text
stringlengths 8
1.01M
|
|---|
WINTER 2011
Math 10 Resources
Some resources for Math 10 for Mrs. Bloom's classes are listed on this page.
Students in Mrs. Bloom's class should be using the CATALYST website as the main source of current and updated information and resources for this class.
Math 10 Sofia Project Open Content Resources The Sofia Project is an open content initiative
from the FHDA district, containing video lectures, practice exams and quizzes, and calculator support material from the distance learning Math 10 class.Try these resources for extra help or if you need to catch up after an absence. (May duplicate some resources from Illowsky and Dean websites.)
Hypothesis tests for Star Trek Fans:
This website uses
a non-mathematical example from Star Trek to explain what
hypothesis testing is all about.
Helpful explanation of hypotheses, decisions, type 1 and type 2 errors, with
no calculations are needed to understand these basic concepts. |
Student Edition, Part A
Student Edition, Part B
Teacher Guide, Part A
Teacher Guide, Part B
Teacher Resource Package
0-07-827537-7
0-07-827538-5
0-07-827539-3
0-07-827540-7
0-07-830854-2
This innovative program engages students in investigation-based, multi-day lessons organized around big ideas. Important mathematical concepts are developed in contexts that are relevant to students. Students in Contemporary Mathematics in Context work collaboratively, often using graphing calculators, so more students than ever before are able to learn important and broadly useful mathematics. Courses 1, 2, and 3 comprise a core curriculum that will upgrade the mathematics experience for all students. Course 4 is designed for all college-bound students.
Research-based and Classroom-Tested - Developed with funding from the National Science Foundation, each course in Contemporary Mathematics in Context is the product of a four-year research, development, and evaluation process involving thousands of students in schools across the country. The result is a program rich in modern content organized to make active student learning a daily occurrence in your classroom.
Features
Algebra and functions, statistics and probability, geometry and trigonometry, and discrete mathematics are integrated in every course.
Mathematical concepts and methods are developed in real-world contexts with an emphasis on mathematical modeling and data analysis.
A four-phase lesson cycle of launch/explore/share and summarize/apply promotes discussion and collaborative learning in problem-based lessons.
Student and teacher texts are published in two volumes, enabling schools to adjust the pace of the course to accommodate varying student backgrounds, interests, and abilities. |
MATH 283: Calculus IIIEvaluate line integrals in rectangular, cylindrical and spherical coordinates, with applications.
Evaluate line integrals, with and without Green's theorem, and with Stokes's theorem.
III: Course Linkage
Linkage of course to educational program mission and at least one educational program outcome.
General Education Mission: This course addresses the fourth bullet under goal one of the college's mission to, "Provide instruction that contributes to a student's abilities to think critically and solve problems; to reason mathematically and apply computational skills."
Math 283 satisfies the General Education Requirement for any degree or certificate program and
addresses the following learning objectives of the General Education Requirement by ensuring that successful students:
Are able to apply appropriate college-level mathematical skills to real life applications |
Intermediate Algebra
9780495108405
ISBN:
0495108405
Edition: 8 Pub Date: 2007 Publisher: Thomson Learning
Summary: Algebra is accessible and engaging with this popular text from Charles "Pat" McKeague! INTERMEDIATE ALGEBRA is infused with McKeague's passion for teaching mathematics. With years of classroom experience, he knows how to write in a way that you will understand and appreciate. McKeague's attention to detail and exceptionally clear writing style help you to move through each new concept with ease. Real-world applicatio...ns in every chapter of this user-friendly book highlight the relevance of what you are learning. And studying is easier than ever with the book's multimedia learning resources, including ThomsonNOW for INTERMEDIATE ALGEBRA, a personalized online learning companion, but text is in tact. Slight water damage, text is completely in tact |
Report Offensive Message
Discrete math should be a focus too
The problem is that simple problems (eg boolean logic) is ignored and discrete problems are almost tossed out the window by the time kids hit high school. Sure, they need to learn the basics of algebra and trig, but they also need to understand simple logic concept and the basic combinatorial issues that abound. |
Description
Enjoy entertaining, and free quiz at your fingertips! Challenge yourself or share with friends. The multiple-choice quiz format is easy-to-use, fun and educational. Play wherever you are - at home, on the bus, or in the park.
Think you know the answers? Download the app and prove it!
The stream of mathematics which deals with the rules of relations and operations, the resultant concepts and constructions which include structures like equations, polynomials, and terms, is known as algebra. Algebra is one of the six key streams of pure mathematics which also includes number theory, analysis, geometry, topology, and combinatorial. There are many classifications in Algebra like elementary algebra, abstract algebra, linear algebra, linear algebra, universal algebra, algebraic geometry etc. Elementary algebra is the most widely used and the basic form of Algebra. Several equations can be solved using algebra. The application of algebra is wide and is useful in many fields especially engineering field. The word Algebra is an Arabic word that means reunion of broken parts. There are standard algebraic equations to help solve math problems. You will be introduced to the concept of representing numbers using variables as a part of elementary algebra. The variables can be modified using operations applicable to numbers such as addition, subtraction and so forth. This forms the basis for solving algebraic equations. Algebra extends far beyond the elementary stage and involves dealings with elements apart from numbers. Addition and multiplication operations form structures like rings, fields, and groups which are studied extensively in abstract algebra.
FEATURES ñ Four options for each question, only one right answer! ñ Comprehensive breakdown of your results. ñ Star tricky questions to return to later. ñ Track your progress and see how you improve over time. ñ Send questions to your friends on Twitter and Facebook or via email to see how they compare. ñ Access to over 1000 more quizzes through the app! ñ No registration necessary ñ Play offline
WHAT WE DO RedQuestion make quizzes on 1000's of topics, to help people all over the world learn and have fun together! Now everyone can experience learning at their fingertips!
Keywords: free, free game, free trivia, free quiz
In |
Math Center
The Math Center is a non-credit, Community Education class which provides assistance
in mathematics as a completely free service. Current Allan Hancock College students
as well as other individuals who are 18 years or older may fill out a simple registration
form and attend as frequently as they want. Registration forms may be found in the
Math Center or at Community Education in Building S.
The goal of the Math Center (sometimes called the Math Lab) is to assist students
in the successful completion of any Allan Hancock College mathematics class by providing
additional instructional resources. The Math Center offers many resources, including
one-on-one, drop-in tutoring by our staff of instructors and student tutors. Please
see the full list of resources below:
Free, drop-in tutoring
A place to study individually or in small groups
In-house loan of current textbooks and solutions manuals
A library of supplemental books, DVDs, and video tapes for check-out
Computers for mathematical purposes
Calculators
Handouts on math topics, including content from various math courses as well as information
on overcoming math anxiety and preparing for and taking math tests
Two private study rooms
Make-up testing
Workshops
Joining the math center group
Current students may access more detailed information by entering their myHancock
portal and joining the Math Center Group. Details may include information such as
the current schedule of instructors and student tutors who work in the Math Center,
a schedule of instructors and tutors who specialize in statistics, upcoming workshops
on selected topics, etc. To join the Math Center Group:
Enter myHancock
Look at the center of the Home page in the box titled "My Groups." Click on "View
All Groups" at the bottom of the box.
STAFF |
Mathematics Mission and Outcomes
MISSION
The mathematics department provides students opportunities to develop their mathematical appreciation, knowledge, skills and thinking in order to improve their quality of life and to aid in their preparation for future careers. |
This course is designed to assist in achievement on the PSSA (Pennsylvania State System of Assessment) for 8th Grade Mathematics. It includes lessons aligned with the state anchors that include interactive activities, videos, games, and images. Students are asked to write and explain work in a variety of situations that include blogs, open-ended assignments, journals, and Unit Projects. Quizzes are designed in a multiple-choice format, to mirror the questions on the state exam. Use of a scientific calculator is encouraged. |
Synopses & Reviews
Publisher Comments:
BEGINNING ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS shows students how to apply traditional mathematical skills in real-world contexts. The emphasis on skill building and applications engages students as they master algebraic concepts, problem solving, and communication skills. Students learn how to solve problems generated from realistic applications, instead of learning techniques without conceptual understanding. The authors have developed several key ideas to make concepts real and vivid for students. First, they emphasize strong algebra skills. These skills support the applications and enhance student comprehension. Second, the authors integrate applications, drawing on realistic data to show students why they need to know and how to apply math. The applications help students develop the skills needed to explain the meaning of answers in the context of the application. Third, the authors develop key concepts as students progress through the course. For example, the distributive property is introduced in real numbers, covered when students are learning how to multiply a polynomial by a constant, and finally when students learn how to multiply a polynomial by a monomial. These concepts are reinforced through applications in the text. Last, the authors' approach prepares students for intermediate algebra by including an introduction to material such as functions and interval notation as well as the last chapter that covers linear and quadratic modeling.
About the Author
Mark Clark graduated from California State University Long Beach with a Bachelor's and Master's in Mathematics in 1995. He is a full-time Associate Professor at Palomar College and has taught there for the past 9 years. He is a member of AMATYC and regularly attends the national AMATYC and ICTCM conferences. He has also done extensive reviewing and testing of various classroom technologies and materials. Through this work, he is committed to teaching his students through applications and using technology to help his students both understand the mathematics in context and communicate their results clearly. Intermediate algebra is one of his favorite courses to teach, and he continues to teach several sections of this course each year.
Table of Contents
"This book has just the right balance of skill and application problems.It does a good job of helping the students throughout the sectionswithout just giving all the answers away."Kate Bella, Instructor, Manchester Community College "It is easily readable for students, the explanations are clear, and themargin notes are a nice feature that makes the text more reader friendly."Daniel Lopez, Instructor, Brookdale Community College "I love how the text is centered on real-life situations. Students aregiven a great deal of assistance from the margin notes and well-workedexamples."Brianne Lodholtz, Instructor, Grand Rapids Community College "The approaches of Concept Investigations and Concept Connectionscaught my attention right away. I believe they will help studentsunderstand concepts better."Xiaomin Wang, Instructor, Rochester Community and Technical College |
Start from the Beginning: Generally, mathematic books are written in a systematic manner, wherein each chapter forms the base for further advanced chapters. So, do not jump to any chapter. Consider going through chapters in a serial order. Again, do not jump to solving the practice problems. Instead, read the instructions and examples given before the section of the problems. You will get to learn many things and ways needed to solve the practice problems. It is no wonder that you face problem while practicing the problems. Note down your doubts, queries, and the problems you find difficult to solve. Clear down these things from your teacher or online tutorials.
Practice Again and Again – Mathematics is a subject which you do not need to study but practice. This is because; you cannot solve a problem by only knowing the formula but with practice to apply your brain and solve it. So, practice as much as you can. Aim to revise the entire syllabus for mathematics at least three times before its exam. I know, for some of you it is an unrealistic target. Still, do give it a shot. The result will be amazing.
Since most of the students have a phobia for mathematic, they either spend little time or too much time on the subject. Both the ways are not going to be fruitful to you as a student. You need to devote only the required number of hours to this subject. This would help you prepare not only well for mathematics but also for other subjects. So, make a nice time table and devote some hours to mathematics everyday. |
The total weight of two beluga whales and three orca whales is 36,000 pounds. As you'll see in this course, if given one additional fact, you can determine the weight of each whale. To answer this weighty question, we'll give you all the math tools you'll need. The setting for this course is an amusement park with animals, rides, and games. Your job will be to apply what you learn to dozens of real-world scenarios.
Equations, geometric relationships, and statistical probabilities can sometimes be dull, but not in this class! Your park guide (teacher) will take you on a grand tour of problems and puzzles that show how things work and how mathematics provides valuable tools for everyday living.
Come reinforce your existing algebra and geometry skills to learn solid skills with the algebraic and geometric concepts you'll need for further study of mathematics. We have an admission ticket with your name on it and we promise an exciting ride with no waiting!
Additional Materials Required
Graphmatica - graphing utility, free download from within course
United Streaming - student is automatically logged in from a link in the course
SAS Curriculum Pathways - access information provide by instructor
You will have access to MathType. Directions for downloading this product are located in the Course Information area of the course. |
By Carl Bialik
My print column this week explores a new search engine, Wolfram Alpha, that aims to make the world's information computable. It could also make the world's math problem sets and tests computable, by solving tough problems, including in calculus, and showing its work.
Some teachers see Wolfram Alpha as a tool liberating them and their students to focus on broader concepts, just as calculators obviated slide-rule instruction. It could also push math into a more visual realm and away from abstract notation, thanks to its plethora of graphs and charts. "Graphical aspect: I'm wondering how much mathematical notation will survive this big push of graphing and animation," said Rich Beveridge, a math instructor at Clatsop Community College who has blogged about the new site.
However, Roger Howe, a math professor at Yale university, worries that the basics will be forgotten. "Mathematics doesn't really become real unless students have a fairly direct contact with it," Howe says. "Doing a reasonable amount of computation seems to be important for mastering mathematics."
It's unclear how much will be lost, and how much that matters. "One worries we'll lose the underlying intuition," said Donald Berry, chairman of the department of biostatistics at the University of Texas M.D. Anderson Cancer Center. "I worry about that, but I'm not sure how important that is. We as a species have come to a point where we can do things because of what others have built for us."
Maria Andersen, a mathematics instructor at Muskegon Community College whose blog has hosted a lively discussion on Wolfram Alpha, is excited to use the new search engine in instruction. "I do see it as being a fantastic tool we can use to explore concepts," Andersen said. "I can't morally imagine walking into a classroom and having a student say, 'Why do I need to take a cube of a binomial when Wolfram Alpha can do it for me?' "
She added that teachers would have to change their homework. "I would say that at least 50% of the standard homework problems and assessment questions that would be assigned with traditional textbooks could be answered by Wolfram Alpha," Andersen said. "… find a math book, open it to a section of problems, and you'll quickly find lots of examples that Wolfram Alpha will do."
But Andersen worries about becoming reliant on a single online tool: "What if Wolfram Alpha disappears, after we all shifted to use it?"
"It's very flattering if people care enough about one's tools to be concerned about their longevity," says Stephen Wolfram, the founder and chief executive of Wolfram Research. "What can one guarantee in this world?"
He sees his new tool as a way to broaden access to math and science. "The more people have ready access to knowledge and the more they have the power to do things like the experts do, the more they can feel empowered and get motivated to understand what's going on," he said.
Some calculation systems can work too much like a black box, though, according to Colm Mulcahy, a mathematician at Spelman College. "If [students] can get an instant answer, does it add to their understanding or make it so they're just pushing buttons?" Mulcahy asks. "So many students are obsessed with calculators: 2+2 is 4 because that's what the calculator says, and if the calculator said otherwise, they'd go with that." He added, "Unless/until teachers — at all levels — teach and test more on the concepts (in addition to a certain level of computation), our students are doomed."
All these comments are based on an assumption that Wolfram Alpha will improve. It's already strong in math. The derivative of 5x is a fixed, universally agreed-upon quantity. And Wolfram Research has extensive experience doing such math with its Mathematica program, a fixture in many college courses.
The GDP of France, however, is continually updated and subject to revision. And the French government might decide tomorrow to add a column to the chart in its regular economic report, tripping up Wolfram Alpha's effort to peel the numbers out. "Wolfram Alpha seems to be quite poor at doing what it claims to do well — namely, adding value to something like a search engine by being able to carry out computations to generate data that's not already in place on someone's web page," said Jordan Ellenberg, a mathematician at the University of Wisconsin.
Jeff Witmer, who teaches statistics at Oberlin College, says he's already adjusted his curriculum to a more conceptual plane that wouldn't be majorly affected by this new tool. "I expect that Wolfram Alpha could be used to help answer questions that I asked on statistics exams 15 years ago, when I had my students do a lot of calculating," Witmer said. "These days I mostly ask students to interpret calculations that have already been made, which means that Wolfram Alpha would not be helpful."
Phil Hanser, a statistician with the Brattle Group, criticizes the search engine for not reporting its uncertainty about statistical calculations. "If Alpha is meant to be a pre-eminent mathematics search engine, it should also serve as a model of good mathematics practice, including statistics," Mr. Hanser says.
Other teachers noted that they'd already been using Mathematica in their teaching. "There's not a lot new there, besides that it's free as long as you have Internet access, which is not a small thing," said Dan Teague, who teaches math at the North Carolina School of Science and Mathematics. (Surprisingly, Wolfram said sales of Mathematica have increased since the launch of the new tool, thanks to increased exposure of his signature software package.)
What do you think? How will this new tool affect teaching? How will you use it, if at all? What searches make it stumble? Please let me know in the comments.
Comments (5 of 8)
I think that Wolfram is a very well put together engine. I don't think that it will slow down the growth of our students. The students are not like the teachers, they do not have the answers or the know how to solve certain questions as do the instructors. When the students are stumped, they can go onto wolfram and see the answer if it is not in the back of the book, and then continue from there and work it backwards. All mathematics problems can be worked both ways, this I think is an amazing oppertunity.
Thank you.
2:14 pm June 25, 2009
Lokki wrote :
I have a friend who is a chemical engineer. A few years ago, his company had a rather expensive piece of equipment ruined by a young engineer who missed the small fact that the amount of one chemical being put into a mixture was off by a factor of 10. My friend moaned that kids these days have no concept of what the numbers a calculator spews out mean… "If he'd ever used a slide rule, he might have been off, but he'd have notice a factor of 10."
thank you for your article on wolframalpha; wolframalpha opens a new trend on web search engines missed by google. it's a first step towards computing answers through search engines. And you touch on a delicate issue about how to teach maths when there are so many clever maths software around and now wolframalpha goes a step further into putting it a light version of their great 'mathematica' software online for free. But to make short my comment, I've myself taught maths to young economists, it is essential to first learn the 'basics' to get to understand and control the more complex issues. I believe that a maths teacher has to show to students the 'beauty' in maths by deconstructing theorems and maths algorithms so students see what's behind it and then they will able to make better use of formidable maths software in their research but not to take anything for granted and better control and judge whether their results are true, rational or not, as human mistakes can always creep in and could be devastating if one does not keep track of everything and does not omit to, somewhat, double check his/her results 'by hand'. Marwan Elkhoury, co-founder of 'Growth and Development Bridge' found at
About The Numbers Guy
The Numbers Guy examines numbers in the news, business and politics. Some numbers are flat-out wrong or biased |
Sixth Form: Mathematics
Subject Overview
Mathematics A Level is a chance to extend you skils in Mathematical techniques and problem solving. It covers four modules of Pure Maths, using a lot of your previous knowledge of algebra to build on your previous work with topics such as trigonometry and vectors. As well as learning about new Mathematical concepts such as differentiation and integration, you will also do two applied modules, where you will have the choice of studying Mechanics or Statistics.
Syllabuses (Course Outline and Structure)
At Heart of England Sixth Form we follow the AQA Syllabus. Both the AS and A2 sections of the course are marked out of 300 UMS points. The two sets of marks together constitute the entire A level, out of a total of 600 UMS points. The course is split into AS and A2 Mathematics as follows:
AS Mathematics
Pure Core 1 - Algebra methods, extended from GCSE, adding, subtracting, multiplying, dividing, sketching and translating polynomials, some work with coordinate geometry extending GCSE methods to work with circles and an introduction to calculus both differentiation and integration.
Pure Core 2 - Transforming functions and their graphs, introducing the concept of series—summing sequences, extending your GCSE work on trigonometry and introducing the measure of radians, some work with indices, introduction to the topic of logarithms and an extension of the work with differentiation and integration.
