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Math mechanics - can you crank out a correct answer?
This is a list of mathematical concepts that incoming graduate students should be able to use or at least define. Many students will have had exposure to these concepts prior to arriving at college, but maybe not to the extent that they can actually use them. The list was developed to encompass math concepts that we use in our own research, and hence would want our students to be able to use as well. This list should be considered a work in progress, and feedback and suggestions are encouraged. Items in bold may be important to include as well.
Basics
graphing, graph interpretation
unit conversion
dimensional analysis
back-of-the-envelope, order of magnitude calculations
substitution of variables
solving systems of equations (link to linear algebra)
Functions
Dependent vs. independent variables
Separation of variables
Types of functions (linear, power, exponential, logarithmic)
Periodic (trig) functions
Time series analysis
Multi-variable Analysis
trigonometry
vectors
directional derivatives
gradient, slope
matrices
linear algebra
sensitivity analysis
eigenvalues
Statistics and Probability
Error analysis (mean, median, std deviation, confidence interval)
regression analysis (R2, χ2)
Conditional probability
Accuracy analysis
Probability distributions
Signal processing/pattern recognition
Bayesian stats
Calculus
Ratio
Rate
Sum and integral
Derivative and Partial derivative
Uncertainty:
Students should appreciate that science is intrinsically uncertain. It is important that they be comfortable with the notion that a deterministic description of a state or a process does not exist, and this does not render the knowledge useless. Sources of uncertainty are numerous, and students should be able to identify and quantify sources of error such as experimental design, measurement error, propagation of error, model inadequacy, etc. Students should be able to quantify uncertainty and demonstrate an ability to use the uncertainty estimates to assess the quality of a solution.
Logical analysis
Students should be able to take a problem, devise strategies for addressing the problem, implement strategies with appropriate tools and skills, and work toward resolution of the problem and understanding the results. These are some of the skills that could be used for various parts of logical analysis.
E) What does this mean for local land use? What are the costs/benefits? What is communicated to the general public? What should be published and where?
Ability to learn independently
Students need to gain the confidence to understand that resources are available that enable them to solve problems. Students should practice using outside resources (e.g, books, web, journals) to gain the tools and methods to solve problems. Students need to gain confidence that they can expand their mathematical skill sets on their own. Transferring skills to new problems underlies the whole research process. It can involve solving quantitative problems with mathematical tools that are not traditionally used. We would like students to pick up tools and techniques from textbooks and modify or combine them appropriately to solve a new problem. |
Math for Electricity and Electronics fresh reader-friendly design, MATHEMATICS FOR ELECTRICITY AND ELECTRONICS, 4E is more current, comprehensive, and relevant than ever before. Packed with practical exercises and examples, it equips learners with a thorough understanding of essential algebra and trigonometry for electricity and electronics technology, while helping them improve critical thinking skills. Well-illustrated information sharpens the reader's ability to think quantitatively, predict results, and troubleshoot effectively, while drill and practice sets reinforce comprehension. To ensure mastery of the latest ideas and technology, the text thoroughly explains all mathematical concepts, symbols, and formulas required by future technicians and technologists. In addition, a new homework solution offers a wealth of online resources to maximize study efforts as well as provides an online testing tool for instructors. |
...The section that covers standard grids and coordinate planes is not multiple choice. Math topics include square roots, circumference, ratios and proportions, multiplying and dividing fractions and decimals, volume, angles, exponents, and the Pythagorean Theorem. Students will also need some basic knowledge of the English and metric measurement systems to answer many of the questions |
The two-line display scientific calculator combines statistics and advanced scientific functions and is a durable and affordable calculator for the classroom. The two-line display helps students explore math and science concepts in the classroom.Color: Orange
The two-line display scientific calculator combines statistics and advanced scientific functions and is a durable and affordable calculator for the classroom. The two-line display helps students explore math and science concepts in the classroom.Color: Lavender
The two-line display scientific calculator combines statistics and advanced scientific functions and is a durable and affordable calculator for the classroom. The two-line display helps students explore math and science concepts in the classroom. Ideal for: General Math Algebra 1 & 2 Geometry Trigonometry Statistics Science Display Two-Line Shows entries on the top line and results on the ...
Two-line 249-function scientific calculator offers a two line editable natural textbook display that shows how a problem is solved, not just the answer. Editable feature means that a few keystrokes are all that are usually needed to correct an error, rather than re-keying the entire expression. Calculator includes a full slate of functions including stats, fractions, trigonometry, combination ...
The two-line display scientific calculator combines statistics and advanced scientific functions and is a durable and affordable calculator for the classroom. The two-line display helps students explore math and science concepts in the classroom.Color: Pink. Color Class: PinkSolar 455 function 2 line alpha numeric LCD.Mathematic ,Trigonometry, Science, Statistics, Computer math, and Algebraic 1&2 functions.Never worry about battery running down in a test. ? Easy to read clear function keys combined with the assistance of a step-by-step instruction manual to make learning scientific calculations almost painless!Comes in a protective hard case and back up battery ... ...
TI s 2-line scientific with more advanced features. 1 brand used by students. Easily scroll review and edit current or previous entries. Perform a variety of conversions and advanced calculations. See both equation and answer. Solar and battery powered. Built to last. Slide on case included. Bulk Packaged. Appropriate for:. General Math. Pre-Algebra. Algebra I and II. Geometry. Trigonometry. ... |
Find a Hialeah Gardens, FL StatisticsThus, I changed majors and started taking chemistry, from intro to chemistry, general chemistry, organic chemistry and biochemistry. I also took physics 1 and 2, biology, microbiology, molecular biology and, as I said, alot of math! From remedial math al the way to calculus 2.
...The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deals with finite sets, particularly those areas relevant to business. Research in discrete mathematics increased in the latter half of the twentieth century partly due to the development of digit... |
Summary: * A one semester precalculus course taught at two- and four-year schools.* Takes the unit circle approach to subject.* Shows how to use formulas in the word problems.* Step-by-step explanations, or side-bar comments, are added to examples |
willMathematics Dictionary is a comprehensive dictionary for maths. If you thinking of learning all those terms or formulae in the maths then you should download this app.
Mathematics Dictionary have all the content of maths related keyword and description which is used in all stream.
Main Features: 1. Equipped with quick dynamic search function – The dictionary will start searching for the words while you type. 2. Bookmark – you are able to bookmark the Mathematics Mathematics
In addition, all the terms are listed alphabetically with faster search facility, easy to navigate through entire app.
This app will work as a great pocket resource for Mathematics terms and definitions.
Please rate this application 5 stars if you find this app benefited you embarrasses |
Understanding Mathematics From Counting To Calculus
$24.95
A comprehensive overview of elementary, middle, and high-school mathematics. Intended as a supplement to any math program, this book provides additional math explanation from basic to advanced levels. Emphasis is placed on why problems are solved in a certain manner. Tailored for those who need simplified, easy-to-read additional explanations of math concepts.
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More information about the Applied Mathematics discipline
Applied mathematics deals with a wide range of disciplines in different areas, as science, technology, business and industry. Applied mathematics aims to solve practical problems using mathematical methods and models, such as materials analysis and processing, weather forecasting, financial services, network management and many more tasks. Applied mathematics can include mathematical disciplines such as mathematics of engineering, linear programming, continuous modeling, numerical analysis, statistics, information theory, game theory, etc.
Suggested Studies Mathematics course has been designed for students who want to continue their mathematics studies by delving more deeply into particular aspects of pure and applied mathematics. The modules may well be of interest to mathematically inclined scientists and engineers as well as to mathematicians.
This programme is offered from 2016.
Are you dedicated to working with applied mathematics and using it in practice? Is it your dream to help develop the newest technology used in for instance computers and robots? In that case, Mathematical Engineering is the programme for you.
Students are trained to apply computational methods, mathematical models and advanced datatools to problems and different tasks in society, including i.e. measurements, data analysis, modeling and simulation of systems and processes.
Artificial Intelligence - This course aims to impart the understanding and skills to develop intelligent software applications, such as those involving evolutionary computation and learning. Students will develop skills in specialist areas with clear applications in industry - including data mining, speech processing and machine vision.
Traditionally number theory used the methods of algebra and analysis, to solve problems such as finding the number of integral of solutions of equations. In recent times geometric methods have been playing a more important role. Also, number theory has important applications in areas such as cryptography, theoretical computer science, and numerical mathematics. The ALGANT master course aims at introducing students into the latest developments of this fascinating subject.
The two-year MSc in Statistics programme targets students from universities in Denmark and abroad. The programme is flexible, allowing students to specialise while at the same time acquiring general competencies in statistics. It is also possible to become a PhD student within the area. The MSc in Statistics programme is open to students with a bachelor's degree with at least 60 ECTS credits in statistics.
This MSc full degree programme in Applied mathematics - research profile is offered in English.
To be accepted into the master's programme in Applied mathematics, you need to complete a relevant bachelor programme.
With a Master's degree in mathematics from the University of Southern Denmark, you will be well qualified for many exciting jobs in private or public organizations (industry, financial institutions, schools, universities, administration) or you may choose to pursue a research career.
The programme offers a solid academic foundation in actuarial science, statistics and finance, providing you the skills to become a successful actuary. During the fourth semester you can take a training post in an insurance company or write a thesis or a project. |
97800705224chaum's Outline of Geometry is a revised edition of this very successful solved-problem outline first published in 1963. "Measure of an angle" terminology and metric as well as customary units are used throughout. Dates and amounts, sections on quantifiers, and laws of reasoning have been updated. Analytic geometry and transformational geometry has been added and the section on solid geometry shortened in line with the recent national curriculum changes. The book integrates plane geometry with arithmetic, algebra, numerical trigonometry, analytic geometry, and simple logic. For plane geometry courses in high schools and colleges and for those who want independent self study. 712 Solved Problems are included. Additionally, this book includes hundreds of supplementary |
Models
College Algebra: Concepts and Models provides a solid understanding of algebra, using modeling techniques and real-world data applications. The text ...Show synopsisCollege Algebra: Concepts and Models provides a solid understanding of algebra, using modeling techniques and real-world data applications. The text is effective for students who will continue on in mathematics, as well as for those who will end their mathematics education with college algebra. Instructors may also take advantage of optional discovery and exploration activities that use technology and are integrated throughout the text. A brief version of this text, College Algebra: A Concise Course, provides a shorter version of the text without the introductory review |
Elementary Linear Algebra with Applications - 3rd edition
This book is intended for the first course in linear algebra, taken by mathematics, science, engineering and economics majors. The new edition presents a stronger geometric intuition for the ensuing concepts of span and linear independence. Applications are integrated throughout to illustrate the mathematics and to motivate the student.Edition/Copyright: 3RD 96 Cover: Hardback Publisher: Saunders College Division Published: 09/08/1995 International: No
View Table of Contents
Preface. List of Applications.
1. Introduction to Linear Equations and Matrices.
Introduction to Linear Systems and Matrices. Gaussian Elimination. The Algebra of Matrices: Four Descriptions of the Product. Inverses and Elementary Matrices. Gaussian Elimination as a Matrix Factorization. Transposes, Symmetry, and Band Matrices: An Application. Numerical and Programming Considerations: Partial Pivoting, Overwriting Matrices, and Ill-Conditioned Systems. Review Exercises.
Third Edition. Books in Fair condition will most likely have markings/highlights on pages or possible binding defects. Moderate to heavy shelf wear and creasing on covers and spine. (Z51)
$59.95 +$3.99 s/h
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Bougey's Books CA Vallejo, CA
1995 Hard Cover Third Edition Fair/No Jacket 0030103479 Third Edition. Books in Fair condition will most likely have markings/highlights on pages or possible binding defects. Moderate to heavy shelf...show more wear and creasing on covers and spine. (Z51) |
This updated and refreshed version of CGP's bestselling Revision Guide is the ideal companion to Foundation Level GCSE Maths - it even includes a free online edition that can be used wherever you have internet access. Every topic is explained in a concise, friendly style, with a sprinkling of CGP humour to keep things interesting. Grade information is included to show the difficulty level of each topic, and there are summary questions at the bottom of each page to test you on the important skills. And finally, a unique code is printed in the book that gives you access to the free online digital version (which also includes fully worked answers to all the test questions in the book |
This course would use Discovery and Exploration to assist in the conceptual understanding of Algebra. Problems covered would include several real life examples. Topics include Functions, equations and inequalities, graphical representations, polynomial, rational, logarithmic and exponential functions. We will focus on hands on problem solving and visualization. Several illustrative examples will be covered in class.
State-of-the-art learning environments.
Discovery and Exploration.
Interactive lectures.
Group work and Discussions. Labs.
Recommended preparation
Aim for good Math Placement Test score.
Revise your High School Algebra course. This will form the foundation on which we build this course.
You may seek assistance from the Quantitative Skills Center (QSC) in addition to class work (contact the QSC for more information).
Class assignments and grading
Online Homework and Textbook: College Algebra 4/e (4th Edition) by Judith Beecher, Judith Penna and Marvin Bittinger. Homework will be completed Online using the Pearson (MyMathLab) system (you will need to purchase a registration code for this). Since this registration code includes a complete electronic version of the textbook, there is no need to buy a hard copy of the text unless you insist on having one. If you need a hard-copy, you can get this cheaper bundled with your Pearson student MyMathLab access code.
Attendance Policy: Class participation is important. If you have to miss a class, let me know as soon as possible Narayani Choudhury
Date: 09/12/2012
Office of the Registrar
For problems and questions about this web page contact icd@u.washington.edu,
otherwise contact the instructor or department directly.
Modified:April 19, 2014 |
Algebra and Trigonometry-Stud. Solution Manual - 2nd edition
Summary: Anyone trying to learn algebra and trigonometry may think they understand a concept but then are unable to apply that understanding when they attempt to complete exercises. This innovative book helps them overcome common barriers to learning the concepts and builds confidence in their ability to do mathematics. The second edition presents new sections on modeling at the end of each chapter as well as new material on Limits and Early Functions. Numerous examples are a...show morelso included that provide more detailed annotations using everyday language. This approach gives them the skills to understand and apply algebra and trigonometry US edition as listed. We ship promptly with good, sturdy packaging! Ask for JR with any product questions!
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The Power of
Google
Just Google it. What does that phrase mean to you? You've probably told somebody to "just Google it", or you
might have just Googled something yourself. You want to know the score of the latest baseball game. Just Google it.
What's the weather for tomorrow? Just Google it. How many calories are in my Chick Fil A sandwich? Just Google it. Why
exactly is the sky blue? Just Google it. The possibilities are endless. Google has become so embedded in our everyday lives
that we turn to it for a lot of our day to day information. And why wouldn't we? Google is a powerful tool that usually gives
us the information that we're seeking. And it does it so quickly. So how is Google so quick and yet also so accurate?
The answer behind the power of Google is Algebra II!
This website will show you just how Google uses Algebra II skills to be successful.
Math is actually a science that can teach us so many things. There are many things to discover about
the way numbers work. A lot of times this takes going through experimentation with different
methods and operations. As you'll see later on in the site, this experimentation often leads to
constant revisions as researchers encounter new problems.
Before we can jump into the math though, there are some things we need to review. Like what
is a network? You've probably heard that word before, but what does it mean for Google?
We also need to review some math back from Algebra I: matrices. You can click the START
button when you are ready to begin. If you've already begun and need to get back to your
previous spot, use the navigation bar to jump ahead. |
Math Applets for Calculus at SLU
These following collection of applets are designed for use in
calculus courses. Another page collects applets for courses
below calculus.
Some of the applets were developed at SLU
and some have been developed elsewhere and are included by
permission. If you would like to host the applets locally, please
contact Mike May, S.J.
Applets for
single variable
calculus
Preliminary material
When working through the understanding of various kinds of functions
it is useful to be able to graph a function with parameters a, b, and
c, in the definition of the function, with the parameters controlled by
sliders. Moving the sliders lets the
student explore families of functions. The Families of
Functions Applet is a GeoGebra applet for
looking at the graph of such a family. Similarly, the Family of
Graphs Applet
is
a JCM applet designed to look at families of
functions.
The Function
Composition
Applet is a JCM applet that links together the
graph of two
functions with the graph
of the function defined by the composition of these two
functions. The Visual
Composition
of Functions Applet is a Banchoff applet
that looks at composition of functions by using three variables, with
y=g(x) and z=f(y). The projection of the curve obtained from the
intersection of the two surfaces is then either the graph of f, g, or
fg, depending on the plane it is projected onto.
Graphers
The 2D Grapher Applet
page collects 3 applets for graphing in the plane. One can either
use
the Cartesian Grapher to graph y as a function of x, or use the
Parameterized Grapher to graph x and y as functions of t, or use the
Polar Grapher to graph r as a function of theta
Continuity
The Epsilon Delta
Applet is
is a JCM
applet designed for a visual exploration
of the delta-epsilon
definition of
continuity. The user highlights an epsilon and delta band around a
proposed limit of a function at a point. It is easy to zoom in or
out, and the applet has a nice collection of pre-set examples. A
second applet also looks at the delta-epsilon definition of continuity of
functions in one
variable. It is not as robust as the JCM applet, but it
generalizes to a applet looking at the delta epsilon definition of continuity for functions
in two
variables.
Differentiation
A standard demonstration in calculus in showing that the tangent is
the limit of a series of secant lines. This is implemented in a
number of applets, each of which has it particular strengths. The
Secant
Tangent applet was developed locally. This applet also
computes a numeric derivative and allows the users to plot their guess
of the derivative for comparison. The GeoGebraSecant to Tangent
Applet lets one easily control the base point and the value of delx
in the secant by sliders. The JCMSecant
Tangent Applet
has
a number of nice pre-loaded examples and nice graphics. We also
have a a Banchoff
applet that looks at secant
lines
converging to a tangent line.
The Slopes
and Derivatives applet is a GeoGebra
applet that traces out the slope of the line tangent to a curve as the
base point is moved along the curve. One can compare this to a
guessed derivative. The First
Derivatives Applet
is a JCM applet that ties together the graph of a
function with the
graph of its first
derivative. (The function and its derivative are plotted in side
by side windows.) A slider moves synchronized points on the two
graphs. A JCMSecond
Derivative Applet
ties together the graph of the function with the graphs of the
first and second derivatives. (The function and its first and
second derivatives are plotted in side by side windows.) A slider
moves synchronized points on the three graphs.
The Linear
Approximation applet is a Banchoff Applet
that explores the issue of the region where the tangent line can be
used as a good approximation of a function.
The Newton's Method
page
illustrates the use of tangent lines to find roots of functions.
It also gives examples where the technique fails. This version
focuses
on moving through the method in a step by step fashion. It lets
the
student focus on how the method works. A second applet
using the Newton-Raphson
method lets you compute up to 200 iterations. This applet
lets the student focus on questions of when the method fails.
The JCMChain Rule
applet is a modification of the Function Composition Applet. It
show that the derivative of the composition of functions is the
product of the derivatives taken at the appropriate points.
Similarly, the Visual
Chain Rule
Applet is a modification of the Banchoff
applet for visual understanding of differentiation of a composition of
functions.
Integration
The Riemann Sums
applet is
designed for a visual exploration of Riemann sums and the relation of
these sums to anti-derivatives. It computes 6 different types of
"Riemann sums", plots a numerical antiderivative, and allows users to
plot their guess at the antiderivative for comparison. The JCM Riemann Sums
Applet also
explores
how Riemann sums converge to the definite integral. It does not
have all the features of the local applet, but the graphics are
smoother and faster.
One of the standard applications of the definite integral is to find
the Area
Between Two Curves. This Banchoff
applet helps develop the visual intuition and check limits with the
curves either to the top and bottom or to the left and right of the
region.
A second application is to find the length of a curve with the curve
defined as
the graph of a function.
A third application of the integral is to find the volume of a solid
for special cases. One special case is a solid of
revolution, finding the volume using either the shell method or the
disk method. A second case is a solid defined by a base and a
given
shape for cross sections. We find volume by using geometry to find
the area function for the cross section and integrating the area
function to find volume.
Sequences and Series
A theme of single variable calculus is how the Taylor polynomials
can be used to approximate functions. A GeoGebraTaylor polynomial
applet
lets you compare a function with its Taylor polynomial approximation
and
the error term of the difference. The base point and degree are
controlled by sliders. A locally developed Taylor
Polynomial
Applet is designed to explores the same themes. These applets
also give formulas for the approximating polynomials in terms of
x-x0. A BanchoffTaylor
Polynomial explores the same themes.
The Sequences and
Series
Applet allows for visual exploration of sequences and series.
It plots a geometric, harmonic and exponential series as well as two
user defined series. The user can choose to plot terms, sums, or
ratios. The applet plots 100 points at intervals of up to 1000
steps. It gives values at specified steps.
The Series
Functions
Grapher Applet graphs functions of x that are defined as a
summation over k of terms in k and x. It is useful for exploring
Taylor and Fourier series. The applet allows the user to plot a
function defined by a series, as well as a closed form function for
comparison, along with the difference of the two.
The JCM Series
Grapher Applet
graphs functions defined as series over k of terms in x and k. It
is similar in functionality to the Series Function Applet above.
General
Another nice Applet done by David
Ecks is the xFunctions
applet. It has seven screens, each of which is a nice applet.
Applets for
Multivariable Calculus
Theses applets are designed to be used for visualization
exercises in multivariable calculus. They are local
implementations of an applet written at Brown University for the
calculus class of Tom Banchoff. The applet is used with
permission. The applet seems to work best with Internet Explorer.
