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Product Information
Sold in packs of 6, this support workbook provides essential extra activities for lowest-level GCSE students working at grades F and G. Part of the Oxford GCSE Maths for Edexcel series, it can be used together with the Foundation Student Book to ensure the best possible support for their learning needs 185 | 677.169 | 1 |
Detailed Description
The purpose of this module is to familiarize you with the basics of Mathematica
programming and its use for generating technology-based classroom materials and
demonstrations as well as student tutorials and laboratories.
Mathematica is
a very powerful software package that allows you to do complicated numerical calculations,
produce and animate beautiful and precise graphical displays, perform messy algebraic and
analytic manipulations as well as to do technical word processing. Moreover, all of these
capabilities can be used in a single environment called a Mathematica notebook that
can be used interactively as an electronic student tutorial, a classroom computer
demonstration, or that can be printed as overhead transparency masters or text
supplements for special classroom units. As such, it has the power to change the way you
teach and the way your students learn mathematics.
To be able to use Mathematica effectively for the above purposes, you need not
be an expert Mathematica programmer. It is not necessary or even advisable to study
a detailed guide to Mathematica programming such as Mathematica by Stephen
Wolfram (Addison-Wesley, 1996) or any less ambitious Mathematica programming guide.
Rather, we have found that a mathematics teacher who is a raw beginner with Mathematica
can learn to use Mathematica more effectively and quickly with a training program
that is structured as follows:
Step 1: Begin by getting a general idea of some of the things that Mathematica
can do by looking at and running some short and simple prepared Mathematica
programs that do things that are related to high school mathematics.
Step 2: Learn a few basic facts about Mathematica syntax to help you to avoid
mistakes when you begin writing your own Mathematica programs. (You will still make
simple mistakes that are annoying but this step will help to reduce the number of
mistakes. It will also help you find and correct the ones that do occur.)
Step 3: Write some very simple programs to do things that would be useful to you in one
of your current classes. Often, you can do this by suitably modifying some program that
you have seen in Steps 1 or 2.
Step 4: Learn how to do some basic procedures that are common ingredients to many
classroom projects created with Mathematica such as: writing and displaying text
and formulas attractively, creating and running animations, creating lists and tables,
entering and using functions, and enhancing graphics so that they are more attractive and
informative.
Step 5: Select and begin a classroom project that you would like to do for one of the
classes that you teach. We will provide you with a file that contains many such projects
that have been done by high school mathematics teachers who were Mathematica
beginners just a few days before they prepared these projects. You can use these sample
projects as a souce of ideas for your own project. You can also use these sample projects
as a source of Mathematica programs that you can copy and modify to suit your own
purposes.
That's it! All of the ingredients necessary to complete these steps are contained in
the files that you will download for this module after you complete your registration. Moreover, you can get help when you need
it by e-mail or phone from our staff. The Step-By-Step Instructions button
below will explain exactly what you need to do to complete this module. | 677.169 | 1 |
Description
An app that delivers three useful, streamlined tools in one easy-to-use package. Perfect as a tool to help understand math concepts or just to speed up the process of solving complicated problems.
-
A Complex Number calculator:
Enter a complex number in the form a + bi, and then add, subtract, multiply, or divide it by another complex number! Perfect for getting quick answers to complicated operations, or for just checking work.
Great for Algebra or Pre-Calculus!
-
A Prime Factor Finder:
Simply enter a number, press "Go, " and if it is prime, a message is displayed telling you that is is, or if it is not, a complete list of its prime factors is displayed.
Related to «Math Toolbox» applicationsFlightPlan is a native iPhone/iPod Touch application for both professional and hobbyist pilots. At its core, FlightPlan functions as an aviation calculator by simplifying many common calculations typically performed with an E6B slide rule computer. FlightPlan makes quick work of your number… more
Radiology Toolbox is the radiologists ectopic brain.Now downloaded by more than 60, 000 users in over 115 countriesRadiology Toolbox is designed by a practicing radiologist to help radiologists, residents, medical students, radiology technologists and technology students.These are the facts you… more
"#1 among 8 Educational iPhone Apps for Small Business Owners" - MashableThis app is released by Learning To-Go, an interactive educational system incorporating text, flashcards and tests into one complete learning app."The information provided in this app is very informative and… more | 677.169 | 1 |
Calculus Problem Solver
Calculus has widespread application in areas like Engineering and Science. Since this
study is pivotal in branching out to other fields, it is important to get the best help right
from the formative years itself.
Solving calculus problems is not easy but with the help of tutorvista's online tutors, this
will become much easy and simple.
Our online tutors will help you out to solve your calculus problems and understand the
concepts with a better hand. Get your help from our tutors and ensure yourself quality
learning on the subject.
Topics Covered in Calculus
Given below are the topics covered by our online calculus help program:
Know More About Formula for Area of a Rectangle
* Functions Limits and Continuity
* Differentiation
* Differential Equations
* Indefinite Integrals
* Definite Integrals
* Application of Derivatives
* Exponential and Logarithmic Series
Understand all these topics with personalized attention and gain quality help online.
Get Calculus Homework Help
Students can get all the Calculus homework help needed from the expert tutors. All the
help required with solving and understanding problems for homework and examinations
can be got online.
As the Calculus help is provided online, students can get help immediately and
accurately with the understanding of the concept.
TutorVista's online help isn't just about working out a few problems and logging off.
Features like regular homework help, and exam prep enable a student to get all the
help he/she needs.
There is also an extensive library of e-learning material like free question banks,
simulations and animations available to help the student ace the subject.
Learn More On :- How do you Find the Area of a Rectangle
Calculus is basically a study of higher grades and Tutorvista has special tutors for
higher grade students who teach the subject with an expertise.
Online Tutoring with an Expert
Get online calculus tutorials from tutorvista. Our Online Tutors will solve all your
Problems.
They are available 24x7 so that, you can connect with them just when you need help.
Our Calculus tutors will help you with your homework and assignments and also give
you step-by-step explanations for all problems making even complex problems simple
and easy.
Algebra Equation Solver
Algebra equations are the equations of the form algebraic variables with some
numerical co-efficient. Algebra equation contains the terms like numbers, integers,
fractions, roots, exponents, ratios, graphing etc.
Pre algebra equation is the simple equation which can be solved easily without any
complex calculations. Linear equation is an algebraic equation in which each term is
either a constant or the product of a constant and with a single variable.
It contains one or more variables. It occurs with great regularity in applied mathematics.
Example on how to solve algebra equations:
Solve Algebra equation 2x + 4 = 0
2x + 4 = 0
2x = - 4
x = −42
X = -2
Algebra Equation Solver
Algebra equation solver is to solve the equation and to get the value of variables. The
following are the important things that need to be noted down in algebra equations
Variables :The variable is the important thing that needs to be considered in equations.
Operations :Operations such as (+, -, x, /) are the operations that plays an important role solving
equations.
Values :We should enter the correct and valid values to get a perfect answer in solving
equations.
Solve x + 3 = 0
Read More On :- Area of Rectangle Formula
To get the value x send +3 to other side, we get x = -3.
Therefore, x is -3.
It is very simple. It only deals with whole numbers in the above example.
Solving Algebraic Equations
Below are the examples on solving algebraic equations:
Example 1 :Solve 2x + 12 = 0
Put all the variables on one side and values on other side.
We get, 2x = -12
Now to get x value divide both sides with 2
2x2 = −122
x = -6
(2) Solve the equation x2 - 4 = 0
Calculus Problem Solver
Calculus has widespread application in areas like Engineering and Science. Since this study is pivotal in branching out to other fields, it is important to get the best help right from the formative years itself. | 677.169 | 1 |
Synopsis
Following the format of the GCSE: Revision and Practice series, this title is targeted at the 3-5 tier of entry. It is aimed at specific tier of entry to ensure that students are focused on the mathematical concepts they need to know. It includes worked examples, showing the key techniques of how to tackle problems and approach questions. | 677.169 | 1 |
A comprehensive guide to quantitative techniques. Its learning-by-doing approach help students understand this tricky subject.
"Sinopsis" puede pertenecer a otra edición de este libro.
Críticas:
'Far too many students steer clear of quantitative methods because they fear that they will be unable to cope with the complexities of statistics and formulae. Louise Swift and Sally Piff have managed to produce a wonderfully clear text that takes students gently through the basic principles behind the most commonly used quantitative methods, simultaneously providing the basis for an understanding of statistical outputs which every researcher requires, regardless of the methods they chose to use in their own work.' -Tony Bryant, Professor of Informatics, Leeds Metropolitan University, UK
'This book is an excellent introduction to the quantitative methods used in business. Swift and Piff succeeded in preparing a well written and comprehensive text book which requires no prior knowledge of statistics and maths. Indeed all the required quantitative background is provided and students may benefit from the abundance of examples, exercises and work cards that will allow them to practice, achieve a high level of understanding of the topics covered in the book as well as confidence in problem solving skills.' -Konstantinos Tolikas, Lecturer in Finance, Cardiff Business School, UK
'Yet again, Swift and Piff have developed and enhanced this essential text, ensuring compatibility with all the latest applications and learning environments. Suitable for both undergraduate and postgraduate study, its practical, no-nonsense approach enables genuine understanding of essential quantitative methods for non-mathematicians.
This is a user friendly text for those who struggle with basic concepts and is versatile enough to be useful for those students with a more in depth knowledge of this subject. It lifts the mystery which often surrounds more difficult quantitative concepts for those studying business and finance.
Subjects are broken down into manageable sections with colour coded reinforcement panels, work cards and assessment tasks. The clarity of this layout provides a supportive platform for ease of learning and self study.' -Hilary Feltham, Director of Administration& Student Affairs, ICMA Centre, Henley Business School, University of Reading, UK
'This new edition of Quantitative Methods has some excellent features. Its four colour text design, companion website and comprehensive range of examples means that it will stay firmly at the top of my reading list for undergraduate Business and Management students.' - Dr. Christina Broomfield, Manchester Metropolitan University, UK
'I highly recommend this textbook as it clearly explains complex mathematical and statistical concepts in a simple, easy to follow manner. Ideally suited to students embarking on an undergraduate or postgraduate degree who in the past have had 'a dislike' for maths, the examples used are relevant and -supplemented with the website - provide an excellent accompaniment to any QM Module. Swift and Piff should be commended for the excellent text which is extremely well written and user friendly. It is also good value for money as the students need only one book to cover most of the topics required at graduate/post graduate level.' - Ann Thapar, Senior Lecturer and Course Leader for Business Management, Westminster Business School, UK
'This book explains how to solve everythingfrom basic maths to complex real-world problems. It starts with simple additions, builds up with derivates, statistics and culminates with real problems like forecasting, quality control or project scheduling. It uses an accessible language and supports theory with many useful examples. It has several entry points according to the level of the reader and is probably the most appropriate textbook for first year undergraduates on the market today.' - Alessio Ishizaka, Senior Lecturer, University of Portsmouth, UK
'This is an excellent text that provides a detailed set of notes covering quantitative methods taught in business schools. The book contains plenty of relevant examples, real data sets, and a very good introduction to the use of SPSS in analysing business related data sets.' -Glyn Davis, Principal Lecturer in e-Business and Data Analysis, Teesside University Business School, UK
'This is one of the best statistics textbooks I've read.The way this book combines statistical theory with real data (using SPSS) is excellent.' - Dr. John Simister, Management Department, Birkbeck College, University of London, UK
'There are large numbers of students on business-related courses who need to learn quantitative methods. This book provides a commendably comprehensive coverage of the material which is typically required. In terms of both style and content the authors have clearly given careful thought to the needs of the target audience.' - Malcolm Farrow, Senior Lecturer in Statistics, Newcastle University, UK
'Swift and Piff's book on quantitative analysis holds the hand of even the most timorous and shows them how important it is to correctly use quantitative models and understand statistical concepts in all areas of business.' - Lyn Thomas, Professor of Management Science, University of Southampton, UK
Reseña del editor:
Quantitative Methods is a comprehensive guide to the techniques any student of business or finance is likely to need. The authors' coaching, learning-by-doing approach coupled with the text's clear structural outline makes these essential mathematical skills far less daunting.
A bestselling and popular text in its previous editions, it has been fully updated with: | 677.169 | 1 |
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Random Walks
Important information
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Online
When: Flexible
Description
Note that Complexity Explorer tutorials are meant to introduce students to various important techniques and to provide illustrations of their application in complex systems. A given tutorial is not meant to offer complete coverage of its topic or substitute for an entire course on that topic.
Important information
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What you'll learn on the course
Distribution
Square Displacement
Spatial Dimension
Central Limit Theorem
First Passage Phenomena
Final Remarks
Applications of First Passage Phenomena
Diffusion Equation
Passage Phenomena
Course programme
Syllabus
Introduction
Root Mean Square Displacement
Role of the Spatial Dimension
Probability Distribution and Diffusion Equation
Central Limit Theorem
First Passage Phenomena
Elementary Applications of First Passage Phenomena
Final Remarks
Homework
This tutorial is designed for more advanced math students. Math prerequisites for this course are an understanding of calculus, basic probability, and Fourier transforms.
Random WalksComplexity Explorer
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Do you see something that is not right in this course? Let us know if there are any mistakes and you will help users like yourself. | 677.169 | 1 |
Calculus and Physics
Perhaps someone who has great knowledge in Physics and Calculus can answer these:
(1). How will mastering Calculus bring beneficial understandings, ones that cannot be seeing easily through other mathematics, to the learning to physics?
(2). What is the true meaning of derivatives, other than just performing some calculations based on some specific rules, at least that is what it appears to be to me, right now.
(3). Physics B, which is a highschool course for students who had trigonometry, will Calculus be a special part here or in Physics C? Assuming the student has very good algebra/geometry/trigonometry background and is enrolled in calculus while taking Physics B.
(4). What are somethings in Physics that only with Calculus knowledge can be proven or solved?
(5). Some tips for learning Calculus and Physics B, XOR C. Assuming the student has great algebra/geometry/trig background and has enrolled in Physics PAP in the freshman year.
Originally posted by PrudensOptimus
(1). How will mastering Calculus bring beneficial understandings, ones that cannot be seeing easily through other mathematics, to the learning to physics?
Calculus is extremely useful for many things (not only for physics).
The reason is that, in many cases, you can measure the rate at which something accumulates, and you want to describe how the accumulated quantity behaves.
When such rates are constant, it is possible to solve things without calculus, but they rarely are constant. Calculus gives you a tool to relate rates with quantities.
Examples:
1. you know that the more people there are, the faster the population increases. This simple description corresponds exactly to a differential equation, whose solution can tell you what population you can expect to have in 10 years.
2. Say you drive your car or 2hrs at 50 miles/hour. How far did you go? 100 miles. That is easy and does not need calculus. But, how often do you keep your speed at exactly 50 mi/h for 2 hours? A varying speed can be used to obtain the total displacement using calculus.
3. Say you have a rocket engine. You can measure how much gas it uses per second. This can be translated in thrust, which gives you the rate of change of speed, which in turn is the rate of change of distance. If you need to determine how much gas you need to cover a specific distance, you definitely need calculus.
4. You probably know F=ma already. Most probably you learned how to use it on problems where a, m and F are constant, which is never the case in real problems.
(2). What is the true meaning of derivatives, other than just performing some calculations based on some specific rules, at least that is what it appears to be to me, right now.
Derivative = rate of change.
Your car's speed is a derivative (of the position of your car with respect to time),
Your bank's interest rate is a derivative (of the ammount you have in your account, again wrt time),
The acceleration of a rocket is a derivative (it tells you how much the speed changes per second)
A pan's handle usually does not get as hot as the pan itself. It is made of a different material. How do you select such material? you want one whose rate of temperature increase with respect to heat received is not as big (for experts: ok, it works a bit differently, but its quite late here ).
(4). What are somethings in Physics that only with Calculus knowledge can be proven or solved?
Pretty much everything once you step out of the introductory book's (frictionless, perfect materials, constant everything, simple relations) examples.
As for course content, you probably would be better off asking people at your school.
HereOriginally posted by HallsofIvy HereAmong others, Napier was looking for a function whose derivative was equal to the function. Logarithms of the usual kinds depended upon the "base"; e.g., the popular logarithm is called "log to the base 10; the log of 2 = 0.30103.. and that means that 10^(0.30103..) = 2. Logarithms to bases other than 10 (such as the base 2 in boolian math)are possible but because of the decimal numbering system, base 10 is popular. Napier discovered that there was an irrational (and also called transcendental) base called "e" that has numerical value equal to 2.7182818.. The Logarithm to the base "e" is labled "ln" to distinguish it from "log to the base 10". For the function y = e^x, the derivative dy = e^x dx. The real value of this simple interdependence resulted in the postulation of the "integration factor" that simplifies cluimsy integrations. Cheers, Jim
PS: "e" can be evaluated with an infinite series.
Calculus is going to be what describes things that are changing. Or any dynamic system. You know, or maybe you don't if you in high school, but that's ok, how the number pi appears in many equations that don't seem to have anything to do with circumfrences or diameters; and how pi also appears in the definition of some physical constants. When you see pi, it is a clue that the result you're looking at came from something that is periodic in nature like a sine wave for instance; or it means that somewhere in arriving at this result you used some kind of circular or spherical symmetry.
Derivatives pop up in the same way. Almost everything you are going to want to study in physics is going to evolve over time. When this happens there will always be derivatives sprinkled everywhere. I haven't been in a physics class in college yet where I haven't encountered derivatives, and I only have 2 physics classes left. They are as common as pi :)
Once you take Calculus it will make sense. The concepts are of biggest importance. If you don't know the concepts, the mathematical techniques are essential useless. It sounds like you know the power rule, but have no idea what it means or what it's used for. Once you learn Calculus you'll find it to be elegant and useful.
I have been practicing all the questions in the book relating to Power Rules, Product Rules, Quotient Rules, and Chain rules. And I have get to know them all and know how to do most of themSo I want to understand why must the change in things relate to "derivatives."
For a particular example, compare the formula for the average velocity of an object over the interval of time [a, a + h]:
vav = (x(a + h) - x(a)) / h
with the formula for the instantaneous velocity of an object at time a:
v(a) = x'(a) = limh->0 (x(a + h) - x(a)) / h
How do they measure and why is it that we can find the change using the same rules?(Prod, Quo, Chain,...)
Look at the proofs in your calculus text, and/or try proving them directly from the limit definition of the derivative... continuing the analogy given above between average rate of change and instantaneous rate of change might help give insight as well.
So I want to understand why must the change in things relate to "derivatives."
the rate of change is the derivative!!!
To understand the rules of derivatives, you must go through their derivation. Then they will make sense as to why you can take these "shortcuts" instead of doing all the work on the problem. Essentially, when you use a rule for finding a derivative, you are skipping the derivation of that rule in that problem, which you would otherwise have to do to get the answer. Since mathematicians are lazy by nature, they realised there is no need to go through these long proofs when an exploitation of a pattern will save them a lot of time and work.
(1). How will mastering Calculus bring beneficial understandings, ones that cannot be seeing easily through other mathematics, to the learning to physics?
Hello, I am new to this forum. As evidenced by this being my first post. But I saw this question and was compelled to reply because I have been asked this on many occassions while tutoring students at my Alma Mater in both Physics and Mathematics.
So, how will mastering calculus help your career in physics? I think that calculus really opened up a new level to my problem solving abilities, including the many different ways to approach a problem and think my way through it to come to the solution. It wasn't apparent to me what I was learning nor how important it was to my educational goals until I was enrolled in caluulus III. Things began to 'click' for me in other areas of study, especially physics. The mastery of the mathematics portion helped me to understand not only how a solution was determined in physics, but why -- especially the proofsStudy ahrkron's posts carefully. The reason that the derivative works can maybe best be understood first with geometry. If you graph y=x, a simple diagonal line, then mark out two values of x, the area under the curve of the graph will be the integral of the function. You might know that the integral is inverse of the derivative,
I mean:
∫x dx = x2/2 ; d(x2/2)/dx = x
Likewise, the derivative of a function is the slope of that function at the point of evaluation. Let's take y=x:
dy/dx at 0 = 1
or y=x2/2
dy/dx at 0 = 0, the slope at 0.
As for a deeper answer as to why it works, I really can;t give you one. Try number theory. My number theory is terrible.
But as for what class you should take, I'd advise taking calculus with physics, esp. if you;ve already had trig. Calculus was invented by people thinking about physics, ya know. They compliment each other, even if the physics class you're taking is introductory. | 677.169 | 1 |
Financial Calculations: A step-by-step guide to the mathematics of financial market instruments
ISBN :
9780273750581
Publisher :
Financial Times Prentice Hall
Author(s) :
Steiner, Bob
Publication Date :
16 Jul 2012
Edition :
3
Overview
Success in today's sophisticated financial markets depends on a firm understanding of key financial concepts and mathematical techniques. Mastering Financial Calculations explains them in a clear, comprehensive way — so even if your mathematical background is limited, you'll thoroughly grasp what you need to know.
