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Diagnostic Algebra Assessment Definitions
As algebra teachers, we all know how frustrating it can be to teach
a particular concept and to have a percentage of our students not get
it. We try different approaches and activities but to no avail. These
students just do not seem to grasp the concept. Often, we blame the students
for not trying hard enough. Worse yet, others blame us for not teaching
students well enough.
Students often learn the equality symbol misconception when they begin
learning mathematics. Rather than understanding that the equal sign indicates
equivalence between the expressions on the left side and the right side
of an equation, students interpret the equal sign as meaning "do
something" or the sign before the answer. This problem is exacerbated
by many adults solving problems in the following way:
5 × 4 + 3 = ?
5 × 4 = 20 + 3 = 23
Students may also have difficulty understanding statements like 7 = 3
+ 4 or 5 = 5, since these do not involve a problem on the left and an
answer on the right.
Falkner presented the following problem to 6th grade classes:
8 + 4 = [] + 5
All 145 students gave the answer of 12 or 17. It can be assumed that
students got 12 since 8 + 4 = 12. The 17 may be from those who continued
the problem: 12 + 5 = 17.
Students with this misconception may also have difficulty with the idea
that adding or subtracting the same amount from both sides of an equation
maintains equality. Kieran gives this example:
In algebra, students learn that a graph is a representation for a function.
Students learn to translate between graphs, equations, and table of values.
But just as the translation between equations and word problems is more
difficult, students sometimes find interpreting the graph of a real world
situation more difficult. Students may forget the algebraic relationships
they have learned and resort to graphical misconceptions. The most common
graphing misconceptions are treating a graph as a picture and slope-height
confusion.
An example of interpreting a graph as a picture might be a problem asking
a student to draw a speed vs. time graph for a biker riding over a hill.
Students with the misconception would draw the hill, and ignore that
speed is asked for. Students do not look at the graph as showing speed
as a function of time, but think of it more literally.
An example of slope/height confusion might use the following graph:
The question could ask "Which internet company costs more per hour
at 2 hours?" A student with the misconception would choose Call.com
since it costs more at 2 hours. The student does not recognize that the
problem asks for slope.
Transitioning from arithmetic to algebra can be a challenging learning
experience for students. One of the key reasons is the use of letters to
represent variables. Even after taking an algebra course, many students
do not understand the use of letters in equations and therefore can not
grasp the concept of a variable.
Booth (1984) explains that letters can be interpreted
as a specific known number, as multiple values instead of one, as an object,
or simply ignored. An example of a typical mistake that students make when
they do not understand the concept of a variable is when asked to "add
4 onto 3n," an
answer of 3n4 or 7n is given. As another example of a
concept of a variable misconception, when students are asked to write an
equation for the following statement using the variables S and P:
"There are six times as many students as professors at this university,"
(Clement, 1982), they interpret the variable P as meaning professor,
instead of number of professors.
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Elementary Algebra, v. 1.0
by John Redden
Preface
It is essential to lay a solid foundation in mathematics if a student is to be competitive in today's global market. The importance of algebra, in particular, cannot be overstated, as it is the basis of all mathematical modeling used in applications found in all disciplines. Traditionally, the study of algebra is separated into a two parts, elementary algebra and intermediate algebra. This textbook, Elementary Algebra, is the first part, written in a clear and concise manner, making no assumption of prior algebra experience. It carefully guides students from the basics to the more advanced techniques required to be successful in the next course.
This text is, by far, the best elementary algebra textbook offered under a Creative Commons license. It is written in such a way as to maintain maximum flexibility and usability. A modular format was carefully integrated into the design. For example, certain topics, like functions, can be covered or omitted without compromising the overall flow of the text. An introduction of square roots in Chapter 1 is another example that allows for instructors wishing to include the quadratic formula early to do so. Topics such as these are carefully included to enhance the flexibility throughout. This textbook will effectively enable traditional or nontraditional approaches to elementary algebra. This, in addition to robust and diverse exercise sets, provides the base for an excellent individualized textbook instructors can use free of needless edition changes and excessive costs! A few other differences are highlighted below:
Equivalent mathematical notation using standard text found on a keyboard
A variety of applications and word problems included in most exercise sets
Clearly enumerated steps found in context within carefully chosen examples
Video examples available, in context, within the online version of the textbook
Robust and diverse exercise sets with discussion board questions
Key words and key takeaways summarizing each section
This text employs an early-and-often approach to real-world In addition to embedded video examples and other online learning resources, the importance of practice with pencil and paper is stressed. This text respects the traditional approaches to algebra pedagogy while enhancing it with the technology available today. In
Flat World Knowledge is the only publisher today willing to put in the resources that it takes to produce a quality, peer-reviewed textbook and allow it to be published under a Creative Commons license. They have the system that implements the customizable, affordable, and open textbook of the twenty-first century. In fact, this textbook was specifically designed and written to fully maximize the potential of the Flat World Knowledge system. I feel that my partnership with Flat World Knowledge has produced a truly fine example in Elementary Algebra, which demonstrates what is possible in the future of publishing.
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Linear algebra is a fundamental area of mathematics, and is arguably the most powerful mathematical tool ever developed. It is a core topic of study within fields as diverse as: business, economics, engineering, physics, computer science, ecology, sociology, demography and genetics. For an example of linear algebra at work, one needs to look no further... more...
The CliffsStudySolver workbooks combine 20 percent review material with 80 percent practice problems (and the answers!) to help make your lessons stick. CliffsStudySolver Algebra I is for students who want to reinforce their knowledge with a learn-by-doing approach. Inside, you'll get the practice you need to tackle numbers and operations withExtend your programming skills with a comprehensive study of the key features of SQL Server 2008. Delve into the new core capabilities, get practical guidance from expert developers, and put their code samples to work. This is a must-read for Microsoft .NET and SQL Server developers who work with data access?at the database, business logic, or presentation... more...
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Synopses & Reviews
Publisher Comments:
INTERMEDIATE ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS shows students how to apply traditional mathematical skills in real-world contexts. The emphasis on skill building and applications engages students as they master concepts, problem solving, and communication skills. It modifies the rule of four, integrating algebraic techniques, graphing, the use of data in tables, and writing sentences to communicate solutions to application problems. The authors have developed several key ideas to make concepts real and vivid for students. First, the authors integrate applications, drawing on real-world data to show students why they need to know and how to apply math. The applications help students develop the skills needed to explain the meaning of answers in the context of the application. Second, they emphasize strong algebra skills. These skills support the applications and enhance student comprehension. Third, the authors use an eyeball best-fit approach to modeling. Doing models by hand helps students focus on the characteristics of each function type. Fourth, the text underscores the importance of graphs and graphing. Students learn graphing by hand, while the graphing calculator is used to display real-life data problems. In short, INTERMEDIATE ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS takes an application-driven approach to algebra, using appropriate calculator technology as students master algebraic concepts and skills.
About the Author
Mark Clark graduated from California State University Long Beach with a Bachelor's and Master's in Mathematics in 1995. He is a full-time Associate Professor at Palomar College and has taught there for the past 9 years. He is a member of AMATYC and regularly attends the national AMATYC and ICTCM conferences. He has also done extensive reviewing and testing of various classroom technologies and materials. Through this work, he is committed to teaching his students through applications and using technology to help his students both understand the mathematics in context and communicate their results clearly. Intermediate algebra is one of his favorite courses to teach, and he continues to teach several sections of this course each year.
Table of Contents
"The quality of the worked examples is first rate. I was pleased to seehow that the writers show what a graph done by hand should look like…. Above all, many of the applications were used as motivating factorsto develop the math, such as the slope."Robert Diaz, Instructor, Fullerton College "The main strength of the book is the great balance of concepts, skills,and applications …."Lenora G. Sheppard, Instructor, Atlantic Cape Community College "The main strengths of this textbook lie with the authors' concept for a strong integration of applied math into the core of the material presentation in each section of the book. The margin notes are highly applicable and well placed, and the story problems and Concept Investigations encourage students to go beyond the operations to really understanding the functions and applications of those functions." Katherine Adams, Instructor, Eastern Michigan University "The Concept Investigations should captivate the students' attention. Most students at this level often ask, 'When will I ever use this?' The Concept Investigations would be effective in addressing this."Mary Legner, Instructor, Riverside City College
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Precalculus : A Problems-Orientedcalculus: A Problems-Oriented Approach offers a fairly rigorous lead-in to calculus using the right triangle approach to trigonometry. A graphical perspective gives students a visual understanding of concepts. The text may be used with any graphing utility, or with none at all, with equal ease. Modeling provides students with real-world connections to the problems. The author is know for his clear writing style and numerous quality exercises and applications.
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Linear Equations
Unit 2
Common Core Math says...
This unit is much more comfortable for me as the teacher. The focus feels clearer and the goals are more familiar. As is states in the Common Core State Standards in the Algebra introduction:
An equation can often be solved by successively deducing from it one or more
simpler equations. For example, one can add the same constant to both sides
without changing the solutions, but squaring both sides might lead to extraneous
solutions. Strategic competence in solving includes looking ahead for productive
manipulations and anticipating the nature and number of solutions.
Keep in mind that just because it is a linear equation chapter, you do not want the students to lose the information you have given them in unit 1. It is a wonderful thing to force students to think outside the units to solve problems.
Standards for Mathematical Practice
4. Model with mathematics
8. Look for and express
regularity in repeated
reasoning
Big Picture Lesson Planning for the Common Core
Big Picture Lesson Planning forces us as teachers to answer the question, "What do I want my students to be able to do in life with the skills they obtain from my class?" Or, "Why am I teaching this?"
The student will understand patterns in business, economics, environment and behaviors to predict future outcomes to make knowledgeable decisions for success. This includes researching and formulating the patterns and understanding the target audience and how that affects the results.
This goal is the same as Unit 1, but will be much more specific to linear equations.
Can the student find a finish date for a project?
Is the student able to take a situation and create a business proposal complete with reasoning and graphs showing future profit?
Can the student decide how much to charge for a job done, such as painting a home?
Lesson Ideas
*Note that this chapter only deals with the linear part of each standard. The exponentials are dealt with in later units.
A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.*
F.IF.1
F.IF.2 Understand the concept of a function and use function notation. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
F.IF.4.* (Emphasize quadratic, linear, and exponential functions and comparisons among them)
F.IF.5 Interpret functions that arise in applications in terms of the context.*
F.IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.?
F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.
F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, give a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
F.BF.1a Write a function that describes a relationship between two quantities. (Emphasize linear, quadratic, and exponential functions). Determine an explicit expression, a recursive process, or steps for calculation from a context. Video explanation
F.BF.3 Video explanation
F.BF.4a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) = 2 x3 or f(x) = (x + 1)/(x - 1) for x ? 1.
F.LE.1a Prove that linear functions grow by equal differences over equal intervals; and that exponential functions grow by equal factors over equal intervals.
F.LE.1b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-?-output pairs (include reading these from a table).
F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context.
S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
Please sign up for the newsletter to receive assessments. It is my small attempt to keep them out of the hands of the kids :)
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Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for).
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Distance Learning Class Critical Information
MAT-160-H1/H3 College Algebra
FAll 2013 Hybrid Course
Dear Student:
Welcome to College Algebra! This hybrid course is a blend of face-to-face instruction and online learning. Each week we will meet for class during our regularly scheduled time. This represents 50% of the normal class time of traditional College Algebra courses. Because our class time is reduced, a significant portion of the learning takes place online. In fact, be prepared to spend at least 10 hours a week outside the classroom reading, watching videos and pencasts, completing homework and quizzes, and preparing for exams. Prepare now to create the necessary time in your schedule before next semester arrives.
We will use MyMathLab to complete the online component of our course. MyMathLab is an Internet based course management system that may be used to read the online textbook, watch videos, view your grades, participate in discussion, and complete your homework and quizzes. You will need Internet access (high-speed preferred) and the most recent version of Adobe Flash Player in order to complete the online requirements of this course.
We will also use the TI-83/84 Plus Graphing Calculator during class and on certain portions of your exams. I find that I can help all students best if we are all using the same calculator technology. You may obtain a calculator for free for the entire semester by checking one out at the library circulation desk. If desired, you may purchase your own.
The prerequisite for this course is a grade of C or better in MAT 121 Intermediate Algebra or assessment into MAT 160. Topics of this course include linear and quadratic equations and inequalities, complex numbers and solutions of higher degree polynomial equations, systems of linear equations, matrices, graphing functions including exponential, logarithmic, polynomial, and rational functions, conic sections, sequences and series. Students may not receive credit for both MAT 160 and MAT 171.
Textbook Information: College Algebra, 11e by Lial, Hornsby, Schneider, Daniels. The textbook is available online with the purchase of a MyMathLab code. You may purchase your code in the SCC Bookstore or online through The hardbound textbook is optional.
Welcome to College Algebra! I am looking forward to helping you reach your mathematical goals.
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More About
This Textbook
Overview
This book presents an introduction to modern (abstract) algebra covering the basic ideas of groups, rings, and fields. The first part of the book treats ideas that are important but neither abstract nor complicated, and provides practice in handling mathematical statements - their meaning, quantification, negation, and proof. This edition features a new section to give more substance to the introduction to Galois theory, updated lists of references and discussions of topics such as Fermat's Last Theorem and the finite simple June 12, 2003
My group theory book of choice!
This is one of the best math books I have ever used. It is very clear and the homework problems are great. The homework problems are illustrative and provide for an excellent understanding of the material. The only thing holding this back from 5 stars for me is that some of the chapters could use a few more examples. Paired with class notes or the internet for reference, you'd be fine. If the prof teaches exactly what's in the book, you don't have to worry about missing some classes! ;-) The book explains everything clearly enough without need for a professor!
Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged.
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Re: Best books for mathematics section of SSC CGL examination?
Hello Dear,To prepare for the Numerical Aptitude Refer to best books available in market for the SSC preparations like:R.S.Agarwal [Arithmetic book ]DR.Lal & Jain [Upkar books ]Quicker Maths by M.TyraRegardsHi,
Friend, i personally recommend you to go with Magical book on Mathematics by M.Tyra or you can either consult any book on vedic mathematics.
It really help you a lot to qualify the mathematics section........
Re: Best books for mathematics section of SSC CGL examination?
hello,
i would refer you R.S. Agarwall for preparing quantitative aptitude , but before referring any book i will suggest you to go through your NCERT books of 10th class to strengthen your concepts then you should take R.S.Agarwall.
Re: Best books for mathematics section of SSC CGL examination?
Friend, SSC conducts CGLE every year to fill up various posts in various ministries and departments of Central Government.
The required qualification for the exam is Graduation in any discipline. The age limit for general category is 18 - 27 only. The reserved category avail the age relaxation.
The question paper of written exam carry 200 marks in total. The question paper is divided into 4 parts namely Reasoning & General Intelligence, General Awareness, General English and Mathematics. All the 4 parts carries the 50 marks each.
I am going to suggest the names of some helpful book for this exam mentioned below Reasoning & General Intelligence : Any book from Upkaar Publication
5. For Current Affairs : Magazine Competition Success Review and Pratiyogita Darpan
Re: Best books for mathematics section of SSC CGL examination?
Dear aspirantMathmatics has a key role in any ssc exame.So you should take most concentration on every parts of mathFor exellent work in math. you should buy r.s.agarwal book or quicker maths by M.tyra.These books are very helpful for math
Re: Best books for mathematics section of SSC CGL examination?
i think all the basic thing are same in all books.
you can follow any kinds of books.
all are good if you can utilize it properly.
you more devoted time give you success.
for your request i give the name----------------
Re: Best books for mathematics section of SSC CGL examination?
Dear Aspirant, Attachment 9152
For the section of Mathematics, Books of R S Agarwal (S. Chand Publication) is best for study. This book is helpful in preparation of all type of Competitive Exams. This Book is one of the Best Book in the Market.
If you want to take those books which has Basic Fundamental of mathematics then You can also take these books from market:
Lucent's Airthematic
Arihant Publication's Mathematics for SSC
Re: Best books for mathematics section of SSC CGL examination?
Dear friend,
there are lots of math books in the market
Now a days . Math is a subject ,the much you precticing
The more you get.
These are some good books which improve your skill.
Quike math ( M.Tyara).
This book is very ifective for objective type math
there are lots of quick mathrod in this book . It save your
Time .
Quantitive aptitude ( R.S.Agarwal).
Arihant.
Just revise more and more you will learn the mathod
You will solve yge question quickly..
Best of luck....
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"With exceptional clarity, but with no evasion of essential ideas, the author outlines the fundamental structure of mathematics."--Carl B. Boyer, Brooklyn College. This enlightening survey of mathematical concept formation holds a natural appeal to philosophically minded readers, and no formal training in mathematics is necessary to appreciate its clear exposition. Contents include examinations of arithmetic and geometry; the rigorous construction of the theory of integers; the rational numbers and their foundation in arithmetic; and the rigorous construction of elementary arithmetic. Advanced topics encompass the principle of complete induction; the limit and point of accumulation; operating with sequences and differential quotient; remarkable curves; real numbers and ultrareal numbers; and complex and hypercomplex numbers. 1959 ed. 27 Figures. Index.
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Computerbasedmath.org -- the radical mathematics education reform organisation -- wants the students of Estonia to use computers to explore mathematical concepts instead of having them spend time solving quadratic equations or factoring polynomialshas
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This utility uses the free Flash player plug-in resident in most browsers to allow the user to plot a parametrically defined surface on a customized scale and dynamically rotate the three-dimensional picture.
This applet performs traditional elementary row operations keeping track of the entire process. It also allows fraction, integer, or decimal entries and preserves these types throughout the row reduction process.
This article explores the symmetry method in elementary differential equations, which uses the invariance of the equation under certain transformations to create a coordinate system in which the equation greatly simplifies.
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Elementary and Inter. Algebra : Graphs and Models - 4th edition
Summary: TheBittinger Graphs and Models Serieshelps readers learn algebra by making connections between mathematical concepts and their real-world applications. Abundant applications, many of which use real data, offer students a context for learning the math. The authors use a variety of tools and techniques-including graphing calculators, multiple approaches to problem solving, and interactive features-to engage and motivate all types of6066.09 +$3.99 s/h
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tenth edition of this bestselling text includes examples in more detail and more applied exercises; both changes are aimed at making the material more relevant and accessible to readers. Kreyszig introduces engineers and computer scientists to advanced math topics as they relate to practical problems. It goes into the following topics at great depth differential equations, partial differential equations, Fourier analysis, vector analysis, complex analysis, and linear algebra/differential equations.
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Singapore Math's Primary Math, U.S. Edition series features the Concrete> Pictorial> Abstract approach. Students begin by learning through concrete and pictorial means before moving into abstract thought and development, which encourages an active thinking process, communication of mathematical ideas and problem solving. Lessons are designed for a mix of teacher instruction and independent work, and students are encouraged to discuss ideas and explore additional problem-solving methods.
This set of textbooks and workbooks is designed specifically for U.S. students. Names, terms in examples, measurement, spellings, currency and other such elements have been changed to reflect American names and stylistic preferences. Review included. 104 pgs, non-consumable and non-reproducible. Paperback.
Higher grade levels lack Instruction
Date:May 2, 2013
Jina
Quality:
3out of5
Value:
4out of5
Meets Expectations:
2out of5
I grew up in Japan and Korea as a kid and love their education systems. As a homeschool parent, I am always looking for affordable curriculum. We are in middle school math now and have had to switch from Singapore Math not because of aging out, but because the books lack the instructions for how to do the harder math it assigns. We use the Textbooks, Workbooks, and Tests books as supplements now, and are using Lifepac math now, but we are still looking for any other math curriculum, our goal for University is Engineering so we want to be prepared.
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Review 2 for Singapore Math: Primary Math Textbook 3A US Edition
Overall Rating:
5out of5
Wonderful Product for Math-Oriented Student
Date:March 16, 2011
melissa745
Quality:
5out of5
Value:
5out of5
Meets Expectations:
5out of5
We have used several other math programs before coming to Singapore. This program is just what my daughter needs. It's fast-moving, with little review. It has challenging word problems that keep her thinking about number and how to manipulate them to get the answer.
She found most of the other programs dreadfully boring, but is excited every day when we pull out her math book.
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Review 3 for Singapore Math: Primary Math Textbook 3A US Edition
Overall Rating:
5out of5
Date:June 25, 2010
D. D.
Excellent resource. We would give all the Singapore Math books 5 stars! The books are visually clear and easy to understand. I recommend taking the placement test to make accurate book selection. We did and ended up starting in a lower book that I thought we would, but quickly gained speed. Now our child is faster than a calculator and loves math!
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Review 4 for Singapore Math: Primary Math Textbook 3A US Edition
Overall Rating:
5out of5
Date:November 10, 2009
Michelle Wheeler
I've been homeschooling my son for three years (this is our fourth) and for the first time, my son loves doing his math work! Singapore gets 5 stars from me, and my son!
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Review 5 for Singapore Math: Primary Math Textbook 3A US Edition
Overall Rating:
4out of5
Date:February 8, 2008
Donna L. Hogue
My daughter, who struggles learning her math concepts, loves this book. The lessons are short and very easy. I am so grateful to have found this book. She will be testing next month so this has come at just the right time.
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1, algebra 2 and prealgebra, algebra 2 and calculus 1, algebra 2 and SAT math geometry, prealgebra and precalculus
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Program Navigation
Lial, et al., College Algebra, 11th Edition
Lial, et al., College Algebra, 11th Edition
College Algebra, Eleventh Edition, by Lial, Hornsby, Schneider, and Daniels, engages and supports students in the learning process by developing both the conceptual understanding and the analytical skills necessary for success in mathematics. With the Eleventh Edition, the authors recognize that students are learning in new ways, and that the classroom is evolving. The Lial team is now offering a new suite of resources to support today's instructors and students.
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Quantitative Literacy: A New Way of Teaching Math and Reasoning Skills
by Professor of Natural Sciences Ben Steele
A common complaint among college faculty members is that too often, students seem unprepared to do simple quantitative manipulations to solve problems they face in their courses. This is especially prevalent in non-math courses where unit conversions, proportions and percentages sometimes stall a student's progress. This complaint is driving a growing movement in higher education for "quantitative literacy" (QL) to replace or supplement math classes.
Quantitative literacy is not the current euphemism for math, but rather a different concept that makes compelling sense. Simply put, rather than help students solve mathematic problems like those at the end of each textbook chapter, QL seeks to ensure that students are able to use their math skills to analyze and solve problems and understand information and issues they encounter in their daily lives.
While QL will not necessarily help students solve (X + 3)(X + 2)= 0, it will help them convert the speed limit in Canada (kilometers per hour) to the miles per hour on their speedometer or evaluate a newspaper story on the escalating national deficit. In short, QL is a habit of mind more than the technical ability to solve mathematical problems.
But how do you teach a habit of mind? A typical college curriculum approaches the issue of quantitative literacy by requiring all students to take a math course, as Colby-Sawyer College has done in the recent past. These courses typically follow a progression in difficulty from college algebra to pre-calculus to calculus. But the value of a pre-calculus course seems questionable for the majority of students who will take just one math course in college.
While Colby-Sawyer will still offer this progression of math courses, college algebra, statistics and liberal arts math will be honed into quantitative literacy courses, and two new courses will be added to our liberal arts curriculum. In all of these courses, students will find opportunities to use the math they learned in high school in various practical contexts. The courses will emphasize the development of problem-solving strategies and allow students to review and practice their math skills.