Understanding
surfaces and graphs of several variables
The Cross Section
applet
looks at how
the graph of
a 2 variable function is built up from the cross graphs of the cross
sections, which are each graphs of single variable functions.
The Level Curve
applet builds
up the
graph from its level sets. It connects the contours of a three
dimensional surface with the contour graph obtained by looking down the
z-axis. (Currently, this one has bugs with Safari.)
The DirectionalSlice
applet lets
you take a cross section of a surface that includes a given line
segment on the x-y plane.
The 3D Grapher Applet
page collects 3 applets for graphing in 3-space. One can either
use the Cartesian Grapher to graph z as a function of x and y, or use
the Cylindrical Grapher to graph r as a function of theta and z, or use
the Spherical Grapher to graph r as a function of theta and phi The Parameterized Surface Applet
lets you see the graph of a parameterized surface. As we did
with the cross section applet above, we can also see a wire frame
constructed from the graphs of lines in the domain.
The Projections, Dot and Cross Products
Applet is a Geometer's
Sketchpad® Applet. It lets you
specify two vectors by dragging their endpoints. It then gives
bit a visualization as well as numerical data for the projection of one
vector on another, their dot product of the two vectors, and the cross
product of the two vectors. with their sum and difference and the
vectors
measured both in polar and rectangular coordinates.
Two similar applets are available to look at cross products.
They differ in the mechanism used to control the vectors.
The first Cross Product
applet gives a visual approach to cross products of vectors in 3-space
with the coordinates of the two vectors controlled by sliders.
The second Cross Product
applet gives a visual approach to cross products of vectors in 3-space
with the coordinates of the two vectors controlled by text boxes.
Continuity in several
variables
The Continuity
applet looks at
a
visualization of the definition of continuity as it applies to
functions of two variables. This is a generalization of an applet
that looks at single
variable
continuity.
Differentiation
of functions of several variables
The Partial
Derivatives applet finds partial derivatives as tangent lines to
the curves in slices where x or y is held constant.
The applet Tangent
Planes,
connects
the tangent lines of the x and y cross sections at a point to the
tangent plane to the surface at that point.
The Line Integral
Applet explores a visualization of the line integral of a vector
field over a parameterized curve.
The Flux Integral
Applet explores a visualization of the flux integral of a vector
field over a parameterized surface.
Several of the applets above are referred to as JCM
applets.
This refers to an NSF sponsored project, the Java
Components for Mathematics project at Hobart and William Smith
Colleges., that
produced a series of JCM-Applets
that are quite useful for calculus and pre-calculus.
Several of the applets above are referred to as Banchoff
applets.
This refers to work done at Brown University under the direction of Tom
Banchoff. The project produced a demonstration applet that is
quite
flexible and can be configured for demonstrations and projects.
The
configurations can be saved as a set of parameters used in calling the
applet. These applets are collected on the Banchoff Applet Page.
Several of the applets above are referred to as Geometer's Sketchpad® Applets. That means that the
applets were created with Java Sketchpad®, a component of
Geometer's
Sketchpad®. More accurately, they were created as a set of
parameter's that can be used to call the Sketchpad® Applet in a
particular configuration. These applets are collected on the Geometer's
Sketchpad® Applets page.
Several of the applets above are referred to as GeoGebra
Applets. That means that the
applets were created with GeoGebra, an open source program created by
Markus Hohenwarter. The program is available from
They applets are more precisely configurations of a master
applet. These applets are collected on the GeoGebra Applets page. |
0840049420
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Mathematics:Master the fundamentals of discrete mathematics and proof-writing with MATHEMATICS: A DISCRETE INTRODUCTION! With a clear presentation, the mathematics text teaches you not only how to write proofs, but how to think clearly and present cases logically beyond this course. Though it is presented from a mathematician's perspective, you will learn the importance of discrete mathematics in the fields of computer science, engineering, probability, statistics, operations research, and other areas of applied mathematics. Tools such hints and proof templates prepare you to succeed in this course.
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Rent Mathematics 3rd edition today, or search our site for Edward A. textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by CENGAGE Learning. |
I am looking for studies which compare students who did not receive mathematical education beyond basic mthematics and those that learned maths upto introductory calculus, with the assumption that both groups recieved similar education in other subjects such as social sciences and natural sciences uptil average high school standards. Has it been found that there is a quantifiable difference in understanding, analytical ability etc between the two groups? In other words, what evidence is there that learning maths beyond the basics has benefited them at the stage of just having completed high school?
I understand a basic science curriculum in this case to include a little mathematics, which both groups should know, and for this purpose a notion of solving linear equations (and hence elementary algebra) besides arithmetic is included in basic mathematics. However, there is no trigonometry or geometry in a basic mathematics course, and in general a person learning basic mathematics knows no more then is the essential to understand basic science.
That is not what I meant. I mean whether there is a benefit uptil the stage of end of their high school? Have they been found to have better understanding, better analytical abilities etc at that stage? Also, I am really looking for empirical studies.
–
ShahabSep 1 '13 at 5:52
@Shahab I am not sure I understand your question. How do you study social science/natural science without math education beyond basic arithmetic?
–
scaaahuSep 1 '13 at 5:53
@scaaahu: Why not? If you know basic arithmetic isn't it possible to learn study history, geography, civics, literature, science etc uptil high school level? Where does one use polynomial division in a history class?
–
ShahabSep 1 '13 at 5:57
1
@Potato: Not only quantitative ability, but also qualitative abilities such as decision making, critical thinking etc. In general what does mathematical training give exclusively (other then a knowledge of the subject), which a non mathematical trained person doesn't have?
–
ShahabSep 1 '13 at 6:19 |
Schaum's Easy Outlines : Trigonometry - 02 edition
Summary: Boiled-down essentials of the top-selling Schaum's Outline series 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 in this series is a pared-down, simplified, and tightly focused version of its predecessor. With an emphasis on clarity and brevity, each new title features a streamlined and ...show moreupdated format and the absolute essence of the subject, presented in a concise and readily understandable form.
Graphic elements such as sidebars, reader-alert icons, and boxed highlights stress selected points from the text, illuminate keys to learning, and give students quick pointers to the essentials.
Designed to appeal to underprepared students and readers turned off by dense text
Cartoons, sidebars, icons, and other graphic pointers get the material across fast
Concise text focuses on the essence of the subject
Delivers expert help from teachers who are authorities in their fields |
part of the market-leading Graphing Approach series by Larson, Hostetler, and Edwards, Precalculus with Limits: A Graphing Approach, 4/e, provides both students and instructors with a sound mathematics course in an approachable, understandable format. The quality and quantity of the exercises, combined with interesting applications, cutting-edge design, and innovative resources, make teaching easier and help students succeed in mathematics. This edition, intended for precalculus courses that require the use of a graphing calculator, includes a moderate review of algebra to help students entering the course with weak algebra skills. |
Secondary Solutions
Curricula Proven to Help All Students Succeed in Math
Carnegie Learning Blended Math Curricula is different; our combination of task-based math textbooks and engaging Cognitive Tutor software is being used across the country to help secondary students achieve success in math. It's a better way to teach, and a better way to learn. And we have over 20 years of research to prove it. With our help, your students can achieve true mathematical understanding, and they'll actually enjoy doing it.
Curricula Offerings
Program Features
Our unique approach involves splitting instructional time between student-centered instruction in the classroom and self-paced learning using our adaptive software. Students spend 60% of the time in the classroom using our textbooks in an approach that involves task-based lessons, collaborative learning, and real-world problems and contexts. The remaining 40% of students' time is spent learning via our Cognitive Tutor software, which offers the most precise method for differentiating instruction available |
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Included are two complete lesson plans guiding students to use the Slope Formula to find the slope of a line. The first lesson uses the formula to find the slope when given two ordered pairs. The second lesson includes finding the slope from the graph of a line.
The lessons include an opening question, minilesson with guided steps through the process, examples, class activities and a worksheet for homework. Answer keys included.
Common Core Standards for 8th grade and High School Algebra included on the cover page |
Number Theory Through Inquiry - 08 edition
Summary: Number Theory Through Inquiry is an innovative textbook designed to help students learn introductory number theory through guided activities and sets of exercises. The book's carefully arranged sequences of challenges allow students to examine methods and discover ideas on their own. Along the way, students develop theorem-proving skills and an understanding of key ideas in the mathematical study of numbers.
Number Theory Through Inquiry is meant to be used...show more with an instructional technique variously known as inquiry-based learning, guided discovery, or the Modified Moore Method. When combined with this participation-driven teaching style, Number Theory Through Inquiry can help students learn to think independently, depend more on their own reasoning, and develop the central ideas behind basic number theory on their own. Students learn that they themselves can create important ideas and effectively handle complicated problems.
Number Theory Through Inquiry is appropriate for a proof transitions course, an introductory abstract mathematics course, or independent study. Whether you're a student, teacher, or just a math enthusiast interested in exploring the mathematical realm of numbers, Number Theory Through Inquiry is perfect for |
Students will solve exponential function problems, graph exponential functions, find the value of logarithms, determine future value, and compound interest. In this Pre-calculus lesson, students will use the properties of logs to solve test problemsIn this radiation and temperature activity, students use 2 methods to derive the Wein Displacement law that shows the relationship between the temperature of a body to the frequency where the Planck curve's value is at its maximum. Students are given data of the temperatures and wavelengths for 12 different bodies and they find a formula that fits the data.
In this precalc lesson, students write out definitions, identify functions, solve integrals and derivatives and graph trig functions as they relate to angles. This is a final exam for precalculus. There are 80 questions on this exam.
Twelfth graders examine the Taylor Series. In this calculus activity, 12th graders explore the representation of a function as an infinite sum of terms calculated form the values of its derivatives at a single point, hence the Taylor Series. Students use a TI-89 to explore the patterns and the command to compute the Taylor series.
Students explore a linear, a parabolic, and a log function. In this Algebra II/Pre-calculus instructional activity students investigate the graph a line, a parabola, and a log function. Students examine the three graphs as they compare and contrast the three in a problem solving context.
For this Calculus worksheet, students use a graphing calculator to boost their understanding of functions and their graphs as they examine the properties of curves. The forty-two page worksheet contains one hundred problems. Answers are not provided.
High schoolers investigate linear, quadratic and exponential equations using the TI calculator. They identify relation and functions using ordered pairs, graph the data, analyze the data, and relate it to real-world situations.
Learners choose a subject of interest and collect related statistical information. They use a graphing calculator to derive the equation for curve of best fit for the data and then predict future trends.
In this integral instructional activity, students estimate the definite integral and find the derivative of functions. They graph functions and determine the range of the velocity. This three-page instructional activity contains approximately 40In this differentiating special functions instructional activity, students solve and complete 5 various types of problems. First, they differentiate each of the given functions. Then, students complete the table using a calculator and plot the points on a graph. In addition they find the slope of the function at a given point.
Students examine the problem of space pollution caused by human-made debris in orbit to develop an understanding of functions and modeling. It allows students an opportunity to use spreadsheets, graphing calculators, and computer graphing utilities.
Students, working on their GED, examine the steps used to resolve the unknown sides of a right triangle. They express the square root function as an exponential function and derive the distance formula using principles of geometryLearners create functions from graphs. In this movement with functions lesson plan, students use motion detectors and create graphs from the movement. Afterward, they describe graphs and write equations for the graphs.
Here's a real-world lesson using a business simulation. Two business accounts are used to find slope and intercept functions. The class graphs and interprets the information to find a break even point. There are plenty of worksheets and assessments included in this lesson |
Teach Algebra:Solve Equations - MATTeaching the skills used to solve single variable equations in Algebra in a fun and meaningful way will set up your students for success. This course, and the accompanying AIMS interactive digital text is the second in a series focused on algebraic principles using hands-on activities. Primarily focused on the Common Core standard 7.EE, these lessons use three big ideas along with activities, video demonstrations and animations to reinforce the concepts. Teachers will reflect on the lessons based on concepts from the National Board for Professional Teaching Standards in an effort to bridge content and pedagogy |
GCSE Mathematics A specification's flexible structure supports your learners' growing understanding of mathematical concepts, giving you real choice to move your learners between routes - unitised, staged or linear - in response to their needs. Your learners will develop analytical and problem solving skills in a range of contexts, which they can take into employment or further study. |
The book "High School Calculus" covers the concepts involved in the various topics of this subject. A few selected problems are solved after each chapter, to aid the understanding of the... More > student. The book finishes with a collection of problems that the student must practice on, to gain expertise. The student is expected to make an honest attempt to solve the problems before looking at the suggested solutions. In doing so, the depth of understanding in the subject improves. Mathematics is not a spectator sport. It requires patience, perseverance and practice. The level of expertise in the subject in some sense is directly proportional to the number of problems solved by the student. The term "solved" is used to imply accuracy of thought, stringing together intermediate steps and accuracy of the final result. In a way, this term refers to the quality of the means to achieve the end goal for each problem. This book is intended to be a comprehensive self-study guide for the students in middle & high schools.<This popular second edition of High School Math Made Simple was specially formatted for e-book readers like the Nook, iPad and Kindle.
The text and graphics help students navigate through all areas... More > of high school mathematics including essential math skills (pre-algebra), algebra 1, geometry, algebra 2, statistics, trigonometry, and calculus.
High School Math Made Simple was written utilizing the principles and standards for school mathematics published by the National Council of Teachers of Mathematics (NCTM). These standards are the cornerstone of basic math principles that ensure the highest quality of learning for students. The rear of the book includes a Scope and Sequence of our content to NCTM's Guidelines.
This book is specially designed and formatted for reading on an e-book reader like the Kindle, Nook and iPad.< Less
Middle schoolers are like no one else. They are not little adults; neither are they taller primary schoolers. Teaching middle school is the most difficult teaching assignment of all. It is also the... More > most rewarding.This book was written to help parents and their middle schoolers successfully integrate into the wonderful world of middle school.< Less
In this book I will be giving advice to graduating high school students or nearly graduated high school students that should help them with their life. I know how hard it is for students who... More > graduate from high school not knowing what to do when they get out or when they are nearly going to get out of school. Their lives have been so regulated from day to day and now they are set free into the real world.
Clearly it will be more difficult for people graduating high school during this time, when the United States is in a recession and jobs are being shipped overseas. What is a student to do, to make their life better, when so many forces are working against them, which keep them from their American dream?
In this book we will be discussing the various aspects of life: education, work, family life, and finances. My goal is to help graduating students avoid the pitfalls that are laid out before them. It is too easy for a person to fall in these pitfalls and my goal is to try to prevent it.< Less
So you've made it through Young Women's and graduated from high school... now what do you do? You get married and have lots of babies, right? Well...
In this insightful book, Lenore... More > Craven helps young women figure out what to do during those pivotal years following high school.
Lenore recommends several Good Girl Goals that will help young women develop into adulthood personally, religiously, and socially. By following these goals, young women will attain a healthy balance in these areas and feel ready to tackle life's top priorities: getting married in the temple and having a family.< Less |
Multiple Representations
On one hand, GeoGebra is a Dynamic Geometry Software (DGS) that supports constructions with points, lines and all conic sections. On the other hand, it provides typical features of a Computer Algebra System (CAS) such as function plotting, root finding, derivatives and integrals. That's why we call GeoGebra a Dynamic Mathematics Software (DMS) for geometry, algebra and calculus.
There is no other way of gaining access to the mathematical objects but to produce some semiotic presentations. [...] There is no true understanding in mathematics for students who do not incorporate into their cognitive architecture the various registers of semiotic representations used to do mathematics. (Duval, 1999)
The basic idea of GeoGebra is to provide two representations of each mathematical object in its algebra and graphics windows. If you change an object in one of these windows, its representation in the other one will be immediately updated. Let's take the example of a quadratic polynomial f and its tangent t through a given point A. Below you see this situation in GeoGebra. When you drag point A with the mouse along the graph of f, its tangent t will change and adapt to your modifications. In the algebra window you will see how the representations of the affected objects are updated accordingly.
Brief Descriptions
Graphics window (right):
Click and drag point A with your mouse.
Click and drag function f with your mouse.
Click on the icon to reset the applet to its initial state
Algebra window (left):
Double click on point A, change the x-coordinate and press Enter.
Click on point A and press the right and left arrow keys on your keyboard.
Right click (Mac OS: apple click) on tangent t to change its equation to "Equation ax + by = c" or "Parametric Form". |
yes but be careful as they do not include the current year's text which is embargoed, although you get the title, and also they do not seem to include graphs and other visual materials which students might need . The text part is brillant though and you can just direct students to this year's hard copy. |
translation of Hilberts "Theorie der algebraischen Zahlkörper" best known as the "Zahlbericht", first published in 1897, in which he provides an elegantly integrated overview of the development of algebraic number theory up to the end of the nineteenth century. The Zahlbericht also provided a firm foundation for further research in the theory, and can be seen as the starting point for all twentieth century investigations into the subject, as well as reciprocity laws and class field theory. This English edition further contains an introduction by F. Lemmermeyer and N. Schappacher.
Editorial Reviews
Language Notes
Text: English (translation) Original Language: German
From the Back Cover
This book is an English translation of Hilbert's Zahlbericht, the monumental report on the theory of algebraic number field which he composed for the German Mathematical Society. In this magisterial work Hilbert provides a unified account of the development of algebraic number theory up to the end of the nineteenth century. He greatly simplified Kummer's theory and laid the foundation for a general theory of abelian fields and class field theory. David Hilbert (1862-1943) made great contributions to many areas of mathematics - invariant theory, algebraic number theory, the foundations of geometry, integral equations, the foundations of mathematics and mathematical physics. He is remembered also for his lecture at the Paris International Congress of Mathematicians in 1900 where he presented a set of 23 problems "from the discussion of which an advancement of science may be expected" - his expectations have been amply fulfilled. |
A Textbook of Engineering Mathematics (Volume II) is a comprehensive text for the students of engineering
Key features Each topic is treated in a systematic and logical manner Incorporates a large number of solved and unsolved problems for each topic Elucidates all basic concepts with the aid of pedagogical features such as Introduction, Definitions Includes question papers from previous years U.P.T.U. examinations. Several Worked out examples drawn from various examination papers of reupted Universities, as well as I.A.S., P.C.S. competitions. An exhaustive list of "objective type of questions" fill in the blanks and matching the answers type of problems are also provided at the end of each chapter.
Get up to speed on Cocoa and Objective-C, and start developing applications on the iOS and OS X platforms. If you dont have experience with Apples developer tools, no problem! From object-oriented programming to storing app data in iCloud, the fourth edition of this book covers everything you need to build apps for the iPhone, iPad, and Mac.
Random-Like Multiple Objective Decision Making ( Rapidgator )
What are the random-like phenomena that can be found everywhere in real-life world? When carrying out a random sampling survey on the traffic situation, we often obtain some descriptive results such as approximately expedite, a little crowded and so on, therefore, the average level should be regarded as the random fuzzy phenomenon, which is one of the random-like phenomena.
Mathematics for 3D Game Programming and Computer Graphics, Third Edition ( Rapidgator )
Applied Basic Mathematics (2nd Edition) ( Rapidgator )
With an emphasis on real world applications, Applied Basic Mathematics, Second Edition, provides students with a new and refreshing perspective on basic math. Paired with a system of structured support, authors Clark and Brechner consistently asks student to relate, reinforce, and review as they learn. This text provides professors with a dynamic way of teaching the material and an approach that encourages students to dive into the math!
Sources in the Development of Mathematics ( Rapidgator )
Sources in the Development of Mathematics Download Filehost: Rapidgator.net : Series and Products from the Fifteenth to the Twenty-first Century by Ranjan Roy English | ISBN: 0521114705 | 2011 | 994 pages | PDF | 5,1 MB
The discovery of infinite products by Wallis and infinite series by Newton marked the beginning of the modern mathematical era. It allowed Newton to solve the problem of finding areas under curves defined by algebraic equations, an achievement beyond the scope of the earlier methods of Torricelli, Fermat, and Pascal. Newton and his contemporaries, including Leibniz and the Bernoullis, concentrated on mathematical analysis and physics.
Mathematics Teaching & Learning in K-12: Equity and Professional Development ( Rapidgator ) |
hi my name is matt and i want to join the military but first i need to take the asvab. i did not finish high school so my math skills are out of date. (i have my GED) anyway i have the most difficulty with word problems and what processes to use and what order to put them in? any help would be great.
Once you've studied the lesson, follow the links at the end of the lesson, which lead to explanations of common sorts of word problems (such as "uniform rate" and "coin" problems). This should give you a good start!
Note: There are books which cover specifically just algebra word problems, such as this book. Your local library or big-box book retailer should have this or similar resources available. Check 'em out! |
bravo!
Bravo is a comprehensive calculator utility for Windows 95. It resembles a standard hand-held calculator and contains virtually all the functions you could possibly want in a calculator. It includes all the normal mathematic and trigonometric, as well as a built-in calendar. You can convert any number between 120 different measurement units grouped in 12 categories, compute all the values of a triangle (sides, angles, area, height) from any three known values, do vectorial and complex calculations, and more. Bravo is even multilingual and can be set to display in English, Italian, German, or Spanish.
Inequality2 This program is intended for students studying intermediate Algebra. It involves step-by-step discussion on absolute value inequalities with illustrations and diagrams.