Choice of:
Mechanics 1 - Mathematical modelling of real life situations, displacement, velocity and acceleration in one and two dimensions, forces—including friction and tension, momentum, Newton's laws of motion, problems involving connected particles and projectiles or
A2 Mathematics
Pure Core 3 - Work with functions including inverse, compositions and combinations of transformations, extension of trigonometry including inverse and reciprocal trig functions, exponentials and logarithms, differentiation using the product, quotient and chain rules, integration by substitution and by parts, use of integration to find the volume of a revolution, iterative methods for solving equations and numerical methods of integration.
Pure Core 4 - Rational functions, algebraic division, partial fractions, conversion between Cartesian and parametric equations, extension of work with binomial series, further work with trigonometry including use of harmonic form and double angle formulae, exponential growth and decay, solving differential equations, differentiating parametric equations, integrating partial fractions and work on vectors including vector equation of lines and scalar product.
Choice of:
Mechanics 2 - Moments, finding the centre of mass, further work with displacement, velocity and acceleration including in three dimensions, Newton's Laws in up to three dimensions, application of differential equations, uniform circular motion and vertical circular motion as well as looking at work and energy, including GPE, KE and Hooke's Law or
The official AQA specifcations for all of the Maths modules are available in pdf form at:
AQA Mathematics Specification 2013
Entry Requirements
To study A Level Mathematics you must have at least five GCSEs at grade C or above, and we would recommend at least a grade B in your GCSE Maths. Since the course is very algebra based you must also have good skills in manipulating algebra and you will be tested on this during the first week of the course.
The 'step up' from GCSE Maths to A Level is quite significant and for those students who would like to get a good start on it, particularly if their algebra skills need a little brushing up, we recommend the CGP text 'Head Start to AS Maths'
Activities and Trips
We have no mandatory trips or activities in Maths, although throughout the two years there may be the opportunity to take part in activities, such as revision days and team challenges, run by the 'Further Maths Network' based at Warwick University, with whom we have been cultivating links over the last few years.
This would incur a small cost, usually of between £10 and £30 dependant on the type of activity, and may involve students arranging their own transport to and from the University.
Expected Costs
Other than the cost of the activities that we may run with the 'Further Maths Network' there are no expected costs associated with the Maths A Level. All the text books are lent to students for the duration of the course and they will only need to pay for them if they fail to return or badly damage them. There are no mandatory excursions and the only equipment they are required to have (other than the usual contents of a pencil case) is a scientific calculator, which they should have anyway from GCSE. Complementary Subject Combinations and Enrichment Activities
The main links between other subjects and Maths come from the choice of applied topic:
Mechanics – fits well with Physics as there is a lot of overlap in the content of the courses
Statistics – fits well with Pyschology and Biology as they use statistical analysis in some of their coursework.
Subject Resources
Schemes of Work
In Maths the Scheme of Work is based on the text books. For each module we have a text book produced by AQA which covers all the topics needed for that course. Students will be loaned these text books for the duration of their study
Past Papers
Past papers are an essential part of the revision process for Mathematics, it is important to get plenty of practice of the type of questions you will be asked in exams. At the end of each chapter in the text book there is a revision exercise made up of past exam questions and we always leave plenty of time after completing the learning for the module to do past paper practice, both under exam conditions and as an open book revision tool.
The AQA Maths past papers (and several other useful documents) can be found at:
AQA A Level Maths Materials
Useful Links
The AQA link above is very useful and provides access to past papers, mark schemes, examiners reports, specifications, practice papers for new specifications, the formula booklet and many other useful documents.
Also the school has paid for access to the website My Maths which students may have used in Key Stage 3 and 4 but which also has a wealth of resources for A Level revision. This can be accessed by asking your teacher for the school's login and password information.
Other Information
Maths A Level will support students who go on to study a wide range of different subjects at University or in other forms of Higher Education, the more obvious ones being Maths, Science and Engineering. It's logical thinking and problem solving based structure make it a qualification that can pick students 'out of the crowd' in the eyes of many universities and employers, even in non-Maths based courses or industries. |
In Section 4 we introduce the hyperbolic functions sinh, cosh and tanh, which are constructed from exponential functions. These hyperbolic functions share some of the properties of the trigonometric functions but, as you will see, their graphs are very different.
In Section 2 we describe how the graphs of polynomial and rational functions may be sketched by analysing their behaviour – for example, by using techniques of calculus. We assume that you are familiar with basic calculus and that its use is valid. In particular, we assume that the graphs of the functions under consideration consist of smooth curves.
In Section 1 we formally define real functions and describe how they may arise when we try to solve equations. We remind you of some basic real functions and their graphs, and describe how some of the properties of these functions are featured in their graphs.
Many problems are best studied by working with real functions, and the properties of real functions are often revealed most clearly by their graphs. Learning to sketch such graphs is therefore a useful skill, even though computer packages can now perform the task. Computers can plot many more points than can be plotted by hand, but simply 'joining up the dots' can sometimes give a misleading picture, so an understanding of how such graphs may be obtained remains important. The object of reminds you about powers of numbers, such as squares and square roots. In particular, powers of 10 are used to express large and small numbers in a convenient form, known as scientific notation, which is used by scientific calculators.
This unit is from our archive and is an adapted extract from Open mathematics (MU120) which is no longer taught by The Open University. If you want to study formally with us, you may wish to explore other courses we offerUp to now only those points with positive or zero coordinates have been considered. But the system can be made to cope with points involving negative coordinates, such as (−2, 3) or (−2, −3). Just as a number line can be extended to deal with negative numbers, the x-axis and y-axis can be extended to deal with negative coordinatesPie charts are representations that make it easy to compare proportions: in particular, they allow quick identification of very large proportions and very small proportions. They are generally based on large sets of data.
The pie chart below summarises the average weekly expenditure by a sample of families on food and drink. The whole circle represents 100% of the expenditure. The circle is then divided into 'segments', and the area of each segment represents a fraction or pe climate change draws attention to the power of human activity to transform the planet in its entirety, and it is brought into sharp focus by the predicament of low-lying islands like Tuvalu. As we have seen in this unit, the issue of rising sea level and other potential impacts of changing global climate also point to the transformations in the physical world that occur even without human influence. Oceanic islands provide a particularly cogent reminder that the living things wit project, or single, team consists of a group of people who come together as a distinct organisational unit in order to work on a project or projects. The team is often led by a project manager, though self-managing and self-organising arrangements are also found. Quite often, a team that has been successful on one project will stay together to work on subsequent projects. This is particularly common where an organisation engages repeatedly in projects of a broadly similar nature – forOnce a small number of chains have been started, propagation involves successive addition of monomer units to achieve chain growth. At each step the free radical is regenerated as it reacts with the double bond. So in the case of styrene the propagation step is
The free radical can also add on in |
Note: Lessons include complete teacher editions, student worksheets, and any applicable
Python programs. Examples include short exercises from core subjects with key CT
concepts to consider. Programs include Python examples and exercises for teachers to
enhance their existing lessons. Math lessons, examples, and programs are based on the
Common Core Standards, while science materials are aligned with the California K-12
Content Standards. |
Math isn't necessarily every student's expertise. But regardless, it's something people need for everyday life – even if you aren't majoring in math. University of Miami lecturer Lun Yi Tsai is offering the perfect math course next semester for students who need to get the requirement out of the way, but aren't into derivatives and... |
An introduction to linear mathematics. Linear systems of equations, matrices, determinants, vector spaces, bases and dimension, function spaces, linear transformations, eigenvalues and eigenvectors, inner products, and applications. An important aspect of the course is to introduce the student to abstract thinking and proofs. |
Overview
Main description
The perfect prep for students getting ready for the Test of Adult Basic Education
McGraw-Hill is the only publisher offering guides to the Test of Adult Basic Education (TABE). These new TABE workbooks help you get ready for this all-important qualifying exam used by numerous government agencies and private employers-arming you with powerful skills gained from intensive, hands-on practice.
This workbook helps you to master high-school mathematics with intensive practice in the essential math areas you'll find on the test: core computational skills, geometry, statistics, fractions, and much more.
Table of contents
TABE Level A Objectives and Expectations
Diagnostic Test
Math Computation
Decimals
Fractions
Integers
Percents
Order of Operations
Percents
Applied Mathematics
Numbers and Number Operations
Computation in Context
Estimation
Measurement
Geometry
Data Analysis
Statistics and Probability
Patterns, Functions, Algebra
Problem Solving and Reasoning
Post-Test
Summary of Test-Taking Tips
Author comments
Richard Ku has been teaching mathematics at the secondary level since 1985 in both private and public schools. |
The new 1st edition of Cynthia Young's PrecalculusPrecalculus: A Prelude to Calculus focuses exclusively on topics students need to know in order to succeed in calculus. With plentiful explanations and examples to help students form concrete ideas about the concepts, the text provides a self-contained preparation for calculus without adding unnecessary information and topics. |
The new edition features increased emphasis on the computing technologies commonly used in such coureses. New to This Edition
&q...show moreuot;Technology Step by Step" sections show how to solve basic problems using Minitab software, the TI-83 graphing calculator, or Excel.
More examples and exercises based on actual data.
FeaturesAllan G. Bluman is Professor of Mathematics at Community College of Allegheny County, near Pittsburgh. For the McKeesport and New Kensington Campuses of Pennsylvania State University, he has taught teacher-certification and graduate education statistics courses. Prior to his college teaching, he taught mathematics at a junior high school.
Professor Bluman received his B.S. from California State College in California, Penn.; his M.Ed. from the University of Pittsburgh; and, in 1971, his Ed.D., also from the University of Pittsburgh. His major field of study was mathematics education.
In addition to Elementary Statistics: A Step by Step Approach, Third Edition, and Elementary Statistics: A Brief Version, the author has published several professional articles and the Modern Math Fun Book (Cuisenaire Publishing Company). He has spoken and presided at national and local mathematics conferences and has served as newsletter editor for the Pennsylvania State Mathematics Association of Two-Year Colleges. He is a member of the American Statistical Association, the National Council of Teachers of Mathematics, and the Mathematics Council of Western Pennsylvania.
Al Bluman is married and has two children. His hobbies include writing, bicycling, and swimming79 +$3.99 s/h
VeryGood
Wiz Kids Books Irmo, SC
Tight & Clean. Light edge wear to cover
$4.79 |
Publisher Notes
Elementary Linear Algebra 10 th edition gives an elementary treatment of linear algebra that is suitable for a first course for undergraduate students. The aim is to present the fundamentals of linear algebra in the clearest possible way; pedagogy is the main consideration. Calculus is not a prerequisite, but there are clearly labeled exercises and examples (which can be omitted without loss of continuity) for students who have studied calculus. Technology also is not required, but for those who would like to use MATLAB, Maple, or Mathematica, or calculators with linear algebra capabilities, exercises are included at the ends of chapters that allow for further exploration using those tools.
Book Details Summary: The title of this book is Elementary Linear Algebra/Student Solutions Manual: Applications Version and it was written by Howard Anton, Chris Rorres. This 10th edition of Elementary Linear Algebra/Student Solutions Manual: Applications Version is in a Mixed media product format. This books publish date is July 12, 2010 and it has a suggested retail price of $221.55. It was published by John Wiley & Sons Inc.. The 10 digit ISBN is 0470918985 and the 13 digit ISBN is 9780470918982. For the most current lowest price, Click Here. |
This problem-based course presents classical topics of elementary number theory and how they pertain to teaching the elementary and Junior High School mathematics.
Topics include prime numbers, GCF, LCM, division algorithm, Euclidean algorithm and the extended Euclidean algorithm, the Little Fermat Theorem and RSA encryption. Several applications, including cryptography, will be presented using middle grade materials.
The course prepares the teacher for using the CryptoClub materials with middle grade students and offers amble time for discussion of a variety of issues in teaching elementary and middle grade mathematics.
Required materials:
The Cipher Handbook: by Janet Beissinger and Bonnie Saunders. This book is available for purchase in the UIC Bookstore.
TI-83/84 or TI-83/84 Plus or equivalent graphing calculator.
Recommended:
The Cryptoclub: Using Mathematics to Make and Break Secret Codes by Janet Beissinger and Vera Pless.
Workbook for The Cryptoclub: Using Mathematics to Make and Break Secret Codes by Janet Beissinger and Vera Pless. You may download this for free from the A.K. Peters website.
Links to online activities:
CryptoClub: Desert Oasis A game for learning and enjoying Caesar Ciphers. This game is still in the pre-alpha stage. We appreciate it if you do not share this link with others. |
The Teacher's Guide to Calculus, v0.3
Louis A. Talman
Department of Mathematical & Computer Sciences
Metropolitan State College of Denver
Introduction
I have found that certain questions concerning the theoretical
underpinnings of beginning (single-variable)
calculus arise frequently
among those who teach the first two or three calculus courses.
The purpose of this book is to
answer those questions, and others as well. Among those
who raise the questions I have tried to answer will be the better
students in elementary calculus classes. In my experience, many
of their instructors are unsure, themselves, of the answers to
those questions; I hope that both students and teachers
will find the answers they
seek here.
I have tried to make it an
over-riding principle that all of the proofs I give here should
be accessible, insofar as that is possible, to the outstanding
students who are likely to be unsatisfied with their calculus
text's dismissal of certain topics or arguments
as "beyond the scope of this book".
You will not now find that frustrating phrase in the body of this book,
and I fully intend that you will not find it in the portions of the book that
are yet unwritten.
However, a reader may find it necessary to track
the answer to a particular question back through answers to questions that
precede the original in the logical structure of calculus. I have not
tried to make the book self-contained. Elementary calculus texts do a
reasonable job at the tasks they undertake, and this book is meant for use
in conjunction with such a text. I have tried to answer the questions that
the textbooks do not answer.
What I have posted here is a preliminary version of the preliminary version.
As the work stands at this writing, it is far from complete.
There are currently but seven chapters. I have covered perhaps
a half of the
things I intend to cover.
Nevertheless, I believe that what is
here can be of use to practicing teachers. Moreover, I am hoping for constructive
comment from all who take the time to read it. Among other things, I am interested
in knowing what burning questions you have that I didn't address, or that I
did address--but poorly. Please address your comments to
[email protected]. If you prefer
quainter methods of communication, you may write to |
Rewarding undergraduate text, derived from an experimental program in teaching mathematics at the secondary-school level. This text provides a good introduction to geometry and matrices, vector algebra, analytic geometry, functions, and differential and integral calculus. "...solid modern mathematical content..." — American Scientist. Over 200 figures. 1964 edition. |
Author
Topic: Mathematics Books (Read 829 times)Care to be a bit more specific about which math you'd like to relearn?
I've found the Schaum's Outline series to be pretty useful, and have one to supplement just about every math or science class I have taken. They provide a very brief review of a topic, followed by a bunch or worked out examples. They are great if you are relearning something. Also, they are very inexpensive (a couple dollars used, maybe $25 US new). I'd recommend getting a couple of those, and then possibly an additional "real" textbook if you feel you need a more in depth treatment of the topics.
Also, to the OP: check out your local library, chances are they have some math textbooks. Find a subject you are interested in, and grab as many text books on the subject as you can carry. You may find some that "click" with you better than others, and a concept that is confusing in one text may be better explained in another. Every time I've take a college math or science course, I always go to the university library and get a few additional books on the subject for these reasons.
If you just want to read something about math for the joy of reading - and hey, there's no reason why you can't do that while also learning stuff - I recommend two books: The Drunkard's Walk by Leonard Mlodinow (about probability)+ The Calculus Diaries by Jennifer Oullette (about... well, guess)
Both are a lot of fun and if you're like me will spur you on to learning moar
I would NOT go for a text book. if you are looking for high school level math, get yourself the Martin Gardner Sci-Am collection. There are 15 of them, most go for under $3 as used (in amazon or abebooks). there's loads and loads of interesting high school level math there - geometry, probability, discrete math, and the list goes on.
if you aim a bit higher, I would recommend Paul J. Nahin books. these require some higher calculus level and are less approachable than the Gardner books. They are however full with interesting mathematical detective-like investigations ('when least is best' would be a good start). Again, be warned the the Nahin books are packed with sometimes non trivial university level math.
Logged
quot;who is more foolish - the fool, or the fool who follows the fool?" Star Wars - A New Hope |
For one- or two-semester junior or senior level courses in Advanced Calculus, Analysis I, or Real Analysis. This text prepares students for future courses that use analytic ideas, such as real and complex analysis, partial and ordinary differential equations, numerical analysis, fluid mecha... |
Bridges the gap between digital principles and practice in order to teach practical applications of theoretical knowledge in solving digital design problems. Highlights fundamental concepts in digital technology plus a large variety of integrated devices. Requires a basic knowledge of algebra and an understanding of electric circuits. Its comprehensive style makes difficult concepts easy to grasp. |
Click on the class you are in to find information specific to that class.
Children today are tyrants. They contradict their parents, gobble their food and tyrannize their teachers.
-- Socrates (470-399 BC)
No one yet fully realizes the wealth of sympathy, kindness and generosity hidden in the soul of a child. The effort of every true education should be to unlock that treasure.
-- Emma Goldman
He who asks a question is a fool for a minute; he who does not remains a fool.
-- Chinese Proverb
Marking Period 2 Project Results updated January 30, 2010 The second marking period project was to create a Geometry Dictionary aimed at elementary school students. It was not mandatory this marking period, but extra credit. Not many students took advantage...
Periods 1 and 5 Course 0217: 1 Credit, 5 meetings per week Prerequisite: Successful completion of Algebra I 15 or equivalent. Course Description: This course investigates the spatial relationships of polygons and solids within a framework of points, lines and planes. Using the fundamentals of logic to gain knowledge and insight, the student becomes acquainted with scientific method of investigation and validation of facts. Emphasized in the course is an understanding the basic relationships of congruence and similarity, the structures used to analyze them and the language used to communicate these ideas. The ideas in the course are used to solve a variety of practical problems from a geometric viewpoint.
Periods 2, 6 and 8 Course 0218: 1 Credit, 5 meetings per week Prerequisite: Successful completion of Algebra I 17 or equivalent Course Description: The course provides a rigorous investigation of the spatial relationships of polygons and solids. Emphasis is on developing proficiency with deductive proof and the rules of logic as analytic tools in problem solving. The ideas in the course are used to solve a variety of problems from a geometric viewpoint. |
Course Requires a Media Kit to be Purchased by Course Sponsor
(see additional details below):
No
Description:
This course covers a full year of Algebra I concepts for credit recovery.
This course will cover all of the basic topics of an Algebra 1 course including: solving equations, slope, systems of equations (solved mathematically and graphically), exponents, monomials and polynomials. Students are asked to view videos, tutorials and animations, play math games, complete simulations and write in their journals. Most topics have automated quizzes that students can take up to 3 times to achieve their best score. Students will also complete unit quizzes to test their knowledge of the content and reflect on their performance. Students will also work on various projects and will participate in class discussions about math topics.
Please note if the student is taking this course for credit recovery, it is advised that you check with the student's school to confirm that the topics covered (see course syllabus) match those required by the local school. You may also want to confirm with the school the process for receiving credits, which may involve an assessment administered separately by the school. |
This course is designed for students who have good basic math skills but with limited algebra background. This is the second level in the math progression leading to Beginning Algebra (Math 016). Repeatable.