We know that college students tend to compartmentalize their areas of knowledge, just as knowledge is somewhat compartmentalized within their courses. By teaching QL skills across the curriculum, we will integrate elements of math and reasoning into many classes, from art to biology and psychology. Students may be asked in an art class to use their math skills to calculate the size of a frame for their painting, or in psychology, to calculate the statistical likelihood of certain mental illnesses within a given population. At Colby-Sawyer and other colleges, we will ensure that students encounter problems with QL components in a variety of courses and contexts.
To meet this challenge, Colby-Sawyer hosted a four-day workshop for faculty last summer to develop quantitative components for their classes. This workshop, supported by a grant from the National Science Foundation, attracted 23 faculty representing all seven academic departments and several student service areas. Participants heard from experts in the field, searched for materials already developed by others and adapted them to their courses, and developed new materials of their own.
Ewa Chrusciel, a poet and assistant Humanities professor, created a project that will ask students to identify fractals in the patterns of word repetition in poetry. Professor Joe Carroll's module analyzes four ways of calculating divorce rates for a sociology class. Students in Robin Burroughs-Davis's first-year seminar will calculate the difference between average and median incomes in the context of promoting different political positions.
With this diverse deployment of QL components in a variety of classes, how can we be sure that all students will encounter these concepts and skills? Could they dodge classes with QL content? Perhaps, but our approach will be to evaluate quantitative skills in a sample of students to be sure they have acquired the skills they will need in our data-driven society.
Many of our students will take an assessment test in quantitative literacy in their first-year Pathway seminar and a similar test during their senior Capstone course. In between we also plan to survey students to measure their attitudes toward, and facility with, quantitative concepts. The test results and survey data will help us to evaluate the effectiveness of our across-the-curriculum approach to teaching quantitative literacy.
The reaction from students? As you might expect, we've heard comments such as "Is this going to be a math class?" and "These look like word problems. I hate word problems." But as our students start to encounter math in several areas of the curriculum, we hope they will come to view it as a useful tool for understanding the world.
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A Workshop on Mathematical Markup Language (MathML)
The tutorial provides a practical introduction to the W3C Mathematical
Markup Language (MathML) 2.0 recommendation. The objective is to provide an
understanding of the role and utility of the standard, to successfully
write W3C MathML documents, and to efficiently navigate the available
documentation and resources. An overview of applications for rendering,
computing, and authoring MathML will be provided.
Participants will use one or more editors to mark-up example math
expressions using MathML content and MathML presentation elements. They
will use the IBM techexplorer hypermedia browser to view the results. The
examples will cover the major components of MathML markup. Participants
will learn which elements to use for what purpose, and how to properly nest
elements to achieve desired results
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In Math C152 students are expected to consistently differentiate and
integrate rational functions and trigonometric functions; apply the
derivative in solving related rates problems; apply the derivative in
solving maximum/minimum problems; apply the integral in solving area
under the curve problems; apply the integral in solving for the volume
of a body of revolution; apply the integral in finding the center of
mass in one and two dimensions; apply the derivative or integral in
solving distance, velocity, and acceleration problems; and solve first
order differential equations with initial conditions. Students
successfully demonstrating these Math C151 skills will be prepared for
Math C152.
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8th Grade Math
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Document Description
ntroduction to English for 8th Grade In this segment of English lesson for 8th grade Math students you will
learn about interrogative sentences and its usage Lesson for 8th Grade - Interrogative ..
Math
Having difficulty working out Math problems? Stuck with your homework and having nightmares before your
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Mathematical Induction
The mathematical induction is one of the numerical proof naturally it is used to find the given statement is
accurate for all normal numbers. It can be a deducted by proving that the 1 st statement may be the countless
succession of the statement is accurate and we have to prove that ..
Mathematical Logic
In this page we are going to discuss about mathematical logic concept .Logic means reasoning. Reasoning
may be legal opinion or mathematical confirmations. We apply certain logics in mathematics. Basic
Mathematical logics are Negation, Conjun..
Business Mathematics
Business mathematics as the term states is related to business which involves mainly profit, loss and interest.
This page is designed to provide you the best help with these basic topics. Below are the important business
math topics that are explained in this page with example:..
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Right Triangle :- A right triangle (American English) or right-angled triangle
(British English) is a triangle in which one angle is a right angle (that is, a 90-
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Curve Fitting :- Curve fitting is the process of constructing a curve, or
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compares the two computer algebra programs, Maple and Mathematica used by students, mathematicians, scientists, and engineers. Structured by presenting both systems in parallel, Mathematica's users can learn Maple quickly by finding the Maple equivalent to Mathematica functions, and vice versa. This student reference handbook consists of core material for incorporating Maple and Mathematica as a working tool into different undergraduate mathematical courses (algebra, geometry, calculus, complex functions, special functions, integral transforms, mathematical equations).Part I describes the foundations of Maple and Mathematica (with equivalent problems and solutions). Part II describes Mathematics with Maple and Mathematica by using equivalent problems.
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books.google.co.jp topics in number theory, algebra, and probability
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Grothendieck's theory of Dessins d'Enfants involves combinatorially determined affine, reflective and conformal structures on compact surfaces. This work presents a general method for uniformizing these dessin surfaces and for approximating their associated Belyi meromorphic functions.
The marriage of analytic power to geometric intuition drives many of today's mathematical advances, yet books that build the connection from an elementary level remain scarce. This engaging introduction to geometric measure theory bridges analysis and geometry, taking readers from basic theory toQuasicrystals and Geometry brings together for the first time the many strands of contemporary research in quasicrystal geometry and weaves them into a coherent whole. The author describes the historical and scientific context of this work, and carefully explains what has been proved and what is …
The differential geometry of curves and surfaces in Euclidean space has fascinated mathematicians since the time of Newton. Here the authors cast the theory into a new light, that of singularity theory. This second edition has been thoroughly revised throughout and includes a multitude of new …
The geometry of power exponents includes the Newton polyhedron, normal cones of its faces, power and logarithmic transformations. On the basis of the geometry universal algorithms for simplifications of systems of nonlinear equations (algebraic, ordinary differential and partial differential) were …
Euclidean plane geometry is one of the oldest and most beautiful topics in mathematics. Instead of carefully building geometries from axiom sets, this book uses a wealth of methods to solve problems in Euclidean geometry. Many of these methods arose where existing techniques proved inadequate. In …
Transformation Geometry: An Introduction to Symmetry offers a modern approach to Euclidean Geometry. This study of the automorphism groups of the plane and space gives the classical concrete examples that serve as a meaningful preparation for the standard undergraduate course in abstract algebra. …
Models of the regular and semiregular polyhedral solids have fascinated people for centuries. The Greeks knew the simplest of them. Since then the range of figures has grown; 75 are known today and are called, more generally, 'uniform' polyhedra. The author describes simply and carefully how to …
Boiling-down essentials of the top-selling, "Schaum's Outline" series is for the student with limited time. What could be better than the bestselling "Schaum's Outline" series? For students looking for a quick nuts-and-bolts overview, it would have to be "Schaum's Easy Outline" series. Every book inVictor Klee and Stan Wagon discuss some of the unsolved problems in number theory and geometry, many of which can be understood by readers with a very modest mathematical background. The presentation is organized around 24 central problems, many of which are accompanied by other, related problems. …
Based on undergraduate teaching to students in computer science, economics and mathematics at Aarhus University, this is an elementary introduction to convex sets and convex functions with emphasis on concrete computations and examples. Starting from linear inequalities and Fourier - Motzkin …
This book shows that some unexplained cosmological and electrodynamic phenomena may be treated and understood in the geometrically based framework of Weyl and Dirac. After a short introductory chapter, Chapters 2 and 3 consider the Weyl-Dirac space-time as a geometric basis appropriate for building …
Develops, discusses and compares a range of commutative and non-commutative invariants defined for projection method tilings and point patterns. The projection method refers to patterns, particularly the quasiperiodic patterns, constructed by the projection of a strip of a high dimensional integer …
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Math Secondary School Curriculum
Starting this year, the Math department is using the International Baccalaureate textbooks for the Middle Years Programme (MYP), grades 7 through 11, and the Diploma Programme (DP), grades 11 and 12. The IB Math curriculum incorporates a multiplicity of cultural and historical perspectives on mathematics.
Math 8: IB-MYP Level 3: This is the third book in our new Middle Years series for international schools which is a continuation of the algebraic, geometric, statistics and probability topics.
Math 9: IB- MYP Level 4: IB- MYP Level 4: This is the fourth book in our new Middle Years series for international schools which is a continuation of the algebraic, geometric, statistics and probability topics.
Math 10: IB- MYP Level 5: This course prepares students for an 'Applications' type of Mathematics course. It is an integrated curriculum that covers various topics in algebra, geometry, trigonometry, Probability and statistics. After 10th grade, the students are offered two tracks: IB Mathematics Studies, or IB Mathematics SL.
Math 11:IB Mathematics Studies SL 1 & 2: Is a two year course that the students take in 11th and 12th grade. This course caters to students with varied backgrounds and abilities. It is designed for students who do not anticipate a need for mathematics in their future studies. The course teaches various topics such as probability, statistics, algebra, trigonometry and financial mathematics.
Math 12:IB Mathematics SL 1 & 2: Is a two year course that is offered for students with sound mathematical background and prepares them for future studies such as chemistry, economics, and business administration. This course focuses on advance algebraic concepts like functions and equations, matrices, vectors, circular functions and trigonometry, statistics and probability, and calculus and its applications.
Science Secondary School Curriculum
Science 7: Life Science: An overview of biology. Topics covered include life characteristics, the cell, classification of living things, and genetics.
Science 10: Chemistry: An introduction to the study of the properties and changes in matter. Topics include classification of matter, chemical shorthand, structure of atoms and compounds, the mole, chemical reactions, solids, liquids, and gases. A special section on nuclear chemistry is included.
IB Biology SL 1 & 2: Is a two year course that the students take in 11th and 12th grade. It covers the relationship of structure and function at all levels of complexity. Students learn about topics such as cell theory, the chemistry of living things, and genetics. Students become aware of scientific studies and applications in the world around us.
IB Biology HL 1 & 2: Is a two year course that the students take in 11th and 12th grade. It offers an extensive study of topics in biology and it is equivalent to a college course of general biology. It covers all the higher objectives identified for the HL biology curriculum. It consists of topics such as cells, genetics, ecology and evolution, and human health and physiology. Throughout this challenging course, students become aware of how scientists work and communicate with each other. Students enjoy multiple opportunities for scientific study and creative inquiry within global context.
IB Chemistry SL:: Is a one year course offered as an elective for students in 11th or 12th grade. This course builds on students knowledge of chemistry in 10th grade and offers them opportunities to appreciate chemistry and its applications. It covers topics of general chemistry such as acids and bases, chemical equilibrium, oxidation reduction, bonding, and organic chemistry.
English Secondary School Curriculum
English 7 Literary Genres and Composition (MYP English A Level 2): The study of various literary genres and themes develops analysis and composition skills. Vocabulary, spelling, and grammar are integrated into the literary themes discussed. Oral presentation and collaboration figure prominently in learning activities and project assignments. Students are introduced to the research process. The focus genre is non-fiction.
English 8 Elements of Literature and Composition I (MYP English A Level 3): Literary elements are studied through theme-based units. The study of writing conventions continues to develop composition skills. Vocabulary, spelling, and grammar continue to be integrated into class work, homework, activities, and discussions. Skills in oral presentation and collaboration are further developed. Students begin to apply knowledge of the research process to create a final product. The focus genre is drama.
English 9- Elements of Literature and Composition II (MYP English A Level 4): Good literature enriches the learning community through inquiry and reflection. The writer communicates a message to the reader, and the reader makes meaningful connections across disciplines. Throughout the genres, there is analysis of literary work, and students come to appreciate the writer's craft and the creative uses of elements and structures. Employing various reading skills and strategies, the reader grasps thematic understandings and responds both orally and in writing. With communication established, the reader becomes the writer; genre choices are made, and a portfolio of creative writing is built. The focus genre is the novel.
English 10- Elements of Literature and Composition III (MYP English A Level 5): Students refine their skills in annotation of texts, oral presentation, and essay writing as they prepare to enter the Diploma Programme. The focus genre is poetry.
IB English 11:This course comprises the first year (Parts 1 and 4) of the two-year International Baccalaureate Diploma Programme English A1 course. During the first semester, students study world literature texts (texts in translation), and examine a variety of features common to literary prose and the effects they have on readers' construction of meaning. Second- semester texts center on the theme of Race and Identity, and include the study of different genres. For second semester, students choose to take either the higher level (HL) or the standard level (SL) course.
IB English 12:This course comprises the second year (Parts 2 and 3) of the two-year International Baccalaureate Diploma Programme English A1 course. During the first semester, students study one (SL) or two (HL) Shakespeare plays, along with texts of other genres, and intensify their study of literary features to prepare for rigorous oral assessments (the Individual Oral Commentary). Second- semester texts center on the genre of the novel. Students take two final written IB examinations in May of their senior year.
Drama 7: This course introduces students to the elements of acting and theatrical production. Students explore the purpose of theater, and learn how to work collaboratively in writing, acting in, and designing skits that have a clear message. Students learn to use correct stage vocabulary and to respond appropriately to theatrical work.
Theater Arts: Students explore theatrical production more in depth by staging a full-length work. Focus is on character analysis and development, correct use of stage vocabulary, and design elements of a production. Students also explore play-writing techniques, with each student writing an original ten-minute play.
Social Studies Secondary School Curriculum
In grades 7 through 11, Social Studies is offered in both English and Arabic.
Social Studies 7: Civics and World Geography:Civics studies the U. S. Constitution and the duties, rights, and privileges of citizens. World Geography studies the world's physical characteristics and the impact of human activity on the environment.
Arabic Social Studies 7: Geography and History:Geography studies the world's physical characteristics; History studies Islamic history from the beginning of Islam until year 40 of the Islamic calendar.
Social Studies 8: Ancient World History: A chronological survey of the development of civilization from the appearance of man to the Renaissance.
Arabic Social Studies 8: Geography studies the physical and human geography of countries with Islamic populations around the world; History studies the Omayaad Empire and the Abassid Empire.
Social Studies 9: Modern World History:A chronological survey of the development of civilization from the time of the Renaissance to the present.
Arabic Social Studies 9Geography studies the physical and human geography of Saudi Arabia and the continents of the world as well as demographic issues such as population increase and migration; History studies the history of Saudi Arabia and its kings.
Social Studies 10: Global Studies: An in-depth geography course emphasizing development and encompassing demographics, population growth, resources, economics, political activity, and cultural and religious systems.
Arabic Social Studies 10/11 Geography and History: Global Studies: Geography studies the geography of the Arabic World, as well as the world superpowers, and Islamic and World Organizations; History studies the lives of the Major Prophets and the life of the Prophet Mohammed.
Social Studies: Grades 11 & 12
IB 20th Century World History—Hl & SL: This course is an in-depth study of specific topics in World History: Communism in Crisis 1976-89 (addresses the major challenges—social, political and economic—facing the regimes in the leading Communist states from 1976 to 1989, and the nature of the response of these regimes); the Origins and Development of authoritarian and single-party states (studies the origins, ideology, form of government organization, and the nature and impact of various 20th century authoritarian and single party states); and The Cold War (addresses the East-West relations from 1945 and aims to promote an international perspective and understanding of the origins, course, and effects of the Cold War).
IB History of Europe and The Islamic World-SL: This prescribed subject covers the Arabian peninsula from the pre-Islamic period to the end of the "Rightly Guided Caliphs". It focuses on the economic, social, political and religious environments into which Muhammad was born, and then examines central issues such as the challenges Muhammad faced in establishing the early Islamic state, questions of succession, the imposition of Islamic rule within the peninsula, and the Arab armies' conquests of Byzantine and Sassanian provinces beyond it.
IB Psychology: HL & SL This course consists of the systematic study of behavior and the mental processes and examines the interaction of biological, cognitive, and socio-influences on human behavior by using an integrative approach. No prior study of psychology is expected and the skills needed for this course are developed within the course itself. Since IB Psychology is a part of the Group 3 subjects, students are given the opportunity to explore the interactions between humans and their environment in time, space, and place.
Art Secondary School Curriculum
Art 7:Introduction to Visual Arts: Students are exposed to a variety of media and are given lessons in drawing, color, painting tempera, watercolors, sculpture, architecture, three dimensional design, crafts, appreciation and aesthetics. This is a ten-week program.
Art 8:Visual Arts: The eighth grade art program progresses from the seventh grade program. The content objectives are similar, but the skills are more refined and the projects are more challenging.
Art Elective:Studio Art: This course offers advanced study in drawing and painting. The class begins by developing a foundation of exploratory experiences in drawing and in painting. This introduces the student to a wide range of experiences before he selects a particular medium for concentrated effort.
Art Elective:Ceramics: This course introduces the basics of working with clay. It includes hand-building using pinch, slab, coil, and drape technique. The students learn methods for hand-building clay objects, glazing and firing them.
Art Elective:Graphics Arts: This course is designed for students who desire to take advanced work in the area of printmaking. Graphic design is primarily concerned with designing and printing the yearbook.
IB Visual Art SL/HL: The Visual Arts Course Higher Level and Standard Level at the Islamic Saudi Academy is designed to meet the needs of a multicultural student body whose ethnicity is a unique association of students from America, Middle Eastern, African and European countries. The aims of the visual arts course at HL and SL are to enable students to investigate past, present and emerging forms of visual arts and engage in producing, appreciating and evaluating these. Students will develop an understanding of visual arts from a local, national and international perspective. Through this practice and investigation they will build confidence in responding visually and creatively to personal and cultural experiences. Students of the Visual Arts Course HL and SL will develop skills in, and sensitivity to, the creation of works that reflect active and individual involvement. Students will take responsibility for the direction of their learning through the acquisition of effective working practices.
The World-Class Instructional Design Assessment (WIDA) is used to assess speaking, listening, reading, and writing levels. All new students take a screener test (W-APT) to determine if they need ESL and the appropriate level. At the end of the year, all students take a benchmark test (WIDA-ACCESS) to measure progress made throughout the year. Students advance to the next level based on their WIDA test results as well as their teacher's recommendation. Feedback from mainstream content area teachers is also considered.
English as a Second Language, Level I: Fundamentals of language and structures are emphasized at this level. Students learn basic vocabulary and grammar tenses. Students learn to form a simple sentence and eventually a paragraph with a topic sentence and supporting details. Capital letters and punctuation are emphasized. We introduce listening and speaking by having students participate in discussions and stating needs. Students receive at least two classes a day in order to move up to the next level.
English as a Second Language, Level II: We read fiction and nonfiction for comprehension and discussion. Here we also start introducing reading strategies, such as prediction, visual cues, inferences, and using references. Then we move into analysis and expressing opinions. In writing we focus on spelling, writing complete sentences, and then paragraphs, all correctly punctuated. Then we move on to complex sentences and paragraphs that distinguish between the general and the specific.
English as a Second Language, Level III: We introduce more advanced themes in reading and comprehension, and we use these as a basis for discussion. Writing is also more advanced. It includes writing essays with a variety of themes and structures. We also introduce the students to basic research and writing longer essays.
English as a Second Language, Level IVIB English B- Diploma Programme, 11th Grade : This course focuses on language acquisition and the development of reading, writing, listening, and speaking skills. Topics include attitudes and values in relationships; effects of modern living; social, political and cultural change; humans and animals; technical and scientific developments. The required IB criteria for both oral and written skills are: Language, Cultural Interaction, and Message. Students take internally moderated oral exams in the early spring and externally moderated written exams in May.
IB English B- Diploma Programme, 12th GradeComputer Science Grade 7: Computer 7 is offered in conjunction with Art 7 and PE. The course is 9 weeks in length, and is followed by or preceded by 9 weeks of Art. The goal for this course is to provide students with the computer knowledge necessary to competently function in other classes, where computer use is required. Topics include: Keyboarding, File Management and Windows, Word Processing, Spreadsheets, Graphics – Using Paint and Print-shop.
Computer Science Grade 8: Computer 8 is offered in conjunction with Art 8 and PE. The course is 9 weeks in length, and is followed by or preceded by 9 weeks of Art. Topics include: Keyboarding, File Management and Windows, Word Processing using Word, PowerPoint, Spreadsheets, and Internet, Graphics, and Designing Web pages using Word. **Students taking Computer 7 and 8 are encouraged to take more advanced computer courses in high school, such as programming.
Grade 10 &11 & 12 Courses :
Computer Applications : This course gives students an extensive overview of computers and computer applications. The main topics of the course are computer vocabulary, spreadsheets, creating multimedia documents, such as web pages, PowerPoint presentations and desktop publishing documents, with an introduction to Database, in addition to some advanced skills in Word processing.
Web Page Design : The Web Design course gives students a solid foundation in good web design techniques. The course has three major components: using and editing graphics, learning html code, and using Dreamweaver MX to create web sites.
Programming I : In this introductory course, students learn to write well-documented, logically structured programs. They learn how the computer can be programmed to perform specific tasks. The course teaches students to solve problems through the use of flowcharts and algorithms. It provides students a chance to hone their analytical skills.
Programming II : Students continue to learn to write original, well-structured programs in the second part to the programming course. The problems given become increasingly more complex and require a deeper knowledge of programming structures. At the close of the course, students will have an extensive background in computer programming concepts and will be able to apply their skills to other programming languages and computer courses
Arabic for Middle and High School
Grade 7: Introduces students to formal linguistic knowledge of Arabic through reading and writing about scientific, literary, and cultural topics.
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books.google.com - Empowering users with the knowledge necessary to begin using mathematical programming as a tool for managerial applications and beyond, this practical guide shows when a mathematical model can be useful in solving a problem, and instills an appreciation and understanding of the mathematics associated... to mathematical programming
Introduction to mathematical programming
Empowering users with the knowledge necessary to begin using mathematical programming as a tool for managerial applications and beyond, this practical guide shows when a mathematical model can be useful in solving a problem, and instills an appreciation and understanding of the mathematics associated with the applied techniques. Surveys problem types, and discusses various ways to use specific mathematical tools. Contains prerequisite material for the study of linear programming, and offers a brief introduction to matrix algebra. Discusses the special structures of four network problems: the transportation problem, the critical path method, the shortest path problem, and minimal spanning trees. Covers compound interest and explores the financial aspects of specific problems considered throughout the book. Touches on "mathematics" oriented (vs. applications) material, with integrated proofs and discussions on such topics basic graph theory, linear algebra, analysis, properties of algorithms, and combinatorics. An extensive appendix section includes answers to many problems, an introduction to the linear programming package LINDO, an overview of the symbolic computation package Maple, and brief introductions to the TI-82 and TI-92 calculators and their applications.
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Linked GCSE Pre-pilot Executive Summary
This resource from Alpha Plus published in December 2010 is the independent evaluation of the pilot of the linked pair of GCSEs in mathematics. The linked pair of GCSE qualifications are: 'Methods in mathematics' and 'Applications of mathematics'. The two qualifications together cover the entire Key Stage Four programme of study for mathematics and contain some additional content.
