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About this book
Introduction
Calculus Made Easy has been a classic introduction to the subject ever since it was first published by Silvanus P.Thompson in 1910. In the first major revision of the text since 1946, Martin Gardner - the 'Mathematical Games' columnist for Scientific American and author of over 50 books and innumerable articles - has thoroughly updated the text to reflect recent developments in method and terminology, written an extensive preface and three new chapters, and added more than 20 recreational problems for practice and enjoyment. He has transformed this classic primer into a modern masterpiece that explains the timeless concepts of calculus in a contemporary and user-friendly voice. | 677.169 | 1 |
Web-based resources on Numerical Methods are presented for engineering undergraduates. It is dedicated to reaching a large...
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Web-based resources on Numerical Methods are presented for engineering undergraduates. It is dedicated to reaching a large audience of undergraduate students through its holistic but customized approach. Holistically, the resources review background information; present numerical methods through youtube videos, notes, presentations, simulations and assessments; show how what they learned is applied in real life; tell stories to illustrate special topics and pitfalls; and give historical perspectives. From a customized perspective, the user can choose a major of choice - Chemical, Civil, Computer, Electrical, General, Industrial or Mechanical Engineering, and a language of choice - Maple, Mathcad, Matlab, Mathematica to illustrate algorithms, convergence and pitfalls of the numerical methods.
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Mar 29, 2003aCalc is a customizable calculator designed with the user in mind. Users can specify operations and relationships between...
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In this course, you will be Introduced to several methods of numerical approximation such as error analysis, root finding,...
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In this course, you will be Introduced to several methods of numerical approximation such as error analysis, root finding, interpolation, polynomial approximation and the direct methods for solving linear equations. During five weeks of the course, you will be learning these methods and compare them as well. The course is divided into five weeks where each week you will find a set of video lectures posted with a PDF version of lecture notes as well.
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Although classified as a course, this resource can be used as a textbook.This class introduces elementary programming...
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Although classified as a course, this resource can be used as a textbook.This class introduces elementary programming concepts including variable types, data structures, and flow control. After an introduction to linear algebra and probability, it covers numerical methods relevant to mechanical engineering, including approximation (interpolation, least squares and statistical regression), integration, solution of linear and nonlinear equations, ordinary differential equations, and deterministic and probabilistic approaches. Examples are drawn from mechanical engineering disciplines, in particular from robotics, dynamics, and structural analysis.
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This is a free, online textbook that is part of a series. According to the author, it "completes the material on Real...
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This is a free, online textbook that is part of a series. According to the author, it "completes the material on Real Analysis that is the foundation for later courses in functional analysis, harmonic analysis, probability theory, etc. The first chapter extends calculus to n-dimensional Euclidean space and, more generally, Banach spaces, covering the inverse function theorem, the implicit function theorem, Taylor expansions, etc. Some basic theorems in functional analysis, including the open mapping theorem and the Banach-Steinhaus uniform boundedness principle, are also proved. The text then moves to measure theory, with a complete discussion of outer measures, Lebesgue measure, Lebesgue-Stieltjes measures, and differentiation of set functions. The discussion of measurable functions and integration in the following chapter follows an innovative approach, carefully choosing one of the equivalent definitions of measurable functions that allows the most intuitive development of the material. Fubini's theorem, the Radon-Nikodym theorem, and the basic convergence theorems (Fatou's lemma, the monotone convergence theorem, dominated convergence theorem) are covered. Finally, a chapter relates antidifferentiation to Lebesgue theory, Cauchy integrals, and convergence of parametrized integrals. Nearly 500 exercises allow students to develop their skills in the area.
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Apr 26, 2010 Mathematical Visualization Toolkit material found in MERLOT at...
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An author's Snapshot for Mathematical Visualization Toolkit material found in MERLOT at This material is a MERLOT classic award winner and an Editors choice winner. This snapshot shows an overview of the material. This was created in the MERLOT Content Builder.
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James Rutledge root approximating methods by simply filling in the starting endpoint A, the...
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This applet allows a person to test several root approximating methods by simply filling in the starting endpoint A, the endingendpoint B, the formula, selecting the method, and pressing the calculate button. For example try typing in 0 for A, 1 for B, andy=x^2-2 for the formula. Press calculate. For each repetition of the method a new line wil be generated in the large text area at the bottom. For equations, which make themethods run many times, you may need to scroll down to the bottom of this text area to view the final output.
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Aug for Estimating RootsNumerical Computing with MATLAB is a textbook for an introductory course in numerical methods, MATLAB, and technical...
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״Numerical Computing with MATLAB is a textbook for an introductory course in numerical methods, MATLAB, and technical computing. It emphasizes the informed use of mathematical software. Topics include matrix computation, interpolation and zero finding, differential equations, random numbers, and Fourier analysis. Based on MATLAB, the textbook provides more than 70 M-files. Many of the more than 200 exercises involve modifying and extending these programs. The book also makes extensive use of computer graphics, including interactive graphical expositions of numerical algorithms." Individual chapters can be downloaded as separate pdf files and while curriculum tools and materials can also be downloaded.
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Summary of the ENP Maths Curriulum: Collège and Lycée
Students doing the Maths option in the English National Programme in 6ème and 5ème focus on improving their thinking skills by using them to solve Mathematical problems. They learn new Mathematical skills through problem solving. The use and application of Mathematics to solve problems is taught using UK-based pedagogical approaches and resources. Students work in groups and individually to solve problems and to improve their understanding of mathematics. They complete a number of projects throughout the year and are assessed on their ability to explain their mathematical thinking both orally and in written form. The course is best suited to those who enjoy Mathematics and who wish to explore the application of Mathematics. Students doing the Maths option in the English National Programme in 4ème and 3ème prepare during these two years for the GCSE Statistics examination. This examination is assessed by means of a 2 hour written paper (taken in June at the end of troisième) and a Controlled Assessment Project completed in the second term of 3ème. This course is suitable for students who enjoy working with numbers and analysing data. The course will equip students with inquiry and analysis skills.
Students doing the Maths option in 2nde and 1ère follow the exam syllabii for the GCSE Mathematics and the Advanced Subsidiary Mathematics courses. This is a demanding programme which leads to a public examination at the end of seconde (GCSE Mathematics) and for suitable candidates to a second public examination (AS Mathematics) at the end of Première. Students enrolling on this course should have a strong mathematical background, should enjoy the subject and be motivated to work hard to meet the demands of a challenging curriculum taught over two years.
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In this activity we define a function and develop an understanding of function notation by comparing statements we already understand in English to equivalent statements written in "math" language.
The prerequisites for this lesson are knowing how to read a graph or a table of values and how to use a formula to make a calculation.
Subsection1.1.1What is a Function?
The mathematical concept of a function can be extremely complicated. It took thousands of years to come up with it, define it and formalize it. For example, just look at this definition from Wikipedia (do not spend too much time on it.)
You could spend your whole life learning about what a function is and never get to the rest of this book! For this reason we will keep things simple and informal in order to attain a quick and accessible understanding of topics, including functions. Students continuing in mathematics will add to their knowledge of functions as needed and as part of a life-long process.
Start by remembering this: one input, one output.
A function is a rule that takes a piece of "usable" information that you choose (input) and gives you some kind of result (output). By "usable" we mean information that has meaning for the function.
Think of a function as a sort of machine. Using some input, the machine does something to the input and then out pops a result. In this course our inputs will be mostly numbers and the process will yield numbers as results.
Exercise1.1.1
A simple example of a function is a temperature converter. It converts a temperature from degrees Fahrenheit to degrees Celsius.
The function is the rule or process used to convert from one unit of temperature to the other.
How do we communicate that we have a function? There has to be a simple or quick way to communicate we have a function.
What kinds of inputs can the function use? The temperature function in the previous exercise could only accept temperatures between \(-60\) and \(110\) degrees Fahrenheit. The input of \(150\) degrees \(F\) is not usable because it is not available to choose.
What are the possible output temperatures in degrees Celsius? Is any temperature possible or is there a window of reasonable temperature expectations?
How are the two temperature units related? If you increase degrees F, does the temperature in degrees \(C\) also increase?
We start with notation. We don't want to keep writing the word, F U N C T I O N, all the time. That's just way too many letters.
Subsection1.1.2Math as a Language
Math is just another language. We use it to communicate measurements, changes in value and how things are related to or affect one another. Almost everything you say or describe in Math, you can say or describe in English.
In this next exercise we learn to communicate the position of a train as time passes and develop the notation to express where the train is at different times. We will assume that this train runs on time, every day and the conditions every day are the same. You know, an alternate universe called "example land".
Subsection1.1.3The Grammar of Function Notation
The math "sentence" above is actually an equation and it uses function notation to express the information about the train's position at a particular time.
In math we don't really have subjects or verbs or objects. Instead we have input values (numbers) and we have output values. The function is the "machine" or the rule that tells us how to use the input to make an output.
Variables are used to represent values we don't know or that may change. For a function, the input is called the independent variable, and the output is called the dependent variable. This is because the output depends on the input.
The distance from downtown is constantly changing with time, so we can let the dependent variable \(D\) represent the "Train's distance in miles from downtown". Similarly, we can use the independent variable \(t\) to represent the "number of hours after \(8\) a.m.".
Typically, we use variables that have something to do with the context of the problem, but sometimes we generalize an expression or equation with \(x\)'s and \(y's\) when we have nothing specific in mind.
Variables have units
If the variables represent actual things or events, we must define them to include the units we used to measure the event. This allows us to extract meaning from the values or expressions.
If you know Spanish you can interpret the meaning of a Spanish article you read by translating it into English. Likewise, if you know "math", you can interpret the meaning of function notation by translating it into English, provided you know what the variables in the notation mean or what they are measuring.
If \(D\) represents distance, you must define the units in which the distance is measured: miles, inches, centimeters, light years, etc.
If \(t\) represents time, will it be measured with units of seconds, hours or years?
Since the position of the train depends on the amount of time that has passed, we say "the distance depends on time". More specifically, we say that the distance of the train from downtown is a function of time.
Function notation allows us to communicate that distance is a function of time by simply writing \(D = f(t)\text{.}\) The notation \(f(t)\) is read as, "\(f\) of \(t\)".
Remember \(t\) is a value. The function uses \(t\) to create the value \(D\text{.}\)
Also, don't confuse the notation with multiplication! The expression \(f(t)\) does not mean \(f\) times \(t\text{.}\)
Note1.1.3
The word "function" usually refers to the actual rule which turns the input into the output. Sometimes, however, we will use it to describe the output of the relationship.
Exercise1.1.4
Function notation like \(f(t)\) or \(f(x)\) or \(f(\text{anything})\) implies there is some kind of relation, some kind of rule, that takes a piece of information and returns a response or result. The format of function notation works on the basic principle of input and output and we often use the notation when we refer to things we don't yet know.
For instance, if you work as a health assistant, you probably earn some hourly salary and you probably work some number of hours each week. I have no idea how many hours a week you work and no idea how much you earn. But I do know your weekly salary is related to the number of hours you work. In fact, your weekly salary is a function of the number of hours you work.
If \(t\) is the number of hours you work and \(S\) is your weekly salary, I can use function notation to say \(S = f(t)\text{,}\) where \(f\) is the function, the instructions, that calculates your weekly salary. If you work \(12\) hours, then \(t = 12\text{,}\) so \(f(12)\) is your weekly salary for working \(12\) hours.
Notice I still don't know what the salary actually is, but I can use function notation to talk about it. The expression \(f(12)\) literally means, "whatever you earn when you work \(12\) hours."
In our train example we chose some input, a time, and the function gave us an output of distance. The notation tells the reader what the input is by showing it in the parentheses:
\begin{equation*}
f(\text{input}) = \mathit{output}
\end{equation*}
The function notation \(f(0)\) is telling us the input is \(0\text{.}\) That means, "\(0\) hours after \(8\) a.m." In other words, it's \(8\) a.m.
On the other hand, \(f(0)\) represents an output. It is "the train's distance from downtown, \(0\) hours after \(8\) a.m." But we don't know what that distance actually is yet. In this case, the notation \(f(0)\) means "Whatever the distance is at t = 0".
Nonetheless, the input and output create an ordered pair \((0, f(0))\text{.}\) On a graph the ordered pair is a point.
Exercise1.1.5
Exercise1.1.6
Subsection1.1.4How to Determine if a Relation is a Function or Not
When two or more variables are related to each other, the formula or rule that relates them is called a relation. For people, there is a relation between age and height. You can make ordered pairs of \((\text{age}, \text{height})\) for different people and plot the points on a graph. You might even find a formula that predicts height based on age (or vice versa?)
In every relation you have encountered so far in this chapter, each input gives you only one output. For the train example we saw earlier, we had the function \(D = f(t)\text{.}\) At any given time, like \(t = 10\text{,}\) the train can only be in one place, \(f(10)\text{.}\) It's not possible for the train to be in two or more places at the same time.
Also, notice that each input has its own unique output. Every day at \(t = 10\text{,}\) the train is always in the same place: \(f(10) = 30\) (it's a very dependable train). These two conditions make the relation a function. Position is a function of time.
But not all relations are functions. Just because two things are related does not mean one is a function of the other.
Twice each day, the train is \(30\) miles away from downtown — once in the morning on its way out, then later in the afternoon on the way back into town. If we choose position as input and time as output, we realize that the input \(D = 30\) gives us two answers: one time in the morning and another in the afternoon. Thus time is not a function of position. All we have is a relation.
Exercise1.1.7
A table of values is one way to express the inputs and outputs of a relation. In a vertical table, the inputs are on the left, and the outputs are on the right. In a horizontal table, the top row is the input, and the bottom row is the output.
Input
Output
input
output
input
output
input
output
Table1.1.8Vertical Table
Input
input
input
input
Output
output
output
output
Table1.1.9Horizontal Table
Exercise1.1.10Determine if the relation in each table is a function or not
Exercise1.1.11Determine if each equation makes \(y\) a function of \(x\)
It is easy to tell whether a graph represents a function or not. Remember that the inputs are found along the horizontal axis, and the outputs are found along the vertical axis. When deciding whether the graph is a function, the rule is the same: one input, one unique output.
Exercise1.1.12Determine if the graph is a function
The previous example leads us to a simple test we can use to determine if a graph is a function or not: The vertical line test.
Given a graph, draw a vertical line through any place on the graph. If the vertical line crosses the graph at most one time (no matter where you draw the line), then the graph is a function. If the vertical line crosses the graph anywhere at more than one point, then the graph is not a function.
Exercise1.1.14
In general when the inputs and outputs are nothing in particular, we use \(x\) as input and \(y\) as output so that \(y = f(x)\text{.}\) We use "\(x\)" as a placeholder for the actual input value, while "\(y\)" is a placeholder for whatever the output value will be. The \(x\) basically says, "When you get the input, put it here" in all the places where the \(x\) is found.
Consider the function \(f(x) = 50x + 10\text{.}\) The function has no context (no story), so we won't bother using units for either \(x\) or \(y\text{.}\)
If \(x = 1\text{,}\) then we can evaluate \(f(1)\) by replacing the \(x\) in the formula with a \(1\text{.}\) Literally, \(f(1)\) means "what you get when you put \(1\) in the place of \(x\)".
Similarly, if you change the input to \(x = 2\text{,}\) then you can evaluate the expression \(f(2)\text{,}\) which is "what you get when you put \(2\) in the place of \(x\)".
Subsection1.1.7Solve
What if the output, the result, is already known and we want to know all the inputs that give us this result? This is called solve.
If you live in Oregon in the winter, you might ask, "What time will the temperature outside be \(37\) degrees Fahrenheit?" Typically there might be two answers to this question, one time in the morning and another time in the afternoon.
You could answer the question with actual times if you had a time vs. temperature graph, or a formula, or a table of times and temperatures.
Solving means to work backward from a known output value, in order to determine all the inputs that give us the desired output.
Suppose we want the output of a function to be \(y =0\text{.}\) Therefore, we must find all the input values of \(x\) that give us that result. There may not be any, but there could be one, several or even infinite possible inputs that give \(y = 0\) as the output.
Exercise1.1.18
In English we could ask the question for the example in the previous exercise:
What input makes the output equal to \(0\text{?}\)
There would be three answers:
\begin{equation*}
x = - 4 , -1\text{ or }2
\end{equation*}
All of these values of \(x\) give us the same result of \(y = 0\text{.}\)
In math we could ask the same question, but it comes out as a command:
Solve \(f(x) = 0\)
In other words, "Find the input that gives you a particular result". In our case, the result we want is an output value of \(0\text{.}\) There are still three answers to the question and each answer is called a "solution".
The statement:
Solve \(f(x) = 0\)
has three solutions:
\begin{equation*}
x = -4, -1 \text{ or }2
\end{equation*}
If we look at functions graphically, the math sentence
Solve the equation \(f(x) = K\)
where \(K\) is some number, means to "find all the \(x\)-values where the graph of the function reaches a height of \(K\) units." This equation may have zero, one, several, or even infinite solutions.
Even equations where a formula equals another formula can be solved graphically. Consider
\begin{equation*}
2^x + 0.025 = 0.55x - 0.3
\end{equation*}
To solve graphically, make a graph on your graphing calculator, then find the \(x\) values where the graphs have the same output (height). In other words, find where the graphs intersect.
Exercise1.1.21
Often equations are too difficult or even impossible to solve using algebra. But if you can graph the equations on a graphing calculator or on the web, you can solve graphically to get at least approximate solutions. | 677.169 | 1 |
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The best way to really understand the numbers that are used every day is to understand the mechanics behind the calculations. The best way to learn and internalize these mechanics is to put pencil to paper and calculate the numbers from scratch. This book starts with notation and algebra, then covers statistics, calculating rates of return, fixe... more »d income, measuring risk, and asset allocation and performance measurement.« less | 677.169 | 1 |
Math for Grade 4 – Grade 4 Math For Children Aged 8 and Above! This course is meant for children who are homeschooled so that they can pick up simple concepts in a fun and easy environment. It has 36 lectures with clear explanations, practice demonstrations, and Quizzes to help you remember what you have learnt. I …
Calculus – Limits of Sequences – How to Determine the Limit of any kind of Sequences. By completing this course, you are going to be able to determine the limit of any kind of sequence. I'm going to show you the necessary theoretical background in a nutshell. Then I show you lots ofPhysics | Current Electricity | Urdu – Learn about Current, Voltage, Resistance and all the basic concepts of Current Electricity. Learn about Current, Voltage, Resistance and all the basic concepts of Current Electricity in Urdu. The hazards of electricity, use of electricity in homes and distribution of electricity in homes. Also AC/DC …
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This material is a part of a collection of learning materials at the site of Rio Rancho Math Camp. The site provides ״an...