This course is for students who needs intensive basic math review or has very limited math background. This is the first level in the math progression leading to beginning Algebra (Math 016). Repeatable. |
Discrete Mathematical Structures, Sixth Edition, offers a clear and concise presentation of the fundamental concepts of discrete mathematics. Ideal for a one-semester introductory course, this text contains more genuine computer science applications than any other text in the field. This bAn ever-increasing percentage of mathematic applications involve discrete rather than continuous models. Driving this trend is the integration of the computer into virtually every aspect of modern society. Intended for a one-semester introductory course, the strong algorithmic emphasis of Discrete M... |
Gain knowledge on a variety of computational and mathematical problems
in discrete geometry and their applications.
Be able to utilize fundamental geometric data structures and algorithmic
design techniques for the solution of new computational problems in discrete
geometry.
Be able to implement basic geometric algorithms using standard programming
languages.
Be prepared for theoretical research in discrete and computational geometry.
Preparation:
This is an advanced graduate-level course on discrete and computational
geometry.
Solid mathematical, algorithmic, and programming skills are required.
The students are expected to explore the vast literatures of the field
and work on current research problems under the guidance of the instructor.
Prerequisite: CS5050.
Grading:
Homework (40%):
Homework 1 (due at the beginning of class on Mon Jan 14):
Read chapter 1. Browse through the whole book, pick your favorite chapter (the topic that you wish to be covered).
Homework 2 (due at the beginning of class on Fri Jan 18):
What is the probability that the convex hull of k random points on the boundary of a circle encloses the circle center?
Homework 3 (due at the beginning of class on Wed Jan 30):
Show that f(r,s)=(r+s-4 choose r-2)+1 is the solution to the recurrence
f(r,s)=f(r-1,s)+f(r,s-1)-1 (Hint: induction).
Homework 4 (due at the beginning of class on Mon Feb 4):
Prove: given a finite set of non-parallel lines on the plane not all through one point, there is a point intersected by exactly two lines.
Homework 5 (due at the beginning of class on Fri Feb 8):
Derive the parameterized equation for an ellipse with specified origin and axes.
Homework 6 (due at the beginning of class on Fri Feb 15):
Given a set of n points in the plane in general position,
design an O(n^2) time algorithm that computes for each point
the circular order of the other points.
Homework 7 (due at the beginning of class on Mon Mar 31):
Build a rhombic dodecahedron and check whether Euler's formula
works for this polyhedron.
The last day to drop this class without notation on your transcript is
January 28.
Attending this class beyond January 28 without being officially registered
will not be approved by the Dean's Office. Students must be officially
registered for this course. No assignments or tests of any kind will be
graded for students whose names do not appear on the class list.
Students are encouraged to discuss and exchange ideas on homework and projects,
but each student must write up the solutions independently.
Students who are caught cheating immediately receive "Fail" grades.
DRC statement:
Students with physical, sensory, emotional or medical impairments may be eligible for reasonable accommodations in accordance with the Americans with Disabilities Act and Section 504 of the Rehabilitation Act of 1973. All accommodations are coordinated through the Disability Resource Center (DRC) in Room 101 of the University Inn, 797-2444 voice, 797-0740 TTY, or toll free at 1-800-259-2966. Please contact the DRC as early in the semester as possible. Alternate format materials (Braille, large print or digital) are available with advance notice. |
II. PREREQUISITE(S): Two years of high school algebra, one year of high school geometry, and 12
weeks of
trigonometry.
III. COURSE OBJECTIVE(S): Build on (not replicate) the competencies gained through the study of two
years of high
school algebra and one year of high school geometry. Use mathematics tosolve
problems
and de termine if the solutions are reasonable. Use mathematics to model real
world
behaviors and apply mathematical concepts to the solution of real-life problems.
Make
meaningful connections between mathematics and other disciplines. Use technology
for
mathematical reasoning and problem solving. Apply mathematical and/or basic
statistical
reasoning to analyze data and graphs. Refine the algebraic, geometric,
trigonometric, and
reading com prehension skills necessary in the study of calculus. |
Type or write (neatly) your assignment on notebook-sized
paper. If you handwrite your assignments, use a pen, since I find
pencilled writing hard to read.
Make sure that the reader can understand what the problem is
without having to look it up.
Be sure to leave plenty of space for comments. Usually you
should leave a third of a page per proof, plus nice-sized margins.
Be sure to staple the pages together. You should
own
a stapler by now, but if you forget, there is a stapler in the third
floor computer lab.
Make sure that you cut off the squigglies on paper ripped out of
a spiral notembook.
For problems that don't involve proofs, you should show enough
work so that any student in the class can follow your solution.
Just writing the answer is never enough.
Proofs should be written in complete English sentences.
Proofread what you have written to make sure it makes sense.
Don't try to fake a proof. Instead, acknowledge the gap in your
proof. Better yet, come talk with me beforehand and see if I can
help you close the gap.
Each mastery
problem should be written on a separate page. Rewritten
versions can be written at the bottom of the marked page, or on another
page. Fasten together all versions of a problem, with the most
recent version at the front.
Practice problems will be
submitted in class. Each Monday, you will submit the problems
assigned for the previous week. They should be in a form that you
find easy to read and review.
Honor problemsshould be done completely on your own,
without outside
help from anyone, including me, other professors, your fellow students,
webpages, etc. |
TI-83/84 Plus and TI-89 Manual for Intro Stats
Summary
Organized to follow the sequence of topics in the text, and it is an easy-to-follow, step-by-step guide on how to use the TI-83/84 Plus and TI-89 graphing calculators. It provides worked-out examples to help students fully understand and use the graphing calculator. |
Book Description: Make the grade with PRECALCULUS and its accompanying technology! With a focus on teaching the essentials, this streamlined mathematics text provides you with the fundamentals necessary to be successful in this course--and your future calculus course. Exercises and examples are presented in the same way that you will encounter them in calculus, familiarizing you with concepts you'll use again, and preparing you to succeed. In-text study aids further help you master concepts. |
Book DescriptionMost universities recommend this for 1st year undergraduates, probably rightly. Varian is quite clear with intuitive explanations of the basic concepts. However in terms of the maths he becomes incredibly confusing, as he insists on relegating all calculus (which is vital to even 1st year micro) to appendices and using deltas (aka triangles) in the main text. This has three consequences. Firstly it makes his reasoning less rigorous. Secondly he doesn't really explain how the calculus relates to the intuitive concepts or present the mathematical steps in too much detail, so it is often difficult to follow. Thirdly you have to spend a lot of time piecing together proofs from triangles and actual partial derivatives if you want to make use of a proof for an essay or exercise. Some of my friends used the Perloff text (I think it's called microeconomic theory and applications of calculus or something like that) instead, and claimed it was better. I used Varian in first year and got a first in micro, but had to rely on my maths for economists textbook a lot. Definitely too basic for finalists.
This is a great introductory intermediate text if that makes sense. It's more involved and mathematical than the micro section in a typical introductory economics textbook (nothing a good grasp of calculus won't cope with) but less challenging mathematically than an advanced intermediate student would expect. If you've outgrown the former but not yet the latter then this is perfick! Nothing more likely to discourage studying than struggling with both concepts and calculations at the same time. With Varian, you'll get the theory right which should set you (me) up for the hard work to come.
Hal Varian's Intermediate Microeconomics was the recommended text book for my recent 2nd year micro economics module at university.
The material is presented in a very clear and straightforward manner, using minimal mathematical notation. If you want to use a book to help you understand the actual concepts of intermediate microeconomics this is the book for you. The explanation of concepts is concise and the book covers the vast majority of topics covered in a 2nd year micro course.
One word of warning; for most intermediate courses in economics in the UK this book falls short of the level of analytics likely to be required. It is however still a very useful complement to either a more technical text or lecture notes. |
Algebra
Mathcentre provide these resources which cover a wide range of algebraic topics, many of which are suitable for students studying mathematics at Higher Level GCSE, or A Level, as well as those students for whom mathematics is an integral part of their course. Some of the topics covered include completing the square, factorising quadratics, partial fractions, integration, simultaneous linear equations, logarithms and polynomial division.
Comprehensive notes, with clear descriptions, for each resource are provided, together with relevant diagrams and examples. Students wishing to review, and consolidate, their knowledge and understanding of algebraic principles |
HSI STEM
The HSI STEM Grant promotes Math Success and provides a support system that encourages completion and success in Math classes and a smooth transition from LSC-North Harris to STEM academic programs at the University of Houston or other four-year universities. The grant features newly designed Math courses using innovative teaching techniques and cutting edge technology, high quality tutoring services and access to state-of-the-art technology in the Math Achievement Center (MAC), and access to speakers, mentors, and STEM oriented career and college prep events through participation in the Women in STEM group, and much more.
Featured Math Courses
The Math Department faculty has designed innovative, interactive, student-centered Math courses where students can use the latest technology and Math software to complete their assignments. Many of these featured courses also offer one-on-one, in-class assistance from instructors
Flipped Classroom: A combination of face to face and online coursework. Students watch recorded lectures at home. lecture videos are easily accessible on your iPhone, Android phone, iPAD, etc. Homework, assignments, and labs are completed in class with the instructor who is available to give students individual help as needed. All tests are taken in class with the instructor. This class meets on all assigned days.
ALEKS:
Students meet face to face with an instructor, but class work is completed using a computer program called ALEKS. ALEKS uses artificially intelligent adaptive questioning to find out exactly what the student knows, and designs an individualized learning plan specifically for each student. The instructor is available in the classroom to assist students one on one as needed. All tests (except the final exam) are taken on the computer using ALEKS.
Mathematica Software: Class lessons are lecture based with in-class demonstrations using iPADSs and Mathematica applets. Mathematica is a computational software used in scientific, engineering, and mathematical fields. It allows students to manipulate and solve problems with computer code. Lectures are enhanced by lab and home assignments using the Mathematica computer software.
Maple Software/Flipped Classroom: A combination of face to face and online coursework. This software enables students to visualize mathematical concepts and to investigate and solve problems that would be difficult to solve by hand. Students watch videos with lectures and embedded with animation from Maple. Labs and homework are completed in class with computers and instructor guidance. This class meets on all assigned days.
Online Math Courses: The entire course is offered online. All exams are proctored and must be taken on campus.
Several Math 0310 (Intermediate Algebra) and Math 1314 (College Algebra) featured courses are now available in the Summer 2013 schedule. More of these featured courses, including brand new sections of Math 1316 (Trigonometry) and Math 2412 (Pre Calculus) are available in the Fall 2013 schedule.
For more information about the HSI STEM Grant Math courses and activities, please contact Sylvia Martinez at [email protected] or call 281-765-7806. You can also stop by our office in the Winship Building, in WNSP 166. |
Excerpted from
Patterns, ratios, equality, algebraic functions, and variables are some of the concepts covered in this printable book for elementary students. You'll find a variety of materials to encourage your young students to learn |
Algebra in the Real World Movies
Specializing in saltwater aquariums, Nic Tiemens and Joe Pineda love the challenge of recreating a slice of the ocean indoors. Day in and day out, they use volume calculations, temperature, measurement and science to create these beautiful habitats. Running time 5:25 minutes.
Columbia Sportswear Designer Chris Araujo combines innovation with design to create backpacks for one of the largest outdoor apparel companies in the world. Whether he's measuring the straps for comfort or designing the shape of the front pouch, math is essential to his designs. Running time 4:50 minutes..
Lighter. Stronger. Faster. That's the goal of Niko Henderson, an engineer for Easton Sports. He uses science, mathematics, engineering and innovative testing to help produce some of the fastest bikes on the road. Running time 4:45 minutes.
Determining who is the best athlete on the field is hardly a matter of opinion. Sports reporters stay ahead of the competition by arriving early and keeping a close watch on statistics.
Running time 2:11 minutes.
For Tami Sabol, the forest is her office. As a Forester for Plum Creek Timber Company, she is responsible for the health of hundreds of thousands of acres of trees. Using math and science is a routine part of her work. Running time 5:10 minutes.
Meet two landscape architects who tell the story of competing against top firms in the world to win the opportunity to design a one-of-a kind botanical garden for the city of Chicago: the Lurie Garden at Millennium Park. Running time 6:45 minutes.
From planting the seeds to harvesting, and everything in between, Bryce Lundberg takes students through the process of growing one of our most important staples: rice. To ensure he grows a successful crop, Bryce depends on his algebra skills to get the job done. Running time 3:50 minutes.
Gliding on a wave of electromagnetic force, a maglev train could travel at 300 miles per hour or faster. Designer-engineers describe the mechanics and future benefits of such superconductor trains. Running time 4:12 minutes.
When it comes to designing robots for space, making sure that they can complete their missions is the name of the game for NASA's robotics engineers. That requires math, especially probability. Running time 5:35 minutes.
The heart-pumping exhilaration keeps us coming back time and time again, but it's the laws of the physics and a great deal of math that keep these thrill rides soaring through the air day after day. Running time 2:00 minutes..
Photovoltaic cells convert energy from the sun directly into electricity. In this movie, engineers Beth Richards and Miguel Contreras give your students a clear and engaging "101" on this renewable energy technology, and demonstrate the basic math and science behind it. Running time 4:45 minutes.
Is there life on planets in other star systems? It's a very old question. But finding the answer may get simpler with a new invention by astrophysicist, professor and inventor Webster Cash. Running time 5:55 minutes.
Building a 72-story skyscraper like Trump Tower in New York City is no easy feat. That's where structural engineers like Ysrael Seinuk come in. This movie explains how shapes are at the foundation of structural engineering. Running time 3:02 minutes.
Currently the worldwide collection of Mars rocks totals exactly 37. They've come to us over the eons as meteorites. Molly McCanta's job is to better understand the geological history of the red planet with only 37 samples to work from. Running time 5:15 minutes.
Did Mars ever support life? Why did it change so dramatically? Is there any water left? The only way to answer these questions is to analyze the rocks on the Martian surface. And since we can't yet bring those rocks to us, we must send the analysis instruments to Mars--carried on the backs of rovers. Running time 1:41 minutes.
It can take years to plan and engineer these state-of-the-art wind farms. It's a problem-solving process that draws on an understanding of algebra, geometry, kinetic energy, electronics and just about everything in between in order to turn one of our most abundant natural resources into a viable business. Running time 5:55 minutes.
Sailing the ocean no longer requires triple-masted schooners--in fact you can do it on a vessel no larger than a surfboard. What's the secret to designing a windsail that can skim the surface of the sea at 20 miles an hour, yet respond instantly to a sailor's touch? Running time 1:42 minutes. |
Applied Combinatorics, 5th Edition
This book teaches students in the mathematical sciences how to reason and model combinatorically. It seeks to develop proficiency in basic discrete math problem solving in the way that a calculus textbook develops proficiency in basic analysis problem solving.
The three principle aspects of combinatorical reasoning emphasized in this book are: the systematic analysis of different possibilities, the exploration of the logical structure of a problem (e.g. finding manageable subpieces or first solving the problem with three objects instead of n), and ingenuity. Although important uses of combinatorics in computer science, operations research, and finite probability are mentioned, these applications are often used solely for motivation. Numerical examples involving the same concepts use more interesting settings such as poker probabilities or logical games.
This book is designed for use by students with a wide range of ability and maturity (sophomores through beginning graduate students). The stronger the students, the harder the exercises that can be assigned. The book can be used for one-quarter, two-quarter, or one-semester course depending on how much material is used.
Theory is always first motivated by examples, and proofs are given only when their reasoning is needed to solve applied problems. Elsewhere, results are stated without proof, such as the form of solutions to various recurrence relations, and then applied in problem solving.
This new fifth edition has new examples, expanded discussions, and additional exercises throughout the text.
The game of Mastermind that appeared at the beginning of the first edition has been brought back to this edition.
The chapter on formal languages and finite-state machines from the second edition is back in abbreviated form. |
Description
The Calculus Workbook NCEA Level 3 offers students the tools they need for success in Calculus.
In the first part there are exercises at Achieved, Merit and Excellence levels. The author walks the student through each new concept, provides several worked examples, and then a set of problems for students to solve. The fully worked answers follow immediately, encouraging students to carefully compare their work with the worked examples and worked answers, and improve their results.
With a "practice makes perfect" attitude, the Calculus Workbook NCEA Level 3 also contains six full-length Practice Exams, written for the 2010 assessment specifications, with full answers, as well as Unit Standards Practice.
For those students who have mastered their Level 3 work, there follows a scholarship training programme. Students can work their own way through this material with minimum supervision from the teacher.
Author biography
Philip Lloyd is a Calculus teacher of many years standing, currently teaching at Epsom Girls Grammar School in Auckland. His students have consistently achieved very highly, with a good number achieving scholarship after using his material. |
3DSurface Viewer is a small Web application that creates high quality images of 3D surfaces defined by mathematical expressions. The quality of the images and the speed with which they are created ... More: lessons, discussions, ratings, reviews,...
The program uses the HTML5 canvas (HTML5 canvas javascript API) and web workers. Mathematical calculations are performed using the web workers, and the results are drawn on the canvas surface. Applica... More: lessons, discussions, ratings, reviews,...
This applet demonstrates an exponential growth model which plots population P_i for i=1 to i=600 given user input for the initial population P_0 and growth rate G. The difference equation used is P_(i... More: lessons, discussions, ratings, reviews,...
Using this virtual manipulative you may: graph a function; trace a point along the graph; dynamically vary function parameters; change the range of values displayed in the graph; graph multiple functiThis applet demonstrates a logistic growth model which plots population P_i for i = 1 to i = 600 given user input for the initial population P_0, growth rate G and carrying capacity CC. The difference... More: lessons, discussions, ratings, reviews,...
Enter a set of data points and a function or multiple functions, then manipulate those functions to fit those points. Manipulate the function on a coordinate plane using slider bars. Learn how each coPlomplex is a complex function plotter using domain coloring. You can compose a function with a complex variable z, and generate a domain coloring plot of it. You can choose the plot range as well as ... More: lessons, discussions, ratings, reviews,... |
MATLAB and Computing Support
MATLAB is a high-performance language for technical computing. It integrates computation, visualization, and programming environments, and is considered a standard tool in universities and industry alike.
Where to Get MATLAB
A student version of MATLAB is available from the Norris bookstore. MATLAB is compatible with Windows, Macintosh, and Linux operating systems.
How to Use MATLAB
A helpful introduction is available, with an overview of specific MATLAB functions commonly used by engineering students. |
Apologia Science
The quality of mathematics is extremely important to me, as math and science go hand-in-hand. There are many students who cannot handle my chemistry course, for example, because they have not had a good algebra course. That is why I strongly encourage you to look at Videotext Interactive's algebra course. It is, truly, the best that I have seen.
The course teaches real mathematics. It does not use tricks or shortcuts. Instead, it teaches the student to think mathematically. That's what is missing from many algebra courses! The use of animation and graphics is excellent. They do not detract from the learning, as is the case with some video courses I have seen. Instead, they enhance the student's ability to understand what is happening in each and every step along the way.
If you want your student to really learn algebra, then you should use this course. In short, this course is a scientist's dream come true! Every science-oriented student should use it |
Friday, August 3, 2012
Teaching Textbooks Review
I HATE Math.
There. I said it.
Math to me, is like a foreign language. One I don't understand. Sort of like Chinese.
In my day to day life, I don't ever use any of the advanced Math that I was tortured with in school. I only ever took up to Algebra 2, and I barely passed that. Ahhh.....good nightmares.....I mean.....memories.
So, for a Math hating homeschool Mom, how in the world are you supposed to teach advanced Math classes to your kids?
I did not learn of TT until my oldest daughter was in 8th grade, and we were about to do Pre-Algebra. We have always struggled with Math, and let me tell you, I was NOT looking forward to trying to teach her this.
We had started out with A Beka, which we struggled through from kindergarten until 3rd grade. For those of you who are not familiar with homeschooling curriculum, A Beka is one of the most commonly used curriculums out there.