This pre-pilot report is the first of seven formative evaluation reports on the pilot of the linked pair of GCSEs in mathematics. A final, summative evaluation report will be presented in December 2013. The pre-pilot report focuses on pre-pilot planning, preparation and communication; pilot centres' state of readiness; and expectations of the impact, risks and issues of the linked pair of GCSEs in mathematics, as identified by centres and wider stakeholder groups before the first delivery of the pilot in September 2010
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UltimaCalc is a collection of mathematical tools wrapped up in one program, for use by scientists, engineers and students. The main window is a calculator that accepts mathematical expressions as plain text and evaluates them to 38 digit precision. UltimaCalc can remain always ready for use. The use of text input means that this window can be small enough to remain open at all times without blocking the view of other windows. This window can be partially transparent when inactive, so you can read documents open underneath it. A major feature of UltimaCalc Professional is its Symbolic Algebra module: Simplify expressions, differentiate them. Integrate a wide range of expressions, and see how the result was obtained. Find Taylor series. Factorise polynomials, divide one polynomial by another or find their GCDs. Analyse a set of measurements, or approximate complicated functions with simpler ones. Use a variety of methods to fit lines to data, plotting the result. Calculate linear regression, or use an absolute deviation fit to minimise the distorting effects of outliers. Perform a multivariate linear regression when one variable is a linear function of several others. Fit polynomials and other non-linear expressions to the data. The Standard Deviation tool calculates the mean, median, standard deviation, skewness, etc of a data set. Other tools solve simultaneous linear or non-linear equations; find the values of parameters that minimise the value of an arbitrary expression; find roots of polynomials up to tenth order; or solve triangles. Plot arbitrary functions. Specify starting and ending conditions and how variables X and Y change at each step. Combine up to 8 plots. Save your results: the calculator window and most special tools can record all calculations in a plain text file. Most special tools can also save their data along with notes to a calculation file future reference. All graphs and plots can be saved as image files in a variety of formats.
Features: UltimaCalc is packed with features on many levels. Percentages, of course, and a large number of functions, including functions for calculating the slope of a line, and calculating definite integrals, as well as the usual trigonometric functions, hyperbolic functions, logarithms (natural, common, and base 2) and exponential. Also factorials, permutations and combinationsUltimaCalc Professional
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There's a new article by the author Nicholson Baker that is not raising as much a fuss as "Is Algebra Necessary?" from The New York Times last year, probably because it's at Harper's behind a paywall. Also, as I write this children are fleeing from algebra all over magazine stands:
The title strikes me as odd, given that the general argument is aimed at all algebra, and the text constantly references algebra as a whole rather than the quite US-specific version of Algebra II. (As far as I'm aware no other country has such a thing; most of them integrate all forms of mathematics together.) What is Algebra II anyway, and where is the cutoff point where Nicholson Baker considers algebra to be too hard to handle? He hints at what he'd like as a replacement, which strikes me as a math appreciation analogous to music appreciation courses:
We should, I think, create a new, one-year teaser course for ninth graders, which would briefly cover a few techniques of algebraic manipulation, some mindstretching geometric proofs, some nifty things about parabolas and conic sections, and even perhaps a soft-core hint of the innitesimal, change-explaining powers of calculus. Throw in some scatter plots and data analysis, a touch of mathematical logic, and several representative topics in math history and math appreciation.
This seems like a truly random collection of topics, but it sounds like Mr. Baker is basing his list off the notion of using The Joy of x by Steven Strogatz as a possible text.
I have had some personal experience with using popular texts; when I team-taught statistics at the University of Arizona we used The Drunkard's Walk, Fooled by Randomness, and Struck by Lightning: The Curious World of Probabilities. While it led to interesting discussions, there just wasn't enough meat to have students do problem solving based solely on the text. The math from the books was purely a passive experience. (We still did just fine by augmenting with our own material.)
I still hold forward the absurd idea that students still solve math problems in a math class. If you're designing a freshman mathematics-teaser course, I might humbly suggest Problem Solving Strategies: Crossing the River with Dogs, which has the virtue of steering away from algebra as the sole touchstone for problem solving.
Back to Mr. Baker's attempt to define Algebra I:
Six weeks of factoring and solving simple equations is enough to give any student a rough idea of what the algebraic ars magna is really like, and whether he or she has any head for it.
Mr. Baker himself seems to have a confused idea of what algebra is like, but he's not alone. (See: my prior post on what is algebra and why you might have the wrong idea.) Also of note: some countries don't bother to factor quadratics. (I haven't made a map comparing countries, but it seems to be continental Europe that ignores it and just says "use the quadratic formula".)
I could see solving equations managed in six weeks, but in a turgid, just-the-rules style that would be the opposite of what we'd want in this kind of appreciation class in the first place. Just the concept of a variable can take some students a month to wrap their head around, making me disturbed by the notion that six weeks would be enough for a student to find "whether he or she has any head for it". (This isn't even touching the issue of just how much is internal to the student. I've heard dyscalculia estimates of up to 7% of all students, but excluding that group a great deal of the attitude seems culturally specific. Allegedly in Hungary [I don't have a hard research paper or anything, this is just from personal anecdotes] it is quite common for folks to say mathematics was their favorite subject in school and the level of disdain isn't remotely comparable to the US.)
They are forced, repeatedly, to stare at hairy, squarerooted, polynomialed horseradish clumps of mute symbology that irritate them
The article's invective along these lines makes me wonder again how much the visual aspect to mathematics is the source of hatred, as opposed to the mathematics itself.
This picture is from the Adventure Time episode "Slumber Party Panic" and is supposed to represent the ultimate in math difficulty. However, the math symbolism is strewn truly at random and there is no real problem here. I am guessing a good chunk of the audience couldn't even tell the difference and for them, any difficult math problem looks like random symbolic gibberish.
This is related to another issue, that of bad writing. Here's Mr. Baker quoting a textbook:
A rational function is a function that you can write in the form f(x) = P(x)/Q(x), where P(x) and Q(x) are polynomial functions. The domain of f(x) is all real numbers except those for which Q(x) = 0.
I claim the above definition is simply bad writing, and a cursory check of the Internet reveals several definitions I'd peg as clearer in a students-who-don't-like-math-are-trying-to-read sense:
"Rational function" is the name given to a function which can be represented as the quotient of polynomials, just as a rational number is a number which can be expressed as a quotient of whole numbers.
Godfrey Harold Hardy admittedly goes on from there, but his text is written for mathematicians. High school texts have no such excuse.
In a similar vein, the article later quotes a 7th grade Common Core standard:
solve word problems leading to equations of the form px + q = r and p(x+q)=r, where p, q, and r are specific rational numbers
which I suppose is meant to be horrifying, but in this case the standards are written for the teachers and aim to remove any ambiguity. Here's problems that matches the standard:
1. You bought 3 sodas for 99 cents each and paid 10 cents in tax. How much money did you pay?
2. You bought 4 candies for 1.50 each and paid $6.20. How much was tax?
The standards can't simply produce many examples and gesture vaguely. They must be exact. Just because 4th grade specifies that students "Explain why a fraction a/b is equivalent to a fraction (n×a)/(n×b)" does not mean students are using variables to do so. (In case you're curious what it does look like to the 4th graders, Illustrative Mathematics has tasks here and here matching the standard.)
There's lots more to comment on, but let me leave off for the moment on this quote, because I'm curious…
Math-intensive education hasn't done much for Russia, as it turns out.
Fold from upper right to lower left (colors added to both sides of the paper for clarity):
Follow up with one more fold:
Voila, a proof that the square root of 2 is irrational.
(Mind you, there is some reasoning involved, but what's the fun in giving that away? Start with "if the square root of 2 is rational, then there is some isosceles right triangle where the sides are the smallest possible integers.")
Teaching is more than telling and explaining, and learning is more than imitating and memorizing. During the last 60 years teachers of mathematics have gradually sensed that, above all else, their pupils should learn the meaning of mathematical terms, principles, operations, and patterns of thought.
So in my last post I opined that the optimal mathematics game in the Tiny Games spirit should "incidentally have some mathematics in them and are the sorts of games one might play even outside of a mathematics classroom." That led to some confusion.
Let me try a do-over:
During a game, when the primary action of the players is indistinguishable from doing traditional homework or test problems, it is a gamified drill.
There's lots of gamified drills. It's easy to do: just take what you normally would do in a math problem review and tack on a game element somewhere (for me it's usually Math Basketball). To be integrated the primary actions of the players will require using mathematics in a way that is linked with the context of the game. That 1-2 Nim requires understanding multiples of 3 is inextricable from the game itself and not interchangeable the same way Math Basketball can be easily switched to Math Darts.
The concept here is to have games suited for different settings that can be described in only a few sentences.
Could one make an all-mathematics variant — mathematical scrimmages, so to speak? The only games I could think of offhand in the same spirit as Tiny Games were some Nim variants and Fizz-buzz.
1-2 Nim (for two players): Start with a row of coins. Alternate turns with your opponent. On your turn you can take either 1 or 2 of the coins. The person who takes the last coin wins.
Fizz-buzz (for a group): Players pick an order. The first player says the number "1″, and then the players count in turn. Numbers divisible by 3 should be replaced by "fizz". Numbers divisible by 5 should be replaced by "buzz". Numbers divisible by both should be replaced by "fizz-buzz". Players who make a mistake are out. Last one in wins the game.
Anyone have some more?
EXTRA NOTE: One condition I'd add is the games need to work as games and not as glorified practice. "Challenge a friend to factor a quadratic you made" meets the "Tiny" but not the "Game" requirement.
EXTRA EXTRA NOTE: Dan Meyer asks "Aside from the counterexample that follows, what are the qualities that make Fizz-Buzz and Nim gamelike and not, say, exerciselike?" In both cases the games incidentally have some mathematics in them and are the sorts of games one might play even outside of a mathematics classroom. Even though Wikipedia claims Fizz-buzz was invented for children to "teach them about division" (?), my first encounter was from The World's Best Party Games. (This still doesn't totally answer the question, I know. A related question is: what is the difference between a puzzle and a math problem?)
Edward L. Thorndike's book The Psychology of Arithmetic (1922) is the earliest I've seen containing criticism of the visuals in textbook design. I wanted to share three of the examples.
Fig. 47.—Would a beginner know that after THIRTEEN he was to switch around and begin at the other end? Could you read the SIX of TWENTY-SIX if you did not already know what it ought to be? What meaning would all the brackets have for a little child in grade 2? Does this picture illustrate or obfuscate?
Fig. 51.—What are these drawings intended to show? Why do they show the facts only obscurely and dubiously?
Fig. 52.—What are these drawings intended to show? What simple change would make them show the facts much more clearly?
While it is still common (and frankly, necessary) to rail at the limitations of learning mathematics via watching videos, my personal umbrage has more to do with presentation than with educational philosophy.
The mathematical video genre is still in its infancy. I am reminded of early films that were, essentially, canned plays.
(From L'Assassinat du Duc de Guise in 1908.)
Oftentimes in videos teaching mathematics with notation they simply duplicate what could be done on a blackboard, without fully utilizing the medium.
However, there are techniques particular to the video format which can strengthen presentation of even mundane notation. For instance, in my Q*Bert Teaches the Binomial Theorem video I made crude use of a split-screen parallel action to reinforce working an abstract level of mathematics simultaneously with a concrete level.
For now, I want to focus on applying animation to the notation itself for clarity.
The video is chock-full of interesting animated moments, but I want to take apart a small section at 5:43. In particular the video shows some algebra peformed on .
Step 1: Multiply the left side by . The variable "falls from the sky" and is enlonged to convey the gravity of motion.
Step 2: Once the variable has fallen, the equation "tilts" to show how it is imbalanced. A second falls onto the right side of the equation.
Step 3: The equation comes back into balance, and the two variables on the left side of the equal side divide.
Step 4: The variables on the right hand side start to multiply, conveyed by a "merge" effect …
Step 5: … forming .
Here's a much more recent example from TED-Ed:
When adding matrices, the positions are not only emphasized by color but by bouncing balls.
When mentioning the term "2×2 matrix" meaning "2 rows by 2 columns" the vocabulary use is emphasized by motion across the rows and columns.
The second matrix is "translated up a bit" by doing a full animation of the matrix sliding to the position.
When the video discusses "the first row" and the "the first column" not only are the relevant numbers highlighted, but they shrink and enlarge as a strong visual signal.
When discussing the problem of why matrix multiplication sometimes doesn't work, the "shrink-and-enlarge" signal moves along the row-matched-with-column progression in such a way it becomes visually clear why the narrator becomes stuck at "3 x …."
These are work-heavy to make, yes, but what if there was some application customized to create animation with mathematics notation? At the very least, there's a whole vocabulary of cinematic technique that has gone unexplored in the presentation of mathematics.
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This third edition of the perennial bestseller defines the recent changes in how the discipline is taught and introduces a new perspective on the discipline. New material in this third edition includes:.:.; A modernized section on trigonometry.; An introduction to mathematical modeling.; Instruction in use of the graphing calculator.; 2,000 solved... more...
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Shop How Much Math-and What Kind of Math-Do We Need
How Much Math-and What Kind of Math-Do We Need
Prakken Publications ED111112 $2.95
Sol Garfunkel, executive director of the Consortium for Mathematics and its applications, and David Mumford, emeritus professor of mathematics at Brown University, want to see a fundamental change in the way math is taught in American schools. In a piece titled "How to Fix Our Math Education," published in the August 24, 2011, New York Times, they write that the "widespread alarm in the United States about the state of our math education" is based on a false assumption. "All this worry . . . [they write] is based on the assumption that there is a single established body of mathematical skills that everyone needs to know to be prepared for 21st-century careers. This assumption is wrong. The truth is that different sets of math skills are useful for different careers, and our math education should be changed to reflect this fact.
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books.google.com thirteen books of Euclid's Elements. The works of Archimedes, including The method. Introduction to arithmetic
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A First Course in Abstract Algebra with Applications
Edition:
3
Publisher:
Pearson/Prentice Hall
Number of Pages:
581
Price:
106.67
ISBN:
0-13-186267-7
This is a comprehensive introduction to the main concepts of abstract algebra, starting with group theory and continuing with ring theory, linear algebra, and fields. It would be appropriate for use in a single-semester introduction to abstract algebra course that covers the basic topics of group theory and ring theory. It would also be quite suitable for a two-semester algebra sequence.
One thing that stands out when reading this book is the quality of the explanations and expositions. Rotman does a very good job of motivating the topics and explaining things in common language. Students using this book would be well-served to have a strong background in discrete mathematics, as Rotman "hits the ground running" by establishing concepts including induction, greatest common divisors, and congruences in the first chapter. As with most texts on this subject, Rotman often pauses to ask open-ended questions when he is about to introduce a new topic. However, in this book these questions often lead to an interesting vignette or history lesson instead of just to the next theorem. With a subject as traditionally difficult as abstract algebra, it is nice for students to be able to see that the reason for proving a theorem is to solve a particular problem, rather than because it is simply the next theorem in the book.
As the book's title indicates, a large portion of the book is dedicated to applications. Unlike some books that tack applications onto the ends of sections, Rotman does a nice job of going into the details of the application, often developing specific notation and theorems. Some of my favorite applications are included, such as the 15-puzzle and using Burnside's lemma to solve counting problems. The attention to detail regarding the applications is apparent, and they do not seem "tacked on" as they often are in other texts.
One drawback of the book is that it is too comprehensive. There is so much material included that one could easily spend a week or two on each section. While Rotman does include some suggested syllabi, it would have been nice to have some more organizational insight given to the prospective instructor. If I were using this book, I would have to spend a large amount of time sorting through the sections ("Should I include Example 2.161?") in order to fit enough material into a 14 or 15-week semester. I would have preferred the book to be organized into a larger number of shorter sections, and a flowchart included so that I could better determine which sections are necessary and which applications and excursions can be omitted.
Overall, I liked Rotman's book, but I think one would have to be very dedicated to making it work within the confines of a semester or two. As many instructors know, well-constructed examples and applications often get discarded when we look at the calendar and see how much time is left in the semester compared with how much material is left to cover. Rotman's book contains great explanations, great examples, and great applications. Unfortunately, it just seems to have too much of everything, and not a lot of advice for the instructor on how to sort it all out.
James Hamblin is an Assistant Professor of Mathematics at Shippensburg University of Pennsylvania. His mathematical interests include origami, quilting, voting theory, and pretty much anything else he can get undergraduates interested in.
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Algebra4.98
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Raise your grades today with the amazing Algebra 1 guide! This 6-page laminated guide covers principles for basic, intermediate, and college level courses. Master and learn the basics quickly and efficiently with QuickStudy.
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...Smooth Operators is a complete solution for learning, practicing, and testing the order of operations. An interactive lesson teaches the math concepts thoroughly with explanations and example problems, including an...
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Video Description: There is more than one type of integral in multivariable calculus. In this lesson, Herb Gross defines and discusses line integrals. He reviews integration with respect to a curve (line) as distinguished from an integral as an area computation (double ...
Video Description: Herb Gross illustrates the equivalence of the Fundamental Theorem of the Calculus of one variable to the Fundamental Theorem of Calculus for several variables. Topics include: The anti-derivative and the value of a definite integral; Iterated integrals. Instructor/speaker: ...
Video Description: With our knowledge of matrix algebra to help, Herb Gross teaches how to find the local maxima and minima of functions of several real variables. Instructor/speaker: Prof. Herbert Gross
Video Description: Herb Gross defines the directional derivative and demonstrates how to calculate it, emphasizing the importance of this topic in the study of Calculus of Several Variables. He also covers the definition of a gradient vector. Instructor/speaker: Prof. Herbert Gross
Video Description: Herb Gross discusses the topic of equations of lines and planes in 3-dimensional space. Topics include: The normal vector to a plane; Parallel planes; Equation of a plane; Equation of a line in space. Instructor/speaker: Prof. Herbert Gross
Video Description: Herb Gross describes the "game" of matrices — the rules of matrix arithmetic and algebra. He also covers non-singularity and the inverse of a matrix. Instructor/speaker: Prof. Herbert Gross
Video Description: Herb Gross shows examples of the chain rule for several variables and develops a proof of the chain rule. He also explains how the chain rule works with higher order partial derivatives and mixed partial derivatives. Instructor/speaker: Prof. Herbert Gross
Video Description: Herb Gross show how the chain rule is involved in finding some integrals involving parameters. He computes the derivatives of integrals with constant limits, as well as derivatives of integrals with variable limits of integration (chain rule). ...
Video Description: Herb Gross reviews the definition of vectors — objects that have magnitude, direction, and sense. He also defines equality of vectors, their components, and rules of arithmetic. Vector arithmetic shares many structural properties with scalar arithmetic including a zero ...
Video Description: Herb Gross teaches us how to calculate infinite double (multiple) sums (for topics in calculus of several variables). This topic is analogous to the use of infinite sums in calculus of a single variable. Instructor/speaker: Prof. Herbert Gross
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Starting at $1628Good addition to private school textMarch 23, 2011 by Colleen Spear
A lot of work went into the production of this book. It's physically well made, and very thoughtfully lay out. This was purchased to supplement a private school text, it's working nicely. I got the product I wanted. It was delivered promptly and i was satisfied with the way the transaction was handled.
The three-step learning system this book provides makes examples easy to follow with frequent support and guidance of an instructor's voice in the annotations. Every page is motivating and you will want to use this book in class.
Summary
Bob Blitzer's unique background in mathematics and behavioral sciences, along with his commitment to teaching, inspired him to develop a precalculus series that gets readers engaged and keeps them engaged. Presenting the full scope of the mathematics is just the first step. Blitzer draws in the reader with vivid applications that use math to solve real-life problems.
These applications help answer the question "When will I ever use this?" Readers stay engaged because the book helps them remain focused as they study. The three-step learning system–See It, Hear It, Try It–makes examples easy to follow, while frequent annotations offer the support and guidance of an instructor's voice. Every page is interesting and relevant, ensuring that readers will actually use their textbook to achieve success! This textbook comes with two CD-ROMs.
Extensive exercise sets at the end of each section are organized into seven categories: Practice Exercises, PracticePlus Exercises, Application Exercises, Writing in Mathematics, Technology Exercises, Critical Thinking Exercises, and Preview Exercises. This variety lets instructors create well-rounded homework assignments, while holding students' interest with an ongoing selection of novel applications. Integrated study aids help students make the most of their time outside of the classroom.
For all readers interested in college algebra College for nearly 30 years. He has received numerous teaching awards, including Innovator of the Year from the League for Innovations in the Community College, and was among the first group of recipients at Miami-Dade College for an endowed chair based on excellence in the classroom. Bob has written Intermediate Algebra for College Students, Introductory Algebra for College Students, Essentials of Intermediate Algebra for College Students, Introductory and Intermediate Algebra for College Students, Essentials of Introductory and Intermediate Algebra for College Students, Algebra for College Students, Thinking Mathematically, College Algebra, Algebra and Trigonometry, and Precalculus, all published by Pearson Prentice Hall.
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TH222 Calculus III
Course Description
A study of sequences, Taylor Polynomials, infinite series, and tests for convergence, and the power series. An overview of ordinary differential equations;
the initial-value Problem; exactness and integrating factors; and Bernoulli and higher-order equations with forcing functions. Graphing calculator is required.
Learning Outcomes
Clearly demonstrate an ability to employ vector operations and properties to include additive, scalar, and vector cross product operations. Using such fundamental properties, the student will provide evidence of employing vectors to define lines and planes in 3-space, and will demonstrate competence in extending such capability to conic surfaces.
Show ability to define vector-valued functions in terms of the scalar functions as components to the basis vectors.
Interpret resulting-properties correctly.
Successfully differentiate and integrate the scalar components.
Provide evidence of understanding and competence in differentiation and integration of functions of more than one variable.
Demonstrate sufficient capability with partial derivatives so as to permit derivations of directional derivatives and gradient functions.
Develop the elements of Jacobean Matrix.
Display capability to incorporate change of variable and other associated applications as specified in the corresponding goal of this syllabus.
Understand the comprehension of the classic theorems of mechanics will be evaluated by application to elementary surface.
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Beginning Topology is designed to give undergraduate students a broad notion of the scope of topology in areas of point-set, geometric, combinator...show moreial, differential, and algebraic topology, including an introduction to knot theory. A primary goal is to expose students to some recent research and to get them actively involved in learning. Exercises and open-ended projects are placed throughout the text, making it adaptable to seminar-style classes.The book starts with a chapter introducing the basic concepts of point-set topology, with examples chosen to captivate students' imaginations while illustrating the need for rigor. Most of the material in this and the next two chapters is essential for the remainder of the book. One can then choose from chapters on map coloring, vector fields on surfaces, the fundamental group, and knot theory
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Synopses & Reviews
Publisher Comments:
Affine geometry and quadrics are fascinating subjects alone, but they are also important applications of linear algebra. They give a first glimpse into the world of algebraic geometry yet they are equally relevant to a wide range of disciplines such as engineering. This text discusses and classifies affinities and Euclidean motions culminating in classification results for quadrics. A high level of detail and generality is a key feature unmatched by other books available. Such intricacy makes this a particularly accessible teaching resource as it requires no extra time in deconstructing the author's reasoning. The provision of a large number of exercises with hints will help students to develop their problem solving skills and will also be a useful resource for lecturers when setting work for independent study. Affinities, Euclidean Motions and Quadrics takes rudimentary, and often taken-for-granted, knowledge and presents it in a new, comprehensive form. Standard and non-standard examples are demonstrated throughout and an appendix provides the reader with a summary of advanced linear algebra facts for quick reference to the text. All factors combined, this is a self-contained book ideal for self-study that is not only foundational but unique in its approach.' This text will be of use to lecturers in linear algebra and its applications to geometry as well as advanced undergraduate and beginning graduate students.
Synopsis:
This text discusses and classifies affinities and Euclidean motions culminating in classification results for quadrics. It features standard and non-standard examples and an appendix that provides the reader with a summary of advanced linear algebra facts.