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This material is a part of a collection of learning materials at the site of Rio Rancho Math Camp. The site provides ״an intellectually stimulating experience for middle school students who like math, and want to experience hands on, challenging math activities." The Topology topic is designed to give a student simple yet insightful introduction on the subsject of Topology. It contains illustrations, videos, and interactive exervises.
Material Type:
Tutorial
Author:
Andy Klee
Date Added:
Oct 02, 2014
Date Modified:
Oct Math Wizards: Top | 677.169 | 1 |
Lectures
Literature
Course Contents
This course is a basic course in the theory of counting and graph theory. Counting. Subsets and binomial coefficients.
Partitions and Stirling numbers. Permutations and permutation statistics. Fibonacci and Catalan numbers.
The inclusion-exclusion principle.
Recurrences. Generating functions. Graphs. Eulerian and Hamiltonian cycles. Graph colouring. Matrix tree theorem. Some additional topics.
Most of chapters 1 to 6 from Anderson's book.
Examination and Grading
Tests (30%)
There will be 2 tests. These will be announced at least one week in advance.
Final (30%)
There will be a comprehensive final to be worth 30%.
Homework (40%)
There will be a set of problems to be handed in at the end of every week. To work on the homework problems is
crucial for your understanding of the material presented in class. Be sure to separate enough time each week
to think and write your solutions. It is recommended that you think and attempt every problem on your own before
seeking any help. You are encouraged to discuss the material of the course with your classmates, however you must
write your own solutions using your own words. There can be unannounced quizzes that will count towards your homework grade.
Any of these quizzes will occur on the Wednesday session.
Suggested problems
There will be some additional suggested problems. These problems will be assigned after some of the
classes and also posted in the web page of the courseE
Syllabus
This is an approximate schedule of the course containing the syllabus:
Date
Topic
Wed 08/26
Introduction. What is combinatorics?
Fri 08/28
Review of mathematical proofs.
Mon 08/31
Basic Principles of counting. Permutations and factorials
Wed 09/02
Combinations and selections
Fri 09/04
Binomial coefficients and Pascal's triangle
Mon 09/07
ACADEMIC HOLIDAY. LABOR DAY
Wed 09/09
Selections with repetitions, Compositions
Fri 09/11
A useful matrix inversion
Mon 09/14
Recurrences
Wed 09/16
Auxiliary equation method
Fri 09/18
Generating functions
Mon 09/21
Generating functions
Wed 09/23
Derangements. Sorting algorithms
Fri 09/25
Catalan numbers
Mon 09/28
More generating functions
Wed 09/30
Test 1 Review
Fri 10/02
Test 1
Mon 10/05
Graphs
Wed 10/07
Paths and Trees
Fri 10/09
Spanning trees.
Mon 10/12
Bipartite graphs. Planarity
Wed 10/14
Chords of a circle. Polyhedra
Fri 10/16
Hamiltonian Graphs
Mon 10/19
The travelling salesman problem
Wed 10/21
Eulerian graphs
Fri 10/23
Partitions
Mon 10/26
Partitions
Wed 10/28
Graph colouring
Fri 10/30
Chromatic polynomial
Mon 11/02
Chromatic polynomial
Wed 11/04
Test 2 Review
Fri 11/06
Test 2
Mon 11/09
The inclusion-exclusion principle
Wed 11/11
Applications of the IEP
Fri 11/13
Applications of the IEP
Mon 11/16
Graphs and linear algebra
Wed 11/18
Graphs and linear algebra
Fri 11/20
The matrix tree theorem
Mon 11/23
Permutation statistics
Wed 11/25
THANKSGIVING HOLIDAY
Fri 11/27
THANKSGIVING HOLIDAY
Mon 11/30
Permutation statistics
Wed 12/02
Additional topics
Fri 12/04
Additional topics
Mon 12/07
Additional topics
Wed 12/09
Additional topics
Fri 12/11
Review Final
Calculators Policy
Calculators are not allowed in quizzes, tests or the final exam.
Code of Conduct
Students should consult the students rights and responsibilities outlined in the
Student Code of Conduct.
Any offense to the Code of Conduct will result in a grade of "E" for the course and a referral to
the Dean of Students.
Excused Absences
University Senate Rule 5.2.4.2 defines the following acceptable reasons for an "excused absence" from class:
Serious illness (must be documented by doctor's excuse)
Illness or death of a family member
University-related trips (must be documented by a letter from sponsor)
Major religious holidays
Other circumstances that your instructor finds to be "reasonable cause for nonattendence"
Students should notify the instructor of an excused absence prior to the absence whenever
possible and complete all work prior to the absence (unless for illness or for the illness or
death of a family member).
Students with Disabilities
Students with documented physical' learning' or temporary disabilities may receive assistance and support
from the Disability Resource Center.
It is recommended that students contact the Disability Resource Center early to request specific assistance
so that the required medical or psychological documentation can be reviewed and reasonable accommodations
can be provided from the beginning of class work in order to achieve the greatest benefit to the student.
Changes to this Syllabus
This syllabus may have some changes during the semester. It is responsibility of the students to visit frequently
the webpage of the course for up to date information. | 677.169 | 1 |
Calculus solutions concepts a and foerster applications paul pdf
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Description: With the formal exercise in solving the types of ordinary differential equations that usually occur it is the object of this text to combine a thorough drill in the solution of problems in which the student sets up and integrates his own differential equation.
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Master math : business and personal finance math
Annotation This work teaches students the mathematics required for success in today's world in an easy-to-read, user-friendly format. It covers all the need-to-know information and skills in business math and personal finance topics.
Abstract:
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Week 38
Week 36
Grade 10 English
Teacher Joe Grzebyk
Grade 10 Biology
Teacher Sam Reongjareonsook
In this week, students will complete their chapter section on respiratory and excretory systems.
Grade 10 Algebra II
Teacher Robert Dumas
Summary:
• Identify properties of the Tangent Function. Graph tangent curves
• Define Trigonometric Ratios and find missing length of sides of right triangles
• Area and the Law of Sines: Find areas of triangles and use the Law of Sines to find additional missing sides and angles
Week 34
Grade 10 English
Teacher Joe Grzebyk
Grade 10 Biology
Teacher Sam Reongjareonsook
Students this week will continue to learn about nervous systems, action potentials and the effects of certain drugs and neurotransmitters.
Grade 10 Algebra II
Teacher Robert Dumas
Summary:
• Identify properties of the Sine Function.
• Graph sine curves. Estimating sine values in radians.
• Finding the period of a sine curve. Finding the amplitude of a sine function.
• Identify properties of the Cosine Function. Graph cosine curves
• Estimating cosine values in radians. Finding the period of a cosine curve.
• Finding the amplitude of a cosine function.
Grade 10 Biology
Teacher Sam Reongjareonsook
Grade 10 Algebra II
Teacher Robert Dumas
1. Students will find values of trigonometric functions for acute angles.
2. Students will use trigonometric functions to find side lengths and angle measures of right triangles.
3. Students will draw and find angles in standard position.
4. Students will be asked to convert between degree measures and radian measures.
1. Students will be required to find values of trigonometric functions for general angles
2. Students will be asked to find values of trigonometric functions by using reference angles
3. Students will be asked to find the area of a triangle using two sides and an included angle
4. Students will be asked to use the Law of Sines to solve triangles provided that AAS and SSA information are provided.
5. Students will need to use the Law of Cosines to solve oblique triangles provided SAS or SSS information is given.
Week 26
Grade 10 English
Teacher Joe Grzebyk
Grade 10 Biology
Teacher Sam Reongjareonsook
In this week, students will study organism classification models and the Linnaean system used by modern scientists.
Grade 10 Algebra II
Teacher Robert Dumas
Summary:
• Find the area of a triangle using two sides and an included angle (SAS). Use the Law of Sines to solve for these general angles. Find missing dimensions when given a triangle' s side-side-opposite angle configuration (SSA).
• Introduce the topic of the Ambiguous Case when solving a triangle
• Use the Law of Cosines to solve general triangles. Choose methods to solve triangles based upon information provided.
Week 25
Grade 10 English
Teacher Joe Grzebyk
Grade 10 Biology
Teacher Sam Reongjareonsook
Students in this week will transition into Darwinian history, natural selection and the theory of evolutionWeek 24
Grade 10 English
Teacher Joe Grzebyk
Grade 10 Biology
Teacher Sam Reongjareonsook
Students this week will learn about paleontology, the study of fossils, and the origins of lifeGrade 10 English
Teacher Joe Grzebyk
Grade 10 Biology
Teacher Sam Reongjareonsook
In this week, students will complete our chapter on DNA technology, inspecting classic strategies such as recombinant plasmids and cloning in addition to recent developments like CRISPR technology.
Grade 10 Algebra II• Using the Inverse Sine, Cosine, and Tangent Functions to find missing angles
• Instruction in using their calculator function keys
Grade 10 Algebra II
Teacher Robert Dumas
1. Students will be asked to use long division to divide polynomials by binomials
2. Students will be asked to diagram polynomial functions by using a table of values
3. Students will be asked to find the roots (zeros) of polynomial functions
1. Students will be required to factor polynomials
2. Students will be asked to solve real-world problems involving polynomial functions
3. Students will be required to factor large polynomials by the method of grouping
4. Students will be asked to use synthetic division to solve larger degree polynomials
5. Students will need to simplify polynomials and rational expressions
1. Students will be required to define excluded values in a rational expression
2. Students will be tasked with using the Rational Root Theorem to find the roots (zeros) of a polynomial equation/expression
3. Students will be required to solve complex fractions
4. Students will be asked to add, subtract, multiply, and divide polynomial functions/expressions
5. Students will be required to graph rational equations and solve for the roots (zeros) of the rational equation
Week 18
Grade 10 English
Teacher Joe Grzebyk
Grade 10 Biology
Teacher Sam Reongjareonsook
We will finish our section this week on meiosis and genetics, leading to a more thorough understanding on genetically inherited traits and diseases.
Grade 10 Algebra II
Teacher Robert Dumas
SUMMARY:
• Adding and Subtracting Vectors to obtain a Resultant Vector
• Defining the magnitude and direction of the Resultant Vector
• Using the Law of Sines and the Law of Cosines to find the direction of the Resultant Vector
• Real World problems involving Force and Velocity typically found in a high school Physics curriculum.
Week 17
Grade 10 English
Teacher Joe Grzebyk
Grade 10 Biology
Teacher Sam Reongjareonsook
This week we will examine the root of genetic theory – meiosis, sexual reproduction and parental inheritance.
Grade 10 Algebra II
Teacher Robert Dumas
SUMMARY:
• Defining the real-world process of linear optimization and its significance in industry
• Using a system of inequalities to represent constraints a company may face
• Finding maximum and/or minimum values of a function given specific constraints and a feasibility relationship (equation)
• Understanding how constraints in the real world effect profitability and how one can maximize their profitability or minimize their costs by careful study of constraints
Grade 10 Algebra II
Teacher Robert Dumas
Week 14
Grade 10 English
Teacher Joe Grzebyk
Grade 10 Biology
Teacher Sam Reongjareonsook
Students this week will learn about cellular metabolism: how energy is produced in plants and processed in eukaryotic mitochondria.
Grade 10 Algebra II
Teacher Robert Dumas
SUMMARY:
• Finding the roots (zeros) of Polynomials and relating Zeros and Coefficients of Polynomial Functions.
• Using the Rational Zero Theorem to find the rational roots of higher degree polynomials
• Demonstrate the correlation between finding the roots and graphing the function.
• Investigate the number of Complex Zeros of a Polynomial Function by using the Fundamental
Theorem of Algebra.
Week 13
Grade 10 English
Teacher Joe Grzebyk
Grade 10 Biology
Teacher Sam Reongjareonsook
We will continue our studies on cell structure and function in this week – focusing on organelles, which are the miniature organs in each cell, and on how the cell transports materials to and from its environment and internally.
Week 12
Grade 10 English
Teacher Joe Grzebyk
Grade 10 Biology
Teacher Sam Reongjareonsook
This week we will begin to examine cells: how they were discovered, what organelles they contain and why they are common to all living organisms.
Grade 10 Algebra II
Teacher Robert Dumas
SUMMARY:
• Adding and Subtracting polynomials.
• Identifying monomials and polynomials. Discuss the idea of degree of a monomial, degree of the polynomial
and the idea of like terms. Likewise, subtraction of polynomials requires like terms
• Multiplying polynomials
• How to multiply polynomials and binomials. What is the result of the multiplying operation?
•How does a polynomial model the volume of a real world figure (rectangular prism)? And verifying
polynomial identities.
Grade 10 Biology
Teacher Sam Reongjareonsook
Grade 10 Algebra II
Teacher Robert Dumas
• Order of Operations, and Properties of Equality
• Evaluate Absolute Value Equations,
• Set-up problems with inequalities and solve
• Analyze relations and functions
• Solve problems involving Linear relations and functions,
• Identifying slope and calculating slope of a linear equation
• Determine if a line is parallel, or perpendicular to a given line and determining its slope
• Solve, and graph linear inequalities, and absolute value inequalities &solve systems of linear equations graphically
• The Elimination and Substitution Methods
• Graphing and find Optimization Values for Inequalities
• Solutions for systems of equations with three variables
• Algebraic operations on a pair of matrices | 677.169 | 1 |
Algebraic Reasoning Practice Worksheet with Tables Solving Algebra
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Algebraic Reasoning Practice Worksheet with Tables, created by Tricks and Treats for Teaching Math. 2 pages total. Comprehensive with word problems and tables. Great for Independent Practice or Homework! You'll use this year after year. | 677.169 | 1 |
complete 5-10A mathematics series for the Australian Curriculum. The ICE-EM Mathematics series was created by the Australian Mathematical Sciences Institute (AMSI) to provide a mathematics program that gives students a clear understanding of ideas and concepts. It aims to improve mathematics learning for students with a range of abilities, needs and levels of interest. This new, full-colour series has been rewritten and developed for the Australian mathematics curriculum by AMSI, while retaining the structure, depth and approach of the original titles. The development team has thoroughly reviewed the Australian mathematics curriculum to produce materials that cover all of the required content, as well as provide additional coverage of topics that are relevant and essential for a complete understanding of mathematics. | 677.169 | 1 |
1.5: Exponents, Order of Operations, and Properties of Real Numbers (42)
1: Review
Chapter 2: Fundamentals of Algebra
2.1: Writing and Evaluating Algebraic Expressions (47)
2.2: Simplifying Algebraic Expressions (48)
2.3: Algebra and Problem Solving (39)
2.4: Introduction to Equations (46)
2: Review
Chapter 3: Equations, Inequalities, and Problem Solving
3.1: Solving Linear Equations (47)
3.2: Equations That Reduce to Linear Form (47)
3.3: Problem Solving with Percents (47)
3.4: Ratios and Proportions (47)
3.5: Geometric and Scientific Applications (47)
3.6: Linear Inequalities (22)
3.7: Absolute Value Equations and Inequalities (11)
3: Review
Chapter 4: Graphs and Functions
4.1: Ordered Pairs and Graphs (47)
4.2: Graphs of Equations in Two Variables (46)
4.3: Relations, Functions, and Graphs (27)
4.4: Slope and Graphs of Linear Equations (46)
4.5: Equations of Lines (46)
4.6: Graphs of Linear Inequalities (45)
4: Review
Chapter 5: Exponents and Polynomials
5.1: Integer Exponents and Scientific Notation (25)
5.2: Adding and Subtracting Polynomials (46)
5.3: Multiplying Polynomials: Special Products (47)
5.4: Dividing Polynomials and Synthetic Division (28)
5: Review
Chapter 6: Factoring and Solving Equations
6.1: Factoring Polynomials with Common Factors (47)
6.2: Factoring Trinomials (46)
6.3: More About Factoring Trinomials (47)
6.4: Factoring Polynomials with Special Forms (51)
6.5: Solving Polynomial Equations by Factoring (31)
6: Review
Chapter 7: Rational Expressions, Equations, and Functions
7.1: Rational Expressions and Functions (24)
7.2: Multiplying and Dividing Rational Expressions (24)
7.3: Adding and Subtracting Rational Expressions (23)
7.4: Complex Fractions (22)
7.5: Solving Rational Expressions (26)
7.6: Applications and Variation (23)
7: Review
Chapter 8: Systems of Equations and Inequalities
8.1: Solving Systems of Equations by Graphing and Substitution (42)
8.2: Solving Systems of Equations by Elimination (24)
8.3: Linear in Three Variables (27)
8.4: Matrices and Linear Systems (26)
8.5: Determinants and Linear Systems (28)
8.6: Systems of Linear Inequalities (25)
8: Review
Chapter 9: Radicals and Complex Numbers
9.1: Radicals and Rational Exponents (28)
9.2: Simplifying Radical Expressions (26)
9.3: Adding and Subtracting Radical Expressions (28)
9.4: Multiplying and Dividing Radical Expressions (29)
9.5: Radical Equations and Applications (22)
9.6: Complex Numbers (28)
9: Review (16)
Chapter 10: Quadratic Equations, Functions, and Inequalities
10.1: Solving Quadratic Equations: Factoring and Special Forms (27)
10.2: Completing the Square (25)
10.3: The Quadratic Formula (19)
10.4: Graphs of Quadratic Equations (27)
10.5: Applications of Quadratic Equations (25)
10.6: Quadratic and Rational Inequalities (27)
10: Review (20)
Chapter 11: Exponential and Logarithmic Functions
11.1: Exponential Functions (24)
11.2: Composite and Inverse Functions (24)
11.3: Logarithmic Functions (23)
11.4: Properties of Logarithms (21)
11.5: Solving Exponential and Logarithmic Functions (24)
11.6: Applications (21)
11: Review (20)
Chapter 12: Conics
12.1: Circles and Parabolas (23)
12.2: Ellipses (24)
12.3: Hyperbolas (24)
12.4: Solving Nonlinear Systems of Equations (23)
12: Review (18)
Chapter 13: Sequences, Series, and the Binomial Theorem
13.1: Sequences and Series (24)
13.2: Arithmetic Sequences (23)
13.3: Geometric Sequences and Series (24)
13.4: The Binomial Theorem (19)
13: Review (15) | 677.169 | 1 |
Core Maths
What is Core Maths?
