symbolic Notation)
Wednesday 10/3/2012
Page 74: #3, 5, 6, 7, 8, 9, 10, 25, 26, 27, 29, 35. If you did not finish Journal #2 Entry #2 in class, finish it at home (it is on today's work sheet). Review the RTN & GP for this section and page 86. The take-home portion (constructions) of your Unit 1 test is due at the beginning of class tomorrow.
Thursday 10/4/2012
Homework: Page 75: #19 – 24, 31, 32.
Finish class work sheets from Lesson 2.2 day 1 and day 2.
RTN & GP Lesson 2.3
Friday 10/5/2012
Review the RTN for lesson 2.3. Stretch your logic and reasoning abilities by completing as many of the logic puzzles and sudoku puzzles as you can!
Monday 10/8/2012
Page 82: #1, 5, 7, 9, 13, 17, 21, 22, 25, 26, 27, 28. Check out the e-textbook animation that goes with this lesson, to help you learn the law of syllogism!
RTN & GP Lesson 2.4 – Please note: you are not expected to memorize postulate numbers or the exact wording of the Point, Line, and Plane Postulates!
Wednesday 10/10/12
Journal #2 is due tomorrow. Retest of the Take home portion of chapter 1 test is due Monday. Finish the 2.4 sheet from class today. RTN & GP Lesson 2.5 - Study the examples very carefully. You will be expected to know the names of all of the properties, and use them to justify each step of an algebraic process. Also notice how Geometric properties are also named as reasons.
Thursday 10/11/12
Lesson 2.5 Day 1 worksheet. Remember to go back to your text book and review the examples in 2.5 that use the segment addition postulate and the angle addition postulate.
Friday 10/12/12
Study the example(s) completed in class, on the Lesson 2.5 Day 2 work sheet. On the back of the sheet, do the proof using different logic, using the hints provided. Carefully read the Chapter 2 project sheets, to decide which project you want to do. Test on Lessons 2.2 - 2.5 on Tuesday 10/16. The retest of the take home portion of the unit 1 test is due on Monday.
Monday 10/15/12
Prepare for Test on Lesson 2.2 - 2.5 tomorrow. Practice! Finish or redo any worksheets from class. Use the on-line text book resources!
Try the proofs on the Lesson 2.6 Day 2 packet - remember to solve the problem in your head first, and developing an overall stategy before you write anything down! If you find some of the proofs frustrating or difficult, don't panic - we'll take care of it in class. However, if you are struggling, do some problems from the text book and check your answers.
Finish any proofs your were not able to complete in class. Test on 2.6 and 2.7 on Friday. RTN & GP Lesson 3.1. All of the highlighted vocabulary terms on page 141 should be familiar to you. Make sure that you realize that these are angle relationship names based on position only, and do not tell you anything about congruence or measures! The two new postulates should make intuitive sense to you.
Thursday 10/25
Prepare for test on 2.6 and 2.7.
Friday10/26/12
Page 142: #3, 4, 5, 6, 15, 16, 17, 28, 29, 30, 31, 32
RTN & GP Lesson 3.2
Monday 10/29/12
Page 150: #22 – 36. For each problem (except #34), copy the diagram, set up an equation and state the postulate or theorem that justifies it, using the acceptable abbreviation.
RTN & GP Lesson 3.3
Monday 11/12/12
WELCOME BACK FROM HURRICATION 2012! No HW
Tuesday 11/13/12
Do pages 1 & 2 ONLY of the 3.2/3.3 packet
RTN & GP Lesson 3.3
Wednesday 11/14/12
Page 150: #22 – 36. For each problem (except #34), copy the diagram, set up an equation and state the postulate or theorem that justifies it, using the acceptable abbreviation.
Practice the 3 constructions on pages 190 & 191, until you can do them neatly, accurately and without looking at the instructions.
RTN & GP Lesson 3.4. Please make note, for each vocabulary term, key concept, postulate and example, which ones you already know, which are new, and which simply need a refresher. PLEASE BRING YOUR TEXT BOOK, or personal technology to access to class on Monday!
Monday 11/19/12
Study for Chapter Test on sections 3.1 – 3.3.
11/20/12 Tuesday
RTN & GP Lesson 3.5. Please make note, for each vocabulary term, key concept, postulate and example, which ones you already know, which are new, and which simply need a refresher.
11/21/12 Wednesday
Have a nice break!
11/26/12 Monday
Finish the 3.4/3.5 intro sheet from class.