Mastering Financial Calculations starts by introducing the fundamentals of financial market arithmetic, including the core concepts of discounting, net present value, effective yields, and cash flow analysis. Next, walk step-by-step through the essential calculations and financial techniques behind money markets and futures, zero-coupon analysis, interest rate and currency swaps, bonds, foreign exchange, options, and more. Making use of many worked examples and practical exercises, the book explains challenging concepts such as forward pricing, duration analysis, swap valuation, and option pricing - all with exceptional clarity.
Whether you are a trader, fund manager, corporate treasurer, programmer, accountant, risk manager, or market student, you'll gain the ability to manipulate and apply these techniques with speed and confidence. | 677.169 | 1 |
d5mathlsur03051e - SUBJECT REPORTS MAY 2003 MATHEMATICS...
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Unformatted text preview: SUBJECT REPORTS MAY 2003 MATHEMATICS
This subject report is written by the principal examiners. Each of the authors provides general comments on performance, taking into account the comments of the assistant examiners and the team leaders. This report is the only means of communication between the senior examiners and the classroom teachers and therefore should be read by all teachers of mathematics HL. The grade award team studied the responses in the G2 forms, the assistant examiners' reports and the grade descriptors (a description of the criteria to be satisfied for each of the individual grade levels) before determining the grade boundaries. Overall grade boundaries
Grade: Mark range: 1 0 - 17 2 18 - 33 3 34 - 43 4 44 - 55 5 56 - 67 6 68 - 79 7 80 - 100 General remarks
With minor variations the remarks made in the report for the May 2002 session apply equally well for this session. Candidates should be encouraged to look at their answers with some critical common sense. Mathematics and common sense should go together. For instance, when the proposed answer is a negative probability, or the sine of an angle is given as 3, candidates should immediately realize that something is wrong. Quite often the error is easy to correct and candidates lose many marks that they could have easily obtained had they spent a minute looking critically at their answers. Candidates should be more careful with their graphs which were often drawn without scales (and therefore meaningless). Many candidates do not seem to know how to deal with accuracy problems: for instance, if an answer is required to 3 decimal places this usually implies working out the problem with 4 or 5 decimals, since errors may accumulate during the computation. Too many candidates err on the side of inaccuracy (better to give more decimals than required than fewer). Generally speaking the candidate should only consider the degree of accuracy required when giving the final answer and use maximum accuracy throughout the computation (when the computation has more than one step). The use of calculators makes this painless. Angles should in general be measured in radians. This is essential when the trigonometric functions are differentiated or integrated (otherwise the standard formulae do not hold!). Candidates should always be encouraged to use radians. If this had been done, many candidates would have avoided costly mistakes in the examination. Candidates should be strongly discouraged from writing their examinations in pencil which makes for very careless, messy and sometimes unreadable scripts. Clearly some schools do not prepare for any option. Schools ought to realize that this is a definite disservice to their candidates who thus waste 30% of their marks on paper 2. In this session, on the whole, candidates used their calculators well. The only relatively common error was overuse of calculators: when exact answers or proofs are required, candidates should realize that they cannot succeed by using their calculators. Some candidates lost a mark for failing to indicate the brand and model of the calculator they were using. Group 5 Mathematics 1 IBO 2003 SUBJECT REPORTS MAY 2003 Internal assessment
Component grade boundaries
Grade: Mark range: 1 0-4 2 5-6 3 7-8 4 9 - 11 5 12 - 13 6 14 - 16 7 17 - 20 In general, candidates did well in their tasks, the majority of which were taken from the Teacher Support Materials (TSM) for mathematics HL. There is also increasing evidence of the use of technology to enhance the work. Shortcomings, however, were still evident under Criterion A in the misuse of calculator notation, and under Criterion B in the lack of presentation skills in technical writing. In several instances, the problems were due to the poor selection of topics or assignments by the teacher. Particularly regrettable was the misuse of tasks taken from the mathematical methods SL TSM as each occurrence was penalised by moderators. Such tasks do not contain the rigour expected of mathematics HL assignments and are inappropriate for inclusion in portfolios. The proliferation of such tasks will likely be penalised more heavily in subsequent sessions. A predictable set of tasks was chosen by teachers from the TSM. Of the tasks not taken from the TSM, those "teacher-designed" type II assignments consisting merely of unrelated questions from past papers or revision questions taken directly from the end of textbook chapters were the most inappropriate. Some teacher-designed type III tasks missed the mark, due in large measure to a lack of understanding of the concept of mathematical modelling. A type III task should require candidates to start with given data and find a mathematical model (equation) that best describes the data. When a task starts with a given model to have candidates confirm its appropriateness with data, the assignment is not considered a type III task. Deductions of 2 marks were made from the total for non-compliance. Type I and type III tasks have in common the search for mathematical patterns. They differ in that a type I task deals with patterns that can be precisely determined through conjecture and proof, whereas a type III task deals with patterns that may be approximated by curve fitting. Paper 1
Component grade boundaries
Grade: Mark range: 1 0 - 20 2 21 - 40 3 41 - 54 4 55 - 68 5 69 - 82 6 83 - 96 7 97 - 120 Results from G2 forms
Comparison with last year's paper: Much easier 2 A little easier 21 Similar standard 88 A little more difficult 14 Much more difficult 1 Group 5 Mathematics 2 IBO 2003 SUBJECT REPORTS MAY 2003 Suitability of question paper: Level of difficulty Syllabus coverage Clarity of wording Presentation of paper Too easy 4 Poor 2 3 1 Appropriate 149 Satisfactory 47 63 51 Too Difficult 3 Good 75 91 100 Areas of difficulty
Candidates were, in general, least comfortable in the areas of vectors, 3-D geometry, probability and statistics. Levels of knowledge, understanding and skill
Apart from the topics listed above, the overall standard of scripts was satisfactory. Most candidates used their calculators effectively. The most common error was carrying out the integration in Question 16 in degree mode; candidates would be well advised to check that they are in radian mode whenever they carry out a process involving calculus. Performance on individual questions
Question 1 Geometric series Answer: (a) (b) 2 3 a=9 r= This was well done by many candidates. Some candidates, however, found it difficult to solve the simultaneous equations for a and r, especially those who wrote 15 = a (1 - r 2 ) (1 - r ) instead of 15 = a(1 + r ) . Candidates who tried to find an equation in a by eliminating r were generally
less successful than those who tried to find an equation in r by eliminating a.
Question 2 Trigonometry Answer: = 0.615, 2.53 (accept 0.196, 0.804) Not all candidates realised that, since roots in the interval [0, ] were asked for, the answers should be given in radians and not degrees. Some candidates gave only the root in the first quadrant.
Question 3 Vectors Answer: 41 Many candidates solved this question correctly although some bad mistakes were seen, eg (i + 2 j - k ) ( -3i + 2 j + 2k ) = -3i + 4 j - 2k and (6i + j + 8k ) (2i - 3 j + 4k ) = 12i - 3 j + 32k . Group 5 Mathematics 3 IBO 2003 SUBJECT REPORTS MAY 2003
Question 4 Remainder and factor theorems Answer: a = -2, b = 6 This question was well done by many candidates. Those who used long division instead of the factor and remainder theorems were usually unsuccessful.
Question 5 Singularity of matrices Answer: = 1 or 6 Solutions were often disappointing with some candidates using trial and error and sometimes spotting = 1 but not = 6.
Question 6 Probability Answer: (a) (b) E ( X ) = 2.5 P( X 2) = 0.526 Most candidates solved part (a) correctly. In part (b), candidates who used their calculators were the most successful; those summing individual binomial probabilities often omitted one of them.
Question 7 Functions: maximum values and roots Answer: (a) (b) f max = 1.17 Roots are -1.32, 0.537 This question was well done by most candidates using their calculators. A fairly common error was to give the x-coordinate of the maximum point instead of the y-coordinate. Some candidates tried to solve the problem analytically; it should be realised at this level that such an approach cannot be used with these particular functions.
Question 8 The sine rule Answer: ^ B = 93.6o or 26.4o ^ Many candidates gave only the acute value of B . Those candidates who started the question ^ by finding the value of b using the cosine rule usually obtained only one correct value of B . ^ ^ Some candidates rounded their obtuse value of C to 124, resulting in a value of 26 for B which incurred an accuracy penalty. Some candidates thought, incorrectly, that the triangle was right-angled.
Question 9 Probability Answer: (a) (b) P( B) = 0.8 0.56 A fairly common error was to confuse `independent' with `mutually exclusive' and therefore to use P ( A B ) = P(A) + P(B) to find P(A) . We were, however, able to follow through in part (b) where the two methods using P(A B) - P(A B) and P(A B) - P(A B) were seen in roughly equal numbers.
Group 5 Mathematics 4 IBO 2003 SUBJECT REPORTS MAY 2003 Question 10 Functions and equations of normals Answer: 4 Equation of normal is y - 1 = ( x - 2) 3 Solutions were often disappointing with algebraic and arithmetic errors made using implicit differentiation; some candidates incorrectly left the `8' on the right-hand side of the equation. Candidates starting from y = 8 x 2 were often the most successful.
Question 11 Complex numbers
-3 Answer: z = -5 - 12i The most successful candidates were those who solved the problem completely using the complex mode in their calculators. Of those who used algebraic methods, the most successful were those who simplified the 2 term first. Candidates who attempted to square the (1 - i) whole expression at the outset usually went down in a mass of algebra with the cross product terms often omitted.
Question 12 Exponents and logarithms Answer: ln 9 ln 8 Many candidates solved this problem successfully. The most elegant solution, seen several times, started by expressing both sides in terms of powers of 2 and 3. The most common error was to assume that the log of a product is the product of the logs.
Question 13 Satisfying inequalities Answer: 1 x -3, 3 Candidates graphing x - 2 and 2 x + 1 were the most successful. Those using algebraic methods often made algebraic errors and sometimes only found one of the critical values.
Question 14 Normal distribution Answer: E ( X ) = 9.19 Solutions were often non-existent with many candidates not knowing where to start.
Question 15 Perpendicular lines and planes Answer: Foot of perpendicular is (5, 3, 7) Solutions to this question were very disappointing. This is a topic that has been well answered in paper 2 questions in recent years but relatively few candidates seemed to know what to do here.
Group 5 Mathematics 5 IBO 2003 SUBJECT REPORTS MAY 2003 Question 16 Kinematics Answer: Distance travelled = 0.852 Many candidates failed to realise that the velocity changed sign half-way through so that the answer 0.387, obtained by simply integrating the velocity between 0 and 2, was often seen. Some candidates used their calculators in degree mode with disastrous consequences.
Question 17 Transformations of graphs Answer: f -1 ( x) = - 1+ x 1- x This question was reasonably well answered although it was fairly common to see the negative sign omitted in the expression for f -1 ( x) . There are still some candidates who think that f -1 means the derivative and others who think that f -1 ( x) means [ f ( x) ] .
-1 Question 18 Integration by substitution Answer: 4 + 4ln 2 - x - (2 - x) + c 2- x Solutions to this question were often disappointing with many candidates seemingly unaware of the mechanics of changing variables, although candidates who tried to solve the problem `otherwise' were even less successful. Candidates should be aware that an `otherwise' method of solution is usually more difficult than the method recommended in the question.
Question 19 Unbiased estimates Answer: (a) (b) x = 31.3 Unbiased esimate = 9.84 Most candidates solved part (a) correctly although some divided by 19. In part (b), only a few candidates appeared to know that an unbiased estimate of the variance is obtained by dividing by n - 1 , 19 here, with most candidates dividing by 20. A fairly common, correct method was to evaluate n-x x 2 2 and then multiply the answer by method, is to evaluate x 2 n -1 ( x) - n . A quicker, and more direct n -1 2 n ( n - 1) . Question 20 Graphing functions It was pleasing to see many reasonably good solutions to this question. Group 5 Mathematics 6 IBO 2003 SUBJECT REPORTS MAY 2003 Paper 2
Component grade boundaries
Grade: Mark range: 1 0 - 17 2 18 - 34 3 35 - 44 4 45 - 55 5 56 - 67 6 68 - 78 7 79 - 100 Results from G2 forms
Comparison with last year's paper: Much easier A little easier Similar standard A little more difficult 12 Much more difficult 0 1 29 63 Suitability of question paper: Level of difficulty Syllabus coverage Clarity of wording Presentation of paper Section A Question 1 Differentiation, maximum points, points of inflection Too easy 3 Poor 12 1 1 Appropriate 129 Satisfactory 73 57 44 Too Difficult 10 Good 54 84 96 Answer : (a) (i) f ( x) = 2 x - x 2 ln 2 22 x x 2 (ln 2) 2 - 4 x ln 2 + 2 2x (ii) f ( x) = x= 2 ln 2 (b) (i) (c) x= 2 2 (= 0.845, 4.93) ln 2 Most candidates - perhaps because the answer was given - answered part (a) (i) satisfactorily. In part (ii) a distressingly large number of candidates thought that the derivative of ln2 is when calculating the second derivative. Far too many candidates ignored the fact (indicated in bold!) that an exact answer was required for part (b) (i) (and therefore could not be produced by a calculator).
Group 5 Mathematics 7 IBO 2003 1 2 SUBJECT REPORTS MAY 2003 In part (ii) again a calculator or a sketch cannot suffice to "show" something (even if they might do the job for "finding" something). The overuse of calculators in this question had the consequence that relatively few candidates thought of evaluating the second derivative and often went into rather contorted and insufficient arguments (occasionally correct) about the values of the first derivative on the right and on the left of the stationary point or indeed even of the function, most of the time with a loss of one or two marks. For part (c), a substantial minority of the candidates chose - correctly - to look for the maximum and minimum of the first derivative while others found the roots of the second. This was all that was required since the question stated that there were two points of inflexion and therefore there was no need to check that the second derivative actually changed sign. Here calculators were used to good effect.
Question 2 Transformation of matrices, solution of linear equations Answer: (i) (a)
(b) -1 0 0 1 0 -1 T1 = ; T2 = 1 0 ; T3 = 1 0 0 -1 1 0 T = (i) 0 -1 (ii) This is a reflection in the x-axis. (ii) (a) (b) (ii) k =1. The general solution is z = , y = (2 - 4) (11 - 7 ) ,x= . 3 3 In part (i) about half the candidates multiplied the matrices in the wrong order. Also too many lost marks because they wrote the matrices in terms of cosine and sine, without giving their numerical values. In part (ii) many candidates seemed to be unable to adopt a precise strategy and went around in circles hoping (mostly in vain since in the process many algebraic mistakes were made) that eventually something would come out that made sense. Many candidates missed the logical point that "not a unique solution" meant "either no solution OR infinitely many solutions". Also, surprisingly, some candidates after stating that the system had an infinity of solutions found only one in part (b).
Question 3 Complex numbers, proof by induction, binomial expansion Answer: (c) (i) (ii) ( z + z -1 ) 5 = z 5 + 5 z 3 + 10 z + 10 z -1 + 5 z -3 + z -5 a = 1, b = 5, and c = 10 Mathematical induction is still largely misunderstood: quite a few candidates stated "assume n=k" (!) instead of "assume the statement is true for n=k" in part (a). Very few bothered to make a concluding statement, yet proof by induction requires a high level of formal correctness. Some candidates worked backwards "assuming the statement is correct for n + 1 let us show that it is true for n". Finally a distressingly large number of candidates did not even attempt to answer this question or made a very limited attempt. Group 5 Mathematics 8 IBO 2003 SUBJECT REPORTS MAY 2003 Some candidates thought that part (b) (i) followed on from part (a) thus confirming that they did not understand proof by induction (-1 is not larger than or equal to 1!). There was a lot of fudging here and in part (ii) as is often the case when the answer is given. In part (c) most candidates who went beyond the binomial theorem part got it right.
Question 4 Probability density functions, median, mode Answer: (a) (i) (ii) 1 x(8 x - x 3 ) dx = E( X ) 12 0 E( X ) = 1.24 2 (b) (c) (ii) m = 1.29 x = 1.63 In part (a) more than half the candidates neglected to multiply the density function by x when computing E(X). In part (b) about half the candidates were able to find the equation for the median. Most of them (as well as those who simply used the given equation) found the median. The most common error here was giving four answers without explaining which one was correct and why. Part (c) was worked out by about half the candidates but many thought that the mode was the value of f(x) rather than x. This was an easy straightforward question and the relatively disappointing results are due to the fact that probability is a part of the curriculum which is apparently often neglected.
Question 5 Functions, integration Answer: (a) (b) R = 2, =
(i) (ii) 3 Range is [1, 2] Inverse does not exist because f is not 1:1. 12 (c) x= In this question many candidates showed signs of confusion. In part (a) some candidates lost marks because they used degrees instead of radians (as a consequence the function was almost constant on the interval [0, 3.14]) and this was encouraged by the fact that some were using their calculators in the degrees mode. Since the answer required was exact, they should not have been using a calculator in the first place. In part (b) (i), many candidates did not take into account the domain and therefore found the range to be [-2, 2]. In part (ii) most answers seem to have been uneducated guesses with Group 5 Mathematics 9 IBO 2003 SUBJECT REPORTS MAY 2003 many nonsensical reasons given and again the problem was often that the domain was not taken into accounts. In part (c), once more an exact answer was required, nevertheless candidates often used their calculators (losing one mark). In part (d) there was a lot of fudging (the answer was given). Some candidates even "found" the answer working in degrees! But other candidates managed well.
Section B Question 6 Statistics Answer: (i) (a) (i) (ii) v = 87.13 s 2 = 215.58 (b) (i) (ii) [86.22, 88.04] [86.37, 87.89]
0.245 0.214 0.0524 (ii) (a) (i) (ii) (iii) (b) (iii) (b) 0.464 (or 0.463) The probability of rejecting H 0 when it is true is 0.05 Parts (i) (a) and (b) were done correctly by a large number of candidates. The usual error about the "unbiased" estimate of the mean was often present (dividing by 999 instead of by 1000). Most candidates rightly used their calculators. Some used them incorrectly and failed to react when getting unbelievable answers (like extremely large confidence intervals, containing all possible reasonable speeds and more). Part (i) (c) was very poorly done, which shows that statistics is too often taught as recipes without a proper attempt at interpretation. Part (ii) (a) was done successfully by most candidates while part (b) was done successfully by almost none. In part (iii) some candidates unaccountably tried to use the binomial law but most candidates successfully tackled part (a) while very few gave even remotely reasonable answers to part (b) (see remark on part (i) (c) above). Group 5 Mathematics 10 IBO 2003 SUBJECT REPORTS MAY 2003
Question 7 Sets, relations and groups Answer: (i) (b) f -1 ( z ) = log 3 ( z ) In part (i) (a) many candidates failed to be concerned about the injectivity and surjectivity of the mapping. Just about everyone got part (b) right. Many candidates dealt incompletely with part (ii) (a), ignoring the determinant condition in all their work. In part (a) many candidates stated that the group was abelian because it was commutative! Others made a logical mistake of failing to realize that a non abelian group may have an abelian subgroup and that therefore the fact that the product of matrices, in general, is not commutative did not imply that G was not commutative. In part (c) many candidates made a serious attempt to deal with the question but often floundered when dealing with transitivity (which some candidates confused with associativity!). Finally part (d) was also often incomplete, with right ideas getting bogged down in confusion. Relatively few candidates successfully tackled part (e).
Question 8 Discrete mathematics Answer : (i) (ii) (a) x = 11 and y = -6 xn = 2 2n = 2n +1 yn = 2n +1 - 3 (iii) (c) AEBACDBDCEDA Candidates who chose this option generally performed well except for parts (i) and (ii). In part (i) most candidates failed to use Euclid's algorithm fully, resorting instead to a trial and error approach and almost no one worked out part (b). In part (ii) again many candidates used a trial and error approach while others tried - with no success - to use the formula for second order difference equations.
Question 9 Analysis and approximation Answer: (i) (b) x = -2.78913 (5 d.p.) x = -0.60135 (5 d.p.)
(i) (c) x5 = -2.78913 (5 d.p.) Most candidates, not surprisingly, did part (i) successfully. They also performed relatively well in part (i) (b). In parts (c) and (d) it was obvious, however, that many were unfamiliar with the fixed point method and therefore, of course, could not give a reason why it did or did not work. Very few candidates received even partial credit in part (ii).