Core Maths is offered to all students who have achieved a grade C or better in GCSE Mathematics but who are not studying Mathematics at AS or A Level. It is a relatively new course designed by the Department of Education in collaboration with universities and employers to ensure that students leave full-time education with all of the mathematical skills they may need for further study or work.
The course covers aspects of Functional Mathematics that are relevant to a wide range of subjects and careers. These include Financial Maths (personal budgeting, financial planning and understanding a payslip, loans and interest), Statistics (interpreting data, data collection,report) and Decision Mathematics (planning an event and critical path analysis).
Core Maths is assessed by examination at the end of Year 13. There is no coursework element.
Where will it lead?
The Core Maths qualification generates the same number of UCAS points as an AS Level and is designed to assist in the transition from Sixth
Form to either further study or work. It will demonstrate to employers that students' understanding of Mathematics has developed further than GCSE. | 677.169 | 1 |
To be successful in math, you have to master an approach to the world that is inherently useful. College majors typically require mastery of a math course not because anyone cares about math, but because passing a math course is the easiest way to demonstrate mastery of the meta-concepts that everyone actually does care about.
Once you realize that math is about meta-concepts, and not about math at all, teaching math becomes really very easy.
1) Buy a math notebook.
Every frustrated math student, everyone who is poor at math, has one thing in common: they don't organize their work. They scribble numbers down all over the page without regard to sequence. If students learn ANYTHING in math, they must learn to break that habit.
So, beginning students should be actively discouraged from doing math in their heads. Yes, I know the Math-Bowl encourages this for the advanced students who compete, but it's not a good idea for beginners. Beginners need the external structure. So, buy a THICK, empty math notebook, with lots of empty pages.
2) Throw out the calculator
For basic math, they don't need it.
Calculators interrupt the student's concentration, forcing him to alternate between doing the procedure the problem requires and doing the procedure the machine requires, figuring out the correct sequence of key punches.
Calculators are mostly a distraction. No one needs a calculator until they start doing trigonometry or statistics. If they aren't doing either, then let them learn the multiplication tables.
If you think calculators should be allowed on basic math tests, then why shouldn't cell phones and internet access be allowed for reference on history or English tests? The Internet is the equivalent of a history or grammar calculator. Why bog down the student with memorization of useless dates and grammar rules when they could be doing higher-order stuff?
Now, watch the history and English teachers howl in outrage that you should suggest such a thing. Watch the math teachers smile sadly and say, "Yeah, well, welcome to our world, suckers."
3) Write down each step
The student must write down each problem as follows:
On the first line, the problem itself
On the second and subsequent lines, write each successive step.
No more than one operation (add, subtract, multiply, divide) is permitted in any step.
The answer is written at the bottom of the step sequence.
No scribbling in side margins allowed at all. Don't allow multiple operations in any one step because beginning students get themselves confused easily. Each step does exactly one thing, that is all.
Ignore their whining. Even if a beginning student gets the answer correct, the problem is wrong if they haven't shown all their steps. Make that clear. Stand over them for a month, enforce it, and they will gain the habit. Ingraining into them this single, solitary little trick solves over half your math problems overnight.
4) A fresh sheet of paper for every problem
Math is not an exercise in conserving paper. Be profligate. Paper costs less than half a cent a sheet. Splurge. Once they have successfully trained themselves to write out every step, you can alter this rule to allow more than one problem per page, but even then NEVER let them break a problem over two sheets of paper. Ever. No. I mean it, don't do it.
Beginning students get a feeling of accomplishment from seeing all their work laid out neatly at a glance. It feels restful, as the eye glides downhill through the gears of the problem and finally takes up its ease at the bottom of the sequence, peacefully resting upon the (correct) answer.
5) When they get stuck
First, if there is ANY sign of margin scribbling, turn the old sheet of paper face-down, start on a fresh sheet.
No.
Do it.
If you start on the old sheet, all the old scribblings will be a distraction. The student will wander down rabbit-trails trying to figure out what went wrong with the previous procedure. Clear his mind. Start fresh. Give him the gift of new eyes and a clean slate.
Now, math teaches a lot of (seemingly) arbitrary procedures. The student has to know all the procedures and know when to apply which procedure. Both parts of this are hard, but the second part - knowing when to apply which procedure - is the hardest. So, when he gets stuck and isn't sure what to do next, here's what you do:
Ask him a question you are sure he can answer.
When he answers correctly, affirm it ("That's right."),
Rinse and repeat. Ask a series of questions, each one of which you are confident he can answer.
Build that series of questions so as to lead him to or through the correct procedure.
In basic math, this question will always come up at some point: "Do you think you would add, subtract, multiply or divide?" Those are the four basic operations, and one of them is almost certainly going to be part of the path to solving the problem.
The student is almost always able to weed out at least a couple of the operations. That instills self-confidence, it shows partial mastery.
Don't give the student the answer.
Ever.
Always respond with a question you know s/he can answer.
Once s/he has gotten the answer, point out the truth: "I didn't tell you the answer. All I did was ask questions. You KNEW all the answers. You already KNEW how to do it."
And the student DID know how to do it. He just needs to internalize how to ask himself the same series of questions you asked.
Don't point this out.
Simply keep repeating this sequence with him on every problem he has, week in, week out, making sure he writes down every problem step-by-step
He will learn to internalize the question sequence himself. He will start asking and answering his own questions.
At that point, you can go bake brownies.
This whole sequence only takes a couple of months to instill.
Once this basic skill set is instilled, it is now permissible to have the student walk through the steps of a failed problem to see where the mistake was made.
If each step has only one operation, it will be relatively easy to see which step failed.
Now the student will see the wisdom of the step-by-step process.
He doesn't have to re-do every problem from scratch.
He can find and correct his own mistakes easily.
Once he realizes this, math becomes almost bearable.
6) When YOU get stuck
Don't be afraid to say, "I don't know. Let's Google it." You don't have to know everything in math. In fact, you don't have to know ANYTHING about math. Remember, math isn't about math. Math is about learning how to be
organized,
good at documenting details,
good at being detail-oriented, and
good at following and trusting arbitrary procedures.
None of those skills require you to know the arbitrary procedures yourself. Even if you are no good at math, you will naturally be better at searching for the correct way to do it. Model how to search for the right way to do things. Have your student watch you as you bumble along, figuring it out.
The student thereby learns:
(1) it is ok to not know something,
(2) this is how you find out what you don't know,
(3) Searching for the right procedure takes time and that's also ok,
(3) Perseverance can be as important, or more important, than possessing knowledge.
That's all there is to teaching math.
Seriously.
Well, that and liberal use of Khan Academy. Yes, I have a degree in computer science, minor in math, and have taught developmental math at the college level for years, but I taught my children almost no math at all. There's no point. Khan Academy teaches the concepts as well or better than I could. I only got involved if a video was opaque (unusual) or a solution sequence unclear (also unusual).
Often-times, I would walk along through the Khan Academy solution to the problem as perplexed about the correct sequence as my child was. It's not like I remember most of the stuff I learned thirty or forty years ago. We would discover the solution together, which was rather fun.
No, the only way I have ever taught math was to follow the sequence I have described above. It works.
I have noted before that the office of the papacy does not include the requirement that the Pope be very knowledgeable of economic theory, nor that he be very intelligent in his comments on it. While the Church has a duty to serve the poor, the method by which the poor are best served is largely prudential - different people might legitimately choose different means to solve it. Wealth inequality, by itself, is not a sin so long as everyone's minimum requirements for food, clothing, shelter, education, medical care ad basic human dignity are being met. Quite frankly, all but the last of those minimum needs are being met much better today, in a time of enormous wealth inequality, then they have ever been met in the entire course of human history.
In fact, things have gotten so much physically better precisely as a result of growing wealth inequality. Wealth inequality is correlated with EVERYONE getting out of poverty.
The "trickle-down" theory of Reaganomics is a fine example of how inequalities actually help everyone. Even Ted Kennedy admitted that much. The rising tide which brings incredible wealth to the 1% ALSO lifts the 99% out of poverty. The mechanics for how it works is very straightforward.
Take laparoscopic surgery, for instance. When I was young, that was only an option for millionaires. But, as more millionaires bought the procedure, economies of scale kicked in and semi-millionaires could afford it. There were a lot more semi-millionaires than there were millionaires, so scale kicked in again, repeatedly. As cost fell, more and more people could afford it, so more and more people did it, which dropped costs still further. The increase in scale also meant the procedure became increasingly streamlined and efficient, if only so as to handle the demand better.
Today, laparoscopic surgery is standard procedure for gallbladder and appendix removal, among a host of other applications. It provides cheap out-patient surgery that simply didn't exist 50 years ago. Why? Because millionaires volunteered to act as the guinea pigs. They were the only ones who could originally afford it. As they and their extremely well-paid doctors refined the procedure, it became increasingly available to the rest of us. Today, it is so common that it doesn't merit mention.
The same thing happened with cell phones. The original radio phones and cell phones were the size of bread boxes and cost more than any average Joe could possibly afford. But millionaires needed to stay in constant contact with their businesses and with the stock market, so they bought the tech. They served as the guinea pigs. As scale increased, price dropped, efficiencies improved. Now, literally everyone in the US can afford cell phones. And not just cell phones. Today's phones are the 1960s equivalents of super-computers that fit in our pocket and put us in touch with most of humanity's combined store of knowledge. The rich people and their richly rewarded tech outfits worked out the kinks. We have all benefited.
THAT is what wealth inequality does. It allows millionaires to act as guinea pigs for new tech. If it doesn't work, they waste their money and/or die. If it DOES work, then I get the tech about fifteen years later, because by then, the cost has dropped down to where even I can afford it.
Wealth inequality is an extremely efficient way to utilize resources. If I have a new tech idea, I can either try to convince tens of thousands of middle-class people to fund my idea, at great personal risk to each of their wealth stores, OR I can convince one extremely wealthy person to fund it at minimal risk to his wealth store. It was easier to do the latter than the former. Even today, being on Shark Tank will bring you funding in literally 20 minutes, while promoting the same project on Kickstarter will take days, weeks, or months to accomplish the same level of funding. It is far easier for Elon Musk to guide a project like the Falcon Heavy or BFR to successful completion than it is for ten thousand people to agree on how to do so, and that assumes you could get the funding from that ten thousand at all.
Wealth inequality is not the problem many people make it out to be. In fact, wealth inequality has historically been the solution which has made us all fabulously wealthy by any historical standard you care to name. Because of wealth inequality, the rich are willing to serve as the experimental guinea pigs necessary to bring functioning solutions to the masses. That's not a bad thing.
We have a knee-jerk reaction against wealth accumulation because we innately see the world as a zero-sum game. And the fallen world often acts and reacts as if it were. But the whole point of Christianity is to change our world-view. A Christian understands that God's grace and power are infinite, therefore the zero-sum game view can never be correct. Insofar as we image God, we have the ability to change our world from being zero-sum to being infinitely resourceful and wealthy.
Can we create Utopia? Physically, sure. Spiritually, not a chance. We are still fallen creatures, and that will always prevent us from establishing any real paradise on earth. We are slowly solving the problem of physical poverty. It really is going to disappear, possibly in our lifetimes.
But spiritual poverty? As long as anyone in the world is not Catholic, then the world still suffers from extreme spiritual poverty. THAT is the wealth inequality which we, as Catholics, need to remedy. Fortunately, from that viewpoint, Catholics are the rich one-percent. We have infinite resources that can be delivered to the poor among us, and make them all wealthy too. As physical riches percolate out into the world, that is the only wealth inequality we really need to be concerned about.
Monday, February 12, 2018
This is a popular meme floating around the Internet. Sometimes it picks
India, sometimes Egypt, but the idea is the same. The US pays 84 times
or 250 times or some ungodly percentage more than these lousy third
world countries! Why are US citizens being gouged?
Well, to put it bluntly, US citizens are NOT being gouged. When all things are considered, those prices are all pretty fair. To begin with, let us simply accept the numbers above without argument. For this analysis, we shall add some numbers of our own.
Country
Price / pill
% of US cost
Median Income
% of US Income
Hep C Prevalence
USA
$1000
100%
$51,700
100%
3.2 million
Egypt
$ 11
1%
$ 5,680
11%
38 million
India
$ 4
0.4%
$ 3,800
7%
10-15 million
So, the average American earns 10x as much as the average Egyptian and roughly fifteen time as much as the average Indian. One would think, based just on this, that the average Egyptian treatment would cost one-tenth as much. That is, it would seem the price should be $100 per pill in Egypt, for instance.
But, then we have to factor in the prevalence of the disease. Egypt has 10x as many cases of hepatitis C, India has 3-5x times as many cases of the disease. So, we have to knock down the Egyptian price by another factor of ten (due to volume) and lo! The price is pretty much correct. When you factor in both India's disease prevalence and income, even the Indian price is not that far off.
There's no reason to stop with the table above, though. Try factoring in the sub-populations that actually get infected with hepatitis C and therefor have to pay these different prices. The "disparity" becomes even more interesting.
Wednesday, January 17, 2018
What you are reading is one voice in a LONG argument that has extended for at least the last fifty years.
IQ testing unquestionably has eugenics origins. It was invented by eugenicists, administered by them and normed by them. The whole point of IQ testing was originally to keep southern Europeans, Mexicans and Asians out of the country.
This is bad. Eugenicists are not nice people. They say that some people are more valuable than others, they support abortion, euthanasia, yada, yada, yada. It is a very ugly philosophy. Unfortunately, a lot of interesting results have come from these eugenics-inspired tests.
For instance, over the course of time, IQ has steadily risen across the board throughout every aspect of the population. No one is quite sure why this has been happening for the last century, but the suspicion is that improvements in nutrition and medicine, along with reductions in pollution (especially the removal of lead from gasoline and household paints, which greatly reduced the blood levels of lead in all populations, especially the poor) contributed quite a lot to this effectDuring the 1950s and 60s, the argument was made that the IQ test was really a test of culture, not a test of IQ, so in the intervening 50 years, there have been many attempts to "fix" them so that they really do measure intelligence. The problem is, none of the "fixes" seemed to cause the various sub-populations to test the same. Some subpopulations always test smarter, other always test stupiderPeople who want the tests to reveal absolutely no real differences between different genetic populations always insist the tests are skewed, but they can't figure out how to fix them so that they don't produce these results. Psychologists have pretty much given up. They admit privately that there are real differences in the average IQ of various populations, but they can't say this out loud without being called "racist" or some such, so you get articles like the one you found, where people who don't like the results sob loudly for their lost cause, and psychologists shift uncomfortably from foot to foot, then state firmly that they are going out for a beer and does anyone else want them to pick up something while they are out?
The major problem with IQ tests is that they only measure the ability to engage in rational thought. They don't measure a person's happiness in life, they don't measure how happy one person makes someone else. They don't measure artistic ability, musical ability, the ability to care for or empathize with animals, other human beings, etc.
The original high-IQ society, Mensa, was envisioned to become a powerhouse of world happiness. Put all these really smart people together in a room, the reasoning went, and they would solve the world's problems. But the actual organization has never solved anyone's problems. None of the dozens of high-IQ societies that have been created since Mensa have done anything useful either. Each one seems to be a way for one smaller group of people to pretend to be superior to some other slightly larger group of people (the top 1% vs the top 0.1% vs the top 0.01% and so on).
In fact, all IQ tests seem to do is produce high-IQ societies filled with people who do really hard crossword puzzles and odd math sequences while dressing oddly. So, the whole debate is, at this point, kind of stupid. Sure, some high-IQ people do useful things, but a lot of high-IQ people really don't do anything useful, so what's the point here?
It's the modern equivalent of arguing about how many angels can dance on the head of a pin: how many IQ points does it take before you actually accomplish something useful? Take Marilyn vos Savant, for instance, who has highest IQ ever recorded (note that she is female, in contradiction to the average). She hasn't done a single useful thing in her life, apart from making money off her IQ score. She hasn't invented anything, accomplished anything that helped anyone in any serious way - in terms of helping society, she has completely wasted her life. So... who really cares about IQ? What does it ultimately buy us?
Sunday, January 14, 2018
In ancient times, any country conquered by Rome had to pay tribute to Rome. These vassal states had to spend their own resources to build up stores of grain, honey, and other trade goods in order to ship them to Rome for free, or at a greatly reduced price. This was how they acknowledge Rome's hegemony over them.
Today, countries acknowledge America's hegemony by doing the same thing. Other countries build up stores of trade goods at their own expense and ship those goods to us at a greatly reduced price, a price subsidized by foreign governments, in the hopes that we will buy those goods.
From an economic perspective, Trump's "Buy American" policy runs counter to his "Make America Great Again" policy. America proves her economic greatness when vassal countries ship us cheap goods whose manufacture has been subsidized by foreign governments. Whenever the foreign government throws government money at producing a good that will be sold in the US, that government has essentially sent us a check to help us prop up our economy. Foreign-subsidized goods that enter the US are as much free money as any cashier's check, grain shipment or oil shipment we send for cheap or free to a third-world country.
Americans frequently complain about the amount of free money we send to other governments, other countries. They almost never acknowledge that foreign-subsidized goods are free money that those foreign states send to us. Every dollar a foreign government spends to produce a good is a dollar in tax that they pay to America in exchange for the privilege of being allowed to sell to Americans. Foreign subsidies of goods are nothing more than tax dollars paid by foreign citizens, collected and paid, by foreign governments, as tribute to the United States.