Page 167: #11, 12, 13, 14, 34, 39, 40, 42
Review your RTN & GP for lesson 3.5
11/27/12 Tuesday
Page 176: #19, 21, 25, 27, 29, 31, 35, 47, 48, 59.
If you were not able to do #42 from yesterday's HW, try again!
11/28/12 Wednesday
Finish the 3.4/3.5 sheets from class.
RTN & GP for lesson 3.6. Notice that the first three theorems don't have names. If you were a math teacher, what do you think would be the best name for each? You should have the next 2 theorems already proven in your notebook. Know how to measure the distance between a point and a line and the distance between parallel lines. Carefully study example #4.
11/29/12 Thursday
Finish the 3.6 sheet from class.
11/30/12 Friday
Page 186: #13, 14, 25, 26, 27.
Test on 3.4 – 3.6 and Constructions on Tuesday 12/4
12/3/12 Monday
Prepare for Test on 3.4 – 3.6 and Constructions.
12/4/12 Tuesday
RTN & GP Lessons 1.6 and 4.1. Know all highlighted vocabulary terms.
12/5/12 Wednesday
Page 44: #8 – 14, 18 - 27
Page 211: #1 - 6, 29 – 37
12/6/12 Thursday
RTN & GP Lesson 8.1
Lesson 8.1 Packet pages 2 & 3. If you are struggling or unsure, try some similar problems in the text book and check the answer key.
12/7/12 Friday
10 point graded HW on sections 1.6, 4.1, & 8.1 should be completed this weekend, but will not be collected until Wednesday. If you are not able to complete the sheet by Monday's class, I will expect you to come in for extra help on Monday or Tuesday! RTN & GP Lesson 4.2.
Complete the coordinate proof from today's activity, two different ways. Do your best to follow the conventions of a "formal coordinate proof" given in the example and notes on Monday.
1/10/13 Thursday
Page 300: #15 – 19, 29, 30
RTN & GP Lesson 5.2
1/11/13 Friday
RTN & GP Lessons 5.3 and 5.4. Review lesson 5.2 and make note of the 4 types of Centers of Triangles including the names and what type of segments create them and any special properties they have. We will be doing constructions next week, so make sure you know where your compass and straight edge are!
1/14/13 Monday
Finish Page 2 ONLY of the construction packet (the 4 centers of acute triangles). Inspect your constructions as you reread lessons 5.2 - 5.4, with a focus on securing the vocabulary and developing an understanding of the properties of each type of center.
1/15/13 Tuesday
Finish the rest of the construction packet. Remember to construct the circle that circumscribes the triangle, with its center at the circumcenter. Remember to construct the circle that inscribes the triangle, with its center at the incenter. Make sure you know how to construct each type of segment, and which type of segment is constructed to find each type of center of a triangle.
1/16/13 Wednesday
Redo any constructions that you are struggling with. Make a graphic organizer to help you know all of the vocabulary and concepts associated with each of the 4 centers.
1/17/13 Thursday
Carefully review the Points of Concurrency Project requirements sheet. The project is due Tuesday 1/29. Put together a plan with your partner, so that you are prepared to review each other's work by the middle of next week. DO NOT treat this like a "divide & conquer" and just put 2 half-projects together at the last minute! LOOKING AHEAD: Plan on a test or quiz on either Tuesday or Friday next week, covering midsegment theorem, coordinate proofs and centers of triangles.
1/18/13 Friday
Work on your Points of Concurrency Project Due Tuesday 1/29. Work on the packet from class today (problems from 5.2 – 5.4). You are not required to complete the packet! Choose several problems from each section that stimulate and challenge you.
Reread the description and examples of indirect proofs in your text book.
Page 340: #11, 12, 13
Work on your Points of Concurrency Project Due Tuesday 1/29.
Start reviewing for your chapter 5 test. Do you know how to use distance formulate, midpoint formula and slope formula in a Midsegment Theorem Verification or any coordinate proof?
1/24/13 Thursday
Prepare for your Chapter 5 Test
IMPORTANT NOTICE:As discussed in class today, tomorrow's test only covers sections 5.1, 5.5 and 5.6. Study the class handouts! Sections 5.2, 5.3 and will be assessed as a partners quiz (multiple choice and short answer, on Tuesday 1/29.
ANOTHER IMPORTANT NOTICE: The Review Guide for the Marking Period 2 Quarterly Assessment is now posted on this website. See the menue on the left side of my homepage.