Question 10 Euclidean geometry and conic sections Group 5 Mathematics 11 IBO 2003 SUBJECT REPORTS MAY 2003 Answer: (i) (a) (b) The conic is an ellipse y= x x + 4 and y = - 4 2 2 As often in the past, this option seems to be chosen at random by candidates whose classmates have chosen another option, giving the impression that most candidates who chose this option do so on their own, without having been prepared for it in class, under the misapprehension that it is an easy option. The result is therefore not surprising: most candidates performed miserably (with, however, some remarkable exceptions). Those candidates that did more than write the heading of the question usually managed to get part or all of part (i) correct. Only a handful of candidates went beyond that. Group 5 Mathematics 12 IBO 2003 ...
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This note was uploaded on 05/06/2010 for the course MATH 1102 taught by Professor Chang during the Winter '10 term at Savannah State. | 677.169 | 1 |
Mathematics
Purpose
Mathematics is a creative and highly inter-connected problem solving discipline developed over centuries. Through history, mathematics has been essential for solving some of the most intriguing problems and today it is just as necessary for everyday life. Although we now have technological advances to solve many difficult calculations, these are a direct result of mathematical knowledge; the need for mathematical thinking in science, technology and engineering, continues to demonstrate its power and importance. The mathematics curriculum provides a foundation for understanding and develops reasoning ability, whilst also developing enjoyment and curiosity for the subject.
Aims
We aim to develop students' understanding of key mathematical concepts and processes to enable students to solve problems using a variety of techniques and skills. This requires students to be fluent in the fundamentals of mathematics and to reason mathematically. This happens through repeated practise to increase fluency and mastery, application of skills to familiar and unfamiliar contexts, learning of formulae, application to calculations, analysis and interpretation of mathematical information, as well as contextualising and applying appropriate elements to situations within which students are familiar.
Areas of Study
Number
Algebra
Ratio, Proportion and Rates of Change
Geometry and measures: learn and apply formulae solve problems.
Probability
Statistics
Years 7 - 11 – from years 7 to 11 we follow a single programme of study leading to a GCSE in mathematics.
Years 7 - 8 - our curriculum is designed to equip students with the mathematical knowledge and skill to successfully embark on their GCSE course in Year 9. It covers the full mathematical spectrum of Number, Ratio, Algebra, Geometry, Statistics and Probability required for their GCSE. We help the students achieve mastery in the use of this knowledge by emphasising the importance of using mathematical reasoning when solving problems in many different contexts.
Years 9 - 11 - our curriculum continues to build towards GCSE mathematics. The syllabus we follow is Edexcel with students either following the foundation or higher specification.
The foundation course covers a range of topics in Number, Algebra, Shape and Data handling. It emphasises students' ability to reason with and use these skills in unfamiliar contexts in order for them to be able to apply them to real life problems. | 677.169 | 1 |
About this product
Description
Description
Based on the author's junior-level undergraduate course, this introductory textbook is designed for a course in mathematical physics. Focusing on the physics of oscillations and waves, A Course in Mathematical Methods for Physicists helps students understand the mathematical techniques needed for their future studies in physics. It takes a bottom-up approach that emphasizes physical applications of the mathematics. The book offers: * A quick review of mathematical prerequisites, proceeding to applications of differential equations and linear algebra * Classroom-tested explanations of complex and Fourier analysis for trigometric and special functions * Coverage of vector analysis and curvilinear coordinates for solving higher dimensional problems * Sections on nlinear dynamics, variational calculus, numerical solutions of differential equations, and Green's functions | 677.169 | 1 |
Product Description:
Tussy and Gustafson's fundamental goal is to build students' conceptual foundation in the "language of algebra" through reading, writing, and talking about mathematics. Their text blends instructional approaches that include vocabulary, varied practice problem sets, and well-defined pedagogy, along with an emphasis on reasoning, modeling, communication, and technology skills. Tussy and Gustafson make learning easy for students with their five-step problem-solving approach: analyze the problem, form an equation, solve the equation, state the result, and check the solution. In addition, the text's widely acclaimed study sets at the end of every section are tailored to improve students' ability to read, write, and communicate mathematical ideas. The Third Edition of ELEMENTARY AND INTERMEDIATE ALGEBRA also features a robust suite of online course management, testing, and tutorial resources for instructors and students. This includes iLrn Testing and Tutorial, vMentor live online tutoring, the Interactive Video Skillbuilder CD-ROM with MathCue, a Book Companion Web Site featuring online graphing calculator resources, and The Learning Equation (TLE), powered by iLrn. TLE provides a complete courseware package, featuring a diagnostic tool that gives instructors the capability to create individualized study plans. With TLE, a cohesive, focused study plan can be put together to help each student succeed in math | 677.169 | 1 |
Mathematics
Did you know that female mathematicians as late as the early 19th century had to pose as men in order to be taught mathematics!
Did Pythagoras really discover THAT theorem?
And why was someone murdered over it?
So what is so fascinating about the Mobius strip as made famous by the Dutch artist, ME Escher?
Why is there no Nobel prize in Mathematics?
The aim of the Mathematics Department at HunterhouseCollege is to ensure that all girls fulfil their mathematical potential.
It is of crucial importance to us that we prepare girls for whatever they go on to do in life, whether that be following a mathematical or scientific career or not.
Key Stage 3
In Key Stage 3 all girls follow the Northern Ireland Revised Curriculum which prepares them for the GCSE course in Mathematics and, if they choose, Additional Mathematics.
GCSE
In Key Stage 4 girls follow the CCEA GCSE course being sitting examinations at the end of year 11 and 12 in GCSE Mathematics.
Additional Mathematics is also an option for girls who enjoy and show a flair for mathematics. The course extends knowledge beyond the scope of the single Mathematics course and provides a sound basis for A level Mathematics.
A Level
It is a truth uniformly acknowledged that A level Mathematics is one of the most difficult A levels that can be taken. However, it is also one of the most rewarding A levels and one that does provide the skills required for any science based degree course.
All girls starting the A level course should have achieved at least a grade B at the Higher tier GCSE course. GCSE Additional Mathematics is not a prerequisite, but would be an advantage. Above all, girls must be prepared to work hard from day 1! | 677.169 | 1 |
There are thousands of thousands of built in functions in mathematica. Knowing a few dozen of the more important will help to do lots of neat calculations. Memorizing the names of the most of the functions is not too hard as approximately all of the built in functions in mathematica follow naming convention (i.e. name of functions are related to objective of their functionality), for example, Abs function is for absolute value, Cos function is for Cosine and Sqrt is for square root of a number. The important thing than memorizing the function names is remembering the syntax needed to use built-in function. Remembering many of built in (built-in) mathematica functions will not only make it easier to follow programs but also enhance own programming skills too.
In mathematica single square brackets are used for input in a function, double square brackets [[ and ]] are used for lists and parenthesis ( and ) are used to group terms in algebraic expression while curly brackets { and } are used to delimit lists. The three sets of delimiters [ ], ( ), { } are used for functions, algebraic expression and list respectively.
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MATHEMATICA originally created by Steven Wolfram, a product of Wolfram Research, Inc. Mathematica is available for different operating systems, such as SGI, Sun, NeXT, Mac, DOS, and Windows. This introduction to Mathematica will help you to understand its use as mathematical and programming language with numerical, symbolic and graphical calculations.
Mathematica can be used as:
A calculator for arithmetic, symbolic and algebraic calculations
A language for developing transformation rules, so that general mathematical relationships can expressed
An interactive environment for exploration of numerical, symbolic and graphical calculations
A tool for preparing input to other programs, or to process output from other programs
Getting Started
Starting Mathematica will open a fresh window or a notebook, where we do all mathematical calculations and do some graphics. Initially windows title is "untitled-1" which can be changed after saving the notebook by name as desired. Mathematica notebook with text, graphics, and Mathematica input and output
Entering Expressions
Type 1+1 in notebook and press ENTER key from keyboard. You will get answer on the next line of work area. This is called evaluating or entering the expression. Note that Mathematica places "In[1]:=" and "out[1]=" (without quotation marks) labels to 1+1 and 2 respectively. You will also see set of brackets on the right side of input and output. The inner most brackets enclose the input and output while the outer bracket (larger bracket) groups the input and output together. Each bracket contains a cell. Each time you enter or change the input you will notice that the "In" and "Out" labels will also be changed | 677.169 | 1 |
BEGINNING ALGEBRA, International Edition employs a proven, three-step problem-solving approach - learn a skill, use the skill to solve equations, and then use the equations to solve application problems - to keep students focused on building skills and reinforcing them through practice. This simple and straightforward approach, in an easy-to-read format, has helped many students grasp and apply fundamental problem-solving skills. The carefully structured pedagogy includes learning objectives, detailed examples to develop concepts, practice exercises, an extensive selection of problem-set exercises, and well-organized end-of-chapter reviews and assessments. Additionally, the clean and uncluttered design helps keep students focused on the concepts while minimizing distractions. Problems and examples reference a broad array of topics, as well as career areas such as electronics, mechanics, and health, showing students that mathematics is part of everyday life. Also, as recommended by the American Mathematical Association of Two-Year Colleges, many basic geometric concepts are integrated in the book's problem-solving sets. The text's resource package - anchored by Enhanced WebAssign, an online homework management tool - saves instructors time while also providing additional help and skill-building practice for students outside of class.
Descripción Softcover. Estado de conservación 978053873982580538739825 | 677.169 | 1 |
DESCRIPTION: Foundation Maths has been written for students taking higher or further education courses, who have not specialised in mathematics on post-16 qualifications and need to use mathematical tools in their courses. It is ideally suited for those studying marketing, business studies, management, science, engineering, computer science, social science, geography, combined studies and design. It will be useful for those who lack confidence and need careful, steady guidance in mathematical methods. Even for those whose mathematical expertise is already established, the book will be a helpful revision and reference guide. The style of the book also makes it suitable for self-study or distance learning | 677.169 | 1 |
Free analytical and interactive math, calculus, geometry and trigonometry tutorials and problems with solutions. Thousands of problems and examples with detailed solutions and answers are included in this site. Also explore topics in mathematics using html 5 apps. Examples related to the applications of mathematics in physics and engineering such as the projectile problem, distance-time-rate...
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WebMath is designed to help you solve your math problems. Composed of forms to fill-in and then returns analysis of a problem and, when possible, provides a step-by-step solution. Covers arithmetic, algebra, geometry, calculus and statistics. Webmath is a math-help web site that generates answers to specific math questions and problems, as entered by a user, at any particular moment. The mathMath explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents. 4 October 2014 14½ Years helping people learn. Started 19th April 2000. Play with the Properties of the equation of a straight line." I want to let you know that your "Algebra 1" product is outstanding. With it I reviewed a lot of Algebra topics and I will use it with my homeschooled kids . Congratulations, this product deserves accolades from everybody. For your information , English is not my first language ( my kids are fully bilingual , English and Spanish ) , but I understood the explanations so well, this guy made...
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QuickMath allows students to get instant solutions to all kinds of math problems, from algebra and equation solving right through to calculus and matrices. The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within...
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About this product
Description
Description
A helpful guide for understanding the mathematical concepts and real-world applications of probability and statistics, including classroom tips, common terms such as outliers, and exercises to encourage hands-on practice -- | 677.169 | 1 |
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Show More principles and practices sections, alowing instructors to adjust the curriculum to meet their needs -Concise workbook format facilitates student learning and simplifies complex tax regulations -Examples show students how to analyze investments using calculators such as the HP 12C -Free Instructor Resource Guide includes a course outline, chapter quizzes, and answer keys | 677.169 | 1 |
You'll gain access to interventions, extensions, task implementation guides, and more for this lesson.
Big Ideas:
A function can be represented in various ways.
Students understand that graphs of nonlinear functions can be derived from a table of values. They make a table from a given scenario, create its corresponding graph and describe the function being modeled.
Vocabulary:
half life
Special Materials:
Graph paper
Straight edge or ruler | 677.169 | 1 |
College Algebra -We continued our investigation into "solving" triangles, this time looking at methods to solve non-right triangles ... using the Law of Sines and the Law of Cosines (Sec. 8.1 and 8.2).
HW for Tuesday - Be prepared to discuss/complete any problem in the worksheet packet distributed in class today.
College Algebra - We completed the online portion of the Ch. 5 Test in class today.
If you missed class today, you may log into MyMathLab anytime over the weekend and complete the assessment:
- password: ch5testsondy
- you may use only your graphing calculator and your Ch. 5 note packet (pgs. 474-477)
- 90-minute time limit, but can "save for later" if you can't complete in first siting
- estimated completion time (by MML) is 33 minutes
- all but 2 of 21 questions are identified at level 2 or easier
- window open until 8:00 am on Monday, Feb. 20
Friday, February 10, 2017
HW for Monday - Complete the worksheet packet that was distributed in class today.
Assessment Alert - We will complete the Ch. 4 Quest
(more than a quiz, less than a test) in class next Tuesday, February
14. Sections covered on this assessment include 4.3, 4.4, 4.5, 4.6,
4.8, and 5.1.
College Algebra - We completed in the Sec. 5.6 - 5.7 quiz in class today.
HW for Monday - Complete the worksheet packet that was distributed in class today.
Thursday, February 9, 2017
HW for Friday - Complete the worksheet packet that was distributed in class today.
Assessment Alert - We will complete the Ch. 4 Quest (more than a quiz, less than a test) in class next Tuesday, February 14. Sections covered on this assessment include 4.3, 4.4, 4.5, 4.6, 4.8, and 5.1.
College Algebra - We worked in the Sec. 5.6 - 5.7 quiz in class today.
Assessment Alert - We will postpone tomorrow's quiz and continue our work with congruent triangles. Instead, we will take a quiz covering Sec. 4.3 - 4.8 (w/ Sec. 5.1) in class next Tuesday, February 14 | 677.169 | 1 |
Solitons are explicit solutions to nonlinear partial differential equations exhibiting particle-like behavior. This is quite surprising, both mathematically and physically. Waves with these properties were once believed to be impossible by leading mathematical physicists, yet they are now not only accepted as a theoretical possibility but are regularly observed in nature and form the basis of modern fiber-optic communication networks. Glimpses of Soliton Theory addresses some of the hidden mathematical connections in soliton theory which have been revealed over the last half-century. It aims to convince the reader that, like the mirrors and hidden pockets used by magicians, the underlying algebro-geometric structure of soliton equations provides an elegant and surprisingly simple explanation of something seemingly miraculous. Assuming only multivariable calculus and linear algebra as prerequisites, this book introduces the reader to the KdV Equation and its multisoliton solutions, elliptic curves and Weierstrass $wp$-functions, the algebra of differential operators, Lax Pairs and their use in discovering other soliton equations, wedge products and decomposability, the KP Equation and Sato's theory relating the Bilinear KP Equation to the geometry of Grassmannians. Notable features of the book include: careful selection of topics and detailed explanations to make this advanced subject accessible to any undergraduate math major, numerous worked examples and thought-provoking but not overly-difficult exercises, footnotes and lists of suggested readings to guide the interested reader to more information, and use of the software package MathematicaA® to facilitate computation and to animate the solutions under study. This book provides the reader with a unique glimpse of the unity of mathematics and could form the basis for a self-study, one-semester special topics, or "capstone" course. | 677.169 | 1 |
Find a Stinson BeachIt needs a strong foundation but the concepts carry through the course that is basically differentiation and integration. After learning the basic skills, application becomes very important. But the depth of understanding in the course by a student leads to a better prepared thinker on a higher level | 677.169 | 1 |
GCSE Maths
In the Maths section we offer revision notes in four main sections: number, algebra, shape and space and handling data. We also have a small section of GCSE maths revision guides and software packages. | 677.169 | 1 |
Science/Technology/Engineering/Math - Keeping it fun!
...
Whether it's an explanation of how to solve equations, understanding word problems, factoring expressions, or creating graphs, Algebra I is all about using mathematical symbols and techniques to reach conclusions that can't be readily | 677.169 | 1 |
This book introduces graduate students and researchers in mathematics and the sciences to the multifaceted subject of the equations of hyperbolic type, which are used, in particular, to describe propagation of waves at finite speed. Among the topics carefully presented in the book are nonlinear geometric optics, the asymptotic analysis of short wavelength solutions, and nonlinear interaction of such waves.
This textbook is designed with the needs of today's student in mind. It is the ideal textbook for a first course in elementary differential equations for future engineers and scientists, including mathematicians.
In this book, there are five chapters: The Laplace Transform, Systems of Homogenous Linear Differential Equations (HLDE), Methods of First and Higher Orders Differential Equations, Extended Methods of First and Higher Orders Differential Equations, and Applications of Differential Equations. | 677.169 | 1 |
Syllabus for Intermediate Algebra
I am teaching intermediate algebra this spring and I wanted to post the syllabus and give a bit of a comment here. You can find the syllabus on my math education page.
The course catalog gives a description:
A study of problem-solving techniques in intermediate-level algebra. The goal is to demonstrate number sense and estimation skills; interpret mathematical ideas using appropriate terminology; manipulate, evaluate, and simplify real-number and algebraic expressions; and translate, solve, and interpret applied problems. Emphasis is on numbers and algebraic properties, graphing skills, and applications drawn from a variety of areas (such as finance, science, and the physical world). Topics include polynomials; factoring; exponents and their notation; rational expressions and equations; rational exponents and radical expressions; linear, quadratic, and other equations; and inequalities.
As we can see, this corresponds to what high school students normally call Algebra II. Let that sink in.
Image by Wokandapix via Pixabay. One day I will run out of generic free math pictures. But that day is not today. | 677.169 | 1 |
Mathematical Tools for Neuroscience
prerequisites: Good working knowledge
of calculus and high school math (e.g., a friendly
relationship with log, exp, trig functions). Programming experience is
helpful but not required.
brief description: This course aims to provide
a comprehensive introduction to the mathematical and
computational tools used for analyzing neural systems and
neural data. The course will introduce students to topics in
linear algebra, differential equations, and probability &
statistics, with a heavy emphasis on applications to
neurobiology. The course will seek to give students both a
good intuitive understanding and a practical mastery of
various mathematical and computational methods, and equip them
with programming and data visualization skills that are
increasingly important to scientific inquiry in general, and
neuroscience in particular. Students will learn to program in
Python, and homework problem sets will focus heavily on
programming. | 677.169 | 1 |
Event Spaces
Volunteer
Lisa Cudd
The following information comes from the named instructor and should describe characteristics general to courses as taught by this instructor. Individual sections of specific courses will deviate from this description in some respects.
Class Format
Lecture plus examples.
Resource Use
Book:
Extensive
Calculator:
Limited
Software:
Limited
For classes with the MyMathLab program, homework is assigned using this. The TI 83/84 calculator is used more in Math 171. For Math 120, a financial calculator is needed, preferably the TI BA 2Plus. Use the textbook as a resource in addition to class lectures and for practicing problems.
Assessment
I generally give a test after a chapter or two of new material. In a semester there will be 4-5 tests. Sometimes there are also short in class quizzes. Plus all classes take a comprehensive final exam.
Homework Policy
Depends on the class, usually turned in once per chapter. It could be a MyMathLab assignment or a worksheet or several problems from the textbook.
Attendance Policy
I don't count attendance in the student's grade. However, I do take attendance and I encourage everyone to attend regularly in order to be successful in class.
Availability
I am an adjunct professor so I am not on campus all of the time. I do, however, list office hours in my syllabus and I make myself available in the math adjunct office in SCI 220. I also encourage students to call me at home or to email with any questions.
Additional Information
I also teach Learning Strategies for Math (LS 174). This is a short, six-week course that meets one hour per week. It starts the second full week of the semester. LS 174 teaches thinking and study skills specifically geared toward the learning of math and is a co-requisite for some math courses. | 677.169 | 1 |
MAT 506 Foundations of the Rational Numbers (3
units)
Course Description
This course
covers the theory and applications of Rational numbers. Topics
central to the course are Number systems, representation of numbers,
equivalence classes, rationality and irrationality, properties of the
rational number system, applications of the central ideas to
proportional reasoning, and developing intuitive models for the
standard rules and algorithms. The course meets for 3 hours of
lecture per week.
Prerequisites
MAT 543 or
concurrent enrollment. Students must have graduate standing and one
year of full time secondary teaching.
Objectives
After completing
MAT 506 the student will be able to
State
definitions of basic concepts
Understand
the rational number notation and equivalence classes
Recognize
irrational numbers and prove that some numbers are irrational
Construct
proofs of mathematical assertions
Construct
intuitive, concrete explanations and models of standard rational
number rules and algorithms
Engage
in problem solving using foundations of Rational numbers and
proportional reasoning
Be
knowledgeable of the current research and theories of proportional
reasoning instruction
Create
short units of instruction that address common misconceptions of
Rational numbers and proportional reasoning
Expected outcomes
Students should
be able to demonstrate through written assignments, tests, and oral
presentations that they have achieved the objectives of MAT 506.