Visual Kalman Filter 2.8 "Visual Kalman Filter " is a visual math tool to simulate Kalman filter for linear or nonlinear system. Only three steps you need do,and you'll get the curve and the estimated results.. |
TI-30XS MultiView: Texas Instruments.
[ILLUSTRATION OMITTED]
Hardware, $15.99
The TI-30XS MultiView is a great choice for general math, geometry,
algebra and higher math, as well as science classes, where visualizing
equations is key to student understanding. Students can enter and view
common notation using the MathPrint mode, display as many as four lines
of calculations, scroll through previous entries looking for Looking for
In the context of general equities, this describing a buy interest in which a dealer is asked to offer stock, often involving a capital commitment. Antithesis of in touch with. patterns,
and toggle To alternate back and forth between two states. toggle - To change a bit from whatever state it is in to the other state; to change from 1 to 0 or from 0 to 1. This comes from "toggle switches", such as standard light switches, though the word "toggle" actually refers to to see different outcome representations. Additional features
include easy to read pull-down menus, including mode settings centrally
located, and a table feature for automatically or manually exploring
(x,y) values for a given function. Fraction computation is in familiar
textbook format, and scientific notationscientific notation, means of expressing very large or very small numbers in a compact form that is easy to use in computations. In this notation, any number is expressed as a number between 1 and 10 multiplied by a power of 10 that indicates the correct position of can be viewed using the proper
superscripted exponents. TI's education site offers a free PDF (Portable Document Format) The de facto standard for document publishing from Adobe. On the Web, there are countless brochures, data sheets, white papers and technical manuals in the PDF format. guidebook downloaded.
COPYRIGHT 2007 Professional Media Group LLC
No portion of this article can be reproduced without the express written permission from the copyright holder. |
TextBook. Class 4. Jayashree Ramadas. Author and primary science co- ordinator. Team for ...Oxford University Press is a department of the University of Oxford. It furthers the .... The School of Mathematics, TIFR, who allowed use of their computer facilities ..... A design of a calendar is given on pages 3-7 in your WorkBook.
The Faculty produces a booklet Study Skills in Mathematics which is distributed to .... Candidates placed in the first class will have demonstrated a good command and secure understanding of .....Oxford University Press 1977 (£22.50 paper- ...7. ANALYSIS I. 24 lectures, Lent term. Limits and convergence. Sequences and ...
The draft Framework for teaching mathematics: Year 7, published in March. 2000 ... This book addresses class organisation, planning and teaching through answers to .....Oxford. OX2 9AT x The National Association of Gifted Children. NAGC |
MAT 107: Math For Elementary Teachers: Real Numbers
Fall 2012.
40 107: Math For Elementary Teachers: Real Numbers
Fall 2011.
30 207: Mathematics for Elementary Teachers: Geometry
Spring 2012.
35 Students were enrolled in this course.
Additional notes:
Professor uses course notes in order to save students approximately $100 for a Textbook typically used in the course.
Textbooks/Resources Used
Student Savings
Savings per student for this course: $0.00
Full Citations for Course Resources
MAT 271: Foundations of Higher Mathematics
Spring 2014.
Student enrollment data not available forFallSpring 307: Foundations of Middle School Mathematics I
Spring 2014.
Student enrollment data not available for 333: Abstract Algebra
Fall 2011.
32 Students were enrolled in 521: Geometry for Teachers
Spring 2014.
Student enrollment data not available for this course.
Additional notes: The textbook is a work-in-progress, given to students of Matt Jones, free of charge. Please see BlackBoard for a link to the book.
A note from Professor Jones: "I teach using an Inquiry-Based Learning, and I develop all of my own materials for most of the courses I teach."
Textbooks/Resources Used
Euclidean Geometry: A Guided Inquiry Approach available to students free of charge. |
An instructor at Boise State University offers his book on elementary algebra for middle school, high school, and college students. The book spans nine chapters and covers both pre-algebra and algebra topics. Clear...
Created by artist Cynthia Wilson at Spokane Falls Community College, this lesson combines art, geometry, and algebra to create two-dimensional models for abstract paintings. On this page, visitors will find a very...
The online math center at Whatcom Community College is intended for a range of audiences, particularly students looking for additional assistance on a variety of math subjects from geometry to calculus. The materials... |
Rates of Change and Limits Calculating Limits Using the Limit Laws Precise Definition of a Limit One-Sided Limits and Limits at Infinity Infinite Limits and Vertical Asymptotes Continuity Tangents and Derivatives
3. Differentiation
The Derivative as a Function Differentiation Rules The Derivative as a Rate of Change Derivatives of Trigonometric Functions The Chain Rule and Parametric Equations Implicit Differentiation Related Rates Linearization and Differentials
Estimating with Finite Sums Sigma Notation and Limits of Finite Sums The Definite Integral The Fundamental Theorem of Calculus Indefinite Integrals and the Substitution Rule Substitution and Area Between Curves
6. Applications of Definite Integrals
Volumes by Slicing and Rotation About an Axis Volumes by Cylindrical Shells Lengths of Plane Curves Moments and Centers of Mass Areas of Surfaces of Revolution and The Theorems of Pappus Work Fluid Pressures and Forces
Sequences Infinite Series The Integral Test Comparison Tests The Ratio and Root Tests Alternating Series, Absolute and Conditional Convergence Power Series Taylor and Maclaurin Series Convergence of Taylor Series; Error Estimates Applications of Power Series Fourier Series
Double Integrals Areas, Moments and Centers of Mass Double Integrals in Polar Form Triple Integrals in Rectangular Coordinates Masses and Moments in Three Dimensions Triple Integrals in Cylindrical and Spherical Coordinates Substitutions in Multiple Integrals
16. Integration in Vector Fields
Line Integrals Vector Fields, Work, Circulation, and Flux Path Independence, Potential Functions, and Conservative Fields Green's Theorem in the Plane Surface Area and Surface Integrals Parametrized Surfaces Stokes' Theorem The Divergence Theorem and a Unified Theory Appendices Mathematical Induction Proofs of Limit Theorems Commonly Occurring Limits Theory of the Real Numbers Complex Numbers The Distributive Law for Vector Cross Products Determinants and Cramer's Rule The Mixed Derivative Theorem and the Increment Theorem The Area of a Parallelogram's Projection on a Plane |
Book Description: This is a widely accessible introductory treatment of infinite series of real numbers, bringing the reader from basic definitions and tests to advanced results. An up-to-date presentation is given, making infinite series accessible, interesting, and useful to a wide audience, including students, teachers, and researchers. Included are elementary and advanced tests for convergence or divergence, the harmonic series, the alternating harmonic series, and closely related results. One chapter offers 107 concise, crisp, surprising results about infinite series. Another gives problems on infinite series, and solutions, which have appeared on the annual William Lowell Putnam Mathematical Competition. The lighter side of infinite series is treated in the concluding chapter where three puzzles, eighteen visuals, and several fallacious proofs are made available. Three appendices provide a listing of true or false statements, answers to why the harmonic series is so named, and an extensive list of published works on infinite series |
Problem – Solving and Selected Topics in Euclidean Geometry. In the Spirit of the Mathematical Olympiads
November 1, 2013 - 06:06 — Anonymous
Author(s):
Sotirios E. Louridas and Michael Th. Rassias
Publisher:
Springer
Year:
2013
ISBN:
978 1-4614–7272–8
Short description:
The book is a wonderful presentation of the essential concepts, ideas and results of Euclidean Geometry useful in solving olympiad problems of various level of difficulties. The theoretical part is excellently illustrated by challenging olympiad problems. The complete solutions to these problems are carefully presented, most of them together with several interesting comments and remarks.
MSC main category:
51 Geometry
MSC category:
51-01
Review:
Geometry is one of the most important and active fields in Mathematics with a substantial and large variety of applications in several disciplines, and with a very high impact in all levels of mathematical education.
This book deals with the essential results in plane Euclidean Geometry that are useful in solving difficult olympiad problems. The reader will become acquainted with well - known theorems such as Menelaus theorem, Ceva theorem, Ptolemy theorem, Stewart theorem, Euler nine point circle and the Euler line, etc., in the context of some complex geometric problems.
This book provides a very synthetic presentation of concepts and ideas in Euclidean Geometry, most of them without proof since its main goal is to illustrate by nonstandard problems how these ideas can be used. The book clearly demonstrates how instrumental it is to use various tools for the formulation of basic geometrical questions in order to find the simplest and the most intuitive arguments to solve a variety of problems. The book under review fully fits this purpose. In several situations and from different points of view the book presents the power of some natural geometric ideas. Most of the material is really suitable for advanced high-school classes and the book itself could offer a great service of attracting bright students to Mathematics.
The textbook is organized into six chapters. The first four chapters present some theoretical results including suggestive examples on the following aspects : Euclid's Elements, logic, methods of proof, fundamentals on geometric transformations and some important theoretical results in solving problems. Chapter 5 contains carefully selected Olympiad - caliber problems and it is organized into three sections : geometric problems with basic theory, geometric problems with more advanced theory, geometric inequalities.
The book concludes with a useful and relevant bibliography containing 99 references. It also contains an index of symbols and a subject index.
I would like to conclude this review with the statement of appreciation of the Fields Medalist Michael H. Freedman who wrote the foreword of the book :
`"........Young people need such texts, grounded in our shared intellectual history and challenging them to excel and create a continuity with the past. Geometry has seemed destined to give way in our modern computerized world to algebra. As with Michael Th. Rassias' previous homonymous book on number theory, it is a pleasure to see the mental discipline of the ancient Greeks so well represented to a youthful audience ".
All in all the text is a highly recommendable choice for any olympiad training program, and fills some gaps in the existing literature in Euclidean Geometry. The book is a very useful source of models and ideas for students, teachers, heads of national teams and authors of problems, as well as for people who are interested in mathematics and solving difficult problems.
Reviewer:
Mihaly Bencze
Affiliation:
PhD, University of Craiova
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The introduction to this site remarks, "If you need help in college algebra, you have come to the right place." Their statement is accurate, as the staff members at the West Texas A&M University's Virtual Math Lab have...
Brought to you by Elizabeth Stapel and purplemath.com, this collection of learning modules contains over 100 mathematics modules designed to teach beginning, intermediate, and advanced algebra concepts. Some algebra...
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For students in college-level math courses, revisiting algebra can be a challenge, and learning for it the first time can prove to be tricky as well. This website, created by Professor John Miller of the City College of...
A non-traditional Algebra text (high school and early college levels) placed on the Web by the Science Education Team at Los Alamos National Laboratory. Browse it on the Web or download a PDF version. Chapter headings... |
... more...
A plain-English guide to the basics of trig Trigonometry deals with the relationship between the sides and angles of triangles... mostly right triangles. In practical use, trigonometry is a friend to astronomers who use triangulation to measure the distance between stars. Trig also has applications in fields as broad as financial analysis, music... more...
Ever since Lorensen and Cline published their paper on the Marching Cubes algorithm, isosurfaces have been a standard technique for the visualization of 3D volumetric data. Yet there is no book exclusively devoted to isosurfaces. Isosurfaces: Geometry, Topology, and Algorithms represents the first book to focus on basic algorithms for isosurface construction.... more...
Presented in an easy-to-follow, step-by-step tutorial format, Puppet 3.0 Beginner?s Guide will lead you through the basics of setting up your Puppet server with plenty of screenshots and real-world solutions.This book is written for system administrators and developers, and anyone else who needs to manage computer systems. You will need to be able... more...
This book is concerned with one of the most fundamental questions of mathematics: the relationship between algebraic formulas and geometric images.At one of the first international mathematical congresses (in Paris in 1900), Hilbert stated a special case of this question in the form of his 16th problem (from his list of 23 problems left over from the... more...
This welcome boon for students of algebraic topology cuts a much-needed central path between other texts whose treatment of the classification theorem for compact surfaces is either too formalized and complex for those without detailed background knowledge, or too informal to afford students a comprehensive insight into the subject. Its dedicated,... more...
Algebraic geometry is a fascinating branch of mathematics that combines methods from both, algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover, Grothendieck's schemes invented in the late 1950s allowed the application of algebraic-geometric methods in fields that formerly... more...
¿¿¿¿This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or... more...
Polyhedral and Algebraic Methods in Computational Geometry provides a thorough introduction into algorithmic geometry and its applications. It presents its primary topics from the viewpoints of discrete, convex and elementary algebraic geometry.The first part of the book studies classical problems and techniques that refer to polyhedral structures.... more...
Originally published in 1985, this classic textbook is an English translation of Einführung in die kommutative Algebra und algebraische Geometrie. As part of the Modern Birkhäuser Classics series, the publisher is proud to make Introduction to Commutative Algebra and Algebraic Geometry available to a wider audience. Aimed at students... more... |
Tyngsboro CalculusUsually this involves doing lots of examples, discussing problem solving strategies and working through practice problems. Algebra is one of the fundamental tools used in theoretical physics. During my physics education it was necessary to become proficient in algebra |
Develop Algebraic Thinking 3-5 - MAT-925Use manipulatives, real-world problem-solving, and captivating activities to engage your students in developmentally appropriate algebraic thinking. This ONLINE course will provide you with numerous opportunities to reflect on current research and pedagogy related to algebraic thinking in the intermediate grades. Make direct application to your own classroom through the design and development of lessons that explore growth patterns, tables, variables, and coordinate graphs. All of the readings and activities are built upon the Common Core standards. Teachers may complete this course with or without students |
Hockessin Algebra can be a difficult topic at first. Like most math classes it has a few elementary parts that once grasped lend incite to the rest of the topic. Knowing what a derivative means and how an integral is used are just two of the basic elementsMy name is Emily and I have experienced a lot in the corporate world that you do not learn in books or college. However, these experiences PLUS COLLEGE make you stronger and more capable of achieving that next promotion coming right around the corner will make you more successful. During colleg... |
gorithms
This text, extensively class-tested over a decade at UC Berkeley and UC San Diego, explains the fundamentals of algorithms in a story line that makes ...Show synopsisThis text, extensively class-tested over a decade at UC Berkeley and UC San Diego, explains the fundamentals of algorithms in a story line that makes the material enjoyable and easy to digest. Emphasis is placed on understanding the crisp mathematical idea behind each algorithm, in a manner that is intuitive and rigorous without being unduly formal. Features include: The use of boxes to strengthen the narrative: pieces that provide historical context, descriptions of how the algorithms are used in practice, and excursions for the mathematically sophisticated. Carefully chosen advanced topics that can be skipped in a standard one-semester course, but can be covered in an advanced algorithms course or in a more leisurely two-semester sequence. An accessible treatment of linear programming introduces students to one of the greatest achievements in algorithms. An optional chapter on the quantum algorithm for factoring provides a unique peephole into this exciting topic. In addition to the text, DasGupta also offers a Solutions Manual, which is available on the Online Learning Center. ""Algorithms" is an outstanding undergraduate text, equally informed by the historical roots and contemporary applications of its subject. Like a captivating novel, it is a joy to read." Tim Roughgarden Stanford University23402 Brand New International edition. 100% Same...New. 0073523402 |
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Comparison of Maths syllabusclass X CBSE ICSE Time 3 hrs 2:45hrs Marks 80 80 Internal marks 20 20 Total marks 100 100 Chapters ... Mathematicssyllabus is designed keeping in mind that the subject is required not only by the science stream but also by the commerce
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Note: Please purchase your textbook before the first day of class.
Required books: Official Guide for GMAT Review 13th Ed. and Kaplan GMAT Math Workbook, 6th Ed.
Class will not meet on May 27, 2013
Sorry, we are no longer accepting registrations for this course. Please contact our office to find out if it will be rescheduled, or if alternative classes are available.
Course Description
This course provides 15 hours of classroom instruction and test-taking strategies on basic arithmetic, algebra, and geometry needed for the mathematics section of the GMAT. Students will practice with sample tests. Book Required.
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0130449415
9780130449412
Mathematics for High School Teachers- An Advanced Perspective: This book gives readers a comprehensive look at the most important concepts in the mathematics taught in grades 9-12. Real numbers, functions, congruence, similarity, area and volume, trigonometry and more. For high school mathematics teachers, mathematics supervisors, mathematics coordinators, mathematicians, and users of the University of Chicago School Mathematics Project materials for grades 7-12 who want a comprehensive reference book to use throughout their careers or anyone who wants a better understanding of mathematics.
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Rent Mathematics for High School Teachers- An Advanced Perspective 1st edition today, or search our site for Anthony textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Pearson. |
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There's the girl who loves to draw. There's the drummer who can't sit still long enough to choke down the basics.
It's those students McHenry hopes will get help from an experimental new approach to teach algebra. Known as aesthetic computing, the approach encourages students to express equations as pictures or stories. It was pioneered not by teachers or education experts, but rather by a computer science professor with a background in simulating complex systems and a fondness for obtuse terms like "multimodeling."
McHenry, one of about a dozen teachers who attended a recent workshop at the University of Florida introducing aesthetic computing, was intrigued enough to say she would give it a try with her 11th- and 12th-graders at North Marion High School in Ocala.
"Hopefully," she said, "this is something my students can do."
Teachers have struggled to engage students' interest in math for as long as math has been taught. All the more so, perhaps, with algebra. Getting already distracted teenagers to focus on abstract, to-their-eyes useless, algebraic concepts can be Herculean, teachers say.
Many educators have tried, but few have come up with memorable solutions. As Tim Ballas, another teacher at the workshop, said, "I'm looking for anything right now that will give my students insights into concepts they will not grasp."
Paul Fishwick, a UF computer and information science engineering professor, has spent nearly a decade cogitating aesthetic computing, a term he coined. He teaches a popular UF undergraduate class on the concept, and his ideas have generated a buzz in academic circles. His course book, a 22-chapter compendium of his and others' thoughts on the concept, will be published by MIT Press later this year.
Fishwick's focus has been on university-level scholarship. But a National Science Foundation grant prompted him to rethink aesthetic computing for younger students. Based on his ideas, he and two secondary-school teachers acting as consultants, Katie Indarawis and Jodee Alice Rose, wrote an introductory curriculum for middle and high school.
The recent workshop was the first introduction of the curriculum to classroom teachers.
"To be honest," Fishwick told the crowd, which also included computer engineering students and UF education professors, "if we can't interest you in this, there's no way we can get it to the students."
The basic idea of aesthetic computing is to make abstract ideas or algebraic formulas "real" through drawings, sculptures or computer graphics — the way concepts in geometry, for example, can come to life in the plans for a house. Fishwick has also likened it to how the graphical user interface changed computer operating systems. When early versions first appeared on the Apple Macintosh, the system made long-opaque operations familiar only to computer experts accessible to lay computer users, popularizing the personal computer.
But just as house plans have dimensions that conform to geometry's rules, so the algebraic representations in aesthetic computing are meant to be rigorous and accurate.
Indarawis and Rose spent a good part of the workshop explaining the method, which involves unpacking a traditional equation into its parts and operations, and then repackaging it in very nontraditional form, one that resembles a diagram with circles and lines. The final step is the fun one: depicting the re-formed equation as a piece of art or a short story.
Rose took the teachers through the process with the equation for a straight line. The final result was "Dorm Life," a picture that included a stereo, lava lamp, power strip, several cords and plugs and an electricity bill. Each object represented a variable or operation in the equation, while the bill represented the solution, or result.
The teachers tried their hand next, seeking to dissect and then depict the Pythagorean Theorem. McHenry wound up with a garden. Ballas, who teaches at a technical high school with a culinary arts program, created a menu. They and the other teachers struggled with reforming the equations in the aesthetic computing mold, but they seemed intrigued.
Julie Edison, a teacher at Dunnellon High, said high school students do not get enough hands-on learning. Aesthetic computing may quench that need, no small achievement for an area that seems hopelessly abstract.
"This idea gives the students a structure to use with any concept, from the real fundamental all the way through trigonometry and higher math," sheSep. 16, 2013 — Researchers have found high school students in the United States achieve higher scores on a standardized mathematics test if they study from a curriculum known as integrated ... full story
Mar. 21, 2013 — Ninth-graders in Chicago Public Schools have significantly benefited from double-dose algebra (attending two consecutive periods of the subject) in ways that were not easily observable in the ... full story
ScienceDaily features breaking news and videos about the latest discoveries in health, technology, the environment, and more -- from major news services and leading universities, scientific journals, and research organizations. |
0078692512
9780078692512
Mathematics with Business Applications, Student Edition:Glencoe Math with Business Applications is a comprehensive text that covers all the skills students need to manage their personal finances and excel at their first jobs and in everyday life. Math with Business Applications is a three-part program that takes students from basic math concepts to sophisticated financial strategies. Basic Math Skills reviews the fundamental math operations, Personal Finance teaches money management skills, and Business Math provides a thorough primer on launching and running a business.Math with Business Applications contains lessons, workshops, features and activities that comprise a well-rounded program.
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Rent Mathematics with Business Applications, Student Edition 6th edition today, or search our site for textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Glencoe/McGraw-Hill. |
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Wednesday, April 16, 2014
Are you in college and struggling in algebra? College algebra also called as algebra 2. College algebra covers inequality, logarithm, exponential, polynomials, quadratic, functions. Linear equations, matrix algebra, graph and line, trigonometry, inverse trigonometry, radical equations, etc. There are some steps which will help you to understand the algebra2 in an easy way.