Algebra <p>Thorough treatment of affine geometry and quadrics </p><p>A useful resource for lecturers in linear algebra and geometry </p><p>Provides an high level of detail and generality that is unmatched by other texts available </p><p>An extensive numbe
"Synopsis"
by Springer,
This text discusses and classifies affinities and Euclidean motions culminating in classification results for quadrics. It features standard and non-standard examples and an appendix that provides the reader with a summary of advanced linear algebra facts
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Mathematics for Elementary Teachers -Text Only - 7th edition
Summary: This leading mathematics text for elementary and middle school educators helps readers quickly develop a true understanding of mathematical concepts. It integrates rich problem-solving strategies with relevant topics and extensive opportunities for hands-on experience. By progressing from the concrete to the pictorial to the abstract, Musser captures the way math is generally taught in elementary schools.
Nice condition with minor indications of previous handling. Book selection as BIG as Texas.46.50 +$3.99 s/h
VeryGood
Bank of Books CA Ventura, CA
2005 Hardcover Very good 7th edition.
$47.77 +$3.99 s/h
VeryGood
Books by Sue Oakdale, CA
This item is in very good condition and if any wear at all it will be minor.
$59.76 +$3.99 s/h
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Charles Byrne Books Oranmore, Co Galway,
Somerset, New Jersey, U.S.A. 2004 Hardcover Very Good
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Review, More Review, Some Algebra II
We started a unit today on factoring in my Algebra II class, and we spent the morning learning to add, subtract and multiply polynomials.
"Who remembers from Algebra I, what you can do when you have a binomial times a binomial?" the teacher Tricia Colclaser asked. (If you need a refresher, think (x+1)(x-1).)
Some of the students were stumped. And FOIL -- one of the all-time famous algebra acronyms which tells you the order of how to solve it (First Outside Inside Last) -- was not ringing too many bells.
A lot of the work we have done in Algebra II this year is review of concepts that were introduced two years ago in Algebra I. (For me, it's all review... but that's different.)
Colclaser is part of a "vertical math team" this year. It's a committee of different grade level math teachers that meets to discuss how they can better organize the curriculum. How, to use a famous example, can we teach fractions in elementary school, so students are not still flummoxed by them in middle school and high school?
The math Standards of Learning, or the state-level teaching standards, are being revised, and committees like this are trying to rethink what they teach. One driving question that Colclaser has is why so many Algebra I concepts end up in Algebra II.
"Maybe we don't need to teach so much, Maybe we should just ask students to become experts in graphing lines and solving linear equations," she said. "I'm still saying to students, 'What's the slope??' and 'How do you find it?'"
Comments
Michael, your post and the "standards" document summarize most of the problems with American math education today.
The post proves that the so-called "standards" are not standards in any real sense, but merely a list of optional things that students may or may not choose to learn. The weak students quickly find out that if they don't know the Algebra I material when they get to Algebra II, somebody from the district will come along and teach it "like it's brand new," at the expense of the good students.
Now take a look at the attachment. Count the number of times the word "calculator" is used. The kids are not being taught to do simple math; they are being taught to run machines that do simple math. Would you expect somebody who relied on books on tape and DVDs to become a great reader?
Finally, recall your post about the "University" of D.C. Students who can't handle Algebra I material even after taking Algebra II know that it doesn't really matter; they can always find an American "university" to teach them middle school math. In short, many of the kids have figured out that the adults running public schools are not serious about the standards, and they therefore treat the adults and their "standards" with the respect they deserve.
The lack of real standards is the problem here. I agree with BradJolly. I'm taking a math class in college and as usual, the professor has to ask, 'How many of you remember ....?' And of course, he 'teaches' it again.
In this case, the class is currently learning recurrent relations (don't even ask!) and the professor asked, 'How many of you remember how to complete the square?'
My teenaged son had just asked me how to complete the square and when I explained it to him (with great pleasure, because I knew how-), his reply was, 'That's way too much work!' It's something not done with a calculator.
The usefulness of completing the square when learning recurrent relations proves it may be too much work but that work pays off.
When the professor whipped through a quick explanation of how to complete the square, I thought that if I didn't know how to do it already, now would not be the time to set about learning it in the space of two minutes. Yet, you can take nothing for granted, apparently, when teaching math. You can't seem to count on it ever having been taught adequately.
You need standards. And you need to have teachers bound to teach by those standards - no deviations, no short-cuts, no excuses.
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An introduction to proof techniques using the many methods of proof that arise in number theory. This course takes a formal look at the properties of the integers and includes topics such as congruencies, quadratic reciprocity, and solution of Diophantine equations. Offered spring semester, even-numbered years, only. Prerequisite: a grade of C or better in MA 260 and MA 261. Liberal Arts Core/University Requirements Designation: DSINQ. (3)
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This second edition of the Math Workbook for ISEE, SSAT, & HSPT Prep: Middle School and High School Entrance Exams has been overhauled from the first edition to reflect the most up-to-date knowledge of the private school admissions exams, as well as to incorporate new insights gleaned by our experts as they used the first edition to prepare students for these exams.Here are some new features you will find in the second edition:* A more logical progression of concepts and exercises* Over 60 new practice sets covering basic arithmetic, algebra, geometry, and advanced topics.* Expanded sections specific to the ISEE and HSPT* An assignment planner to help students track their practice sets andMore... measure scores* A formula sheet containing the most vital math rules and information* A thorough explanation of the major differences between the ISEE, SSAT, and HSPT* Updated answer key with easier navigationThe philosophy of this math workbook remains the same as in our first edition; rigor and drill. Because these are the first tests that actively try to trick students at every turn, those who sit for these exams need reflexive familiarity with mathematical computation , problem types, and strategy. The entrance exams are the first standardized tests for which budgeting time is a significant issue. Students need to spend the majority of time on analysis, rather than computation, to avoid getting tricked. By building skills, speed, and confidence, we hope to eliminate anxiety and give students a solid foundation on which to build excellent scores. This book is intended as a supplement for our highly trained staff, so it does not include strategies. However, motivated students can use it successfully with occasional help from a teacher or parent. Each chapter is comprised of units, with each unit comprised of problem sets with difficulty increasing in a logically progressive manner. Students should do as many of the problem sets for each unit as it takes to achieve a 90% accuracy rate. As a general rule, students taking lower level exams should complete chapters 1-8, and stick to "basic" questions in chapters 9-16. Students preparing for high school entrance exams should go through the entire book.While private school entrance exam preparation is the primary purpose of this book, we recognize that it may serve other purposes as well. This book would be useful for anyone looking for a workbook that encompasses all fundamental math concepts up through an 8th grade math program.For further information about the book and our test prep offerings, check out our website at Education (c) 2012
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Calculus is one of the
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Solve a wide array of problems in the physical, biological, and social sciences, engineering, economics, and other areas with the skills you learn in Understanding Calculus II: Problems, Solutions, and Tips. This second course in the calculus sequence introduces you to exciting new techniques and applications of one of the most powerful mathematical tools ever invented. Professor Bruce H. Edwards of the University of Florida enriches these 36 lectures with crystal-clear explanations, frequent study tips, pitfalls to avoid, and—best of all—hundreds of examples and practice problems that are specifically designed to explain and reinforce key concepts to the formation of Earth to the many twists and turns in our planet's evolution. In a course suitable for scientists and nonscientists alike, Professor Hazen recounts Earth's story through 10 stages of mineral evolution.
Examine groundbreaking research on the enigmatic phenomenon of sleep, straight from a scientist at the forefront of the field. In these 24 engrossing lectures, award-winning Stanford University professor H. Craig Heller reveals what happens in the sleeping brain all the way down to the cellular and molecular level as you investigate coping mechanisms for jet lag, shift work, and insomnia; parasomnias such as sleepwalking and night terrors; and much more.
Time rules our lives. From the rising and setting of the sun to the cycles of nature, the thought processes in our brains, and the biorhythms in our day, nothing so pervades our existence and yet is so difficult to explain. Time seems to be woven into the very fabric of the universe. But why? In 24 riveting half-hour lectures, Mysteries of Modern Physics: Time shows how a feature of the world that we all experience connects us to the instant of the formation of the universe—and possibly to a multiverse that is unimaginably larger and more varied than the known cosmos.
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More About
This Textbook
Overview
Get a good grade in your precalculus course with PRECALCULUS, Seventh Edition. Written in a clear, student-friendly style, the book also provides a graphical perspective so you can develop a visual understanding of college algebra and trigonometry. With great examples, exercises, applications, and real-life data--and a range of online study resources--this book provides you with the tools you need to be successful in your course.
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Meet the Author
David Cohen, a senior lecturer at UCLA, was the original author of the successful, well-respected precalculus series--COLLEGE ALGEBRA, ALGEBRA AND TRIGONOMETRY, PRECALCULUS: A PROBLEMS-ORIENTED APPROACH, and PRECALCULUS: WITH UNIT CIRCLE TRIGONOMETRY
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Algebra for College basic concepts of algebra are presented in a simple, straightforward manner. Algebraic ideas are developed in a logical sequence, through examples, continuously reinforced through additional examples, and then applied in a variety of problem-solving situations. In the examples, students are guided to organize their work and to decide when a meaningful shortcut might be used.
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Monponsett Calculus precalculus at Plymouth State University, and used this class as a prerequisite for Calculus and differential equations. I received an A in probability and statistics for scientists at Plymouth State University. The course was designed to teach statistics so that they could be applied to scientific researchThe axioms and common understandings of Algebra 1 are common to all other algebras, such as vector algebra, and are therefore the essential foundation for all further study in mathematics. Algebra 2 skills, including factoring, finding roots, solving sets of equations and classifying functions b...
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{"currencyCode":"GBP","itemData":[{"priceBreaksMAP":null,"buyingPrice":38,"ASIN":"0198534566","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":24.95,"ASIN":"1852336625","isPreorder":0}],"shippingId":"0198534566::OXoLXccpG%2BRQwuLHalfUNYxgnoIOMaP9UcBGJyULiY46yvZAxGUWftt6PBrXEfJFYti9agwzJ9Hr8lHcVBsw7cyXrPBXFNhR,1852336625::j4CCMcnoCYhg2TQCc1usmvAKfdifgNC4pix%2B5C6djx5Bzb9vLNBSj9DM20EUDqDQmuCcWEu56NZJxwa5b%2FQreSloRip6uiA introductory book about Basic Geometry, written in a brief british style, for beginning undergraduate students. The book can be read by (and can be taught to) anyone with some background in traditional high school Mathematics. The book begins with Euclidean Geometry and ends with a brief introduction to Differential Geometry of curves and surfaces. It is an interesting read (and a pleasant teach, unlike most undergraduate text books) with nice historical threads and good classical problems. The author provides hints and short solutions to almost all the problems at the end of the book. The problems are an essential ingredient of the book, so don't miss them! The author probably did not quite intend to write a yellow "Geometry for Dummies" so he does not dwell (not for too long at least) on the trivial stuff. Geometry was never part of the Trivium! You will feel good about yourself and about Geometry, one of the oldest disciplines of science, after reading this book. I did.
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ISBN-139781412073813
ISBN-101412073812
Original list price$0.00
Amazon.com description:Product Description: The authors have made this book a thorough review of basic courses in Trigonometry. In addition to traditional studies of common trigonometric functions and basic trigonometric identities, the book covers various methods for solving trigonometric equations and inequalities. It also introduces an innovative graphic approach to solving complex trigonometric inequalities and systems of trigonometric inequalities by using graphing calculators.
With a wide variety of topics, diverse exercises with answers, and logical explanations, this book will be an excellent reference for students who want to excel in Trigonometry classes and to be ready for deeper college math study
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The differentiation is the subfield of calculus and there are various application of
differentiation in real world. The differentiation is very important part of math as
it is used in many scientific ...
Anti derivative of function f is the function F whose derivative is function f. We can understand it by an equation as F'=f. This process is also known as anti differentiation. This term is related ...
Expressions for velocity and acceleration of a particle moving along a curve
(curvilinear motion) are more complicated than for a particle moving in a straight line.
The equation of the curve can be ...
Integration is an important concept in mathematics and, together with its inverse,
differentiation, is one of the two main operations in calculus. Given a function f of a real
variable x and an ...
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Definition, Testing and Application of Aloe Vera and Aloe Vera Gel Definition, Testing and Application of Aloe Vera and Aloe Vera Gel Definition Aloe Vera is the colourless mucilaginous gel obtained from the parenchymatous cells in the fresh leaves of Aloe vera (L) Burm. f. (Liliaceae) (1,2). Nomenclature Aloe barbadensis Mill., Aloe chinensis Bak., A. elongata Murray, A. indica Royle, A. afficinalis Forsk., A. perfoliata L., A. rubescens DC, A. vera L. var. littoralis König ex Bak., A. vera L. var chinesis Berger, A. vulgaris Lam. (25). Most formularies and reference books regard Aloe barbadensis Mill. As the correct species name, and Aloe vera (L.) Burm. f. as a synonym. However, according to the International Rules of Botanical Nomenclature, Aloe vera (L.) Burm. f. is the legitimate name for this species (24). The genus Aloe has also been placed taxonomically in the family called Aloeaceae. The Story of Aloe Vera The plant Aloe Vera has a history dating back to biblical time. Aloe vera plant is not a cactus, but a member of the tree lily family, know as Aloe barbadensis. It produces a tubular yellow flower in the spring that is typical of the lily family. There are over 250 species of aloe grown around the world. Only two species are grown commercially: Aloe barbadensis Miller and Aloe aborescens. The Aloe plant is grown in warm tropical areas and cannot survive freezing temperatures. In the United States, most of the Aloe is grown in the Rio Grande Valley of South Texas, Florida and Southern California. Internationally, Aloe can be found in Mexico, the Pacific Rim countries, India, South America, Central America, the Caribbean, Australia and Africa. The original use of the Aloe plant was in the production of Aloin, a yellow sap used for many years as a laxative ingredient by the pharmaceutical industry. Another main ingredient: Aloe Gel, a clear colorless semisolid gel that was also stabilized and marketed. This Aloe Vera Gel, beginning in the 50's, has gained respect as a commodity used as a base for nutritional drinks, as a moisturizer, and a healing agent in cosmetics and OTC drugs. Chemical analysis has revealed that this clear gel contains amino acids, minerals, vitamins, enzymes, proteins, polysaccharides and biological stimulators. Public interest is Aloe has grown quickly, and now there is a considerable amount of research into the various components of Aloe to find our more about their properties and to characterize these components so that more specific research can provide clues to the "magic" that is attributed to Aloe Vera. For more information go to the Aloe Research studies links. 1 Definition, Testing and Application of Aloe Vera and Aloe Vera Gel Description Succulent, almost sessile perennial herb; leaves 3050 cm long and 10 cm broad at the base; colour peagreen (when young spotted with white); bright yellow tubular flowers 2535 cm in length arranged in a slender loose spike; stamens frequently project beyond the perianth tube. Liquid Gel from the fresh leaf Aloe Vera Gel is not to be confused with the juice, which is the bitter yellow exudate originating from the bundle sheath cells of the leaf. The drug Aloe consists of the dried juice. General appearance The gel is a viscous, colourless, transparent liquid. Organoleptic properties Viscous, colourless, odourless, taste slightly bitter. Geographical Probably native to North Africa along the upper Nile in the Sudan, and subsequently introduced and naturalized in the Mediterranean region, most of the tropics and warmer areas of the world, including Asia, the Bahamas, Central America, Mexico, the southern United States of America, southeast Asia, and the West Indies. Identity Test NMR Microbiology The test for Samonella spp. In Aloe Vera Gel should be negative. Acceptable maximum limits of the other microorganisms are as follows. For external use: aerobic bacteria –not more than 10²/ml; funginot more than 10²/ml; enterobacteria and certain Gramnegative bacteria not more than 10¹/ml; Staphylococcus spp. –0/ml. (Not used internally.) Moisture Contains 98.5% water Pesticide residues To be established in accordance with the national requirements. For guidance, see WHO guidelines on quality control methods for medicinal plants and guidelines on predicting dietary intake of pesticide residues. Heavy metals Recommended lead and cadmium levels are not more than 10 and 0.3 mg/kg, respectively, in the final dosage form. Radioactive residues For analysis of strontium90, iodine131, caesium134, caesium137, and plutonium239, see WHO guidelines on quality control methods for medicinal plants. 2 Definition, Testing and Application of Aloe Vera and Aloe Vera Gel Other Tests Chemical test for Aloe Vera Gel and tests fro total ash, acidinsoluble ash, alcohol soluble residue, foreign organic matter, and watersoluble extracts to be established in accordance with the national requirements. Chemical assays Carbohydrates (0.3%), water (98.5%). Polysaccharide composition analysis by gasliquid chromatography. Major chemical constituents Aloe Vera Gel consists primarily of water and polysaccharides (pectins, hemicelluloses, glucomannan, acemannan, and mannose derivatives). It also contains amino acids, lipids, sterols (lupeol, campesterol, and βsitosterol0, tannins, and enzymes. Mannose 6phosphate is a major sugar component. Dosage forms The clear mucilaginous gel. At present no commercial preparation has been proved to be stable. Because many of the active ingredients in the gel appear to deteriorate on stage, the use of fresh gel is recommended. Preparation of fresh gel: harvest leaves and wash them with water and a mild chlorine solution. Remove the outer layers of the leaf including the pericyclic cells, leaving a "fillet" of gel. Care should be taken not to tear the green rind, which can contaminate the fillet with leaf exudates. The gel may be stabilized by pasteurization at 7580˚C for less than 3 minutes. Higher temperatures held for longer times may alter the chemical composition of the gel. Medical uses Uses described in pharmacopoeias and in traditional systems of medicine. Aloe Vera Gel is widely used for the external treatment of minor wounds and inflammatory skin disorders. The gel is used in the treatment of minor skin irritations, including burns, bruises, and abrasions. The gel is further used in the cosmetics industry as a hydrating ingredient in liquids, creams, sun lotions, shaving creams, lip balms, healing ointments, and face packs. Aloe Vera Gel has been traditionally used as a natural remedy for burns. Aloe Vera Gel has been claimed to be effectively used in the treatment of first and seconddegree thermal burns and radiation burns. Both thermal and radiation burns healed faster with less necrosis when treated with preparations containing Aloe Vera Gel. In most cases the gel must be freshly prepared because of its sensitivity to enzymatic, oxidative, or microbial degradation. Aloe Vera Gel is not approved as an internal medication, and internal administration of the gel has not been shown to exert any consistent therapeutic effect. Uses described in folk medicine, not supported by experimental or clinical data. The treatment of acne, hemorrhoids, psoriasis, anemia, glaucoma, petit ulcer, tuberculosis, blindness, seborrhoeic dermatitis, and fungal infections. 3 Definition, Testing and Application of Aloe Vera and Aloe Vera Gel Pharmacology Wound healing Clinical investigations suggest that Aloe Vera Gel preparations accelerate wound healing. In vivo studies have demonstrated that Aloe Vera Gel promotes wound healing by directly stimulating the activity of macrophages and fibroblasts. Fibroblast activation by Aloe Vera Gel has been reported to increase both collagen and proteoglycan synthesis, thereby promoting tissue repair. Some of the active principles appear to be polysaccharides composed of several mosaccharides, predominantly mannose. It has been suggested that mannose 6phosphate, the principal sugar component of Aloe Vera Gel, may be partly responsible for the wound factor receptors on the surface of the fibroblasts and thereby enhance their activity. Furthermore, acemannan, a complex carbohydrate isolated from Aloe leaves, has been shown to accelerate wound healing and reduce radiationinduced skin reactions. The mechanism of action of acemannan appears to be twofold. First, acemannan is a potent macrophageactivating agent and therefore may stimulate the release of fibrogenic cytokines. Second, growth factors may directly bind to acemannan, promoting their stability and prolonging their stimulation of granulation tissue. The therapeutic effects of Aloe Vera Gel also include prevention of progressive dermal ischaemia caused by burns, frostbite, electrical injury and intraarterial drug abuse. In vivo, analysis of the injuries demonstrates that Aloe Vera Gel acts as an inhibitor of thromboxane A2, a mediator of progressive tissue damage. Several other mechanisms have been proposed to explain the activity of Aloe Vera Gel, including stimulation of the complement linked to polysaccharides, as well as the hydrating, insulating, and protective properties of the gel. Because many of the active ingredients appear to deteriorate on storage, the use of fresh gel is recommended. Studies of the growth of normal human cells in vitro demonstrated that cell growth and attachment were promoted by exposure to fresh Aloe Vera leaves, whereas a stabilized Aloe Vera Gel preparation was shown to be cytotoxic to both normal and tumour cells. The cytotoxic effects of the stabilized gel were thought to be due the addition of other substances to the gel during processing. Antiinflammatory The antiinflammatory activity of Aloe Vera Gel has been revealed by a number of in vitro and in vivo studies (See studies section). Fresh Aloe Vera Gel significantly reduced acute inflammation in rats (carrageenininduced paw oedema), although no effect on chronic inflammation was observed. Aloe Vera Gel appears to exert its anti inflammatory activity through bradykinase activity and thromboxane B2 and prostaglandin F2 inhibition. Furthermore, three plant sterols in Aloe Vera Gel reduced inflammation by up to 37% in croton oilinduced oedema in mice. Lupeol, one of the sterol compounds found in Aloe Vera, was the most active and reduced inflammation in a dosedependent manner. These data suggest that specific plant sterols may also contribute to the antiinflammatory activity of Aloe Vera Gel. Burn treatment Aloe Vera Gel has been used for the treatment of radiation burns. Healing of radiation ulcers was reported in one study in patients treated with Aloe Vera cream, although the fresh gel was more effective than the cream. Complete healing was reported in another study, after treatment with fresh Aloe Vera Gel, in patients with radiation burns. Twenty seven patients with partialthickness burns were treated with Aloe Vera Gel in another placebocontrolled study. The Aloe Vera Geltreated lesions healed faster than the burns treated with petroleum jelly gauze (18.2 days), a difference that is statistically significant (ttest, P<0.002). 4 Definition, Testing and Application of Aloe Vera and Aloe Vera Gel Contraindications Aloe Vera Gel is contraindicated is cases of known allergy to plants in the Liliaceae's family. Precautions No information available concerning general precautions, or precautions dealing with carcinogenesis, mutagenesis, impairment of fertility; drug and laboratory test interactions; drug interactions; nursing mothers; paediatric use; or teratogenic on nonteratogenic effects on pregnancy. Adverse reactions There have been very few reports of contact dermatitis and burning skin sensations following topical applications of Aloe Vera Gel to dermabraded skin. Posology Fresh gel or preparations containing 1070% fresh gel. References 1. WHO monographs on selected medicinal plants. 2. Bruneton J. Pharmacognosy, phytochemistry, medicinal plants. Paris, Lavoisier, 1995. 3. Grindlay D, Reynolds T. The Aloe Vera phenomenon: a review of the properties and modern uses of the leaf parenchyma gel. Journal of ethnopharmacology, 1986, 16:17151. 4. Newton LE. In defense of the name Aloe Vera. The cactus and succulent journal of Great Britain, 1979, 41:2930. 5. Tucker AO, Duke JA, Foster S. Botanical nomenclature of medicinal plants. In: Cracker LE, Simon JE, eds. Herbs, spices and medicinal plants, Vol. 4. Phoenix, AR, Oryx Press, 1989:169 242. 6. Hänsel R et al., eds. Hagers Handbuch der Pharmazeutischen Praxis, Vol. 6, 5 th ed. Berlin, Springer, 1994. 7. Youngken HW. Textbook of pharmacognosy, 6 th ed. Philadelphia, Blakiston, 1950. 8. Quality control methods for medicinal plant materials. Geneva, Word Health Organization, 1998. 9. Deutsches Arzneibuch 1996. Vol. 2. Methoden der Biologie. Stuttgart, Deutscher Apotheker Verlag, 1996. 10. European pharmacopoeia, 3 rd ed. Strasbourg, Council of Europe, 1997. 11. Rowe TD, Park LM. Phytochemical study of Aloe Vera leaf. Journal of the American Pharmaceutical Association, 1941, 30:262266. 12. Guidelines for predicting dietary intake of pesticide residues, end rev. ed. Geneva, World Health organization, 1997 (unpublished document WHO/FSF/FOS/97.7; available from Food Safety, WHO, 1211 Geneva 27, Switzerland). 13. Pierce RF. Comparison between the nutritional contents of the aloe gel from conventional and hydroponically grown plants. Erde international, 1983, 1:3738. 14. Hart LA et al. An anticomplementary polysaccharide with immunogical adjuvant activity from the leaf of Aloe Vera. Planta medica, 1989, 55:509511. 15. Davis RH et al. Antiinflammatory and wound healing of growth substance in Aloe Vera. Journal of the American Pediatric Medical Association, 1994, 84:7781. 16. Davis RH et al. Aloe Vera, hydrocortisone, and sterol influence on wound tensile strength and antiinflammation. Journal of the American Pediatric Medical Association, 1994, 84:614621. 17. Heggers JP, Pelley RP, Robson MC. Beneficial effects of Aloe in wound healing Phytotherapy research, 1993, 7:S48S52. 18. McCauley R. Frostbitemethods to minimize tissue loss. Postgraduate medicine 1990, 88:6770. 19. Shelton RM. Aloe Vera, its chemical and therapeutic properties. International journal of dermatology, 1991, 30:679683. 20. Haller JS. A drug for all seasons, medical and pharmacological history of aloe. Bulletin of New York Academy of Medicine, 1990, 66:647659. 21. Tizard AU et al. Effects of acemannan, a complex carbohydrate, on wound healing in young and aged rats. Wounds, a compendium of clinical research and practice, 1995, 6:201209. 5 Definition, Testing and Application of Aloe Vera and Aloe Vera Gel 22. Roberts DB, Travis EL. Acemannancontaining wound dressing gels reduce radiationinduced skin reactions in C3Hmice. International journal of radiation oncology, biology and physiology, 1995, 15:10471052. 23. Karaca K, Sharman JM, Norgren R. Nitric oxide production by chicken macrophages activated by acemannan, a complex carbohydrate extracted from Aloe Vera. International journal of immunopharmacology, 1995, 17:183188. 24. Winters WD, Benavides R, Clouse WJ. Effects of aloe extracts on human normal and tumor cells in vitro. Economic botany, 1981, 35:8995. 25. Fujita K, Teradaira R. Bradykininase activity of aloe extract. Biochemical pharmacology, 1976, 25: 205. 26. Udupa SI, Udupa AL, Kulkarni DR. Antiinflammatory and wound healing properties of Aloe vera. Fitoterapia, 1994, 65:141145. 27. Robson MC, Heggers J, Hagstrom WJ. Myth, magic, witchcraft or fact? Aloe Vera revisited. Journal of burn care and rehabilitation, 1982, 3:157162. 28. Collin C. Roentgen dermatitis treated with fresh whole leaf of Aloe vera. American journal of roentgen, 1935, 33:396397. 29. Wright CS. Aloe Vera in the treatment of roentgen ulcers and telangiectasis. Journal of the American Medical Association, 1936, 106:13631364. 30. Rattner H. Roentgen ray dermatitis with ulcers. Archives of dermatology and syphilogy, 1936, 33:593594. 31. Loveman AB. Leaf of Aloe vera in treatment of roentgen ray ulcers. Archives of dermatology and syphilogy, 1937, 36:838843. 32. Visuthikosol V et al. Effect of Aloe vera gel on healing of burn wounds: a clinical and histological study. Journal of the Medical Association of Thailand, 1995, 78:403409. 33. Hormann HP, Korting HC. Evidence for the efficacy and safety of topical herbal drugs in dermatology: Part 1: Antiinflammatory agents. Phytomedicine, 1994, 1:161171. 34. Hunter D, Frumkin A. Adverse reactions to vitamin E and Aloe vera preparations after dermabrasion and chemical peel. Cutis, 1991, 47:193194. 35. Horgan DJ. Widespread dermatitis after topical treatment of chronic leg ulcers and stasis dermatitis. Canadian Medical Association Journal, 1988,138:336338. 36. Morrow DM, Rappaport MJ, Strick RA. Hypersensitivity to aloe. Archives of dermatology, 1980, 116:10641065. This information is provided so that current & prospective buyers will have complete knowledge about the historical and documented uses of Nature*4*Science Nutraceutical ingredients. N4S does not recommend any of its Nutraceutical ingredients for any particular use. Each buyer must determine, with regulatory and legal advice, the kinds of products and product claims that are suitable and appropriate for their respective markets and customers. N4S does not provide this advice. 6
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Mathematics is a grand subject in the way it can be applied to various problems in science and engineering. To use mathematics, one needs to understand the physical context. The author uses mathematical techniques along with observations and experiments to give an in-depth look at models for mechanical vibrations, population dynamics, and traffic flow. Equal emphasis is placed on the mathematical formulation of the problem and the interpretation of the results. In the sections on mechanical vibrations and population dynamics, the author emphasizes the nonlinear aspects of ordinary differential equations and develops the concepts of equilibrium solutions and their stability. He introduces phase plane methods for the nonlinear pendulum and for predator-prey and competing species models.