1/25/13 Friday
Work on your Points of Concurrency Project Due Tuesday 1/29.
RTN & GP Lesson 8.2
1/28/13 Monday
Your project is due tomorrow!
Partner Quiz on 5.2-5.4 tomorrow!
Page 512: #7, 11, 15, 31, 33
RTN & GP Lesson 8.3 – Know the 5 new theorems, and how they differ from the theorems in 8.2. These will be justifications you can use if you already know relationships involving angles, sides and/or diagonals and you are concluding that the figure is a parallelogram. Study the examples carefully.
1/29/13 Tuesday
Bring in any questions you have about the Quarterly Assessment.
1/30/13 Wednesday Page 521 #15, 16, 17, 34, 35, 36
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1/31/13 Thursday
Period 6 – finish preparing for tomorrow's quarterly. (The HW listed below for period 8 will be your HW tomorrow night!)
Period 8 – finish the 8.2 and 8.3 sheets from class. RTN & GP Lesson 8.4 – Know the formal definitions of a rhombus, rectangle and square. Notice how the Venn diagram presented is justified by the definitions. Notice that the corollaries on page 527, restate the definitions, without having to mention anything about parallelograms! The three new theorems on page 529 pack a lot of information about rectangles and rhombuses. Since they are biconditionals, you should write each of the 3 theorems as two separate conditionals that are converses of each other. Then reread each one, and create a diagram that allows you to see what it is actually telling you about the figure.
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2/1/13 Friday
Period 6 – finish the 8.2 and 8.3 sheets from class. RTN & GP Lesson 8.4. See yesterday's period 8 HW posting for RTN details. (The HW listed below for period 8 will be your HW Monday night!)
Period 8 – Page 531: #25, 27, 29, 33, 35, 39, 41, 45, 47, 49
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2/4/13 Monday
Period 6 – Page 531: #25, 27, 29, 33, 35, 39, 41, 45, 47, 49
Period 8 – finish preparing for tomorrow's quarterly.
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2/5/12 Tuesday
Period 6 & 8 are back in sync NOW! Complete as much as you can in the 8.4 packet. ALL problems must be at least reasonably attempted!
2/6/12 Wednesday
Complete the 8.4 packet.
RTN & GP Lesson 8.5. Know the formal definition of a trapezoid, isosceles trapezoid and a kite. The first two theorems about isosceles trapezoids make sense if you see that is like an isosceles triangle with the top sliced off! Notice that the third theorem makes sense when you look at the symmetry. There is not much to know about trapezoids that are not necessarily isosceles, except for which pairs of angles must be supplementary, and that the midsegment is parallel to the bases, and its length is the average of the length of the bases. The kite theorems should be very clear and intuitive if you look at the symmetry of a kite in one direction, and from the other direction look at it as two non-congruent isosceles triangles. You can also see it as 4 right triangles.
Page 586: 19, 21, 26 (do this twice – once with compass and straight edge and once with ruler and protractor)
Review for Quiz tomorrow on 4.3, 4.9, 9.1, 9.3, 9.4.
3/1/13 Friday
No new HW. Self assess, regarding Friday's quiz. What do you need to review, practice and/or reinforce? Choose problems appropriately. Also review/practice/reinforce Thursday's lesson, performing reflections with a compass and straight edge, as well as performing them with a ruler and protractor. Consider the advantages and disadvantages of each.
3/4/13 Monday
Complete the 9.5 compositions packet. RTN & GP Lesson 9.5.
3/5/13 Tuesday
Complete the 9.5 Day 2 compositions packet.
3/6/13 Wednesday
Page 604: #13 - 22
Go to the online text book. In Chapter 9 go to the Videos & Activities tab and find the Animated Math section. Do the Activity for Extension 9.5: Tessellations
3/7/13 Thursday
Use the square template and the class handout to create a unique shape that tessellates. This is just practice, so don't get too complicated, but do not copy the author's seahorse. You do not have to fill the page, but you should show 8 – 10 interlocking copies of your figure.
3/8/13 Friday
Use the equilateral triangle and/or regular hexagon template, today's handouts and tracing paper to practice a different method for creating a unique shape that tessellates. You do not have to fill the page, but you should show 8 – 10 interlocking copies of your figure.
Finish the Law of Cosines sheet started in class today. Use the Law of Cosines to find each missing value. Then use the triangle sum theorem to check your angle measures, and then check using the Law of Sines.