Method of Evaluating Outcomes
Evaluations are
based on homework, class participation, short tests, scheduled
presentations and group projects that cover students' understanding
of topics.
Grading Policy
Students' grades
are based on homework, class participation, short tests, and
scheduled presentations and group work. The instructor determines the
relative weights of these factors.
Text
No
single text will be assigned, as no single book exists that is
suitable for the course. Library research by students and class
handouts will be used instead.
Course Schedule
Week 1: Common misconceptions about fractions and proportional
reasoning group discussion
Week 2: Delving into theory. Building the Rational numbers from
scratch, number systems, representing numbers and equivalence
classes
Week 3: Continuing the development of the theory of Rational
numbers. Equivalence classes
Week 4: Incompleteness of the Rational Numbers: Irrationality and
Rationality
Week 5: Arbitrarily close: The density of the Rational numbers in
the real number system
Week 6: Developing concrete models for the addition and subtraction
of fractions
Attendance Requirements
Policy on Due Dates and Make-Up Work
Due dates of
assignments and projects will be announced in class. No late work
will be accepted.
Schedule of Examinations
The instructor
sets all test dates. Students will be notified well in advance. The
final group project is due on the last day of class.
Academic Integrity
The mathematics
department does not tolerate cheating. Students who have questions or
concerns about academic integrity should ask their professors or the
counselors in the Student Development Office, or refer to the
University Catalog for more information. (Look in the index under
"academic integrity".) | 677.169 | 1 |
GeoGebra
An advanced mathematics software
GeoGebra is an application designed for all those interested in geometry, algebra and mathematics in general. It can very well meet the needs of any user (novice and advanced) as it brings together all the necessary tools for performing basic calculations as well as more complex mathematical operations.
You can work with various dedicated tools and commands to create mathematical objects combining several geometric representations with other specific objects used for calculus and algebra. One can design lines and vectors, points and segments, conic sections, arcs and curves and then perform different calculations.
There are options to hide and rename objects, resize them and edit their properties, add labels and captions, trace objects and points position or animate free numbers and angles. Moreover, you can create equations using pre-defined operators and functions as well as sequences of commands to modify objects (GGBScript and JavaScript are both supported).
At the end, you can export your dynamic worksheets as HTML files or share them with others via GeoGebraTube. | 677.169 | 1 |
June 4, 2011
Math 147 Notes
Math 147 - Calculus I
Or, a course leading up to dierential calculus
The Well-Ordering Principle.
If S is a non-empty subset of N, then it must have a least element.
The Induction Principle.
Suppose that P (n) is some statement
MATH 147 Homework 1
Due in class Monday, September 21
1. Three young men accused of stealing donuts from the C&D make the
following statements:
1. Ed: Fred is guilty, and Ted is innocent.
2. Fred: If Ed is guilty, then so is Ted.
3. Ted: Im innocent, but
Calculus 1 (Advanced Level) Advice
Showing 1 to 1 of 1
Great professor. Very clear lecture. Returns emails very quick. Very patient with questions. Assignments are hard but you will have plenty of time while exams are easy with a large proportion of questions coming from assignments. Plus, both are heavily curved.
Course highlights:
The assignments were fairly challenging, but our grades were soooo generously curved!! So if you're interested in pmath, don't hesitate to take this course
Hours per week:
3-5 hours
Advice for students:
Make sure you actually attempt the assignments, because they are very enriching. However, even if you decide to half-ass them you will probably end up with 85+ | 677.169 | 1 |
Physical Oceanography with MATLAB provides an introduction to the fundamental analytical and computational tools necessary for modeling ocean currents, focusing on partial differential equations (PDEs) of geophysical fluid dynamics (GFD). Requiring only a basic familiarity with advanced engineering mathematics, the text presents topics, such as multivariate calculus and the integral theorems of Gauss and Stokes, in the context of fluid dynamics. MATLAB® is used throughout the book in the exercises as well as in the development of the mathematics. The author discusses current research problems in the mathematical ocean modeling community and features computational projects at the end of every chapter, ranging from elementary (box models of basins) to intermediate (quasi-geostrophic and multilayer). A CD-ROM containing all MATLAB programs accompanies the text. | 677.169 | 1 |
Main menu
Advanced Engineering Mathematics eBook
The value of mathematics in engineering cannot be overstated. Thousands of years before the Industrial Revolution brought modern technology into existence, the ancient Egyptians were using their advanced knowledge of mathematics to calculate the dimensions of their pyramids and palaces. The Babylonians were skilled engineers too, and it was these people who gave us the 24-hour day and the 360-degree angle. Today, students who seek a career in engineering need to study mathematics as it pertains to their chosen field. This article will discuss the textbook Advanced Engineering Mathematics 10th Edition. The first edition of the book was printed in 1963.
What the textbook is about
Advanced Engineering Mathematics 10th Edition is one of the best textbooks on the subject that any teacher can choose was written by Ernin Kreyszig, Hernan Kreyszig, Edward J. Norminton. It provides the student with everything that he or she will need in order to succeed in the course and, hopefully, in his or her engineering career. All the information given in the book has been checked to make sure that it is both accurate and up to date, and the examples have been made as simple as possible.
A close look at the contents
The book has been greatly changed since its previous edition. As a reflection of changes in engineering mathematics, some of the problem sets now have more problems than others. The fifth chapter has been shortened and more information on orthoganal functions has been included. The openings and parts of chapters, as well as parts of sections, have been completely rewritten to give students a better intuitive understanding of the material.
Advanced Engineering Mathematics is divided into seven parts:
Ordinary Differential Equations
Linear Algebra, Vector Calculus
Fourier Analysis, Partial Differential Equations
Complex Analysis
Numeric Analysis
Optimisation, Graphs
Probability, Statistics
Each of these parts is divided into a total of 25 chapters, which are further subdivided into sections. For instance, Part E, Numeric Analysis, is divided into three chapters, titled "Numerics in General," "Numeric Linear Algebra" and "Numerics for ODEs and PDEs." "Numerics in General" has an introduction plus sections titled "Solutions of Equations by Iteration," "Interpolation," "Spline Interpolation" and "Numeric Integration and Differentiation." At the end of every chapter is a set of review questions and problems and a summary of the chapter.
All formulas cited in the book are given on a separate line, separated from the preceding and succeeding text by a blank space. Charts and graphs also occur throughout the textbook. The problems in each set are separated according to the section to which they apply.
E-text format
Advanced Engineering Mathematics 10th Edition is available in two e-book formats, one of which is simpler and less expensive than the other. The simple e-book can be viewed both on- and offline on a PC, tablet or smartphone, and the student can insert notes on it. The WileyPLUS format includes advanced study tools not found in the less expensive format. | 677.169 | 1 |
Kaufmann and Schwitters have built this text's reputation on clear and concise exposition, numerous examples, and plentiful problem sets. This traditional text consistently reinforces the following common thread: learn a skill; practice the skill to help solve equations; and then apply what you have learned to solve application problems. | 677.169 | 1 |
Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material.
Beginning with reviews of vector algebra and differential and integral calculus, the book continues with infinite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations. Discussions of numerical analysis, nonlinear dynamics and chaos, and the Dirac delta function provide an introduction to modern topics in mathematical physics.
This new edition has been made more user-friendly through organization into convenient, shorter chapters. Also, it includes an entirely new section on Probability and plenty of new material on tensors and integral transforms | 677.169 | 1 |
Math essay introductions
Feb 13, 2013 · Compossing an essay 1. Republic of Moldova Ministry of Education ―Ion Creangă‖ State Pedagogical University Faculty of Foreign. Hundreds of fun educational games and activities for kids to play online. Topics include math, geography, animals, and more. Get the best free essay test taking tips and strategies that will help you achieve the best results on your test. The remainder of this document focuses on possible components of a math lesson plan template. Of course, such a template will include the components of the general.
Office: Science Center 512 Tel: (617) 495-3352 Fax: (617) 495-5132 Email: [email protected] Postal Address: Department of Mathematics Harvard … New Mathematics or New Math was a brief, dramatic change in the way mathematics was taught in American grade schools, and to a lesser extent in European countries.
Math essay introductions
A collection of some of the best math books, divided by area of mathematics. Easily author, edit, customize, and curate curricula using LearnZillion's powerful Curriculum Manager and readily share the materials through your LMS. This USB drive contains 100 of the top This I Believe audio broadcasts of the last ten years, plus some favorites from Edward R. Murrow's radio series of the 1950s.
Would you rather take six aptitude tests than make one introduction? Then cheer up -- and settle down to learning the whys and wherefores of introductions. The AP Biology exam has two large essays and six short answer questions that make up 50% of your score. Learning to quickly write intelligent, direct answers to the. Pearson Prentice Hall and our other respected imprints provide educational materials, technologies, assessments and related services across the secondary curriculum. PTC Mathcad is math software that allows you to solve, analyze and share your most vital engineering calculations. Office: Science Center 512 Tel: (617) 495-3352 Fax: (617) 495-5132 Email: [email protected] Postal Address: Department of Mathematics Harvard …
Qualified and Experienced Help. There are many companies today which offer assistance with essay writing. However, it doesn't mean that you'll be satisfied with. Bayes' Theorem for the curious and bewildered; an excruciatingly gentle introduction. Do you need help teaching your child how to write a personal narrative essay? Here is a short video that explains an easy way to organize and write a personal… BYU-Idaho values suggestions and ideas that can improve the university. Use our Feedback Form to let us know what you think.
Our Professionals will present you Essay Help Online. Maybe English is not your main subject, but does not mean that there is no need look for college essay help. A collection of some of the best math books, divided by area of mathematics. Students can use this checklist to edit and revise their peer's persuasive essay. The checklist focuses on strong topic sentences and conclusions, using text For resources for younger kids, see MATH I. MATH WAR! What to teach? How to teach? How much to teach? Does everybody need higher math? Opposing theories and …
Our The Math Forum's Internet Math Library is a comprehensive catalog of Web sites and Web pages relating to the study of mathematics. This page contains sites relating. | 677.169 | 1 |
Abstract: Resumen: Con base en la perspectiva de modelos y modelación, en este artículo se analiza la relación entre las herramientas conceptuales utilizadas para modelar una situación sobre costo de envíos de paquetería y los ciclos de entendimiento que los estudiantes van desarrollando sobre los conceptos de función y variación. Las preguntas que guían la discusión son ¿Qué registros de representación utilizan estudiantes del primer semestre de una licenciatura en Turismo para describir y analizar situaciones problemáticas cuyo modelo subyacente es una función escalonada' ¿Cómo apoyan las diferentes representaciones el desarrollo de ciclos progresivos de entendimiento de los conceptos de función y variación en los estudiantes' Los resultados muestran que la utilización de diversas representaciones, el análisis de éstas, su modificación y refinamiento, son indicadores de la construcción de niveles progresivos de entendimiento de los conceptos de función y variación.Abstract: In this paper we analyze the relationship between the conceptual tools (representations) used by students enrolled in a college tourism program, to model a situation about cost of sending packages, and the cycles of understanding that the students develop about the concepts of step function, function, and variation. Based on the perspective of Models and Modeling, the questions that guide the discussion are: What kind of representations did first semester students use to describe and analyze problematic situations where the underlying model is a step function' To what extent did the representations support the development of different cycles of understanding of the concepts of function and variation' The results show multiple representations that students construct, analyze, modify, and refine. The representations helped to acquire meaning of mathematical concepts as function and variation.
Abstract: Resumen: La representación de la multiplicación en el sistema numérico de los números complejos suele presentarse con un fuerte énfasis en lo algebraico, lo que lleva a una comprensión parcial de esta propiedad. A partir de lo anterior, en el presente trabajo se investiga sobre el proceso de aprendizaje de la multiplicación de los números complejos, con el objetivo de enseñar este contenido privilegiando el registro gráfico a partir de la teoría de Espacio de Trabajo Matemático. En esta investigación cualitativa se ha implementado una propuesta de aprendizaje en una primera fase con 34 estudiantes de ingeniería; y en una segunda fase con 4 estudiantes de Matemática, ambos grupos de estudiantes pertenecientes a primer año universitario (18-19 años). A partir de los resultados se evidencia que al realizar tratamientos y conversiones entre los registros semióticos usados con un artefacto de tipo software, no sólo se permite la activación de las distintas génesis del ETM, sino que también produce circulaciones en el ETM personal del estudiante, lo que lleva a una mejora en la comprensión del objeto matemático en cuestión.Abstract: The representation of multiplication in the number system of the Complex Numbers is usually presented with a strong emphasis in the algebraic aspect that brings a partial comprehension of this property. On the basis of the foregoing, the current study investigates the learning process of the multiplication of complex numbers in order to teach this content facilitating the graphic register according to the theory of Mathematical Working Space. In this qualitative research, there has been implemented a learning proposal that includes 34 engineering students in the first stage and 4 mathematics students in the second stage; both groups of students are in their first year at university (18-19 years old). Based on the results it is clear that carrying out processes and conversions between the semiotic registers used with a software artefact not only permit the activation of certain genesis of the ETM, but also produce circulations in the personal ETM of a student which leads to a better comprehension of the mathematical object in question.
Abstract: Resumen: Este artículo muestra evidencias del conocimiento exhibido por dos profesoras de bachillerato en España en relación con el uso de ejemplos y ayudas en la clase de álgebra lineal. Se trata de un estudio de caso instrumental cualitativo enfocado desde un paradigma interpretativo. Utilizamos el modelo Mathematics Teacher's Specialised Knowledge para analizar el conocimiento de las profesoras, centrándonos particularmente en uno de los subdominios del conocimiento didáctico del contenido, el Conocimiento de la Enseñanza de las Matemáticas. A partir de la observación de las cualidades y tipos de ejemplos empleados por las profesoras, los resultados dan cuenta del conocimiento de estas acerca de la potencialidad y el uso didáctico de los ejemplos. Análogamente, el uso de diversas técnicas de andamiaje permite identificar conocimiento de las profesoras sobre la diversificación y focalización de las ayudas.Abstract: This paper examines the kind of mathematical knowledge, which lies behind the use of examples and provision of support for students by two Baccalaureate (16-18) teachers in Spain. The methodological approach is that of a qualitative instrumental case study within an interpretative paradigm. Analysis is carried out through the Mathematics Teacher's Specialised Knowledge model, with particular focus on one of the sub-domains of pedagogical content knowledge, Knowledge of Mathematics Teaching. The detailed consideration of the types of examples used and their particular features sheds light on the teachers' awareness of the potential these have in the educational context. At the same time, the use of various scaffolding techniques on the part of the teachers points to knowledge about the variety of learner support available and how this focuses on specific aspects. | 677.169 | 1 |
Instead of using a simple lifetime average, Udemy calculates a course's star rating by considering a number of different factors such as the number of ratings, the age of ratings, and the likelihood of fraudulent ratings.
Algebra for Beginners
Taking the mystery out of algebra...
4.4 beginners, those who are just starting out or who are unfamiliar with basic algebra and wanting to refresh their knowledge and skills. It is broken down into bitesize chunks making it suitable for both learning and revising. You will gain an understanding and be able to put in to practice knowledge and skills in the areas of:
Positive and Negative Numbers
Order of Operations using BODMAS/BIDMAS/PEMDAS
Constants, Variables and Expressions
Collecting Like Terms
Forming and Solving Equations and more...
If you are wanting to prepare for what lies ahead or simply gain a better understanding in these areas then this course is ideal for you. The engaging and informative videos, course notes and practice questions with worked answers, will help you add algebra to your growing list of mathematical strengths.
Who is the target audience?
This course is ideal for you if you:
…have little or no understanding of algebra.
…are just starting out.
...are a beginner.
…just 'didn't get it' at school.
…are home-schooled.
…want to refresh your basic algebraic skills.
…are a parent or carer wanting to support your child with their learning.
This video will help you understand how positive and negative numbers work when adding and subtracting. Remember you can pause and rewind at anytime which makes it ideal for both learning and revising. When you're satisfied you have sufficient understanding move on to the next lecture.
This video shows some worked examples of adding and subtracting positive and negative numbers. Remember you can pause and rewind at anytime which makes it ideal for both learning and revising.
Worked Examples - Adding and Subtracting Positive and Negative Numbers
04:00
Using what you have learnt from the previous two lectures see how many of the following questions you can answer correctly. If it helps draw a number line like the one shown in the Worked Examples.
Positive and Negative Number Question Practice
10 questions
Have a go at these questions to help reinforce what you have learnt about positive and negative numbers. Download and print out the worksheet if it makes it easier. Remember NO CALCULATORS allowed. The answer sheet is downloadable for you to check how well you have done. Good Luck!
Adding and Subtracting Negative Numbers - Further Practice
1 page
This video explains what happens when you multiply and divide using positive and negative numbers. A Summary is available as a download to help you with your learning. When you are happy that you have sufficient understanding move on to the next lecture (quiz) for some practice. Good luck!
Multiplying and Dividing with positive and negative numbers
03:07
Multiplying and Dividing Positive and Negative Numbers
12 questions
This video explains exactly what the BODMAS Rule is and how it works. Remember you can pause and rewind at anytime which makes it ideal for both learning and revising.
Order of Operations - (BODMAS) - Introduction
04:21
This video shows worked examples of using the BODMAS Rule. Watch, rewind and watch again until you feel ready to move on to some practice of your own. When you are ready move on to the next lecture and have a go at the exercises to help reinforce what you have learnt about using the BODMAS Order of Operations rule.
BODMAS Worked Examples
03:45
Download and print out the attached question sheet then have a go at completing the questions using the knowledge and skills you have learnt so far. Remember NO CALCULATORS allowed. The answer sheet is downloadable too so you can check and see how well you have done. Good Luck!
BODMAS Practice Questions
1 page
Here are some further exercises to help reinforce what you have learnt about using the BODMAS Order of Operations rule. Download and print out the worksheet if it makes it easier. Remember NO CALCULATORS allowed. In the next lecture the answer sheet is downloadable or if you prefer there is a video showing worked answers for this question sheet. Either way you can check and see how well you have done. Good Luck!
This video gives an introduction into simplifying algebra by collecting like terms. It shows you how a basic example in real life can be translated into maths and then simplified.
Collecting Like Terms - Introduction
03:37
This video shows worked examples of Collecting Like Terms. Watch, rewind and watch again until you feel ready to move on to some practice of your own.
Collecting Like Terms - Examples
05:22
When you feel ready, attached are some exercises to help reinforce what you have learnt about collecting like terms. Download and print out the worksheet if it makes it easier. The answer sheet is downloadable so you can check and see how well you have done. Good Luck!
Collecting Like Terms - Practice Questions and Answers
3 pages
Magic Pyramids are a great way to practise your number and algebra work. This video gives examples of how they are constructed so that you can then go on and download the attached sheet and have a go yourself. When you are happy with your understanding move onto the next lecture which deals with Expression Pyramids. Good luck.
Magic Number Pyramids
02:41
This lecture explains how you can use Expression Pyramids to practise collecting of like terms. Watch the video through, pause and rewind if you need to and then go on to download the attached sheet to complete the Expression Pyramids. The answers are there to download too. Good luck.
Expression Pyramids
08:10
This lecture introduces how we translate real life problems into algebra. The introduction is followed by examples and a brief summary.
Translating English to Mathematics Introduction & Examples
04:24
The aim of this quiz is to correctly select the algebraic statement for each statement.
Translating English to Mathematics Practice
14 questions
As well as creating algebraic expressions we can evaluate them too. This short video explains how you can substitute values in place of variables and evaluate an expression. Also included in with this lecture is a downloadable question sheet where you can practice evaluating expressions. The answer sheet has been included as a download too.
Evaluating Algebraic Expressions
03:05
+–
Linear Equations
11 Lectures
52:40
This video gives an introduction as to what an equation is. It will give you a clearer view as to how an expression leads on to an equation. The following lecture looks at how to solve an equation by balancing scales.
What is an Equation?
01:55
This video explains how we solve an equation. It shows how by using both algebra and balancing. Watch, rewind and watch again until you feel ready to move on and practise some balancing of equations.
Solving an Equation
04:22
Download this question sheet and Balance the Equations to find the value of the unknown variable. I have included a short video demonstration to help you. The answer sheet is also included as a download. Good luck.
Download the question sheet and solve the equations to find the value of the unknown variable. I have included a short video demonstration that shows you how best to set out your workings. The answer sheet is also included as a download. Good luck.