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Calm down - it will be okay. The Algebra Helper software can help you with your homework. It makes your homework faster to do and easier to learn...so don't panic practical applications algebraic fractions
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Week 5: What do YOU think should be the kind of math competence we require students to learn? And, is it important for students to see the relevance of math to jobs and everyday life?
Sol Garfunkel
At COMAP (Consortium for Mathematics and Its Applications) we work with teachers, students, and business people to create learning environments where mathematics is used to investigate and model real issues in our world. In our 2009 paper, Math to Work we argued for offering curricular alternatives in math that would emphasize how discrete ideas taken from high school math courses apply to a variety of careers and your everyday lives. These alternatives would help students like you make connections between what they are learning and how you would use those skills in future jobs.
COMAP further argued that too many people have accepted a false argument that continuous mathematics is essential for all students. Continuous mathematics are highly technical subjects that teach a good deal of symbol manipulation (like using "x" and "y" in Algebra II) and typically lead up to calculus and analysis. This kind of math learning is necessary for future engineers and epidemiologists, but for the large majority of students it won't be needed. The false argument goes like this: All students need to learn mathematics (so far so good). We shouldn't discriminate against any group of students (still hard to argue). All students must be given the opportunity to reach some basic level of mathematical competence. That basic level of mathematical competence can be defined by the content of Algebra II (as exhibited on a particular test). Criminal!
In the name of giving everyone an equal chance to succeed, we merely give them an equal chance to fail. The simple truth is that there is an enormous choice of mathematical topics we could (and should) be teaching. If you read the short paper, you'll learn some examples of good, well-paying jobs where Algebra II is simply not required but other math concepts are used to some extent. In other words, we could say, as a nation, that the "basic level of math competence" is not about being well-along in the path toward calculus and more about having math skills for work and life. This would not mean that anyone who wants to pursue continuous mathematics necessary for their own future careers would be prevented from doing so (but even exposing such students to how what they're learning will apply to their careers and lives would be a good idea.)
My questions:
1. To what extent have you been told that continuous mathematics is important for all students? Have you heard varying ideas about this from different people? What do you think of the idea that every student must learn Algebra II to be successful at a well-paying job?
2. Do you think there is there a relationship between students' motivation to learn math and their understanding of how it will be useful in future jobs and in their everyday lives? (Generally? In their specific areas of interest?) How so?
3. Some have suggested: If teens don't see clear connections between school, work and jobs, they might see dropping out of college (or maybe even high school) as a rational choice--especially in today's economy where financing for four-year college is out of reach for many. The paper I just linked suggests that this is because other pathways to well-paying jobs aren't obvious (the "false argument" prevails). Would high school students benefit from increased guidance about the variety well-paying jobs available, whether you attend college or not? About what kind of math and other knowledge you'll need to do the jobs well? Do you think this could have an impact on dropout rates?
4. Your working question in this project is "What is Student Achievement?" Read the third paragraph above one more time for my opinion. What do YOU think should be the basic level of math competence we require students to learn? Need it be associated with "continuous mathematics"?
Failing to see the point of math--partiucalrly what Sol has termed continuous math-- is a longtime hobby of mine, so I've asked every math teacher I've had from seventh grade on to explain its relevance and justify its continued existence in secondary school curricula. They all open with a vague insistence that "we use math all the time, we just don't realize it." When I pressed them further, (Isn't it a problem that I don't realize the practical applications of what I'm learning? What are they, anyway?) one forced me to watch the CBS procedural Numb3rs (their spelling, not mine), one admitted that I would only need enough algebra to calculate interest and enough geometry to grasp basic measurements, and everything else wouldn't come up again unless I pursued a career in mathematics/engineering/hard sciences etc. All the others pointed out that the continuous math sequence was a college entrance requirement.
I find that last one bizarre. My teachers were right: most state universities explicitly require at least three years of math. (Colorado universities require four.) More often than not, they also mandate that those three years consist of Algebra I, Geometry, and Algebra II and specifically indicate that other math courses, such as finances and statistics, will not count towards the three year total. This seems backwards to me. Wouldn't those last two be more applicable to and useful in many more careers and fields of study, to say nothing of day-to-day life?
It appears to me that our obsession with teaching the calculus sequence has already hurt our nation. I realize, of course, that our current economic climate is the result of a perfect storm of any number of factors, but I would venture to say that at least one of those was consumers who didn't quite grasp the economic realities of exotic mortgages and predatory lending practices. Would so many have agreed to adjustable-rate mortgages and NINA loans had they received an education that empowered them to detect a too-good-to-be-true financial product?
To that end, I would be inclined to believe that proficieny standards should be geared less towards AP calculus and more towards financial independence. Can you do basic arithmetic? Can you balance a checkbook? Calculate interest? Keep a budget? These are the sorts of things that keep a person afloat in Grown-Up Land, not y=mx+b. Most of my teachers in subjects other than math , by their own admission, would have trouble breaking 400 on the math section of the SAT. But despite what some of my past math teachers would have me believe, they are all still happy, succesful people who can, to the best of my knowledge, put their pants on without bruising themselves.
As for the question of motivation, what I've just said more or less illustrates my interest in continuous math and my opinion of its worth, and I'd wager that my attitude is widespread. And it isn't just young people who are skeptical about the very idea of staying in school anymore. If I had a dollar for every op-ed I read that declared college degrees worthless, bemoaned the ever-shrinking job market, and urged would-be college students into vocational schools instead (to receive training in a job sector said to be "growing"), I'd be tempted to drop out of high school myself, in order to live full time on the island (Corsica) I bought with the money.
And only now do I notice my glaring typos. What a "succesful" demonstration of my "proficieny" in spelling. Sorry everyone..."partiucalrly" indeed.
I have certainly been told continous mathematics is a good idea for anyone possibly pursuing a career in an engineering, science, etc. field. However, for those not interested in a future with mathematics, I don't think it's very stressed. Honestly, I think Algebra II was an important class for me, and while every student will not directly benefit in their career from this class, I felt more confident in my algebra skills and thought it was a good basic class to have. As for students' motivation to learn math, I think if their not interested, they're not interested. Students understand why we take classes, and even if they realize it will benefit them later, I think its hard to get excited about math when that's not your passion. While clear connections between work/school might motivate many students to continue with their education, I think a lot of the motivation for a higher education comes from a love of learning. And while a guidance and knowledge of jobs that are possible with/without a college education would be helpful, I'm not sure how effective it would be in impacting dropout rates. For mathematical competence, I think Algebra II is sufficient right now. An integrated approach might be more effective though, combining Algebra I/Geometry/Algebra II. As I haven't taken anything beyond Algebra II yet, I do not yet see the advantages of taking a Calculus class.
I also agree with Miriam, having pre-calculus as the requirement could be beneficial because it gives students the option to pursue calculus in college, if during their junior/senior years in high school and freshmen year in college, they choose to go into a different career path. Why spend money taking pre calculus and more advanced classes when you can get it for free in high school?
In general, I don't like math much. But I feel like the thing I like the least about math (especially algebra) is that I struggle to find a real-world connection to the subject. I don't see how taking classes like Algebra I and II really apply to a wide variety of future professions. No one has really mentioned to me the need to take Algebra II to be successful later in life, but I have always somewhat assumed that I would have to take these classes no matter what, and not thought about the reasons why. Right now I am taking, Geometry, and I find I can enjoy it much more because I can find many more connections between the class and the real world. It's not that I don't consider algebra important, it's just that I think it needs to be taught in a way that students can connect with real-world issues. For me, there is definately a connection between my motivation to learn math and my understanding of how it connects to the real world. In Algebra I, I found that I didn't care about the work, didn't treat it with reverance, mostly because I couldn't see its importance. I also found it much harder to understand for this reason. In Geometry, I feel like I try much harder to do well because I can see more connections to how it might help me in the future.
i have almost been told by all my teachers that taking or learning mathematics is good for you because you use it everywhere and you will keep on using it in the future. They say its very imortant to learn and use mathematics. My mom says math is very important and my math teacher of course, and my science teacher because even though physics isnt math i still do problems in physics with math in it. I think every student should take Algebra II beacuse you never know that you are going to use it in your job. I dont think there is a relationship when students are motivated to learn math because if thats something they dont like they wont really care. But later on they will realize that math is important for all types of jobs and then they might be motivated.Yes giving more guidance to students about well-pay jobs and weather they have to attend college or not, will help their self awareness to choose their destiny. (hopefully not dropping out of school). I think it should be pre-caculus because their they have the choice to further study math but still stop while functioning in society.
Continuous mathematics at my public high school, Harry D. Jacobs, is recommended for most students however, some choose not to do so. Entering high school, all freshmen are required to take an Algebra I course. Depending on what track you take (general, advanced, or honors) determines the course length throughout the year. For example, a general class is all four terms and an honors class is only first and second term. As the year progresses, an honors student moves on to honors geometry for term three and four while a general student is still behind in algebra I. A general student would begin with geometry the following year as an honors student would advance to Algebra II. As you can see, a general student is hindered from the start and by their senior year may only reach Trigonometry, if they choose to do so. Many general students do not continue past Algebra II as it is the minimum math requirement to graduate at Jacobs. I am currently in the honors track and my honors friends agree continuous mathematics is beneficial to our future. The higher the math level course, the more it is likely for one to test out of math courses in college. My general class-level friends do not have the desire to continue math throughout their high school career and typically stop at algebra II. I think that every student should take algebra II and BEYOND in order to be successful in a well-paying job. The standards are being raised for this generation and students should take the courses offered to them, despite the challenge, in order to be prepared for their future.
I believe there is a correlation between a student's desire to learn math and their knowledge of how it will pertain to them in the future. If students aren't provided with the motivation to learn in high school, it's most likely they will not pursue higher level careers that require beyond algebra II math skills. I see how this may lead to the increase of drop-out rates. If motivation is not instilled in high school, it is likely this will carry on to the professional world.
I believe there should not be a basic level of math for students, I think math should be REQUIRED for all students, all four years of high school. This way students have the knowledge from the beginning of high school on the importance of math throughout their educational experience.
1. Math to me is the subject I find is most hotly debated on importance. I have heard equally throughout my life that math is one of the most important subjects and one of the least important. While I feel one would probably expect to mostly hear students say math is not important, I find I hear a fair amount of disregard for math from adults (even educators) as well as praise for math by a lot of students. I personally don't believe one needs to have taken courses in any particular subject to be succesful since often times success is not determine by skill but by luck, ( such as being born into an already "succesful" family).
2. I believe that it's the way math is taught in school that sways the way students feel about it I also feel there is this idea in society that being good at math makes one intelligent beyond all else and somehow more capable than anyone else. I' not sure I'm expressing it right here and if I need to explain again please ask.
3. Yes I do believe that high school students would benefit from understanding there is a wide range of career options, as for attending college, I am honestly unsure. I feel students dropout for all kinds of reasons, but mostly probably due to stress of college work and the feeling that pay-off my be minimal in comparison, at least this is a complaint I hear from fiends I have in college.
I don't think I was entirely clear. I meant to say, if the math class requirements were done away with and it was only required that you take four years of math, any class, would classes that are currently viewed as slacker classes but that are useful in life become more popular? Do you all think that less people would feel pressured to take calculus and be more likely to take stats, or econ, or something of the sort?
Nora, Given Michael's point about people seeing discrete mathematics courses as a joke, I don't know if choosing any 4 math courses would have helped you avoid the calculus predicament you're in? Something more seems necessary... Which brings me to my next question (which I'd love for you to weigh in on).
Michael, do you think implementation would be as hard as the job of getting people to widen their definition of what can be considered achievement in math? I think you've gotten at a really big aspect of what it would take to gain acceptance. What are barriers to acceptance and what do you suggest for overcoming them?
In answer to Michael's question there are several branches of discrete mathematics which are both deep and useful. Two that come to mind are game theory and graph theory. These are subjects which can be studied at various levels and can certainly be introduced in high school. They differ from calculus in that they don't require an enormous amount of algebraic machinery. Both of these branches have applications to decision making, such as the kind of behavioral economics that Michael suggests. They simply provide the ability to explore these areas in more depth.
I also think that it is a good thing when different subjects overlap. Certainly every college physics course teaches two weeks of calculus, so that students know what velocity and acceleration mean in order to talk about gravity. Any serious biology course today has to do some combinatorics if it is to explain anything about genetics. In fact, I believe that the increased importance and popularity of the life and environmental sciences will eventually make my case.
It seems to me that nearly everyone agrees that math is an important part of life but there is debate on what should be required of students in terms of math. I am in calculus class not by my own choosing but by that of my parents. I have been on the math fast track, which led up to calculus this year, for years. I have had a hard time not only understanding the subject but also in wrapping my head around how I will ever use it. I do not plan on going into the math field, so calculus will most likely never benefit me, besides in applying to colleges. While I don't think that this was the right course for me to take, I definitely believe that I should be taking some math course, just maybe one that will be useful for me later on.
Do you think that there should continue to be required math courses to take to graduate high school or would just taking four years of math suffice? What if you just had to pick any four math classes to take during high school? Do you think that that would be helpful in spiking interest in math?
The main issue logistically here seems to be implentation. Dr. Garfunkel, how would you suggest different branches of math be added into the high school curricula? Earlier on Marie mentioned the topic of real-world applications such as checking books, calculating interest, maintaing a budget, ect. As it happens, at my school anyways, these topics are covered--albeit in a very different setting. Where I'm attending high school all enrolled students must take a semester's credit of economics. The standard year, as recomended by our guidance advisors, to take the course is Junior year. One has two choices. One may take the 'advanced' option, which focuses on preperation for the AP Macro Econ test, or the 'regular' option, which ignores theory altogether in favor of personal economics like the formentioned skills brought up by Marie.
I have no doubt there are highly challenging branches of math outside of calculus, but as it stands the alternatives sometimes already exist (although I would be interested to hear what specificaly has not, but should, be introduced in highschool), but are considred "joke" classes. Because no student in the class is relying on a good education in the subject matter for AP, SAT, or ACT tests, the teacher (in my experience) is often under much less pressure to teach it rigorously, or worse, in some cases at pressure not to teach it rigorously.
Actually, Kim has raised a mathematical point as well, i.e. what do you mean by best. The theory of optimization is almost never mentioned in high school math, but it is crucial in the world of work and in daily life. How do I make the most money? How do I incur the least costs? What's the fastest way to do something? where's the best place to put the fire station? These ideas from discrete mathematics are simply not addressed.
I want to be clear here. I think that learning mathematics and doing mathematics is a good thing. It might even be reasonable for colleges to look at achievement in math as a predictor of future success. But what math? The mathematics we teach in schools today is mathematics (for the most part) that we've already taught machines to do. Adults are teaching children to do perform computations that they themselves never perform - see long division. There is almost no recognition of technology whether it be computational or algebraic. Machines can solve equations and perform routine algebraic manipulations.
Think about other subjects. when you take a 10th grade biology course or a college course called biology 101, you learn something about the different parts of the subject and what a biologist does. The same for chemistry and physics. In mathematics you get a run up to calculus. while calculus is an important branch opf mathematics, it is just that - a branch. If after high school or after a year or two of college mathematics you were to ask a student what mathematics is about, you would likely get an answer that was partial at best and more likely to be total nonsense.
Michael and Annika -- Welcome to Students Speak Out. I am glad you are part of the discussion and contributing so thoughtfully.
Michael -- I, too, hear three commentators in defense of continuous mathematics. But I also hear two questioning it. And I hear 1 saying that better connections between math and life/work could be made in any case. You make a good point, Michael, that perhaps we're all caught up in the game. It can be hard to see clearly while playing...
So, here's a question: To what extent does the current definition of math achievement influence the defense of continuous mathematics?
Marie wrote about the state of Colorado requiring some kinds of math, but not being open to other kinds. I also read Sol's 2nd paragraph below. Their points are that getting into college requires all to meet certain continuous math standards. But there is much evidence that when school is said and done there are many people who are in well-paying careers, and even doing well in colleges or other post-secondary work, who are using other kinds of math. Perhaps poorly because they weren't educated in this kind of math.
IMPORTANTLY: This is not to say we ought to abandon math. This is also not to suggest that we abandon continous math across the board (there are some who will use it and need it). This is to say that all math is not continuous math, and to question whether we can see that as truth.
Semeo made a point that students' views on "what is math learning" comes from what they've been told and surrounded with. I see Semeo's point, and extend it to adults. Among policymakers and education leaders there are a lot of people who think we must solve achievement questions by accepting as given what we currently do. Make tweaks within those givens... We don't have to address our problems that way. Part of why we're here and working on these challenging questions is to examine where we might, as a nation, need to stretch ourselves in the discussion about "what is student achievement".
Some related questions:
1. Do you think there are well-paying jobs that require math, but not necessarily continuous math? Brett has put down some points here that I sense contibute to how people think about this question, which leads me to my next question.
2. What is the balance between "access" and actual experiences of life? The nation's discussion about student achievement is focused a lot on "access". Sol touched on this in his question. Every student should have the opportunity to get into the "best" colleges. Every student should have the opportunity to get into the "best"; most well-paying careers. But, from here is where we start to make leaps. The leaps come at many levels. Can you identify any leaps?
Consider some of these ideas:
--What is "best"?
--How much are plumbers (who use a ton of math) making now that supply is low given the continuous mathematics focus?
--If you were a teen parent (of your own child, of your siblings), would you want access to college admission? Would you want options in math-learning? Why would you want those? If you want both, in what balance? What if you were a teen from a long line of plumbers who stood to inherit a profitable business? Does our prevailing math learning structure assume "one path for all"? Or do we accept there might be other pathways?
--How much is the "access" discussion related to our "adolescence" discussion from a couple of weeks ago?
--Is access to college and post-college entrance really a reason for our nation to ask ALL students to score well in continuous mathematics? Or should math learning for jobs people will be in matter more?
--I suspect we all hear the stats in Brett's post more than we hear the stats in Sol's post. The question that emerges after I read Brett's post is who else uses math and how else. Arguably, many students had access to continuous math and the options Brett outlined. They didn't choose them. At the same time, they're now in college with many choices. Have we now, in the name of access, lost the opportunity to teach them other math skills they might use more in their jobs?
As I said, our job here is to consider new ideas and push out of the box in terms of what could be. That said, ALL answers are respected here. If our current way of doing things still reigns supreme in your mind, by all means say so.