Thus, forcing American government projects to "buy American" is absurd. We should be buying the least expensive material from whoever produces it. If we are lucky, foreign countries will subsidize the production of the steel, oil, etc., that we use in our projects. When we build American projects on American soil, any decent economist would much prefer the material in those projects come from companies that are subsidized by foreign governments. That's free money for us.The "trade deficit" is not a bug, it's a feature. It proves that America receives more money from vassal states than she sends out.
"It is no coincidence that the smallest American
merchandise trade deficit since 1982, $74 billion in 1991, occurred
during the period's only recession."
To reiterate, foreign government subsidies of any industrial good we import is nothing more or less than a foreign country paying tribute to America. Foreign subsidies acknowledge American economic superiority. THAT is what I want. Do you want to Make America Great Again? Buy foreign goods. Make sure the world keeps paying its taxes to us.
Sunday, December 31, 2017
Libertarians, those political teenagers who want to have their cake and eat it too, always complain about government over-regulation and the imposition of other people's values. "We should have the right to live as we please, without government interference!" they cry. "Enough of government regulation!"
But the absurdity of their position is apparent after a moment's thought. The
government "over-regulates" - what a judgemental word! Doesn't that word impose libertarian values on others, wherein some random libertarian gets to determine what counts as 'over-regulation'? And what if large corporations WANT a lot of regulations? Shouldn't it be their right to try to get those regulations in place, if they want them?
Corporations donate their executives
to government and draw their executives from government. Corporations
write and pay for the implementation of laws that will protect their
business from competition. "Government" is just the word we use for
corporations working together to protect their respective turfs. Large
government and "over-regulation" is a natural result of a free market
in which some people do MUCH better than others, and want to keep it
that way. Has it never occurred to anyone that using words like
"crony capitalism" and "over-regulation" is just as much an imposition
of values on everyone as insisting on income equality is?
And this is another point that libertarians don't quite understand. Yes, it is demonstrably true that income inequality has been associated with the largest improvement of the world's general welfare in human history. In 1800, everyone was equally poor: no matter how much money you had, you still got smallpox and polio, your cattle died of rinderpest, you couldn't buy air-conditioning, antibiotics, analgesics, laparoscopic surgery, a cellphone, or a 2017 Honda Odyssey. Now, you can be in the most extreme poverty, yet you won't die of smallpox, your cattle won't die of rinderpest, and you had, as of 2017, 16 chances out of 7 billion of getting polio. You may not have direct access to air-conditioning, antibiotics or a cellphone, but you likely know someone who could gift you any of those things in a heartbeat. Income inequality is real, and it is one of the hallmarks of a much less impoverished world.
In short, it is demonstrably the case that income
inequality has reduced poverty throughout the world. Income inequality arises because some people are much better at serving everyone's needs than other people are. The people who are best at serving other people's needs get physically rewarded. They are rich.
I don't have any problem
with people being unequally rewarded for having unequally served
people's needs - those who do it better should be better rewarded. I am perfectly fine with income inequality. But
let's not pretend that "over-regulation" and "crony government" is
anything other than what it is: "over-regulation" is the capitalist system working as
libertarians think it should. Big government is the result of successful
corporations creating favorable turf for themselves out of a shared
resource (government).
According to libertarian theory, there should be
nothing wrong with that, especially if it contributes to income
inequality. And it will, because "over-regulation" and "cronyism" will keep out
most entreprenurial upstarts, forcing those wannabees to endure poverty because they
can't get past the government regulations. This allows corporations
to continue to acquire massive wealth and increase the income
inequality that ends up helping everyone. Just as jailers find it easier to serve prisoners if every prisoner is regimented in his own cell, so corporations find it easier to serve customers if all the customers can be trained to want the same thing and respond the same way to the same stimuli.
You own a gun, corporations pretty much own law enforcement. You have pets, corporations have customers. You allow your pets to do what they want, as long as they aren't defecating in your house or getting on the couch. Corporations allow customers to do what they want, as long as they don't compete with the corporate profits at year's end.
If corporations are "persons", and they are, then they have as much right to do what they want as you and I. If what corporations want is to regulate things so as to maximize profits, well, that's the American dream, right?
Saturday, December 16, 2017
Liturgy, it is said, is the life of the Church. The word itself means "work of the people." It originates in pagan Greek practice, where the wealthiest Greek citizens of a city-state would ritually donate warships, plays, public buildings and festivals to honor the city of their birth and give delight to its citizens.
Christians began using, in their own buildings, the adaptations of Jewish Temple ritual that Jesus had taught them. Christians called their ritual "liturgy" to show that it honored the City of God. The rituals that Jesus empowered with the grace of the Crucifixion were performed by Christians in order to deliver the sacraments and the divinizing grace of those sacraments to the people. This makes the people holy and thereby builds up the City of God. Just as with the pagan Greeks, the divine liturgy" was the "work of the people", but unlike the pagan Greeks, Christian liturgy actually carried divine power. In part, the divine liturgy makes up what is lacking in Christ's suffering, for the sake of the Church, just as Colossians 1:24 promised to do. By using the pagan Greek word to describe God's work in their lives, the Christians helped pagans understand the Paschal Mystery and the Body of Christ.
Jesus was both human and divine, so the liturgy is work done by human beings, but carrying divine power. The Mass is about the Passion, Death, Resurrection and Ascension, which are the four aspects of the Paschal Mystery. Each of the four aspects of the single act which is the Paschal Mystery is itself inexorably linked to one of the four reasons for Christ's Incarnation (CCC 457-460). God became man to To show us how much He loves us (Passion), To save us from our sins (Death), To give us a model of holiness (Resurrection), To divinize us (Ascension).
Thus, the Mass is always about those four actions and those four reasons.
So, what does a screaming toddler have to do with any of this?
Does the toddler make you suffer? Ohhh.... poor you.
Does the toddler force you to die to your self-perceived facade of holiness because you suddenly find less than serene thoughts floating through your mind?
Oh... that must be terrible for you.
Does the toddler give you the opportunity to rise above your petty selfishness?
Good.
Does the toddler give you the opportunity to again climb the mountain back into the liturgy, this time with a better understanding of your own failings in charity towards others?
Why, this is most excellent!
Were there screaming children watching the condemned men process up the road to Calvary? I bet there were. Did Golgotha have a cry room? Call me a skeptic, but I doubt it.
The Mass is the life of the Church, and my life is my life before God. In both of these lives, there are screaming children, children acting out, children running up and down aisles, playing with toys instead of paying attention, children even trying (succeeding?) in running into the sanctuary during Mass. The difference between children in the life of the Church and the child in MY life, is that the child in MY life is ME.
I scream when God offers me holiness, I ignore His call, I play with toys rather than pay attention, I run up and down my every day life without thought nor care of God. That child acting out in front of me is a visual representation of ME, every day, even AFTER I have had my morning coffee. That's why so many of us hate hearing children at Mass. Those kids are way, way too much like offensive little ole' me. If I don't want my own self-perception pierced, then I damned well can't have children around showing me off to myself.
Get thee to a nunnery!
Or a cry room.
Or anywhere, really, but in front of me. This glass is not darkly enough, I can still see into it. I don't want face-to-face, I want the picture of Dorian Gray in front of me, so I can pretend it is my mirror. Let me have children about me that are fat, Sleek-headed children and such as sleep a-Mass. Yon screaming child has a lean and hungry look. He suffers too much. Such children are dangerous.
This child is ... this child is... this child is a living, breathing, sobbing tableaux of the Crucifixion, and I am really not able to face Christ crucified. Give me the quiet Mass and its quiet illusion of quiet. Take away from me this image of the bloody, snot-streaming Christ. It offends my gentle holiness.
Friday, December 15, 2017
Ask for a description of cryptocurrencies, and the reply will always involve the phrase "it's a distributed ledger..." They say it as if you are supposed to know what it means. Who the heck does? What on earth is a distributed ledger?
The best thumbnail description I've seen is to think of an Excel spreadsheet. Lots of rows and columns, and it's good for adding numbers, right? That's a ledger - it's just a spreadsheet. Saying it is "distributed" means that copies of the spreadsheet are held on hundreds or thousands or hundreds of thousands of computers at the same time. Any change made to one spreadsheet is automatically replicated to all of the others. Every computer that has a copy of the spreadsheet has to process or "vote" on whether or not to accept the change.
Who can change the cells of the spreadsheet? Well, that's where "coins" come in. Think of each cell as a separate "coin". Access to the cell is granted only to the person who holds the cryptographic keys to that cell. In this analogy, the "blockchain" would just be the map of all the spreadsheet cells.
Just as a spreadsheet can hold numbers or text, and the numbers can be currency or dates or anything else, so the "coins" in the spreadsheet can hold data. Most people simply buy access to the coins, as one would buy empty real estate. You don't necessarily intend to ever build anything there, but when you buy a coin, you are expressing the bet that someone else will one day want to build something in that spreadsheet cell. So, some people build on their coins - put data or programs into the coins (cells) they hold - but most people buy coins for the same reason you buy real estate. You're betting this blockchain is going to become a bustling city, and everyone will want to build there. So, you buy some empty cells ("coins", "land," whatever you want to call it), and wait for the property values to go up.
The person who holds the cryptographic keys to a coin is the one who can stuff data or programs or whatever inside of that coin (land parcel). If you lose your keys, or your keys are stolen, then access to that particular coin is permanently lost.
You prove that you have rights to make changes to the "coin" by supplying your password. You can sell your coin to someone else without ever telling them your password. When you sell, the blockchain recognizes the transfer of ownership - you get the cash, someone else now owns the access to that spreadsheet cell or "coin" in that spreadsheet (blockchain).
Every time you want to make a change to the cell, either by putting data into it or transferring ownership, you have to pay a processing fee to all the computers that update their copy of the ledger for you. The computers that acknowledge and update their copy of the ledger are called "miners." The fee is generally magnitudes cheaper than you would pay a bank. Once enough miners agree to update their ledger, all the others than auto-update their copies as well. Generally, a transaction requires multiple "confirmations", three or six or nine or whatever, to initiate the auto-update on all the other thousands of copies.
Every change to the "coin" or cell is permanently written to the cell and visible to everyone. So, every transfer of ownership, every content addition or change, all of it is permanently recorded in the cell, impossible to erase. Everyone can see the whole history of everything that happened in that cell and to that cell, right down to the last niggling little detail. Forever.
So, if you want permanent records and don't mind them being publicly visible to everyone with access to a computer, this is a great feature. Every public record could be permanently recorded into a blockchain. Medical records could be put in a blockchain, instantly accessible by medical personnel anywhere. You might think "Good heavens! I don't want everyone to know I had my gallbladder out!" Not a problem - encrypt the data before you stuff it into the cell. Now everyone can see the encrypted data in the blockchain, but only you have the key. When you show up at the hospital, the doctors check the blockchain with the key you supply for that record, and they can see the relevant details about your gallbladder. Without the key, no one else can read the cell contents. Win-win, the record can be updated by the doctors with your permission and the payment of the very nominal processing fee to update the blockchain. These are a couple of use cases. There are many more.
Some blockchains have no upper limit to the number of cells in their spreadsheet, so new "coins aka "land" aka "spreadsheet cells" are continually created. Other blockchains have a hard upper limit - only so many coins will ever be created and that's it. Some blockchains generate new "coins" at a steady rate, a certain percentage a minute/hour/day. Other blockchains generate new "coins" according to other methods. Some blockchains come with all the coins they will ever have already in existence when they first publish their Initial Coin Offering (ICO).
As I pointed out before, each blockchain has its own unique characteristics. How, and how many of, the new coins are generated (and how new coins are generated) affects the value of the coin. Just as there is no single agreed upon "best set" of qualities, there is no single agreed upon "best method" for coin generation. People are still figuring out what works best for which applications. All of these unknowns are why values fluctuate so steeply.
Is cryptocurrency overvalued, in a bubble? It really is impossible to tell. It should be obvious that this is a pretty new technology, a new way of thinking about how to deal with information. How useful is it? Well, that's what the market is trying to figure out. The more people think about it, the more useful it seems to be, which is why the "coins" or the "real estate value" of the various distributed ledgers are steadily increasing. Is a lot of it pure mis-calculation? Could it be that this thing is really a lot less useful than it appears? Sure.
It's a penny stock, land speculation, stock market gambling, all wrapped up in a portable package that transcends both national boundaries and national currencies. It allows anyone with a cell phone to become his own personal uninsured bank and banker. Is it safe? Probably not, but maybe it will be once we figure out what it is and how to cage it. Is it fun? Yes. | 677.169 | 1 |
Fully explained and written solutions to the OCR 2017 AS Mathematics Core 2 exam paper. The questions are split by each part so that you can easily navigate to the parts you and the students want to look at.
If you find this useful there are many other free exam solutions on my youtube channel: MissPennyMaths
40 slide Powerpoint for Advanced Higher Maths Unit 2: Complex Numbers.
There is a brief revision of the basics of Complex numbers followed by a series of questions.
The 24 questions (many of them multi-part) require the construction of Argand Diagrams, use of the quadratic formula, polynomial long division, and simultaneous equations.
There are fully worked solutions (including diagrams) for complex number topics relating to:
Equating Real and Imaginary Parts;
Finding square, cube, fourth, fifth and sixth roots of complex numbers (including unity) and plotting them on an Argand diagram;
Verifying and finding roots of complex number polynomials;
Expanding and simplifying complex numbers using the Binomial Theorem and De Moivre's Theorem;
Interpreting geometrically loci in the complex plane;
Conversions between polar and rectangular forms;
Complex Conjugates;
Exponential Form;
Trigonometric identities, substitutions and simplification.
The questions are grouped in approximate order of difficulty and to match the usual order of progress through this topic.
*Animated workings come up line by line on mouse clicks.*
Presentation covering the whole of chapter 8 (4-6hrs) from the Pearson Edexcel Pure Mathematics Year 1/AS book. Includes examples and notes for;
Pascal's triangle
Factorial notation
The binomial expansion
Solving binomial problems
Binomial estimation
Suitable for the new A-Level specification year 1 or AS-level.
Presentation designed to be used as teaching aid for entire block of lessons. Opportunities for students to work through examples, and notes on key points. All learning objectives included and maintained throughout the presentation. Editable for you to select you own questions or add consolidation work. | 677.169 | 1 |
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New question banks for new AS and A-level Mathematics and Further Mathematics specifications. Currently containing all specimen papers plus Pure Core module questions re-mapped to the new specifications. Regular free updates will complete all question banks by early 2018. | 677.169 | 1 |
From the people who brought you the Dummies instructional book series, brings you the same non-intimidating guides in video form. This is Mathematics for Dummies. Just watch this video tutorial to learn how to connect slopes and derivatives, For Dummies.
Finding a derivative on a curve reveals the slope or steepness at graph points. This video tutorial shows you how calculus connects to algebra formulas you already know. | 677.169 | 1 |
Algebra Interval Notation Task Cards plus HW
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Algebra Interval Notation Task Cards plus HW
This activity is appropriate for all levels of Algebra. Interval notation is an important concept that students have traditionally had difficulty with. This set of task cards reinforces the relationship between interval notation, inequalities, and graphing on a number line.
Included:
☑ 24 Task Cards.
#1 – 10 Given a number line graph, students are to determine the interval in both interval notation and as an inequality. There are two versions of these cards, one with ( ] notation and the other with open and closed circle notation. Print out the version you prefer.
#11 – 17 Given an inequality and students are to determine the interval notation, and graph it using the real number line.
#18 – 25 Given an interval, students are to determine the inequality, and graph it using the real number line.
☑ Master List of questions with answer key included. This can also be used as a worksheet.
☑ Student response sheets with blank graphs for selected problems.
☑ Additional Handout with15 questions. This can be used for Homework, Assessment, or Enrichment | 677.169 | 1 |
Topics in Mathematics for the 10th Grade Robert Neumann
$25.00
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This
series, "Mathematics for the High School," in mathematics was
specifically designed with math teachers in mind. Not only are the books
a useful resource for gaining familiarity with teaching approaches used
in a Waldorf school, but they are also a source of inspiration –
offering fresh perspectives and new insight – for course that have
perhaps been taught many times.
The
material is not only described theoretically, but includes many
examples, exercises and "hands-on" hints for the lessons. Some
information about the historical background of the major themes rounds
out many of the contributions. | 677.169 | 1 |
Learning Mathematics
From Hierarchies to Networks
How and why is mathematics taught? This book seeks to improve on our current answers. The contributors provide various perspectives in this richly cross-referenced work. Relevant to policy makers, practitioners and researchers. | 677.169 | 1 |
Practical algebra lessons that emphasize the practicalities of understanding the questions and intelligently and simply Formatting Math as Text (how to type math when e-mailing or posting Reviews of. Internet Sites: Free Help Free math lessons and math homework help from basic math to algebra , geometry and beyond. Students, teachers, parents, and everyone can find solutions to Free algebra lessons, games, videos, books, and online tutoring. We can help you with middle school, high school, or even college algebra , and we have math Algebrahelp .com is a collection of lessons, calculators, and worksheets created Math Resources. ·Prime Numbers List ·Perfect Squares Chart ·Study Tips Pre- Algebra , Algebra I, Algebra II, Geometry: homework help by free math tutors, solvers, lessons. Each section has solvers (calculators), lessons, | 677.169 | 1 |
10th grade geometry textbook PDF
Review of "10th grade geometry textbook"
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Solutions to exercises in geometry textbooks more. regardless of the subject. having a real person explain it 10th grade geometry textbook like a teacher or looking up help based upon the page number of his math textbook is for my 10th grade son in geometry 10th grade curriculum. world history us government us history european history enter your math …. the lessons offer a convenient way. tenth grade is when students should find themselves as more comfortable in math (10) environmental science textbook and digital. classzone book angela bofill i try free download finder. 10th grade math students typically study geometry, 10th grade geometry textbook although that is not always the case because students have progressed at different rates. spanish latin french more languages. this 10th grade geometry textbook replacement course covers all of the topics in a standard geometry textbook. find great deals on ebay for geometry textbook grade 10. shop with confidence test and improve your knowledge of 10th grade geometry textbook with fun 10th grade geometry textbook multiple choice exams you can take online with study.com. | 677.169 | 1 |
Course Description: The course reviews and expands incrementally upon the content taught in SaxonMath 5/4 with increased emphasis upon the methods and tools of mathematical problem solving. Mental computations, patterns and functions, statistics, and probability, are reviewed with expanded study of geometry, fractions, mixed numbers, and decimals. Percentages and negative numbers are introduced. | 677.169 | 1 |
Math education by exam3.0
Publisher Description
Base skills for pre-kindergarten through high school and soon, skills cover it all from level 0, 1 to 12!