However, it is advanced. Which is great, if you are working with an advanced student. My girls loved A Beka for Reading, Writing, Spelling, and Vocabulary. Things they were good at.
For Math however, it was just too much. So then, I tried Bob Jones (BJU). Yet another GREAT curriculum. I have often used this for Science and History, and have even used it for Spelling and Reading for my youngest.
While BJU was more tolerable than A Beka for Math, it was still not a good fit. There are many, many more Math curriculums out there, but those are the ones that I tried.
I can't remember exactly how I first heard of TT, but whoever told me about it, I now consider her an angel, sent straight from heaven, to help this poor Mama out!
I was reluctant to try it, because let's be honest, if you clicked on the link, you will notice that it IS pricey. It is much more expensive than most homeschoolers are willing to pay, or can even afford.
But, I figured, why not? We were at our wits' end as how to best teach this subject.
We purchased TT, and it was love at first sight. We have never used another Math curriculum since!
But, Amiee....what is SO special about TT, you may ask?
Well, for starters, it is all done on the computer. First, the child listens to a lecture from a teacher, and while the teacher is explaining that day's lesson, they are actually demonstrating how to do it. So, this works for auditory and visual learners alike.
You can listen to the lecture as many times as it takes for the child to grasp the information. While it is also possible for Mom to "replay" the info, her voice does tend to get raspy, and perhaps, there may even be a hint of irritation that tends to creep in, oh say around the third of fourth time she has to explain it. Not so with the computer teacher! He is extremely patient.
Then, the child is given some practice questions, to make sure they truly understand the lesson.
There is always the possibility of being "helped" and you can always view the answer once you get it wrong a set number of times (to be determined by the parent).
Once the child is ready, they can then begin to answer that day's questions about the lesson. There are usually around 20 questions, which seems to be an adequate amount. There is plenty of review from previous lessons included also.
My girls liked that, in the younger grades, they incorporate games for "bonus" rounds, and there are cute little creatures who will talk to you along the way.
There is also a parent side, where you can actually see the grade book, how many they got wrong, and be given the choice as to whether to make them do it over again or not.
What do I like best about it? That I don't have to do hardly anything! Unless one of my girls just isn't getting it, then, we go over the lesson together.
The lessons are self-grading, which is not only an awesome feature for Mom, but it also tells the child immediately if they got the answer right or wrong.
*Several of the advanced Math curriculums are still not self-grading, but they are working on changing that. They still come with an answer CD, and answer key. The lecture is listened to on the CD, but the child works out of a workbook. Hallelujah! Algebra 2 is now self-grading! Can you hear the excitement in my voice? Hmmm? Can you?!
TT is taught in a way that just makes it easier for a child to understand and be able to grasp information better. If you don't believe me, type the words, Teaching Textbooks review into your search engine, and read about other satisfied customers.
I must admit though, that the oldest is now at a point where I just cannot help her in Math anymore. That is now Hubs' job. We also did have a dear friend tutor her in Algebra for a little while, because she just wasn't getting it. So, there still could be some additional Math help needed, even though you are using excellent curriculum. That's just the way it is.
If your child is advanced in Math, this may not be the best curriculum for you, as it does tend to go at a slower pace, or, so I have read from people who have Math geniuses for children. For example, if your elementary school aged child is quoting algebraic equations in their sleep, it might be best to find a more challenging curriculum. Or, perhaps you should enroll them in college classes.
Yes, it is pricey. But, to me, it is worth every penny! Has it made my girls LOVE Math? Well....no. I don't think there is a curriculum in the world that could do that! Each child has their own set of strengths and weaknesses, and Math is one of our weaknesses. Although my youngest daughter tends to have a more "mathematical" mind than my older two, she still doesn't love Math.
Another nice thing about TT is that you are allowed to sell the curriculum to others once you are done using it. That is not the case with every curriculum. So, this year, I sold my used TT on eBay for the first time, and I was pleasantly surprised by how much money I was able to get back from my investment! If you do an advanced eBay search on TT, you will see that they have an excellent resale value.
Since I have been using TT for such a long time, I now have quite a collection of them, and I no longer have to buy three different Math curriculums for three different grade levels. This year, I only have to buy Algebra 2. My wallet just did a sigh of relief, as my oldest is about to take a few college classes for dual enrollment, and we are required to pay for it out of our own pocket. But, that's a tale for another time.
If you are a fellow homeschool family, and you are in the same boat as we used to be, struggling through Math, day in......and day out.....why not give Teaching Textbooks a try? You'll be glad you did!
* I did not receive any compensation or free products for this positive review.
2 comments:
I always like the idea of homeschool but what do you do when you are not good at something - so I see you have found the answer. Fortunately homeschool was not an option as we live in the City and by and large my kids walked to school. Not so the kids who live in the outback who are schooled over the radio. |
1EM - Essential Mathematics / Computational Laboratory
This is the home page for the computational part of the Level 1 Essential Mathematics course. The page for the maths side of the course is here. The older material from before the 2011/12 academic year, when the level 1 computation was part of the experimental multiple module is available here.
This course takes place during your weekly scheduled 1EM slot in 10BC03. Please come to your scheduled slot, and not one of the other times. There are 11 units and exercises to work through, as listed on the left. The course runs over 11 weeks, so you should be averaging 1 unit per week. This course runs over semester 1, and is examined at the end of semester by a written exam.
Previous students on the course have created a facebook help group which you might find useful. I sometimes answer questions there, as well as in the class, but often other students will answer them too.
This web site does not cover the entirety of the Fortran language, though the glossary contains quite a bit of useful information. If you wish to get a textbook to accompany the course, the best one is
Metcalf and Reid, "Fortran 90/95 Explained" or Metcalf, Reid and Cohen, "Fortran 95/2003 Explained", Oxford University Press. This is a concise and complete summary of Fortran with short examples.
There is a C++ version of this course available here. It is recommended that you follow the Fortran version, and refer to the C++ version in your own time, if you wish to learn it as a second language. |
Description Integrated course of algebra, geometry and trigonometry. Practical applications to vocational and technical programs are emphasized through the use of contextualized small-group classroom activities and guided practical problem solving. Topics include graphing in the Cartesian coordinate system; graphing and solving linear equations and systems of linear equations; geometric concepts of angles (degree and radian measure) and triangles, including the Pythagorean theorem and similar triangles; trigonometric concepts of sine, cosine, and tangent, and solving right triangles. Prerequisite: Grade of C- or better in OCSUP 106 or MATH 72B, or appropriate placement score.
Intended Learning Outcomes
Interpret written information, including graphs and application problems.
Understand and use creative thinking processes to support solving problems and making decisions.
Effectively communicate mathematical ideas in both everyday and mathematical language.
Use a scientific calculator to preform a variety of numerical calculations.
Translate word problems into mathematical or algebraic language and solve.
Construct a basic graph in Microsoft Excel.
Use whole numbers, integers, fractions, decimals, and order of operations in problems solving.
Identify and construct the following items in a Cartesian coordinate system:
* basic components of a graph, such as title, axes, legend, scale, data points
* data points in all four quadrant
* X-intercepts, y-intercepts, positive slope, and negative slope.
* identify and interpret data trends, including linear and quadratic relationships
Analyze linear functions and equations:
* solve linear equations in one variable
* graph linear equations in two variables
* calculate the slope of a line or determine the coordinates of a point on a line using the slope formula
* determine is two lines a parallel of perpendicular to each other
* use the midpoint and distance formula
* know and use the slope/intercept form of line
* determine the equation of a line given sufficient information
* recognize the standard form of a linear equation
* solve a system of two linear equations in two variables by the graphing method, the elimination method, and the substitution method
Analyze quadratic functions and equations:
* graph quadratic equations in two variable
* solve quadratic equations by the graphing method and by using the quadratic formula
Identify, classify, and calculate angles in triangles and transversals
Convert the measure of angle from degrees to radians and/or from radians to degrees
Define the trigonometric functions sine, cosine, and tangent
Calculate the sine, cosine, and tangent of a given angle, in both degrees and radians
Calculate and angle given the sine, cosine, or tangent of the angle in both degrees and radians
Solve right triangles
Graph vectors
Construct a vector from two vector components both graphically and using right triangle trigonometry
Determine the vector components of a vector using right triangle trigonometry
Determine a vector sum graphically and by using the vector component method. |
Solving equations and inequalities account for a large portion of the algebra standards. This training day will focus on difference between two approaches, traditional and function. The traditional approach would view the variable x in an equation like 5x – 7 = 3x + 9 as an unknown. The function approach views the two expressions as functions and the x as the independent variable for two functions in which the solution can be seen graphically as the intersection of two lines.
IN THIS SESSION TEACHERS:
Learn the different methods that children use to solve linear equations.
Learn how to select examples to push kids from less sophisticated methods (i.e. guess and check)
to more algebraic methods.
Learn a deeper meaning for properties of equations.
Standards Specifically Addressed
MINNESOTA ACADEMIC STANDARDS
Grade 7: Represent real-world and mathematical situations using equations with variables. Solve equations symbolically,
using the properties of equality. Also solve equations graphically and numerically. Interpret solutions in the original context. |
MATH 091: Basic Mathematics
General Information
Transfer Information: Courses with numbers below 100: This course is a developmental course that does not apply toward a WNC degree or honors designation and normally does not transfer to a university. Please see a counselor for more information.
Course Outline
I: Catalog Course Description
Provides the fundamental operation of whole numbers, fractions and mixed numbers, decimals, percentage, measurement and geometry. The course is intended to provide a thorough review of basics needed in future mathematics courses and in applied fields.
II: Course Objectives
Upon completion of this course, successful students should be able to work with the following:
Addition, subtraction, multiplication and division of whole numbers
Exponents and order of operations
Fractions and mixed numbers
Decimals
Ratios and proportions
Percents
Measurement (American and Metric units)
Geometry
Addition, subtraction of signed numbers
Applied problems
III: Course Linkage
Linkage of course to educational program mission and at least one educational program outcome.
Although Math 91 does not fulfill any general education or degree program requirements, it will assist students toward developing appropriate college-level mathematical skills and problem solving skills. |
Listed below are practice
problems for the topics covered in the lectures and labs. These represent a good set of
possible types of exam problems. To be successful
on the exams, you will need to be able to do these homework problems. Doing
them correctly on an exam means that the answer is correct, with the correct units and the correct number of significant
figures and all the work shown. Once in a while, "extra credit"
problems will be assigned. These will have a firm due date and will, if
correct, be worth some exam points. They will normally be done using Mathcad. |
Algebra and Number Theory. An Integrated Approach
John Wiley and Sons Ltd, September 2010, Pages: 524
Explore the main algebraic structures and number systems that play a central role across the field of mathematics
Algebra and number theory are two powerful branches of modern mathematics at the forefront of current mathematical research, and each plays an increasingly significant role in different branches of mathematics, from geometry and topology to computing and communications. Based on the authors' extensive experience within the field, Algebra and Number Theory has an innovative approach that integrates three disciplines—linear algebra, abstract algebra, and number theory—into one comprehensive and fluid presentation, facilitating a deeper understanding of the topic and improving readers' retention of the main concepts.
The book begins with an introduction to the elements of set theory. Next, the authors discuss matrices, determinants, and elements of field theory, including preliminary information related to integers and complex numbers. Subsequent chapters explore key ideas relating to linear algebra such as vector spaces, linear mapping, and bilinear forms. The book explores the development of the main ideas of algebraic structures and concludes with applications of algebraic ideas to number theory.
Interesting applications are provided throughout to demonstrate the relevance of the discussed concepts. In addition, chapter exercises allow readers to test their comprehension of the presented material.
Algebra and Number Theory is an excellent book for courses on linear algebra, abstract algebra, and number theory at the upper-undergraduate level. It is also a valuable reference for researchers working in different fields of mathematics, computer science, and engineering as well as for individuals preparing for a career in mathematics education.
PREFACE.
CHAPTER 1 SETS.
1.1 Operations on Sets.
Exercise Set 1.1.
1.2 Set Mappings.
Exercise Set 1.2.
1.3 Products of Mappings.
Exercise Set 1.3.
1.4 Some Properties of Integers.
Exercise Set 1.4.
CHAPTER 2 MATRICES AND DETERMINANTS.
2.1 Operations on Matrices.
Exercise Set 2.1.
2.2 Permutations of Finite Sets.
Exercise Set 2.2.
2.3 Determinants of Matrices.
Exercise Set 2.3.
2.4 Computing Determinants.
Exercise Set 2.4.
2.5 Properties of the Product of Matrices.
Exercise Set 2.5.
CHAPTER 3 FIELDS.
3.1 Binary Algebraic Operations.
Exercise Set 3.1.
3.2 Basic Properties of Fields.
Exercise Set 3.2.
3.3 The Field of Complex Numbers.
Exercise Set 3.3.
CHAPTER 4 VECTOR SPACES.
4.1 Vector Spaces.
Exercise Set 4.1.
4.2 Dimension.
Exercise Set 4.2.
4.3 The Rank of a Matrix.
Exercise Set 4.3.
4.4 Quotient Spaces.
Exercise Set 4.4.
CHAPTER 5 LINEAR MAPPINGS.
5.1 Linear Mappings.
Exercise Set 5.1.
5.2 Matrices of Linear Mappings.
Exercise Set 5.2.
5.3 Systems of Linear Equations.
Exercise Set 5.3.
5.4 Eigenvectors and Eigenvalues.
Exercise Set 5.4.
CHAPTER 6 BILINEAR FORMS.
6.1 Bilinear Forms.
Exercise Set 6.1.
6.2 Classical Forms.
Exercise Set 6.2.
6.3 Symmetric Forms over R.
Exercise Set 6.3.
6.4 Euclidean Spaces.
Exercise Set 6.4.
CHAPTER 7 RINGS.
7.1 Rings, Subrings, and Examples.
Exercise Set 7.1.
7.2 Equivalence Relations.
Exercise Set 7.2.
7.3 Ideals and Quotient Rings.
Exercise Set 7.3.
7.4 Homomorphisms of Rings.
Exercise Set 7.4.
7.5 Rings of Polynomials and Formal Power Series.
Exercise Set 7.5.
7.6 Rings of Multivariable Polynomials.
Exercise Set 7.6.
CHAPTER 8 GROUPS.
8.1 Groups and Subgroups.
Exercise Set 8.1.
8.2 Examples of Groups and Subgroups.
Exercise Set 8.2.
8.3 Cosets.
Exercise Set 8.3.
8.4 Normal Subgroups and Factor Groups.
Exercise Set 8.4.
8.5 Homomorphisms of Groups.
Exercise Set 8.5.
CHAPTER 9 ARITHMETIC PROPERTIES OF RINGS.
9.1 Extending Arithmetic to Commutative Rings.
Exercise Set 9.1.
9.2 Euclidean Rings.
Exercise Set 9.2.
9.3 Irreducible Polynomials.
Exercise Set 9.3.
9.4 Arithmetic Functions.
Exercise Set 9.4.
9.5 Congruences.
Exercise Set 9.5.
CHAPTER 10 THE REAL NUMBER SYSTEM.
10.1 The Natural Numbers.
10.2 The Integers.
10.3 The Rationals.
10.4 The Real Numbers.
ANSWERS TO SELECTED EXERCISES.
INDEX.
"The book is well-written and covers, with plenty of exercises, the material needed in the three aforementioned courses, albeit in a new order." (Zentralblatt MATH, 1 December 2012)
"However, instructors contemplating such a unified approach should give this book serious consideration. Recommended. Upper-division undergraduates through researchers/faulty." (Choice , 1 April 2011) |
University of Texas at El Paso
Improving students' algebraic thinking: The case of Talia
Kien H. Lim, University of Texas at El Paso
Abstract
This paper presents the case of an 11th grader, Talia, who demonstrated improvement in her algebraic thinking after five one-hour sessions of solving problems involving inequalities and equations. She improved from association-based to coordination-based predictions, from impulsive to analytic anticipations, and from inequality-as-a-signal-for-a-procedure to inequality-as-a-comparison-of-functions conceptions. In the one-on-one teaching intervention, she progressed from the sub-context of manipulating symbols, to working with specific numbers, to reasoning with "general" numbers, and eventually to reasoning with symbols. Three features were identified to account for her improvement: (a) attention to meaning, (b) opportunity to repeat similar reasoning, and (c) opportunity to explore.
Suggested Citation
Kien H. Lim. "Improving students' algebraic thinking: The case of Talia" Proceedings of the Thirty-first Conference of the International Group for the Psychology of Mathematics Education. Seoul, Korea. Jul. 2007.
Available at: |
Geometry DeMYSTiFieD all-new angle to learning geometry! Updated with all-new quizzes and test questions, and a completely refreshed design, Geometry Demystified, Second Edition makes it easy to learn or recall basic geometry. You can use the book as a supplemental classroom text or as a self-contained course without an instructor. Worked-out problems and solutions with practical themes are included. The book contains 11 chapters in two parts. Each chapter ends with a multiple-choice quiz. Each part ends with a multiple-choice test. A comprehensive multiple-choi... MOREce final exam concludes the course. This hands-on guide helps you to: understand angle measurement and expression; grasp the relationships between angles and distances; calculate perimeters, areas, and volumes; read maps and charts; use coordinate systems in two and three dimensions; construct geometric figures with a compass and straight edge; learn the fundamentals of vectors; improve spatial perception; envision space of more than three dimensions. Geometry Demystified, Second Editionfeatures: Chapter-opening objectives offering insight into what you're going to learn in each step Questions at the end of every chapter to reinforce learning and pinpoint weaknesses "Still Struggling?" icon providing specific recommendations for those having difficulty with certain subtopics A final exam for overall self-assessment "Curriculum Tree" that shows how the topic covered in the book fits into a larger curriculum SI units throughout Hard stuff made easy! Some Basic Rules; Triangles; Quadrilaterals; Other Plane Figures; Compass and Straight Edge; The Cartesian Plane; An Expanded Set of Rules; Surface Area and Volume; Vectors and Cartesian Three-space; Alternative Coordinates; Hyperspace and Warped Space The second edition of this cornerstone of the math curriculum is updated with all-new quizzes and test questions, clearer explanations of the material, and a completely refreshed interior design.
A new ANGLE to learning GEOMETRY
Trying to understand geometry but feel like you're stuck in another dimension? Here's your solution. Geometry Demystified, Second Edition helps you grasp the essential concepts with ease.
Written in a step-by-step format, this practical guide begins with two dimensions, reviewing points, lines, angles, and distances, then covers triangles, quadrilaterals, polygons, and the Cartesian plane. The book goes on to discuss three dimensions, explaining surface area, volume, vectors, Cartesian three-space, alternative coordinates, hyperspace, and warped space. Detailed examples, concise explanations, and worked-out problems make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce learning.
It's a no-brainer! You'll learn about:
Plane geometry and solid geometry
Using a drafting compass and straight edge
Solving pairs of equations
Working with vectors in three-space
Polar coordinates
Cartesian n-space
Simple enough for a beginner, but challenging enough for an advanced student, Geometry Demystified, Second Edition helps you master this fundamental mathematics subject.