I have no doubt that some very bright mathematics majors do well on entrance exams in those respective fields. It is not so surprising to me, that discipline definitely has the rigor to help prepare its majors for further schooling. Yet, to say continuous mathematics is making better lawyers/doctors seems to me to be stretching the truth. According to tables on national medical school acceptance, a whole host of unrelated fields had statistically high acceptance rates. Of Mathematics majors who applied to a medical school, only 40% were admitted, compared to 50% of Philosophy majors, 50.5% of English majors, 53% History majors, and 53.5 % anthropology majors. The point here is not to begin recommending prospective medical students to read more Dickens or brush up on Leibniz hoping to maximize their chances, but to recognize the only thing these statistics show decisively is that medical schools like diversity among their students—which should hopefully not be news to anyone. The truth of the matter could have easily been guessed, students of all majors can be accepted if they are bright enough, but ultimately, for every one accepted applicant majoring in a non-science field there are three accepted Biology majors.
On a side note, I'd like to take a liberal quote from the paper linked by the guest speaker. I think it very well matches my own opinion and would be interested to hear others' agreement or protest:
"I mentioned that the colleges must act first, if we are to have change at the school level. Colleges can give lip service day and night to any set of ideas, but admissions criteria and college placement tests rule! Students and parents are less interested in what colleges say than what they do. Any alternative path into mathematics must be valued and endorsed at the college level if we are to expect any change at the secondary level. And parents must be brought along so that the change is seen to make sense and to benefit their children."
If a person does partake on the continuous mathematics pathway, what benefits are out there for someone with a major in mathematics? Well, it is statistically one of the best majors for getting high scores on either the LSAT or GMAT (graduate school entrance exams). Math majors taking entrance exams for both law school and medical school do better than their pre-law and pre-med student counterparts (just to provide more specifics on that fun fact). When compared to English majors, math majors make 37.7% more on their starting salaries immediately after college. On that note, math related jobs fall in the top five spots in job satisfaction ratings.
In reading the thoughts of this week's guest and his respective student commentators, I see several points seem to be in consensus among near everyone here. The 'real-world' applicable skills taught by of high school level mathematics are dubious at best and more often, laughable, such as in the case of the cynical student's mock thankfulness described in Annika's post. Nevertheless, among the student commentators, one upheld the current requirement of Algebra II as minimum graduation requirement, one wanted to see the minimum be moved to pre-calc (a class, as a side note, shadier in intent than any other in the high school math curriculum; my school, in the desire to teach a host of techniques necessary in some Calculus courses—trigonometry, vectors, mathematical induction, etc.—gave up the title pre-calculus entirely in favor of the vaguer "Math-Analyses"), and one postulated a four-year requirement of math courses, regardless of the level that the students reach at graduation. This staunch defense of what I believe falls under Dr. Garfunkel's definition of continuous mathematics, despite recognition that much of the math taught in a high school is irrelevant to the average person's life, is a clear sign of what is wrong with the American education system.
Let me be clear: I am a hypocrite. I am in an advanced track in my school's math program. I am not interested in pursuing a career that benefits from higher math, yet I plan on taking all four years of math myself—likely culminating with an AP test or two. I wish this was not the case. I do not blame those who recommend the previously mentioned requirements. They are on to something—that certain math courses, even when not actually used in the career of choice, are nearly essential to success. Like Dr. Garfunkel said, "[students] take the exam to impress the admissions officers at the colleges of their choice, not because they ever intend to do anything with the mathematics they mastered." It is my belief that math, rather than be taught for regularly applicable skills or recommended as a necessity for those who wish to specialize in a study or career that requires it, has become a mere benchmark; just another way for colleges and universities to help determine which students to admit to their gates.
There needs to be change. The system, as it stands, is being clogged by the bureaucratic insistence by school administration that every student achieve a certain level of achievement in fields that, by practical applications anyway, are irrelevant to most. When I was taking an Honors Geometry course, my teacher was taken away mid-year and our class split up among other class periods. Why? All because so many students, poorly taught and inspired by earlier courses, failed Algebra I and had to be moved into a newly created class, requiring a two-hour class block, to prepare them for Algebra with another year of Pre-algebra. My teacher had the lovely assignment of teaching it. I am blessed to go to a good school with high academic standards, but all the same my learning is disrupted by these sorts of shenanigans. I can not help but fear for those less lucky than I am and how their schools handle similar problems.
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Modeling Quadratic Behavior Curriculum:
Math Grade Level:
9-12
Description:
This WebQuest is designed to facilitate the understanding of quadratic functions by associating them with real-life applications. The students will explore various applications on quadratics. They will then be required to model free-fall, an application of quadratics, by creating a stop motion animation. Keywords:quadratics, applications, models, real-life, free-fall, stop motion, animation, mathematics, high school and functions Author(s): Elias Youhanna
Unit Circle Discovery Curriculum:
Math Grade Level:
9-12
Description:
The unit circle is generally a circle used in trigonometry with a radius of one. Here students will learn how to work with the unit circle. They will complete tasks that are designed to cause an understanding of the relationship between right triangle trigonometry and unit circle trigonometry. Students will also use angle measures in degrees and radians interchangeably as well as will be able to recognize and use the reciprocal relationships of the six trigonometric functions. Keywords:Unit Circle, degrees, radians, trig, trigonometry, pre-calculus and algebra Author(s): Rebecca Snider
Using Area and Perimeter Curriculum:
Math Grade Level:
9-12
Description:
This webquest will add the students' knowledge in manipulating the Area and Perimeter to design a house. Keywords:area and perimeter in designing a house Author(s): Marnelie Quines
Number Theory Curriculum:
Math Grade Level:
9-12
Description:
Number theory (or arithmetic) is a branch of pure mathematics devoted primarily to the study of the integers, sometimes called "The Queen of Mathematics". Keywords:Math Number Theory and its Application Webquest Author(s): Remelie Acob
Solving two-step equations Curriculum:
Math Grade Level:
9-12
Description:
Students will be able to solve a two step equation. Students will start with simple one step equations, using correct vocabulary, and find solutions using the correct procedures. They will end by being able to apply prior knowledge for solving a two-step equation. Keywords:Solving two-step equations Author(s): Neil Furnish
Exponential Growth and Decay Curriculum:
Math Grade Level:
9-12
Description:
This wequest will help you determine if a problem is exponential growth or exponential decay by using equations. Keywords:Helpful, Resourceful, Math, Growth and Decay Author(s): De'shawna Mosley
Studying Tessellations Curriculum:
Math Grade Level:
9-12
Description:
This WebQuest is designed to allow students to not only learn about the four types of symmetry, but also create their own tessellation and identify different examples of tessellations in nature. Keywords:pattern, tessellations, math and geometry Author(s): Ashley G
Learning Concepts in Math Geometry Curriculum:
Math Grade Level:
9-12
Description:
Through this WebQuest, all concepts in Math would be accesible to everyone. Worksheets are available here to practice one's Math skills. Keywords:All in Math Geometry Author(s): Donna Marie Boter
Exploring the Math with Automobile Ownership and Driving Data Curriculum:
Math Grade Level:
9-12
Description:
Owning and Operating an automobile is a tremendous responsibility. In this unit, students will examine and work with some of the math behind automobile ownership. Student will explore strategies to pricing a used vehicle, better understand the terminology used in obtaining adequate insurance coverage, and compute data using formulas and unit conversion to gain a better understanding of driver safety. Keywords:automobiles, pricing, safety, insurance and driving Author(s): Angela Rice
SMART HOME APPLIANCES:-for a better tomorrow Curriculum:
Math Grade Level:
9-12
Description:
•Children will collect data information from the Electricity board for the past 20 years for the yearly electricity consumption in their locality. They will also calculate the rate of increase in the consumption of electricity in the city for every 5 years based on the collected data. Observe and assess how the demand of electricity has changed over the years.• Students will then take two home appliances (Refrigerator and Air Conditioner) which are available in many star ratings in the market.... Keywords:DATA ANALYSIS, STATISTICS, FREQUENCY POLYGON, HISTOGRAM and LINE GRAPH AND BAR GRAPH Author(s): Sushirta Sachdeva, Gurpreet Bhatnagar, Anamika Verma
Logical Nonsense Curriculum:
Math Grade Level:
9-12
Description:
Students will be looking at a scene at the tea party, from the famous children's novel, "Alice's Adventures in Wonderland." Students will be looking at logic sentences. Students will have to decide if the sentences are true or false, using converse, inverse and contrapositive definitions. Keywords:Mathematics, geometry, logic, converse, inverse and contrapositive Author(s): Colleen Coon
Mathematics Quest Solutions Curriculum:
Math Grade Level:
9-12
Description:
The WebQuest is designed to assist students in enhancing their techniques in handling topics in Mathematics. The topics that I will be focusing on is Statistics. Keywords:Data, information, gathering, Pie Chart and Bar Chart and Pictograph Author(s): Edward Carter
The Concept Of Pythagoras' Theorem Curriculum:
Math Grade Level:
9-12
Description:
This WebQuest outlines the concept of Pythagoras'Theorem. It shows how to find the length of a side of right angled triangle by finding the square root of the sum of the squares of the other two sides. Keywords:Pythagoras' Theorem, Rectangles, Right- angle Triangles, Area, Formula, Hypotenuse, Adjacent and Opposite Author(s): Monique Bookal
Volume of a Solid of Revolution Curriculum:
Math Grade Level:
9-12
Description:
This WebQuest is designed for students taking AP Calculus. The topic is how to determine the volume of a solid of revolution by using the disk method and the washer method Keywords:calculus, volume, disk and washer Author(s): Will Kellogg
GRAPHS AND CHARTS Curriculum:
Math Grade Level:
9-12
Description:
This webquest is to inform and teach students about the main types of graphs and charts Keywords:Graphs Charts Author(s): Asavari Goberdhan
Unpacking the Unit Circle Curriculum:
Math Grade Level:
9-12
Description:
With this lesson, students will see that working with the unit circle is easy and fun. Keywords:unit circle, trigonometry, pre-calculus and algebra Author(s): James Molloy
Quadratic Formula Curriculum:
Math Grade Level:
9-12
Description:
This Webquest is designed to help students learn the quadratic formula and how to use it to solve problems. Keywords:Algebra 2 and Quadratic Formula Author(s): Jason Wapnick
Roots Can Be Complex Curriculum:
Math Grade Level:
9-12
Description:
Your task in this Webquest will be to gain an understanding of how imaginary numbers can be represented using trigonometry and to demonstrate this understanding by explaining with a powerpoint presentation, a poster or some other means how we can use trigonometry to find all of the nth roots of a complex number. Keywords:imaginary numbers, complex numbers, polar form, square roots, nth roots, de Moirve's formula, trigonometric form and cis Author(s): Kevin Gilliam
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Math Strategies
Taken from "How to be a Great Math Student" By Richard Manning Smith, Ph.D.
Before Class
Begin with an open mind. The most important quality that will affect your success is your attitude.
If you can achieve success in a "difficult" math course, your awareness of that success can inspire you to pursue challenging projects in the future without becoming demoralized.
Recognize that you have control over how well you will do in the course.
Decide now that you will make an honest effort to do well in the course.
Decide now that you will work not merely to pass the course but to do much better than pass.
Decide now that you will persist in working hard in the course until the end, regardless of any setbacks that might occur along the way.
Make an exceptional effort from the beginning. Be over dedicated for the first two or three weeks of the course.
Select your teacher with care. Ask for recommendations from your counselor or tutor.
Buy the textbook early. Get a head start by reading appropriate sections before the course starts.
In Class
Feel free to ask questions in class. Don't put off questions until later.
Attend all classes. Missing even one class can put you behind in the course by at least two classes.
Arrive on time or a little early, get out your notes and homework, and identify any questions you have for the instructor.
Sit in the front and center of the class.
Use one three-ring binder devoted exclusively to math. Keep all your notes and tests in order.
Take a complete set of notes. Compare notes with another person in class to fill in any parts you missed.
Take a tape recorder to class to tape the lecture in addition to taking notes in class.
Studying for Class
Plan your study schedule carefully. Give yourself a number of hours to study math every day.
Choose a time of day to study math when you are especially alert.
Work with a tutor, the instructor, or a study buddy every day.
Read your math notes on the same day that you wrote them.
Read the textbook and understand the concepts before starting your homework.
A math textbook needs to be read slowly. You do not have to read the whole chapter at once. Read through a section, and then go through the examples. Rework the examples without looking at the solution.
Avoid test anxiety with solid preparation.
Begin to prepare at least a week before the test.
Write a list of all the topics the test might cover. List each kind of word problem separately on your topics list.
Find specific problems for each topic on your list. Work out problems one topic at a time, until you are completely confident you understand that topic.
Make up practice tests that have the same form as the test you will take.
Think of ways to distinguish each type of problem from any other. Write a list of similarities and differences. Check that you have accurately identified the correct method for solving each problem.
Aim for getting 100% on the test. Over learn the material. You can't study too much.
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Math at Woodstock Academy
Woodstock Academy offers various mathematics courses to meet the students' needs at all ability levels. Students are not restricted to one sequence of study and may enroll in courses based on teacher recommendation and course prerequisites. Regardless of the level, all mathematics courses at the Academy seek to develop and refine each student's skills in logical thinking, creative problem solving, deductive and inductive reasoning, data analysis, and inquiry.
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Math Calculators
Our math calculators are
interactive and unique. These calculators are best used to check
your work, or to compute a complicated problem. Remember that math
calculators are a problem-solving tool, and should not replace
conventional math skills. Choose one of the calculators
below to get started.
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Introduces the student to numerous mathematical topics and their applications in the modern world. The main emphasis is on developing quantitative reasoning, that is, an ability to read and write mathematics, as well as on developing an appreciation for the role of mathematics in contemporary society. Topics include: graph theory, mathematical modeling, consumer mathematics, descriptive statistics, geometry, and symmetry.
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Synopses & Reviews
Publisher Comments:
This book arose out of the authors' desire to present Lebesgue integration and Fourier series on an undergraduate level, since most undergraduate texts do not cover this material or do so in a cursory way. The result is a clear, concise, well-organized introduction to such topics as the Riemann integral, measurable sets, properties of measurable sets, measurable functions, the Lebesgue integral, convergence and the Lebesgue integral, pointwise convergence of Fourier series and other subjects.
The authors not only cover these topics in a useful and thorough way, they have taken pains to motivate the student by keeping the goals of the theory always in sight, justifying each step of the development in terms of those goals. In addition, whenever possible, new concepts are related to concepts already in the student's repertoire.
Finally, to enable readers to test their grasp of the material, the text is supplemented by numerous examples and exercises. Mathematics students as well as students of engineering and science will find here a superb treatment, carefully thought out and well presented , that is ideal for a one semester course. The only prerequisite is a basic knowledge of advanced calculus, including the notions of compactness, continuity, uniform convergence and Riemann integration.
Synopsis:
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Videos Will Help Students "Ace" Math
02/01/97
Ace-Math, an award-winning video tutorial series, is suited for students trying to grasp fundamental mathematical concepts, parents who want to help their child with their homework, or people who need to brush up on math skills for a specialized license or test.
There are nine separate series, each with many individual videos: Basic Mathematical Skills, Pre-Algebra, Algebra I, Algebra II, Advanced Algebra, Trigonometry, Calculus, Geometry, and Probability and Statistics. Each series except Algebra I consists of 30-minute videotapes explaining various concepts. Algebra I has 16 hour-long videos.
For only $29.95, Ace-Math purchasers get a 30-minute tape with the right to make two back-up copies. This lets educators keep the tape in the learning center and let students check out a copy to take home -- with the added security of another back-up copy!
These innovative tapes have been purchased by institutions such as NASA, the U.S. Coast Guard and IBM, and are in use at institutions such as the Los Angeles Public Library and New York Public Library.Video Resources Software, Miami, FL, (888) ACE-MATH
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more details
The Art of Proof is designed for a one-semester or two-quarter course. A typical student will have studied calculus (perhaps also linear algebra) with reasonable success. With an artful mixture of chatty style and interesting examples, the student's previous intuitive knowledge is placed on solid intellectual ground. The topics covered include: integers, induction, algorithms, real numbers, rational numbers, modular arithmetic, limits, and uncountable sets. Methods, such as axiom, theorem and proof, are taught while discussing the mathematics rather than in abstract isolation. The book ends with short essays on further topics suitable for seminar-style presentation by small teams of students, either in class or in a mathematics club setting. These include: continuity, cryptography, groups, complex numbers, ordinal number, and generating functions.7.5
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Product Description
Review
"Every prospective teacher should read it. In particular, graduate students will find it invaluable. The traditional mathematics professor who reads a paper before one of the Mathematical Societies might also learn something from the book: 'He writes a, he says b, he means c; but it should be d.' "--E. T. Bell, Mathematical Monthly
"[This] elementary textbook on heuristic reasoning, shows anew how keen its author is on questions of method and the formulation of methodological principles. Exposition and illustrative material are of a disarmingly elementary character, but very carefully thought out and selected."--Herman Weyl, Mathematical Review
"I recommend it highly to any person who is seriously interested in finding out methods of solving problems, and who does not object to being entertained while he does it."--Scientific Monthly
"Any young person seeking a career in the sciences would do well to ponder this important contribution to the teacher's art."--A. C. Schaeffer, American Journal of Psychology
"Every mathematics student should experience and live this book"--Mathematics Magazine
Polya prescribes different forms to approaching a problem through some guide questions that a solver should ask ("Is there a related problem"). The exposition is quite short, majority of the book is devoted to a glossary of heuristic terms which prove very helpful. Polya uses common problems in high school geometry to demonstrate his point which make it easily understandable.
I'm glad I have discovered an excellent book on problem solving which would prove indispensable in my programming career. Other programming books mainly demonstrate features of an OS or a computer language but this book goes into the heart of the computer science which is problem solvingI got this book because I saw good reviews and heard that this was a classic...so I got it.
This is the first book that I ever encountered that teaches problem-solving. Further more, it teaches it through the use of heuristics(noun: A commonsense rule (or set of rules) intended to increase the probability of solving some problem). Half of the book cantains what the author calls The Dictionary - which contains a large number of heuristics that a problem-solver can use in his attempt to dissolve a problem. The author also describes in the first few chapters of the book on how to go about solving problems. Really gave me a new perspective on problem solving...Can't wait to apply what I have learned.
It's delightful to see this book is still in bookstores after 60 years, and I can still remember how much fun it was to read it 30 years ago. I came across it recently in a local bookstore, and after poring over it again, I was inspired to write a little review about it.
The most important thing about the book is Polya's little heuristic method for breaking down math problems and guiding you thru the process of solving them. Try to visualize the problem as a whole. Diagram it at first, even if you don't have all the details. Just initially try to get the most important parts of the problem down. Then try to get some sense of the relationship of the parts to the whole. Then tackle each of the component parts. If you get stuck, ask yourself if you could approach it another way, what could be missing, and so on. To this end, the questions at the back of the book are worth their weight in gold.
Polya's little heuristic and methods book is a timeless classic. This and Lancelot Hogben's "Mathematics for the Millions" have done more good for suffering math students than all the the dry textbooks put together that really don't teach you "how to solve it."
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Algebra 1 : Basic Operations On Whole and Rational NumbersMathematics program intended for Middle School pupils (age 12-14) This Title comprises 17 chapters of complete courses completed with exercises covering every subject undertaken. The exercises are corrected step by step using the Evalutel Teaching Method which reconciles the struggle against failure in school and the valorisation of the most talented students. Among the subjects covered: Introduction of negative integers on an axis, addition and multiplication of whole numbers, proof of the sign rules, operations on fractions, prime numbers LCM' and GCD', setting and solving linear equations in one variable.
What's new in this version: New courses, exercises, and
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MATH Developmental CoursesMAT-098 Algebra I, 3 credits
Topics in this course include a review of the basic concepts of arithmetic
and algebra with real numbers, solving first degree equations and inequalities of one variable, graphs
and equations of lines in Cartesian co-ordinates, simplifying algebra expressions with exponent rules
and properties, and operations on polynomials.
Prerequisite: By Placement
MAT-099 Algebra & Applications, 3 credits
This course consists of selected topics that include simplifying and
operations on algebraic expressions and solving equations involving polynomials, rational expressions,
and roots and radicals; and solving systems of linear equations and inequalities.
Prerequisite: MAT-098 or placement
MATH 100-Level CoursesMAT-106 Math for the Liberal Arts , 3 credits
Math for the Liberal Arts is an introduction to non-technical applications of mathematics in the modern world. The course is designed to cultivate an appreciation of the significance of mathematics in daily life and develop students' mathematical reasoning. Subjects include Quantitative Information in Everyday Life, Financial Management, Statistics, and Probability. OLD
Prerequisite: MAT-098 or By Placement
MAT-107 Quantitative Reasoning , 3 credits
This course is an introduction to non-technical applications of mathematics in the modern world. The course is designed to cultivate an appreciation of the significance of mathematics in daily life and develop students' mathematical reasoning. Subjects include Statistics, Probability, Exponential Growth, and Geometry.
Prerequisite: MAT-098 or By Placement
MAT-110 College Algebra, 3 credits
This course contains algebraic techniques, functions, and graphs which are essential in
order to understand and use higher level mathematics. Topics include solving equations and inequalities,
graphing equations and functions, identifying types of functions and characteristics of graphs, and solving
application problems.
Prerequisite: MAT-099 or By Placement
MAT-111 Pre-Calculus, 3 credits
This course is an introduction to algebraic techniques, functions and graphs which are
essential in order to understand and use higher level mathematics in courses beginning with calculus. Topics
include exponential, logarithmic, trigonometric, and inverse trigonometric functions.
Prerequisite: MAT-110 or placement
MAT-114 Elementary Statistics I, 3 credits
This course is designed for students who need an elementary knowledge
of statistics. The basic ideas of descriptive statistical methods are considered, including frequency
distribution, measures of location and variation. It also includes permutation, combination and rules of
probability, together with well-known probability distributions such as binomial, poisson, geometric,
hyper geometric and multinomial.
Prerequisite: MAT-110
MAT-115 Elementary Statistics II, 3 credits
This course is a continuation of MAT 114. Among the topics covered are estimation, hypothesis
testing, design of experiments, chi-square, analysis of variance, regression analysis, covariance
analysis, and nonparametric approaches. Emphasis will be placed on interpretation and use of the
computer software packages. Prerequisite: MAT-114
MAT-117 Finite Mathematics, 3 credits
This course is designed for students in the Social Sciences, The goal of
the course is to give the student a working knowledge of the areas of mathematics that are most
applicable to his or her particular discipline. Among the topics studied will be elementary matrix
algebra, linear programming, logarithms, progressions, and the mathematics of finance.
Prerequisite: MAT-110
MAT-120 Calculus for Life Science and Social Science Majors, 4 credits
This course studies differential and integral calculus with a focus on its
applications to business and economics. Topics to be covered are increments and rates, limits, the
derivative, rules of differentiation, logarithmic differentiation, methods of integration, and applications
of the definite integral to business and economics.
Prerequisite: MAT-117
MAT-121 Calculus I, 4 credits
This is the first course in the calculus sequence designed for students intending to major in mathematics, the natural sciences, and engineering. The topics covered will include: limits and continuity; derivatives rules of algebraic, trigonometric and inverse trigonometric, exponential and logarithmic functions; extreme values and graphing of functions; and applications to optimization, related rate, and initial value problems.
Prerequisite: MAT-111
MAT-122 Calculus II, 4 credits
This is the second semester course in the Calculus sequence designed for students intending to major in mathematics, natural sciences, and engineering. The topics covered will include: integration, geometrical applications, integration techniques, and infinite series.