We're constantly adding new skills for pre-kindergarten through high school and soon, we're introducing calculus! From exciting and interactive to rigorous and cognitively demanding, skills cover it all from level 0, 1 to 12!
Math Academy app covers basic skills and high school. It categorizes different aspects of math in such a way that you can pick up what you plan to learn and start learning. We plan to cover all the topics in math general education. You can enjoy the following topics
If you have a suggestion or issue with this app please kindly let us know through email. We always try to respond immediately
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Math education by exam is a free software application from the Kids subcategory, part of the Education category.
The app is currently available in English and it was last updated on 2016-01-23. The program can be installed on iOS.
Math education by exam (version 3.0) has a file size of 141
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The latest version is 3.0 and it was updated on soft112.com on 2018-01-25.
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Description: The present text is the result of several years of study and trial in the classroom in an effort to make an introduction to college mathematics more effective, rational and better suited to its place in a scheme of education under modern conditions of life.
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Endorsed by the OCR for use with "Additional Maths (FSMQ)", this textbook covers the exact requirements of the specification. It should be a useful text for Higher Tier students taking their GCSE early as they can gain a recognised qualification without having to embark on their AS modules. It gives students a taster of AS/A Level maths and aids their choice of AS/A Level modules. It should also be ideal for students who intend to follow AS/A Level further maths by giving them a "head start" on their course. The content of the course covers four areas from pure mathematics: algebra, coordinate geometry, trigonometry and calculus and three areas from applied mathematics: statistics, mechanics and decision and discrete maths.
Product Details
Table of Contents
1 Algebra: review Linear expressions Solving linear equations Changing the subject of an equation Quadratic expressions Solving a quadratic equation that factorises Completing the square Simultaneous equations 2 Algebra: techniques Linear inequalities Solving quadratic inequalities Manipulating algebraic fractions Solving equations involving fractions Simplifying expressions containing square roots 3 Algebra: polynomials Operations with polynomials The Factor Theorem The Remainder Theorem 4 Algebra: applications The binomial expansion The binomial distribution 5 Co-ordinate geometry I Co-ordinates The gradient of a line Parallel and perpendicular lines The distance between two points Midpoint of a line joining two points The equation of a straight line Drawing a line given its equation Finding the equation of a line Intersection of two lines The circle 6 Co-ordinate geometry II, applications Inequalities Using inequalities for problem solving 7 Trigonometry I Using trigonometry in right angled triangles Trigonometrical functions for angles of any size Solving trigonometrical equations Identities involving sintheta, costheta, and tantheta The area of a triangle The Sine and Cosine rules 8 Trigonometry II - Applications Applications of the Sine and Cosine rules in 2-D Height and distance problems in 3-D 3-D problems involving solids 9 Calculus I - Differentiation Finding the gradient of a curve Differentiating by using standard results Tangents and normals Stationary points Curve sketching 10 Calculus II - Integration Reversing differentiation Using integration to find areas 11 Calculus III - Applications to kinematics Variable acceleration problems The formulae for constant acceleration
Promotional Information
Teach with confidence, knowing your students will be fully prepared for their exams, with this detailed textbook, endorsed by OCR.
About the Author
Val Hanrahan has been Head of Maths at an Independent school. She has also written several Pure Maths A/AS texts.Roger Porkess has written and edited books for GCSE, A/AS level and Key Stage 3.
Reviews
This is the officially endorsed course text and as such represents the best text book offering for the Additional Maths OCR qualification. It covers all of the topics in a clear fashion and is well presented. However, I would say that it needs more questions for practice and it lacks some of the more challenging, quirky-style of problem which candidates will meet on the examination. Overall it is a good text book but will need to be supplemented with other material (such as the practice book!). -- Mr Stephen Black * Abigail Lambert * ...it contains all the information you'll need for the course as well as a HUGE number of questions for practice and makes it all very interesting. * Additional Mathematics for OCR | 677.169 | 1 |
CalculusMathematics 005)
Authors:
Catherine Hutchings (4th edition revision). Illustrations by Stacy Stent
The 4th edition of 'Studying at University: A guide for first year students' is intended to provide new students with the knowledge and skills required for coping with their studies and academic assig
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Teaching & Learning Context:
This guide is intended to help new students adjust to university life, with a particular focus on studies in the Humanities. However, much of the information is relevant to all students new to studying at university.These materials include teacher notes and student instructions for 1 hour activity for a module on Laban Movement Analysis. The activity is designed to give students an opportunity to practice and apply movement analysis, observational skills and documentation skills to film analysis. The activity specifically addresses turning actions. However, any movement theme may be featured such as aerial forms, gestures, circular paths, or floor plans.
Image from ?Songs of Near and Far Away. Illustrated and written by E. Richardson?, 003093646
Author: RICHARDSON, Emmeline.
Page: 38
Year: 1900
Place: pp. 80. Cassell & Co.: 153 Nidderdale: upon notes and observations other than geological, made during the progress of the Government Geological Survey of the district, 1867-1872?, 002276447
Author: LUCAS, Joseph F.G.S
Page: 152 227 24 195 421 196 707 | 677.169 | 1 |
Sunday, February 28, 2010
Like most non-traditional college students, I really struggled and had trouble with college algebra. One of the issues I had was that it had not just been too long since taking algebra in high school, it had been too long since I had used much math at all. I discussed this with the introductory algebra teacher, and eventually tried to make the same case for my own students who were having math issues, but the main problem is that colleges will not go back into basic math to help students get to the point that algebra makes sense.
Fortunately, I had homeschooled my son through high school. When he had trouble with algebra, we did a grade level exam and found that he had missed some information from 4th and 6th grade math. Once we went back and addressed those problems, we started with pre-algebra, and he whizzed through all his math courses after that, without much help from mom (since I was not able to do the same work he was doing).
I used his pre-algebra book to relearn fractions, ratios, percentages, review basic multiplication and division, and reacquaint myself with all the stuff you have to learn before doing well with algebra. Because I had worked some with my son while he was learning algebra, my understanding was spotty, but I knew enough to do well on the ACT. I had to pressure my advisor to let me into the introductory algebra class, but will always be grateful I knew myself well enough to insist. I could not have passed algebra without taking the time to work through some pre-algebra work and work through introductory and intermediate algebra.
The textbooks my son used in his high school work, and that I borrowed to help me learn algebra, are available from Amazon.com.
I like these books, because they don't expect you to understand or know anything. Alan Wise is thorough in his explanations, and the books are not designed to have an instructor helping you understand the material, unlike many school textbooks. They have the material for the chapter, then a section on worked problems that explain step by step how to do the problems, then a list of what you need to have learned, followed by a few pages of problems for you to try. At the very end of each chapter are the answers to all problems, so that you can check to see if you correctly did the work.
I can't recommend these books highly enough. They helped me make it through my college algebra courses with an A in both introductory algebra and intermediate algebra, and a B in college algebra. If you are having trouble with algebra, I believe these books will help in your efforts to pass algebra.
Wednesday, February 24, 2010
Every five weeks, I see a new group of students beginning their college careers. Some of these students are traditional students, but most fit into the nontraditional or even untraditional categories. Nontraditional students are usually defined as anyone who has been out of high school for more than six months, or has a family. Untraditional students are usually older adults (meaning out of high school for five or more years), and can be adults returning for second career training.
Some untraditional students may have had college courses before, may even have completed college degrees before, but have been out of college for many years. Even with previous degrees behind them, untraditional students often feel out of place and concerned over their ability to complete the course work. Untraditional students may be in college due to loss of a job and inability to locate comparable work, death of a spouse who supplied the family income, divorce, another life changing event, or may have just decided that it was their turn to get an education. Whatever the reason, untraditional students seem to have strong emotions such as fear of the unknown. They are out of their comfort zone, so to speak, and don't know what to do, how to do it, or even if they can do it.
As an untraditional student who started classes in January 1998 and just never quit going to college, I can relate. One thing to keep in mind when starting something new, however, is something Lou Tice of The Pacific Institute tells his students, "It is OK to be afraid. It is not OK to stay afraid." New experiences can be frightening, but with determination, study, and perseverance, we can make it through the education process to walk across the stage and receive a diploma well earned.
One way Lou Tice recommends to help you do this is to create affirmations. Affirmations are single sentence goals that are always positive and always present tense. "I have accomplished my goal of earning my degree," is a sample affirmation. Make up several affirmations and say them out loud several times every day and you will find that they come true, just because you unconsciously start looking for ways to make them come true. Learning requires students to go beyond their comfort zone. Take a deep breath, settle your nerves, and get started. Come on in--the water is fine.
Tuesday, February 9, 2010
Stepping onto a campus, of any size, after several years absence, or for the first time ever, can be a bit overwhelming. Fear is normal. It is also normal to feel like all the younger students are staring at you, and that you will never fit in. Don't worry. You don't have to fit in or be popular, this is not high school. You are in college to learn, fulfill your dreams and start anew. Relax, the chances are you will excel in your new environment.
Scheduling is Everything
Before you ever begin a class you have to create your schedule. Many students find this preparation the most confusing time of their school career. Non-traditional students must consider two things when selecting their class schedules, what else is going on in their life, and can they be reasonably sure that they can make it to their classes.
Children, spouses and work all make big impacts on your schedule. Many classes require a lot of outside studying. Can you commit to the hours needed for class preparation, projects and activities? If not, you better select a different class. Some teachers are more lenient towards non-traditional students, but they will still expect your best efforts. If you can't give them, don't bother.
Also, consider you time constraints. Do you have to be somewhere every Thursday, does PTO meet on Mondays? What about driving time, carpool? Does the class you're considering conflict with any of these things? If so, you may want to choose a different class, or make a commitment determining what things you are going to give up during that particular class time. Don't make these decisions on impulse. Carefully consider all your options before committing to a class.
Confidence Determines Success
The very first day of class the pressure may seem unbearable. Walk into class with your head held high, and with your most inviting smile on your lips. A smile can actually break the tension in the class. There are many students that are just as scared as you are.
Make eye contact with people. This eye contact may actually help you make friends. A person's response will also help you to decide if he is a possible partner for any group projects that may be assigned during the class.
Notes are Key
On the first day of class you will always have an A. It is your job to keep it. Properly formulated notes can be the key to keeping high marks. Consider what the teacher is saying. You do not have to record everything he says.
If your teacher is fond of telling pointless stories, don't take write them into your notes. It is a waste of paper, and it will also waste your studying time. Leafing through pages of notes to find a few lines of pertinent information is never fun. Record things that are related to the class or the things that the teacher says will be on the test.
Develop Your Own Note Taking System
Make use of colored pens, highlighters or computer software to keep track of important information. Programs like Microsoft OneNote are perfect for recording notes and important facts. The OneNote program allows the user to create folders for individual classes, as well as daily pages under a class heading.
Remember, you will succeed as a non-traditional student. Be your biggest cheerleader and keep on trucking | 677.169 | 1 |
Pages
Sabtu, 18 April 2015
Spectrum Math, Grade 7
Best Book Spectrum Math, Grade 7
Product Description
Test with success using the Spectrum Math workbook! This book helps students in grade 7 apply essential math skills to everyday life. The lessons focus on ratio and proportion, fractions, percents, calculating interest, perimeter, volume, and statistics, and the activities help extend problem-solving and analytical abilities. The book features easy-to-understand directions, is aligned to national and state standards, and also includes a complete answer key. --Sales Rank: #1609 in Books
Brand: Spectrum
Model: MGH0769636977
Published on: 2007
Released on: 2002-06-01
Original language: English
Number of items: 1
Dimensions: 10.80" h x .38" w x 8.40" l, .76 pounds
Binding: Paperback
188 pages
Features
10.80L 8.40W 0.375H
0769636977
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Algebra 2 - Linear Programming
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Abstract:
This introductory text walks readers from the fundamental mechanics of lift to the stage of being able to make practical calculations and predictions of the coefficient of lift for realistic wing profile and platform geometries.Read more...
Reviews
Editorial reviews
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This book is a very useful digest of key points from the literature, carefully structured and presented with helpful pointers as to how the successive aerodynamical models can be implemented in the now so readily available interactive matrix computation systems. (Aeronautical Journal, 1 August 2013)Read more... | 677.169 | 1 |
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This book is an "impedance match" between high school math and science, and university physics-with-calculus at the level of Halliday-Resnick. It is for students who have done reasonably well in the standard high school courses but who need practice with the applications of quantitative methods. The topics covered are those fundamental skills and techniques that are most needed and assumed in introductory physics, but that many students do not have. Students who have taken a course based on this book have established a good record of doing well in their subsequent physics course | 677.169 | 1 |
Calculus tutorial
Introduction. Welcome to the SageMath Calculus Tutorial! From initial concepts to increasingly complex techniques and applications, this tutorial is meant to. Learn differential calculus for free—limits, continuity, derivatives, and derivative applications. Full curriculum of exercises and videos. Calculus is the study of the changes taking place in a system over time. Mathematicians, scientists, and engineers use calculus in their work to make predictions. Calculus 1 studies rate of change in functions while learning methods, techniques and applications as a whole. Isaac Newton used calculus to develop his laws of.
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Calculus tutorial
Directory of calculus links for tutorials, homework help, history sample tests, and tips on exam preparation. Cheat Sheets & Tables Algebra, Trigonometry and Calculus cheat sheets and a variety of tables. Class Notes Each class has notes available. Most of the classes have. Short descriptions and examples for limits, derivatives, and integrals. Various plug-ins are needed to view some of the pages.
Flash Tutorials for the Calculus Phobe Chapter One: Limits and Continuity Lesson 1: What Is a Limit? Lesson 2: When Does a Limit Exist? Lesson 3: How do you evaluate. Calculus for Beginners and Artists. Chapter 1 Why Study Calculus? Chapter 2 Numbers; Chapter 3 Linear Functions; Chapter 4 Quadratics and. An introduction to the basic concepts of calculus. The derivative and integral are explained. Calculus resource links are included. Calculus is the study of the changes taking place in a system over time. Mathematicians, scientists, and engineers use calculus in their work to make predictions. | 677.169 | 1 |
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Description: This classic introduces the concepts and uses of probability theory. It demonstrates, without the use of higher mathematics, the application of probability to games of chance, physics, reliability of witnesses, astronomy, insurance, democratic government, and many other areas. It also shows how scientists can express complex ideas in simple terms.
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Probability Course by Gian-Carlo Rota - David Ellerman In 1999, Gian-Carlo Rota gave his famous course, Probability, at MIT for the last time. The late John N. Guidi taped the lectures and took notes which he then wrote up in a verbatim manner conveying the substance and the atmosphere of the course. (1397 views)
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Subscription based homework help videos in science (physics, biology and chemistry), math (algebra 1 and 2, geometry, trigonometry, pre-calculus and calculus) and English (writing and grammar). The site also offers U.S. high school test prep (AP, SAT, ACT,...
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Based on the authors' three decades of teaching experience, Advanced Engineering Mathematics presents the fundamentals and theoretical concepts of the subject in an intelligible and easy-to-understand style. The carefully planned chapters make this book an effective tool for teaching the application of mathematics to engineering and scientific problems.
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Jacobs Elementary Algebra
CalmingTea
Reviewed on Tuesday, July 19, 2016
Grades Used: 9th
Dates used: 2016
My son used Saxon from 2nd through 8th grade, and then used AOPS (Art of Problem Solving) for most of Algebra 1. AOPS is a very intense, discovery based method for extremely gifted learners and lost my son at the end.
We picked up Jacobs to finish the year. I must say, Jacobs is an interesting text, friendly, well written and it has some challenging word problems mixed in for those who want to stretch their thinking.
However, my son found it frustrating that there were few examples, and no teacher's manual, or solutions...just answers. Now you can purchase some of those items from Ask Dr. Callahan website. But even with those helps, I will echo one of the previous reviewers and say that Jacob's is for the intuitive math student. It doesn't give a lot of examples so the student has to read the short intro, see one example, and then the problem sets are what lead the student into the intuitive understanding of the algorithms and also the concepts.
My son is very good at math and maybe even nearing the gifted range, but this is not the style for him. He prefers to learn the math, and then look up the concepts...
For mom, this is a lot more difficult to use, because it doesn't include all the helps that Saxon, Math U See or other popular publishers offers. So keep that in mind as well. You will spend a lot more time teaching, and talking about the math using Jacobs. If you're great at math, then that is a bonus. If not, or if you have a student that prefers to learn on his own, you may find this exhausting.
bec-rockz
Reviewed on Thursday, February 6, 2014
Grades Used: 9th
Dates used: 2013-14
I agree with other reviewers that this is not a good fit for a child who is weak in math. This course was TOUGH for my dd15, although I, as the teacher mainly liked it. My dd went straight to Algebra from Saxon with no pre-algebra, and did fine the first half of the book through the mid-term. We then took an extended summer break, and I thought we would never muddle our way through the second half of the book. Thankfully, Mr. Jacob's has PLENTY of practice problems. the book is set up with 4 sets of problems per lesson. Set 1 is review of previous lessons/concepts. Set 2 is practice problems for that day's lesson. The answers to Set 2 problems are in the back of the book, if the student needs to see if they got something correct or not, but there are no solutions to see HOW the answer was arrived at. (and if you have a child like mine, who feels checking her answers is cheating, they are useless anyway, lol). Set 3 problems are identical to the set 2 problems, using different numbers, so the student can have an extra day of practice if they need to. Set 4 is a challenge problem, for fun or extra credit. On a normal day my daughter did all the set 1 and set 2 problems. We would then move on to the next lesson the next day, unless she got a C or below on the set 2 problems. If that happened, we did the set 3 problems the following day before moving on to the next lesson. Each set 2 and set 3 section had between 50 and 65 problems, and for us, algebra took an average of 2 hours per day, including the lesson, the problems, and correcting any mistakes.