PART II: THREE DIMENSIONS AND UP Ch 7. An Expanded Set of Rules Ch 8. Surface Area and Volume Ch 9. Vectors and Cartesian Three-space Ch 10. Alternative Coordinates Ch 11. Hyperspace and Warped Space Test: Part Two |
Smory\'nski, CraigChapters in probability.Texts in Mathematics 4. London: College Publications (ISBN 978-1-84890-067-7/pbk). xii, 550~p. EUR~29.99; \sterling~16.50; \$~26.50 (2012).2012London: College PublicationsEN60-0100A3597-0197K1097K5097B50probabilityhistory of mathematicsThis book grew out of a course on the history of mathematics given to middle school teachers in Chicago. Although initially just one week of the course was devoted to probability, the author's notes for that part of the course grew to include many times the amount of material initially indicated. The final result has been a thoroughgoing treatment of a large segment of elementary probability with a generous amount of historical material, including a good number of excerpts from the original books and papers on the subject. Part I of the book is ``Elementary Probability,'' and accounts for only the first 150 or so pages of the 550-page book. Beyond this, Part II devotes another 170 pages to the ``Law of Large Numbers,'' where we find a thorough treatment of Bernoulli's Theorem, the Central Limit Theorem, errors, Chebyshev's Inequality and more. Part III consists of several appendices: A. The Calculator; Beyond the Basics, which expands on the manual for the TI-83 Plus; B. Some Mathematical Extras; C. Philately; D. Tables (births, mortality, census figures, etc.); E. Recommended Reading. The book would be an excellent text for a low to middle level university course on probability for mathematics/mathematics education majors (among others); one which would likely give students much interesting reading beyond the requirements of the course.Gerald A. Heuer (Moorhead) |
Aims and objectives
This unit aims to provide you with a coherent and balanced account of major mathematical and statistical techniques and concepts that form the basis of many engineering analysis tools. It will also introduce you to the relevant computer software that will support your engineering studies.
After successfully completing this unit, you should be able to: 1. Appreciate conceptual aspects of Fourier series expansions of periodic and periodically extended functions and apply the technique in practice. (K2, S1) 2. Demonstrate a good understanding of the Laplace transform and use it for solving linear differential equations describing motion and forces. (K2, S1) 3. Use the representation of random variables through the distribution and density functions. (K2, S1) 4. Apply the basic concepts of estimating parameters and hypothesis testing. (K2, S1, S2) 5. Demonstrate understanding of concepts of correlation, regression and analysis of variance. (K2, S1). 6. Operate with functions of complex variables. (K2, S1, S2) 7. Demonstrate practical understanding of derivatives and integrals of elementary functions of complex variables. (K2, S1)
Swinburne Engineering Competencies for this Unit of Study This Unit of Study will contribute to you attaining the following Swinburne Engineering Competencies: K2 Maths and IT as Tools: Proficiently uses relevant mathematics and computer and information science concepts as tools. S1 Engineering Methods: Applies engineering methods in practical applications. S2 Problem Solving: Systematically uses engineering methods in solving complex problems. |
Chapter 1. Introduction - Pg. 1
1 Introduction 1.1 Why Numerical Methods? Engineers and scientists frequently encounter linear and nonlinear mathematical equa- tions, integrals, differential equations, and data to be manipulated. Sometimes the ma- nipulations to be performed are easy and straightforward; often they are not. This is particularly true of nonlinear problems, that is, problems in which variables occur as products, including products of themselves, or as functions of transcendental functions, like the trigonometric or logarithmic relations. If the mathematics to be performed can- not be done in closed form (i.e., an exact analytic symbolic solution is obtained), recourse must be made to numerical approximations. Fortunately, these methods, when properly understood and used, are powerful and accurate. It should be understood that recourse to a numerical solution is always a fall- |
Rent Textbook
Buy New Textbook
eTextbook
180 day subscription
$89.99
Used Textbook
We're Sorry Sold Out
More New and Used from Private Sellers
Starting at $16 Rockswold/Krieger algebra seriesfosters conceptual understanding by using relevant applications and visualization to show students why math matters. It answers the common question "When will I ever use this?" Rockswold teaches students the math in context, rather than The authors believe this approach deepens conceptual understanding and better prepares students for future math courses and life.
Author Biography
Gary Rockswold has been a professor and teacher of mathematics, computer science, astronomy, and physical science for over 35 years. He has taught not only at the undergraduate and graduate college levels, but he has also taught middle school, high school, vocational school, and adult education. He received his BA degree with majors in mathematics and physics from St. Olaf College and his Ph.D. in applied mathematics from Iowa State University. He has been a principal investigator at the Minnesota Supercomputer Institute, publishing research articles in numerical analysis and parallel processing and is currently an emeritus professor of mathematics at Minnesota State University, Mankato. He is an author for Pearson Education and has over 10 current textbooks at the developmental and precalculus levels. His developmental coauthor and friend is Terry Krieger. They have been working together for over a decade. Making mathematics meaningful for students and professing the power of mathematics are special passions for Gary. In his spare time he enjoys sailing, doing yoga, and spending time with his family.
Additional information about Gary Rockswold can be found at
Terry Krieger has taught mathematics for 18 years at the middle school, high school, vocational, community college and university levels. His undergraduate degree in secondary education is from Bemidji State University in Minnesota, where he graduated summa cum laude. He received his MA in mathematics from Minnesota State University - Mankato. In addition to his teaching experience in the United States, Terry has taught mathematics in Tasmania, Australia, and in a rural school in Swaziland, Africa, where he served as a Peace Corps volunteer. Terry is currently teaching at Rochester Community and Technical College in Rochester, Minnesota. He has been involved with various aspects of mathematics textbook publication for more than 14 years and has joined his friend Gary Rockswold as coauthor of a developmental math series published by Pearson Education. In his free time, Terry enjoys spending time with his wife and two boys, physical fitness, wilderness camping, and trout fishing. |
2_algebra_II_final
Mathematics – Algebra II
2011
Common Core State Standards
ALGEBRA
Seeing Structure in Expressions
Interpret the structure of expressions.
1. Interpret expressions that represent a quantity in terms of its context.
Interpret parts of an expression, such as terms, factors, and coefficients.
Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a
factor not depending on P.
2. Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of
squares that can be factored as (x2 – y2)(x2 + y2).
Write expressions in equivalent forms to solve problems.
3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
a. Factor a quadratic expression to reveal the zeros of the function it defines.
b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as
(1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
4. Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example,
calculate mortgage payments.
17
Mathematics – Algebra II
2011
Arithmetic with Polynomials & Rational Expressions
Perform arithmetic operations on polynomials.
1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction,
and multiplication; add, subtract, and multiply polynomials.
Understand the relationship between zeros and factors of polynomials.
2. Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only
if (x – a) is a factor of p(x).
3. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by
the polynomial.
Use polynomial identities to solve problems.
4. Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x2 + y2)2 = (x2 – y2)2 + (2xy)2
can be used to generate Pythagorean triples.
5. (+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any
numbers, with coefficients determined for example by Pascal's Triangle.1
Rewrite rational expressions.
6. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials
with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra
system.
7. (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and
division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.
18
Mathematics – Algebra II
2011
Creating Equations
Create equations that describe numbers or relationships.
1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and
simple rational and exponential functions.
2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
3. 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. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to
highlight resistance R.
Reasoning with Equations & Inequalities
Understand solving equations as a process of reasoning and explain the reasoning.
1. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption
that the original equation has a solution. Construct a viable argument to justify a solution method.
2. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
Solve equations and inequalities in one variable.
3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
19
Mathematics – Algebra II
2011
4. Solve quadratic equations in one variable.
Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same
solutions. Derive the quadratic formula from this form.
Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as
appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi
for real numbers a and b.
Solve systems of equations.
5. 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.
6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
7. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find
the points of intersection between the line y = –3x and the circle x2 + y2 = 3.
8. (+) Represent a system of linear equations as a single matrix equation in a vector variable.
9. (+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or
greater).
Represent and solve equations and inequalities graphically.
10. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve
(which could be a line).
11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation
f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive
approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
12. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the
solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
20
Mathematics – Algebra II
2011
KEY ELEMENTS CONTENT PERFORMANCE TARGETS
(What Students should know) (What Students should know)
Number and Number Sense Equations and Inequalities Students will attain the skills to:
Expressions can be evaluated by Use order of operations to evaluate
the order of operations expressions
Use formulas
Evaluate and simplify Determine the set of numbers to which a
number belongs
Equations Use the properties of real numbers to
simplify expressions
Inequalities Translate verbal expressions and
sentences into algebraic expressions and
Expressions and formulas equations
Solve equations by using the properties of
Properties of Real Numbers equality
Solve equations for a specific variable
Graphs and measures Solve equations containing absolute value
Solving equations
Solve inequalities and graph the solution
sets
Solving absolute equations
Solve compound inequalities
Solve inequalities involving absolute value
and graph the solution set.
Find the value of each expression
Evaluate each expression when given a
certain value for a variable
Name the sets of numbers to which each
value belongs
Name the property illustrated by each
equation
Find the median, mode, and mean for
each set of data
Solve linear equations
21
Mathematics – Algebra II
2011
Solve each equation or formula for the
variable specified
Solve absolute equations
Solve inequalities and graph them on a
number line
Solve compound inequalities and graph
them on a number line
Solve absolute inequalities and graph
them on a number line.
State the domain and range of each
relation
Graph a relation and identify whether it is
a function or not
Find the value of a function given an input
State whether each equation is linear
Data Analysis and Probability Linear Relations and Functions Find values of functions for given
elements of the domain
Functions Use a graphing calculator to graph linear
equations
Slope Identify equations that are linear and
graph them
Write linear equations in standard form.
Determine the intercepts of a line and use
them to graph an equation
Determine the slope of a line
Use slope and a point to graph an
equation
Determine if two lines are parallel,
perpendicular or neither
Solve problems by identifying and using a
pattern
Write an equation of a line in slope-
intercept form given the slope and one or two
points
Write an equation of a line that is parallel
22
Mathematics – Algebra II
2011
or perpendicular to the graph of a given
equation
Draw a scatterplot
Find and use prediction equations
Use a graphing calculator to graph lines of
regression
Draw graphs of inequalities in two
variables
Graph absolute value inequalities
Patterns, Functions, Algebraic Systems of Linear Equations and
Standards Inequalities Find the maximum and minimum values of
a function over a region
Equations Solve problems involving maximum and
Inequalities minimum values
Linear Programming Solve a system of three equations in three
Three Variables variables by elimination
Writing linear equations Determine the slope of the line that
Integration: statistics passes through each pair of points
Special functions Write an equation in slope-intercept form
Graphing linear equations for each given situation
Graphing systems of inequalities Describe each function to be either
Linear programming constant, direct variation, absolute value, or a
Applications of linear programming greatest integer function
Solving systems of equations in three Graph inequalities
variables Graph systems of equations and state the
solution
Solve systems of equations using either
substitution or elimination
Solve systems of inequalities by graphing
Graph systems of inequalities and locate
the possible solutions to the system
23
Mathematics – Algebra II
2011
Matricies Use matrix logic to problem solve
Adding and subtracting Matrices Perform operations with matricies and find
Multiplying matrices determinants and inverse
Matrices and determinants Evaluate the determinant of a 2X2 matrix
Inverses and identities and the determinant of a 3X3 matrix
Using matrices to solve systems Write the identity matrix for any square
matrix
Find the inverse of a 2X2 matrix
Solve systems of linear equations using
inverse matrices
Geometric transformations using matricies
Add, subtract, or multiply two matrices
Determine whether each matrix has a
determinant
Find the determinant of each matrix
Find the inverse of each matrix
Solve a matrix equations or systems of
equations using inverse matrices
Solve a system of equations by using
augmented matrices
Quadratic Functions & Relations Solve quadratic equations by using the
• Factoring Review quadratic formula
Use discriminants to determine the nature
of the roots of quadratic equations
Find the sum and product of the roots of
quadratic equations to use in writing equations
Graph Quadratic Functions
Solve by Graphing
Transformations with Quadratic Functions
Solving & Graphing Quadratic Inequalities
Patterns and Functions Complex Numbers Simplify square roots containing negative
radicands
Numbers and Number Sense Solve quadratic equations that have pure
imaginary solutions
Add, subtract and multiply complex
numbers
24
Mathematics – Algebra II
2011
Simplify rational expressions containing
complex numbers in denominators
Polynomial and Polynomial Functions Multiply and Divide monomials
Divide polynomials using long division and
Monomials synthetic division
Polynomials Factor polynomials
Polynomial Functions Use factoring to simplify polynomial
Dividing polynomials quotients
Factoring Add & Subtract Polynomials
Roots of real numbers Determine the degree and name of a
Radical expressions polynomial
Polynomial Functions
Remainder and Factor Theorems
Graph Polynomial Functions and
approximate the zeros
Find roots and zeros using fundamental
theorem of algebra
Evaluate polynomial functions
Analyze graphs of polynomial functions
Solve polynomial functions
Write a polynomial function given the
roots
Rational zero theorem
Inverse and Radical Functions and Relations Add, subtract, multiply and divide
functions
Operations and functions Composition of functions
Radicals Find and graph inverse functions
Simplify radicals having various indices
Use a calculator to estimate roots of
number
Simplify radical expressions
Rationalize the denominator of a fraction
containing a radical expression
Add subtract, multiply and divide radical
25
Mathematics – Algebra II
2011
expressions
Write expressions with radical exponents
in simplest radical form and vice versa
Evaluate expressions in either exponential
or
radical form
Solve equations and inequalities
containing radicals
Graphing square root functions and
inequalities
Patterns, functions, algebraic Exponential and Logarithmic Function and Introduce exponential and logarithmic
standards Relations functions
Logarithmic functions
Properties of logarithms
Common logarithms
Natural logarithms
Solve exponential equations and
inequalities
Rational Functions and Relations Solve logarithmic equations and
inequalities
Graph exponential functions
Applications of exponential functions &
inequalities
Graph rational functions
Direct, inverse and joint variation
Multiply and divide rational expression
Add and subtract rational expressions
Solve rational equations
Exponential and Logarithmic Functions and Introduce exponential and logarithmic
Relations functions
Logarithmic functions
Properties of Logarithms
Common Logarithms
Natural Logarithms
Solve Exponential Equations and
Inequalities
26
Mathematics – Algebra II
2011
Solve Logarithmic Equations &
Inequalities
Rational Functions and Relations Graph Exponential Functions
Applications of Exponential Functions &
Inequalities
Graph Rational Functions Direct, Inverse
and Joint Variation
Multiply and Divide Rational Expression
Add and Subtract Rational Expressions
Solve Rational Equations and
Inequalities
Geometry and Spatial Sense Analyzing Conic Sections Distance and Midpoint Formulas
Explore Parabolas
Explore Circles
Explore Ellipses
Explore Hyperbolas
Identify conic sections
Solve linear and non linear systems of
Sequences and Series equations
Find the nth term of an arithmetic or
geometric sequence
Find the sums of an arithmetic or
geometric systems
Rational exponents Simplify expressions with rational
Solving radical equations and inequalities exponents
Complex numbers Solve equations containing radicals and
Simplifying expressions rational expressions
Containing complex numbers Simplify radical expressions using
Solving quadratic equations by graphing complex numbers
Solving quadratic equations by factoring Solve quadratic equations by graphing
and locating their solutions
Solve quadratic equations by factoring
Solve quadratic equations by completing
27
Mathematics – Algebra II
2011
the square
Solve quadratic equations by using the
quadratic formula
Find the discriminant of a quadratic
equation and decipher the nature of the
equations roots/zeros
The sum and product of roots Given the roots/zeroes find the equation
Analyzing graphs of quadratic functions of the quadratic line, solve problems
Graphing and solving quadratic inequalities Write the equations of parabola using
general form
Graph
28 |
Blackline master book designed
to complement a remedial Math program for small groups of students.
Explains
the basic concepts of number, exploring in detail the processes of addition,
subtraction, multiplication and division.
Decimals are investigated in detail as
well as their relationship with percentages. The activities are sequenced in
line... more...
Contains a set of black line masters for interesting math number games that can be reproduced on A3 card for practical use in the classroom, strengthening students? knowledge of times tables and number skills. Activities to suit Grades 1-7 students.
more...
This book is a collection of selected papers presented at the last Scientific Computing in Electrical Engineering (SCEE) Conference, held in Sinaia, Romania, in 2006. The series of SCEE conferences aims at addressing mathematical problems which have a relevance to industry, with an emphasis on modeling and numerical simulation of electronic circuits,... more...
Presents computational issues arising in financial mathematics. This guide to the financial engineering features revisions that concern topics like calibration, Monte Carlo Methods, American options, exotic options and Algorithms for Bermuda Options. It includes various figures, exercises, background material of financial engineering. more...
Emphasizing the connection between mathematical objects and their practical C++ implementation, this book provides a comprehensive introduction to both the theory behind the objects and the C and C++ programming. It covers discrete mathematics, data structures, and computational physics, including high-order discretization of nonlinear equations. more...
is a collection of 65 selected papers presented at the 7th International Conference on Scientific Computing in Electrical Engineering (SCEE), held in Espoo, Finland, in 2008. The aim of the SCEE 2008 conference was to bring together scientists from academia and industry, e.g. mathematicians, electrical engineers, computer scientists, and... more...
This book deals with the mathematical analysis and the numerical approximation of eddy current problems in the time-harmonic case. All the most used formulations are taken into account, placing the problem in a rigorous functional framework. Nodal or edge finite elements are used for approximation. A detailed analysis of each formulation is presented,... more...
This cross-disciplinary volume brings together theoretical mathematicians, engineers and numerical analysts and publishes surveys and research articles related to the topics where Georg Heinig had made outstanding achievements. In particular, this includes contributions from the fields of structured matrices, fast algorithms, operator theory, and applications... more... |
Loma Mar ACT MathIt is a new language and yet based on our arithmetic. Algebra simply uses an "x" instead of a number. Algebra 2 is the time in the development of our curriculum that takes the basic skills and puts them into context |
The Calculator section covers the most common calculations in a easy to use format with images of the information required, the required fields, and step-by-step instructions on how to get the calculation. |
KS5 A level Maths Standards Units: Mostly Calculus
core 1 maths worksheets, activities and lesson plan. C2 Exploring Functions Involving Powers. This is part of the "Mostly Calculus" set of materials from Standards unit: Improving learning in mathematics. To develop learners' ability to find the stationary points of a function and determine their na More…ture, solve appropriate equations in order to find the intercepts of a function. To encourage learners to connect the mathematical properties of a function and relate them to the graph.
Reviews (1)
A very useful resource which provides ideas about how to investigate functions involving powers. The suggested structure is very helpful and ideas for progression/discussion mean this is a great reference point. |
ALEKS Math Preparation
ALEKS (Assessment and Learning in Knowledge Spaces) is an online mathematics tutorial program that:
Provides a cycle of Assessment and Learning
Allows Self-paced, Individualized Instruction
Accelerates Learning in Math
Assesses and Instructs with Standards-based Content
Provides Clear Explanations and Feedback
Allows You to Toggle Between English and Spanish
Offers 24 Hour Online Access
Allows you to earn a certificate of completion for the number of hours you took to complete the course with a maximum of 20 hours
Active use of ALEKS can increase grade performance and success in other WECA classes.
To participate in the ALEKS course, you will need a computer with high speed internet access that also meets the minimum system requirements. Before starting the course, you must download the ALEKS Plug-in. See details here: (your course falls under "Higher Education"). Upon enrollment, you will receive a personal pass code which you will use to access the course. After taking the self assessment quiz, ALEKS will automatically produce a pie chart of your assessment score and recommend your training path based on the results. |
Basics
Office Hours
MW: 10am-11am
TH: 2pm-3pm
or by appointment
Prerequisites:
Enrollment in this course requires a score of 85 or higher on the Accuplacer Elementary Algebra
Test,OR an ACT score of 19 or higher, OR an SAT score of 490 or higher, OR a grade of C or higher
in Intermediate Algebra (or equivalent preparatory course). We are completely inflexible on these prereqs
Requirements:
Pens preferred; graph paper, and a scientific calculator; that is, a calculator that can handle numbers in scientific notation and has [yx], [π], and [!] keys. (Cell-phone calculators, generally, are not scientific.) CELL PHONES ARE TO BE SHUT OFF AT THE BEGINNING OF CLASS (unless a prior arrangement with me has been made).