If you had 2 congruent cookies named A and B, and you cut A into congruent halves named 1 and 2 , and you cut B into congruent halves 3 & 4, you KNOW (and you CAN prove!!!) that 1 & 4 are congruent and 2 & 3 are congruent. Its just a bit of delightfully tediaous algebra.
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Emne: Clifford algebras. Data processing ; Clifford algebras. Data processing ; Clifford algebras Summary: The author defines "Geometric Algebra Computing" as the geometrically intuitive development of algorithms using geometric algebra with a focus on their efficient implementation, [...]and the goal of this book is to lay the foundations for the widespread use of geometric algebra as a powerful, intuitive mathematical language for engineering applications in academia and industry. The related technology is driven by the invention of conformal geometric algebra as a 5D extension of the 4D projective geometric algebra and by the recent progress in parallel processing, and with the specific conformal geo
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Numerical Methods in Electromagnetism
Electromagnetics is the foundation of our electric technology. It describes the fundamental principles upon which electricity is generated and used. This includes electric machines, high voltage transmission, telecommunication, radar, and recording and digital computing. This book will serve both as an introductory text for graduate students and as a reference book for professional engineers and researchers. This book leads the uninitiated into the realm of numerical methods for solving electromagnetic field problems by examples and illustrations. Detailed descriptions of advanced techniques are also included for the benefit of working engineers and research students.
Audience Students, engineers, scientists, and researchers involved in numerical methods for solving electromagnetic field problems in electrical machinery, as well as in high frequency devices; students and professors in electrical engineering departments.
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Microsoft Mathematics 4.0 for solving Mathematics problem
If you are a Windows user , you might have atleast come across the default calculator which is quite often used for some basic operations . But , here comes another program from Microsoft called "Microsoft Mathematics 4.0″ that helps the users to solve all kinds of maths problems . Whats more , its a free download and you can download Microsoft Mathematics 4.0 from the Microsoft Download Center .
Microsoft Mathematics provides a graphing calculator that plots in 2D and 3D, step-by-step equation solving, and useful tools to help students with math and science studies.
Students involved in any kind of Mathematical calculations might find this tool helpful . Students can learn to solve equations step-by-step while gaining a better understanding of fundamental concepts in pre-algebra, algebra, trigonometry, physics, chemistry, and calculus.
Microsoft Mathematics includes a full-featured graphing calculator that's designed to work just like a handheld calculator. Additional math tools help you evaluate triangles, convert from one system of units to another, and solve systems of equations.
Another special feature of the Microsoft Mathematics 4.0 is that inclues a Ribbon UI . so the Microsoft Office users might find it really easy to use it .
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Evolution of the Mathematics Curriculum
The mathematics curriculum responded to both internal factors
(e.g. department expertise, college requirements) and external factors
(e.g. textbook trends, demand for teachers and engineers). Although
the evolution was almost continuous, the following divisions reflect
some of the key periods in the changing curriculum.
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aths for Chemists
Publication Details
The two volumes of Maths for Chemists provide an excellent resource for all undergraduate chemistry students but are particularly focussed on the needs of students who may not have s...
The two volumes of Maths for Chemists provide an excellent resource for all undergraduate chemistry students but are particularly focussed on the needs of students who may not have studied mathematics beyond GCSE level (or equivalent). The texts are introductory in nature and adopt a sympathetic approach for students who need support and understanding in working with the diverse mathematical tools required in a typical chemistry degree course. Maths for Chemists Volume II: Power Series, Complex Numbers and Linear Algebra builds on the foundations laid in Volume I, and goes on to develop more advanced material. The topics covered include: power series, which are used to formulate alternative representations of functions and are important in model building in chemistry; complex numbers and complex functions, which appear in quantum chemistry, spectroscopy and crystallography; matrices and determinants used in the solution of sets of simultaneous linear equations and in the representation of geometrical transformations used to describe molecular symmetry characteristics; and vectors which allow the description of directional properties of molecules.