Step 1) Revise Pre algebra concepts:
Revise all the fundamentals of pre algebra concepts. Go through all the concepts as far as necessary to refresh your memory. Most of the college students go forward and later on feel difficulty to understand the algebra2 concepts. You can arrange a self pre algebra test before the college semester starts or can ask live math tutor to facilitate you.
Step 2) Attend regular classes even optional one:
Attend classes regularly, this will help you to understand topic clearly. Algebra topics are connected to each other if you miss any class, then it may be hard you to infer the next topic. Attend all the optional classes they are very important.
Steps 3) Follow the pattern:
Algebra2 topics are related to each other so it is necessary to follow the pattern. Start with the linear equation then go to the polynomial and quadratic, etc. If you immediately start with the inequality or quadratic equation then it will be hard you to infer. It is necessary to follow the pattern to make algebra2 easy.
Steps 4) Make a proper notes:
Maintain the proper notes this will help you to study for exam. Write down everything which professor explain in the class. Notes will help you to keep track on the topic.
Step 5) Complete assignment:
Assignment and homework are nothing but the practice for the exam. Practice is the key for success Do as much as homework or assignment problem you can do. Recheck your homework this will help you to understand the fundamental of the subject. Ask question on based on the assignment or you can get online college algebra help.
Step 6) Learn algebraic technology tools:
Make use of algebraic tools like scientific calculator and programing. Many other online tools are available, make use of them this will make your work easier and faster.
Step 7) Discus with your professor:
If you do not understand something, then do not hesitate to ask your professor. Ask your professor for extra time.
Step 8) Practice:
Practice as many as problems you can do. Practice makes you perfect. Practice all the example problems.
Important points:
• Make use of scientific calculator.
• Be a master of pre algebra.
• Complete assignment on time.
• Use algebraic tools online.
• Solve sample paper.
• Get a help from tutors on Online Algebra 2 Help.
Thursday, April 10, 2014
Common 6th grade math coverup number system, arithmetic operations, geometry, measurement, functions, pre algebra, data, statistic, mensuration, ratios and proportions, etc. If you have a good command on all this topic then it is easy to survive with 6th grade math. To understand the 6th grade math in a right way follow the below article.
Number system:
Numbers are the basic building stone of the mathematics. Understand all the properties of the numbers and types of numbers. Rational numbers, irrational numbers, real numbers, whole numbers, natural numbers etc.
Arithmetic Operations:
Addition, subtraction, multiplication and division are the basic arithmetic operations. Follow the order of operations PEMDAS to solve problem.
Geometry:
Geometry is all about the shape and their properties. Understand the probability of different shape like cube, square, triangles, circles, etc. To know more about the it get geometry help online. 6Th grade math caved 2D shape.
Pre Algebra:
Pre algebra deal with linear equation, quadratic equation, factorization, simple root and power, etc. these all are basic of the Algebra. Be a master of these basic algebra.
Statistic:
Be a master of basic statistic terms like mean, median, mode, etc. To survive with 6th grade statistic you can take live statistics help.
Data:
Analyze the data to justify the conclusions or to make predictions.
Important points to survive 6th grade math:
1. Attend classes regularly.
2. Be attentive in the classroom.
3. Do not hesitate to ask questions from your teacher.
4. Do your homework every day.
5. Understand the topic. Do not memorize the things.
6. Do not give up. Try problem until you get the solution.
7. Practice as many as problem you can.
8. Make use of a calculator. This makes math easier.
9. Take online math help.
Wednesday, April 2, 2014
Math exam anxiety is very common in most of the students. Math anxiety develops from childhood. Child's mind use to develop according to their age. When they start learning math problem, apply logic and still get unsuccessful results, then they lead to stress and anxiety. Math anxiety especially develop in exam time because there is the added stress and pressure. Parents and teacher play the most important role to reduce math anxiety in the students. Anxiety can not be reduce with in a day. You need to put enough effort to reduce it. Here are some points to reduce math exam anxiety.
1) Find the root of math anxiety
What is the cause of your anxiety? Some students simply believe that math is not necessary in the real life, which is not true. Some believe that men are better at math than women. Many believe that math is so tough, he/she can not learn it. Some students are afraid of math logic. This all are not so true. Find your anxiety reason and work on it.
2) Do not wait for the last moment
Make a study plan at least 2-3 week before of your exam. Do not wait for the last moment. Create a plan for the your study and work according to schedule.
3) Know the exam material well
If you know the exam material, then you can prepare well for the exam. This is the best way to reduce the math anxiety. If the material well know then you don't have to take stress and extra work load.
4) Extra help
Analyze which part of math is hard to understand. Ask extra help from your teacher. If you are not getting any help the from your teacher then asks help from free live math tutor.
5) Self doubt
Self doubt is the main reason for anxiety. To solve any math problem you need to be confident. The problem will become more tougher if you have self doubt because you will not confident with your answer. Self doubt work as fuel for anxiety.
6) Time management
Many students are slow in math they need more time to solve a problem. That can be the reason for math anxiety. To reduce the math anxiety learn time management because in the exam you get limited time.
7) Physical Stress
Do not get any kind of mental stress. Many students get sick just before the math test this is a symptom of the anxiety. Many students are forced to sit and solve the math problem which prevent them from putting full efforts in the exam.
8) Take self test
Conduct a self test analysis yourself where you realize mistakes and workout on those errors. When you are struggling with any problem do not waste your time and do not feel lost just move on to the other problem. This will help you to maintain time in exams.
9) Give proper rest to your mind
Just before one day of the exam take a proper sleep, eat healthy food and do not take any kind of stress. If you are prepare well for the exam, then no need to get anxious.
10) During exam
During exam read your exam paper carefully and be positive in yourself. If there is time then, recheck your answer sheet.
Important Tips
• Take test as a homework so that you will not become stressed and pressure.
Monday, March 10, 2014
Do you want to pass in 5th grade math? Are you having trouble with 5th grade maths? Commonly 5th grade math coverup basic arithmetic, measurement, geometry, basic algebra, probability, etc. If you are good at all this then it is very easy to pass in the 5th grade math exam.
Follow the list of basic concepts provided below. Arithmetic: • Be a master in addition, subtraction, multiplication and division. • Understand the place value in graph. Negative goes left and positive goes right. Measurement: • Understand the terms like inches, feet, centimeter, yard ,meter, kilometer, etc. • Learn Unit Conversion Like 1 kilometer =1000 meters. • Solve measurement problems like circumference, volume, capacity, perimeter, and area ,etc. Explain the problem and make use of the rule. • Learn units like for time we use minute or second. Algebra: • Learn basic algebra like to find the missing term in the equation. • Determine the value of the equation. • Understand the basic rule of algebra. Geometry: • Geometry is all about the shapes and their properties. • Understand the all 2D shapes and their properties. • Clarify all types of triangles. • Learn the coordinate system of the graph. Just go through the tips for more help. 1: Attentive In The Class: If you really want to be good in maths and want to pass with good grade, then you need to be attentive in the class room. In order to cross in a class exam initial thing which often you must do is usually give attention in the class room. Make an effort to crystal clear your current subject matter related doubts from your math tutor. 2: Practice: Keep in mind practice makes you perfect. Practice daily at least for 30 min, what your teacher has covered in the class. Divide equal time for each topic. You could also try Online Game And Worksheets for practice. 3: Do Your Homework: Homework is also a part of your practice. Try to finish your homework on a regular basis. Write each step that you've taken so that it will enable you to cross check your problem. If you happen to be stuck among them,then can take Math Question Helpfrom online.
4: Group Study: Group study is often a nice way to tern your own math into fun as well as games. If you don't want to take a seat and study ,then ask your friends and carry out group study. This will refresh your brain and you may understand a few tough problems. 5: Take Your Time In Exam: When you give equal time for each question in your exam, then you do less silly mistakes. Read all question at least twice. Try to give your best in exam. Solve effortless problem first then select tough one. Get more tips on Tutoring 5th Grade Math
Tuesday, March 4, 2014
A math problem can be solved in many ways. There is a general way to solve any math problem. Do not get bored by seeing math problem. If you approach any problem with the clear mind, then half of your worried will be over.
Different people follow different method to solve a problem and take different time to finish the problem. There are some simple and general steps to solve a math problem. Step 1: Read out the problem carefully twice and get an idea about it. Determine the area of the problem like trigonometry, algebra and calculus, etc. In some problem there are some significant topic in which you should have the particular knowledge about that topic. Write down what is given and what you have to find. Step 2: Think in a roughly way what is needed to get the solution, whether you have enough knowledge about the area of your problem and what formula should use, etc. If not then seek for help from your teacher or any math solver. There are many websites or free online math tutor that offers the basic math concept. Collect all important information related to the problem. Step 3: Start solving your problem. Divide your problem into sub parts. Proceed problem logically by part by part. If needed draw graph, table and figure. Apply your math skills. Step 4: Write down all the step and calculation. Avoid solving full problem in your mind and come up with the solution directly. Writing down all the steps will help you to cross check your problem. Step 5: Once you get the solution cross check all the calculation part and check if you did any writing error or did you miss any step. Step 6: Check your solution with the answer sheet. Whether your solution is correct or not. Step 7: If you can not find the exact solution to your problem, don't give up. If you try to solve it once more. Constantly facing the same questions, you will be able to find the right solution and learn how to solve the problem. Finding difficult to complete your homework problems, not to worry Math Homework Help Tutor Online Freegives you complete solution to your homework problems and assignments. |
XV. Mathematics, Grade 10
Grade 10 Mathematics Test
The spring 2008 grade 10 MCAS Mathematics test was based on learning standards in the
Massachusetts Mathematics Curriculum Framework (2000). The Framework identifies five major
content strands listed below.
Number Sense and Operations
Patterns, Relations, and Algebra
Geometry
Measurement
Data Analysis, Statistics, and Probability
The grades 9–10 learning standards for each of these strands appear on pages 72–75 of the
Mathematics Curriculum Framework, which is available on the Department Web site at
In Test Item Analysis Reports and on the Subject Area Subscore pages of the MCAS School Reports
and District Reports, Mathematics test results are reported under five MCAS reporting categories,
which are identical to the five Framework content strands listed above.
Test Sessions
The MCAS grade 10 Mathematics test included two separate test sessions, which were administered
on consecutive days. Each session included multiple-choice and open-response questions. Session 1 also
included short-answer questions.
Reference Materials and Tools
Each student taking the grade 10 Mathematics test was provided with a grade 10 Mathematics
Reference Sheet. A copy of the reference sheet follows the final question in this chapter.
During session 2, each student had sole access to a calculator with at least four functions and a square
root key. Calculator use was not allowed during session 1.
The use of bilingual word-to-word dictionaries was allowed for current and former limited English
proficient students only, during both Mathematics test sessions. No other reference tools or materials
were allowed.
Cross-Reference Information
The table at the conclusion of this chapter indicates each item's reporting category and the Framework
learning standard it assesses. The correct answers for multiple-choice and short-answer questions are
also displayed in the table.
384
Mathematics
SeSSion 1
You may use your reference sheet during this session.
You may not use a calculator during this session.
DIRECTIONS
This session contains fourteen multiple-choice questions, four short-answer questions, and
three open-response questions. Mark your answers to these questions in the spaces provided in your
Student Answer Booklet.
ID:250907 335s_10ma_s07MCAS.eps B Common ID:254546 C Common
●
1 The table below shows a linear
relationship between the values of
●
2 Which of the following is closest to the
value of the expression below?
x and y.
52 8
x y
A. 1.4
1 1
B. 2.2
2 6 C. 4.1
3 11 D. 8.5
4 16
Item: TBD Art: TBD
Based on the relationship in the table,
Source: MP
?
what is the value of y when x = 7
MCAS\07-08\Gr10\Math\335s_10ma_s07MCAS.ai (10/16/2007, 11:47 am)
A. 35
B. 31
C. 28
D. 21
385
Mathematics Session 1
ID:250896 545S_10ma_s07MCAS.eps C Common ID:261521 B Common
●
3 Sharon took 24 nighttime photographs.
The exposure times, in seconds, for her
●
4 Which of the following is equivalent to
the expression below?
photographs are represented in the stem-
and-leaf plot below. 100 3 109
A. 1010
Exposure Times (in seconds)
B. 1011
1 8 9 9 C. 1012
2 0 2 3 3 4 4 4 4 6 8 9 9 D. 1018
3 0 1 2 4 5 6 7
4 2 3
ID:273058 A Common
Key
●
5 The first five numbers of a quadratic
sequence are shown below.
3 2 represents 32
4, 6, 11, 19, 30, . . .
What is the median exposure time for
her photographs? What is the next number in the
sequence?
A. 24 seconds
A. 44
B. 25 seconds
B. 43
C. 27 seconds
C. 42
D. 28 seconds
D. 41
386
Mathematics Session 1
ID:253151 CMH015_quadrilateral.eps C Common ID:273059 C Common
●
6 A polygon and expressions representing
its dimensions, in meters, are shown
●
7 A square has an area of 75 square meters.
Which of the following is closest to the
below. length of a side of the square?
2x A. 7.8 meters
B. 8.2 meters
5 – x
C. 8.7 meters
D. 9.1 meters
3x
x + 5
ID:253160 A Common
●
8 What are the solutions of the equation
below?
Which of the following represents the
perimeter, in meters, of the polygon? 2n(3n 12) 0
A. 5x A. 0 and 4
B. 15x B. 0 and 12
C. 5x 10 C. 2 and 4
D. 7x 10 D. 2 and 12
387
Mathematics Session 1
ID:273061 CMH001_points.eps C Common ID:254620 C Common
●
9 Shantel made the line plot below to show
the numbers of points she and the other
●
10 What is the value of the expression below?
members of her team scored. 2 ( 3 2 ) 2 (1) 2
A. 18
X
X X X X B. 22
X X X X X C. 49
0 1 2 3 4 5 6 D. 51
Numbers of Points Scored by Team Members
Exactly three players scored more points ID:253851 A Common
than Shantel. Based on the line plot, ●
11 Jessica wrote the equations below.
what is the number of points that
Shantel scored? r 27 • n
s 45 • n
A. 2
Which of the following expressions is
B. 3 equivalent to s r ?
C. 4
A. (45 27)n
D. 5
B. 45(27 n)
C. (45 n)(27 n)
D. (45 27)(n n)
388
Mathematics Session 1
ID:250911 589s_10ma_s07MCAS.eps D Common ID:254607 C Common
●
12 A line is shown on the coordinate grid
below.
●
13 What is the value of the expression below?
3 8 5 (2 )
y
A. 14
6
5 B. 2
4 C. 4
3 D. 8
2
1
x
–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6
–1 ID:254292 A Common
–2
–3
●
14 The heights, in inches, of the members
of a soccer team are listed below.
–4
–5
66, 61, 71, 62, 64, 70, 64, 63, 72, 68
–6
After a new member joined the team,
Which of the following best represents the median height of all the members
an equation of the line? was 66 inches.
Which of the following could be the
A. y 2x 2
height, in inches, of the new member?
B. y 1 x 4 A. 68
2
B. 65
C. y 1 x 2
2 C. 64
D. y 2x 4 D. 61
389
Mathematics Session 1
Questions 15 and 16 are short-answer questions. Write your answers to these questions in the boxes
provided in your Student Answer Booklet. Do not write your answers in this test booklet. You may do
your figuring in the test booklet.
ID:254582 Common
●
15 Laila is having shirts made with a logo printed on them to promote her band. The total cost
consists of a one-time fee of $75 to have the logo designed plus $8 per shirt to print the logo.
Write an equation that Laila can use to determine the total cost, C, in dollars, to make
x shirts.
ID:253231 CMH033_KLMN.eps Common
●
16 Rectangle KLMN and its dimensions are shown below. Point P lies on KL .
K P L
15 cm
N 20 cm M
What is the area, in square centimeters, of NPM ?
390
Mathematics Session 1
Question 17 17 in the space provided in your Student Answer Booklet.
ID:254600 Common
●
17 Line j is represented by the equation below.
line j: y 2 x 4
a. What is the slope of line j? Show or explain how you got your answer.
b. What is the slope of any line that is parallel to line j? Explain your reasoning.
c. Write an equation for the line, k, that is parallel to line j and passes through the point
with coordinates (3, 7). Show or explain how you got your answer.
d. Write an equation for the line, h, that is perpendicular to line j and passes through
the point with coordinates (8, 10). Show or explain how you got your answer.
391
Mathematics Session 1
Questions 18 and 19 are short-answer questions. Write your answers to these questions in the boxes
provided in your Student Answer Booklet. Do not write your answers in this test booklet. You may do
your figuring in the test booklet.
ID:229969 Common
●
18 Davis is on the high school track team. The table below shows the number of laps he ran around the
school's track each day for 7 consecutive days.
Number of Laps Each Day
Day Mon. Tue. Wed. Thu. Fri. Sat. Sun.
Number of Laps 8 11 7 9 10 11 12
What is the numerical difference between the median of the number of laps and the mode of the
number of laps?
ID:254135 Common
●
19 What is the value of the expression below?
3 26
392
Mathematics Session 1
Questions 20 and 21 are open-response questions.
• BE SURE TO ANSWER AND LABEL ALL PARTS OF EACH QUESTION.
• Show all your work (diagrams, tables, or computations) in your Student Answer Booklet.
• If you do the work in your head, explain in writing how you did the work.
Write your answer to question 20 in the space provided in your Student Answer Booklet.
ID:258329 Common
●
20 Glenn sells clothing at his store. He changes some prices each month.
a. The original price of a jacket was $30. Glenn increased the price by 10%. What is the
new price of the jacket after the increase? Show or explain how you got your answer.
b. The original price of a pair of sneakers was $50.
• Glenn increased the price by 20% in April.
• He then increased the price again by 20% in July.
What is the new price of the sneakers after both increases? Show or explain how you got
your answer.
c. The original price of a shirt was $16.
• Glenn increased the price by 25% in April.
• He then decreased the price by 30% in July.
Is the final price of the shirt the same as if the original price had been decreased by 5%?
Show or explain how you got your answer.
d. The original price of a coat was $80. Glenn increased the price to $100. By what percent
did the price increase? Show or explain how you got your answer.
393
Mathematics Session 1
Write your answer to question 21 in the space provided in your Student Answer Booklet.
ID:254373 Common
●
21 Jason launched a model rocket from the ground. The formula below can be used to determine
the height of the rocket above the ground at any time during the rocket's flight.
h 16 t ( 7 t )
In the formula, h and t are defined as follows:
• t = the time, in seconds, that has elapsed since the rocket was launched
• h = the height, in feet, of the rocket above the ground at time t
Use the formula to answer the following questions.
a. What was the height, in feet, of the rocket 1 second after it was launched? Show
your work.
b. What was the height, in feet, of the rocket 6 seconds after it was launched? Show
your work.
c. The value of h was 0 when the rocket hit the ground. How many seconds after the rocket
was launched did it hit the ground? Show your work.
d. How many seconds after the rocket was launched was the height of the rocket 160 feet?
Show your work.
394
Mathematics
SeSSion 2
You may use your reference sheet during this session.
You may use a calculator during this session.
DIRECTIONS
This session contains eighteen multiple-choice questions and three open-response questions.
Mark your answers to these questions in the spaces provided in your Student Answer Booklet.
ID:253202 CMH005_parallelogram.eps A Common ID:250983 503s_10ma_s07MCAS.eps D Common
●
22 A parallelogram and its dimensions are
shown below.
●
23 In the diagram below, line l is parallel to
line m, and line k intersects both lines.
k
6 in. l
4 in. 37°
3 in.
What is the area of the parallelogram? m
x°
A. 12 sq. in.
B. 13 sq. in.
Based on the angle measure in the
C. 18 sq. in. diagram, what is the value of x?
D. 24 sq. in.
A. 37
B. 53
C. 127
D. 143
395
Mathematics Session 2
ID:253143 CMH008_zero_slope.eps [op A Common ID:253188 D Common
●
24 In which of the following graphs does
line k best represent a line with a slope
●
25 A large organization uses a phone tree
to contact members.
of 0?
• The director first contacts
3 members. This is the 1st set
A. y of calls.
• Each member who was contacted
in the 1st set of calls then contacts
x 3 different members who were
k not previously contacted. This is
the 2nd set of calls.
• The pattern continues with each
member contacting 3 different
B. y members who were not
previously contacted.
x The table below shows the number of
members contacted in each set of calls.
k Phone Tree Calls
Number of
C. y
k Set of Calls Members Contacted
in This Set of Calls
1st 3
x
2nd 9
3rd 27
4th 81
D. k y If the pattern continues, what is the
number of members who would be
contacted in the 6th set of calls?
x
A. 216
B. 324
C. 486
D. 729
396
Mathematics Session 2
ID:273056 CMH019_cross.eps D Common ID:229576 3207734_AR1.eps B Common
●
26 The rectangle below is a cross section
of a three-dimensional object.
●
27 An international basketball court has a
region called the free-throw lane, shown
as the shaded part in the diagram below.
• The free-throw lane is shaped like
an isosceles trapezoid.
• A semicircle, shown as the unshaded
part in the diagram, is attached to
the shorter base of the trapezoid.
The rectangle could not be a cross • The radius of the semicircle is
section of which of the following 1.8 meters.
objects?
A. a cylinder
B. a prism
C. a cube
D. a cone 1.8 m
6.0 m
5.8 m
Based on the dimensions in the
diagram, what is the area of the
shaded free-throw lane?