Solving Equations (1)
04:19
True or False
10 questions
Use your knowledge and skills that you have learnt so far to Crack the Code and solve the riddle. You can view the answers in the attached download. Good luck!
Can you crack the code?!
2 pages
Download the attached question sheet and solve the equations to find the value of the unknown variable. I have included a video demonstration that shows you how best to set out your workings. The worked answers are in the next lecture. Good luck.
Solving Equations with Variables on Both Sides
08:06
This video works through the answers to the question sheet from the previous lecture. Feel free to pause and rewind to ensure you have a good understanding of how to approach these types of questions.
Solving Equations with Variables on Both Sides Answers
17:33
This video demonstrates how to solve equations using the skills and knowledge that you have learnt throughout this course. No more pictures of scales but instead we just use algebra showing all workings as we solve each equation. You can download the attached worksheet and practise your technique. The worked answers have been included as a download too. Good luck!
Solving Equations Using Algebra
05:50
This video explains how to use the knowledge and skills you have learnt so far to form and solve equations. Watch the video and when you are ready download the attached question sheet and complete the questions showing all of your working out. The answer sheet is also available as a download. Good luck.
Forming and Solving Equations
02:49
This Magic Maths Pyramid is based on an actual MENSA Maths Pyramid. It requires you to put in to practice what you have learnt about expressions and forming and solving equations. The same rules apply as with the Magic Pyramids you completed earlier. Adding together two blocks gives you the total in the block directly above.
Download the attached worksheet and have a go. Can you work out the value of the ?. Remember to show all of your working out. Good luck!
The answer with working out is in the next lecture.
MENSA Maths Pyramid
1 page
Watch this video to see how the MENSA Maths Pyramid was solved. How did you get on? If you managed to get the answer and show all of your working out then well done!
Maths need not be difficult but we understand that it may take you a while to grasp a concept.
Our courses are designed by maths experts who know how to express mathematical ideas in a clear and engaging manner. Each of our bitesize lectures reinforce your learning and encourage practical application, so that you develop the necessary skills to be a successful, confident mathematician. Our maths courses are designed to appeal to a variety of different learning styles by using a variety of delivery methods. | 677.169 | 1 |
This complete guide to numerical methods in chemical engineering is the first to take full advantage of MATLAB's powerful calculation environment. Every chapter contains several examples using general MATLAB functions that implement the method and can also be applied to many other problems in the same category.
The authors begin by introducing the solution of nonlinear equations using several standard approaches, including methods of successive substitution and linear interpolation; the Wegstein method, the Newton-Raphson method; the Eigenvalue method; and synthetic division algorithms. With these fundamentals in hand, they move on to simultaneous linear algebraic equations, covering matrix and vector operations; Cramer's rule; Gauss methods; the Jacobi method; and the characteristic-value problem. Additional coverage includes:
The numerical methods covered here represent virtually all of those commonly used by practicing chemical engineers. The focus on MATLAB enables readers to accomplish more, with less complexity, than was possible with traditional FORTRAN. For those unfamiliar with MATLAB, a brief introduction is provided as an Appendix.
Over 60+ MATLAB examples, methods, and function scripts are covered, and all of them are included on the book's CD
REVIEWS for Numerical Methods for Chemical Engineers with MATLAB | 677.169 | 1 |
Description
This quick and easy-to-use guide provides a solid grounding in the fundamental area of complex variables. Copious figures and examples are used to illustrate the principal ideas, and the exposition is lively and inviting. In addition to important ideas from the Cauchy theory, the author also includes the Riemann mapping theorem, harmonic functions, the argument principle, general conformal mapping, and dozens of other central topics. An undergraduate taking a first look at the subject, or a graduate student preparing for their qualifying exams, will find this book to be both a valuable resource and a useful companion to more exhaustive texts in the field. For mathematicians and non-mathematicians alike.
Create a review
About Author
Steven G. Krantz is currently Deputy Director of the American Institute of Mathematics. He is the holder of the Chauvenet Prize and the Beckenbach Book Award, both awarded by the Mathematical Association of America, and is a recipient of the UCLA Alumni Association Distinguished Teaching Award. | 677.169 | 1 |
Learning Objectives
This course is intended to expose you to the basic ideas of Differential Equations combined with some ideas from Linear Algebra. To be successful, a student must be able at the end of the class to solve the majority of the problems with no external help. All assignments and exams are geared towards and measure how much this goal has been accomplished.
Specific Learning Objectives
To learn about
Separable Differential Equations
Linear and Non-Linear Differential Equations
First- Order Differential Equations
Second- Order Differential Equations
Modelling with Differential Equations
Solving Differential Equations using Numerical Methods
Solving a system of two linear equations; Eigenvalues
Solving systems of Differential Equations
The Laplace Transform
General Learning Objectives
To learn (or at least start learning) how to think mathematically/critically. You will have to
Memorize and explain definitions, formulas, equations and theorems.
Learn certain techniques.
Formulas, equations, techniques etc… these are your mathematical tools and as a bare minimum you have to know what they are.
Learn when certain formulas, equations, techniques etc. can be applied.
Combine different tools and techniques.
Identify the correct tools and techniques to deal with unknowns situations.
Solve problems that look different from what you have seen before.
Engage in mathematical arguments.
3. Actively participate in this class
Be present; ask questions; answer questions; take notes.
Contribute your thoughts.
Work with other students outside class about this class. Working with a group of other students is highly encouraged, but not during the exams!
It is advisable that you study Differential Equations with the intend to remember it | 677.169 | 1 |
Word Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
0.08 MB | 9 pages
PRODUCT DESCRIPTION
This activity includes 40 problems to practice the parts of an algebraic expression. This activity is set up in a quiz, quiz, trade format but it could also be used for a partner activity or for flash cards. Students will identify the terms, like terms, coefficients and constants for each expression | 677.169 | 1 |
... More Description
difficult than the ones for first grade. Many of the problems are circuit representations for generating algebraic functions such as [n!], n^2, n^3, 2^n, and so on. It develops a curiosity in the student to experiment with other similar graphs on their own. Visual skills are highly desired in the fields of science and engineering. The books in the Visual Mathematics Series are geared to help build the foundations for a career in science, engineering, and mathematics. Similar networks are used in semiconductor chips for parallel operations using logic gates. The addition problems have a simple format. A set of pre-determined input values are provided for each problem. The goal is to find intermediate values based on addition of the inputs. The final result is provided in the problem itself. A few solved examples are provided in the beginning for illustration purposes. Solutions are provided for all problems at the end of the book.Also available directly from the publisher, an Amazon company, at: CreateSpace eStore: | 677.169 | 1 |
Equations & Answers every student who has ever found the answer to a particular calculus equation elusive or a certain theorem impossible to remember, QuickStudy comes to the rescue! This 3-panel (6-page) comprehensive guide offers clear and concise examples, detailed explanations and colorful graphsall guaranteed to make calculus a breeze! Easy-to-use icons help students go right to the equations and problems they need to learn, and call out helpful tips to use and common pitfalls to avoid. | 677.169 | 1 |
table to equation 2
Presentation (Powerpoint) File
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0.3 MB | 18 pages
PRODUCT DESCRIPTION
This lesson is foundational skill for algebra 1. It is made in the direct instruction and guided practice method. There are 3 opportunutiy for students write out their understanding and questions are tailored for conceptual understanding. Please enjoy | 677.169 | 1 |
Synopses & Reviews
Publisher Comments
This book is an introduction to manifolds at the beginning graduate level. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields. Its guiding philosophy is to develop these ideas rigorously but economically, with minimal prerequisites and plenty of geometric intuition. A course on manifolds differs from most other introductory mathematics graduate courses in that the subject matter is often completely unfamiliar. Unlike algebra and analysis, which all math majors see as undergraduates, manifolds enter the curriculum much later. It is even possible to get through an entire undergraduate mathematics education without ever hearing the word "manifold." Yet manifolds are part of the basic vocabulary of modern mathematics, and students need to know them as intimately as they know the integers, the real numbers, Euclidean spaces, groups, rings, and fields. In his beautifully conceived introduction, the author motivates the technical developments to follow by explaining some of the roles manifolds play in diverse branches of mathematics and physics. Then he goes on to introduce the basics of general topology and continues with the fundamental group, covering spaces, and elementary homology theory. Manifolds are introduced early and used as the main examples throughout. John M. Lee is currently Professor of Mathematics at the University of Washington.
Review
This book is an introduction to manifolds on the beginning graduate level. It provides a readable text allowing every mathematics student to get a good knowledge of manifolds in the same way that most students come to know real numbers, Euclidean spaces, groups, etc. It starts by showing the role manifolds play in nearly every major branch of mathematics.
The book has 13 chapters and can be divided into five major sections. The first section, Chapters 2 through 4, is a brief and sufficient introduction to the ideas of general topology: topological spaces, their subspaces, products and quotients, connectedness and compactness.
The second section, Chapters 5 and 6, explores in detail the main examples that motivate the rest of the theory: simplicial complexes, 1- and 2-manifolds. It introduces simplicial complexes in both ways---first concretely, in Euclidean space, and then abstractly, as collections of finite vertex sets. Then it gives classification theorems for 1-manifolds and compact surfaces, essentially following the treatment in W. Massey's \ref[ Algebraic topology: an introduction, Reprint of the 1967 edition, Springer, New York, 1977
Synopsis
Manifolds play an important role in topology, geometry, complex analysis, algebra, and classical mechanics. Learning manifolds differs from most other introductory mathematics in that the subject matter is often completely unfamiliar. This introduction guides readers by explaining the roles manifolds play in diverse branches of mathematics and physics. The book begins with the basics of general topology and gently moves to manifolds, the fundamental group, and covering spaces.
Synopsis
This is an introductory text on manifolds, the technical detail of the definition and the applications in topology, geometry, complex analysis, algebra and classical mechanics.
Description
Includes bibliographical references (p. [359]-361) and index.
Table of Contents
Introduction.- General Topology.- New Spaces From Old.- Compactness and Connectedness.- Surfaces.- Homotopy and the Fundamental Group.- The Circle.- Some Group Theory.- Fundamental Groups of Surfaces.- Covering Spaces.- Classification of Covering Spaces. | 677.169 | 1 |
This book contains a detailed account of all important relations in the analytic theory of determinants from the classical work of Laplace, Cauchy and Jacobi in the 18th and 19th centuries to the most recent 20th century developments. Several contributions have never been published before. The first five chapters are purely mathematical in nature and make extensive use of the column vector notation and scaled cofactors. They contain a number of important relations involving derivatives which prove beyond a doubt that the theory of determinants has emerged from the confines of classical algebra into the brighter world of analysis. The whole of Chapter 4 is devoted to particular determinants including alternants, Wronskians and Hankelians. The contents of Chapter 5 include the Cusick and Matsuno identities. Chapter 6 is devoted to the verifications of the known determinantal solutions of several nonlinear equations which arise in three branches of mathematical physics, namely lattice, soliton and relativity theory. They include the KdV, Toda and Einstein equations. The solutions are verified by applying theorems established in earlier chapters and in the extensive appendix. The book ends with an extensive bibliography and an index. Mathematicians, physicists and engineers who wish to become acquainted with modern developments in the analytic theory of determinants will find the book indispensable. | 677.169 | 1 |
Algebraic Proofs - Reasons and Practice
Word Document File
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0.1 MB | 4 pages
PRODUCT DESCRIPTION
The first page of this file gives students a list of commonly used reasons in algebraic proofs (e.g., addition property of equality). The second page has three practice two-column proofs and quicker practice identifying properties that change one equation into four equivalent equations.
Common Core Standard(s):
A-REI.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 | 677.169 | 1 |
Mathematics
Mathematics forms an essential part of the curriculum at Carterton Community College and is taught in 8 fortnightly lessons for key stage 3 and 7 for key stage 4, by a team of 8 specialist Mathematics teachers. Lessons take place in one of the 7 dedicated Mathematics classrooms in the newly built department block. All classrooms are equipped with interactive whiteboards.
The Mathematics Department aims to encourage all learners to enjoy Mathematics and motivate them to extend their understanding, develop mental skills applicable to real life situations, develop problem solving skills, and help learners to hypothesise, calculate and communicate their solutions in a variety of forms.
Teaching Staff
MrRBaileyTeacher
MrIainBiltonHead of School
MrsSJamesTeacher
MsLLansleyTeacher
MrAScullySecond in Faculty, Mathematics & Computing Faculty
MrKSlaterAssistant Headteacher
KS3 Curriculum
In Years 7, 8 and 9 lessons follow the Key Stage 3 Mathematics framework covering work in 6 areas of Mathematics: Number and the Numbering system; Algebra; Handling Data; Shape, Space and Measures; Calculating; Using and Applying. Learners experience a wide variety of activities throughout each term and they are assessed using APP success criteria on a day to day basis, by using bi-termly assessments and through the use of Rich Tasks. This ongoing individual assessment then aids the planning of future schemes of work.
KS4 Qualifications
In Years 10 and 11 Learners follow the Edexcel linear GCSE course, and much like Key Stage 3, learners in Years 10 and 11 experience a variety of lesson activities and detailed personalised assessment.
Our more able key stage 4 Mathematicians are advised about the opportunity and advantages of going on to study AS/A2 Mathematics and the course is offered by the Department.
KS5 Qualifications
Our Year 12 and Year 13 learners follow the Edexcel A level Mathematics course. This comprises of 6 modules throughout the 2 year course; Core 1,2,3,4 and 2 applied modules; a choice of Mechanics 1, Statistics 1, or Decision 1.
Three Modules are taught each year and all 3 module exams are sat in the summer of that academic year.
A level Mathematics is an extremely challenging and rewarding course which can lead to a huge variety of higher education and career pathways.
SMSC / Enrichment
The Mathematics department is a tenacious, forward thinking team, striving for the very best standards for its students and staff. All 3 curriculum areas encourage students to develop a wide variety of transferable skills to help learners take on board the careers of the future that don't even yet exist, tackling the problems that we don't even know are problems yet.
Through the cooperative raising over standards over recent years, the department now boasts A*-C GCSE results consistently above 73%. With at least 75% of students making the required level of progress and over 30% making above the required level of progress. (Both well above average)
All members of the team have high expectation for their learners and teach using a wide variety of challenging and engaging resources covering a wide variety of real life topics which address the SMSC curriculum.
The Department is now a member of the Further Mathematics Support Programme which regularly invites a variety of learners to various mathematically enriching activity days.
Our more able learners from each year group take part in the UKMT Maths Challenges including the team challenge day held in Oxford.
Maths Clinic is held every Monday lunch time for students to be able to 'drop in' and get support with all aspects of the Mathematics.
Student Resources
A huge resource with lessons and homework activities. (login and password advertised at school) | 677.169 | 1 |
Home
The TalkMaths project provides functionality for creating mathematical equations hands-free, using speech recognition. This is useful for anyone who prefers to speak rather than use keyboard and mouse. TalkMaths can be seen as an enhancement of existing assistive technology or simply as a tool to boost productivity.
Students can create mathematical e-content without the need to learn LaTeX. Academics can enhance their productivity by dictating lecture notes and research papers. | 677.169 | 1 |
You are here
Northern S.D. Math Contest
Northern's mathematics faculty members will write tests that cover specific areas of mathematics. Divisions included in the contest are (1) elementary algebra, (2) geometry, (3) advanced algebra, and (4) senior division. Each test usually consists of 35-50 multiple choice questions and a tie breaker. The test usually takes about 50 minutes.
To be added to the contest mailing list or for more information,call 605-626-2456 or emailLinda Richards.
History
Northern State University's Mathematics Department started offering a mathematics contest in 1953. The contest was developed to give area high school teachers an opportunity to compare the mathematical skills of their students with the skills of students from other schools. In addition, the contest served to promote interest in mathematics.
Two members of the NSU mathematics faculty - Scout Mewaldt and Edwin Williamson -created the contest, and its popularity has grown throughout the years. The contest started in 1953 with approximately 40 students from eight area schools in attendance. Today, more than 1,000 students from dozens of schools participate. | 677.169 | 1 |
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MATLAB Student Version
04/01/03
Students in engineering, math or science have a new technical computing resource designed for their needs. The MathWorks' MATLAB Student Version includes full-featured versions of MATLAB and Simulink, the software products used by engineers, scientists and mathematicians at leading universities, research labs, technology companies and government labs. MATLAB integrates computation, data analysis, visualization and programming in one environment. Simulink is one of the leading interactive environments for modeling, simulating and analyzing dynamic systems. In addition, there is no difference between the student and professional versions of the program, which, according to the company, is important because students are learning skills with the same tools they may use in a professional arena. The program also comes with MATLAB and Simulink books to help students get started. This product has a special student price of $99. The MathWorks, (508) 647-7000,
This article originally appeared in the 04/01/2003 | 677.169 | 1 |
Express and explain mathematical techniques and arguments clearly in words.
Assessment
Weekly assignments or quizzes: 30% Final examination (3 hours): 70%
Students are required to achieve at least 45% in the total continuous assessment component and at least 45% in the final examination component and an overall mark of 50% to achieve a pass grade in the unit. Students failing to achieve this requirement will be given a maximum of 45% in the unit. | 677.169 | 1 |
Graph theory is very much tied to the geometric properties of optimization and combinatorial optimization. Moreover, graph theory's geometric properties are at the core of many research interests in operations research and applied mathematics. Its techniques have been used in solving many classical problems including maximum flow problems, independent set problems, and the traveling salesman problem. Graph Theory and Combinatorial Optimization explores the field's classical foundations and its developing theories, ideas and applications to new problems. The book examines the geometric properties of graph theory and its widening uses in combinatorial optimization theory and application. The field's leading researchers have contributed chapters in their areas of expertise. | 677.169 | 1 |
Approximation Theory and Methods functions that occur in mathematics cannot be used directly in computer calculations. Instead they are approximated by manageable functions such as polynomials and piecewise polynomials. The general theory of the subject and its application toMore...
Most functions that occur in mathematics cannot be used directly in computer calculations. Instead they are approximated by manageable functions such as polynomials and piecewise polynomials. The general theory of the subject and its application to polynomial approximation are classical, but piecewise polynomials have become far more useful during the last twenty years. Thus many important theoretical properties have been found recently and many new techniques for the automatic calculation of approximations to prescribed accuracy have been developed. This book gives a thorough and coherent introduction to the theory that is the basis of current approximation methods. Professor Powell describes and analyses the main techniques of calculation supplying sufficient motivation throughout the book to make it accessible to scientists and engineers who require approximation methods for practical needs. Because the book is based on a course of lectures to third-year undergraduates in mathematics at Cambridge University, sufficient attention is given to theory to make it highly suitable as a mathematical textbook at undergraduate or postgraduate | 677.169 | 1 |
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The Open University of Sri Lanka
Department of Mathematics & Philosophy of Engineering
Mark Sheet
Course Code : MPZ 3132
Name of Programme: Diploma in Technology
Engineering Mathematics IB
CAT#1 -2012
Date: 22/03/2013
No
Reg No
Result
No
Reg No
Result
No
Performance Assessment Task
Dons Shapes
Grade 2
The task challenges a student to demonstrate understanding of the attributes of two-dimensional
shapes. Students must be able to identify shapes and make comparisons between and among shapes.
Students must m
LEARNING TEAM EVALUATION
LEARNING TEAM_A_ ASSIGNMENT _CURRICULM NIGHTCRIPT
Curriculum Night
DEVONIA MOURNING-TAYLOR/MATH 214
Course Description
This course is a seven week course designed to
introduce applications of mathematics in graphs,
probability, and geometry.
This course is an extension of the problem
solving skills taugh
Financial Accounting I
1st Year Examination
August 2011
Paper, Solutions & Examiners Report
1
Financial Accounting I
August 2011
1st Year Paper
NOTES TO USERS ABOUT THESE SOLUTIONS
The solutions in this document are published by Accounting Technicians Ir
RUNNING HEADER: Math of Life
1
Math of Life
Amber Ancheta
University of Phoenix
8/15/16
Math 214
MATH OF LIFE
2
Math of Life
Math is not for everyone, take it from me when I was younger I never liked math.
I always had a fear of math not being something I
Tessellation Example
MTH/214 Version 6
1
University of Phoenix Material
Tessellation Example
The following is an example of a tessellation that was created using the Microsoft Paint program.