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This book is an essential resource for anyone who ever encounters binomial coefficient identities, for anyone who is interested in how computers are being used to discover and prove mathematical identities, and for anyone who simply enjoys a well-written book that presents interesting, cutting edge mathematics in an accessible style. Wilf and Zeilberger have been at the forefront of a group of researchers who have found and implemented algorithmic approaches to the study of identities for hypergeometric and basic hypergeometric series. In this book, they detail where to find the packages that implement these algorithms in either Maple or Mathematica, they give examples of and instructions in how to use these packages, and they explain the motivation and theory behind the algorithms. The specific algorithms that are described are Sister Celine's Method, an algorithm from the 1940's that underlies most of the current research; Gosper's Algorithm, the first of the powerful proof techniques to be implemented with a computer algebra package; Zeilberger's Algorithm which extends and generalizes Gosper's approach; the WZ Method which is guaranteed to provide a proof certificate for any correct identity for hypergeometric series and which can be used to determine whether or not a ``closed form'' exists for any given hypergeometric series. The book is also sprinkled with examples, exercises, and elaborations on the ideas that come into play. [D.M.Bressoud (St.Paul)]
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Elementary Numerical Analysis
9780471433378
ISBN:
0471433373
Edition: 3 Pub Date: 2003 Publisher: John Wiley & Sons Inc
Summary: Offering a clear, precise, and accessible presentation, complete with MATLAB programs, this new Third Edition of Elementary Numerical Analysis gives students the support they need to master basic numerical analysis and scientific computing. Now updated and revised, this significant revision features reorganized and rewritten content, as well as some new additional examples and problems. The text introduces core areas... of numerical analysis and scientific computing along with basic themes of numerical analysis such as the approximation of problems by simpler methods, the construction of algorithms, iteration methods, error analysis, stability, asymptotic error formulas, and the effects of machine arithmetic
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Summer School - Mathematics
The following courses are offered within the Mathematics Department. All math courses run from Monday, July 1-Friday, August 2 (5 weeks).
Algebra I -- Credit
Prerequisite: Successful completion of Math 7, Algebra 1 8B, or an introductory Algebra course, and, for Horace Mann students, approval of the Middle Division Department Chair. Non-Horace Mann students entering grade 8 may enroll for this course. Please be aware that Horace Mann students may not use this course for the purpose of acceleration in the summer after their 7th grade year.
The course begins with a thorough review of the material studied in the Math 7 course. Topics such as coordinate graphing and polynomials continue to be investigated on a more abstract level. Factoring, quadratic equations, algebraic fractions, systems of equations, inequalities, irrational numbers, and the quadratic formula are taught. Word problems remain an integral part of the course.
Five of six periods per day.
Mr. Luis Franco will teach this course.
Geometry -- Credit
Prerequisite: Satisfactory completion of Algebra I and, for Horace Mann students, approval of the Upper Division Math Chair. This course covers a full year's work in Geometry and is designed for Horace Mann students who are entering the 10th grade in the next school year and who have had a full course in Algebra I (or who will be new to the school and have passed our placement test for entry into Geometry). Horace Mann students may NOT take this course for the purpose of acceleration in the summer after their 8th grade year.
The course is designed to convey an appreciation of geometry as a deductive system. Starting with undefined terms, postulates, and definitions, the students follow the progressive development of theorems and their proofs to create a mathematical structure with rich aesthetic and practical value. In building this axiomatic structure, they improve their ability to recognize and organize the various relationships among points, lines, triangles, polygons, and circles in the plane. Throughout the summer, students will engage in a series of guided explorations using the dynamic software program, Geometer's Sketchpad.
Algebra II & Trigonometry -- Credit
Prerequisites: Algebra I and Geometry. This course is equivalent to a full-year Algebra II course. This workload is intensive. Horace Mann students may take this course for credit only if they are repeating the course. Students from outside of Horace Mann may take this course for credit provided their schools have granted permission.
Five of six periods per day.
Mr. Chance Nalley will teach this course.
Pre-Calculus -- Credit
Prerequisite: Satisfactory completion of Algebra II and Trigonometry and approval of the department chair for Horace Mann students. Within the Horace Mann community, this course is open ONLY to students who will be seniors in the following academic year.
This course lays the foundation for college-level Advanced Placement Calculus AB. As problem-solving is a central theme of this course, students will develop their ability to solve problems that require them to apply what they have learned in new and seemingly unfamiliar situations.
In terms of content, this course is a combination of theoretical study and practical applications of the elementary functions, including trigonometric, polynomial, exponential, and logarithmic. Other major topic areas include combinatorics, elementary probability, sequences, series, the conic sections, and an introduction to the intuitive concept of a limit.