A. 22.62 square meters
B. 27.84 square meters
C. 34.80 square meters
D. 55.68 square meters
397
Mathematics Session 2
ID:261482 295S_10ma_s06MCAS.eps D Common
●
28 The box-and-whisker plot below shows the distribution of the daily high temperatures, in
degrees Fahrenheit, in the town of Clifton during the year 2004.
Daily High Temperatures (in degrees Fahrenheit)
30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
Based on the box-and-whisker plot, in which of the following intervals of temperatures is it
most likely that exactly 50% of the daily high temperatures are located?
A. 38°F to 54°F
B. 38°F to 81°F
C. 54°F to 72°F
D. 54°F to 81°F
ID:253841 C Common ID:273062 A Common
●
29 For all nonzero values of x and y, which of
the following expressions must equal 0?
●
30 The circumference of Sophie's circular
flower garden is 75 feet. Which of the
following is closest to the diameter of
A. x0( y0 ) her flower garden?
B. x y y x A. 24 feet
B. 12 feet
C. xy yx C. 10 feet
D. 5 feet
D. (x y) (x y)
398
Mathematics Session 2
Question 31 31 in the space provided in your Student Answer Booklet.
ID:261495 278S1_10ma_s06MCAS.eps, 2 Common
●
31 The first six rows of a pattern are shown in the triangular array below.
Row 1 2
Row 2 2 2
Row 3 2 4 2
Row 4 2 6 6 2
Row 5 2 8 12 8 2
Row 6 2 10 20 20 10 2
Row 7 ? ? ? ? ? ? ?
Each number in the array, other than 2, can be found by adding the two numbers in the
preceding row that are diagonally above it. For example, 6 2 4, as shown in the
triangular array.
a. If the pattern continues, what are the seven numbers in Row 7? Show or explain how you
got your answer.
Copy the table below into your Student Answer Booklet.
Sum of the
Numbers in Each Row
Row Sum
1
2
3
4
5
6
7
b. Determine the sum of the numbers in each of the first seven rows of the pattern. Complete
your table with these sums.
c. If the pattern continues, what row will be the first row in which the sum of the numbers is
greater than 600? Show or explain how you got your answer.
d. Write a rule in terms of n that can be used to find the sum of the numbers in Row n.
Show or explain how you got your answer.
399
Mathematics Session 2
Mark your answers to multiple-choice questions 32 through 40 in the spaces provided in your Student
Answer Booklet. Do not write your answers in this test booklet. You may do your figuring in the test
booklet.
ID:253219 B Common ID:261490 248S_10ma_s06MCAS.eps A Common
●
32 Each of two different-sized boxes is in ●
33 On the spinner shown below, the sizes
of the sections are as follows:
the shape of a right rectangular prism.
The volume of the larger box is • Sections S and U are equal in size.
4 times the volume of the smaller box.
The dimensions of the smaller box are • Sections R and T are equal in size.
represented below. • The size of section S is half the
size of section T.
• length: l
• width: w
• height: h S
T
Which of the following could represent
the dimensions of the larger box?
R
A. l, 4w, 4h U
B. 2l, 2w, h
C. 2l, 2w, 4h
D. 4l, 4w, 4h If Darryl spins the arrow one time, what
is the probability that it will land on
section S?
A. 1
6
B. 1
4
C. 1
3
D. 1
2
400
Mathematics Session 2
ID:273057 C Common ID:253181 B Common
●
34 Manuel is using a small paper rectangle
and a large paper rectangle for an art
●
35 Melinda invested $1000 in a retirement
account. The formula below shows the
project. amount of money, A, that will be in her
account at the end of t years.
• The length of the small rectangle
is half the length of the large A 1000(1 r)t
rectangle. In the formula, r is the interest rate,
• The width of the small rectangle expressed as a decimal. Melinda's
is half the width of the large account has an interest rate of 6%.
rectangle. Which of the following is closest to the
amount that will be in Melinda's account
The area of the small rectangle is
at the end of 2 years?
how many times the area of the large
rectangle? A. $1120
B. $1124
A. 1
16
C. $1256
B. 1 D. $1360
8
C. 1
4
ID:227872 3007141_AR1.eps A Common
D. 1
2 ●
36 In circle D, BC is a diameter, DA is a
radius, and m AB 60°.
A
B
D
C
What is mCAD ?
A. 30°
B. 50°
C. 60°
D. 70°
401
Mathematics Session 2
ID:253264 CMH012_eq_triangle.eps B Common ID:227925 D Common
●
37 In the diagram below, ST is equilateral,
R ●
38 Jeremy calculates his car's gas mileage
every time he buys gas for his car. The
and U is the midpoint of RT .
chart below shows the data from the last
S 5 times he bought gas.
Gas Mileage for Jeremy's Car
Gas Mileage
Miles Gallons of Gas
(miles per gallon)
20 cm
370 11.3 32.74
352 9.5 37.05
303 8.9 34.04
298 9.7 30.72
R U T 398 11.2 35.54
If the length of ST is 20 centimeters, Based on the data in the chart, what is the
range of gas mileage for Jeremy's car?
what is the length of SU ?
A. 2.80 miles per gallon
A. 10 cm
B. 4.31 miles per gallon
B. 10 3 cm
C. 4.82 miles per gallon
C. 20 cm D. 6.33 miles per gallon
D. 20 3 cm
402
Mathematics Session 2
ID:250619 588S_10ma_s07MCAS.eps B Common ID:253189 D Common
●
39 The vertex-edge graph below represents
all the paths in a park.
●
40 The only coins that Alexis has are
dimes and quarters.
N • Her coins have a total value
of $5.80.
M • She has a total of 40 coins.
P
Which of the following systems of
K equations can be used to find the
number of dimes, d, and the number
J of quarters, q, that Alexis has?
Mike is at point J and wants to walk A. d q 5.80
along each path exactly one time. At 40d 40q 5.80
which point will Mike finish his walk?
B. d q 40
A. point K 5
.80d 5.80q 40
B. point M
C. d q 5.80
C. point N 0
.10d 0.25q 40
D. point P
D. d q 40
0
.10d 0.25q 5.80
403
Mathematics Session 2
Questions 41 and 42 are open-response questions.
• BE SURE TO ANSWER AND LABEL ALL PARTS OF EACH 41 in the space provided in your Student Answer Booklet.
ID:251149 072S_10ma_s07MCAS.eps Common
●
41 A water dunking tank at a carnival is in the shape of a right circular cylinder. Its height is 5 feet,
and the radius of each base is 3 feet, as shown in the picture below.
a. What is the lateral surface area, in square feet, of the tank? Show your work.
b. On the first day of the carnival, the dunking tank was filled with water to a height of
4 feet. What was the volume, in cubic feet, of the water in the tank on the first day of
the carnival? Show your work.
At the end of the second day of the carnival, some water was drained from the tank. The
volume of water drained was 35.3 cubic feet.
c. Using your answer from part (b), determine the height, in feet, of the water remaining in
the tank after the water was drained at the end of the second day. Show your work.
The water that was drained from the tank was poured into containers, each in the shape of
a right rectangular prism. Each container was 2 feet in length, 1.5 feet in width, and 3 feet
in height.
d. What was the least number of containers needed to hold all the water that was drained at
the end of the second day? Show your work.
404
Mathematics Session 2
Write your answer to question 42 in the space provided in your Student Answer Booklet.
ID:251661 324S1_10ma_s07MCAS.eps, 3 Common
●
42 Felicity's class helped scientists study monarch butterflies. The students caught butterflies, put
an identifying tag on each one, and then released them.
The next year scientists caught 24 of the tagged butterflies. They sent Felicity's class the table
below, which shows the distance flown by each of the 24 butterflies.
Distances Flown by Butterflies
(in miles)
613 1366 1600 1371 1696 884
842 1886 239 1779 1604 2122
1090 1678 1885 1476 1803 1662
104 1665 1697 1669 120 857
a. What is the range of the distances, in miles, that the 24 butterflies flew? Show or explain
how you got your answer.
b. Copy the table below into your Student Answer Booklet. Complete your table by
determining the number of butterflies that flew within each distance interval.
Distance Intervals
Flown by Butterflies
Distance Interval Number of
(in miles) Butterflies
0 –600
601–1200
1201–1800
1801–2400
c. In your Student Answer Booklet, create a circle graph that shows the information in your
table from part (b). Be sure to do the following:
• Draw the sectors in your circle graph so that their sizes are reasonably accurate.
• Label each sector of your graph with the distance interval it represents and the
percent of the butterflies that flew within that distance interval.
• Show how you determined each percent.
• Include a title for your graph.
405
Massachusetts Comprehensive Assessment System
Grade 10 Mathematics Reference Sheet
AREA FORMULAS VOLUME FORMULAS
square ..................... A = s2 cube .........................................V = s3
(s = length of an edge)
rectangle ................. A = bh
right rectangular prism ............V = lwh
parallelogram ......... A = bh OR
V = Bh
triangle ................... A = 1 h
b (B = area of a base)
2
4
trapezoid ................. A = 1 (b1 + b2)
h sphere ......................................V = 3 pr3
2
circle ....................... A = pr2 right circular cylinder ............V = pr2h
.
1
right circular cone ...................V = 3 pr2h
LATERAL SURFACE AREA FORMULAS
1
right rectangular prism .......... LA = 2(hw) + 2(lh) right square pyramid ...............V = 3 s2h
right circular cylinder ........... LA = 2prh
right circular cone ................. LA = pr CIRCLE FORMULAS
( = slant height)
right square pyramid ............. LA = 2s C = 2pr
( = slant height) A = pr2
SPECIAL RIGHT TRIANGLES
TOTAL SURFACE AREA FORMULAS
cube ....................................... SA = 6s2
45˚ x
2
right rectangular prism ......... SA = 2(lw) + 2(hw) + 2(lh) x
sphere .................................... SA = 4pr2
45˚
right circular cylinder ........... SA = 2pr2 + 2prh x
right circular cone ................. SA = pr2 +pr
( = slant height) 60˚ 2y
right square pyramid ............. SA = s2 + 2s y
( = slant height)
30˚
y
3
406
Grade 10 Mathematics
Spring 2008 Released Items:
Reporting Categories, Standards, and Correct Answers*
Correct Answer
Item No. Page No. Reporting Category Standard
(MC/SA)*
1 385 Patterns, Relations, and Algebra 10.P.1 B
2 385 Number Sense and Operations 10.N.3 C
3 386 Data Analysis, Statistics, and Probability 10.D.1 C
4 386 Number Sense and Operations 10.N.2 B
5 386 Patterns, Relations, and Algebra 10.P.1 A
6 387 Patterns, Relations, and Algebra 10.P.3 C
7 387 Number Sense and Operations 10.N.3 C
8 387 Patterns, Relations, and Algebra 10.P.5 A
9 388 Data Analysis, Statistics, and Probability 10.D.1 C
10 388 Number Sense and Operations 10.N.2 C
11 388 Number Sense and Operations 10.N.1 A
12 389 Patterns, Relations, and Algebra 10.P.2 D
13 389 Number Sense and Operations 10.N.2 C
14 389 Data Analysis, Statistics, and Probability 10.D.1 A
C 8x 75
15 390 Patterns, Relations, and Algebra 10.P.7 or equivalent
16 390 Measurement 10.M.1 150 cm2
17 391 Geometry 10.G.8
18 392 Data Analysis, Statistics, and Probability 10.D.1 1
19 392 Number Sense and Operations 10.N.2 12
20 393 Number Sense and Operations 8.N.12
21 394 Patterns, Relations, and Algebra 10.P.7
22 395 Measurement 10.M.1 A
23 395 Geometry 10.G.3 D
24 396 Patterns, Relations, and Algebra 10.P.2 A
25 396 Patterns, Relations, and Algebra 10.P.7 D
26 397 Geometry 10.G.10 D
27 397 Measurement 10.M.1 B
28 398 Data Analysis, Statistics, and Probability 10.D.1 D
29 398 Number Sense and Operations 10.N.1 C
30 398 Measurement 10.M.1 A
31 399 Patterns, Relations, and Algebra 10.P.1
32 400 Measurement 10.M.3 B
33 400 Data Analysis, Statistics, and Probability 8.D.4 A
34 401 Measurement 10.M.3 C
35 401 Patterns, Relations, and Algebra 10.P.7 B
36 401 Geometry 10.G.3 A
37 402 Geometry 10.G.6 B
38 402 Data Analysis, Statistics, and Probability 10.D.1 D
39 403 Geometry 10.G.11 B
40 403 Patterns, Relations, and Algebra 10.P.8 D
41 404 Measurement 10.M.2
42 405 Data Analysis, Statistics, and Probability 10.D.1
* nswers are provided here for multiple-choice items and short-answer items only. Sample responses and scoring guidelines for
A
open-response items, which are indicated by shaded cells, will be posted to the Department's Web site later this year. |
Description:
Created by Illumination: Resources for Teaching Mathematics, this unit plan includes four lessons covering correlation and regression. Students will use interactive computer-based tools to investigate the relationship between a set of data points and a curve used to fit the data points. Students will be able to investigate relationships between variables using linear, exponential, power, logarithmic, and other functions for curve fitting. This is an excellent collection of statistical applets for students to interact with. |
PAPERBACK Fair 0130676993 Student Edition. Missing many pages. Heavy wrinkling from liquid damage. Does not affect the text. Heavy wear, wrinkling, creasing, Curling or tears ...on the cover and spine May be missing front or back cover. May have used stickers or residue. Poor binding causing loose and torn pages. Heavy writing, highlighting and marker.Read moreShow Less
More About
This Textbook
Overview
The engaging Martin-Gay workbook series presents a user-friendly approach to the concepts of basic math and algebra, giving readers ample opportunity to practice skills and see how those skills relate to both their lives and the real world. The goals of the workbooks are to build confidence, increase motivation, and encourage mastery of basic skills and concepts. Martin-Gay enhances readers' perception of math by exposing them to real-life situations through graphs and applications and ensures that readers have an organized, integrated learning system at their fingertips. The integrated learning resources program features book-specific supplements including Martin-Gay's acclaimed tutorial videotapes, CD videos, and MathPro 5. This book covers topics such as multiplying and dividing fractions, decimals, ratios and proportion, percent, geometry, statistics and probability, as well as an introduction to algebra. For anyone who wishing to brush up on their basic mathematical skills.
Editorial Reviews
Booknews
An introductory textbook for students needing math in non-mathematical courses. The author covers standard math topics from place value and adding; through statistics and geometry, to basic algebra. Annotation c. by Book News, Inc., Portland, Or.
From The Critics
This text provides a foundation in basic college mathematics, covering whole numbers, fractions and decimals, ratio and proportion, percent, and measurement, and introducing geometry, statistics and probability, and algebra. Emphasis is on applications, interpretation, problem solving, writing, use of technology, and critical thinking. Learning features include worked examples following a four-step process of understanding, translation, solving, and interpretation. This second edition contains new material on study skills integrated throughout, and an increased integration of geometry concepts. The author teaches mathematics at the University of New Orleans. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Related Subjects
Meet the Author
An award-winning instructor and best-selling author, Elayn Martin-Gay has taught mathematics at the University of New Orleans for more than 25 years. Her numerous teaching awards include the local University Alumni Association's Award for Excellence in Teaching, and Outstanding Developmental Educator at University of New Orleans, presented by the Louisiana Association of Developmental Educators.
Prior to writing textbooks, Elayn developed an acclaimed series of lecture videos to support developmental mathematics students in their quest for success. These highly successful videos originally served as the foundation material for her texts. Today, the videos are specific to each book in the Martin-Gay series. Elayn also originated the Chapter Test Prep Video CDs to help students during their most "teachable moment" ---as they prepare for a test.
Elayn's experience has made her aware of how busy instructors are and what a difference quality supports make. For this reason, she created the Instructor-to-Instructor video series. These videos provide instructors with suggestions for presenting specific math topic and concepts in basic mathematics, prealgebra,beginning algebra, and intermediate algebra. Seasoned instructors can use them as a source for alternate approaches in the classroom. New or adjunct faculty may find the CDs useful for review. They are a great resource for suggestions regarding areas they may wish to emphasize, or common trouble areas students experience, that instructors my wish to highlight.
With her textbooks series, the Chapter Test Prep Video Cd, and CD Lecture series, Elayn has sought to put success within the reach of every student and instructor.
Prefacedevelop student proficiency in algebra and problem solving, and to prepare students for future courses.
Introduction developstudent proficiency in algebra and problem solving, and to prepare students for future courses.
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Barnes & Noble.com Review Rules |
Sequences, combinations, limits. Translated and adapted from the Russian by Leslie Cohn and Joan Teller. Reprint of the 1969 ed. (English)Zbl 1011.40001
Mineola, NY: Dover Publications. x, 142 p. $ 8.95 (2002).
This Dover reprint is the third book in the series "The Library School of Mathematics". This little book is designed as a self-reading experience for 9th and 10th grade students. There are three chapters: Sequences, written by Gelfand, Combinations, by Gerver and Kushnirenko, and Limits, prepared by Kirillov and Konstantinov. Complete solutions for the 140 problems in the text are provided in the appendix. The first chapter also contains a section on mathematical induction. The remaining chapters also contain a number of problems for which mathematical induction is the proof tool. The book is well written for a European audience, but is probably a bit too challenging for most American public school students. |
Book Description: A flexible program with the solid content students needGlencoe Algebra 1 strengthens student understanding and provides the tools students need to succeed—from the first day your students begin to learn the vocabulary of algebra until the day they take final exams and standardized tests |
Book DescriptionEditorial Reviews
Book Description
Adding Excel to Your Analysis Arsenal
About the Author
As a naval architect and marine engineer, David M. Bourg performs computer simulations and develops analysis tools that measure such things as hovercraft performance and the effect of waves on the motion of ships and boats. He teaches at the college level in the areas of ship design, construction and analysis. On occasion, David also lectures at high schools on topics such as naval architecture and software development. In addition to David's practical engineering background, he's professionally involved in computer game development and consulting through his company, Crescent Vision Interactive.
It is often either inconvenient or financially unfeasible to solve every mathematical problem with a standalone procedural language or an expensive application such as Matlab or Mathematica. Since Excel has such advanced computational capabilities built into it and is ubiquitous in offices and homes, it would make sense to mine this application for numerical problem solving techniques. Bourg does a masterful job of presenting the tools available in Excel and showing the reader how to put them to work to solve real world engineering and mathematical problems. First, he spends a couple of chapters briefly going over Excel and its language VBA (Visual Basic for Applications). Next he goes over some intermediate level tasks such as collecting and cleaning up data, charting including 3D charts, and statistical analysis tasks such as correlating data and generating random numbers. Next Bourg moves into purely mathematical tasks such as working with discrete Fourier transforms, manipulating matrices and vectors, as well as working with basic mathematical functions. Once you have learned to use these mathematical tools in Excel, Bourg uses them to show you how to perform curve fitting and regression, solve equations, perform integration and differentiation, and solve both ordinary and partial differential equations. He even spends time on performing multivariable calculus and the finite element method in Excel. Chapter 13, on optimization, was my favorite chapter. Here, Bourg is actually getting into a little algorithm analysis and design via linear programming and genetic algorithms. This chapter showed me some truly innovative uses of Excel. The final chapter deviates from the scientific flavor of the book and concentrates on more traditional financial applications. The writing is very accessible, the examples are clear and very creative, and the author does a tremendous job of capturing the range of Excel's mathematical capabilities. Do not expect mathematical theory in this book. Bourg assumes you already know how to set up a mathematical problem and that you just need a computational platform and tools with which to perform your work. It is nice to know I am not necessarily held hostage by Mathworks(maker of Matlab) every time I need to solve a mathematical problem of any level of sophistication. Highly recommended. The table of contents is as follows: 1. Using Excel 2. Getting Acquainted with Visual Basic for Applications 3. Collecting and Cleaning Up Data 4. Charting 5. Statistical Analysis 6. Time Series Analysis 7. Mathematical Functions 8. Curve Fitting and Regression 9. Solving Equations 10. Numerical Integration and Differentiation 11. Solving Ordinary Differential Equations 12. Solving Partial Differential Equations 13. Performing Optimization Analyses in Excel 14. Introduction to Financial CalculationsRead more ›
No, I mean no sarcasm here at all. With all the books in O'Reilly's "Cookbooks" line, I find that it's really hit or miss. Sometimes the books are good, sometimes great, sometimes it's a big whiff.
Not here folks.
I can say without question that the 'Excel Scientific and Engineering Cookbook' by David Bourg is the BEST line in the Cookbook series I have read thus far. Neatly compact at just over 400 pages and full of actual, useful tips and tricks throughout, this is must read for anyone that uses the mathematical side of Excel and wants to learn how to take their car into the next gear!!
After reading this book you will be amazed at all the things you can do in Excel and I have little doubt that you will learn something new and ENJOY doing it while you take a bite out of this great manual!!
I am very surprised that there are only 2 reviews here. This is a must have book for all engineering students. The book totally leverage all of excel powers commingled with vba. While other vba books talk about loops and looping, this book did that in just one chapter. The other chapters talk about all what engineering students want: solving and writing codes for non-linear equation (a must for solving for z factor in thermo), numerical differentiation, numerical integration, differential equations, partial differential equations, statistical analysis and valuable things about excel. Combined this book with any standard vba text, and you are set. Kudos to David Bourg.