Prerequisite: MAT-121
MATH 200-Level CoursesMAT-210 Foundations and History of Mathematics ,120 or MAT-221
MAT-211 College Geometry,121 and MAT-213
MAT-212 Mathematical Modeling, 3 credits
This course is an introduction to the development and study of mathematical models. It is
designed in such a way that students from other disciplines will find it useful as a summary of
modern mathematical methods, and mathematics majors will benefit from applications of
mathematics to real life problems. Undergraduate students from the Natural and Social Sciences
will find most of the material accessible because the prerequisite is basic calculus. Prerequisite: MAT-120 or MAT-121
MAT-221 Calculus III, 4 credits
This is the third course in the Calculus sequence designed for students intending to major in mathematics, natural sciences, and engineering. The topics covered will include: power series, parametric equations, polar co-ordinates, vector calculus, partial derivatives, multiple integrals, and applications.
Prerequisite: MAT-122
MAT-222 Differential Equations, 3 credits
Topics include solution methods and applications of first order differential equations, solution of higher order differential equations using the characteristic equation, the undetermined coefficients and variation of parameters methods, existence and uniqueness theorems for initial value problems, and Laplace transforms.
Prerequisite: MAT-122
MAT-240 Combinatorics, 3 credits
Combinatorics is frequently described as the mathematics of "counting without counting." It has
a wide variety of applications in computer science, communications, transportation, genetics,
experimental design, scheduling, and so on. This course is designed to introduce the student to
the tools of Combinatorics from an applied point of view. Prerequisite: MAT-099 or MAT-110
MATH 300-Level CoursesMAT-310 Methods of Teaching Mathematics, 3 credits
This course is a study of strategies, techniques, materials, technology, and current research used in the teaching of mathematical concepts to high school students. Students will review the traditional and contemporary standards involved in teaching mathematics at the secondary school level; develop an awareness of the professional resources, materials, technology and information available for teachers; prepare unit and lesson plans with related assessment procedures on a variety of topics; and acquire teaching experience by taking part in individual tutoring, observation at a high school, and/or presenting lessons at the appropriate level.
Prerequisite: Junior Education MajorCo-requisite: MAT-211
MAT-313 Numerical Methods, 3 credits
Modern computational algorithms for the numerical solution of a variety of applied mathematics problems are considered. Topics include numerical solution of polynomial and transcendental equations, acceleration of convergence, Lagrangian interpolation and least-squares approximation, numerical differentiation and integration.
Prerequisite: MAT-122 and CSC-158
MAT-325 Modern Algebra I
This course covers the following topics: set theory, functions and mappings, permutations, theory of groups, rings and ideals, homomorphisms, integral domains and fields.
Prerequisite: MAT-213 and MAT-214
MAT-341 Mathematical Statistics I, 3 credits
This is a first course in a year-long sequence designed for Mathematics majors. The topics include the algebra of sets, probability in finite sample spaces, random variables and probability functions, including the mean, variance, and joint probability functions, the binomial distribution, and applications.
Corequisite: MAT-221
MAT-342 Mathematical Statistics II, 3 credits
This is the second course in a year-long sequence designed for Mathematics majors. The topics include distribution of random variables, conditional probability and stochastic independence, special distributions including the (t) and (F) distributions, moment generating techniques, limiting distributions, and the central limit theorem.
Prerequisite: MAT-341
MATH 400-Level CoursesMAT-400 & 401 Topics in Mathematics I & II, 3 credits each
These courses cover various topics chosen by the faculty as being of interest to current students in the Mathematics program.
.
Prerequisite: Permission of the instructor
MAT-421 Analysis I, 3 credits
This course is designed as an introduction to the rigorous development of the fundamentals of analysis. The following topics will be covered in this course: analytic and algebraic structure of the set of real numbers, sequences and series of real numbers, limits and continuity of functions.
Prerequisite: MAT-213 and MAT-221
MAT-422 Analysis II, 3 credits
This is the second semester course in a one-year sequence that is designed as a rigorous development of fundamentals of analysis for Mathematics majors. The following topics will be covered in this course: differentiation of functions, integration of functions, infinite series, and sequences and series of functions.
Prerequisite: MAT-421
MAT-423 Introductory Complex Variables I, 3 credits
Topics include complex numbers, analytic functions, contour integration, residues, and power series.
Prerequisite: MAT-221
MAT-475 Seminar I, 3 credits each
This course will focus on involving students in independent projects dealing with current topics or research interests in higher Mathematics. Students will be required to conduct a literature survey, carry out independent investigations projects, prepare a report, and defend their work in an oral presentation.
Prerequisite: Junior or Senior Math Major
CSC 100-Level CoursesCSC-151 Computer Applications, 3 credits
This course is designed to give the students an introduction to applications of computers in the area
of spreadsheets, database management, presentation, structured programming, and web programming.
Desktop software such as Microsoft office as well as a programming language compiler will be utilized
in this course.
Prerequisite: MAT-098 or placement
CSC-152 Introduction to Programming, 3 credits
This introductory programming course is designed for non-computer science majors.
This course introduces the student to principles of computer programming via a visual programming language.
The students will learn to create graphical user interface forms and apply visual programming to problem solving.
Topics will include basic control statements. Event-driven programming will be an integral part of the course.
Prerequisite: MAT-098 or placement
CSC-158 Computer Programming I, 3 credits
This course is the first course in a year- long sequence required for Computer Science majors. It
introduces the student to principles of computer programming via a structured programming
language. The students will write, test, and debug a wide variety of problems drawn from several
disciplines. The course will also address program design and program style. Prerequisite: MAT-110
CSC-159 Computer Programming II, 3 credits
This course is a continuation of CSC-158. The students will use a structured programming
language in problem solving. This course examines advanced features of programming
languages. Topics include file processing, and object oriented and event-driven programming.
As a preparation for CSC-254, this course will also include an introduction to data structures
such as queues and stacks. Prerequisite: CSC-158
CSC 200-Level CoursesCSC-201 Web Programming, 3 credits
This course is an introduction to web design with an emphasis on the scripting languages.
Both server-side and client-side scripting will be studied. HTML programming is an integral
part of the course. Topics include database processing for the web using SQL language and
Internet security.
Prerequisite: CSC-158
CSC-202 Introduction to Computer Animation, 3 credits
This is course is a study of the art and science of computer animation. Both programming and
utilization of animation software will be covered with an emphasis on the latter. The topics
include NURBS and Polygon modeling, rendering techniques, motion path, and introductory applications
of mathematics and algorithms in computer gaming.
Prerequisite: CSC-159
CSC-254 Data Structures, 3 credits
This course will focus on algorithms, analysis, and the use of basic and advanced data structures.
Among the specific data structures covered are strings, stacks, records, linked lists, trees and
graphs. Recursion will also be covered. Sequential and random files, hashing and indexed
sequential access methods for files will be discussed. Finally, some standard computer science
algorithms (sorting and searching) will be discussed. Prerequisite: CSC-159
CSC-290 Special Topics, 3 credits
Computer Scince department may occasionally offer special courses of interest such as COBOL. This course can count as a general elective course toward 120 crredits, but it may not count toward the CSC major curriculum requirements.
CSC 300-Level CoursesCSC-353 Computer Organization and Assembly Language, 3 credits
This course is intended as a first introduction to the ideas of computer architecture-both hardware
and software. Assembly language programming is the central theme of the course. The attributes
and operations of a macro assembler are discussed in some detail. Prerequisite: CSC-254
CSC-354 Database Management, 3 credits
This course will introduce students to the principles of single and multiple applications of database systems.
In addition, it will develop graphical and logical skills that are used to construct logical models of information
handling systems. Topics include normalization and removal of data redundancies, insertion, deletion, and update
anomalies; logical and physical views of data, the entity-relationship model, data description and data
manipulation languages, relational, hierarchal, and network approaches, as well as data security and integrity
and database processing for the web. Prerequisite:CSC-254
CSC-355 Operating Systems, 3 credits
An operating system is a program that acts as the link between the computer and its users. A well
written operating system makes it easy and fun to use a computer. This course will introduce the
student to the principles and concepts of operating systems design, discuss major issues of
importance in the design, and show how different widely used operating systems have
implemented the design ideas. In short, this course will teach what operating systems does, how
it may do it, and why there are different approaches. Prerequisite: CSC-254
CSC-357 Computer Architecture, 3 credits
This course is intended to explore the interface between a computer's hardware and its software.
The interface is often called computer architecture. Starting from the basic ideas of assembly
language programming, this course will give the students an idea of where the software stops and
the hardware begins, and what things can be done efficiently in hardware and how. Prerequisite: CSC-353
CSC-358 Artificial Intelligence, 3 credits
This course is intended to explore the ideas and developments in Artificial Intelligence. Artificial intelligence algorithms in pattern recognition, game playing, image analysis, and problem solving will be covered.
Also included among the topics are rule-based expert systems, fuzzy logic, neural networks, and learning systems. Prerequisite: CSC-254
CSC 400-Level CoursesCSC-451 Computer Simulations 3 credits
This course demonstrates to the student how computers may be used to represent selected
characteristics of real world systems by utilizing mathematical models. The simulation projects
will be done using a simulation software package and a structured programming language.
Statistical analyses are carried out. Prerequisite: CSC-254
CSC-452 Computer Graphics 3 credits
This course develops and applies the mathematical theory of computer graphics. The theory
includes rotation, translation, perspective projection, and curve and surface description. The
course will use a structured programming language. In addition, it will use available commercial
graphic packages. Prerequisite: CSC-254 and MAT-122 and MAT-213
CSC-454 Software Engineering 3 credits
This course will introduce the student to the principles and techniques involved in the generation
of production quality software items. The emphasis will be on the specification, organization,
implementation, testing and documentation of software products. Prerequisite: CSC-254
CSC-455 Mathematical and Statistical Software 3 credits
This course will introduce the student to the currently available mathematical and statistical
software on personal computers in particular, and mainframes in general. Hands-on activities
with software items will form a major part of the course. The student will be trained not only to
use the software items, but also interpret the results meaningfully as related to specific
applications situations. The course is designed primarily for students interested in scientific and
statistical computing and analysis. Report writing will be required on all projects. Prerequisite: CSC-159 and MAT-117
CSC-456 Operations Research 3 credits
Operations Research is a very important area of study which tracks its roots to business
applications. It combines the three broad disciplines of Mathematics, Computer Science, and
Business Applications. This course will formally develop the ideas of developing, analyzing, and
validating mathematical models for decision problems, and their systematic solution. The course
will involve programming and mathematical analysis. Prerequisite: CSC-151 and MAT-117
CSC-498 & 499 Topics in Computer Science I & II, 3 credits each
This course will focus on involving students in independent projects dealing with current topics
of current research interest in Computer Science. Students will be required to conduct a literature
survey, carry out independent investigations projects, prepare a report, and defend their work in
an oral presentation. Prerequisite: Senior Status in Computer Science
Please consult with the department chairperson for any program updates or corrections which may not be yet reflected on this site. Also, please forward suggestions about this page to abarimani@lu.lincoln.edu.
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Mathematics for Elementary School Teachers, 2/e, provides a unique opportunity for students to develop a clear understanding of mathematical concepts, procedures, and processes, to communicate these ideas to others, and to apply them to the real world.The goal is to achieve the optimum balance between presenting a thorough development of mathematical content and presenting it in a way that is understandable by students. The material has been revised so that it powerfully embodies the new Principles and Standards for School Mathematics of the National Council of Teachers of Mathematics.
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In Mastering Algebra I: Course II, students begin by examining rational and irrational numbers and then investigate polynomial expressions and operations. With these skills in hand, they graph parabolas and identify relationships between graphs and equations. Following this analytic investigation, students use a variety of techniques, including applying the quadratic formula, to solve equations in one variable. Throughout the course, the mathematics arises from real-life situations, and students refine and expand their skills through interactions, practice problems, and workout questions.
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Pacemaker Geometry
Help your students grasp geometric concepts Through a clear and thorough presentation, this program fosters learning and success for students of all ...Show synopsisHelp your students grasp geometric concepts Through a clear and thorough presentation, this program fosters learning and success for students of all ability levels with extensive skills practice, real-life connections, projects, and study aids. The accessible format helps students gain the understanding and confidence they need to improve their performance on standardized tests. Margin notes provide links to postulates and concepts previously taught; theorem boxes help students identify the big ideas in geometry. Featured lessons address calculator usage, applications, as well as paragraph proofs and constructions. Pre-taught vocabulary provides students with relevant background. Lexile Level 670 Reading Level 3-4 Interest Level 6-12Hide synopsis
Description:2003. A good used copy with clean pages, usual school markings...2003. A good used copy with clean pages, usual school markings and moderate cover wear.
Description:Good. 0130238376 Shipped from CA. This book may have a school...Good. 0130238376 Shipped from CA. This book may have a school stamp or sticker. Book may contain some highlighting and other markings throughout book and on binding. Book shows backpack wear.
Description:Very Good. 0130238414 MULTIPLE COPIES AVAILABLE-Very Good...Very Good. 0130238414
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Saxon Math 76: Third Edition
You have chosen the Dr. Aarsma's Saxon Math 76: Third Edition Checker. This Checker
is designed to be used with the following set of
three books.
1. Student Textbook
Saxon Math 76: Third Edition
Student Textbook
ISBN:1-56577-153-2
The Student Textbook is divided into 138 lessons, all of which are included in the
Checker. The textbook also contains 6 investigations, supplemental practice problems for remediation, an illustrated
glossary, and a comprehensive index.
2. Homeschool Packet
Saxon Math 76: Third Edition
Homeschool Packet
ISBN:1-56577-156-7
The Homeschool Packet contains step-by-step solutions for all test questions and answers
for textbook questions. This booklet also contains the answers for all supplemental materials.
3. Test Forms
Saxon Math 76: Third Edition
Test Forms
ISBN:1-56577-157-5
The Test Forms booklet provides all the worksheets and tests needed by one student to complete the program. There are 28 tests,
all included in the Checker. There are a large number of Facts Practice worksheets. We recommend use of Dr. Aardsma's Math Drill (see link in navigation bar at left) in place of these worksheets.
The booklet also contains optional student answer forms.
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Discrete Mathematics
An ever-increasing percentage of mathematic applications involve discrete rather than continuous models. Driving this trend is the integration of the ...Show synopsisAn ever-increasing percentage of mathematic applications involve discrete rather than continuous models. Driving this trend is the integration of the computer into virtually every aspect of modern society. Intended for a one-semester introductory course, the strong algorithmic emphasis of Discrete Mathematics is independent of a specific programming language, allowing students to concentrate on foundational problem-solving and analytical skills. Instructors get the topical breadth and organizational flexibility to tailor the course to the level and interests of their students
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Expanding their bestselling curriculum into the younger math years, Math 6 retains the features that homeschoolers have come to love. A textbook written directly to the student, answer booklet and CD-ROM collection with step-by-step audiovisual solutions to every one of the thousands of homework and test problems are included to start your students on the right track to upper-level math. Topics covered include fractions, decimals, percents, simple geometry (e.g. area and perimeter), units of measure, probability, bar and circle graphs, and equation-solving. Math 6 also features a digital gradebook that grades answers as soon as they are entered, providing immediate feedback while the problems are still fresh in the student's minds. 116 lessons and 19 quizzes. Teaching Textbooks Grade 6.
This kit includes:
546-page consumable workbook, softcover and spiralbound
Answer booklet
4 hybrid CD-ROMs
The new hybrid CD-ROMs feature multiple improvements, including:
Easy multiple user setup (built into program)
An area where parents can access all of their students' gradebooks.
An editable gradebook where you can reset a particular lesson(s) without having to uninstall and reinstall.
Do you have to use the computer for Teaching Textbooks?
Can you just use the workbook and write the answers? I do not want to use the computer for Math right now.
Thanks!
asked 1 month ago
by
Anonymous
va
on Teaching Textbooks: Math 6 Kit (Windows & Macintosh)
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1 answer
Answers
answer 1
You can certainly use the program without the CDs, however they are such a good value (120-160 hours of teaching) that the publisher recommends anyone who can afford them should definitely make the investment. Students who use the CDs generally learn more and enjoy the program more than ones who don't.
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Mathematical Tools for Physisists is a unique collection of 18 review articles, each one written by a renowned expert of its field. Their professional style will be beneficial for advanced students as well as for the scientist at work. The first may find a comprehensive introduction while the latter use it as a quick reference. The contributions rangeContains some of the invited lectures presented at the International Conference Analysis, PDEs and Applications, held in Rome in July 2008, and dedicated to Vladimir G Maz'ya on the occasion of his 70th birthday. This title present surveys as well as fresh results in the areas in which Maz'ya gave seminal contributions. more...
This title adopts the view that physics is the primary driving force behind a number of developments in mathematics. Previously, science and mathematics were part of natural philosophy and many mathematical theories arose as a result of trying to understand natural phenomena. This situation changed at the beginning of last century as science and mathematics... more...
Vector analysis provides the language that is needed for a precise quantitative statement of the general laws and relationships governing such branches of physics as electromagnetism and fluid dynamics. more...
Innovative developments in science and technology require a thorough knowledge of applied mathematics, particularly in the field of differential equations and special functions. These are relevant in modeling and computing applications of electromagnetic theory and quantum theory, e.g. in photonics and nanotechnology. The problem of solving partial... more...
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Everyday Math DemystifiedSay goodbye to dry presentations, gruelling formulas, and abstract theories that would put Einstein to sleep, now there's an easier way to master the disciplines you really need to know Everyday Math Demystified has everything you need to know about essential mathematics, including arithmetic, ratios, and proportions, working with money, the International System of Units, perimeter and area, graphs, stock returns, square roots, rates of change, and much more. This unique self-teaching guide helps to decipher number... MOREs and arithmetic, measurements, fractions and graphs, and puts them into the context of real-life situations you're sure to encounter.
Chapter 10. Surface Area and Volume
Chapter 12. Graphs in Three Dimensions
Test: Part Three
PART FOUR: SCIENCE AND ENGINEERING
Chapter 13. Logarithms and Exponentials
Chapter 14. Angles and Distances
Chapter 15. Magnitudes and Directions
Chapter 16. Rates of Change and Accumulation
Test: Part Four
Final Exam
Answers to Quiz, Test, and Exam Questions
Suggested Additional Reading and Reference
Index
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Mathematical Reasoning Writing And Proof
9780131877184
ISBN:
0131877186
Edition: 2 Pub Date: 2006 Publisher: Prentice Hall
Summary: Focusing on the formal development of mathematics, this book shows readers how to read, understand, write, and construct mathematical proofs. Uses elementary number theory and congruence arithmetic throughout. Focuses on writing in mathematics. Reviews prior mathematical work with " Preview Activities" at the start of each section. Includes " Activities" throughout that relate to the material contained in each sectio...n. Focuses on Congruence Notation and Elementary Number Theorythroughout. For professionals in the sciences or engineering who need to brush up on their advanced mathematics skills. Mathematical Reasoning: Writing and Proof, 2/E Theodore Sundstrom
Sundstrom, Ted is the author of Mathematical Reasoning Writing And Proof, published 2006 under ISBN 9780131877184 and 0131877186. One hundred forty one Mathematical Reasoning Writing And Proof textbooks are available for sale on ValoreBooks.com, eleven used from the cheapest price of $53.45, or buy new starting at $112.32
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Physics for High School Students
If you are look at this page now, you are probably a high school student looking for help in physics.
You probably studied other sciences before physics such as biology and chemistry but have never encountered any other science subject that was this math intensive.
Well have no fear!
This Fizzics Fizzle intermediate level physics guide will help you along with some of those difficult problems.
This section assumes that you have a basic background with algebra and trigonometry and that you have the basic knowledge covered in our beginner's guide.
So why is physics so math intensive anyway?
Biology describes life functions; chemistry describes the interaction of matter; but physics describes the fundamental mechanisms of the universe.
These mechanisms, such as why objects fall and why we have electricity, are based on mathematics.
In addition, these mechanisms are the same no matter where you are, whether on earth or on some distant planet across the universe.
Physics tries to descibe all interactions using pure mathematics.
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Offering
10 subjects
including discrete math discrete math discrete math discrete math
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Ron Larson - The Pennsylvania State University, The Behrend College Robert P. Hostetler - The Pennsylvania State University, The Behrend College Bruce H. Edwards - University of Florida
Student Success Organizer This is an innovative study aid, in the form of a notebook organizer, that helps students develop a section-by-section summary of key concepts.
Graphing
Calculator Programs Use these sample calculator programs to solve
many of the applications in this book. The TI-82, TI-83, TI-83 Plus.
TI-89, TI-92 Plus, and Voyage 200 are the calculators featured in
this guide.
Graphing Technology Guide This guide contains keystroke level commands and instructions in order to help you use your graphing calculator as a problem-solving tool.
Historical
Notes These notes provide information relating to
a specific concept or vignettes of individuals who were responsible
for advancements in their fields of study.
Chapter Projects These projects are extended applications with the use of real data, graphs, and modeling to enhance studentsí understanding of mathematical concepts.
ACE Practice Tests Take these newly enhanced ACE quizzes and improve your understanding of the course concepts. These quiz questions include step-by-step tutorial help and are based on problems from your textbook. And since the content is algorithmically generated, you'll get virtually unlimited practice!
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Description:This lesson focuses on finding appropriate non linear functions to model real world phenomena. Various cases are examined before the absolute value function and equations and inequalities are introduced.
This lesson focuses on finding appropriate non linear functions to model real world phenomena. Various cases are examined before the absolute value function and equations and inequalities are introduced.
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Covina ACTIt is necessary to develop a solid foundation of algebra principles here so that later classes will not present problems. Moving up from prealgebra I make sure to focus on the properties of algebra, how to solve equations and more complex problems. Algebra II is a return to an algebra based class, even though it usually follows geometry
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MATH LAB (Math N01 F, Improving Math Skills)
The Fullerton College Math Lab has been in continuous operation since 1967 as an integral part of the
Mathematics and Computer Science Division. This Lab provides students with the support they need to
acquire basic math skills necessary to their timely advancement toward their goals. Students will find
instructors and qualified tutors available for assistance in solving mathematical problems or in
understanding mathematical concepts. Students can also access online math resources in the Lab.
Math Lab Policies and Procedures
The Fullerton College Math Lab is located in the Library/Learning Resource Center, Room 807. All students
using the Lab must be enrolled in Math N01 F, a zero-unit, no cost, non-credit tutoring course. Students
enrolled in Math 010 F, 015 F, 020 F, 030 F, 040 F, 129 F, 141 F, 141 HF and 142 F are eligible to enroll
in this course and use the Math Lab. Your instructor will explain how to access these services at your
first class meeting.
A complete list of Math Lab policies and procedures can be found here.
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Summary: Solving word problems has never been easier than with Schaum's How to Solve Word Problems in Algebra! This popular study guide shows students easy ways to solve what they struggle with most in algebra: word problems. How to Solve Word Problems in Algebra, Second Edition, is ideal for anyone who wants to master these skills. Completely updated, with contemporary language and examples, features solution methods that are easy to learn and remember, plus a self-test....show more...070071343077
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need a good math book
It's becoming more and more likely that whatever I get my bachelor's in, calculus is going to be involved at some point. Which means given my complete ineptitude at math I need to start prepping now in hopes of either CLEPing it before college or at least being ready to take it. The nature of my job lets me have a good amount of study time so I'd like to have a book I could go over during those periods. And as much as I'd like to jump straight in to calculus, one that covered the basics of algebra and geometry would probably be necessary since I barely passed that CLEP.