This course may be used for advancement within the Horace Mann sequence in the following ways: (i) A student who achieves a grade of C+ or higher and has the approval of the department chair will be eligible for Contemporary Calculus (0450) (ii) A student who achieves a grade of B or higher and has the approval of the department chair will be eligible for Advanced Placement Statistics (0462) (iii) A student who achieves a grade of B+ or higher and has the approval of the department chair will be eligible for Advanced Placement Calculus AB (0451)
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Introduction
This is an introductory course in mathematical systems theory. The
subject provides the mathematical foundation of modern control theory,
with application in aeronautics, electrical networks, signal
processing, and many other areas. The aim of the course is that you
should acquire a systematic understanding of linear dynamical systems,
which is the focus of this course. The acquirement of such knowledge
is not only very useful preparation for work on system analysis and
design problems that appear in many engineering fields, but is also
necessary for advanced studies in control and signal processing.
Course goals
The overall goal of the course is to provide an understanding of the
basic ingredients of linear systems theory and how these are used in
analysis and design of control, estimation and filtering systems. In
the course we take the state-space approach, which is well suited for
efficient control and estimation design. After the course you should
be able to
Analyze the state-space model with respect to minimality,
observability, reachability, detectability and stabilizability.
Explain the relationship between input-output
(external) models and state-space (internal) models for linear systems
and derive such models from the basic principles.
Derive a minimal state-space model using the Kalman decomposition.
Use algebraic design methods for state feedback design with pole
assignment, and construct stable state observers by pole assignment
and analyze the properties of the closed loop system obtained when the
observer and the state feedback are combined to an observer based
controller.
Solve the Riccati equations that appear in optimal control and
estimation problems.
Design a Kalman filter for optimal state estimation of linear
systems subject to stochastic disturbances.
Apply the methods given in the course to solve example problems (one
should also be able to use the ``Control System Toolbox'' in Matlab to
solve the linear algebra problems that appear in the examples).
For the highest grades you should be able to integrate the tools you
have learnt during the course and apply them to more complex
problems. In particular you should be able to
Explain how the above results and methods relate and build on each other.
Understand the mathematical (mainly linear algebra) foundations of
the techniques used in linear systems theory and apply those
techniques flexibly to variations of the problems studied in the
course.
Solve fairly simple but realistic control design problems using the
methods in the course.
Course material
The required course material consists of the following lecture and
exercise notes on sale at ``studentexpeditionen'' on Lindstedtsv 25.
Course requirements
The course requirements consist of an obligatory final written
examination. There are also three homework sets we strongly encourage
you to do. All these optional activities will not only give you bonus
credits in the examination, but also help you understand the course
material better.
Homework
Each homework set consists of maximally five problems. The first three are
methodology problems where you practice on the topics of the course
and apply them to examples. The last one or two problems are of more
theoretical
nature and helps you to understand the mathematics behind the
course. It can, for example, be to derive an extension of a result in
the course or to provide an alternative proof of a result in the
course.
Each successfully completed homework set gives you maximally 5 points for
the exam. The exact requirements will be posted on each separate
homework set. The homework sets will be posted roughly ten days before
the deadline on the course homepage.
Homework 1: This homework set covers problems from the first
three chapters in compendium. [Solution] (Due on Wednesday February 6, 17:00).
Written exam
This is an open book exam and you may bring the lecture notes, the
exercise notes, your own classnotes and Beta
Mathematics Handbook (or any equivalent handbook). The exam will
consist of five problems that give maximally 100 points. These
problems will be similar to those in the homework assignments and the
tutorial exercises. The preliminary grade levels are distributed
according to the following rule, where the total score is the sum of
your exam score and maximally fifteen bonus points from the homework
assignments (max credit is 115
points). These grade limits can only be modified to your advantage.
Total credit (points)
Grade
>90
A
76-90
B
61-75
C
50-60
D
45-49
E
41-44
FX
The grade FX means that you are allowed to make an appeal, see below.
The first exam will take place on March 15, 2013 at 08:00-13:00.
The second exam will take place on May 30, 2013 at 14:00-19:00.
Appeal
If your total score (exam score + maximum 15 bonus points from the
homework assignments) is in the range 41-44
points then you are allowed to do a complementary examination for
grade E. In the complementary examination you will be asked to solve
two problems on your own. The solutions should be handed in to the
examiner in written form and you must be able to defend your solutions
in an oral examination. Contact the examiner no later than three weeks
after the final exam if you want to do a complementary exam.