Bourg's book is an excellent collection of analytical recipes suitable for undergraduates, graduate and postdocs in all scientific disciplines. Engineers will find good treatment of important topics such as optimization and numerical integration. Statistical analysis is also covered, although no theoretical background is provided, and in this format, none should be expected, as the author indicates. An excellent and useful book.
This book is good not just for the examples that are in here, but also for the ideas and techniques it gives you to solve your own unique problems. Each recipe describes the problem, presents a solution in screenshots and code, and then does a good job describing that solution. And through that the book teaches not only a specific solution, but also a generic approach that will help you solve other related problems.
I learned alot from this book. I learned how to use Excel to properly model complex mathametical calculations, and I rounded out some mathematics knowledge (eg PDE implementations, data smoothing via moving average). there are a few areas that this book doesnt cover, which may be appropriate for scientific computing using Excel: 1) VSTO C# coding against Excel, 2) SQL Server Analysis Services integration with PowerPivot for Excel, 3)Excel Services and UDFs, 4) Solver Foundation, and 5) Windows HPC Excel Services for distrubted workbook processing.
1. Sharable and somewhat powerful tool for numerical calculation. 2. Quick and easy way to compare and prove the results of expensive math tools.
I have thought EXCEL might be the best one. That's why I have bought and read this book.
I was delighted that I was right and this book was fun also. I'll point out just one thing how good it is for a mechanical engineer like me: "solver": the optimization tool and more. I have been looking for something like that tool since I started the graduate school.
Well, here maybe I am just telling I am so ignorant about the excel, but anyway I really enjoyed this book and I strongly recommend it. |
Studying Mathematics at Brookes, you will focus on the subject's modern applications - the structures and techniques which underpin science and technology.
Why choose this course
Mathematics is an elegant and exciting subject encompassing structures and techniques which underpin science and technology.
The mathematics courses at Oxford Brookes University focus on modern applications of the subject.
Mathematics graduates have excellent career prospects and our courses enable students to develop key skills which are highly valued by employers.
100 per cent of maths students said Brookes staff were "good at explaining things" in the 2012 National Student Survey.
The Sunday Times University Guide (2013) rated Brookes 10th best in the UK for maths subjects.
Our modular system gives you the flexibility to develop your mathematical skills according to your interests and ambition.
This course in detail
During Year 1 you will develop essential knowledge and skills in pure mathematics, mathematical methods and mathematical modelling (and statistics in the single honours course).
In Year 2 and the final year on the single honours course, you will spend most of your time on mathematics but you will also have the opportunity to study some statistics. On the combined honours course, modules in mathematics are complemented by those in your other field of study. Throughout the course we will encourage you to acquire and develop your computing abilities through the extensive use of up-to-date mathematical (and, for single honours, statistical) software.
Study modules
As courses are reviewed regularly the module list you choose from may vary from that shown here. Some modules will be compulsory.
Year 1
For single honours
Applied Probability
Statistical Inference
Algebra and Calculus (double)
Introductory Mathematics
Basic Survey Methods
Modelling and Computation
Word-Processing and Spreadsheet IT skills.
For combined honours
Algebra and Calculus (double)
Introductory Mathematics
Applied Probability
Modelling a Computation
Word-Processing and Spreadsheet IT skills.
Year 2 and final year
For single honoursIndependent Study in Mathematics
Mathematics Project (double)
Mathematics for Decision Making
Quantitative Research Methods
Linear Algebra and Analysis I
Linear Algebra and Analysis II
Honours Topics in Mathematics (double)
Time Series Analysis
Sampling and Surveys
Communicating Statistics
Simulation and Modelling Linear Regression Models
Linear Regression Models
Honours Topics in Statistics
Medical Statistics.
For combined honours
Simulation and Modelling
Linear Algebra and Analysis I
Linear Algebra and Analysis IIHonours Topics in Mathematics
Independent Study in Mathematics
Mathematics for Decision Making
Mathematics Project (double)
Mathematics Interdisciplinary Project.
Work placements
It is possible to study combined honours Mathematics as a four-year sandwich course, the third year being spent in supervised work experience. This is possible if you are combining Mathematics with certain subject areas such as computing.
Study abroad
Great opportunities to study or work abroad
You may be able to go on a European or international study exchange while you are at Brookes. Most exchanges take place in the second year.
Free language courses for students - the Open Module
Free language courses are available to full-time undergraduate and postgraduate students on many of our courses, and can be taken as a credit on some courses.
Please note that the free language courses are not available if you are:
studying at a Brookes partner college
studying on any of our teacher education courses or postgraduate education courses.
Teaching, learning and assessment
Teaching and learning
We use a wide range of teaching methods, including lectures, problem-solving classes and group work, as well as guided reading and research. Lecturers will generally supply extensive handouts and booklets during sessions. Our experienced staff provide tutorial support in practical classes and on a one-to-one basis where required. You will also be able to access online educational materials through our virtual learning environment.
Approach to assessment
Coursework is an
important element in assessment and is highly valued by students for the
feedback it provides. Most modules are assessed using a combination of
coursework and examination, although some rely solely on coursework.
Assessment methods include individual work, group assignments,
presentations and project work.
Learning outcomes
When you have successfully completed this course, you will have:
an understanding of the foundations, techniques, limitations and applications of selected areas of mathematics
the confidence to tackle mathematical problems and to formulate and analyse mathematical and numerical models
experience in the selection and use of mathematical software
enhanced ability to communicate within and across discipline boundaries, and to work independently and as a member of a team
a range of transferable skills in self-management, communication, problem-solving, information technology, and logical and analytical reasoning.
In addition, if you take the single honours course you will have an understanding of the foundations of statistics, some knowledge of statistical modelling and some experience in the use of statistical software.
How to apply / Entry requirements
Typical offers
IB Diploma:
32 points, to include at least a 6 in Standard Mathematics (single honours). 31 points, to include at least 6 in Standard Mathematics (combined honours).
BTEC National Diploma with two distinctions and one merit PLUS grade B minimum in A-level Mathematics (single honours). BTEC National Diploma with one distinction and two merits PLUS grade B minimum in A-level Mathematics (combined honours).
For combined honours, normally the offer will lie between the offer quoted for each subject.
Country specific entry requirements
If you are studying outside the UK, for more details about your specific country entry requirements, translated information and local representatives who can help you to apply, please have a look at our country specific information pages.
How to apply
Conditions of acceptance
When you accept our offer, you agree to the conditions of acceptance. You should therefore read those conditions before accepting the offer.
Credit transfer
Oxford Brookes operates the European Credit Transfer System (ECTS). All undergraduate single modules are equivalent to 7.5 ECTS credits and double modules to 15 ECTS credits. More about ECTS credits.
Student experience
Why Oxford is a great place to study this course
As a student in Oxford you'll be at the heart of the UK's most successful economic region and in a centre for leading industries which will provide you with a host of work placement and other learning opportunities.
One of the world's great academic cities, Oxford is a key centre of debate, with conferences, seminars and forums taking place across education, science, the arts and many other subjects. It is a vibrant city with plenty of attractions for its large student population, from theatres and cinemas to museums, art galleries and music venues. A bustling and stunning cosmopolitan city, Oxford has excellent shopping, restaurants, cafes, pubs and clubs.
Situated in the heart of England and home to around 150,000 people, Oxford offers students a clean and safe environment less than an hour from London and international airports.
Specialist facilities
You will have access to excellent computer facilities. The department is located in modern buildings with its own networks of computers as well as full use of the university's extensive PC networks. We emphasise the importance of developing computer skills and give our students many opportunities to use specialist software packages during their course.
We want your time at Brookes to be as enjoyable and successful as possible. That's why we provide all the facilities you need to be relaxed, happy and healthy throughout your studies.
After graduation
Professional accreditation
The single honours course and our honours degree courses in which Mathematics is combined with Statistics have been recognised by the Institute of Mathematics and its Applications (IMA). These courses will meet the educational requirements of the Chartered Mathematician designation, awarded by the Institute of Mathematics and its Applications, when they are followed by subsequent training and experience in employment to obtain equivalent competences to those specified by the Quality Assurance Agency (QAA) for taught master's degrees.
Career prospects
Recent research has shown that graduates in mathematical disciplines enjoy one of the highest earning potentials of all graduates. Employers recognise that mathematical knowledge and skills are essential to the solution of many current problems, not only in science and technology but also in business and commerce.
As well as using their knowledge directly in scientific research and teaching, graduates in Mathematics go on to develop careers in accountancy, computing, actuarial, market research or management work where they can use their numeracy and skills such as problem-solving and statistical modelling. Many of our graduates also progress to postgraduate study, both MSc and PhD.
Graduates in Mathematics are particularly well equipped for a career in information technology and related areas. For example, demand is strong for graduates capable of developing error-free software that is mathematically based and also for those who can exploit sophisticated software and technology effectively.
As mathematics is a National Curriculum subject, a combined or single honours mathematics degree will equip you to proceed directly to a teaching qualification. There is high demand for mathematics graduates in the teaching profession.
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Elementary Education
Mathematics for Elementary Teaching I
Class Level: Junior
Credits: 2
Department: Education
Term:
Description: This course is the first foundational course in the mathematics content area for elementary education majors. It includes problem solving, sets, functions, exploration of our number system including properties, place value, basic operations and algorithms
Overheard
"
Franklin College has prepared me by teaching me how to adapt to situations quickly." |
Course Description: This is the first course in the college preparatory math sequence. Students will review the language of algebra, operations with signed numbers, and the basic properties for simplifying and solving equations. Students will learn techniques to solve first and second degree algebraic sentences. Students will use problem-solving techniques in working with word problems involving fractions, decimals, and percents. Students will be introduced to graphing first-degree equations and inequalities in one and two variables. Students will also be introduced to basic geometrical terminology and problems. |
0321849248
9780321849243
Survey of Mathematics with Applications, A:This is the eBook of the printed book and may not include any media, website access codes, or print supplements that may come packaged with the bound book. In a Liberal Arts Math course, a common question students ask is, "Why do I have to know this?" A Survey of Mathematics with Applications continues to be a best-seller because it shows students how we use mathematics in our daily lives and why this is important. The Ninth Edition further emphasizes this with the addition of new "Why This Is Important" sections throughout the text. Real-life and up-to-date examples motivate the topics throughout, and a wide range of exercises help students to develop their problem-solving and critical thinking skills. Angel, Abbott, and Runde present the material in a way that is clear and accessible to non-math majors. The text includes a wide variety of math topics, with contents that are flexible for use in any one- or two-semester Liberal Arts Math course.
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Rent Survey of Mathematics with Applications, A 9th edition today, or search our site for Allen R. textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Pearson. |
MATLAB及其在理工课程中的应用指南 (第3版)
Written for undergraduate students in science and engineering, this book provides a comprehensive introduction to MATLAB. The revised third edition contains three sections. The first section introduces the student to MATLAB language and environment. The second section focuses on mathematics and shows how to use MATLAB to solve calculus, linear algebra, and statistics problems. The third section focuses on applications, and contains numerous examples using MATLAB to solve problems in physics, mechanics, electronics, and signals and systems.
The book includes an introduction to MATLAB. In addition, a supplemental set of MATLAB M-files is available for download. |
Harmonic analysis is the branch of mathematics that studies the representation of functions or signals as the superposition of basic waves, and Gelfand pairs refer to pairs of groups satisfying certain properties on restricted representations. This book contains written material of lectures on the topic which might serve as an introduction to the topic. more...
This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that... more...
An insightful presentation of the key concepts, paradigms, and applications of modeling and simulation Modeling and simulation has become an integral part of research and development across many fields of study, having evolved from a tool to a discipline in less than two decades. Modeling and Simulation Fundamentals offers a comprehensive and authoritative... more...
The importance of partial differential equations (PDEs) in modeling phenomena in engineering as well as in the physical, natural, and social sciences is well known by students and practitioners in these fields. Striking a balance between theory and applications, Fourier Series and Numerical Methods for Partial Differential Equations presents an introduction... more...
In time series modeling, the behavior of a certain phenomenon is expressed in relation to the past values of itself and other covariates. Since many important phenomena in statistical analysis are actually time series and the identification of conditional distribution of the phenomenon is an essential part of the statistical modeling, it is very important... more...
Recent years have seen a significant rise of interest in max-linear theory and techniques. Specialised international conferences and seminars or special sessions devoted to max-algebra have been organised. This book aims to provide a first detailed and self-contained account of linear-algebraic aspects of max-algebra for general (that is both irreducible... more...
This guide book to mathematics contains in handbook form the fundamental working knowledge of mathematics which is needed as an everyday guide for working scientists and engineers, as well as for students. Easy to understand, and convenient to use, this guide book gives concisely the information necessary to evaluate most problems which occur in concrete... more...
WILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations... more... |
More About
This Textbook
Overview
Prealgebra, Second Edition, helps students not only learn but also retain, mathematical concepts - an important challenge that math instruction must meet in order to ensure the current and future success of mathematics students. A strong revision that includes a new design, a new art program, and key content enhancements, our text incorporates a careful development of mathematical concepts, a focus on the ""why"" behind the mathematics, and a problem-solving approach that can be applied in all math courses, as well as in everyday life. Refine pedagogy and an enhanced supplements package also provide maximum help and support for both instructors and students.
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Meet the Author
Marvin Bittinger has been teaching math at the university level for more than thirty-eight years. Since 1968, he has been employed at Indiana University Purdue University Indianapolis, and is now professor emeritus of mathematics education. Professor Bittinger has authored over 190 publications on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy and his election to the Manchester College Board of Trustees from 1992 to 1999. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled "Baseball and Mathematics." His hobbies include hiking in Utah, baseball, golf, and bowling. In addition, he also has an interest in philosophy and theology, in particular, apologetics. Professor Bittinger currently lives in Carmel, Indiana with his wife Elaine. He has two grown and married sons, Lowell and Chris, and four granddaughters |
Practice division withThis book contains some tricks extracted from Vedic Mathematics
Which are useful in making Calculations in short peroid of time or
While solving some problems.The book is very useful,the thing is
Some practise need to be done,these tricks help make calculations
In less peroid of time.
The Author of the book, Kiran Anil Parulekar has been researching number theory and practical numbers. He is a number wizard and carries a vast experience in Elementary Number Theory and Calculation of Numbers. "Amazing Properties of Squares & Their Calculations" is the result of Kiran's personal experience in working with large natural numbers over a period of 25 year.
Integration is the algebraic method of finding the integral. I was fun of Math and I conducted research in mathematics in my free time. I worked as adviser of Central Bank of the USSR in 1920-s and I was arrested during the Great Terror in 1930-s.
I started writing of this book in 1931 in terrible Verhneuralsk prison in Russia. This book is in Russian and my dream is to translate it in English.
GCSE Maths Teachers Pack
Learn GCSE Maths on your Smartphone
GCSE Maths receipt.
How much is a trillion? How high would a stack of a trillion dollars be? How much space would a trillion candies might take up? How many people can a trillion kernels of popped corn feed? These questions, and more, are posed, answered and explained in words and math.
Is it possible for Algebra to be easy, fun or cool?
Is it even possible to read any Math book and not get bored?
Math Is Super Cool – The Ultimate Guide for Understanding Algebra is one of few Math Books that will leave you wanting for more. This book teaches Algebra in a simple, cool, exciting, fun and I must admit a little crazy way trigonometric ratios, the trigonometric ratios of standard triangles, the sine rule, the cosine rule, the formula to calculate the area of a triangle as well as generic trigonometric equations equation of a circle, the graphs of cos x, sin x and tan x, transformed trigonometric graphs as well as the graph and CAST methods of solving trigonometric equations in a given ..
This eBook reviews simultaneous equations and inequalities. We introduce simultaneous equations as systems of equations, and consider some relatively simple pairs of simultaneous equations, one pair involving a pair of linear equations, and another pair involving one linear equation and one quadratic equation. We go on to introduce the two methods of solving simultaneous equations, elimination.. |
MA 125 Intermediate AlgebraPerhaps more than any subject, the successful learning of mathematics depends upon previously acquired knowledge and skill. Because of this, active participation in daily activities such as asking questions in class, reading the text, and working the assigned problems on time is essential.
I am here to help you learn. If you need any additional help or have questions, please come see me or email me.
Class Assessment:
Students will be evaluated based on performance of homework, quizzes, exams, and the final.
Homework - Homework is assigned at the end of each class, and expected to be completed by the next class meeting. The homework set will be collected on the exam day
Quizzes - The quiz will be given at the beginning of each class, and the quiz problems will come from homework.
Exams - There will be two in-class exams, Mid-term and Final. Test dates will be accounced ahead of time.
Final - The final exam will be comprehensive areLate submission of homework will not be accepted except in extreme cases as determined by the instructor. Homework must be turned in at the beginning of class on the day it is due1. Attend all classes and be in class on time.
2. Be prepared. Work all homework problems and ask questions
3. Know your material. Complete the readings and homework with the purpose of LEARNING.
4. Do respect others, property, and yourself.
5. Do give 100% effort, 100% of the time!
Be certain all cell phones & pagers are turned off. If there is an emergency for which you need to leave your phone on, please inform me before the start of the class.
Course Topic/Dates/Assignments:
Week1
Chapters 1
Homework #1 is assigned
Week2
Quiz #1
Chapter 2
Homework #1 is due
Homework #2 is assigned
Week3
Quiz #2
Chapter 3
Homework #2 is due
Homework #3 is assigned
Week 4
Homework #3 is due
Midterm Review
Midterm Exam
Week 5
Chapter 4
Homework #4 is assigned
Week 6
Quiz # 3
Chapter 5
Homework #4 is due
Homework #5 is assigned.
Week 7
Quiz #4
Chapters 6
Homework #5 is due
Homework #6 is assigned.
Week 8
Homework #6 is due
Final Exam ReviewMakeup Test/Quiz
may be granted at the sole discretion of the instructor and only in the event of
unavoidable and documented absence has been provided to the instructor. Each student will be
permitted only one make-up exam per term. NO EXCEPTIONS.
Copyright:
This material is protected by copyright and can not be reused without author permission. |
Course Information
MATH 100: The Mathematics of Democracy
We aspire to live in a democratic society, but what exactly does this mean? How can we decide, for example, which candidate in an election has the support of the people? How can Congressional seats be apportioned to the States "according to their respective numbers?" Are these things even possible? Recently, mathematical analysis has brought new insight to these old questions, often with surprising results. We will study some of this work and its implications for our democratic aspirations, and perhaps gain some appreciation for the power and elegance of mathematics along the way.
MATH 101: Calculus with Problem Solving
An introduction to the central ideas of calculus with review and practice of those skills needed for the continued study of calculus. Problem solving strategies will be emphasized. (Meets Monday through Friday).
Prerequisites: Not open to students who have received credit for Math 111. 6 credit; Mathematics and Natural Sciences, Formal or Statistical Reasoning; offered Fall 2013 · D. Haunsperger
MATH 106: Introduction to Mathematics
This course is designed to provide an understanding of fundamental concepts, and examples of applications, of mathematics. It attempts to provide insights into the nature of mathematics and its relation to other branches of knowledge, and helps students develop skill in mathematical reasoning. No prerequisites.
MATH 115: Statistics: Concepts and Applications
Introduction to statistical concepts with emphasis on understanding and interpretation of statistical information, especially in the context of media reports and scholarly articles. Examples taken from a wide-range of areas such as public policy, health and medicine, and the social and natural sciences. Computationally less intensive than Math 215. Students will learn how to use statistical software. Topics include: Uncertainty and variability, statistical graphs, types of studies, correlation and linear regression, two-way tables, and inference.
MATH 206: A Tour of Mathematics
A series of eight lectures intended for students considering a Mathematics major. The emphasis will be on presenting various striking ideas, concepts and results in modern mathematics, rather than on developing extensive knowledge or techniques in any particular subject area.
Prerequisites: Not open to students who have already received credit for Math 115, Psychology 200/201 or Math 275. Students who have taken Math 211 are encouraged to consider the more advanced Math 265-275 probability-statistics sequence. 6 credit; Formal or Statistical Reasoning, Quantitative Reasoning Encounter; offered Winter 2014 · Staff
MATH 236: Mathematical Structures
Basic concepts and techniques used throughout mathematics. Topics include logic, mathematical induction and other methods of proof, problem solving, sets, cardinality, equivalence relations, functions and relations, and the axiom of choice. Other topics may include: algebraic structures, graph theory, and basic combinatorics.
Extended departmental description for MATH 236
This course is intended to introduce students to certain features of the mathematical enterprise including: (1) basic structures in mathematics; (2) the nature of formal arguments that establish the validity of theorems; (3) strategies for problems-solving; and (4) analogies that exist among various mathematical concepts. Amidst all of this mathematical formality, you will discover some remarkable facts. In particular, you will learn that when Buzz Lightyear said "To infinity and beyond!", he was being mathematically precise.
Math 236 is the last course in the math sequence that is required of all math majors, and is the first course that suggests what being a math major (as opposed to a math user) is all about. If you are undecided about majoring in math, taking this course before you make the decision might prove helpful.
MATH 237: Designing a Curriculum for Math GED
We will help local communities respond to the latest changes in GED requirements by observing how GED mathematics is currently taught and preparing new curricular materials to teach it in the future.Prerequisites: Mathematics 236 and permission of the instructor. 2 credit; S/CR/NC; Does not fulfill a curricular exploration requirement; offered Spring 2014 · D. Haunsperger
MATH 241: Ordinary Differential Equations
An introduction to ordinary differential equations, including techniques for finding solutions, conditions under which solutions exist, and some qualitative analysis.