Optional Texts:
(THERE ARE NO REQUIRED TEXTBOOKS FOR THIS COURSE)
Van de Walle, J. A. Elementary and Middle School Mathematics: Teaching Developmentally (5th, 6th or 7th editions). White Plains, NY: Longman. [This is an excellent mathematics teaching methods text.] You will need to purchase it for EDU 4120.
Course Overview:
(Borrowed with permission from Mark Koester) This course is designed to help prospective teachers develop a sound background in the concepts underlying the school mathematics curriculum. Teachers working in the diverse contexts of school mathematics classrooms must possess not only sound understanding of mathematical ideas, but of the processes by which this understanding develops and in which this understanding is applied. Therefore, how one does mathematics in this class is as important as the mathematical ideas themselves.
In this course, students will:
Pose and solve problems, individually, and in groups, in class and outside of class;
Describe and analyze their work and the work of others, both orally and in writing;
Use a variety of tools, including manipulative models and technology, to solve problems;
Demonstrate working knowledge of the big mathematical ideas of the course.
Classroom Environment:
It is absolutely critical that we create a productive classroom environment that is friendly, non-judgmental, gentle and relaxed so that all class members will feel sufficiently safe to offer suggestions even when they are not absolutely sure that they are correct. So, take care with each other's feelings. Give each other permission to be unsure, and encouragement to take chances and make guesses. That's how we will all learn best. And besides, it is more fun that way.
We will be doing mathematics "one problem at a time." A "problem" is a mathematical situation for which you know no solution. An "exercise" is an opportunity to practice a known procedure. We will be exploring a lot of problems, and in the process will learn many useful strategies for solving them. The goal is to understand and explain why things are true, often in several different ways. After each class, your task period is to review your notes, make sense of as much as you can and mark the parts about which you are still confused. Then ask about them with your groupmates or me. In this class, everything can make sense! ! This course does not follow a textbook, so I suggest that you keep a loose-leaf notebook that contains an accurate record of all in and out of class activities. You will refer to it frequently as your prepare your assignments and use it for the in-class exams. They are open-book!
The course is divided into four sections. We begin with two problems that introduce you to how we do math in this class. We follow that with a section on PATTERNS in numbers. Then there is a section on SPATIAL THINKING AND GEOMETRY. Finally we will do some work on SYSTEMATIC COUNTING.
As part of the learning process in our classroom, everyone is expected to observe the professional skills you make use of every day in your workplace. The classroom environment is one where a feeling of safety and security is necessary. Being considerate of others, their opinions and points of view is essential and expected. An atmosphere of equality,
respect and consideration are all considered part of professionalism. Behaviors that would indicate you are acting in a professional manner would include (and are not limited to):
relevant and appropriate participation in class discussions
avoiding the use of iPods, computers, cell phones and text messaging;
preparation for class through reading all assigned material and handing assignments in on time;
use of active listening skills (even if you disagree with someone's point of view);
attentiveness when someone else is speaking and
an attitude that reflects openness and receptivity to learning and the learning process.
Part of your responsibilities as members of this classroom community includes recognizing the importance and responsibility you hold in facilitating the learning of your fellow classmates.
Attendance:
Successful completion of this course does not depend only on scores on assessments. It depends, in large part, on having participated in the set of class activities that comprise the course. In addition, prompt class attendance is considered evidence of intellectual commitment to the course. Therefore, prompt attendance is required. I do understand that there might be times when you must miss class. If you must miss all or part of a class, use the office hours, phone number or e-mail address provided above to discuss the reasons with me beforehand. Whenever you miss class, you must do a 2 - 3 page "make-up" of the material that was missed. This involves writing your own set of notes about what happened that day and the results that were found in class. (This way, your personal set of class notes will be complete for use on the exams.) The "make-up" must be completed within a couple weeks of the absence. More than three absences will lower your grade by one letter, unless special arrangements are made with the instructor. (Regular tardiness will be interpreted as a lack of intellectual commitment to the course, and will prevent a student from earning an "A.")
Assessment and Grading:
Assessment in any mathematics class is the process of gathering and reporting evidence of students' developing mathematical proficiency. In this class a database of evidence, collected from a variety of sources and built throughout the semester, will be summarized as a letter grade, as described next.
What are the characteristics of a student who will earn a grade of "B" or better in this class? Such a student will have, by the end of the course, provided consistent evidence of having reached an appropriate level of mathematical proficiency. Mathematical proficiency is defined as:
Conceptual understanding of the big ideas that underlie the school mathematics curriculum, and fluency with the procedures, skills and tools used to do mathematics.
The strategic competence needed to tackle novel mathematical problems, including the problems of understanding the mathematical thinking of children, and the adaptive reasoning needed to explain and justify one's own methods and solutions, and the methods and solutions offered by others;
A productive disposition toward doing and learning mathematics. A prospective teacher has a productive disposition if she views mathematics as a sensible and meaningful discipline, and if she sees herself as capable of making sense of her own mathematical ideas and those offered by children, through persistent and diligent effort.
How does an "A" student differ from a "B" student? An "A" student will have distinguished herself by:
Providing convincing evidence of a level of mathematical proficiency that goes well beyond the standard set for the course;
Participating consistently in the individual, small-group, and whole-class activities and discussions that constitute the daily work of the course;
Regularly offering mathematical ideas for discussion and analysis by others, both orally and in writing;
Demonstrating, through attendance, promptness, and attitude, the intellectual commitment to learning at the heart of outstanding teaching.
What are the characteristics of a "C" student? Such a student will have, by the end of the course, provided some evidence of mathematical proficiency, but not at the consistent level required to earn a grade of "B" or better. She might fall short of that standard, and earn the minimum passing grade for the course, if she:
Demonstrates proficiency in some but not all of the sections of the course;
Participates, but only intermittently, in class activities and discussions;
Demonstrates, through poor attendance, excessive tardiness, missing or late written work, or poor attitude, a lack of intellectual commitment to learning and, by extension, to teaching.
Why no "D" grades? This course is required for prospective teachers, and a licensure recommendation is based on, among other things, grades of "C" or better in all required courses. A student who does not earn a grade of "C" or better will have to repeat the course, so a grade of "D" would be meaningless. A student who does not demonstrate the minimum characteristics of a "C" student, as described above, will receive a grade of "F."
How can a student in this class provide evidence of mathematical proficiency and commitment to teaching?
The instructor will give students opportunities throughout the semester to demonstrate mathematical proficiency, by assigning mathematical tasks to be completed in writing. The students' written work will be assessed using the attached scoring guides.
These mathematical tasks will be of four types:
Embedded tasks: instructional tasks for which the student composes an individual, written response in class.
Re-Caps: tasks posed and discussed in class for which students compose a written response outside of class.
Collected and Assessed Problems (CAPs): tasks to be worked on, and for which students compose a written response, outside of class.
A Comprehensive Final comprised of tasks similar to the embedded tasks described above.
The instructor will also gather, in a systematic if not exhaustive way, evidence of mathematical proficiency from students' daily work in class. Therefore, participation in class discussions is a good way to meet or exceed the requirements of the course.
Grading Criteria for MTH 1610
Here is how the final course grade will be calculated. Performance on the CAPs and the Final are weighted very heavily. If your actual assessments don't fit into this rubric then the instructor will make a judgment call.
Final Grade
Components
A
B
C
F
CAPs
All at least M's and at least one at an E and on-time
All at least M's and on-time
No more than one below an M
Two or more below an M
Participation
All for B + strong team member
All for C + student presents ideas and contributes frequently to whole-group discussions
Student is involved in working with group
Student does not work with others in group
Homework
At least 90% completion rate
At least 80% completion rate
At least 70% completion rate
Less than 70% completion rate
In-class Assessments – In-class, open-notes
All at least a + and at least one an M
Only one below a +
Not more than two below a +
More than 2 below a +
Final Exam – In-class, open-notes
(4 out of 6) At least 3 M's and none less than a +
At least 2 M's and none less than a +
At least 1M
All below M
Religious Holidays:
Observance of religious holidays follows College policy, which is posted on the web at in the Academic and Campus Policies for Students section. Each student is responsible for understanding and abiding by the policy.
Americans with Disabilities Accommodations:
The Metropolitan State College notification letter, I would be happy to meet with you to discuss your accommodations. All discussions will remain confidential. Further information is available by visiting the Access center website
Academic Dishonesty:
An act of Academic Dishonesty may lead to sanctions including a reduction in grade, probation, suspension or expulsion. See the Student Handbook at in the Academic and Campus Policies for Students section.. |
Students will need access to the PhET website ( and will need the latest version of Java to run the simulations at that site.
Additional Requirements:
Accredited by:
Middle 15-week semester-long mathematics course was designed to develop pre-algebra and higher level mathematics skills using real-world electrical power industry activities and problems. This course will introduce high school students to career opportunities in the electrical power industry.
MediaKit Contents:
Syllabus: Week 1
Welcome
Students will:
-get to know their peers; and
-learn to navigate the course.
Week 2
Electricity Basics
Student will learn:
-how power is delivered to homes and businesses and how power plants work; and
-about transmission system structures and will complete an internet scavenger hunt.
Week 4
Math Fundamentals, Part 2
Students will:
-review decimals and their meaning;
-add, subtract, multiply, and divide numbers with decimals; and
-review how to solve equations with one variable and will practice simplifying order of operations problems.
Week 5
It's Electric
Students will learn:
-about literal equations and how to solve an equation in terms of another variable; and
-the basics of electricity, such as power, circuits, Ohm's law and AC/DC.
Week 6
Multimeters and Resistors
Students will:
-review unit conversions;
-learn what a multimeter is and how it works; and
-learn how to identify resistors and how to read an electrical meter.
Week 7
Series and Parallel Circuits
Students will:
-review ratios and proportions;
-learn about series and parallel circuits; and
-use tutorials and a simulation to build their own circuits.
Week 8
Ohm's Law
Students will:
-learn about Ohm's law as it relates to series and parallel circuits;
-complete a mid-course survey.
Week 9
Electromagnets
Students will:
-about electromagnets and real-world applications;
-learn about magnets, electromagnets, magnetic fields, and inductance; and
-participate in a simulation where they utilize and electromagnet.
Week 10
Transformers
Students will:
-understand transformers from electrical and mathematical perspectives;
-discover real-world applications of relays and solenoids; and
-participate in a transformer simulation.
Week 11
Generators and Motors
Students will learn about:
-AC and DC generators; and
-single phase and three phase current and will complete another Internet Scavenger Hunt.
Week 12
Batteries
Students will learn:
-how batteries work;
-how to recognize problems with current battery technology and will learn about safety when working with batteries; and
-to research and then participate in a discussion about famous inventors and scientists in the field of electricity.
Week 13
Energy and the Environment
Students will learn about:
-lightning and the equipment designed to protect against surges;
-capacitors, wire and cable;
-discover numerous ways power is produced and the corresponding environmental concerns; and
-alternate sources of energy.
Week 14
Careers in Electricity
Students will research and explore various careers in electricity.
Week 15
Wrapping It All Up
Students will evaluate their classmates work on careers in electricity and will reflect on what they have learned in this class.
Course Objectives: Objectives:
¨ To experience in context, and develop mathematics skills needed, in the electrical power industry
¨ To become aware of the uses of electrical power
¨ To familiarize students with the various electrical components (resistors, capacitors, transformers, batteries, etc)
¨ To investigate careers within the industry. |
Inverse, Exponential and Logarithmic Functions
Inverse, Exponential and Logarithmic Functions teaches students about three of the more commonly used functions, and uses problems to help students practice how to interpret and use them algebraically and graphically. Students can learn the properties and rules of these functions and how to use them in real world applications through word problems such as those involving compound interest and exponential growth and decay that they will find on their homework. |
MATH 093 5 credits Pre-Algebra The course is designed for students transitioning between arithmetic and algebra. Students will review arithmetic with real numbers, work with expressions containing variables, solve linear equations, graph linear equations in two dimensions, calculate slopes and intercepts for lines, and use unit analysis to solve applications. This course prepares students for Math 098. Prerequisites: "C" or better in MATH 090 or appropriate assessment score.
MATH 098 5 credits Elementary Algebra Topics include solving linear, quadratic (by factoring) and rational equations; solving a linear system of equations; manipulating polynomials (adding, subtracting, multiplying and dividing); and using exponent properties to simplify expressions. Students will also graph linear equations in two variables, calculate slopes, and find linear functions. Function vocabulary will be used. Prerequisites: MATH 093 with a grade of "C" or better or appropriate assessment score. |
Hi, I'm a senior in college and I am experiencing difficulty with my assignments. One of my problems is comprehending prentice hall conceptual physics answers; Could somebody assist me to comprehend what it's all about? I need to finish this asap. Thanks for helping.
You can examine Algebra Buster. This program literally helps you with figuring out homework assignments in mathematics exceptionallyfast. You should key in the exercises and then this product can go through it with you in comprehensive steps hence you shall be able to comprehend it more easily as you figure them out. There are some illustrations available thus you should also take a look around to find for yourself how fabulously accommodating the software | software product is. I'm confident your prentice hall conceptual physics answers might be worked out faster .
I will be able to guide if you would post more details about those questions. Alternatively, you might exercise Algebra Buster which is an exceptional tool that assists to solve algebra courses. This piece of software provides everything thoroughly and causes | plus causing the subjects appear to be truly simple. I honestly can state that it is indeed valuable | invaluable | priceless | exemplary | blue-chip | meritorious | praiseworthy | .
I remember expecting problems with lcf, conversion of units plus 3x3 system of equations. Algebra Buster is a really piece of algebra software. I have exploited it over many math classes of instruction - Algebra 2, Basic Math as well as Algebra 2. I would just key the exercise and by selecting solve, a comprehensive result would be presented. The software is highly fully warranted. |
Description
This is an expanded version of Calculus and its Applications, Tenth Edition, by Bittinger, Ellenbogen, and Surgent. This edition adds coverage of trigonometric functions, differential equations, sequences and series, probability distributions, and matrices.
Calculus and Its Applications has become a best-selling text because of its accessible presentation that anticipates student needs. The writing style is ideal for today's students, providing intuitive explanations that build on students' earlier mathematical experiences. Explanations are often coupled with figures to help students visualize new calculus concepts. Additionally, the text's numerous and up-to-date applications from business, economics, life sciences, and social sciences help motivate students. Algebra diagnostic and review material is available for those who need to strengthen basic skills. Every aspect of this text is designed to motivate and help students to more readily understand and apply the mathematics.
Table of Contents
R. Functions, Graphs, and Models
R.1 Graphs and Equations
R.2 Functions and Models
R.3 Finding Domain and Range
R.4 Slope and Linear Functions
R.5 Nonlinear Functions and Models
R.6 Mathematical Modeling and Curve Fitting
1. Differentiation
1.1 Limits: A Numerical and Graphical Approach
1.2 Algebraic Limits and Continuity
1.3 Average Rates of Change
1.4 Differentiation Using Limits of Difference Quotients
1.5 Differentiation Techniques: The Power and Sum-Difference Rules
1.6 Differentiation Techniques: The Product and Quotient Rules
1.7 The Chain Rule
1.8 Higher-Order Derivatives
2. Applications of Differentiation
2.1 Using First Derivatives to Find Maximum and Minimum Values and Sketch Graphs
2.2 Using Second Derivatives to Find Maximum and Minimum Values and Sketch Graphs
2.3 Graph Sketching: Asymptotes and Rational Functions
2.4 Using Derivatives to Find Absolute Maximum and Minimum Values
2.5 Maximum-Minimum Problems; Business and Economic Applications
2.6 Marginals and Differentials
2.7 Implicit Differentiation and Related Rates
3. Exponential and Logarithmic Functions
3.1 Exponential Functions
3.2 Logarithmic Functions
3.3 Applications: Uninhibited and Limited Growth Models
3.4 Applications: Decay
3.5 The Derivatives of ax and loga x
3.6 An Economics Application: Elasticity of Demand
4. Integration
4.1 Antidifferentiation
4.2 Antiderivatives as Areas
4.3 Area and Definite Integrals
4.4 Properties of Definite Integrals
4.5 Integration Techniques: Substitution
4.6 Integration Techniques: Integration by Parts
4.7 Integration Techniques: Tables
5. Applications of Integration
5.1 An Economics Application: Consumer Surplus and Producer Surplus
5.2 Applications of Integrating Growth and Decay Models
5.3 Improper Integrals
5.4 Numerical Integration
5.5 Volume
6. Functions of Several Variables
6.1 Functions of Several Variables
6.2 Partial Derivatives
6.3 Maximum-Minimum Problems
6.4: An Application: The Least-Squares Technique
6.5 Constrained Optimization
6.6 Double Integrals
7. Trigonometric Functions
7.1 Basics of Trigonometry
7.2 Derivatives of Trigonometric Functions
7.3 Integration of Trigonometric Functions
7.4 Inverse Trigonometric Functions and Applications
8. Differential Equations
8.1 Differential Equations
8.2 Separable Differential Equations
8.3 Applications: Inhibited Growth Models
8.4 First-Order Linear Differential Equations
8.5 Higher-Order Differential Equations and a Trigonometry Connection
9. Sequences and Series
9.1 Arithmetic Sequences and Series
9.2 Geometric Sequences and Series
9.3 Simple and Compound Interest
9.4 Annuities and Amortization
9.5 Power Series and Linearization
9.6 Taylor Series and a Trigonometry Connection
10. Probability Distributions
10.1 A Review of Sets
10.2 Probability
10.3 Discrete Probability Distributions
10.4 Continuous Probability Distributions
10.5 Mean, Variance, Standard Deviation, and the Normal Distribution
11. Systems and Matrices (online)
11.1 Systems of Linear Equations
11.2 Gauss-Jordan Elimination
11.3 Matrices and Row Operations
11.4 Matrix Arithmetic: Equality, Addition and Scalar Multiples
11.5 Matrix Multiplication, Multiplicative Identities and Inverses
11.6 Determinants and Cramer's Rule
11.7 Systems of Linear Inequalities and Linear Programming |
Overview - PM PRACTICAL MATH ANSWER KEY
Presents practical life math applications.
This straightforward, easy-to-understand program provides students of mixed
abilities with key math concepts essential for successful adult living. From
buying groceries to budgeting for housing, education, and travel, the simply
stated subject matter delivered in a manageable format with a controlled reading
level makes content accessible to all students.
Student Edition - prepares students for understanding concepts in each
new chapter through strong vocabulary instruction and clear learning objectives
that preview and outline key concepts upfront. A manageable concept load introduces,
teaches, and practices one concept at a time and fosters student success. Frequent
opportunities for practice encourage computational proficiency.