The second page of this handout includes step-by-step instructio
RUNNING HEADER: Math for Elementary Educators
Math for Elementary Educators
Amber Ancheta
Math 213
University of Phoenix
7/11/16
1
MATH FOR ELEMENTARY EDUCATORS
2
Math is a general subject that elementary teachers need to teach to students. It is an
essen
Geometry Manipulative Handout
Prepare an activity involving a geometric manipulative designed to teach a geometric concept to
an elementary school student. You may create your own activity or modify an existing activity; if
you are modifying an existing a
Mathematics for Elementary Educators II Advice
Showing 1 to 1 of 1
Math 213 and 214 at the University of Phoenix covered most aspects of basic college math. It was a perfect refresher for me since I have been out of school for a very long time. The online practice problems were so helpful.
Course highlights:
We covered fractions, root values, order of operations, geometry, graphing, functions, polynomials, exponents, and more. The textbook was helpful but the online practice problems and tests made all the difference. You could practice until you understood the concept.
Hours per week:
12+ hours
Advice for students:
Use the online platform and take the practice tests frequently before the final. | 677.169 | 1 |
Learning Framework
Mathematics
Mathematics in the Senior Years, aims to instil in students an appreciation of the elegance and power of mathematical reasoning. Mathematical ideas
have evolved across all cultures over thousands of years, and are constantly developing. Digital technologies are facilitating this expansion
of ideas and providing access to new tools for continuing mathematical exploration and invention.
The curriculum focuses on developing increasingly
sophisticated and refined mathematical understanding, fluency, logical reasoning, analytical thought and problem–solving skills. These
capabilities enable students to respond to familiar and unfamiliar situations, by employing mathematical strategies to make informed decisions
and solve problems efficiently.
Year 10
Mathematics in Year 10 forms part of the integrated Years 7–10 Mathematics Curriculum. In Years 9–10, there are three specific course
pathways available to cater more effectively for the full range of learners. Please refer to the Middle Years Mathematics content.
Years 11–12
Higher School Certificate (HSC)
In the HSC, students can study Mathematics General, Mathematics, Mathematics Extension 1 and Extension 2.
Mathematics General
In Year 11, the Preliminary Mathematics General course is highly contextualised and provides opportunities for creative thinking, communication
and problem–solving. Students learn to use a range of techniques and tools, including relevant technologies, in order to develop solutions
to a wide variety of problems relating to their present and future needs and aspirations.
Satisfactory completion of the Preliminary Mathematics General course may be followed by study of the HSC Mathematics General 2 course.
The HSC Mathematics General 2 course builds on the knowledge, skills and understanding gained through the study of the Preliminary Mathematics
General course.
The Preliminary Mathematics General/HSC Mathematics General 2 pathway provides a strong foundation for a broad range of vocational pathways, as
well as for a range of university courses.
Mathematics
The Mathematics 2 Unit course has general educational merit and is also useful for studies in Science and Commerce. It is a sufficient basis for
further studies in Mathematics as a minor discipline at tertiary level, in support of courses such as the Life Sciences or Commerce. Students
who require substantial Mathematics at a tertiary level, supporting the Physical Sciences, Computer Science or Engineering, should undertake
the Extension 1 or Extension 2 courses.
Mathematics Extension 1
The content of the Extension 1 course, which includes the whole of the 2 Unit course, is intended for students who have demonstrated a mastery
of the skills in the Stage 5.3 course and who are interested in the study of further skills and ideas in Mathematics.
The Extension 1 course has general educational merit and is also useful for studies in Science, Industrial Arts and Commerce. It is a recommended
minimum basis for further studies in Mathematics as a major discipline at a tertiary level, and for the study of Mathematics in support of
the Physical and Engineering Sciences. Although the Extension 1 course is sufficient for these purposes, it is recommended that students of
outstanding mathematical ability should consider undertaking the Extension 2 course.
Mathematics Extension 2
The Extension 2 course is designed for students with a special interest in Mathematics, and who have shown that they possess special aptitude in
the subject. It represents a distinctly high level of school Mathematics, involving the development of considerable manipulative skill and
a high degree of understanding of the fundamental ideas of algebra and calculus. These topics are explored in depth, which provides a sufficient
basis for a wide range of useful applications, as well as the foundation for the further study of the subject
International Baccalaureate (IB) Diploma
In the IB Diploma, students can study Mathematical Studies, Mathematics Standard Level and Mathematics Higher Level. These courses serve to accommodate
the range of needs, interests and abilities of students, and to fulfil the requirements of various university and career aspirations.
The aims of these courses are to enable students to:
develop mathematical knowledge, concepts and principles
develop logical, critical and creative thinking
employ and refine their powers of abstraction and generalisation
Students are also encouraged to appreciate the international dimensions of Mathematics and the multiplicity of its cultural and historical perspectives. | 677.169 | 1 |
Project Based Pre-Algebra unit is meant to provide supplemental support to a standard Pre-Algebra course.The topics covered are typical to a standard Pre-Algebra course. The projects are meant to connect the world of math to that of art. They will allow you to make connections that would not normally occur while completing problem sets. These projects follow the typical sequence of a standard 7th/8th grade Pre-Algebra course. The major concepts covered will be integers, equations, factors and fractions, rational numbers, ratios, proportions, percents, inequalities, functions, graphing, right triangles, and two-dimensional figures. These projects are to be used in conjunction with a standard Pre-Algebra curriculum.
Sequence: The projects are listed and organized by the topics that they cover below. The material assessed in each project will be revisited, but following the prescribed order would be recommended. | 677.169 | 1 |
Description of the book "AQA Certificate in Further Mathematics":
Motivates and challenges more able students by providing more complex introductions, worked examples and exercises for all topics. This specification is ideal for students to prepare for A level mathematics. A range of algebraic and geometric topics are covered and it provides an introduction to Matrices and Calculus. Written by experienced teachers, this book: - Offers complete support for students throughout the course as it is an exact match to this new specification - Includes an introduction to each topic followed by worked examples with commentaries - Provides plenty of practice with hundreds of questions
Reviews of the AQA Certificate in Further Mathematics
Up to now concerning the publication we've AQA Certificate in Further Mathematics feedback users haven't however left his or her article on the overall game, or otherwise read it yet. But, in case you have already see this book and you're simply wanting to make their particular conclusions convincingly require you to spend time to go away an evaluation on our site (we are able to post equally bad and the good opinions). Basically, "freedom involving speech" All of us wholeheartedly recognized. Your own feedback to book AQA Certificate in Further Mathematics -- various other audience should be able to make a decision in regards to e-book. This sort of help can make people far more Joined!
David Pritchard
Unfortunately, presently we really do not have information regarding the actual musician David Pritchard. Nonetheless, we may take pleasure in when you have just about any details about this, and are also willing to provide the idea. Send out the idea to us! We have all of the verify, in case all the info are correct, we'll release on the site. It is vital for us that most real with regards to David Pritchard. Most of us thanks a lot in advance to get prepared to head to meet people! | 677.169 | 1 |
Product Description:
For many students interested in pursuing - or required to pursue - the study of mathematics, a critical gap exists between the level of their secondary school education and the background needed to understand, appreciate, and succeed in mathematics at the university level. A Concise Introduction to Pure Mathematics provides a robust bridge over this gap. In nineteen succinct chapters, it covers the range of topics needed to build a strong foundation for the study of the higher mathematics. Sets and proofsInequalities Real numbersDecimals Rational numbersIntroduction to analysis Complex numbersPolynomial equations InductionIntegers and prime numbers Counting methodsCountability FunctionsInfinite sets Platonic SolidsEuler's Formula Written in a relaxed, readable style, A Concise Introduction to Pure Mathematics leads students gently but firmly into the world of higher mathematics. It demystifies some of the perceived abstractions, intrigues its readers, and entices them to continue their exploration on to analysis, number theory, and beyond.
21 Day Unconditional Guarantee
REVIEWS for A Concise Introduction to Pure Mathematics | 677.169 | 1 |
Intro to Algebra - Adding and Subtracting Equations
PDF (Acrobat) Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
0.24 MB | 12 pages
PRODUCT DESCRIPTION
These worksheets are a great way to introduce students to solving for missing terms. The worksheets include adding, subtracting, and a combination of both. I use these in tutorials with lower level students. Once they can successfully complete some of these worksheets, we add a variable in the circle and practice showing work to solve an equation. This allows me to make these worksheets a little harder as the student progresses and/or for different levels of kids within your classroom. Enjoy | 677.169 | 1 |
RELATED INFORMATIONS
Articles, problems, games and puzzles - Algebra and many of which are accompanied by interactive Java illustrations and simulations.. Elementary algebra encompasses some of basic concepts of algebra, one of main branches of mathematics. It is typically taught high school students and .... Mathematics fiction, music and other offbeat links: Which Mathematical Structure is Isomorphic our Universe? by Max Tegmark Mathematics Fiction and .... Mission Statement. It is mission of Blount Elementary and its staff create safe and caring environment where teachers teach and students learn higher levels.. Mathematics. Math lessons, lesson plans, and worksheets. Basic math, telling time, calendars, money skills, and algebra.. View Your Algebra Answers Now. Free. Browse books below find your textbook and get your solutions now.. | 677.169 | 1 |
Christian Haesemeyer
Contact
This subject introduces the theory of groups, which is at the core of modern algebra, and which has applications in many parts of mathematics, chemistry, computer science and theoretical physics. It also develops the theory of linear algebra, building on material in earlier subjects and providing both a basis for later mathematics studies and an introduction to topics that have important applications in science and technology.
In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include | 677.169 | 1 |
This thread should serve as an interactive resource to help people bridge the gap to undergraduate mathematics. I anticipate people will be discussing topics covered in a typical undergraduate course with emphasis on, though certainly not limited to, the first years of those respective courses. People should feel free to have tangential discussions including everything from the philosophy of mathematics to more practical things like choosing modules and subject areas. That said, we should aim to avoid discussing A-level material as well as topics from postgraduate courses as these will be of little interest to the majority of people participating in this thread. Also, most of the content here is taken from JKN's original post and all credit goes to him.
Target audience
I am assuming that the majority of people participating will be those who are currently preparing for the first year of their undergraduate course in mathematics at Cambridge. That said, this thread is in no way exclusive and so I hope that everybody feels welcome! This is also why I am choosing to use the topic headings for the Cambridge mathematics course as the basis for the resource library. I hope that many do not find this in any way elitist or discouraging as I believe that most undergraduate courses cover almost identical material in the first year.
Introduction to number systems and logic
Overview of the natural numbers, integers, real numbers, rational and irrational numbers, algebraic and transcendental numbers. Brief discussion of complex numbers; statement of the Fundamental Theorem of Algebra. Ideas of axiomatic systems and proof within mathematics; the need for proof; the role of counter-examples in mathematics. Elementary logic; implication and negation; examples of negation of com-pound statements. Proof by contradiction. [2 lectures] Sets, relations and functions
Union, intersection and equality of sets. Indicator (characteristic) functions; their use in establishing set identities. Functions; injections, surjections and bijections. Relations, and equivalence relations.Counting the combinations or permutations of a set. The Inclusion-Exclusion Principle. [4 lectures] The integers
The natural numbers: mathematical induction and the well-ordering principle. Examples, including the Binomial Theorem. [2 lectures] Elementary number theory
Prime numbers: existence and uniqueness of prime factorisation into primes; highest common factors and least common multiples. Euclid's proof of the infinity of primes. Euclid's algorithm. Solution in integers of .
Modular arithmetic (congruences). Units modulo . Chinese Remainder Theorem. Wilson's Theorem;the Fermat-Euler Theorem. Public key cryptography and the RSA algorithm. [8 lectures] The real numbers
Least upper bounds; simple examples. Least upper bound axiom. Sequences and series; convergence of bounded monotonic sequences. Irrationality of and . Decimal expansions. Construction of a transcendental number. [4 lectures] Countability and uncountability
Definitions of finite, infinite, countable and uncountable sets. A countable union of countable sets is countable. Uncountability of R. Non-existence of a bijection from a set to its power set. Indirect proof of existence of transcendental numbers. [4 lectures]
Examples of groups
Axioms for groups. Examples from geometry: symmetry groups of regular polygons, cube, tetrahedron.Permutations on a set; the symmetric group. Subgroups and homomorphisms. Symmetry groups as subgroups of general permutation groups. The Möbius group; cross-ratios, preservation of circles, thepoint at infinity. Conjugation. Fixed points of Möbius maps and iteration. [4 lectures] Lagrange's theorem
Cosets. Lagrange's theorem. Groups of small order (up to order 8). Quaternions. Fermat-Euler theorem from the group-theoretic point of view. [5 lectures] Group actions
Group actions; orbits and stabilizers. Orbit-stabilizer theorem. Cayley's theorem (every group is isomorphic to a subgroup of a permutation group). Conjugacy classes. Cauchy's theorem. [4 lectures] Quotient groups
Normal subgroups, quotient groups and the isomorphism theorem. [4 lectures] Matrix groups
The general and special linear groups; relation with the Möbius group. The orthogonal and specia lorthogonal groups. Proof (in ) that every element of the orthogonal group is the product of reflections and every rotation in has an axis. Basis change as an example of conjugation. [3 lectures] Permutations
Permutations, cycles and transpositions. The sign of a permutation. Conjugacy in and in . Simple groups; simplicity of . [4 lectures] | 677.169 | 1 |
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In this product you will have:
1. Absolute Value Functions Investigation - Students graph different abs.value functions in different colors to see the transformations. They compare these transformations with the parent functions.
2. Notes - After the investigation, students summarize what they learned by using the form f(x)=a|x+h|+k and comparing the transformation with the parent function. Lastly, there are two examples that can be completed with teacher's guidance.
3. Practice - 15 practice problems graphing absolute value functions and labeling the vertex, min/max, transformation, domain and range.
4. Graphic Organizer - filled in or blank. see preview | 677.169 | 1 |
Chapter 6 "Number Theory and the Real Number System" has a revised discussion of the properties of the real number system.
Algebra coverage is streamlined into a single Chapter 7 "Algebraic Models and Linear Systems".
In Chapter 8 "Consumer Mathematics" examples in consumer mathematics have been clarified, computations on refinancing loans have been streamlined, and new information on inflation is added. Examples use notation consistent with TI-83 Plus and TI-84 Plus calculators, and Using Technology exercises demonstrate how to use TI's TVM Solver.
Chapter 9 "Geometry" presents updated and simplified examples.
Chapters 10 "Apportionment" and 11 "Voting" provide a streamlined discussion of apportionment. New Between the Numbers feature encourages readers to investigate viable alternatives to the current plurality voting method.
Using Technology exercises in Chapter 14 "Descriptive Statistics" illustrate Excel's built-in statistical functions as well as its Analysis ToolPak to simplify computations. | 677.169 | 1 |
Anyone Can Do Algebra
Description
Arithmetic deals with operations using numbers, but algebra is needed to thoroughly understand the concept of number, which is vital in our society. The natural sequel to the author's previous book Anyone Can Do Arithmetic, Anyone Can Do Algebra aims to promote genuine understanding of one of the most important foundation stones of Mathematics. Within his book, Brian Fletcher deals with the fundamental aspects of algebra in order to combat the common misconception that algebra is too difficult. Focusing on how these algebraic rules can be applied, topics range from quadratic equations and powers of numbers, to graphs and how they provide an alternative method of solving any equation. Through the examination of such topics, Anyone Can Do Algebra can provide a full and proper understanding of an important mathematic concept. Unlike other algebra based books, this book focuses on the steady build up of understanding to provide a more solid foundation, rather than simply learning and repeating rules. This book will appeal to those who have previously struggled with maths, in particular algebra, and wish to improve their understanding of a vital aspect of learning.
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About Author
Having previously worked as a research physicist, Brian Fletcher became a teacher of Mathematics. The final five years of his career were spent teaching Information Technology to adults. He is now retired and a governor at his local primary school. | 677.169 | 1 |
...
Show More algebra. Additionally, sufficient work in measurements has been provided to prepare students for future work in the sciences. Whole Numbers. Expressions and Equations. Integers. Fractions. Decimals. Rates, Ratios, and Percents. Linear Equations | 677.169 | 1 |
There are dozens of books on ODEs, but none with the elegant geometric insight of Arnol'd's book. Arnol'd puts a clear emphasis on the qualitative and geometric properties of ODEs and their solutions, rather than on theroutine presentation of algorithms for solving special classes of equations.Of course, the reader learns how to solve equations, but with much more understanding of the systems, the solutions and the techniques. Vector fields and one-parameter groups of transformations come right from the startand Arnol'd uses this "language" throughout the book. This fundamental difference from the standard presentation allows him to explain some of the real mathematics of ODEs in a very understandable way and without hidingthe substance. The text is also rich with examples and connections with mechanics. Where possible, Arnol'd proceeds by physical reasoning, using it as a convenient shorthand for much longer formal mathematical reasoning. This technique helps the student get a feel for the subject. Following Arnol'd's guiding geometric and qualitative principles, there are 272 figures in the book, but not a single complicated formula. Also, the text is peppered with historicalremarks, which put the material in context, showing how the ideas have developped since Newton and Leibniz. This book is an excellent text for a course whose goal is a mathematical treatment of differential equations and the related physicalWell differential equaitons are all about change, and this book changed my life. I read this more than 30 years ago, and all the mathematics I know, I mean really know, I learned from this book. Along with Aristotle's ethics, it is probably the most important book in my life.
ARNOLD==The MASTER!!! Aug 18, 2006
No doubt the best book on ODE by a master!! Ecuaciones Diferenciales Ordinarias (Fondos Distribuidos) Kiseliov Krasnov is another great book! Translated in English!! Like Spivak's Calculus on Manifolds, thin but good!!!
MDC Jul 13, 2006
This is a classic in the field. Excellent presentation and geometric perspective of dynamical systems. Most definitely a book to be kept as reference.
wow! differential equations made appealing Dec 20, 2005
I had always hated d.e.'s until this book made me see the geometry. And I have only read a few pages.
I never realized before that the existence and uniqueness theorem defines an equivalence relation on the compact manifold, where two points are equivalent iff they lie on the same flow curve. This instantly renders a d.e. visible, and not just some ugly formulas.
He also made me understand for the first time the proof of Reeb's theorem that a compact manifold with a function having only 2 critical points is a sphere. If they are non degenerate at least, the proof is simple. Each critical point has a nbhd looking like a disc. In between, the lack of critical points means there is a one parameter flow from the boundary circle of one disc to the other, i.e. thus the in between stuff is a cylinder.
Hence gluing a disc into each end of a cylinder gives a sphere! It also makes it clear why the sphere may have a non standard differentiable structure, because the diff. structure depends on how you glue in the discs.
What a book. I bought the cheaper older version, thanks to a reviewer here, and I love it. No other book gives me the geometry this forcefully and quickly. Of course I am a mathematician so the vector field and manifold language are familiar to me. But I guess this is a great place for beginners to learn it.
One tiny remark. He does not mind "deceiving you" in the sense of making plausible statements that are actually deep theorems in mathematics to prove. E.g. the fact that in a rectangle it is impossible to join two pairs of opposite corners by continuous curves that do not intersect, is non trivial to prove.
Hence the staement on page 2 that the problem is "solved" merely by introducing the phase plane, is not strictly true, until you prove the intersection statement above. All the phase plane version does for me is render the problem's solution highly plausible, and show the way to solving it. You still have to do it. But it was huge fun thiunking up a fairly elementary winding number argument for this fact.
Good teachers know how to deceive you instructively by making plausible statements that a beginner is willing to accept. I presume a physicist, e.g., would not quarrel with the statement above about curves intersecting.
This is the best differential, equaitons book I know of if you want to understand what they are, as opposed to learn to calculate canned solution fornmulas for special ones. He even makes clear what it is that is special about the special ones, e.g. linear equations are nice not just because the solutions are familiar exponential functions, but because the flow curves exist for all time,...
Amazing Nov 18, 2005
This is an amazing book. Arnold's style is unique - very intuitive and geometric. This book can be read by non-mathematicians but to really appreciate its beauty, and to understand the proofs that sometimes are just sketched, it takes some mathematical culture. This is the way ordinary differential equations should be taught (but they are not | 677.169 | 1 |
Compressed Zip File
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This r squared creation PowerPoint and Worksheet is a review of the topics that will be covered on the Chapter 9 Test. The materials covered in the assessment are standards based (even has released test questions) and are aligned to Chapter 9 "Quadratic Functions & Equations" of the Holt Algebra textbook. Concepts covered are how to determine if a point is on a graph, if a parabola opens up or down, where is the vertex, how to find the zero and vertex of a quadratic function, how to graph a quadratic function, how to solve a quadratic equation by graphing, how to solve a quadratic equation by factoring when in standard form, how to solve a quadratic equation by factoring when not in standard form, how to solve a quadratic equation by using square roots, how to find the discriminant and state the number of solutions to a quadratic equation, how to solve a quadratic equation by using the quadratic formula when in Standard Form, and how to solve a quadratic equation by using the quadratic formula when not in Standard Form.