Course evaluation
At the last tutorial exercise you will be asked to complete a course
evaluation form. The evaluation form will also be posted on the course
homepage and it can be handed in anonymously in the mailbox opposite
to the entrance of "studentexpeditionen" on Lindstedtsv 25. We
appreciate your candid feedback on lectures, tutorials, course
materials, homeworks and computer exercises. This helps us to
continuously improve the course.
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Intermediate Algebra, 5th Edition, is designed to provide students with the algebra background needed for further college-level mathematics courses. The unifying theme of this text is the development ...
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Title
Patterns and Relationships
Body
Things are getting pretty exciting in mathematics! In addition to one step and two step equations. We are discovering the meaning of a function. This describes the relationship between to numbers and can be displayed in a chart, graph, and an equation. Please utilize the web links for math to practice these hot topics.
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Upcoming News
» Education
This article discusses about the latest version of openSIS, one of the most popular student information system round the globe. Recently OS4ED launched openSIS ver5.2, the developers of the product demands that this will be better, faster and more secured compared to previous versions.
A System of equations is basically a collection of Linear Equations and includes the same Set of the variables in each and every equation of the system. This system of equations is also known as the Linear System.
A number which is divided by itself and by 1 is called a prime number. Prime number can also be defined as the Odd Numbers which are not divided by any odd number except 1 and itself. Prime numbers are mainly 1, 2, 3, 5, 7, and 11 and so on.
Numbers starting with 1, 2, 3, 4.…… are called Natural Numbers. Natural numbers are denoted by 'N'. These numbers are put into different groups. The group may be of Even Numbers, odd numbers, prime numbers or even composite numbers.
When we deal with algebra, we mainly focus on equations and expression. These two terms can be defined as the heart of the algebra, as whenever we solve any problem we have to solve different equations.
The elements are subdivided into molecules which further divided into atoms. The atoms for long considered to be indivisible but with the discovery of the sub atomic particle, like electrons and protons, it was understood that there were more smallest and fundamental particles then the atom.
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MATH 500: Fundamentals of Mathematics
This course provides students with a thorough foundation in the topics of whole numbers, fractions, decimals, ratios and proportions, percents, geometric figures and measurement. (Offered in lab and lecture formats.) Lecture: 3 hours
Credits:0
Overall Rating:0 Stars
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Thanks, enjoy the course! Come back and let us know how you like it by writing a review.
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Algebra 2 is a mathematics course designed for students who have completed Algebra 1 and includes the study of linear, quadratic, square root, rational, exponential, and logarithmic functions, equations, and inequalities. Real-world problem solving situations will also be covered. This course is for Toltech T-STEM Academy sophomores and is rigorous in its study of algebraic theory and situations; studying outside of class time is an absolute necessity.
vWarm Ups are a daily grade due at the beginning of each class period and cannot be made up. If you miss a warm up due to an absence, an alternative assignment will be given.
vClass work is due before the end of the period on the day it is assigned, no exceptions. You may attend tutoring to complete class work not finished in class. If you miss class work due to an absence, you must attend tutoring to make up the assignment.
vHomework is the due the class period after it is assigned and is graded on completion. If it is not completed, it will be accepted one (Pre-AP) to three (non Pre-AP) class periods after it is assigned. If homework is not turned in within this time frame, it's a zero. The highest grade a late homework assignment can receive is an 80.
ATTENDENCE:
Mathematics can be very challenging; therefore, instructional time is very important. Students who are absent miss vital pieces of information, fall behind completing coursework, and risk credit denial.If a student is absent, it is his/her responsibility to collect missing assignment(s) and notes.These can be obtained from the website, a classmate, or by making an appointment with the teacher.For each day a student has an excused absence, one additional class day will be given to complete missing assignment(s).If a student is absent on the day of a test, the test can be made-up by making an appointment with the teacher. It is the student'sresponsibility to make appointments and turn in all missing assignments and tests completed and in a timely manner.
CLASS ORGANIZATION:
Notebooks/Binders are required for this class.The notebook should be a 1.5 to 3 inch 3-ring binder and should consist of items in the following order: Course Syllabus, Classroom Policies, List of Assignments, and then dividers. We will discuss notebook organization in detail in class. Notebooks will be graded two or three times each nine-weeks.
SCHOLASTIC INTEGRITY:
Scholastic dishonesty shall include, but not be limited to: cheating on tests, copying of homework, and the discussion of tests with other classes before all classes have completed the test.The consequence of scholastic dishonesty will come in the form of a zero (0) for that assignment, test, or project.
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