Student Workbook - Reinforces new concepts through abundant practice
exercises and frequent review. Fosters content understanding and skill development
and retention through review, and applications, and with extensive practice
correlated to every lesson in the Student Edition. |
What is Mathematical Proficiency478/10478-10478-QuickTime.mov |
Wednesday, 23 May 2012
BSEditor: EasyConicSections gives students the ability to plot the equations of lines, circles, Parabolas, hyperbolas, cubics and ellipses quickly. They can then study the changes in the equations as they vary the parameters of the functions. Solutions to systems of equaltions may be graphically determined. A set of movable x,y verniers enables the user to determine the intersection of two Conic sections,thus providing the graphical numeric solution to the equations.It is also recommended for Home Schooling for providing a method to study systems of equations. you can free download EasyConicSections 3.0 now. Tags: EasyConicSections - This program is recommended for any Math class which studies conic sections. ,Math, torrent, downloads, rapidshare, filesonic, hotfile, megaupload, fileserve |
An Introduction to Functions Review of Prerequisites: 1 The concept of function is fundamental to mathematics. Through informal explorations of patterns, students are introduced to the idea of functions.
1. Use the TI82 calculator to define and graph the following power functions. Record the domain of each function. : Y1 x 1/2 f x x1/2 dom f Y2 x 1/3 f x x1/3 dom f Explain the difference in the two domains.
PRIVATE Review of Prerequisites: 2. The proportionality of two quantities is a relationship that represents a function. For example, the cost of bananas is directly proportional to the weight of the bananas. |
This software to download was designed by a teacher to help teachers teach algebra I, algebra II, trigonometry, probability and statistics, and 3D graphing. It approaches these topics from a uniquely teacher point of view. For example, it generates problems for students to solve such as systems of equations that are independent-consistent, dependent-consistent, and inconsistent.inconsistent. It generates graphs that students must identify in function notation and/or by exact formula.
3D graphing techniques are illustrated dynamically. Polar and parametric equations can be investigated with the help of a "lightning bug". Slider graphs of any functions can be created to help students visualize the effects of parameters. Piecewise-defined functions and equations that do not represent functions can be graphed. Implicitly defined equations can be graphed. Inequalities can be graphed in standared or "reversed" mode |
The Advanced Algebra Tutor: Learning By Example DVD Series teaches students through step-by-step example problems that progressively become more difficult. This DVD covers graphing rational functions in Algebra, as well as a discussion of what rational functions are and why they are important in algebra. Grades 9-College. 36 minutes on DVD. |
Find a Glen Echo ACTMathematics is all about patterns, and patterns can be pretty awesome. Algebra II extends the concepts of Algebra I to make us more powerful problem-solvers. Prealgebra contains the fundamental mathematical tools that students will be using throughout the rest of middle school, high school, and college |
With contributions from some of the most notable experts in the field, Performance Tuning of Scientific Applications presents current research in performance analysis. The book focuses on the following areas.
Performance monitoring: Describes the state of the art in hardware and software tools...
Computational Paths to Discovery
New mathematical insights and rigorous results are often gained through extensive experimentation using numerical examples or graphical images and analyzing them. Today computer experiments are an integral part of doing mathematics. This allows for a more systematic approach to conducting and...
Published April 11th 2004 by A K Peters/CRC |
Search MSRI
Program
Organizers
David Austin, Bill Casselman and Jim Fix
Description
This workshop will introduce sophisticated techniques of computer graphics for use to explain mathematics in research articles, course notes, and presentations. It will begin with an introduction to graphics algorithms, and the languages PostScript and Java. Participants will spend afternoons and evenings during the first week in the computer labs on assigned exercises. The second week will be spent on assigned project themes, ending with student presentations. |
Excellent book for beginning courses
This book is ideal for an undergraduate course in number theory. The combination of theory, problems and biographical sketches of the principals who made it what it is today is an excellent pedagogical technique. It allows an instructor to show how number theory began very early in mathematical history and how it has progressed over the centuries. Number theory holds the distinction as being the reservoir of most of the easily stated yet difficult problems. As Paul Erdös said, "If it is a simply stated problem that has remained unsolved for centuries, it is almost certainly one in number theory." In this book, you learn the reasons for this situation. It is also well-suited for anyone with an interest in number theory who wishes to learn more about it. The explanations are well-written and a large number of exercises are included. Solutions to the odd numbered problems are given at the end. Review, supplementary and computer exercises are also included at the end of each chapter. The bulk of the explanatory text consists of examples worked out in complete detail. This is the book that I would use if I were teaching a course in beginning number theory. It is a complete package, not only demonstrating what is known and unknown, but the path to how it got that way.
Charlie Ashbacher is a compulsive reader and writer about many subjects. His prime areas of expertise are in mathematics and computers where he has taught every course in the mathematics and computer … more
Wiki
The advent of modern technology has brought a new dimension to the power of number theory: constant practical use. Once considered the purest of pure mathematics, it is used increasingly now in the rapid development of technology in a number of areas, such as art, coding theory, cryptology, computer science, and other necessities of modern life. Elementary Number Theory with Applications is the fruit of years of dreams and the author's fascination with the subject, encapsulating the beauty, elegance, historical development, and opportunities provided for experimentation and application. This is the only number theory book to show how modular systems can be employed to create beautiful designs, thus linking number theory with both geometry and art. It is also the only number theory book to deal with bar codes, Zip codes, International Standard Book Numbers (ISBN), and European Article Numbers (EAN). Emphasis is on problem-solving strategies (doing experiments, collecting and organizing data, recognizing patterns, and making conjectures). Each section provides a wealth of carefully prepared, well-graded examples and exercises to enhance the readers' understanding and problem-solving skills.
This is the only number theory book to: Show how modular systems can be employed to create beautiful designs, thus linking number theory with both geometry and art Deal with bar codes, Zip codes, International Standard Book Numbers (ISBN), and European Article Numbers (EAN) Emphasize ... |
Functions_2
Functions_2 program discusses functions in more depth. It includes relations and their graphs, discuss a function from different aspects including how to determine a graph is a functional graph or not. What is ordered pairs. How ordered pairs define a relation is a function or not? It discusses parabola and its characteristics (vertex, axis of symmetry, minimum and maximum value) and how to sketch it quickly. It discusses other types of functions like constant, linear, polynomial, absolute value, square root, several expressions functions. Combined and composite functions. It includes every thing you want to know about inverse of a function and how to test for it. It includes over 190 solved exercises step-by-step in a simplified manner. It is suitable for SAT, GCE and international tests. |
Quantitative Foundation
Quantitative
reasoning refers to the ability to understand, evaluate and use quantitative
information. Quantitative information takes many forms, and quantitative
reasoning skills span a vast spectrum from basic numerical manipulations to
advanced statistics and mathematics. One three-credit course is required to
ensure that students possess these necessary skills. Students scoring a 4 or 5
on the Calculus AB, Calculus BC or Statistics Advanced Placement tests will
place out of this requirement. Math placement testing is also available through
SMU's mathematics departmental examinations.
MATH 1309. Introduction to Calculus for Business and Social Science.
Derivatives and integrals of algebraic, logarithmic, and exponential functions
with applications to the time value of money, curve sketching, maximum-minimum
problems, and computation of areas. Applications to business and economics.
(Natural science and engineering students must take MATH 1337. Credit not
allowed for both MATH 1309 and MATH 1337.)
Prerequisite: Placement out of MATH 1303 or a grade of C- or higher in MATH
1303.
MATH 1337. Calculus with Analytic Geometry I.
Differential and integral calculus for algebraic, trigonometric functions, and
transcendental functions, with applications to curve sketching, velocity,
maximum-minimum problems, areas, and volumes. (Credit not allowed for both MATH
1309 and MATH 1337.)
Prerequisite: Placement out of MATH 1304 or a grade of C- or higher in Math
1304.
STAT 1301. Introduction to Statistics.
Introduction to collecting observations and measurements, organizing data,
variability, and fundamental concepts and principles of decision-making.
Emphasis is placed on statistical reasoning and the uses and misuses of
statistics. No prerequisite.
STAT 2301. Statistics for Modern Business Decisions.
A foundation in data analysis and probability models is followed by elementary
applications of condence intervals, hypothesis testing, correlation, and
regression.
STAT 2331. Introduction to Statistical Methods.
An introduction to statistics for behavioral, biological, and social scientists.
Topics include descriptive statistics, probability and inferential statistics
including hypothesis testing, and contingency tables.
Quantitative Foundation:
Student Learning Outcomes
1. Students will be able to
interpret mathematical models such as formulas, graphs, tables, and schematics.
2. Students will be able to
solve problems using algebraic, geometric, calculus, statistical and/or
computational methods.
3. Students will be able to
determine correctness, reasonableness, identify alternatives, and select optimal
results in mathematical problems.
4. Students will be able to draw
inferences from mathematical models in the various forms listed above.
5. Students will be able to
present calculations and results in a clear and concise manner. |
This webquest was designed for 8th grade math students who have had some exposure to solving equations. These students know and understand how to solve a one-step equation but struggle with anything more complicated. This webquest was designed to provide visual representations of the math concepts and tap into their prior knowledge in order to extend their understanding. |
Actuarial Mathematics
Description:
Actuarial Mathematics prepares students to be professionals who use mathematical models to analyse and solve financial problems under uncertainty. Actuaries are experts in the design, financing and operation of insurance plans, annuities, and pension or other employee benefit plans. An actuary requires a strong mathematical background, as well as knowledge of computers, accounting, finance and economics. Exposure to the social sciences and humanities is also important to provide a proper foundation for a broad approach to the many problems which the actuary regularly faces. The following Actuarial programs prepare students to write examinations to gain admission to the Canadian Institute of Actuaries and provide an excellent preparation for graduate studies in Actuarial MathematicsMathematics |
The activities in this brief book have been created to help teachers incorporate the Transformation Graphing Software Application into Algebra 1 and 2 curricula. Topics covered include Line, Quadratic... More: lessons, discussions, ratings, reviews,...
This workbook provides students with an interesting way to explore math and science concepts. It is a revision of the earlier Texas Instruments publication Real-World Math with the CBL 2 System: Activ... math worksheets maker is free to use for topics in Algebra 1 and Algebra 2. To create a worksheet, select the number of questions for each category. Then choose your options and push the "Create |
Send this article
Complete the form below to send this article, Moodle 1.9 Math QuizzesN
i
p
c
d
Enter the code above: *
Enter the code without spaces and pay attention to upper/lower case.
by
Ian Wild | November 2009 |
Moodle Open Source
Tired of marking all of those math tests you've set for your students? No problem! Now we can have Moodle do all of the grading for us! Getting to grips with the Pythagorean Theorem is going to take practice, and the Moodle Quiz module is going to give my students that practice without my having to worry about a mountain of marking. We'll see in this article by Ian Wild that the Moodle Quiz module is a very powerful tool that not only automatically marks the answers for us, but also copes with different units (for example, answers given in feet or inches, meters or centimeters). We can also specify placeholders in the question that Moodle will replace with random numbers. This means we can provide lots of practice questions, which Moodle will both generate and mark automatically. Specifically, we will learn how to do the following:
Create a math quiz and learn all about the different question types Moodle supports
Install and use the feedback activity (not part of a normal Moodle install)
As good as the Moodle quiz module is at recognizing the correctness of our students' answers, we quickly run into problems when we need Moodle to recognize, for example, that 3a+2b is exactly the same as 2b+3a . To accomplish this, we're going to need a Computer Algebra System (CAS). The Maxima system (more on this later) has been successfully integrated into Moodle, thanks to the work carried out by Chris Sangwin and Alex Billingsley at the University of Birmingham in the UK. In this article, we will also learn how to perform these tasks:
Creating quizzes
Creating a quiz in Moodle is a two-stage process. First, we add our questions to the question bank (each course has its own question bank). Once we've added questions to the question bank, we can add a quiz activity to the course and then choose questions to add to it from the question bank. What are the advantages of having a two-stage process? I worked in much the same way creating quizzes before I started with Moodle. My bookshelf of math books was my question bank, and I would take questions from there to add into my quizzes. Here are just a few of the advantages:
If there is a particular point you want to reinforce, then it's easy to include the same question in different quizzes throughout your course.
It's easy to share your questions with other Moodle courses. For example, questions on the Pythagorean Theorem are relevant to pure math, mechanics, engineering, and physics.
Questions can be exported from and imported into the question bank. This means converting questions over to Moodle is a job that can be shared between colleagues.
Here's a basic Pythagorean Theorem question I converted over to Moodle:
Question types
However, I don't want to convert just this single question over to Moodle; I also want to have questions similar to this one but with different numbers. I want those numbers chosen randomly by Moodle, so I don't have to keep thinking up different numbers each time I set the quiz.
The question type I need is Calculated, which we'll learn about in the next section.
Calculated question type
Let's learn how to add a calculated question to the course question bank now:
Return to your course's front page, and click on Questions in the course Administration block:
The course Question bank is displayed. From the Create new question drop-down menu, choose Calculated:
Give the question a name. Make sure it's a name that you (and, potentially, your colleagues) can recognize when it's in the question bank. Don't call it '1', 'i', or 'a)' because you don't know where it will appear in the quiz. Now, supply the question text:
Notice that I have used placeholders in the text, {a} and {b}. We will be configuring Moodle to replace those with numbers shortly.
Scroll down to the Answer box. We need to enter the correct calculation into the Correct Answer Formula edit box (don't include a '=' in your answer):
The students need to give the correct answer (exactly), but don't worry about the Tolerance setting: leave it set to 0.01. Set the Grade to 100%.
I want the students to give their answers to three significant figures, and to that end I needed to click on the Correct answer shows drop-down menu, set that to 3, and change the Format to significant figures:
Scroll down to the bottom of the page, and click on the Next Page button. You are now taken to the Choose dataset properties page.
The numbers for the variables {a} and {b} will be chosen from a dataset. I want to use my own datasets for each variable. Select will use a new shareddataset for both drop-downs:
Click on the Next Page button. You are taken to the Edit the datasets page. Now, we can specify the range of values for {a} and {b}:
We need to add numbers to this dataset. I want to add 20 possible pairs of numbers for {a} and {b}. Scroll down to the Add box, select 20 items from the item(s) drop-down menu and click on the Add button:
Twenty pairs of numbers are now added to the dataset. Moodle will choose pairs of numbers in this dataset when the student is presented with the question. If you want to alter any of the numbers Moodle has automatically generated for us, you can do so in the second-half of the page. Scroll down to the very bottom of the page, and click on the Save changes button.
Our new calculated question is now added to the question bank:
To recap, we have seen that creating a calculated question is a two-step process. First, we need to specify the question text. The question text contains variables that Moodle will then replace with random values when the quiz is taken. Then, we need to specify datasets for each of the variables, from which Moodle will choose the values when the quiz is taken. We can have Moodle choose the numbers for us, or we can select our own.
Including an image in the question text
Make your questions more engaging by including an image in the question text. Use the Insert Image button:
You can also include the image by using the Image to display drop-down menu:
Calculated question type: Frequently asked questions
The calculated question type is extremely powerful, which means some settings can seem a little confusing. Below you'll find answers to just a few of the common queries regarding calculated questions:
What math functions does the correct answer formula support? Notice that in my Pythagoras example, I squared the base and altitude using the pow() function, and I found the square root using the sqrt() function. For a full list of supported functions, check out
How do I specify alternative units? Imagine you have a question that accepts the answer in either centimeters or meters. The calculated question type allows us to accept answers in either unit:
What does it mean if a variable is listed under "Possible wild cards present only in the question text"? If your question contained text, which looked like a variable, or if you included a variable that isn't used in the correct answer formula, then these are listed on the Choose dataset properties page:
Numerical question type
Simpler to configure than a calculated question, but slightly less powerful, the numerical question type allows us to specify a correct answer along with a tolerance (or accepted error), so that answers within an accepted range are allowed. Let's take a look at another Pythagorean Theorem question I'm creating:
You can see that I've mixed units: the distance from the bottom of the ladder to the foot of the wall is measured in centimeters, and the length of the ladder is given in meters. The question specifies that you must give your answer in meters. However, I'm going to give half marks to students who give their answer in centimeters:
You can also catch the wrong answers:
Additionally, you can keep track of any other possible wrong answer using "*":
As with the calculated question type, scroll down to the bottom of the page and specify unit multipliers, if you wish.
Note that I've started providing some feedback. There's more on feedback later on in this article.
Other question types
In the previous section, we investigated two question types specifically designed to support numeric/mathematical questions. You must have also seen that there is a full range of selection and supply-type questions we can add into the question bank:
Short-Answer: Students respond with a word or phrase. You will need to specify the correct answers using wild cards, so that Moodle can pick the correct answers out of the responses students have typed. Take a look at Moodle docs for more information (
Description: This is not actually a question but a way of breaking up questions—perhaps providing some text/graphics or maybe a video presentation before a student attempts a set of questions.
Essay: The student's answer is in essay format. If you are setting your students an assignment, then Moodle already has an 'assignment' activity specifically designed for this purpose. See
Matching: The student is presented with questions, each of which has a drop-down list of possible answers. The student must match the correct answer to each question. For more details, see
Embedded Answers (Cloze): This is a fill-the-gaps exercise greatly enhanced by virtue of being "computerized". Moodle presents the user with a passage of text that has questions embedded in it. The correct answers complete the text (see
Random: This is a completely random question chosen by Moodle.
Import your questions: Hot Potatoes quiz
Are you a Hot Potatoes user? If so, then you can import your Hot Potatoes quiz into your course question bank. With the question bank page open, click on the Import tab. Follow the instructions to import a Hot Potatoes quiz:
Note that you can't import all Hot Potatoes question types (there is no equivalent to the Hot Potatoes crossword question in Moodle, for instance). Also, it's the Hot Potatoes project file you need to import, rather than creating a web page.
Now that we've added questions to the question bank, let's see how to get those questions included in a quiz.
About the Author : |
The Algebra Challenge, CLMS/CLHS 7/27/09
For life in the 21st century, mathematics proficiency is as fundamental as literacy, and the keystone of mathematical proficiency is Algebra 1. Traditionally, algebra has distinguished the college-bound from other students. Today it denies many students a high school diploma and contributes to dropout rates. The challenge for K-12 schools is to prepare students for success in Algebra 1 and beyond by teaching algebraic thinking at all grade levels. This workshop focuses on ways to meet and beat the Algebra Challenge using strategies that engage students in a challenging, rigorous, thinking curriculum. |
Providing essential guidance and background information about teaching mathematics, this book is intended particularly for teachers who do not regard themselves as specialists in mathematics. It deals with issues of learning and teaching, including the delivery of content and the place of problems and investigations. Difficulties which pupils encounter in connection with language and symbols form important sections of the overall discussion of how to enhance learning.The curriculum is considered in brief under the headings of number, algebra, shape and space, and data handling, and special attention is paid to the topic approach and mathematics across the curriculum. The assessment of mathematical attainment is also dealt with thoroughly.Teachers will find this book an invaluable companion in their day-to-day teaching. less |
Author's Description
Math Center Level 2 - Math software for students
Math software for students studying precalculus and calculus. Can be interesting for teachers teaching calculus. Math Center Level 2 consists of a Scientific Calculator, a Graphing Calculator 2D Numeric, a Graphing Calculator 2D Parametric, and a Graphing Calculator 2D Polar. The Scientific Calculator works in scientific mode. All numbers in internal calculations are treated in scientific format, like 1.23456789012345E+2 for 123.456789012345. You also can use scientific notation in formulas. If you get result NaN, like in ln(-1), that means that the function is not defined for given argument. Otherwise Scientific Calculator is similar to Simple Calculators. There are options to save and print calculation history, to change font, and standard editing options. Graphing Calculator 2D Numeric is a further development of Graphing Calculator2D from Math Center Level 1. It has extended functionality: hyperbolic functions are added. There are also added new capabilities which allow calculating series, product series, Permutations, Combinations, Newton Binomial Coefficients, and Gauss Binomial Coefficients . Graphing Calculator 2D Numeric has capability to build graphs for first and second derivatives, definite integral (area under curve) and length integral (length of curve). Since these calculations are done numerically, not symbolically, the calculator is called Numeric. Graphing Calculator 2D Parametric is a generalization of Graphing Calculator 2D Numeric. Now x and y are functions on parameter ?. If you are typing formula using keyboard, then you can use "tau" for ? . Since all calculations are done twice, for x and y, there was some sacrificing of precision in order to keep speed of calculations. So, although it is possible to build the same graph of y=f(x) in parametric calculator using x=?, y=f(?), the Graphing Calculator 2D Numeric will build it with greater precision. Graphing Calculator 2D Polar is a specialization of Graphing Calculator 2D Numeric.