So, recommend away. For what it's worth I have access to UH's bookstore for one more week in addition to the various stores on my island.
I know you said book, but I'd suggest at least checking Khan academy out even though you can't do it at work. It was much more effective than dealing with any of the textbooks I've ever come across.
As far as one that covers algebra, trig and calc ... I honestly have no idea. The calc book I used was Calculus - James Stewart which was solidly passable (covers through approx calc 2 or 3). For the other stuff, if I find my precalc book I'll toss the name up here, but if I can't then maybe just being directed at pre-calc books will help.
edit: Another option: if you had one, could you use a netbook at work? If you can, can you use audio on it (with headphones maybe)? If so, I'm actually going to suggest a netbook and downloading khan academy (or just queuing up a bunch of lectures) instead of a pair of books (cost will be about the same)
James Stewart is the author when it comes to calculus textbooks. You should be able to pick up an older edition on the cheap. I'm not sure how much trig/algebra it'll cover again, but that stuff is relatively easy to pick up (although you may want a separate book for that).
gonna third Stewart calculus
it is fantastic and covers everything up to calculus three
you should know that you can't teach yourself calc one but by the end of calc II you can teach yourself the rest
it is weirdIt has been. I'm not so much learning from scratch as re-learning because I'm going to jump back in to final year degree level study having put it on hold about six years ago, but I basically needed to go from zero to calculus independently and that's exactly what it was useful forIn terms of books; I would suggest schaum outlines. They are maybe $10 or $15 bucks.
Cheaper if you buy used or any and all libraries will have a copy.
It's very dry; but they are great resources. They are outlines as the name implies
Working though them till you get stuck and find external resources to teach that topic (see below).
I promise you, if you can work though a schaum outline on a topic and know everything in that, you will be light years ahead of any formal class on the topic.
For other books, find whatever is a) cheap and b) college level. There is a ton of "outdated" editions on Amazon for super cheap. Math hasn't changed that much. It's not like there have been any major break thoughts in calculus in the last 10 years' so find some used book for $1.02 or whatever and use that to help with a schaum outlineThis seems like it might be exactly what I'm looking for. Thanks a lot. Hope to get it in timeYep; in the videos he goes over them. But there is no problems or exercises [yet]. I think it's hard to learn without those Also, like I said; it's a great supplementary material, but think it would be difficult to learn just from the videos as he tends to jump around and sometimes leaves holes in topics.
Self studying math will take a ton of discipline. Good luck sir! Remember that you will apply it some day.
I was able to do it to CLEP college math, and that was before I spent hours shut in a room with little to do for months at a time. I know this will be significantly harder but boredom gets me to study all sorts of things I don't like.
I've always found it to be much easier to read and learn from than Stewart.
Having re-read the OP I'd think you need to jump back in with a Precalculus book rather than going straight to Calc I material. You're more likely to sink than swim without a solid knowledge of Algebra basics. If you don't know exponent rules, inverses, function compositions, and exponentials/logs try as you might the Calc I stuff just isn't going to make a whole heck of a lot of sense.
Of the modern books Blitzer is the lowest level precalculus, Stewart is the hardest. I like Dulgoposki (sp?) as well since its got a better description of matrices and trigonometryHaving taken college calc based on the Stewart book, I agree. Half the time the explanations and proofs made no sense until the teacher stepped through them for us.
It's good as a reference book and has lots of problems to test your understanding, but the idea of using it to learn independently strikes me as an exercise in futility unless you're exceptionalYes, this one (in fact, I think I recommended it to you). It's the best maths book I've come across in my travels.
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Microsoft® Mathematics for Educators
Step-by-Step
Microsoft® Mathematics for Educators
Step-by-Step
Familiarize yourself with the interface
When you first open Microsoft Mathematics, you'll see the following elements displayed:
1. The Calculator Pad which includes a number pad and the following button groups: Statistics, Trigonometry, Linear Algebra, Calculus, Standard, and Favorite Buttons.
2. The Worksheet tab is displayed by default, and is where you will do most of your numerical computing. This tab includes both an input and output pane. The input pane gives you the option of using the graphing calculator, keyboard or ink input. When you click buttons on the calculator pad, you construct a mathematical expression in the keyboard input pane.
3. The Graphing tab can be used to create most mathematical graphs. This tab includes an input pane to enter the function equation, inequality, data sets, or parametric equations that you want to plot.
4. Math Tools : On the Home tab, in the Tools group, you'll see buttons for additional math tools:
* Equation Solver to solve a single equation or a system of equations.
* Formulas and Equations to find frequently used equations from science and math, and explore them graphically or by solving for a particular variable.
* Triangle Solver to find the measures of the remaining sides and angles of a triangle when some sides and angles are known.
* Unit Conversion Tool to convert measurements in one system of units to another.
1
1
4
4
3
3
2
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Using the Graphing Calculator
The primary tool in Microsoft Mathematics is a full-featured scientific calculator with extensive graphing and equation-solving capabilities.
You can use it just like a handheld calculator by clicking buttons, or you can use your keyboard to type the mathematical expressions that you want the calculator to evaluate.
Solve an equation:
Our sample problem is to find the area of a walkway that surrounds a...
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Practicing College Learning Strategies, 5th Edition
PRACTICING COLLEGE LEARNING STRATEGIES, Fifth Edition, is a straightforward text with ample exercises and a "Survival Kit" — a quick roadmap that provides an overview of keys to academic success. This roadmap is perfect for the first few days of class, because it helps you gain confidence as a new college student. You're in the driver's seat and this book will teach you how to use the tools that are at your disposal. Structured activities and exercises guide you in the reflection process to make the information personal and useful and to provide practice opportunities.
The Fifth Edition features a revised appendix, Principles of Studying Math. Organized around the learning strategies presented in the text, the appendix gives you concrete strategies for not just getting through your math class, but for becoming completely engaged in the learning96.95
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In a rapidly evolving local and global economy, skills related to mathematical problem solving, scientific inquiry, and technological innovation are becoming more critical for success in and out of school. Thus, Demystify Math, Science, and Technology addresses the need to cultivate these skills in young students so that ingenuity, teamwork,... more...
Now, 2 owls are ready to play. Hippity-hop, bip-bop, jive and sway! Hootenanny, hootenanny--it's time for fun. Hootenanny, hootenanny--the party has begun! In this jazzy ebook with audio, a hilarious cast of owls are working their way from the bottom to the top of the Old Oak Tree for a party on a Saturday night. Along the way these owls sing,... more...
Every year, thousands of students go to university to study mathematics (single honours or combined with another subject). Many of these students are extremely intelligent and hardworking, but even the best will, at some point, struggle with the demands of making the transition to advanced mathematics. Some have difficulty adjusting to independent... more...
Teach lessons that suit the individual needs of your students with this SQA endorsed and flexibly structured resource that provides a suggested approach through all three units. This 'without answers' textbook completely covers the latest National 4 syllabus. Each chapter includes summaries of key points and worked examples with explanatory... more...
Teach lessons that suit the individual needs of your students with this SQA endorsed and flexibly structured resource that provides a suggested approach through all three units. This 'without answers' version textbook completely covers the latest National 5 syllabus. Each chapter includes summaries of key points and worked examples with... more...
Mathematics Education identifies some of the most significant issues in mathematics education today. Pulling together relevant articles from authors well-known in their fields of study, the book addresses topical issues such as:
gender
equity
attitude
teacher belief and knowledge
community of practice
autonomy and agency
assessment... more...
This alternative textbook for courses on teaching mathematics asks teachers and prospective teachers to reflect on their relationships with mathematics and how these relationships influence their teaching and the experiences of their students. Applicable to all levels of schooling, the book covers basic topics such as planning and assessment, classroom... more...
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ustafson and Frisk's Intermediate Algebra: Student Solutions Manual
This manual provides worked-out, step-by-step solutions to the odd-numbered problems in the text. This gives students the information as to how these ...Show synopsisThis manual provides worked-out, step-by-step solutions to the odd-numbered problems in the text. This gives students the information as to how these problems are solved
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This Algebra course will provide an introduction to various topics, including problem solving, variables, graphs and equations, statistics, systems of equations, linear relationships, quadratics, inequalities, rational equations, radicals, and functions and relations. This course will also focus on using multiple representations to make connections. » read more...
This Algebra 2 course will provide an introduction to various topics, including investigations of functions, sequences and equivalence, exponential functions, transformations of parent graphs, solving and intersections, inverses, logarithms, 3-D graphing, trigonometric functions, polynomials, probability and counting, conic sections, series, and analytic trigonometry. This course will also focus on utilizing the graphing calculator and using multiple representations to make connections. » read more...
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yeah, its just a bunch of proofs with hw and a final. the professor is really hard to understand too and he doesnt go by the book so theres no way of going back. he was wicked unclear for the first hw assignment.
Unfortunately, "a bunch of proofs" isn't very informative. I'm sure it's daunting - pure math always is at first. Can you tell us specifically what ideas are covered? Can you link us to the Syllabus?
Generally (pending seeing the syllabus), my gut says it will likely be useful at some point. After all, understanding the reason that a model works is what really lets you understand its applications and possible extensions in actual depth.
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Hello math wizards, I need some urgent help. I have a set of math problems that I need to answer and I am hopelessly lost. I don't know where to begin or how to go about and this paper is due next week. Kindly let me know if you are good in distance of points or if there is a good site which can assist me.
The best way to get this done is using Algebrator . This software provides a very fast and easy to learn technique of doing math problems. You will definitely start loving math once you use and see how effortless it is. I remember how I used to have a hard time with my Intermediate algebra class and now with the help of Algebrator, learning is so much fun. I am sure you will get help with aptitude questions and answers(math) problems here.
I always use Algebrator to help me with my math homework. I have tried several other online help tools but so far this is the best I have encountered. I guess it is the simple way of explaining the solution to problems that makes the whole process appear so effortless. It is indeed a very good piece of software and I can vouch for it.
I'm so happy I got these answers so fast, I can't wait to try Algebrator. Can you tell me one more thing, where could I find this software? I'm not so good at searching for things like this, so it would be great if you could give me a link. Thanks a lot!
Registered: 24.10.2003
From: Where the trout streams flow and the air is nice
Posted: Thursday 04th of Jan 11:52
I am a regular user of Algebrator. It not only helps me complete my assignments faster, the detailed explanations provided makes understanding the concepts easier. I suggest using it to help improve problem solving skills.
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Algebra: Word Problems Help and Practice Problems
Find study help on linear applications for algebra. Use the links below to select the specific area of linear applications you're looking for help with. Each guide comes complete with an explanation, example problems, and practice problems with solutions to help you learn linear applications for algebra.
Study Guides
Introduction to Percent Word Problems
To many algebra students, applications (word problems) seem impossible to solve. You might be surprised how easy solving many of them really is. If you follow the program in this chapter, you will find ...
Introduction to Work Problems
Work problems are another staple of algebra courses. A work problem is normally stated as two workers (two people, machines, hoses, drains, etc.) working together and working separately to complete a task. Often ...
Distance, Rate, and Time
Another common word problem type is the distance problem, sometimes called the uniform rate problem. The underlying formula is d = rt (distance equals rate times time). From d = rt , ...
Introduction to Formulas in Word Problems - Cost and Profit
For some word problems, nothing more will be required of you than to substitute a given value into a formula, which is either given to you or is readily available. The most difficult ...
Mathematical Reasoning in Word Problems
Consecutive Integers that Differ by One
Many problems require the student to use common sense to solve them—that is, mathematical reasoning. For instance, when a ...
Word Problems About Grades
Finding the Grade Needed to get a Specific Average Grade
Grade computation problems are probably the most useful to students. In these problems, the formula for the course grade and ...
Introduction to Money Word Problems
Coin problems are also common algebra applications. Usually the total number of coins is given as well as the total dollar value. The question is normally "How many of each coin is there?"
...
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23 STATE NORMAL SCHOOL.
SUBJECTS OF INSTRUCTION.
MATHEMATICS.
Mr. Steffensen
Mr. Smith.
Mr.
Algebra a. This course affords a thorough and complete treatment of elementary algebra ; including quadratic equations, equations in quadratic form; simultaneous quadratic equations, theory of quadratic equations; ratio, proportion, and variation, arithmetical, geometrical and harmonica) progressions; imaginary numbers; logarithms.
Wells's The Essentials of Algebra is the text book used.
Five hours per week throughout the year.
Algebra b. Review of algebra a, and a brief course in advanced algebra.
Two hours per week throughout the year.
Plane Geometry. This course covers the five books in plane geometry. It aims to familiarize the students with the forms of rigid deductive reasoning, and to develop accuracy of statement and the power of logical proof. Considerable time is devoted to the demonstration of original theorems and to the solution of practical problems.
Two hours per week throughout the year.
Solid Geometry. Wentworth's Solid Geometry.
Two hours per week throughout the year.
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Sign in to YouTube
• General discussion of mathematics Standards • Aspirations for mathematics instruction at higher levels • Greater mastery through focus and coherence • Review of groups involved • General discussion of mathematics progressions • What is and is not included at the elementary level • What happens at middle school • Discussion of migration away from strands and into domains of mathematics
• General discussion of mathematics Standards and goals • Description of domains and increased focus and coherence • Discussion of domains' discrete life spans • General description of the differences for high school mathematics, including real-world applications and modeling
• In-depth description of coherence in mathematics, with examples • Need for mathematics domains to fit together for college and career preparation • Flows of the domains in mathematics; moving into a unified whole • Algebra as an example
• First-year college remediation challenges • Mismatch between higher education and K-12 -- more mastery of fewer topics vs. covering more • Focus as it relates to teachers' needs to build a solid foundation in early grades • Solid early foundation enabling greater success later
• Detailed description of the three domains of numbers and operations (Operations and Algebraic Thinking; Number and Operations in Base Ten; and Numbers and Operations -- Fractions) • Arithmetic as a rehearsal for Algebra
• Careful, prescribed sequence of mathematics that builds skills and mastery for elementary and middle school • Explanation of two reasons for a different approach to high school • How mathematics is better connected and cohesive at high school levels • Modeling and probability/statistics in all math subjects
• General discussion • Clear expectations • Balance between skills and understanding • Higher cognitive demand • More time for teachers to go more deeply with their students • Preparing students to not only "do" the math, but "use" the math
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Writing Math Research Papers: A Guide for Students and Instructors
Book Description: Students often need help learning to write well. This book serves as a student text and a resource for implementing a mathematics research program. The book details how to write a research paper, from pre-writing to presenting the paper. It provides interesting research topics, a bibliography of periodicals and problem-solving books and information about mathematics contests
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p... read moreAn Introduction to Differential Geometry by T. J. Willmore This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.
Introduction to Differential Geometry for Engineers by Brian F. Doolin, Clyde F. Martin Acquaints engineers with basic concepts and terminology of modern global differential geometry. It introduces the Lie theory of differential equations and examines the role of Grassmannians in control systems analysis. 1990Einstein's Theory of Relativity by Max Born Semi-technical account includes a review of classical physics (origin of space and time measurements, Ptolemaic and Copernican astronomy, laws of motion, inertia, more) and of Einstein's theories of relativity.
Elements of Relativity Theory by D. F. Lawden The basic concepts of relativity theory are conveyed through worked and unworked examples in this text, which requires only elementary algebra and emphasizes physical principles and concepts. 1985 edition.
The Principle of Relativity by Albert Einstein, Francis A. Davis Eleven papers that forged the general and special theories of relativity include seven papers by Einstein, two by Lorentz, and one each by Minkowski and Weyl. 1923 edition.
Relativity: The Special and General Theory by Albert Einstein The great physicist's own explanation of relativity, written for readers unfamiliar with theoretical physics, outlines the special and general theories and presents the ideas in their simplest, most intelligible form.
Relativity and Its Roots by Banesh Hoffmann Entertaining, nontechnical demonstrations of the meaning of relativity theory trace development from basis in geometrical, cosmological ideas of the ancient Greeks, plus work by Kepler, Galileo, Newton, others. 1983 edition.
Theory of Relativity by W. Pauli Nobel Laureate's brilliant early treatise on Einstein's theory consists of his original 1921 text plus retrospective comments 35 years later. Concise and comprehensive, it pays special attention to unified field theoriesProduct Description:
physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Starting with an introduction to the various curvatures associated to a hypersurface embedded in Euclidean space, the text advances to a brief review of the differential and integral calculus on manifolds. A discussion of the fundamental notions of linear connections and their curvatures follows, along with considerations of Levi-Civita's theorem, bi-invariant metrics on a Lie group, Cartan calculations, Gauss's lemma, and variational formulas. Additional topics include the Hopf-Rinow, Myer's, and Frobenius theorems; special and general relativity; connections on principal and associated bundles; the star operator; superconnections; semi-Riemannian submersions; and Petrov types. Prerequisites include linear algebra and advanced calculus, preferably in the language of differential forms
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Most linear algebra texts neglect geometry in general and linear geometry in particular. This text for advanced undergraduates and graduate students stresses the relationship between algebra and linear geometry. It begins by using the complex number plane as an introduction to a variety of transforma... read more
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Most linear algebra texts neglect geometry in general and linear geometry in particular. This text for advanced undergraduates and graduate students stresses the relationship between algebra and linear geometry. It begins by using the complex number plane as an introduction to a variety of transformations and their groups in the Euclidean plane, explaining algebraic concepts as they arise. A brief account of Poincaré's model of the hyperbolic plane and its transformation group follow. Succeeding chapters contain a systematic treatment of affine, Euclidean, and projective spaces over fields that emphasizes transformations and their groups, along with an outline of results involving other geometries. An examination of the foundations of geometry starts from rudimentary projective incidence planes, then gradually adjoins axioms and develops various non-Desarguesian, Desarguesian, and Pappian planes, their corresponding algebraic structures, and their collineation groups. The axioms of order, continuity, and congruence make their appearance and lead to Euclidean and non-Euclidean planes. Lists of books for suggested further reading follow the third and fourth chapters, and the Appendix provides lists of notations, axioms, and transformation groups
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0495387916
9780495387916
Study Guide for Stewart/Redlin/Watson/Panman's College Algebra: Concepts and Contexts:Reinforces student understanding with detailed explanations, worked-out examples, and practice problems. Lists key ideas to master and builds problem-solving skills. There is a section in the Study Guide corresponding to each section in the text.
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Rent Study Guide for Stewart/Redlin/Watson/Panman's College Algebra: Concepts and Contexts 1st edition today, or search our site for Scott textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by CENGAGE Learning.
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Imaginary Numbers -- Introduction to Imaginary Numbersm21990Imaginary Numbers -- Introduction to Imaginary Numbers1.12009/01/31 09:51:47.200 US/Central2009/04/16 07:53:20.269 GMT-5KennyFelderKenny FelderKFelder@RaleighCharterHS.orgKennyFelderKenny FelderKFelder@RaleighCharterHS.orgKennyFelderKenny FelderKFelder@RaleighCharterHS.orgAlgebra 2FelderImaginary NumbersTeacher's GuideMathematics and StatisticsAn introduction to the teacher's guide on imaginary numbers.enThis is a fun day, or possibly two days. The first exercise is something that, in theory, they could walk all the way through on their own. But it sets up all the major themes in imaginary numbers.In practice, of course, some groups will have problems, and will need help at various points. But beyond that, almost no groups will see the point of what they have done, even if they get it right. So a number of times in class, you are going to interrupt them and pull them back together into a classwide discussion, and discuss what they have just done. The ideal time to do this is after everyone in the class has reached a certain point—for instance, after they have all done #2 (or struggled with it in vain), you pull them back and talk about #2. All my suggested interruptions are described below.Before you start, remind them that the equation
x2=–1 has no answer, and talk about why. Then explain that we are going to pretend it has an answer. The answer is, of course, an "imaginary" number, so we will call it i. The definitions of i is therefore i=−1 size 12{ sqrt { - 1} } {} or, equivalently, i2=–1.There are two ways to play this. One is to go into the whole "why i is useful" spiel that I spelled out above. The other approach, which is the one I take, is to treat it as a science fiction exercise. I always start by telling the class that in good science fiction, you start with some premise: "What if time travel were possible?" or "What if there were a man who could fly?" or something like that. Then you have to follow that premise rigorously, exploring all the ramifications of that one false assumption. So that is what we are going to do with our imaginary number. We are going to start with one false premise: "What if you could square something and get –1?" And we are going to follow that premise logically, using all the rules of math, and see where it would lead us.Then they get started. And in #2, they get stopped in their tracks. So you give them a minute to struggle, and then walk it through on the board like this.–i means –1•i (*Stress that this is not anything unusual about i, it is a characteristic of –1. We could just as easily say –2 means –1•2, and so on. So we are treating i just like any other number.)So i(–i) is
i•–1•i.But we can rearrange that as i•i•–1. (You can always rearrange multiplication any way you want.)But i•i is –1, by definition. So we have –1•–1, so the final answer is 1.The reason to walk through this is to get across the idea of what I meant about a science fiction exercise. Everything we just did was simply following the rules of math—except the last step, where we multiplied
i•i and got –1. So it illustrates the basic way we are going to work: assume that all the rules of math work just like they always did, and that
i2=-1.The next few are similar. Many of them will successfully get
−25 size 12{ sqrt { - "25"} } {}on their own. But you will have to point out what it means. So, after you are confident that they have all gotten past that problem (or gotten stuck on it), call the class back and talk a bit. Point out that we started out by just defining a square root of -1. But in doing so, we have actually found a way to take the square root of any negative number! There are two ways to see this answer. One is (since we just came off our unit on radicals) to write
−25 size 12{ sqrt { - "25"} } {}=25⋅−1 size 12{ sqrt {"25" cdot - 1} } {}=−25 size 12{ sqrt { - "25"} } {}−1 size 12{ sqrt { - 1} } {}=5i. The other—which I prefer—is to say,
−25 size 12{ sqrt { - "25"} } {} is asking the question "What number squared is -25? The answer is 5i. How do you know? Try it! Square 5i and see what you get!"Now remind them of the subtle definition of square root as the positive answer. If you see the problem x2=-25 you should answer x=±5i
(take a moment to make sure they all got the right answer to #4, so they see why (-5i)2 gives -25). On the other hand,
−25 size 12{ sqrt { - "25"} } {} is just 5i.Next we move on to the cycle of powers. Again, they should be able to do this largely on their own. If a group needs a hint, remind them that if we made a similar table with powers of 2 (21,
22, 23, and so on), we would get from each term to the next one by multiplying by 2. So they should be able to figure out that in this case, you get from each term to the next by multiplying by i, and they should be able to do the multiplication. They will see for themselves that there is a cycle of fours. So then you can ask the whole class what i40 must be, and then i41 and so on, and get them to see the general algorithm of looking for the nearest power of 4. (I have tried mentioning that we are actually doing modulo 4 arithmetic and I have stopped doing this—it just confuses things. I do, however, generally mention that the powers of –1 go in a cycle of 2, alternating between 1 and –1, so this is just kind of like that.)#13 is my favorite "gotcha" just to see who falls into the trap and says it's 9–16.After they do #18, remind them that this is very analogous to the way we got square roots out of the denominator. And this is not a coincidence—i is a square root, after all, that we are getting out of the denominator! You may want to introduce the term "complex conjugate" even at this stage, but the real discussion of complex numbers will come later.Homework:"Homework: Imaginary Numbers"When going over this homework the next day, make sure they got the point. Our "pattern of fours" can be walked backward as well as forward. It correctly predicts that i0=1 which it should anyway, of course, since
anything0=1. It correctly predicts that
i-1=-i which is less obvious—but remind them that, just yesterday, they showed in class that
1i size 12{ { {1} over {i} } } {} simplifies to –i!
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