Overall, my dd did fairly well with this program, although she struggled a bit the last few chapters we did. We ended up skipping the last 2 chapters (16 and 17), which Mr. Jacob's says is fine, as that is for the student who is advanced in Algebra or plans to pursue a career in math. I feel the lessons were explained very well, the examples were perfect for the lesson and assignments, and there was more than ample practice and review throughout the book.
My only 2 cons to Jacob's Algebra were: 1.) He sometimes gave far too lengthy introductions to the lesson before getting on to simply explaining HOW to do the actual math, which was confusing to both me, as the teacher, and my dd, as the student, but we soon learned to skim over his passionate introductions and get down to the lesson, and 2.) to view solutions to the problems we had to buy a separate solutions manual, written by Mr. Jacobs and Cassidy Cash 30 years after the original textbook was published. We very rarely used the solutions manual until the last few chapters, but then it was worth having. Also, the tests were in yet another book, the Test Masters book.
Overall, I feel Jacob's Algebra was a good, solid Algebra 1 program. I would use it again, and hope to, with my younger daughter when she is ready for it. I would hesitate to recommend it for a child weak in math, though. I have heard many people say this program is more of a pre-algebra course....I beg to differ. This course covered everything one would need to be a full credit of Algebra and then some. Looking over scope and sequence of other Algebra TWO programs, we have already covered much of the material, a good 50-75%. If rating this on a scale of 1 to 5, I would give Jacob's 4 stars.
NancyR
Reviewed on Saturday, July 14, 2012
Grades Used: 8th & 9th
Dates used: 2006-2008
I consider the Harold Jacobs Algebra and Geometry curriculum to be one of the best investments I have made for my son and daughter. I purchased the Student Text, Tests, and Solutions Manual from Rainbow Resource Center, which currently lists them as available on their web site. Although the set is much more expensive than most other curriculum, I am convinced that Jacobs Algebra and Jacobs Geometry provided a very strong foundation for my kids, and also was the primary factor for high Math scores on their SAT s (which resulted in scholarship money for both). My son is starting his third year of college in Engineering, while my daughter is majoring in English. Although my daughter is bright, math is not her natural strength, yet she managed to earn a higher SAT math score than some fellow students who are actually more gifted in that area than she is and who used other math curricula. This curriculum is best suited for students who plan to continue math at least through Pre-Calculus. If a student struggles with math and only needs the basics, this is more thorough than necessary. Each lesson is structured so the homework is not just practice, but continues to guide the understanding of the student. My kids both spent about 1 - 1 ½ hours per lesson. Each lesson also includes optional problems that are similar to those found on the ACT/SAT. The Jacobs Geometry curriculum includes doing proofs that start with a few steps and builds to proofs that require multiple steps. Based on my own experience, I found this process prepared me for the logic involved in the multiple steps of Calculus, so I wanted proofs included in my son's math background.
Eli Robert
Reviewed on Saturday, April 3, 2010
Grades Used: 9th-10th
Dates used: 2009-2010
I love the Jacobs Algebra text, but I would agree that it is difficult to use without a solutions manual; the teacher's guide from Freeman (the publisher) offers limited support, often in the form of tiny copies of transparencies meant for a classroom, and it only includes a basic answer key.
But I was pleased to learn that a Dr. Callahan and his daughter Cassidy have released video lectures and a supplemental teacher's guide that work with the text. Also, they have worked with Mr. Jacobs to publish a solutions manual, released this year (2010). To me, this finally makes Jacobs a very usable text for homeschool families and tutors. | 677.169 | 1 |
Please contact your nearest Dymocks store to confirm availability
Email store
This book is available in following stores"e; Discrete and Computational Geometry"e; offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science.
This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincare conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also features numerous exercises and unsolved problems. The essential introduction to discrete and computational geometry Covers traditional topics as well as new and advanced material Features numerous full-color illustrations, exercises, and unsolved problems Suitable for sophomores in mathematics, computer science, engineering, or physics Rigorous but accessible An online solutions manual is available (for teachers only). To obtain access, please e-mail: Vickie_Kearn@press.princeton.edu the | 677.169 | 1 |
Demonstrates how a simple (no leak) solution can be adapted to solve more complex problems in which there is a bottom leak or...
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Demonstrates how a simple (no leak) solution can be adapted to solve more complex problems in which there is a bottom leak or a side leak. The side leak solution combines the no-leak and bottom-leak solutions.
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Animation
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Steve Reed, Susan Phares, Jeff Sale
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Jun 10, 2009Emphasizes the distinction between simple and compound interest as examples of linear and exponential growth. Application to...
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Emphasizes the distinction between simple and compound interest as examples of linear and exponential growth. Application to both earning and owing interest.
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Animation
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Bob Hoffman, Steve ReedRequires estimating and adjusting parameters to improve goodness-of-fit of linear and exponential models of population...
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Requires estimating and adjusting parameters to improve goodness-of-fit of linear and exponential models of population growth. Investigates extrapolation to predict future growth.
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Steve Reed, Bob Hoffman how the same equation applies across a variety of problems that differ in story content. Shows different methods...
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Illustrates how the same equation applies across a variety of problems that differ in story content. Shows different methods for solving the same problem.
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Steve Reed, Susan Phares, Jeff SaleSymmetry properties of the 4x4 array. The invariance of symmetry displayed in the author's Diamond 16 Puzzle (online)...
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Symmetry properties of the 4x4 array. The invariance of symmetry displayed in the author's Diamond 16 Puzzle (online) suggests insights into finite geometry, group theory, and combinatorics.
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Steven Cullinane
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Apr 17, 2002
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Apr 17 book is intended for a one semester introduction to abstract algebra. Most introductory textbooks on abstract algebra...
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״This book is intended for a one semester introduction to abstract algebra. Most introductory textbooks on abstract algebra are written with a two semester course in mind.
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Feb 01 children who are being home schooled. It provides a plethora of information to help children understand...
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This website is for children who are being home schooled. It provides a plethora of information to help children understand math.
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Nov 24 School Math to Bookmark material or Course ePortfolio | 677.169 | 1 |
Confusing Textbooks? Missed Lectures? Not Enough Time? Table of Contents: 1. Graphs and Digraphs. 2. Connectivity. 3. Eulerian and Hamiltonian Graphs. 4. Optimization Involving Trees. 5. Shortest Path Problems. 6. Flow, Connectivity, and Combinatorics. 7. Matchings and Factors 8. Graph Embeddings. 9. Colorings of Graphs. | 677.169 | 1 |
Algebra Survival Guide: A Conversational Handbook for the Thoroughly Befuddled
th the Algebra Survival Guide's First Edition, written by longtime teacher/tutor Josh Rappaport, the Second Edition takes a hard look at algebra's word problems and offers time-tested advice for cracking them. With a new 62-page chapter devoted to these word problems, the new edition tackles the ultimate math nightmares of the puberty years: problems involving rate, time and distance, work performed, and mixture formulas, among others.
With twelve additional content chapters that explain fundamental and advanced areas of algebra, the 352-page Second Edition guides students to success in pre-algebra and Algebra I. The Guide features a unique question/answer format so students hear their own questions echoed in the text. The book's answers, written in the voice of a friendly tutor, provide lucid explanation and answers, along with step-by-step instructions with explanations in English right next to the math steps. At the end of each one-page lesson, the book presents practice problems, giving students instant feedback on their grasp of the math. Additional chapter tests provide comprehensive checks for understanding.
The new edition boasts an expanded glossary and index, and contains a navigation tool that helps students know exactly where they are in the program. In addition, the Guide is adorned with lively illustrations by award-winning artist Sally Blakemore. These cartoons not only provide well-deserved comic relief for math learners, they also offer a visual way to grasp algebra's challenging abstractions. (Example: to illustrate the Reflexive Property of a = a, the cartoon shows a sad 'x' variable looking in the mirror while experiencing a 'bad hair day.') With all of these features, the Second Edition Algebra Survival Guide is ideal for homeschoolers, tutors and students striving for algebra excellence.
The Second Edition also aligns with the current Common Core State Standards for Math, so it's ideal for today's teachers, as well. Its content chapters tackle the trickiest topics of algebra: Properties, Sets of Numbers, Order of Operations, Absolute Value, Exponents, Radicals, Factoring, Cancelling, Solving Equations, and the Coordinate Plane. Loaded with thorough explanations, practice problems and answers, the new Algebra Survival Guide gives students the boost they need in a style they'll enjoy to master the skills of algebra....more
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thems themselves. It would be a good book for a tutor or a parent to quickly review Algebra 1 in an orderly fashion....morefrom Terri: of students over 10 years' time. He has seen first-hand the confusion students have with the vocabulary and the explanations of the typical algebra textbook. The guide uses the question and answer process to explain algebra concepts in clear and user-friendly language. The questions are typical questions other students have asked and the author offers the best answers to those questions. The guide uses great illustrations by Sally Blakemore to make the explanations fun, quirky and the algebraic concepts memorable for the student. The guide can be used as a quick reference guide, as a memorization tool, as a self-teaching program or as your survival buddy that shows you all the common mistakes and misunderstandings a typical student faces with Algebra. The Algebra Survival Guide has the stamp of approval from the Parent's Choice Foundation and 2011 winner of the Golden Porch Award for top tutoring products. Whether this is your first brush with Algebra or you want to clear up past algebra confusion, this is a great book to guide you on your way!...more
h her problem, go over them, and build from there.
My one complaint about the book (although not the companion workbook), is that the answers are right next to the problems. This makes it difficult for even the most dedicated learners to keep from peeking, which, of course, diminishes effectiveness....more | 677.169 | 1 |
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MTH1003 - General Mathematics
Course Description
A course designed to provide mathematical concepts and skills to assist students in using mathematics in their ministry, personal, and professional lives. The students will be given exposure to problem solving, set theory, historical systems of numeration, algebraic equations, geometry, consumer mathematics, and statistics.
Course Objectives
The following intended learning outcomes will be achieved by this course:
Develop critical thinking and problem solving skills.
Develop an understanding of the history and development of the base-ten numeration system.
Solve real number system applications using rules and properties of operations | 677.169 | 1 |
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Publisher Comments
Common Core Mathematics is the most comprehensive Common Core State Standards-based mathematics curriculum available today.
The modules are sequenced and paced to support the teaching of mathematics as an unfolding story that follows the logic of mathematics itself.
They embody the instructional "shifts" and the standards for mathematical practice that are fundamental to the CCSS.
Each module contains a sequence of les- sons that combine conceptual understanding, fluency, and application to meet the demands of each topic in the module.
Formative assessments are included to support data-driven instruction.
The modules are written by teams of master teachers and mathematicians.
In Common Core Mathematics, Geometry students explore more complex geometric situations and deepen their explanations of geometric relationships, moving towards formal mathematical arguments. Important differences exist between this Geometry course and the historical approach taken in Geometry classes. For example, transformations are emphasized early in this course. Close attention should be paid to the introductory content for the Geometry conceptual category found in the high school CCSS. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.
About the Author
Common Core ( is a non-profit organization formed in 2007 to advocate for a content-rich liberal arts education in America's K-12 schools. To improve education in America, Common Core creates curriculum materials and also promotes programs, policies, and initiatives at the local, state, and federal levels that provide students with challenging, rigorous instruction in the full range of liberal arts and sciences. Common Core is not affiliated with the Common Core State Standards Initiative. | 677.169 | 1 |
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Why UMS is better ?
In every mathematical topic covered by Universal Math Solver, the software can solve and present a step by step solution to any problem, regardless of how complex the problem is. All our competitors can only solve a limited subgroup of fairly simple problems in every area.
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These competing solvers either cannot solve these very elementary problems or worse yet, give incorrect or incomplete answers. Would you trust these programs with your complex homework?
UMS works like a "live" teacher. It allows for entering the problem in the same format as it written in a notebook and then presents a step by step solution accompanied by the voice of a professional teacher (available in 7 languages).
UMS can create a problem similar to one just presented to it by a user. Unlike other educational math programs that just have large collections from a particular topic, UMS can create a problem that utilizes the exact same mathematical concepts; no more and no less than the one just presented to it.
UMS offers an absolutely Free Algebra Equation Solver – our software with "Equations" section enabled. It will solve all you equations and systems of equations. There is no registration required nor there is a time limit. | 677.169 | 1 |
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MathCAD is a software for the personal computer that lets you create documentation and perform calculations in the technological and scientific fields. Mathcad belongs to a computer algebra system and allows you automatically to perform engineering calculations and complex calculations. Mathcad has an intuitive and easy to use user interface.
More detail information about it You can find in this category in our lessons, posts and articles. | 677.169 | 1 |
The Story of Stuff - Chapter 6 A seven part video explaining the life cycle of the products we buy and the ethical choices necessary presented with playful chalkboard diagrams and an energetic Annie Leonard. This sixth chapter gives an explanation of the disposal process in the cycle of creating materials. Chapter 1 introduces the life cycle and chapters 2-6 explain different parts of this cycle. Chapter 7 is a summary. Author(s): No creator set
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Solving Equations with the Distributive Property, Part 1 - Khan Academy In this video, Sal Khan demonstrates how to solve equations with the distributive property. Mr. Khan uses the software (with different colors) to illustrate his points. Sal Khan is the recipient of the 2009 Microsoft Tech Award in Education. (06:04) There is a lot of information on the screen--the viewer may want to open the video to 'full screen.' Author(s): No creator set
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Harmonic Motion, Part 2 Instructor tests whether Acos (wt) can describe the motion of the mass on a spring by substituting into the differential equation F=-kx. This video, which is suitable for high school students, starts with a black screen because the instructor, in his conversational tone, uses it as a 'chalkboard.' Instructor uses different colors for clarification. Run time 09:45. Author(s): No creator set
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9.66J Computational Cognitive Science (MIT) hu Author(s): Tenenbaum, Joshua
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Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative C
Lugosi teaches math - Positive series2 Béla Lugosi teaches advanced mathematical concepts in this video. This video shows a variety of tests to prove positive series. He begins with what is called a comparison test and formulates proofs. Lugosi's hidden love for mathematics is illuminated by his animated teaching style. This video is geared to older, advanced mathematics learners. Author(s): No creator set
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Anchises Excerpts from a video of a collaborative performance piece by Jonah Bokaer and Harrison Atelier. Ariane Lourie Harrison is a visiting lecturer in SA+P's Department of Architecture. Author(s): No creator set
Finding Percentages of a Whole Number The instructor uses a chalkboard to demonstrate how to figure out a percentage of a whole number. He uses a step by step approach by showing that you multiply the whole number by the percentage in decimal form. Author(s): No creator set
Morocco's King Mohamed visits France French President Francois Hollande welcomes the Moroccan King Mohammed VI at the Elysee palaceu Author(s): No creator set
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The Need for Achieving Appropriate Information Sharing and Information Protection David Bray describes the Information Sharing Environment, exploring post-9/11 information sharing in the United States, and the efforts being made towards information sharing and national security. In the aftermath of the September 11 terrorist attacks, the United States began a historic transformation aimed at preventing future attacks and improving its ability to protect institutions at home and abroad. As a result, the US is now better informed of terrorist intentions and plans, and better pr Author(s): No creator set
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Col. Leo Thorsness on Ethical Leadership in Combat and Prison When his wingman's plane was shot down over North Vietnam in 1967, Col. Leo Thorsness fought back. He relayed its position to search and rescue personnel, used his plane to distract the enemy while fellow airmen parachuted to the ground, destroyed two aircraft and turned back three others. Less than two weeks later he became a prisoner of war. He received the Medal of Honor for extraordinary heroism upon his return and went on to serve in the Washington State Senate. He currently serves on the B Author(s): No creator set
The nominal frequency range of human hearing is 20 Hz to 20 kHz, though most people cannot hear to 20 kHz. However, the pitches used in music correspond roughly to frequencies in the range from 20 Hz to 2.5 kHz. Generally, musical tones are not pure sine waves but are mixtures of sine waves with frequencies that can extend well beyond 2.5 kHz. However, although they are mixtures of sine waves, they are usually heard as having a single pitch.
How to Draw a Cartoon Character Outline Outlining helps you get a good foundation for the characteryou will draw. Work on finding the dimensions-how tall, how wide-creating a road map to draw your cartoon. Step-by-step narration by artist Danny Page. English captions. (2:06) Author(s): No creator set
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TALAT Lecture 3202: The Liquid Metal This lecture provides an introduction to factors affecting the quality of molten aluminium. Basic knowledge of foundry practice is assumed. The student should be able to appreciate the differences between good and bad melting practices in a foundry. Author(s): TALAT,Richard A Harding, Interdisciplinary Researc | 677.169 | 1 |
great introduction to the tricky concept of differentiation. Fully animated graphical display of how we use tangents to curves to differentiate a function, with regular examples for the teacher to explain key concepts. Solomon Worksheet Questions and Answers provided and embedded throughout the Powerpoint. If you like these resource, please review so I can see if there would be interest for my other A-Level / IB resources.
This bundle includes the Chain, Product and Quotient rule match-up activities. All with answers. All as pdfs file as well as the original powerpoint files for easy editing. Bonus resource = Chain Rule Practice activity. A well thought out series of questions based on variation theory for students to progress through learning how to use the chain rule and product rule match-ups.
Three match-up puzzles for pupils to practice product rule and quotient rule match-ups match-up product and quotient rule questions.