The worksheet reinforces the lessons taught in the PowerPoint and includes both .doc and .pdf formats. The PowerPoint is also editable if you would like to make any changes (you may need to download MathType for free3.98. | 677.169 | 1 |
Overview
About The Product
MATHEMATICAL EXCURSIONS, Third Edition, teaches students that mathematics is a system of knowing and understanding our surroundings. For example, sending information across the Internet is better understood when one understands prime numbers; the perils of radioactive waste take on new meaning when one understands exponential functions; and the efficiency of the flow of traffic through an intersection is more interesting after seeing the system of traffic lights represented in a mathematical form. Students will learn those facets of mathematics that strengthen their quantitative understanding and expand the way they know, perceive, and comprehend their world. We hope you enjoy the journey.
Features
Content includes a subsection on Reading and Interpreting Graphs, a section on Right Triangle Trigonometry, and a section on Stocks, Bonds, and Mutual Funds.
An Excursion activity and corresponding Excursion Exercises conclude each section, providing concept reinforcement and opportunities for in-class cooperative work, hands-on learning, and development of critical-thinking skills.
Use of the Aufmann Interactive Method ensures that students try concepts and manipulate real-life data as they progress through the material. Every objective contains at least one set of matched-pair examples, the first of which is a completely worked-out example with an annotated solution. Students then actively practice the concept under discussion by trying the second problem, called Check Your Progress, using the example as a model. Each Check Your Progress problem includes a reference to a fully worked-out solution in the back of the text.
A section on Problem-Solving Strategies in Chapter 1 introduces students to the inductive and deductive reasoning strategies they will use throughout the text.
A Question/Answer feature encourages students to pause and think about the current discussion and to answer the question. For immediate reinforcement, the Answer is provided in a footnote on the same page.
Extension exercises at the end of each exercise set include Critical Thinking, Cooperative Learning, and Explorations, which may require Internet or library research.
The Math Matters feature throughout the text helps to motivate students by containing an interesting sidelight about mathematics, its history, or its applications.
Supporting margin notes include Take Note, alerting students to a concept requiring special attention; Point of Interest, offering motivating contextual information; Historical Notes, providing background information or vignettes of individuals responsible for major advancements in their field; and Calculator Notes, providing point-of-use tips.
About the Contributor
AUTHORS
Richard N. Aufmann
Richard Aufmann is the lead author of two bestselling developmental math series and a bestselling college algebra and trigonometry series, as well as several derivative math texts. He received a BA in mathematics from the University of California, Irvine, and an MA in mathematics from California State University, Long Beach. Mr. Aufmann taught math, computer science, and physics at Palomar College in California, where he was on the faculty for 28 years. His textbooks are highly recognized and respected among college mathematics professors. Today, Mr. Aufmann's professional interests include quantitative literacy, the developmental math curriculum, and the impact of technology on curriculum development.
Joanne S. Lockwood
Joanne Lockwood received a BA in English Literature from St. Lawrence University and both an MBA and a BA in mathematics from Plymouth State University. Ms. Lockwood taught at Plymouth State University and Nashua Community College in New Hampshire, and has over 20 years' experience teaching mathematics at the high school and college level. Ms. Lockwood has co-authored two bestselling developmental math series, as well as numerous derivative math texts and ancillaries. Ms. Lockwood's primary interest today is helping developmental math students overcome their challenges in learning math.
Richard D. Nation
Richard Nation received a B.A. in mathematics from Morningside College and a M.S. degree in mathematics from the University of South Dakota. Mr. Nation also attended a National Science Foundation academic year institute in mathematics at San Diego State University. Mr. Nation taught math at Palomar College in California, where he was on the faculty for 20 years. He has over 38 years' experience teaching mathematics at the high school and college levels. He is the co-author of several Aufmann titles. Today, Mr. Nation's professional interests include the impact of technology on curriculum development and on the teaching of mathematics at the precalculus level.
Daniel K. Clegg
Daniel Clegg received his B.A. in Mathematics from California State University, Fullerton and his M.A. in Mathematics from UCLA. He is currently a professor of mathematics at Palomar College near San Diego, California, where he has taught for more than 20 years. In addition to writing with the Aufmann team, he co-authored "Brief Applied Calculus" with James Stewart. He has also assisted James Stewart with various aspects of his calculus texts and ancillaries for almost 20 years.
New to this Edition
The Third Edition's table of contents has been reorganized and rearranged to group the chapters by broad topics that you can cover sequentially.
In the News exercises, based on media sources, have been added to this edition, providing another way to engage students by demonstrating the contemporary use of mathematics.
Chapter Summaries now appear in an easy-to-use grid format organized by section. Each summary point is now paired with the page numbers of an example that illustrates the concept, and exercises that allow students to practice the relevant skill or technique.
All application Examples, Exercises, and Excursions have been updated to reflect the most recent data and trends.
Definitions are now boxed and highlighted for greater prominence throughout the text, facilitating study and review.
All graphing calculator notes have been updated to refer to the TI-84 Plus.
In the Answer Section, answers to Chapter Test exercises now include a reference to a similar example in the text, making it easy for students to review relevant material for exercises that they answer incorrectly.
Components
Teacher Components your students need to retake the course and you are using the same book AND edition then they will not need to buy a new code.
This instant access code will be delivered via email when purchased. If you are not certain this is the correct access code for your course, please contact your Cengage Learning Consultant.
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Enhanced WebAssign - Start Smart Guide for Students
(ISBN-10: 0495384798 | ISBN-13: 9780495384793)
This guide helps students navigate Enhanced WebAssign. It includes instructions on how to use the Assignment page and its Summary, tips on using MathPad for providing easy input of math notation and symbols, an overview of the Graphing Utility's drawing tools for completing graphing assignments, and information on how to access grades and scores summary.
Price = 38.25
Student Supplements you need to retake the course and your instructor is using the same book AND edition then you will not need to buy a new code.
This instant access code will be delivered via email when purchased. If you are not certain this is the correct access code for your course, please contact your instructor.
Price = 59.16
Enhanced WebAssign - Start Smart Guide for Students
(ISBN-10: 0495384798 | ISBN-13: 9780495384793)
If your instructor has chosen to package Enhanced WebAssign with your text, this manual will help you get up and running quickly with the Enhanced WebAssign system so you can study smarter and improve your performance in class.
Price = 38.25
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Choose the Format that Best Fits Your Student's Budget and
Course Goals | 677.169 | 1 |
Keep Learning
AlgebraHelp.com contains lessons for basic algebra concepts such as equations, proportions, word problems, combining like terms, distribution, the FOIL method, exponents of numbers, exponents of variables, solving equations by factoring, completing the square, and the quadratic formula. Worksheets cover such topics as simplifying, multiplication, exponents, factoring, advanced equations, and graphing. In addition, AlgebraHelp.com has different calculators for help with solving and simplifying equations and expressions and graphing functions. Also included are math resources such as a prime numbers list, a perfect squares chart, and study tips for students who wants to take their algebra competency to the next level. | 677.169 | 1 |
Los Angeles PrecalAnna M.
...The math sections measure a student?s ability to reason quantitatively, solve mathematical problems, and interpret data presented in graphical form. These sections focus on four areas of mathematics that are typically covered in the first three years of American high school education: Arithmetic... | 677.169 | 1 |
Limits from a Graph with GOOGLE Slides
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2.29 MB | 32 pages
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Limits from a Graph with GOOGLE ® Slides Paperless and NO Prep for you designed for Calculus and/or PreCalculus
In this fun, challenging activity your students find the limits of functions visually from a graph. Functions include piecewise defined, trigonometric, absolute value, and more. Some answers are DNE, Does Not Exist.
This resource includes 24 digital task cards plus a digital answer sheet. A printable answer sheet is also included should you want a blended activity. Your students can enter their answers on the individual slides or use the response sheet. Because each student has their own digital copy, they can also make notes on the slides and refer to them later for review. As with traditional task cards, students can work alone or in groups. This activity can also be used for HW or an assessment. | 677.169 | 1 |
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Unformatted text preview: M316K Section 1.4- At the simplest level, a representation is a picture-- a picture of your image of a prob- lem- It can take many forms: diagrams, graphs, tables, sketches, equations, words, etc...- One of the key ideas: most problems and most mathematical concepts can be represented in different ways Section 1.5- Standard 7: Reasoning and Proof (Principles and Standards:- Recognize reasoning and proof as fundamental aspects of mathematics- Make and investigate mathematical conjectures- Develop and evaluate mathematical arguments and proofs (formal proofs in high school and children can construct informal proofs)- Select and use various types of reasoning and methods of proof as appropriate- Another maladaptive belief: Making sense of math is reserved only for the smart stu- dents and for the rest, the best advice is just do it.- Mathematical reasoning is often categorized as:- Quantitative: using quantities (numbers)- Qualitative: not using quantities (no numbers)- More specific kinds of mathematical reasoning: numerical, proportional, algebraic, and...
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This note was uploaded on 02/21/2009 for the course M 316K taught by Professor Ermer during the Spring '09 term at University of Texas at Austin. | 677.169 | 1 |
The monograph is written with a view to provide basic tools for researchers working in Mathematical Analysis and Applications, concentrating on differential, integral and finite difference equations. It contains many inequalities which have only recently appeared in the literature and which can be used as powerful tools and will be a valuable source for a long time to come. It is self-contained and thus should be useful for those who are interested in learning or applying the inequalities with explicit estimates in their studies.
Contains a variety of inequalities discovered which find numerous applications in various branches of differential, integral and finite difference equations
Valuable reference for someone requiring results about inequalities for use in some applications in various other branches of mathematics
Highlights pure and applied mathematics and other areas of science and technology
REVIEWS for Integral and Finite Difference Inequalities | 677.169 | 1 |
How How ThisBrian Brian
Develop DevelopBanach function algebras are complete normed algebras of bounded, continuous, complex-valued functions defined on topological spaces. BanProblems Problems This Dr
This This
This This course in a two-semester sequence on astrophysics. Topics include galactic dynamics, groups and clusters on galaxies, phenomenological cosmology, Newtonian cosmology, Roberston-Walker models, and galaxy formation. This is the second course in a two-semester sequence on astrophysics. Topics include galactic dynamics, groups and clusters on galaxies, phenomenological cosmology, Newtonian cosmology, Roberston-Walker models, and galaxy Theough turning the shell body at the National Projectile Factory, Birtley 14 | 677.169 | 1 |
Book Description:
This classic outline provides practical applications of basic mathematics for science, technology, and astronomy students. This edition will a) add new material to the Decimal Fractions and Measurement and Scientific Notation chapters, b) introduce the use of calculators for arithmetic operations, and c) provide a new chapter on descriptive statistics.
About the Author:
Ramon A. Mata-Toledo, Ph.D. (Harrisonburg, VA) is an associate professor of computer science at James Madison with 30 years of teaching experience. Pauline K. Cushman, Ph.D. (Harrisonburg, VA) is an assistant professor of integrated science and technology and computer science at James Madison University. | 677.169 | 1 |
Common Core Math Courses
San Lorenzo Valley Middle School has fully implemented the new Common Core Standards in Mathematics, and has revamped both the math courses and sequence of courses for our students. District-wide, the decision was made to follow the International or Integrated Math course sequence.
There are no longer be courses teaching only one type of math, such as Pre-Algebra, Algebra, Algebra Readiness or Geometry.
Courses integrate developmentally appropriate concepts from each of these courses into the three grade-level math courses to be taught at the middle school.
These courses are 6th Grade Math, 7th Grade Math, and 8th Grade Math, and will be the courses most students take at SLVMS during their time in middle school.
The process of accelerating advanced math students has also changed.
Students who have completed 5th grade math at the elementary level will all take the 6th Grade Math course at SLVMS during their 6th grade year.
We now accelerate students going into their 7th grade year.
SLVMS will offer a course called Accelerated Math 7. Students who are recommended to advance after sixth grade will be placed in this class and learn both the 7th and 8th grade standards during their 7th grade year. Students who successfully complete this course will be placed in a section of High School Math 1 during their 8th grade year. High School Math 1 is the first-year High School Math course.
Accelerated students who successfully complete their advanced courses will be one full year ahead of their peers on the grade-level math track.
Incoming advanced students used to take Pre-Algebra in 6th, Algebra in 7th, and then Geometry - the 1st year of HS math - in 8th grade.
Current advanced math students will take 6th grade math, then be placed in Accelerated Math 7, then HS Math 1- the 1st year of HS Math - in 8th grade.
We feel that both the new courses and the new placement for those on the advanced track will have students better prepared to take Math 2, Math 3, and both HS AP math courses while in high school. | 677.169 | 1 |
The equation editor is used throughout the Maple demonstration movies.In particular, see:
Clickable Math "Clickable Math" techniques redefine what is possible in mathematics, engineering and science education. During this brief demonstration, you will see firsthand how Maple's easy-to-use equation editor, context menus, palettes, and other clickable interface features allow you to focus on the concepts, not the tool.
How to Buy/Licensing Options: | 677.169 | 1 |
Right menu
Featured resource
Developing and maintaining a professional learning community is an essential element of a well-functioning school. This book will help school leaders conduct ongoing, structured learning opportunities tailored to the needs and interests of the participating mathematics teachers.
Navigating through Reasoning and Proof
in Grades 9-12
Expanding from 'reasoning to obtain solutions' to 'reasoning to justify ideas and validate results' is a significant development for the student of mathematics. Activities highlight the cycle of exploration, conjecture and justification. Supported by blackline masters, the activities build on and extend problem solving and reasoning to include proof; through Number, Algebra, Geometry, Data Analysis and Probability and Measurement. The book is accompanied by a CD-ROM which includes further reading for teachers, files for the blackline masters, and computer applications for students to use in their investigations. | 677.169 | 1 |
Mathematics Courses
Requirement: All students are required to take three years of a Mathematics course sequence.
Algebra I
This course is a modern introduction to Algebra which leads to the understanding of the basic structure of algebra through an informal and intuitive approach. Students will be provided with an in-depth study of the language of Algebra. A substantial amount of time is spent on skills and concepts to enable students to make the transition from arithmetic to Algebra. Application of these skills and concepts is also enforced. The graphing calculator, TI-84, will be introduced when graphing is studied. (Grade 9) (Course # 3101)
Algebra I – Honors
This course is a modern introduction to Algebra which leads to the understanding of the basic structure of Algebra through an informal and intuitive approach. Appropriate emphasis is placed on mastering more rigorous skills, concepts and mathematical content. Students are encouraged to develop thinking and problem solving skills throughout the course, and applications of these skills will be of primary importance. The graphing calculator, TI-84, will be introduced when graphing is studied. (Grade 9) (Course # 3102)
Algebra I - High Honors
This accelerated course is a modern approach to algebra in which the concepts, principles and basic structure of algebra are explored. Emphasis will be placed on problem solving and real-life applications so that the students can be given a greater appreciation for the relevance of algebra in their lives and careers. Additional topics that will be covered beyond the scope of an Algebra I course include radical expressions, quadratics and an introduction to probability and statistics. The graphing calculator, TI-84, will be introduced when graphing is studied. (Grade 9) (Course # 3103)
Geometry
A modern approach to the basic principles of Geometry aims to develop a knowledge of geometric elements and their relationships in order to help the student grow in mathematical awareness and conceptual understanding. This course will cover all the basic ideas and terms of traditional geometry. A non-rigorous approach to the deductive method of proof will be presented to promote logical reasoning skills. The key concepts of Algebra will be re-enforced throughout the year. TI-84 Graphing Calculator is required for the 3rd quarter. (Grade 9 or 10) (Course # 3201)
Plane and Solid Geometry – Honors
A modern approach to the basic principles of geometry aims to develop a knowledge of geometric elements and their relationships in order to help the student grow in the use of the deductive method of proof. Formal proofs will be explored in detail throughout the entire course. A study of three-dimensional solids including their lateral areas, surface areas and volumes will be studied during the fourth quarter. TI-84 Graphing Calculator is required for the 3rd quarter. (Grade 9 or 10) (Course # 3202)
Plane and Solid Geometry - High Honors
This course provides an in-depth study of geometry with heavy emphasis on deductive proofs from the outset. Allof the traditional topics of Euclidean geometry will be studied in detail as well as coordinate geometry and an introduction to right triangle trigonometry. A study of three-dimensional solids including their lateral areas, surface areas and volumes will be studied during the fourth quarter as well as an introduction to geometric probability. TI– 84 Graphing Calculator is required for the 3rd quarter. (Grade 9 or 10) (Course # 3203)
Algebra II
A modern integrated course in Algebra consists of a thorough review of Algebra I. A complete study of quadratic equations, factoring, completing the square, the quadratic formula, graphing, problem solving, solving systems of equations and inequalities and polynomial equations will be provided. Additional topics will include operations on rational expressions and radicals. TI–84 Graphing Calculator is required. (Grade 10 or 11) (Course # 3301)
Algebra II - Honors
An extended study of the topics introduced in Algebra I is made. The real number system with emphasis on linear functions and relations, systems of equations and inequalities, rational expressions, radicals and irrational numbers, complex numbers, polynomial functions, conic sections, and exponential and logarithmic functions are included in the course of the year. Students review and expand their knowledge of problem solving. (Grade 10 or 11) (Course # 3302)
Algebra II - High Honors
An extended study of the topics introduced in Algebra I is made. The real number system with emphasis on linear functions and relations, systems of equations and inequalities, rational expressions, radicals and irrational numbers, polynomial functions, conic sections, exponential and logarithmic functions, sequences and series, and probability. The course is fast-paced and emphasis will be placed on higher order thinking and problem solving. TI–84 Graphing Calculator is required. (Grade 10 or 11) (Course # 3303)
Precalculus
This course is a continuation of Algebra II. Topics will include a complete study of trigonometry, conic sections,exponential and logarithmic functions, probability, and sequences and series. TI–84 Graphing Calculator is required. (Grade 11 or 12) (Course # 3411)
Precalculus – Honors
This course is a preparation for Calculus. Topics will include a complete study of trigonometry, functions and their inverses, advanced graphing techniques, exponential and logarithmic functions, sequences and series, the binomial theorem and probability. Applications of these concepts will also be included. An introduction to limits and continuity may also be explored. (Grade 11 or 12) (Course # 3412)
Precalculus – High Honors
This rigorous course will provide the students with a strong background for Calculus (AB) or Calculus HH. Topics include trigonometry, advanced graphing, polynomial functions, logarithm and exponential functions, complex numbers in polar form, polar graphing, limits, and continuity will be studied in depth. An introduction to Differential Calculus will also be included. The course will also focus on the theoretical development of each of these topics, and emphasis will be placed on higher order thinking skills and challenging applications. Use of the graphing calculator will be essential to the course. (Grade 11 or 12) (Course # 3413)
Calculus
This course is open to students who have successfully completed Precalculus. The course will include a study of limits, continuity, the basic rules of differentiation, as well as applications of differentiation to curve sketching and word problems involving related rates and optimization. The derivative of the exponential and logarithmic functions will also be studied. Techniques of integration will be introduced. Limits of trigonometric functions and differentiation and integration of trigonometric functions will not be studied in this course. (Grade 12) (Course # 3401)
Calculus – High Honors/Middle College Program
In this course, students will continue to study the concepts of limits and continuity. The basic concepts of the derivative with its applications to velocity, acceleration, curve sketching, related rates, and max-min problems will be studied in the first semester. The definite and indefinite integral will be introduced during second semester. Techniques of differentiation and integration of the trigonometric functions, the natural logarithmic function, the exponential function and the inverse trigonometric functions will be studied. Integration will be applied to finding area and volume. (Grade 12) (Course # 3403)
Calculus (AB) - Advanced Placement
Students will continue to study limits and continuity begun in Precalculus. An introduction to the basic concepts of differential and integral calculus with applications to velocity, acceleration, curve sketching, related rates and max-min problems will be given. Techniques of differentiation and integration will be studied and applied to areas, radioactive decay, and volumes and surface areas of revolution. The theoretical development of each of these topics will be stressed. The course concludes with the Advanced Placement Examination in May. (Grade 12) (Course # 3404)
Additional Mathematics Courses
Probability and Statistics
This full-year mathematics course will cover basic concepts in statistics and probability. Emphasis will be placed on the collection, processing, analysis and interpretation of numerical data, as well as probability theory and combinatorics. This course will be highly beneficial not only to students planning to study mathematics and science but also to those who wish to pursue a career in the social sciences or business (for example Sociology, Psychology, Economics). TI-84 Graphing Calculator is required. (Grade 12) (Course # 3421)
Statistics - Advanced Placement
This course is open to juniors and seniors who have successfully completed Precalculus-Honors or Precalculus-High Honors or who are taking either of these courses simultaneously with AP Statistics. The focus of this course is on problem solving. The course will introduce students to the major concepts and tools for collecting, analyzing and drawing inferences from data. Students will concentrate on the following topics: exploring data, planning a study, anticipating patterns and statistical inferences. TI-84 Graphing Calculator is required. (Grade 11 or 12) (Course # 3424)
Introduction to Computer Science
Introduction to Computer Science is a full year course which handles fundamental ideas of Computer Science. Through lecture and projects, students will be given hands on experience with computer, programming and coding skills that gear towards the technology industry. Students will be given insight into the many career opportunities that study in Computer Science can make them available to. (Grade 10, 11 or 12) (Course #3801)
Computer Science A - Advanced Placement
The AP Computer Science A course is equivalent to a first-semester, college-level course in computer science. The course continues to make students familiar with fundamental computer science topics such as: problem solving, design strategies, organization of data, approaches to processing data, analysis of potential solutions, data structures, abstraction and the ethical and social implications of computing. The course uses the programming language Java to emphasize object-oriented programming methodology with a focus on problem solving and algorithm development. (Grade 11 or 12) (Course # 3704) | 677.169 | 1 |
This book details developments that have led to the introduction of many innovative statistical tools for high-dimensional data analysis. It takes a broad perspective, covering both linear and nonlinear methods graduate level text based partly on lectures in geometry, mechanics, and symmetry given at Imperial College London, this book links traditional classical mechanics texts and advanced modern mathematical treatments of the subject. more... | 677.169 | 1 |
Overview
The best-selling A TRANSITION TO ADVANCED MATHEMATICS, 8TH EDITION helps students bridge the gap between calculus and advanced math courses. Students gain a foundation in the major concepts needed for continued study as they learn to express themselves mathematically, analyze a situation, extract pertinent facts, and draw appropriate conclusions. The authors introduce modern algebra and analysis with an emphasis on reading and writing proofs and spotting common errors in proofs. Clear explanations and detailed examples support concepts, while exercises provide practice in routine and more challenging problems. Students master the mathematical reasoning for later courses while learning how mathematicians approach and solve problems.