MATH 244: Geometries
Euclidean geometry from an advanced perspective; projective, hyperbolic, inversive, and/or other geometries. In addition to foundations, various topics such as transformation and convexity will be treated. Recommended for prospective secondary school teachers.
MATH 245: Applied Regression Analysis
A second course in statistics covering simple linear regression, multiple regression and ANOVA, and logistic regression. Exploratory graphical methods, model building and model checking techniques will be emphasized with extensive use of statistical software to analyze real-life data.
MATH 280: Statistical Consulting
Students will apply their statistical knowledge by analyzing data problems solicited from the Northfield community. Students will also learn basic consulting skills, including communication and ethics.
MATH 295: Seminar in Set Theory
Introduction to set-theoretic foundations of mathematics. The axiom system of Zermelo-Fraenkel, cardinal and ordinal numbers, and the Axiom of Choice. As time permits, additional topics may include construction of the real number, transfinite induction, or consistency/independence proofs.
An independent study course intended for students who have completed an external activity related to the mathematics major (for example, an internship or an externship) to communicate (both in written and oral forms) and assess their mathematical learning from that activity.
MATH 312: Elementary Theory of Numbers
Properties of the integers. Topics include the Euclidean algorithm, classical unsolved problems in number theory, prime factorization, Diophantine equations, congruences, divisibility, Euler's phi function and other multiplicative functions, primitive roots, and quadratic reciprocity. Other topics may include integers as sums of squares, continued fractions, distribution of primes, integers in extension fields, p-adic numbers.
Covers sampling design issues beyond the basic simple random sample: stratification, clustering, domains, and complex designs like two-phase and multistage designs. Inference and estimation techniques for most of these designs will be covered and the idea of sampling weights for a survey will be introduced. This course will also teach methods for graphing complex survey data and exploring relationships in complex survey data using regression and chi-square tests.
MATH 341: Fourier Series and Boundary Value Problems
Fourier series and their applications to boundary value problems in partial differential equations. Topics include separation of variables, orthogonal sets of functions, representations of functions in series of orthogonal functions, Sturm-Liouville theory, and Fourier transforms.
MATH 349: Methods of Teaching Mathematics
Cross-listed with EDUC 350.
Methods of teaching mathematics in grades 7-12. Issues in contemporary mathematics education. Regular visits to school classrooms and teaching a class are required.
Prerequisites: Junior or senior standing and permission of the instructor. 6 credit; Does not fulfill a distribution requirement, Does not fulfill a curricular exploration requirement; not offered 2013–2014
Extended departmental description for MATH 351
What happens to calculus when you replace the real variable x by the complex variable z = x + iy and the real-valued function y = f(x) by the complex-valued function w = f(z)? For starters, the statement "f is differentiable" becomes more powerful while the idea of integration becomes more flexible---you can now integrate along various paths in the complex plane. This subject is inherently elegant – arguably among the most beautiful subjects in mathematics. But, perhaps surprisingly, this subject is also one of the most practical and can be applied to "real" mathematical and physical problems in which no complex number occurs. This course has connections with many other upper-level math courses. Those who have taken other courses should enjoy discovering some of those connections. However, Math 211 is really the only prerequisite.
MATH 352: Topics in Abstract Algebra
An intensive study of one or more of the types of algebraic systems studied in Mathematics 342.
MATH 354: Topology
An introduction to the study of topological spaces. We develop concepts from point-set and algebraic topology in order to distinguish between different topological spaces up to homeomorphism. Topics include methods of construction of topological spaces; continuity, connectedness, compactness, Hausdorff condition; fundamental group, homotopy of maps.
MATH 395: Topics in Algebraic Number Theory
Study of integers in algebraic extensions of the rationals. Motivated by a failed attempt to prove Fermat's last theorem, we define the ring of integers, examine the failure of unique factorization, and rehabilitate it somewhat by showing that ideals have unique factorization into prime ideals. Further topics may include the finiteness of the class number, units in rings of integers, relations to Galois theory, cyclotomic fields, class number formulas, and the Chebotarev density theorem. Where appropriate for comps projects, links to arithmetic dynamics will be given.
MATH 395: Combinatorics of Symmetric Functions
Study of symmetric functions with an emphasis on the underlying combinatorics. Course opens with several bases for the space of symmetric functions, including elementary symmetric functions, complete homogeneous symmetric functions, power sum symmetric functions, and Schur functions. The rest of the course is devoted to combinatorial answers to algebraic questions; topics may include standard and semistandard tableaux, Kostka numbers, the hook length formula, the Robinson-Schensted-Knuth correspondence, Cauchy's identity, the Pieri rules, lattice paths and the Jacobi-Trudi identities, the Murnaghan-Nakayama rule, the Littlewood-Richardson rule, Knuth equivalence on words, jeu de taquin, and compositions and quasisymmetric functions. |
This eBook introduces the topic of polygons, tessellations and symmetry, through a review of what polygons are, a review of angles within polygons, a review of what tessellation of 2D planar shapes is, and the various forms of symmetry that exist with regard to 2D planar shapes and 3D solidsAs parents, we know that every mom and dad strives to help their kids develop an appetite for learning that will last a lifetime. But, if we want our kids to "think different", we need to first acknowledge that they "learn different"...then help them learn to play to those learning strengths.
This eBook introduces the topic of inequalities, the meaning of the inequality symbols, how to rearrange and solve inequalities as well as the use of inequalities and number lines and the use of inequalities in graphs.
A Unit Study to use while Reading the novel.
This unit study DOES NOT include the novel.
This unit study offers many wonderful activities to use while having students read the book. There are between 6 and 10 lessonsSo many of us have gmail accounts, but are we really using them to their fullest potential? This guide will help you take a different look at your Gmail account and offer you many options for increasing productivity and efficiency, saving your seconds for the more important things in life! |
ALEX Lesson Plans
Title: Why so Cross?
Description:
This lesson will help students develop a deep understanding of what the solution to a system of linear equations means. They will investigate the graphs of systems as well as experiment with an online graphing calculatorSubject: Mathematics (8 - 12) Title: Why so Cross? Description: This lesson will help students develop a deep understanding of what the solution to a system of linear equations means. They will investigate the graphs of systems as well as experiment with an online graphing calculator.
Title: Systems of Equations: What Method Do You Prefer?
Description:
TheStandard(s): [MA2013] (8) 10: Analyze and solve pairs of simultaneous linear equations. [8-EE8] [MA2013] AL1 (9-12) 19: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. [A-REI5] [MA2013] AL1 (9-12) 23 ALC (9-12) 2: Solve application-based problems by developing and solving systems of linear equations and inequalities. (Alabama) [MA2013] ALT (9-12) 22: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [A-CED3]
Subject: Mathematics (8 - 12) Title: Systems of Equations: What Method Do You Prefer? Description: The
Web Resources
Lesson Plans
Title: Supply and Demand
Description:Supply and Demand
Title: Graphing Lines
Description:
Students explore the world of lines by investigating the relationships between linear equations, slope, and graphs of lines. This interactive tool requires Javascript.
Standard(s): [MA2013] (7) 2: Recognize and represent proportional relationships between quantities. [7-RP2] [MA2013] (8) 10: Analyze and solve pairs of simultaneous linear equations. [8-EE8] [MA2013] AL1 (9-12) 17: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. [A-REI3] [MA2013] GEO (9-12) 31: Prove the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). [G-GPE5]
Graphing Lines
Students explore the world of lines by investigating the relationships between linear equations, slope, and graphs of lines. This interactive tool requires Javascript. |
In the minds of many, calculus is college mathematics. Using calculus we can calculate exactly how much force to apply to send a spacecraft to mars, or the rate at which a medication will be absorbed into the bloodstream. Calculus connects mathematics to our natural world.
You might be surprised to learn that all of calculus is built on three not so difficult concepts: limits, rates of change, and areas under a curve. As one well-known mathematics professor has put it, "A typical calculus textbook has 5 pages to explain the concepts and 1200 pages of examples."
Of Special Note: For students with a background in college math, The Empire State College Course, Math Modeling, is for students ready to go beyond the basics and learn about the math models used in science and economics. |
Text Size:
AAA
MATH070 - Developmental Mathematics
Credits: 3
The content of the course is designed to either review or to enhance the mastery of basic mathematical concepts and skills that are needed to successfully complete future courses in math. The inclusion of numerous real-data and real-world applications relating to everyday life or to other academic disciplines will enable the student to begin the development of a firm foundation of math facts and problem-solving skills. Calculators will not be used in this course until the very end of the term. Credits do not count toward graduation requirements. |
How to evaluate progress in problem solving by Randall I Charles(
Book
) 8
editions published
between
1987
and
1994
in
English
and held by
414 WorldCat member
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"This book puts the goals of problem-solving evaluation in sharper foucs, describes several classroom evaluation techniques, and illustrates how these techniques might be used in practice." -- from p. 1
Scott Foresman - Addison Wesley mathematics by Randall I Charles(
Book
) 93
editions published
between
2004
and
2008
in
English
and held by
366 WorldCat member
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worldwide
This sixth-grade textbook focuses on key ideas in mathematics, rich problem-solving lessons that build the reading and writing skills necessary for powerful problem solving, and differentiated instructional options to meet the needs of varied learners
Mathematics by Randall I Charles(
Book
) 42
editions published
between
2004
and
2012
in
English
and held by
363 WorldCat member
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Scott Foresman-Addison Wesley middle school math by David L Stout(
Book
) 9
editions published
between
1998
and
2002
in
English
and held by
135 WorldCat member
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A middle school math program consisting of three courses: course 1 focuses on numerical reasoning; course two focuses on proportional reasoning;; course 3 focuses on algebraic reasoning
Addison-Wesley pre-algebra : a transition to algebra by Phares G O'Daffer(
Book
) 10
editions published
between
1987
and
1992
in
English
and held by
120 WorldCat member
libraries
worldwide
Pre-algebra text with accompanying workbook and teacher's materials provides a program in mathematics which is a transition from arithmetic to algebra. Includes decimals, number theory, equations, percent, ratio, area and volume, statistics, and square roots
Prentice Hall mathematics(
Book
) 28
editions published
between
2004
and
2012
in
English
and held by
103 WorldCat member
libraries
worldwide
Prentice Hall mathematics(
Book
) 24
editions published
between
2004
and
2013
in
English
and held by
92 WorldCat member
libraries
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Prentice Hall mathematics(
Book
) 25
editions published
between
2003
and
2012
in
English
and held by
88 WorldCat member
libraries
worldwide
Scott Foresman-Addison Wesley enVisionMATH(
Book
) 12
editions published
between
2009
and
2012
in
English
and held by
84 WorldCat member
libraries
worldwide
Daily problem-based interactive learning followed by visual learning strategies deepen conceptual understanding by making meaningful connections for students and delivering strong, sequential visual/verbal connections through the visual learning bridge in every lesson. Ongoing diagnosis & intervention and daily data-driven differentiation ensure that enVisionMATH gives every student the opportunity to succeed. - Publisher
Addison-Wesley mathematics by Robert E Eicholz(
Book
) 10
editions published
between
1985
and
1992
in
English
and held by
72 WorldCat member
libraries
worldwide
An introduction to the mathematical concepts and skills involved in personal money management and in being a consumer. Discusses such topics as shopping, banking, investments, and taxes
Pre-algebra by Randall I Charles(
Book
) 14
editions published
between
2004
and
2009
in
English
and held by
71 WorldCat member
libraries
worldwide
High school textbook on mathematics, with North Carolina mathematics standard course of study handbook |
MAT117 Week 9 Discussion 1
Course: MAT 117, Spring 2013
School: University of Phoenix
Word Count: 1284
Rating:
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Week 99 Week.
RESPONSE 1 1) From the concepts you have learned in this course, provide a real-world application of something that you think has been the most valuable to you? Why has it been valuable? From the concepts that I have learned in this course, algebra in this class has showed me that it can be a useful tool that can be used in various amount of ways. First of off to start out with that math can be used to determine things like distance, measurement, and percentage. The use of equations has helped better my knowledge solving quadtraic, polynomial and radical equations. The concept in how it has provided a real-world application to myself is how I will be able to use rational expressions to solve like baking and cooking and also calculating my past and taxes. The my math lab helped me a lot with equations because it gave examples that explained how to solve each problem making it easier for me while taking my tests because I was already was doing them and had notes to help me out. Also the use of mymath lab helped break the equations in steps making it less complex and easier to understand. I suggest that students taking this course are well organized and very good with keeping up with due dates and studying. 2) How do you think you will use the information you learned in this course in the future? The way I think I will use the information I have learned in this course will be applied to any type of jobs that require me to use math. Right now currently Im in the army so
I will not be using any of the concept that I have learned in this class, but I hope to use them later in the future to better myself and keep it in the brain as a reminder.
3) Which concepts will be most important to you? Explain why. The main concept to me that will be most important will be the quadratic equations . The reason I say that quadratic equations is most important, is because they were the easiest of all the concepts to solve for me and didnt give me that much of an issue. 4) Which do you anticipate will be the least important? Explain why. Well to me the one concept that I feel will be least important to me is trying to solve radical equations. For some odd reason when it came to solving radical equations I just had issues solving them. As much as i looked over my notes and tried following examples it still would not come out right. RESPONSE 2 A real world application for my future career in accounting would be compounding interest. A client has $1,500 to put into an interest account. They want to know how much annual interest is paid and how much would be in the account after five years. We compound monthly with an annual rate of 6%. To find out how much is in the account after five years we know there are 12 months in a year and 5 years of compounding. The account would compound 60 times. P = 1500 r=0.06 n=12 t=5. The formula: A = P(1 + r/n)^nt. A = 1500(1 + 0.06/12)^12*5. A=1500(1.005)^60. A = $2023.28 I will use some algebra in the future because my accounting career will deal with a lot of math. We will need to know How formulas. to plug in the correct numbers. We will double check our work. We may have two numbers and need to find a third. We will use percentages, interest, maybe even log and exponents. I feel the concepts of interest and percent change will be beneficial in my future. They will come in handy when we deal with interest on accountants and how much a client will gain and maybe to choose the best solution to saving and investing money. Percent change will help when we look at annual amounts and how they changed from year to year.
The concept I feel would be least important would be quadratic formulas and functions. I do not see that being used in accounting from what I have learned so far. RESPONSE 3 From the concepts that I have learned throughout this course, I would say that in Chapter 5 and Chapter 12, in these chapters it explains that you can figure out compound interest for a savings account using as expression. I am sure I will always have a savings account and now I know how to make more off of the money I put into my account in the future by using concepts that I have learned in this class. I am going into the accounting field so I think that concepts that help me figure out compound interest and wages are the most important concepts that I have learned. When I first started this course I thought that I would not use any of the concepts again but I am seeing more and more how the concepts are used in everyday life. The concept that I anticipate will be the least important is multiplying and dividing fractions. RESPONSE 4 Of the concepts we learned throughout this class, I think the quadratic equations is something I will use now and in the future. We can use a lot of the information we learned for many reasons. An example is when doing home remodeling we can use the quadratic equations to add more patio room, or measure the diagonal of a window to change the glass. It is a great way to measure and determine what amount of supplies I will need to complete the work at hand. The other concept we learned that I think I will use a lot in life, is proportions. In every aspect of life, there is a way to use proportions. Whether it is cooking, making a cleaning solution, putting gas, or determining how much money will be left after bill paying, ratios and proportions are found everywhere. I think we learned this when we were little, but after taking this class, we learned a harder approach with variables. The concept that I think will be less important in life, is graphing. I am still confused about how to graph sometimes and I don't think I will use graphing of information in any profession I go into.
RESPONSE 5 The concept that I believe will be the most valuable in my future were quadratic equations. Quadratic equations can determine a variety of solutions to a mathematical problem that has multiple terms. Quadratic equations can also be used to determine areas for a variety of things including cooking areas and temperatures, restaurant space, and home projects. I will use different concepts that I learned in this course to aid me with labor rates, efficiency, and later in life when I want to open my own restaurant. I do not see myself using radicals and logarithms in the near future, if at all. Many of the concepts we have learned have real world application but do not need to be used in those applications. Some of the applications could be reduced to simple math and hands on trial.
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"Week 4 DQ 1 Please post a 150-300-word response (signature block not included or question) to the following discussion question by clicking on Reply. Answer all parts of the DQ completely. What defines a rational expression? How would you explain this con"
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What is the difference between solving and evaluating? 2) Provide a detailed example of both. 3) Provide one example for your classmates to solve and one for them to evaluate.
RESPONSE 1 Solving an equation is when you are looking to find t"
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"Table lists data regarding the average salaries of several professional athletes in the years 1991 and
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Use the data points to find a linear function that fits the data
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HUM/111 Version 5
Associate Level Material
Appendix D
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thinking? Wh"
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"Appendix E
ETH/125 Version 7
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Appendix E
Part I
Define the following terms:
Term
Definition
Racial formation
A theory that states that the importance of race is a social construct.
Within this construct, race has a different " |
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This Flash Forum tutorial not only discusses the programming involved in rendering simple polyhedra in Flash CS3, but it also gives an elementary discussion of the mathematics behind 3D rendering on a 2D computer screen.
The "area function" is often discussed as part of an introduction to the definite integral. This applet provides an innovative approach to producing functions drawn with a mouse in the context of an exploration/demonstration of the area function.
This interactive Geogebra applet allows exploration of a linear transformation in terms of images of a set of points. The Geogebra interface allows dragging of points and vectors to make for versatile explorations of basic linear algebra ideas. Suggested activities are included. |
CliffsQuickReview course guides cover the essentials of your toughest classes. Get a firm grip on core concepts and key material, and test your newfound knowledge with review questions.<p>Whether you're new to fractions, decimals, and percentages or just brushing up on those topics, <i>CliffsQuickReview Basic Math and Pre-Algebra</i>... more...
Your complete guide to a higher score on the CSET: Mathematics. Features information about certification requirements, an overview of the test - with a scoring scale, description of the test structure and format and proven test-taking strategies Approaches for answering the three types of questions: multiple-choice... more...
CliffsQuickReview course guides cover the essentials of your toughest subjects. Get a firm grip on core concepts and key material, and test your newfound knowledge with review questions. Whether you're new to limits, derivatives, and integrals or just brushing up on your knowledge of the subject, CliffsQuickReview Calculus can help. This guide covers... more...
CliffsQuickReview course guides cover the essentials of your toughest classes. Get a firm grip on core concepts and key material, and test your newfound knowledge with review questions. From planes, points, and postulates to squares, spheres, and slopes — and everything in between — CliffsQuickReview Geometry can help... more...
Boost Your grades with this illustrated quick-study guide. You will use it from college to graduate school and beyond. FREE Geometry Background and Triangles chapters in the trial version. Clear and concise explanations. Difficult concepts are explained in simple terms. Illustrated with graphs and diagrams. Table of Contents. Geometry Background. Euclidean... more... |
Matrices and determinants are very nice ways to vepresent bunch of number. matrices as well as determinants dlong with some very nice properties that each of then have, prove to be very useful in solving equations, finding area of polygons etc. Matrices a also find use in Linear Algebra which is beyond the scope of JEE syllabus. So, Let us study these in details.
Matrices And Determinants MATRICES
A rectangular away of elements or symbols.along sows and wlumns in colled a matricx .
Equal MAtrices :- Two matrices are eqnal if they have the same order and each element of ove is equal to the corresponding of the other.
Classification (Secondaty Information) :-
Row Matrix A mstrix lhaving a single row .
Column Matrix A matrix with a single column .
Square Matrix An m X n matrix is said to be a square matrix if m = n i.e. no. of rows = no. o of columns.
eg: A - Trace of a Matrix The sum of the elements of O square matrix A lying along the principal diagonal .
Properties of trace of a matrix (Secondary Information) :-
(i) tr (A) =tr (A)
(ii) tr (A + B) = tr (A) + tr (B)
(iii) tr (A B) = tr (B A)
Diagonal Matrix (Secondary Information) :-
A square matrix with all the elemente O except the diagonal elements.
Scalar Matrix :- A diagonal matrix whose all the leading elements are equal.
Unit or Identify Matrix :-
A diagonal matrix of order n which has only unity for all its diagonal elements. is called unit or Identify matrix of order n and is denoted by In.
Triangnlar Matrix (Secondary Information) :
A square matrix in which all the elements below the diagonal are zero is called upper triangnlar and square matrix in which all the elements above diagonal are zero is called lower triangnlar matrix . |
Math Problems and Solutions Guide
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Improve your homeschooler's understanding of K-12 math concepts with the easy-to-follow Math Problems and Solutions Guide. With chapters and sections that correspond to the best-selling Understanding Mathematics: From Counting to Calculus, this 305-page companion workbook provides more hints, examples, explanations, and exercises to eliminate issues that arise when solving specific problems.
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Description
Written to complement the explanations provided in the popular Understanding Mathematics: From Counting to Calculus, this informative guide contains over 10,000 additional problems and solutions that cover numbers, addition and subtraction, multiplication and division, fractions and percentages, negative numbers, exponents, pre-algebra, algebraic equations, graphs, geometry, trigonometry, logarithms, and more.