Set of questions of progressive difficulty, based on variation theory and grouped into clear sections for students to familiarise themselves with the chain rule, answers included. Tried and tested successfully in the classroom many times. This download includes a pdf file as well as the original word file for easy editing | 677.169 | 1 |
This booklet was designed to provide information on secondary school mathematics courses being developed or revised, reinforcing a National Council of Teachers of Mathematics recommendation calling for "a flexible curriculum with a greater range of options." A survey of mathematics supervisors led to the identification of over 450 persons who might be developing new courses; 147 replies were received, of which 74 courses were selected for this publication. Courses are presented in 12 categories: advanced mathematics, algebra, applications, business mathematics, computer mathematics, consumer mathematics, general mathematics, geometry, integrated mathematics, problem solving, statistics, and technical mathematics. For each course, information on 19 points are given: title of course, grade level(s)/length, site, date first taught, students allowed to enroll, why developed, objectives, prerequisites, course it precedes, persons involved in development, materials used, community resources utilized, teaching modes, special teaching skills/experience, number of students enrolled/completing, evaluation or indication of success, changes considered, course outline and topic/time, and contact person. Some sequences of courses are also listed. (MNS) | 677.169 | 1 |
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MATH TREK Algebra 1
04/01/04
For curriculum-based algebra instruction, teachers and students can use MATH TREK Algebra 1. The multimedia program includes tutorials, assessments and student tracking. Students can use the program's scientific calculator, glossary and journal to help them complete the various exercises and activities. The assessment and student-tracking features provide immediate feedback to students so that they can stay on top of their progress. This engaging program, complete with sound, animation and graphics, can be used on stand-alone computers or a network. NECTAR Foundation, (613) 224-3031, | 677.169 | 1 |
STEP BY STEP HELP WITH ALGEBRA
Step by step help with algebra
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The Best Book For Learning Mathematical Modeling
The best all-around introductory book on mathematical modeling is How to Model It: Problem Solving for the Computer Age by Starfield, Smith, and Bleloch. The book dates back to 1994, but is just as relevant today. When most direct marketing people talk about "modeling", they either mean predictive response models, or they mean financial spreadsheet P&L models. This book goes far beyond these applications, and teaches the skill of crafting novel models to help provide insight into a wide range of problems. It teaches the reader how to think about a problem, craft a mathematical representation, then use that representation Topics include model scope, heuristics, spreadsheets, risk, stochastic modeling, rudimentary optimization, dynamics, trade-offs, and expert systems. The book isn't a dry academic text book. Rather, it is a series of exercises and questions that teach modeling concepts in a hands-on manner. Highly recommended for analysts in any field. | 677.169 | 1 |
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The Little Green Math Book reads like a collection of math recipes to help us blend problems, principles, and approaches in creating our own lineup of splendid math cuisine. The book's four chapters include: (1) Basic Numeracy Ingredients, (2) Wonderful Math Recipes, (3) Favorite Numeracy Dishes, and (4) Special Math Garnishments. Along with 30 of the most fundamental, recurring math principles and rules, readers will find a three-tier system to rate the difficulty level of all problems -- one chili ("mild"), two chilies ("hot"), and three chilies ("very hot").
Fine-tune your numerical mindset with a quantitative review that serves as a refresher course and as a tool for perceiving math in a new way. Whether you're a high school or college student, test-prep candidate, or working professional, this book's wealth of explanations and insights makes it a perfect learning companion.
Enjoy the benefits of your own self-paced math course: *Contains 120 all-star problems to help readers discover the secrets of basic math. *Develop a feel for how numbers behave and what makes math problems tick. *Learn to solve equations by translating math into words and thinking conceptually. *Watch for pitfalls when working with percentage increase and decrease. *Use simple math to solve "business" scenarios involving price, cost, volume, profit, and break-even, as well as how to calculate markup versus margin and efficiency. *Be able to glance at graphs and grasp their underlying meaning. *Understand correlation: weak or strong, positive or negative, linear or nonlinear. *Gain a newfound confidence with an increased competency with numbers. | 677.169 | 1 |
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This resource is a demonstration lesson presented at the 2014 Write for Texas Summer Institute. It provides a snapshot of a four to five week unit that engages students in the reading and writing workshop modelStudents will learn to develop mathematical relationships and make connections to geometric formulas; use geometry to solve problems; use one-variable equations or inequalities in problem situations; and use multiple representations to develop foundational concepts of simultaneous linear equations. | 677.169 | 1 |
Wednesday, September 9, 2015
A Book of Abstract Algebra: Second Edition PDF Download
Accessible but rigorous, this outstanding text encompasses all of the
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Math Studies
Research Objectives
In our research it is a purpose to analyze various phenomena of the nonlinear dynamics. One is fluctuation effect of synchronization in the chaotic dynamics. The elements in heterogeneous systems are easy to synchronize than those in homogeneous systems, and we analyzed it with the use of the probability density function. Now, we consider more rigid and more detailed analysis. The other is the research of dynamics in coupled map lattices using nonlinear Frobenius-Perron equation. For the piecewise linear system, calculations in the nonlinear Frobenius-Perron equation are simpler, we research the dynamics of the infinite system size. As for classes for basic education, one of the big purposes is to provide understandable lectures and then to contribute to pharmacy studies. In mathematics and statistics as liberal arts, we aim to continue education to help professional studies in pharmacy. | 677.169 | 1 |
How can we help you?
Math for Pre-Health 2
Enrol in Math for Pre-Health 2
Course Code: MATH140
Learn to evaluate a variety of arithmetic and algebraic expressions and apply these principles to typical problems that arise in the health care fields. Concepts studied include numeracy fundamentals; systems of measurement and dimensional analysis; algebra, with an emphasis on analytical techniques; and evaluating systems of linear equations. You will develop essential critical thinking and problem-solving skills through exposure to application problems, including dosage calculations, solution dilutions, concentrations, and pH. Learn to use numerical methods along with graphs, charts, and tables to effectively describe data, calculate the empirical and theoretical probability of simple events using key rules of probability, and apply descriptive and inferential statistics to applications from the health care fields. Prerequisite: Math for Pre-Health 1 | 677.169 | 1 |
Book Details
ISBN 139781787123663
Paperback480 pages
Book Description
Physics is really important for game programmers who want to add realism and functionality to their games. Collision detection in particular is a problem that affects all game developers, regardless of the platform, engine, or toolkit they use.
This book will teach you the concepts and formulas behind collision detection. You will also be taught how to build a simple physics engine, where Rigid Body physics is the main focus, and learn about intersection algorithms for primitive shapes.
You'll begin by building a strong foundation in mathematics that will be used throughout the book. We'll guide you through implementing 2D and 3D primitives and show you how to perform effective collision tests for them. We then pivot to one of the harder areas of game development—collision detection and resolution.
Further on, you will learn what a Physics engine is, how to set up a game window, and how to implement rendering. We'll explore advanced physics topics such as constraint solving. You'll also find out how to implement a rudimentary physics engine, which you can use to build an Angry Birds type of game or a more advanced game.
By the end of the book, you will have implemented all primitive and some advanced collision tests, and you will be able to read on geometry and linear Algebra formulas to take forward to your own games!
Table of Contents
Chapter 1: Vectors
Introduction
Vector definition
Component-wise operations
Dot product
Magnitude
Normalizing
Cross product
Angles
Projection
Reflection
Chapter 2: Matrices
Introduction
Matrix definition
Transpose
Multiplication
Identity matrix
Determinant of a 2x2 matrix
Matrix of minors
Cofactor
Determinant of a 3x3 matrix
Operations on a 4x4 matrix
Adjugate matrix
Matrix inverse
Chapter 3: Matrix Transformations
Introduction
Matrix majors
Translation
Scaling
How rotations work
Rotation matrices
Axis angle rotation
Vector matrix multiplication
Transform matrix
View matrix
Projection matrix
Chapter 4: 2D Primitive Shapes
Introduction
2D points
2D lines
Circle
Rectangle
Oriented rectangle
Point containment
Line intersection
Chapter 5: 2D Collisions
Introduction
Circle to circle
Circle to rectangle
Circle to oriented rectangle
Rectangle to rectangle
Separating Axis Theorem
Rectangle to oriented rectangle
Oriented rectangle to oriented rectangle
Chapter 6: 2D Optimizations
Introduction
Containing circle
Containing rectangle
Simple and complex shapes
Quad tree
Broad phase collisions
Chapter 7: 3D Primitive Shapes
Introduction
Point
Line segment
Ray
Sphere
Axis Aligned Bounding Box
Oriented Bounding Box
Plane
Triangle
Chapter 8: 3D Point Tests
Introduction
Point and sphere
Point and AABB
Point and Oriented Bounding Box
Point and plane
Point and line
Point and ray
Chapter 9: 3D Shape Intersections
Introduction
Sphere-to-sphere
Sphere-to-AABB
Sphere-to-OBB
Sphere-to-plane
AABB-to-AABB
AABB-to-OBB
AABB-to-plane
OBB-to-OBB
OBB-to-plane
Plane-to-plane
Chapter 10: 3D Line Intersections
Introduction
Raycast Sphere
Raycast Axis Aligned Bounding Box
Raycast Oriented Bounding Box
Raycast plane
Linetest Sphere
Linetest Axis Aligned Bounding Box
Linetest Oriented Bounding Box
Linetest Plane
Chapter 11: Triangles and Meshes
Introduction
Point in triangle
Closest point triangle
Triangle to sphere
Triangle to Axis Aligned Bounding Box
Triangle to Oriented Bounding Box
Triangle to plane
Triangle to triangle
Robustness of the Separating Axis Theorem
Raycast Triangle
Linetest Triangle
Mesh object
Mesh optimization
Mesh operations
Chapter 12: Models and Scenes
Introduction
The Model object
Operations on models
The Scene object
Operations on the scene
The Octree object
Octree contents
Operations on the Octree
Octree scene integration
Chapter 13: Camera and Frustum
Introduction
Camera object
Camera controls
Frustum object
Frustum from matrix
Sphere in frustum
Bounding Box in frustum
Octree culling
Picking
Chapter 14: Constraint Solving
Introduction
Framework introduction
Raycast sphere
Raycast Bounding Box
Raycast plane and triangle
Physics system
Integrating particles
Solving constraints
Verlet Integration
Chapter 15: Manifolds and Impulses
Introduction
Manifold for spheres
Manifold for boxes
Rigidbody Modifications
Linear Velocity
Linear Impulse
Physics System Update
Angular Velocity
Angular Impulse
Chapter 16: Springs and Joints
Introduction
Particle Modifications
Springs
Cloth
Physics System Modification
Joints
What You Will Learn
Implement fundamental maths so you can develop solid game physics
Use matrices to encode linear transformations
Know how to check geometric primitives for collisions
Build a Physics engine that can create realistic rigid body behavior
Understand advanced techniques, including the Separating Axis Theorem
Create physically accurate collision reactions
Explore spatial partitioning as an acceleration structure for collisions
Resolve rigid body collisions between primitive shapes
Authors
Gabor Szauer
Gabor Szauer graduated from Full Sail University with a bachelor's degree in game development. He has been making video games professionally for over 6 years. He has worked on games for the Nintendo 3DS, Xbox 360, browser-based games, and mobile games.
In his free time Gabor makes video games, researches video game-related technologies, and likes to design and construct furniture. Gabor currently resides in San Francisco, working in the mobile game industry | 677.169 | 1 |
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Adequate texts that introduce the concepts of abstract algebra are plentiful. None, however, are more suited to those needing a mathematical background for careers in engineering, computer science, the physical sciences, industry, or finance than Algebra: A Computational Introduction. Along with a unique approach and presentation, the author demonstrates how software can be used as a problem-solving tool for algebra. | 677.169 | 1 |
Distribution Guide is a program allowing to build various graphs of statistical distributions. It enables you to enter the parameters of the particular distribution and display the graphs of such functions as PDF, CDF, and others.
A short ebook explaining a simple way to subtract integers for people who have trouble subtracting integers. This uses a method based on simply changing a subtraction problem to an addition problem based on helping people with algebra.
Calcul will help your elementary school students practice mental arithmetic or to do fractions. Choose addition, subtraction, multiplication, division or fractions; then set the range of numbers and the number of calculations for an exercise.
Curvilinear: Easy Learning Plane Analytic Geometry An Intuitively-Easy-To-Use visual interactive software, oriented to overcome the abstraction that exists in the Plane Analytic Geometry (PAG), this is a tool that makes it easy to learn and master th | 677.169 | 1 |
Description: The text for beginning graduate students of mathematics, engineering, and the physical sciences. The book covers elements of Hilbert space, distributions and Sobolev spaces, boundary value problems, first order evolution equations, implicit evolution equations, second order evolution equations, optimization and approximation topics.
Topics in Real and Functional Analysis by Gerald Teschl - Universitaet Wien This manuscript provides a brief introduction to Real and (linear and nonlinear) Functional Analysis. It covers basic Hilbert and Banach space theory as well as basic measure theory including Lebesgue spaces and the Fourier transform. (8937 views) | 677.169 | 1 |
Candida Barny, MT
The way this tool works, the step-by-step approach it provides to complicated equations it makes learning enjoyable. Great work! Jeff Brooks, ID | 677.169 | 1 |
Description
Applied Calculus 5th Edition is praised for the creative and varied conceptual and modeling problems which motivate and challenge students. The 5th Edition of this market leading text exhibits the same strengths from earlier editions including the ""Rule of Four,"" an emphasis on concepts and modeling, exposition that students can read and understand and a flexible approach to technology. Updated data and fresh applications throughout the book are designed to build student confidence with basic concepts and to reinforce skills. As in the previous edition, a Pre-test is included for students whose skills may need a refresher prior to taking the course.
PROJECTS: A HEATER IN A ROOM, OPTIMIZING RELATIVE PRICES FOR ADULTS AND CHILDREN, MAXIMIZING PRODUCTION AND MINIMIZING COST: "DUALITY" 401
FOCUS ON THEORY 403
DERIVING THE FORMULA FOR A REGRESSION LINE 403
9 MATHEMATICAL MODELING USING DIFFERENTIAL EQUATIONS 409
9.1 MATHEMATICAL MODELING: SETTING UP A DIFFERENTIAL EQUATION 410
9.2 SOLUTIONS OF DIFFERENTIAL EQUATIONS 414
9.3 SLOPE FIELDS 418
9.4 EXPONENTIAL GROWTH AND DECAY 424
9.5 APPLICATIONS AND MODELING 430
9.6 MODELING THE INTERACTION OF TWO POPULATIONS 439
9.7 MODELING THE SPREAD OF A DISEASE 445
REVIEW PROBLEMS 450
STRENGTHEN YOUR UNDERSTANDING 452
PROJECTS: HARVESTING AND LOGISTIC GROWTH, POPULATION GENETICS, THE SPREAD OF SARS 455
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11. THE FLU IN WORLD WAR I 504
ANSWERS TO ODD-NUMBERED PROBLEMS 507
PRETEST 535
INDEX 539
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New case studies on medicine by David E. Sloane, MD.
Many new problems have been added, designed to build student confidence with basic concepts and to reinforce skills.
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Chapters 6 and 7 have been rearranged and combined, putting an introduction to antiderivatives before the applications to consumer surplus and present value. This gives instructors the choice of evaluating definite integrals numerically or using the Fundamental Theorem of Calculus.
As in the previous edition, a Pre-test is included for students whose skills may need a refresher prior to taking the course.
In additional to the new math functionality and administrative features you'll find in the 5th edition of the Applied Calculus WileyPLUS course, the author team has been hard at work improving the assessment question content to further enhance the link between the text and the WileyPLUS course to help ensure a seamless experience for instructors and students.
Pre-created assignments available to instructors for each section are based on the suggested assignments authors themselves use, and that are also available in the Instructor's Manual.
Each question has been checked for accuracy by the author team, including the testing of algorithmically-generated parameters and testing of tolerance levels.
The hint for each question has been reviewed and rewritten where necessary to provide more descriptive guidance for students.
The popular ConcepTests, questions designed to promote active learning during class which are modeled on the pioneering work of Harvard physicist Eric Mazur, are now available for automatic grading in WileyPLUS. Evaluation data shows that students taught with ConcepTests outperformed students taught by traditional lecture methods 73% versus 17% on conceptual questions, and 63% versus 54% on computational problems. | 677.169 | 1 |
AQA GCSE Maths (2017-18) Collection
Here you will find the complete collection of quizzes written by AQA to help you and your students in Years 9 to 11 prepare for the demands of the Maths GCSE.
You can click here to sign up to the completely free AQA Diagnostic Questions Schemes of Work. These schemes cover Years 9, 10 and 11 (Higher and Foundation), and are fully customisable to match the schemes of work you follow in your school. Once set up your students will automatically receive a year's worth of AQA quizzes - one immediately after each topic unit to identify misconceptions, and one three weeks later to test retention and understanding. Via our in depth insights you will learn more about your students' understanding of mathematics than ever before.
Alternatively, you might want to make use of the questions in class, or set individual quizzes for homework. The questions are fantastic for whole class discussions, identifying key misconceptions and encouraging students to provide their reasons. See our series of In the Classroom videos for more on this.
Disclaimer
These Diagnostic Questions have been written for the topics which feature in AQA's GCSE Maths 8300 Specification. We have released these questions to support teaching and learning for the new GCSE, rather than attempting to cover all of the content that could be asked. Real examinations may feature questions of a different style to those used here.
These questions have not been through the full AQA Question Paper production process, therefore they have not been through all the accuracy checks. If you spot a mistake, let us know by emailing maths@aqa.org.uk and we'll investigate. | 677.169 | 1 |
My daughter is dyslexic and has always struggled with math. Your program gave her the necessary explanations and step-by-step instructions to not only survive grade 11 math but to thrive in it. Thanks. Sharon Brightwell, WA Mr. Tom Carol, NY
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My son was in a major car wreak and was homebound for several months. I feared that he would fall behind in his classes. His math teacher recommended Algebra Helper, which literally took him through each problem step by step. Once my son was able to return to school, he had a better understanding of math then before he left. I would recommend this software to anyone! Barbara, LA Sonja Goyco, MS08-08:
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Mathematics for College Technology: MCT4C (Grade 12, College Preparation)
Availability
Semester 1, Semester 2
Prerequisite
Functions and Applications, Grade 11, University/College Preparation
Credit Value
1.0
Required Text
A textbook is not required for the course
This course enables students to extend their knowledge of functions. Students will investigate and apply properties of polynomial, exponential, and trigonometric functions; continue to represent functions numerically, graphically, and algebraically; develop facility in simplifying expressions and solving equations; and solve problems that address applications of algebra, trigonometry, vectors, and geometry. Students will reason mathematically and communicate their thinking as they solve multi-step problems. This course prepares students for a variety of college technology programs.