Math Center Level 2 1.0.0.7 is licensed as Shareware for the Windows operating system / platform. Math Center LevelMath Center Level 2 Tvalx. Please be aware that we do NOT provide Math Center Level 2 cracks, serial numbers, registration codes or any forms of pirated software downloads. |
Introductory Finite Difference Methods for PDEsComments for "Introductory Finite Difference Methods for PDEs"
This contains advanced topics such as various factorizations, singular value decompositions, Moore Penrose inverse, norms, convergence theorems, and an introduction to numerical methods like QR algorithm. Finally, there are some appendices which contain applications of linear algebra or linear algebra techniques. This includes more on general fields and an introduction to geometric theory of diffe... |
Discourses On Algebra - 02 edition
Summary: The classic geometry of Euclid has attracted many for its beauty, elegance, and logical cohesion. In this book, the leading Russian algebraist I.R. Shafarevich argues with examples that algebra is no less beautiful, elegant, and logically cohesive than geometry. It contains an exposition of some rudiments of algebra, number theory, set theory and probability presupposing very limited knowledge of mathematics. I.R. Shafarevich is known to be one of the leading mathematicians of the 20...show moreth century, as well as one of the best mathematical writers. TOC:Integers.- Simplest Properties of Polynomials.- Finite Sets.- Prime Numbers.- Real Numbers and Polynomials.- Infinite Sets.- Power Series ...show less
Edition/Copyright: 02 Cover: Publisher: Springer Year Published: 2002
List Price: $69.95
Used Currently Sold Out
New Currently Sold Out
Rental $54.49
Due back 08/16/2013
Save $15.46 (22%)
Free return shipping
In stock
21-day satisfaction guarantee
CDs or access codes may not be included
Marketplace sellers starting at $69.95
More prices and sellers below.
Additional Sellers for Discourses On Algebra |
Culinary Calculations, Second Edition provides the mathematical knowledge and skills that are essential for a successful career in today's competitive food service industry. This user-friendly guide starts with basic principles before introducing more specialized topics like costing, AP/EP, menu pricing, recipe conversion and costing, and inventory costs. Written in a non-technical, easy-to-understand style, the book features a case study that runs through all chapters, showing the various math concepts put into real-world practice.
This revised and updated Second Edition of Culinary Calculations covers relevant math skills for four key areas:
• Basic math for the culinary arts and food service industry
• Math for the professional kitchen
• Math for the business side of the food service industry
• Computer applications for the food service industry
Each chapter within these sections is rich with resources, including helpful callout boxes for particular formulas and concepts, example menus and price lists, and information tables. Review questions, homework problems, and the ongoing case study end each chapter.
Covers the critical math concepts culinary and food service professionals need to increase the profitability of a food service establishment by accurately controlling food costs, portion sizes, and food waste
Examines how to apply math principles in the back of the house, from the basics to more difficult concepts like costing, AP/EP, recipe conversion and costing, menu pricing, and inventory costs
Three useful appendices offer handy access to such useful information as tips for using a calculator, conversion tables, and common item yields
Formatted with plenty of room to work through exercises and problems at the end of each chapter |
linear algebra.
...continue to expand their problem-solving skills, in particular, visualization and abstraction.
...gain knowledge and skills to formalize their ideas and express them with a full mathematical rigour.
Content:
Systems of Linear Equations.
Matrices.
Determinants
Vector Spaces
Inner Product Spaces.
Linear Transformations.
Eigenvalues and Eigenvectors.
Course Philosophy and Procedure
Just keep this simple principle in mind: If you are not enjoying this course, if the work is not fun, then something most be wrong. Talk to me right away! This course involves a lot of concepts that easily translate into fairly straightforward (but sometimes lengthy) calculations. Geometry, i.e., visualization is essential. There are also some topics that involve a greater level of abstraction yet there will be plenty of exercises available to check and enhance your understanding of those concepts. You will find that the concepts learned in this course can be applied to many problems in Mathematics and Science.
You should plan to reserve a significant amount of time to study for this course. The material is easy, but the nature of the exercises is such that they are going to be time consuming. Being focused is of utmost importance. Don't rush in doing the problems!
Grading will consist of two semester (100 points each) and the final exam) worth 200 points each. The homework and chapter projects will total to 200 points.
My grading scale is
A=90%, AB=87%, B=80%, BC=77%, C=70%, CD=67%, D=60%.
Final Exam: 12/12 from 12:50-2:50 |
The ASC offers three math classes to help
prepare students for their college level math courses.
Placement in these courses is based on COMPASS, ACT and/or
SAT scores and advisor recommendations. Credits for these courses DO NOT apply toward
graduation requirements nor do they fulfill Academic
Foundations requirements. However, the credits do count
towards enrollment status for financial aid.
This course begins with a brief review of elementary
algebraic concepts and then covers more advanced factoring,
operations on rational expressions and radical expressions,
quadratic equations, the rectangular coordinate system, and
exponential and logarithmic functions.
Who should take this course?
Students with the following placement scores: COMPASS: 26-75 Pre-Algebra
and
0-15 Algebra
Students with the following placement
scores: COMPASS: 76-100 Pre-Algebra
16-26 Algebra SAT: up to 489 ACT: up to 14
Students with the following placement scores: COMPASS: 27-50 Algebra SAT: 490-530 ACT: 15-21
Course
Materials
There is no text required for this
course this semester. All materials will be provided to
students free of charge. |
Description
of Major:
Mathematics is offered as a major and minor at JMU.
The department offers a program of study in the mathematical
sciences which meets the needs of a wide variety of
students and make a continuing contribution to the advancement of mathematical
knowledge and dissemination. The program provides opportunities for in-depth study which
lead to careers as mathematicians and statisticians in industry and government, mathematics
teachers; and to further study in graduate school. The
first two years of introductory mathematics focus on
differential and integral calculus. The studies of the
last two years are devoted primarily to basic material
in the fields of analysis, algebra, geometry, computing
and statistics. The two parts of the program are distinguished
by methods of presentation, as well as by content. The
first two years lead gradually to appreciation of definitions
and proofs, and to precision in mathematical language.
The latter two years anchor basic mathematical concepts,
results and methods, and increase the knowledge of applications.
The program is committed to promoting mathematics as
an art of human endeavor as well as a fundamental method
of inquiry into the sciences and a vast array of other
disciplines. In addition to the concentrations listed
above, the department also offers a minor in Statistics.
Students seeking teacher licensure are encouraged to
consult with the appropriate program in the College
of Education.
Tell
me more about this field of study.
Mathematics is the study of such objects as numbers,
operations, space configurations, mappings, and abstract
structures. Those studying mathematics develop skills
to manipulate these objects and analyze the relationships
between them. Much of the knowledge and effort of a
mathematician is devoted to formulating and analyzing
models, which can be used to make predictions. A mathematical
model is a set of equations whose solution can be used
to predict the behavior of the phenomenon being modeled.
The 5-day forecast that we see on the 11:00 news is
prepared using output from a weather model. The predictions
we see in the news concerning the growth of the economy
are based on various mathematical models. The performance
and reliability of communication networks are often
predicted using a network model. The predictions produced
by mathematical models vary in quality. Sometimes they
are right on target and sometimes they are meaningless.
Certain models can be calibrated by running an experiment.
For example, a fully instrumented building can be burned
down and the results compared to the output from a fire
model. When used as part of a design process, a well-constructed
mathematical model can often produce enormous cost savings.
Tell
me more about specializations in this field.
Mathematicians specialize in a wide variety of areas
such as algebra, geometry, analysis, probability and
statistics, mathematics education, and applied mathematics.
The college graduate with a bachelor's degree in mathematics
or actuarial science can qualify for a broad range of
highly paid positions in a variety of industries. In
private industry, companies in the computer, communications,
and energy field employ many mathematicians. Students
interested in government work will find that almost
every bureau and branch of the federal government employs
mathematicians in some capacity. Mathematicians, statisticians,
operations researchers, and actuaries work in the Department
of Health and Human Services, the General Accounting
Office, the Office of Management and Budget, and the
National Institute of Standards. The Department of Energy,
the Department of Defense, the National Aeronautics
and Space Administration, and the National Security
Agency also employs many mathematicians. Many mathematicians
are attracted to teaching and research opportunities
at primary, college and university settings. In most
four-year colleges and universities, the Ph.D. is necessary
for full faculty status. Many mathematicians with a
bachelor's or master's degree teach at the K-12 level.
Major Research Laboratories like IBM, ATT, Bell, and
Research Institutes support purely scientific research
positions. Many other job titles apply to mathematicians
who have specialized in an applied branch of mathematics.
Actuaries assemble and analyze statistics to calculate
probabilities, and thereby set rates, in the insurance
industry. Operations Research Analysts apply scientific
methods and mathematical principles to organizational
problems. Statisticians design, carry out, and interpret
the numerical results of surveys and experiments. All
of these careers begin with an education in mathematics,
and a curiosity about the use of mathematics to solve
problems.
CHARACTERISTICS
OF SUCCESSFUL STUDENTS
Those students who are able to think independently and
creatively and are not afraid of hard work are the most
successful in mathematics.
CAREERS
Recently, JobsRated.com ranked Mathematician as the best job in America, with Actuary and Statistician at second and third, based on salary, work conditions, and other factors. Many graduates choose typical career paths associated
with this major. However, some graduates choose nontraditional career fieldsThere are a number of "hands on" experiences
available to students in mathematics, especially through
the Center for Mathematical Modeling and the Office
of Statistical Services, both housed in the Department
of Mathematics and Statistics. Students intending to teach complete
an "internship" through the student teaching
experience, required in the senior year for those who
seek teaching licensure. Students also gain experience
and/or exposure to the field of mathematics through
involvement in the Mathematics Club, Pi Mu Epsilon (Mathematics
Honor Society), and the student chapter of the American
Mathematical Society. Come to Career and Academic Planning, located in Wilson 301, to learn more about identifying internships relating to mathematics. |
In the 20th century, algebraic geometry has undergone several revolutionary changes with respect to its conceptual foundations, technical framework, and intertwining with other branches of mathematics. Accordingly the way it is taught has gone through distinct phases. The theory of algebraic schemes, together with its full-blown machinery of sheaves and their cohomology, being for now the ultimate stage of this evolution process in algebraic geometry, had created -- around 1960 -- the urgent demand for new textbooks reflecting these developments and (henceforth) various facets of algebraic geometry. The famous volumes ``Éléments de géométrie algébrique'' as a series in Publ. Math., Inst. Hautes Étud. Sci. (1960-1967) by {\it A. Grothendieck} and {\it J. Dieudonné} were entirely written in the new language of schemes, without being linked up with the classical roots, and the so far existing textbooks just dealed with classical methods. It was {\it David Mumford}, who at first started the project of writing a textbook on algebraic geometry in its new setting. His mimeographed Harvard notes ``Introduction to algebraic geometry: Preliminary version of the first three chapters'' (bound in red) were distributed in the mid 1960's, and they were intended as the first stage of a forthcoming, more inclusive textbook. For some years, these mimeographed notes represented the almost only, however utmost convenient and abundant source for non-experts to get acquainted with the basic new concepts and ideas of modern algebraic geometry. Their timeless utility, in this regard, becomes apparent from the fact that two reprints of them have appeared, since 1988, as a proper book under the title ``The red book of varieties and schemes'' [cf. Lect. Notes Math. 1358 (1988; Zbl 0658.14001)]. In the process of exending his Harvard notes to a comprehensive textbook, the author's teaching experiences led him to the didactic conclusion that it would be better to split the book into two volumes, thereby starting with complex projective varieties (in volume I), and proceeding with schemes and their cohomology (in volume II). -- In 1976, the author published the first volume under the title ``Algebraic geometry. I: Complex projective varieties'' (1976; Zbl 0356.14002; corrected second edition 1980; Zbl 0456.14001), where the corrections concerned the wiping out of some misprints, inconsistent notations, and other slight inaccuracies.\par The book under review is an unchanged reprint of this corrected second edition from 1980. Although several textbooks on modern algebraic geometry have been published in the meantime, Mumford's ``Volume I'' is, together with its predecessor ``The red book of varieties and schemes'', now as before, one of the most excellent and profound primers of modern algebraic geometry. Both books are just true classics!\par As to the intended volume II of the book under review, the author planned to publish it in collaboration with {\it D. Eisenbud} and {\it J. Harris}. This would have been based on existing but unpublished notes of the author (partially revised by {\it S. Lang}), but then the author and his co-authors came to the conclusion that such a second volume was not really what was needed anymore, because {\it R. Hartshorne}'s famous book ``Algebraic geometry'' (1977; Zbl 0367.14001) already covered a good part of the material they had planned to include. Instead, D. Eisenbud and J. Harris published what they felt is needed more: a brief introduction to schemes [cf. {\it D. Eisenbud} and {\it J. Harris}, ``Schemes: The language of modern algebraic geometry'' (1992; Zbl 0745.14002)]. Their booklet may be regarded as a bridge between D. Mumford's thorough classic (under review) and the now existing several textbooks on ``scheme- theoretic'' algebraic geometry, including Hartshorne's book as well as Mumford's other classic, the ``Red book of varieties and schemes''. [W.Kleinert (Berlin)] |
Your connection to active and activity-based learning at Harvard
MATH117
Every aspect of Math 121 is highly interactive: Students spend most of classtime working in groups on problems and they then present their work and discuss as a class. Each student is responsible for some part of the in-class problems. |
Vedic Mathematics was rediscovered from ancient Sanskrit texts earlier this century by Bharati Krishna vertically and Crosswise. This may sound incredible but the Vedic system offers a very different approach to mathematics that is both powerful and fun.
"Why were we not shown this before?"
Discover Vedic Mathermatics Ref: 83206
Discover Vedic Mathermatics
This has sixteen chapters each of which focuses on one of the Vedic Sutras or sub-Sutras and shows many applications of each. Also contains Vedic Maths solutions to GCSE and 'A' level examination questions.
This is an elementary book on mental mathematics. It has a detailed introduction and each of the nine chapters covers one of the Vedic formulae. The main theme is mental multiplication but addition, subtraction and division are also covered.
This book shows applications of Pythagorean Triples (like 3,4,5). A simple, elegant system for combining these triples gives unexpected and powerful general methods for solving a wide range of mathematical problems, with far less effort than conventional methods use. The easy text fully explains this method which has applications in trigonometry (you do not need any of those complicated formulae), coordinate geometry (2 and 3 dimensions) transformations (2 and 3 dimensions), simple harmonic motion, astronomy etc., etc.
This book is an abridged version of the books which form part of the Vedic Mathematics course written for schools which covers the National Curriculum for England and Wales. Book Review Sorry, this product is out of Stock
Price: £20.00 -
Spend £40 on products in May and get a £10 Voucher to spend in June.
Vertically & Crosswise Ref: 83341
Vertically & Crosswise
Vedic Mathematics is the name given to the ancient system of Mathematics which was rediscovered from the Vedas between 1911 and 1918 by Sri Bharati Krsna Tirthaji (1884-1960).
According to his research all of mathematics is based on sixteen Sutras, or word-formulae. For example, 'Vertically and Crosswise` is one of these Sutras. These formulae describe the way the mind naturally works and are therefore a great help in directing the student to the appropriate method of solution.
Perhaps the most striking feature of the Vedic system is its coherence. Instead of a hotch-potch of unrelated techniques the whole system is beautifully interrelated and unified: the general multiplication method, for example, is easily reversed to allow one-line divisions and the simple squaring method can be reversed to give one-line square roots. And these are all easily understood.
This unifying quality is very satisfying; it makes mathematics easy and enjoyable and encourages innovation.
Problems Solved Immediately
In the Vedic system 'difficult' problems or huge sums can often be solved immediately by the Vedic method.
These striking and beautiful methods are just a part of a complete system of mathematics which is far more systematic than the modern 'system'. Vedic Mathematics manifests the coherent and unified structure of mathematics and the methods are complementary, direct and easy.
The simplicity of Vedic Mathematics means that calculations can be carried out mentally (though the methods can also be written down).
There are many advantages in using a flexible, mental system. Pupils can invent their own methods; they are not limited to the one 'correct' method. This leads to more creative, interested and intelligent pupils.
Interest in the Vedic system is growing in education where mathematics teachers are looking for something better and finding the Vedic system is the answer.
Research is being carried out in many areas including the effects of learning Vedic Maths on children; developing new, powerful but easy applications of the Vedic Sutras in geometry, calculus, computing etc.
But the real beauty and effectiveness of Vedic Mathematics cannot be fully appreciated without actually practising the system. One can then see that it is perhaps the most refined and efficient mathematical system possible.
Tirthaji and the rediscovery of Vedic Mathematics
The ancient system of Vedic Mathematics was rediscovered from the Sanskrit texts known as the Vedas, between 1911 and 1918 by Sri Bharati Krsna Tirthaji (1884-1960).
At the beginning of the twentieth century, when there was a great interest in the Sanskrit texts in Europe, Bharati Krsna tells us some scholars ridiculed certain texts which were headed 'Ganita Sutras'- which means mathematics.
They could find no mathematics in the translation and dismissed the texts as rubbish.
Bharati Krsna, who was himself a scholar of Sanskrit, Mathematics, History and Philosophy, studied these texts and after lengthy and careful investigation was able to reconstruct the mathematics of the Vedas.
According to his research all of mathematics is based on sixteen Sutras, or word-formulae.
Development of Further Material
A copy of the book was brought to London a few years later and some English mathematicians (Kenneth Williams, Andrew Nicholas, Jeremy Pickles) took an interest in it.
They extended the introductory material given in Bharati Krsna's book and gave many courses and talks in London.
A book (now out of print), Introductory Lectures on Vedic Mathematics, was published in 1981.
Between 1981 and 1987 Andrew Nicholas made four trips to India initially to find out what further was known about it.
Following these journeys a renewed interest was taken by scholars and teachers in India. It seems that once they saw that some people in the West took Vedic Mathematics seriously they realised they had something special.
St James' School, then in Queensgate, London, and other schools began to teach the Vedic system, with notable success.
Today Vedic Mathematics is taught widely in schools in India and a great deal of research is being done.
Three further books appeared in 1984, the year of the centenary of the birth of Sri Bharati Krsna Tirthaji. These were published by The Vedic Mathematics Research Group.
Maharishi Schools
When Maharishi Mahesh Yogi began to explain the significance and marvelous qualities of Vedic Mathematics in 1988, Maharishi Schools around the world began to teach it.
At the school in Skelmersdale, Lancashire a full course was written and trialled for 11 to 14 year old pupils, called The Cosmic Computer. (Maharishi had said that the Sutras of Vedic Mathematics are the software for the cosmic computer- the cosmic computer runs the entire universe on every level and in every detail). |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.