Meet the Author
Doug Smith,
University of North Carolina at Wilmington
The authors are the leaders in this course area. They decided to write this text based upon a successful transition course that Richard St. Andre developed at Central Michigan University in the early 1980s. This was the first text on the market for a transition to advanced mathematics course and it has remained at the top as the leading text in the market. Douglas Smith is Professor of Mathematics at the University of North Carolina at Wilmington. Dr. Smith's fields of interest include Combinatorics / Design Theory (Team Tournaments, Latin Squares, and applications), Mathematical Logic, Set Theory, and Collegiate Mathematics Education.
Richard St. Andre,
Central Michigan University
Richard St. Andre is Associate Dean of the College of Science and Technology at Central Michigan University. Dr. St. Andre's teaching interests are quite diverse with a particular interest in lower division service courses in both mathematics and computer science.
Features & Benefits
The authors follow a logical development of topics, and write in a readable style that is consistent and concise. As each new mathematical concept is introduced the emphasis remains on improving students' ability to write proofs.
Worked examples and exercises throughout the text, ranging from the routine to the challenging, reinforce the concepts.
A flexible organization allows instructors to expand coverage or emphasis on certain topics and include a number of optional topics without any disruption to the flow or completeness of the core material.- | 677.169 | 1 |
book is an independent source of problems with detailed answers beneficial for anyone interested in learning complex analysis. The problems cover such topics as: power series, Cauchys theorem, Laurent series, singularities and meromorphic functions, the calculus of residues, conformal mappings, and Jensens formula. All the exercises from this volume were derived from Serge Lang's fourth edition of Complex Analysis and can also serve as a companion guide to it.
is a collection of exercises in the theory of analytic functions, with completed and detailed solutions. We wish to introduce the student to applications and aspects of the theory of analytic functions not always touched upon in a first course. Using appropriate exercises we wish to show to the students some aspects of what lies beyond a first course in complex variables. We also discuss topics of interest for electrical engineering students (for instance, the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). Examples of important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space) are given. The book also includes a part where relevant facts from topology, functional analysis and Lebesgue integration are reviewed.
The book Complex Analysis through Examples and Exercises has come out from the lectures and exercises that the author held mostly for mathematician and physists . The book is an attempt to present the rat her involved subject of complex analysis through an active approach by the reader. Thus this book is a complex combination of theory and examples. Complex analysis is involved in all branches of mathematics. It often happens that the complex analysis is the shortest path for solving a problem in real circum stances. We are using the (Cauchy) integral approach and the (Weierstrass) power se ries approach . In the theory of complex analysis, on the hand one has an interplay of several mathematical disciplines, while on the other various methods, tools, and approaches. In view of that, the exposition of new notions and methods in our book is taken step by step. A minimal amount of expository theory is included at the beinning of each section, the Preliminaries, with maximum effort placed on weil selected examples and exercises capturing the essence of the material. Actually, I have divided the problems into two classes called Examples and Exercises (some of them often also contain proofs of the statements from the Preliminaries). The examples contain complete solutions and serve as a model for solving similar problems given in the exercises. The readers are left to find the solution in the exercisesj the answers, and, occasionally, some hints, are still given.
In the pages that follow there are: A. A revised and enlarged version of Problems in analysis (PIA) . (All typographical, stylistic, and mathematical errors in PIA and known to the writer have been corrected.) B. A new section COMPLEX ANALYSIS containing problems distributed among many of the principal topics in the theory of functions of a complex variable. C. A total of 878 problems and their solutions. D. An enlarged Index/Glossary and an enlarged Symbol List. Notational and terminological conventions are to be found for the most part under Conventions at the beginnings of the chapters. Spe cial items not included in Conventions are completely explained in the Index/Glossary. The audience to which the current book is addressed differs little from the audience for PIA. The background of the reader is assumed to include a knowledge of the basic principles and theorems in real and complex analysis as those subjects are currently viewed. The aim of the problems is to sharpen and deepen the understanding of the mechanisms that underlie modern analysis. I thank Springer-Verlag for its interest in and support of this project. State University of New York at Buffalo B. R. G. v Contents The symbol alb under Pages below indicates that the Problems for the section begin on page a and the corresponding Solutions begin on page b. Thus 3/139 on the line for Set Algebra indicates that the Problems in Set Algebra begin on page 3 and the corresponding Solutions begin on page 139.
Over 1500 problems on theory of functions of the complex variable; coverage of nearly every branch of classical function theory. Topics include conformal mappings, integrals and power series, Laurent series, parametric integrals, integrals of the Cauchy type, analytic continuation, Riemann surfaces, much more. Answers and solutions at end of text. Bibliographical references. 1965 edition. | 677.169 | 1 |
Writing 116: Writing in the Natural Sciences
Habecker/ Spring 2017
Technical Explanation for a Lay Audience (TELA)
Topic:
Select a relatively current scientific topic that interests you; topics can be found in original research
articles, in the news, in p
J.G. Pieters, G.G.J. Neukermans, M.B.A. Colanbeen, Farm-scale Membrane Filtration
of Sow Slurry, Journal of Agricultural Engineering, No. 73, 403-409, 1999.
One way to assess the uses of membrane filtration is to test it against the most complex and
chall
Math 46 Sec 1
Ordinary Differential Equation
What is a differential Equation?
We learned a lot about solving equations in pre-calculus
and calculus. For example, we learned to solve
x^2+ 3x+2=0
or
sin(y) +y =0
where the unknowns in the equations are numbe
LECTURE 2, WHAT IS DIFFERENTIAL EQUATION?
PO-NING CHEN
Here are the things we will learn today:
(1)
(2)
(3)
(4)
(5)
(6)
What is a differential equation?
What is an ordinary differential equation?
What is the order of a differential equation?
How to verify
LECTURE 5: SEPARABLE EQUATION
PO-NING CHEN
Today we will first review the Bernoulli equation and then we will derive the general
solutions of the separable equations.
y0 =
(1)
(2)
(3)
(4)
(5)
F (x)
G(y)
Review of Bernoulli equation
General Solution of sep
Lecture 15
Variation of Parameter
Mar 7th, 2017
Outline
Today, we use the method of Variation of Parameter to solve
y 00 + p1 (x)y 0 + p2 (x)y = q(x)
where p1 (x), p2 (x) and q(x) can be arbitrary functions.
The method is based on the solution of the homo
Lecture 3
Linear equation
Topics for today
Today, we will learn the following topics:
(1) Classification of first order equations.
(2) Linear first order equations
Classification of first order equations
We also observed that a differential equation might
LECTURE 4, LINEAR FIRST ORDER DIFFERENTIAL EQUATIONS
PO-NING CHEN
Today we will learn the classification of first order equation and learn how to solve the
inear first order equation
y 0 + p(x)y = q(x)
using the method of integrating factors.
(1) Classifi
Lecture 16
Higher order linear equation
Mar 8, 2016
Outline
Today, we introduce higher order linear equation.
We will first go over the general theory of higher order linear equation and
homogenous equation.
Then, we study higher order homogenous equation
Lecture 11
Repeated root and reduction of order
Feb 21, 2017
Outline
Last time, we studied 2nd order linear equation with constant coefficients
y 00 + ay 0 + by = 0
where the characteristic equation
r 2 + ar + b = 0
has a repeated root.
This is also a nat | 677.169 | 1 |
David Rayner Mathematics 9 Answers
... contains important information and a detailed explanation about david rayner mathematics 9 answers ... which is also related with , cord algebra part b answers pdf, precalculus - sites.math.washington.edu, precalculus - university of washington.
What general ideas will guide the way you will teach math- ematics? ... message the mathematics taught at each grade level needs to focus, go . Principles and Standards for School Mathematics 3 logical thinking that helps us decide if and why our answers excellent resources to help you envision your role as a.
ebook.dexcargas.com is a PDF Ebook search engine and unrelated to Adobe System Inc. No pdf files hosted in Our server. All trademarks and copyrights on this website are property of their respective owners. | 677.169 | 1 |
Derivatives of Trig Functions Digital Task Cards with GOOGLE Slides
PDF (Acrobat) Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
1.71 MB | 24 including key and directions pages
PRODUCT DESCRIPTION
This Google® resource is a new engaging way to have your students practicing finding derivatives of the trig functions while using technology in a paperless environment. Plus, it is NO PREP for you.
Activity Based Learning with Task Cards really works to help reinforce your lessons. Task Cards get your students engaged and keep them motivated without overwhelming then with a huge boring worksheet. This set of 16 task cards will help students practice finding the derivative of Trigonometric Functions using the Chain Rule.
This lesson is designed for AP Calculus AB, AP Calculus BC and College Calculus 1 and is designed to help your students stay involved and thoroughly understand and master the concepts in this section.
Included in this GOOGLE resource:
✓ 16 Digital task cards finding the derivative of trig functions involving the chain rule.
✓ Answer keys
✓ Optional QR code answer sheet which you can post or project on the board via a computer for checking.
✓ A digital Drag & Drop interactive students response sheet. After finding the derivative, student go to the last slide and Drag and Drop the correct solution onto the answer blanks. There are more choices than problems, making sure they don't guess. I have also included a printable version of the student response sheet should you want that.
✓ Additional printable handout worksheet with 10 problems. This can be used as HW, an assessment, or enrichment.
Note: You and your students must have access to the internet and have individual FREE Google Drive Accounts to use this resource. Increases student engagement and can be accessed from anywhere | 677.169 | 1 |
Richard H. Enns, «Computer Algebra Recipes for Mathematical Physics»
Over two hundred novel and innovative computer algebra worksheets or "recipes" will enable readers in engineering, physics, and mathematics to easily and rapidly solve and explore most problems they encounter in their mathematical physics studies. While the aim of this text is to illustrate applications, a brief synopsis of the fundamentals for each topic is presented, the topics being organized to correlate with those found in traditional mathematical physics texts. The recipes are presented in the form of stories and anecdotes, a pedagogical approach that makes a mathematically challenging subject easier and more fun to learn. Key features: * Uses the MAPLE computer algebra system to allow the reader to easily and quickly change the mathematical models and the parameters and then generate new answers * No prior knowledge of MAPLE is assumed; the relevant MAPLE commands are introduced on a need-to-know basis * All recipes are contained on a CD-ROM provided with the text * All MAPLE commands are indexed for easy reference * A classroom-tested story/anecdote format is used, accompanied with amusing or thought-provoking quotations * Study problems, which are presented as Supplementary Recipes | 677.169 | 1 |
Calculator Prompter is a math expression calculator. Calculator Prompter has a built-in error recognition system that helps you get correct results. With Calculator Prompter you can enter the whole expression, including brackets, and operators | 677.169 | 1 |
PreCalculus: Conics in the Real World Stations Activity
PDF (Acrobat) Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
2.99 MB | 15 + 2 Keys pages
PRODUCT DESCRIPTION
PreCalculus: Conics in the Real World *Task Cards* Activity
This activity is designed to help your Pre-Calculus students review key concepts at the end of the unit on Analytic Geometry. There are 10 stations in the activity. Great fun for students to collaborate and cooperate. The activity includes a student answer sheet for recording work.
Concepts include the following:
1. Equations for Circles of a Ferris wheel
2. Properties of elliptical ceilings
3. Finding a parabola to model the Golden Gate Bridge
4. Halley's comet, eccentricity and maximum distance of orbit.
5. Hyberbolic pathways of atom
6. Creating a parabolic satellite dish
7. Earth's orbit around the Sun.
8. Air traffic control flight path for a plane
9. Apogee and Perigee of the Moon'a orbit around Earth.
10. Ability to pass under a parabolic shaped bridge | 677.169 | 1 |
...
Show More practice with excellent examples and computer programs. The programs help students perform 3 types of calculations; relatively simple calculations, calculations designed to provide solutions for steady state system operation, and unsteady flow simulations | 677.169 | 1 |
Successful game programmers understand that in order to take their skills beyond the basics, they must have an understanding of central math topics; however, finding a guide that explains how these topics relate directly to games is not always easy.
Is the art for your video game taking too long to create? Learning to create Pixel Art may be the answer to your development troubles. Uncover the secrets to creating stunning graphics with Pixel Art for Game Developers.
Successful game programming requires at least a rudimentary understanding of central math topics. While most books neglect the point-by-point details that are necessary to truly hone these skills, Beginning Pre-Calculus for Game Developers tackles each task head on, using easy-to-understand, hands-on exercises.
Successful game programmers understand that in order to take their skills beyond the basics, they must have an understanding of central math topics; however, finding a guide that explains how these topics relate directly to games is not always easy. Beginning Math Concepts for Game Developers is the solution! | 677.169 | 1 |
Based on a lecture course at the Ecole Polytechnique (Paris), this text gives a rigorous introduction to many of the key ideas in nonlinear analysis, dynamical systems and bifurcation theory including catastrophe theory. Wherever appropriate it emphasizes a geometrical or coordinate-free approach which allows a clear focus on the essential mathematical structures. Taking a unified view, it brings out features common to different branches of the subject while giving ample references for more advanced or technical developments | 677.169 | 1 |
7th Grade Math Worksheets – Topics To Study
You know you are going to be faced with the same hurdle – 7th grade math worksheets – only this time you are doing more advanced topics than those you encountered in the 6th level. Actually, there's just a bit of an addition that's going to happen. Meaning, some of the things you've learned from math 6 are carried over to the 7th level, some of these are even repetitions or reviews of topics back a year ago.
7th Grade Math Worksheets – Generalizations Of Past Concepts
But there are really new concepts that are somehow alienated from the topics a year ago, little different topics but advanced. For instance, there's Geometry part dealing with the figures – segments, rays, angles, parallel lines, parallelograms, quadrilaterals, etc. – that you have learned in the 6th. This time around, you will take up generalizations about them. So, instead of just counting the angular measures and trying to illustrate these figures, your worksheets will be filled with general statements, axioms, theorems and proving assumptions or theories.
An Example
Let us take parallel lines in grade 6. They form pairs of equal angles when these lines are cut or intersected by another line. As part of your worksheet exercises, you will be asked to show or prove that indeed these pairs of angles are equal in measure. Conversely, you will have to show that two lines are parallel, given that some angles are either supplementary or equal in measure.
That sort of stuff is an example of new topics ahead. It's going to make your head spin, like it did to me, but there's a clean way out of this predicament.
7th Grade Math Worksheets – Start Ahead
That is the way to do it – work out some of the coming math loads while you have free time. While the 6th grade concepts are fresh in your mind, do some advanced learning. Some of the important questions that you should ask while tackling new topics are:
What does the new topic mean? What are the new terminologies that are used for this section of the book or manual? What is the coverage of these new topics? In short, define clearly these new topics.
What are the theorems, postulate, kinds of exercises, and types of questions in this section? What is the standard way of solving these problems? What should I expect the teacher to ask of me? What are the given items for each type of problems? Do I have to reviews past concepts as preparation for learning these new topics?
The Topics In Brief Overview
Above, I mentioned about parallel lines. That example is a part of Geometry learning. Apart from this part, you will have to study about similar triangles and congruent triangle. A special section in Geometry is devoted to studying right triangles and non-right triangles (properly called oblique triangle).
Probability and Statistics is another main topic. This one tackles the methods by which we gather data and interpret data. Your teacher will be talking a lot about percentages, predictions and central tendencies in this part of the study.
You will also deal with relations and functions. This is where you will have to graph lines, circles, parabolas, hyperbolas and so on and so forth. Study how to graph these figures as early as you can because the concepts in this part of the study you can use when you go to college.
I wouldn't like to tax your mind more. What I have mentioned here is about 75% of the things you will be dealing with. The 25% will come naturally in the course of your discussions.
Remember to take things in your stride. Relax. Hurdling 7th grade math worksheets is easier if you will approach the task this way. | 677.169 | 1 |
Specialist Mathematics with CD-Rom
Overview
The original text has been completely rewritten for the 2000 Mathematics Study Design and has taken in the many suggestions and requests provided by teachers. Essential Specialist Mathematics provides a single unified course of study which addresses all the key knowledge and skills outcomes. It includes new graphics calculator questions, exercises and theory and includes revision chapters for efficient examination preparation. Included are analysis exercises, multiple choice questions and applications. Current technology is addressed with applications to theory and exercises, and there are answers to all questions. The CD includes navigation by chapter and chapter section as well as the Cambridge Specialist Mathematics Tutor CD-ROM which is a self-help bank of multiple choice questions to consolidated knowledge. | 677.169 | 1 |
9th Grade Math
9th
grade math lessons are planned and introduce
in different activities. 9th grade math help is provided for the 9th
grade students in all segments to cover all the math lesson plans which are categorized into Arithmetic, Algebra, Geometry and Mensuration.
All types of solved
examples on different topics are explained along with the step-by-step solutions.
9th
grade math practice sheets
are arranged in such a way that students can learn math while practicing math
problems.
Keeping in mind the mental level of student
in ninth grade, every efforts has been made to introduce new concepts in a
simple and easy language, so that the students can understand the problems easily.
The difficulty level of the 9th grade math problems
has emphasized the theoretical as well as the numerical aspects of the
mathematics course. Each topic contains a large number of examples to
understand the applications of concepts. | 677.169 | 1 |
Aimed at effectively delivering the 2008 framework, the Pupil Books are packed with functional maths questions and spreads and ensure progression by providing differentiated material for each level. Year 7 Pupil Book 1 will help students working at levels 3- 4 to make a smooth transition from Key Stage 2 to Key Stage 3. The Pupil Book offers: * Fully integrated functional maths questions and exciting real-world spreads to put maths into context and help your pupils to develop vital functional skills * Colour-coded levelling on every piece of content so that pupils always work at the right level and progress with ease * "Student friendly" learning objectives from the New Framework for every chapter, promoting personalised learning and self assessment * Level boosters for every chapter to put learning into pupils' hands, telling them what they need to know and how to improve * Worked examples to aid understanding, easing the class into each exercise * Extension activities to stretch and challenge * Test-style levelled questions providing excellent test preparation * Full colour artwork to engage students See Teacher Pack for additional support and answers.
"synopsis" may belong to another edition of this title.
About the Author:
Collectively, Evans, Gordon, Speed and Senior have over 100 years of teaching experience, both in the classroom and leading maths departments. They all currently hold senior positions within examining bodies and have been extensively involved in the development and piloting of new specifications. With an incredible range of outside interests, including flying planes, riding motorbikes, starring in local productions and travelling the world, they bring maths to life with an outstanding range of engaging real-life situations and applications. | 677.169 | 1 |
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