A valuable resource for teaching math, the Math Problems and Solutions Guide contains problem sets for commonly taught topics from first grade through high school, and it gives students more confidence and expertise when studying for standardized tests or college entrance exams. This supplemental resource from Alpha Omega Publications also includes a bonus section with extended math explanations, helpful hints to accelerate problem solving, and real-world problem scenarios to assist learning |
Glencoe Secondary Mathematics to the Common Core State Standards, Geometry SE Supplement
Reading and Writing in the Mathematics Classroom
Summary
Math Triumphsis an intensive intervention resource for students who are two or more years below grade level. The series accompanies GlencoeAlgebra 1,Geometry, andAlgebra 2and provides step-by-step intervention, vocabulary support, and data-driven decision making to help students succeed in high school mathematics.. |
Imported EditionPrinciples Of Mathematical Analysis is the first in Walter Rudin's series of books on mathematical analysis and is a leading introductory text on the subject.
Summary of the Book
Principles of Mathematical Analysis provides a comprehensive introduction to some of the major theories of mathematical analysis. First published in 1953, the book is a standard text for undergraduate and first year graduate students.
The book begins with a discussion on Real and Complex numbers and Basic Topology. Here, students are introduced to the background required to understand rest of the topics in the book. The book goes on to discuss Numerical Sequences and Series, Continuity, Differentiation, Riemann-Stieltjes Integral, Integration of Differential Forms, and The Lebesgue Theory. Appropriate appendices and exercises follow each chapter. The book, in its third edition, includes a new section on the gamma function, and interesting, new exercises.
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Nice
The Good thing about this book is that there is a detailed solution manual of the exercises in this book available on the internet. So you can tackle the exercises with assurance. The book is not written in the most simplest language there is a great deal of intuition required from the reader but hey that is mathematics. Enjoy
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Good book for Real Analysis
It's not a particularly easy read, as is widely known, but with some patience and work, it's very useful and rewarding. Starts basic and reaches advanced topics; better to have some experience with a proof-based course before-hand. |
This course will help you to learn PTC Mathcad in 25 live lessons of an hour each. These cover worksheets, functions, plotting, programming, units, statistics, calculus, vectors and matrices, linear and non-linear equations and differential equations. Some hundred exercises include examples from applied math, physics, chemistry and physiology.
To begin, download the lessons and exercises from the PTC website. Open the first lesson in Prime 3.0 and work through it. The course consists of read-only Mathcad files, which can be viewed and modified in the free Mathcad Express. The course is also available as a book from Delft Academic Press. This can be ordered via Amazon.
What is New: The largest change in Prime 3.0 compared to Prime 2.0 is in the editing of equations. These are handled in lesson 6. You will find the new method of editing to be more natural than the old one: it closely follows that of other Windows programs. There are smaller changes in lesson 1 (the interface), lesson 3 (templates), lessons 7,8 an 9 (plotting) and lessons 10 (labels and global variables). We have partly rewritten lessons 11 and 12 on programming and lessons 13 through 16 on statistics.
Worksheets marked with use PTC Mathcad premium features, otherwise they are Express compatible. All worksheets created in PTC Mathcad Prime 3.0.
PTC Mathcad is very useful for problems where you need to be flexible and creative: when you are learning a subject, doing homework, designing, or developing a new product or theory. You can even write a book in it, as this text shows.
PTC Mathcad has one great advantage over other programming languages: it is self-documenting. You will still be able to understand this Mathcad file if you load it in a years time. The program is not a full-fledged text editor, but as you can see in this chapter, text handling is good enough for many purposes.
When doing a quick calculation, you may not worry about the layout of your worksheet. However, for a report or a book, the layout needs to be chosen such that it does not distract the reader. For that, PTC Mathcad has integrated lots of features.
3D plots in PTC Mathcad are similar to 2D plots. However, there are differences of which you should be aware of. PTC Mathcad has two kinds of 3D plots: the true 3D plot with three axes as well as the contour plot. Two find out more about them check out this chapter.
In practical calculations you often need to use the same letter to describe different entities. For example the letter 'g' might be used to describe a variable, the unit gram, the gravitational acceleration and some function g(x). You can do this in PTC Mathcad without any confusion by giving these entities a different label.
PTC Mathcad contains a programming environment that greatly extends its capabilities. Despite the small number of commands you can construct the three main elements of any programming language: actions, branches and loops. That combined with the many other parts of Mathcad that you have learned in the previous chapters gives you humongous possibilities.
In this lesson (and the following ones) we look at data which will be regarded as two vectors of equal length. We will show how to summarize the behaviour of data by the mean and the standard deviation. Further we discuss two of the random number generators in PTC Mathcad.
In this chapter we look at how to handle data, specifically how to find relations between variables from experiments. We will look at two techniques for handling experimental data: Data fitting (regression analysis) and interpolation between data points.
PTC Mathcad is a layout program in which you can place text and math regions. In the previous chapters, the math regions have been numerical. However, you can also use these to do 'symbolic' calculations. These will allow you to redo classic 'calculus' on the computer: differentiation, integration, limits, series... and all these operation with equations as you would write them.
In this chapter we explore variations of symbolic evaluation using keywords and modifiers. We apply these to get a symbolic solution of equations, and to approximate a function as a series of polynomials.
You may know a lot about this subject without having realized. Calculations in Excel are vector and matrix operations. You can do these in PTC Mathcad with the advantage that calculations are much easier to follow and you are less likely to make any mistakes.
PTC Mathcad can solve implicit sets of linear and non-linear equations. It does this with a clever multi-variable interation technique. If you provide an approximate solution, then the program will improve your estimate. Because of that you must understand the behavior of the functions that you are studying.
We like to end with two bits of advice. Firstly that real problems take longer and secondly there is a lot more in PTC Mathcad that you have seen in these chapters. For more details, check out this chapter. |
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Math in the Middle School
Course Type:
Undergraduate
Course Prefix:
EDU
Course Number:
380
Credits:
3 sem. hrs.
Semesters Offered:
Spring
Focus is upon methods and techniques of teaching math concepts and skills in grades 4 through 9. Emphasis is upon building positive attitudes toward math, on-going formal and informal pupil assessment and the use of active hands-on participation. The Ohio Math Model will provide the concepts and skills for the method development. Short and long-range planning along with the use of materials and technology will be covered. Research of related professional literature is included. (Field experience required.) Prerequisites: 3.0 GPA, Junior level, C- or higher in PSY 101, EDU 220, EIS 265, EDU 230, and EIS 285. Corequisite: EDU 350, 375 and one of the following: 360, 373 or 390. |
Description of Algebra 1: Test Forms by Saxon
Geared specifically toward the homeschool classroom, Saxon Algebra 1 is a college-prep course designed to build the mathematical foundation necessary for students to transition successfully into higher-level math courses.
Ideal for additional students joining the Algebra 1 course, this set includes 30 test forms with step-by-step test solutions, plus an answer key with answers to all student textbook practices and problem sets.
This helped my first two children to be ready for calculus in college--they were able to test out of college algebra. My youngest child needed to go at a slower rate and had to take college Math in college. So it is great for those who have a bent for math and science. |
This course teaches the art of guessing results and solving problems without doing a proof or an exact calculation....
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This course teaches the art of guessing results and solving problems without doing a proof or an exact calculation. Techniques include extreme-cases reasoning, dimensional analysis, successive approximation, discretization, generalization, and pictorial analysis. Applications include mental calculation, solid geometry, musical intervals, logarithms, integration, infinite series, solitaire, and differential equations. (No epsilons or deltas are harmed by taking this course.) This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.
Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some...
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Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the plane) and its point-set topology. Option C (18.100C) is a 15-unit variant of Option B, with further instruction and practice in written and oral communication.
Analysis I covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability,...
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Analysis I covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and interchange of limit operations.
This course is meant as a first introduction to rigorous mathematics; understanding and writing of proofs will be emphasized....
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This course is meant as a first introduction to rigorous mathematics; understanding and writing of proofs will be emphasized. We will cover basic notions in real analysis: point-set topology, metric spaces, sequences and series, continuity, differentiability, and integration.
This course continues from Analysis I (18.100B), in the direction of manifolds and global analysis. The first half of the...
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This course continues from Analysis I (18.100B), in the direction of manifolds and global analysis. The first half of the course covers multivariable calculus. The rest of the course covers the theory of differential forms in n-dimensional vector spaces and manifolds.
18.104 is an undergraduate level seminar for mathematics majors. Students present and discuss subject matter taken from...
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18.104 is an undergraduate level seminar for mathematics majors. Students present and discuss subject matter taken from current journals or books. Instruction and practice in written and oral communication is provided. The topics vary from year to year. The topic for this term is Applications to Number Theory.
This is an advanced undergraduate course dealing with calculus in one complex variable with geometric emphasis. Since the...
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This course covers harmonic theory on complex manifolds, the Hodge decomposition theorem, the Hard Lefschetz theorem, and...
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This course covers harmonic theory on complex manifolds, the Hodge decomposition theorem, the Hard Lefschetz theorem, and Vanishing theorems. Some results and tools on deformation and uniformization of complex manifolds are also discussed. |
3146776X / ISBN-13: 9780131467767
Intermediate Algebra
The Sullivan/Struve/Mazzarella Algebra program is designed to motivate students to "do the math"- at home or in the lab-and supports a variety of ...Show synopsisThe Sullivan/Struve/Mazzarella Algebra program is designed to motivate students to "do the math"- at home or in the lab-and supports a variety of learning environments. The text is known for its two-column example format that provides annotations to the left of the algebra. These annotations explain what the authors are about to do in each step (instead of what was just done), just as an instructor would do.Hide synopsis
Description:Very Good. 013146776X MULTIPLE COPIES AVAILABLE-Very Good...Very Good. 013146776 |
Getting from Arithmetic to Algebra
Balanced Assessments for the Transition
Getting from Arithmetic to Algebra by Judah L. Schwartz
Book Description
The title of this book is Getting from Arithmetic to Algebra and is written by author Judah L. Schwartz. The book Getting from Arithmetic to Algebra is published by Teachers' College Press. The ISBN of this book is 9780807753200 and the format is Paperback. The publisher has not provided a book description for Getting from Arithmetic to Algebra by Judah L. Schwartz.
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MTH60 Introductory Algebra- 1st Term
Introduction to algebraic concepts and processes with a focus on linear equations and inequalities in one and two variables. Applications, graphs, functions, formulas, and proper mathematical notation are emphasized throughout the course. A scientific calculator is required. The TI-30X II is recommended. Prerequisites: MTH 20 and RD 80 (or ESOL 250). Audit available.
(For detailed information, see the Course Content and Outcome Guide ).
Credits:
4.00
Distance Education: Telecourse + Web Course
Information
CRN 20310
Special Note: You may view my TVWEB packet on-line at
then click on Math 60 TVWEB Course Information and scroll down to TVWEB PACKET (REQUIRED) or purchase it from the bookstore.
SUMMER TERM ONLY: You may opt to take it in 8 weeks if you are using YouTube or webstreaming the lectures AND you notify me by email within the 1st week of the course.
INFORMATION
ABOUT MTH 60 TVWEB:
****The TVWEB videos are now available for free on You Tube. With these videos, the use of Desire2Learn and the optional use of MyMathLab (Course Compass) you can consider this a modified Web Course!
The majority of your learning comes from viewing videos created by 3 talented PCC instructors, reading your text and working problems from your text. You can also use the optional MyMathLab that accompanies your text for computer generated problems that have video instruction and hints. Many students find this a valuable resource. ***
**Make sure you check Desire2Learn at least once a week for course announcements, additions and corrections.**
which links to more information about Math 60, the text (We use the same text as regular campus courses), and resources on campus and on the web.
Here are a few things to consider:
Are you aware that Distance Learning (web or TVWEB) is often a bigger time commitment than on campus classes? You must be an independent learner.
Can you make the time to work on this class effectively? This course, like other math courses, is time-intensive. In addition to watching 3 hours of videos each week ('attending' class), these types of classes typically require at least 3-5 hours a week reading and learning from the text, and the additional 8-12 hours doing homework, studying and practicing to successfully complete all course assignments and activities (recommended for ALL math classes.)
Please assess your situation before enrolling in this course, and determine if you will be able to commit this kind of time to the class.
Also think about the type of learner you are. Distance Learning classes (web or telecourse) are a terrific option, especially for independent, self-motivated learners. If this does not describe you consider why it is you are thinking about taking this type of class and if it really is a choice that will allow you to experience success.
For all my math 60 students (on-line, TVWEB and campus) I recommend that BEFORE STARTING they should be comfortable working WITHOUT A CALCULATOR with fractions, positive and negative numbers and order of operations. If not, that dramatically increases the time needed for learning algebra.
Make sure you have the proper pre-requisites: See Placement Info on the Math Department Web Page
If you have never had any algebra before that also increases the time needed to process and retain the new information.
If you had algebra before, and did well, it should come back relatively quickly and you will probably spend less time the 2nd time around.
If you had algebra before, and did not do well you would probably need to spend the recommended time on the course
HOW THIS CLASS WORKS:
All Math Distance Learning classes (Web and telecourse) require 2 proctored exams, (Midterm and a final exam) and a possibility of written worksheets and take home quizzes. More details forthcoming in the telecourse packet which you can view on my web site, or purchase at the bookstore with your text.
Consider these factors when deciding if this course is for you!
If you are trying to register, and the class is full get on the wait list. Usually some spaces become available. Many spots open up - ESPECIALLY THE FIRST WEEK OF THE TERM! There is no guarantee, however, that you will get into the class, but this is your best chance.
Course Specific Requirements:
There are two proctored no calculator, paper-and-pencil exams (Midterm and the Final). There will be scheduled times to take those exams at the Sylvania Campus, but if you cannot make those times you can make alternative arrangements to take them at the Sylvania Testing center if you live in the district or at an accredited college testing center if you do not. Otherwise, the entire course can be completed by viewing the videos and mailing in 4 worksheets and one quiz.
The TVWEB PACKET is located on my web site at
then click on Math 60 TVWEB Course Information and scroll down to TVWEB PACKET (REQUIRED) or purchase it from the bookstore.
Students with disabilities should notify their instructor if accommodations are needed to take this class. For information about technologies that help people with disabilities in taking Web based distance learning classes please visit the Office for Students with Disabilities website. |
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MATH 1034 - College Algebra of Functions
This course includes topics such as polynomials, radicals, exponents, coordinate geometry, rational expressions and equations, and solutions to linear and quadratic equations. Students are introduced to the concept of functions and their graphs. Additional topics may include conic sections, matrices, variation, and nonlinear inequalities. Emphasis will be placed on problem solving. A graphing calculator is required. The course is designed to give students additional time above that allotted in MATH 1033 working on mastery of concepts and skills in the student learning outcomes. Students cannot receive credit for MATH 1034 if they have credit for MATH 1033 or for MATH 1054. Students cannot receive credit for MATH 1034 if they have credit for MATH 1063, MATH 1084, or any course for which MATH 1063 or MATH 1084 are prerequisites. A grade of C or better is required to take MATH 2043, College Trigonometry. |
Math 201
Calculus III (Multivariable Calculus)
Third semester of the 3-semester calculus sequence 103/104/201. Introduces mathematical methods needed to understand real world questions involving quantities changing over time in 3-space. Students must move beyond thinking about mathematics as a set of rules and algorithms to memorize. Instead they learn to approach problems with greater independence and maturity. Exams test for thorough conceptual understanding and computational fluency in standard cases. In other words, although demanding, the exams do not typically involve proofs, and there is little emphasis on exceptional cases.
The first part of the course introduces basic objects in space: lines, planes, curves, (quadric) surfaces, and basic properties like arc length, surface area and volume.
The second part moves on to quantities that change with position in 3-space, like temperature or population density, which can be described by functions of several variables. We study their graphs, level sets, rates of change (partial derivatives) and their extreme points (maxima/minima) using Lagrange multipliers and Taylor's theorem.
The third part is devoted to vector fields, quantities that change with both position in space and with time. Think of how storms move, how radio signals make cell phones work or how blood flows. Although we do not explicitly study such applications, we lay the mathematical foundation for more advanced courses in science, engineering, and economics. The course ends with the theorems of Green, Gauss, and Stokes.
Classes: meet 3 times per week, for 50 minutes. Generally offered MWF at 10, 11 and 12:30 in both Fall and Spring semesters. The course is organized into small precepts of 20 to 30 students. There is one course head who coordinates with all the instructors to write the exams. All students have the same homework assignments and take the same midterm and final exam. These exams count for most of your course grade. They are graded by all the instructors together to ensure uniformity across sections. In addition there are two to four take-home quizzes, the same for all sections.
Notes:
Usually followed by 202 (Linear Algebra). Although 201 and 202 can be taken in either order, we recommend you take 201 first.
Students may get Princeton credit for only two of the three courses 200, 201 and 202.
Who Takes This Course?
The typical student plans to major in engineering or science; however, many other students interested in quantitative aspects of their discipline (e.g. economics or other social sciences) with possible graduate work in mind take this course. Intended for students who want to use mathematics and mathematical thinking as a tool in later studies in other fields. Most students are freshmen; in the fall they are students who got a 4 or 5 on the BC exam in high school (or its equivalent) and in the spring, they are mostly students continuing from MAT104.
Students who took AB calculus only should take 104 instead. Although some topics at the beginning of 104 will be familiar, the second half of 104 is needed to qualify for 201 (or for 200).
Exceptions:
Students who consider a major in physics or engineering with strong mathematical interest and aptitude (as evidenced by a BC calculus score of 5 and a math SAT score of 750 or more) should consider 203 or 215 instead.
Prospective math majors should probably take 218 instead (after 215). Some who are more interested in applied math opt instead for 203.
Some economics majors (or others interested in a finance certificate) take 200 instead.
AB COS majors are not required to take 201. They need only 202 (or 204 or 217).
Placement and Prerequisites
A very solid knowledge of single-variable calculus and precalculus is needed: how to analyze and graph functions, how to compute and interpret derivatives, how to interpret, set up, and calculate definite integrals with speed and accuracy.
Must have an interest in thinking rigorously about problems involving space and time.
If your background is weak or rusty consider 104 to get an excellent review of the knowledge assumed in this course.
General information about placement and contact information for the placement officer can be found on the
math placement page.
Sample Problems
Working problems from these sample quizzes and exams can give you a good idea of the expectations and content in this course as you think about which course is right for you. Just reading the questions or the solutions can be very misleading however. Try the problems yourself!
FAQ
I already took multivariable in high school, do I have to take this course?
Most students in 201 have had some multivariable calculus and/or linear algebra before, but rarely with the same depth and thoroughness. If you need the course for upper division courses in your major, then you are probably better off to take 201 even though some material will be review.
Take the sample final. Can you do any of the problems? For most students, the answer will be no. Review your old notes and try again. Can you do at least 60% of the exam?
In rare cases, the placement officer will decide that your prior work is indeed equivalent to 201 at Princeton. It will be helpful if you can bring your graded exams from the course you took to show the placement officer. He/she may also require you to take an exam to demonstrate your knowledge. Contact info for the placement officer can be found at the adept rep home page.
Can I take 201 and 202 in the same semester?
It is not impossible, but we do not recommend it. It makes midterm week particularly unpleasant, but if you have a very good reason for it and you are a very strong student, it can be done. It will likely mean that you will get a lower grade in one of them that you would otherwise have done.
How much work is this course?
It requires a steady time commitment. We expect that the weekly problem sets will take at least 3 hours to complete. To do well on exams, you need to work a lot of extra problems from old exams. So all in all we expect this course to take a minimum of 10 hours/week outside of class, on average.
If I think 201 is too hard, what should I do?
Try an old final exam in 104. If you can do most of the problems with confidence, you should stay in 201. Otherwise, you may want to switch to 104 to get a thorough review of all the math assumed in 201. Starting in 104 won't throw you off-track if you are a BSE student and taking the time to strengthen your foundations can really pay off in the long run.
If I think 201 is too easy, what should I do?
Have you had a quiz yet? You may be in for a surprise. Homework will be much easier than exams in this course. The general math FAQ page has a whole section on how Princeton's calculus courses work which may give you a more realistic view of the situation.
If you are also taking PHY103, you might consider just enjoying the fact that MAT201 is too easy. The combination of a demanding physics class and a demanding math class has been responsible for quite a few academic distress stories at Princeton.
I need both 104 and 201 for my major. After checking the math placement information, I think 201 is probably the right course for me, but I don't qualify for AP credit for 104. Do I have to take 104 or can I sign up for 201 instead?
Be cautious. Students often underestimate the difficulty of 104 and of 201 because many have seen some of the techniques taught in the first few weeks of these courses. Consider the information in the previous two questions as you think about your decision.
If you are really sure that you belong in 201, you can sign up for it. If you pass 201 in your freshman year, you will automatically receive AP credit for 104. Just be ready to re-consider and switch down to 104 early on if necessary.
If I want to switch courses, what should I do?
Talk with your 201 teacher. You may also want to talk with the teacher in charge of the other course. If you are going to
switch, do it soon!
I would like to switch sections within 201, what should I do?
If you have a time conflict, there is no problem. If you want to switch to another section at the same time, be prepared for a possible refusal --- the instructor may not have room for another student. Course and section changes must be made through SCORE.
I can't fit this course into my schedule. Can I take this course for Princeton credit at another university?
Yes, but it may be difficult to find an equivalent course. Many multivariable courses at other universities cover only about half of 201. More info at the adept rep home page.
I have more questions that are not answered here. What should I do?
First, check the general math FAQ page for more information. (There is a whole section there on how Princeton's calculus courses work.) If you still have questions, representatives from the math department will be available at freshman registration. |
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