MCT4C is based on Mathematics, The Ontario Curriculum, Grades 11 and 12, Ministry of Education, Revised 2007. It is comprised of 7 units, each of which has from five to 7 activities (lessons and assignments). The first 6 units are term work; the final unit is the culminating task. | 677.169 | 1 |
Have Math Formulas on Hand (on Your iPhone or iPad) for Quick Reference
As you may know from my past posts, I'm always on the lookout for math apps that are more than just arithmetic. While not a teaching app, I have found another that fits the bill.
Math Formulas is a reference app that contains over 100 formulas covering topics such as Algebra, Geometry, Calculus, Trigonometry, Probability and Statistics, and more. Also, within each category, the formulas are broken down further into sub-categories, such as 2D Shapes and 3D Shapes within Geometry.
Tap on the formula you want and it is shown, along with examples of how it is used. From each formula page, you can navigate up and down to other formulas, or go back in the menu structure. For equations you use often, tap the star on their page, and they will be available in your Favorites list on the main menu.
Image: Mobile Formulas
You probably won't use all of the included formulas unless you're in school or do math for a living, but many of them will come in handy. I have often had to look up formulas for area and volume, or combinations and permutations. Or what the letters in the Greek alphabet are, or math prefixes (such as "nano"). This app would have come in handy for those purposes.
Some of the formulas have an explanation of what the variables and placeholders stand for, but not all of them do. If this improvement could be made, it would be more useful than it already is.
Math Formulas is a simple app, but for $1.99 in the iTunes store, it's handy for reminding you of math formulas on the fly | 677.169 | 1 |
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Mathematics is the music of science, and real analysis is the Bach of mathematics. There are many other foolish things I could say about the subject of this book, but the foregoing will give the reader an idea of where my heart lies. The present book was written to support a first course in real analysis, normally taken after a year of elementary calculus. Real analysis is, roughly speaking, the modern setting for Calculus, "real" alluding to the field of real numbers that underlies it all. At center stage are functions, defined and taking values in sets of real numbers or in sets (the plane, 3-space, etc.) readily derived from the real numbers; a first course in real analysis traditionally places the emphasis on real-valued functions defined on sets of real numbers. The agenda for the course: (1) start with the axioms for the field ofreal numbers, (2) build, in one semester and with appropriate rigor, the foun- dations of calculus (including the "Fundamental Theorem"), and, along the way, (3) develop those skills and attitudes that enable us to continue learning mathematics on our own. Three decades of experience with the exercise have not diminished my astonishment that it can be done | 677.169 | 1 |
Maths for GCSE and IGCSE® Textbook, Higher (for the Grade 9-1 Course)
New Maths for GCSE and IGCSE® Textbook, Higher (for the Grade 9-1 Course)
This superb Textbook is bursting with thousands of practice questions for Higher Level GCSE and IGCSE Maths — all fully up-to-date for all the new Grade 9-1 GCSE and IGCSE specs. It's a fantastic source of classwork and homework throughout the course, with answers included at the back of the book!
For each topic, there are worked examples that show students how to approach problems step-by-step, followed by a huge number of questions that build up in difficulty as they gain confidence.
And if you'd rather not hand out the printed books for homework, there's a brilliant Online Edition that students can read on a PC, Mac or tablet. There's also a money-saving bundle containing a printed Textbook and two Online Editions!
This book is also available for (this link will take you to the amazon.co.uk website). You don't need a Kindle to read it — just download the free Kindle App for your computer or tablet. | 677.169 | 1 |
A Discovery-Based Approach to Learning about Algebraic Structures Abstract Algebra: Structures and Applications helps students understand the abstraction of modern algebra. It emphasizes the more general concept of an algebraic structure while simultaneously covering applications. The text can be used in a variety of courses, from a one-semester introductory course to a full two-semester sequence. The book presents the core topics of structures in a consistent order: Definition of structure Motivation Examples General properties Important objects Description Subobjects Morphisms Subclasses Quotient objects Action structures Applications The text uses the general concept of an algebraic structure as a unifying principle and introduces other algebraic structures besides the three standard ones (groups, rings, and fields). Examples, exercises, investigative projects, and entire sections illustrate how abstract algebra is applied to areas of science and other branches of mathematics. "Lovett (Wheaton College) takes readers through the variegated landscape of algebra, from elementary modular arithmetic through groups, semigroups, and monoids, past rings and fields and group actions, beyond modules and algebras, to Galois theory, multivariable polynomial rings, and Gröbner bases." Choice Reviewed: RecommendedAbstract Algebra: Theory and Applications is an open-source textbook that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many non-trivial applications. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second-half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory.
A new approach to conveying abstract algebra, the area that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras, that is essential to various scientific disciplines such as particle physics and cryptology. It provides a well written account of the theoretical foundations; also contains topics that cannot be found elsewhere, and also offers a chapter on cryptography. End of chapter problems help readers with accessing the subjects. This work is co-published with the Heldermann Verlag, and within Heldermann's Sigma Series in Mathematics.
Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 editionThis textbook provides an introduction to abstract algebra for advanced undergraduate students. Based on the authors' lecture notes at the Department of Mathematics, National Chung Cheng University of Taiwan, it begins with a description of the algebraic structures of the ring and field of rational numbers. Abstract groups are then introduced. Technical results such as Lagrange's Theorem and Sylow's Theorems follow as applications of group theory. Ring theory forms the second part of abstract algebra, with the ring of polynomials and the matrix ring as basic examples. The general theory of ideals as well as maximal ideals in the rings of polynomials over the rational numbers are also discussed. The final part of the book focuses on field theory, field extensions and then Galois theory to illustrate the correspondence between the Galois groups and field extensions. This textbook is more accessible and less ambitious than most existing books covering the same subject. Readers will also find the pedagogical material very useful in enhancing the teaching and learning of abstract algebra.
Praise for the Third Edition ". . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . ."— begin to perform computations using abstract concepts that are developed in greater detail later in the text. The Fourth Edition features important concepts as well as specialized topics, including: The treatment of nilpotent groups, including the Frattini and Fitting subgroups Symmetric polynomials The proof of the fundamental theorem of algebra using symmetric polynomials The proof of Wedderburn's theorem on finite division rings The proof of the Wedderburn-Artin theorem Throughout the book, worked examples and real-world problems illustrate concepts and their applications, facilitating a complete understanding for readers regardless of their background in mathematics. A wealth of computational and theoretical exercises, ranging from basic to complex, allows readers to test their comprehension of the material. In addition, detailed historical notes and biographies of mathematicians provide context for and illuminate the discussion of key topics. A solutions manual is also available for readers who would like access to partial solutions to the book's exercises. Introduction to Abstract Algebra, Fourth Edition is an excellent book for courses on the topic at the upper-undergraduate and beginning-graduate levels. The book also serves as a valuable reference and self-study tool for practitioners in the fields of engineering, computer science, and applied mathematics.
Abstract Algebra: A Gentle Introduction advantages a trend in mathematics textbook publishing towards smaller, less expensive and brief introductions to primary courses. The authors move away from the 'everything for everyone' approach so common in textbooks. Instead, they provide the reader with coverage of numerous algebraic topics to cover the most important areas of abstract algebra. Through a careful selection of topics, supported by interesting applications, the authors Intend the book to be used for a one-semester course in abstract algebra. It is suitable for an introductory course in for mathematics majors. The text is also very suitable for education majors who need to have an introduction to the topic. As textbooks go through various editions and authors employ the suggestions of numerous well-intentioned reviewers, these book become larger and larger and subsequently more expensive. This book is meant to counter that process. Here students are given a "gentle introduction," meant to provide enough for a course, yet also enough to encourage them toward future study of the topic. Features Groups before rings approach Interesting modern applications Appendix includes mathematical induction, the well-ordering principle, sets, functions, permutations, matrices, and complex nubers. Numerous exercises at the end of each section Chapter "Hint and Partial Solutions" offers built in solutions manual | 677.169 | 1 |
Linear algebra will have the most direct application to geometry transformations used in rendering and physics. Diff Eq. and Calculus will be more in the realm of physics, statistics, with applications also in AI and graphics.
The more math the better though. Plan to learn all 4 if you can, and take now what will serve you best and most immediately, or in better shape to pursue the others later. If you're in college there's no rule against taking more classes than you need, it'll only cost you money and time -- be careful about keeping minimum grades up though, if you intend to take a heavier course-load than usual.
Edited October 3, 2014 by Ravyne
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I found multi-vector calculus to be far more useful than one would initially imagine. I like linear algebra, but the later stuff tended to be (as you mentioned) more proofs and less applicable to games.
- to each vector exists exclusive vector that when added result in the addition neutral vector (zero vector)
- to each vector exists exclusive multiplication inverse vector ( if multipled with, result in multiplication neutral vector= I so that I*x=x)
- a vector multiplied by vector is a vector of the space
--7
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Computer graphics is like 70% linear algebra, 20% calculus, 10% misc. But that doesn't mean a course in linear algebra is useful, partly because a lot of courses and books on linear algebra are !@#$ing terrible. The proofs in particular are completely pointless unless you have aspirations towards a master's degree or PhD in mathematics.
2 - to each vector exists exclusive vector that when added result in the addition neutral vector (zero vector) - to each vector exists exclusive multiplication inverse vector ( if multipled with, result in multiplication neutral vector= I so that I*x=x) - a vector multiplied by vector is a vector of the space -You are spreading misinformation.
85But I insist that in linear algebra generaly, there are axioms about multiplication operation if multiplication gets introduced onto vector space , having to be fullfilled with the new space and operations to keep it being a vector space .0
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Share on other sitesI can tell you that. In modern mathematics (after Grothendieck, I believe), you don't just study objects like vector spaces: You also study the morphisms between them that preserve the structure. In the case of vector spaces, the corresponding morphisms are linear mappings(*). When we talk about matrix multiplication being associative and all those things you mention, we are looking at matrices as representing linear mappings between vector spaces. A column vector represents a vector, and a row vector represents a co-vector, which is a linear mapping from the vector space to the field of scalars. The whole thing makes perfect sense without introducing a mechanism to multiply vectors.
(*)- Other examples are sets and functions, topological spaces and continuous functions, differentiable manifolds and smooth functions, and groups and group morphisms (they are just called that).
Edited October 5, 2014 by Álvaro
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looking at matrices as representing linear mappings between vector spaces.
I understand it similiary. The vector of N dimnesion has a space, and a space is well defined by N vectors of N dimension. If vector is to functionaly relate to those base vectors, it must have multilplication relation with a vector . Then vector can get expressed by other base vectors (transform).
At this point matrix is a set of vectors, that does not introduce further properties, the properties will emit only from the multiplication relation definition of vectors.
Of course, there is no requirement for multiplication relation of vector to be defined, so I know that when one says, linear Algebra, there is too much of subset having nearly disappearing common inclusion.
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Share on other sitesOpenGL uses the same data type for several different things, not just geometric vectors. In particular, it uses them for colors. The component-wise multiplication is in fact very useful in this case. Code implementations of mathematical concepts are rarely completely equivalent to their theoretical version.
2When we speak about matrix multiplication in the context of graphics programming we are speaking practically almost always about endomorphisms only (that is, mappings from a vector space \(V\) into \(V\) itself. The matrices are in this case always square. Square matrices form a ring, which includes the properties you are alluding to (like some matrices having a multiplicative inverse or associativity). These are properties of square matrices only, not any matrix. Again, linear algebra only defines a multiplication between matrices for: \( \cdot: \mathbb R^{n \times m} \times \mathbb R^{m \times k} \rightarrow \mathbb R^{n \times k}\) It should be obvious it is not possible to multiply just any matrices (or vectors if we chose to model them as a special case of matrix) together any way you please. It should also be noted that matrix multiplication is always associative (that is \( (A\cdot B)\cdot C = A\cdot (B\cdot C) \)) provided the dimensions of the matrices allow that multiplication in the first place. It is left as an exercise to the reader to show that the associativity does not interfere with the restricted multiplication operator above.
Edited October 6, 2014 by BitMasterThat is the usual definition of number theory. Study of properties of integers. As such it is useful in cryptography but not very useful for games. Numerical Analysis (also called Numerical Methods) is useful for physics programming etc.
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which includes the properties you are alluding to (like some matrices having a multiplicative inverse or associativity).
These are properties of square matrices only, not any matrix. Again, linear algebra only defines a multiplication between matrices for:
I apointed the rules only for multiplication of a vector, it does not automaticly imply rules about matricies.There is no need to have matricies invertable, to have multiplication operation on a vector space.Yes, you're right, I was mixed up.
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Linear Algebra (upper div with lots of proofs) (last chance to take it also)
Take this. You will examine questions to reasonings, proofs being honest (rare), and if you do, you will master a plenty . I am not smart myself (whaether I have strenghts or not in a smart field), but I handled it and it catalyzed me to master everything (except paranormal world we live in)
Linear Algebra is fair and flexing powerfull , making you able to aproximate paranormal real world. Linear Algebra is simple and honest and pasionate
(I thiknk I need a poem about linear algebra, it is an orgastic discipline, dive to it. It is no hard, being hardest)
Edited October 6, 2014 by JohnnyCode
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Share on other sitesAs the last time we talked about that: you can certainly add additional stuff (like operators) to a vector space. You might even be able to do more with it then (although the polite way in mathematics is to give it's proper name then), but that doesn't suddenly give all vector spaces that property.
Even so, if I remember correctly the last time that discussion came up you needed something like getting rid of a vector \(v\) on the right in an expression \(Av\) for a suitable matrix \(A\). Even if you have an inner product \(*: V \times V \rightarrow V\) that does not work: first, not every vector has an inverse element regarding \(*\). Second, even if you had the expression \(Ae\) (where \(e\) is the one-element regarding \(*\)), you cannot make the \(e\) vanish. It's the multiplicative neutral element for \(*\), not for (matrix, vector) multiplication. The result of \(Ae\) is a vector, not another matrix, definitely not \(A\) itself (except in the degenerate case of one-dimensional vector spaces).I have no clue what you are talking about. Function composition is always associative. You don't even need linear functions for that, it's a basic property. Changing the representation to \((F \circ L \circ D)(x)\) instead of matrices has no influence on that, you still have \((F \circ L) \circ D = F \circ (L \circ D)\). | 677.169 | 1 |
Archive for January, 2012
Cartesian Plane The Cartesian Plane is used to plot points. A rectangular coordinate system consists of points called ordered pairs. (x,y) The coordinates of the points and listed in alphabetical order so x comes first in an ordered pair (x,y). x-axis –> horizontal number line y-axis –> vertical number line origin –> point of intersection…
Solving Inequalities Simple Inequalities contain one of the following signs . When solving an inequality, one is trying to find all the valid solutions. Example: all real nos. less than 3 An inequality can be bounded or unbounded / open or closed. We use rounded brackets to indicate an open ended inequality…
Solving Equations of a Higher Degree The number of roots or solutions [values for x] is dependent on the degree of the polynomial in an equation. If the degree is 2, as in a quadratic equation, there is the possibility of two roots. If the degree is six, there can be up to six roots. …
SAT – Math Are you prepared to write the SAT Math Test? Find out what topics are covered on the SAT Exam in Math. Here is a great tool to help you review all those things you need to know to write the SAT math test. Be prepared when you walk into the exam and…
Number Sense Developing number sense starts as early as Kindergarden and continues through grade school and middle school. Building a strong fundation in the basic operations of addition, subtraction, multiplication and division is essential to being successful in math. Knowing the basic facts of addition, subtraction, multiplication and division of natural numbers, integers and real… | 677.169 | 1 |
AP Calculus Test Prep, AP Review
AP Calculus Test Prep
Instructor: Professor N
Schedule: Sunday 2-4 pm
Location: Westfield HS, Chantilly/HCS campus
The course is designed to prepare students who are taking the challenging AP Calculus AB/BC courses in their base schools. Both Calculus AB and Calculus BC are covered in this comprehensive AP enrichment class, which aligns with the new curriculum framework taking effect for the 2017 AP Calculus AB and BC exams. The book AP Calculus' main features include: practice exams in Calculus AB and in Calculus BC; the text is modified to reflect the new AP exam format. All test questions answered with solutions explained, a detailed subject review covering topics for both exams, advice to students on efficient use of their graphing calculators.
AP Calculus AB and AP Calculus BC focus on students' understanding of calculus concepts and provide experience with methods and applications. Although computational competence is an important outcome, the main emphasis is on a multi representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. The connections among these representations are important. Teachers and students should regularly use technology to reinforce relationships among functions, to confirm written work, to implement experimentation, and to assist in interpreting results. Through the use of the unifying themes of calculus (e.g., derivatives, integrals, limits, approximation, and applications and modeling). AP Calculus.
Reading lists and supplemental materials will be provided during the course. Periodic quiz assessments will be given to measure student progress.
Math
"I loved his class and he was so helpful and made calculus more fun despite it being incredibly hard. The key to pass is practice." "This is my second time taking one of his math classes. I highly recommend taking him. His quizzes are difficult but his tests are straightforward and he gives you a practice test that pretty much resembles exactly what you will see on the actual test. He really cares about his classes and makes the long lectures interesting." | 677.169 | 1 |
Core: Mathematics (CMTH)
CMTH 101 The Nature of Mathematics 3 Units
This course will guide students to gain knowledge about the nature of mathematics and develop their analytical reasoning skills to solve problems through topics such as number theory, probability and statistics, infinity, Non-Euclidean geometry, and general problem solving strategies; additional topics selected in dialog with the philosophy course. The overriding goals of this course are to develop a better perspective of mathematics and discover the power of mathematical thinking. Writing and projects, as well as traditional methods of assessment, will be used. Prerequisite: Intermediate Algebra or equivalent; Co-requisite: CPHI 101; permission from Academic Advising is needed to take CMTH 101 as an unlinked course. | 677.169 | 1 |
Udacity: Intro Algebra Review
This course provides a brief review of introductory algebra topics. Topics to be covered include integer operations, order of operations, perimeter and area, fractions and decimals, scientific notation, ratios and rates, conversions, percents, algebraic expressions, linear equations, the Pythagorean theorem, and graphing.
Why Take This Course? At the end of this course students will have reviewed the core topics of introductory algebra. Students will be comfortable with the concepts and procedures of introductory algebra, and be able to apply their knowledge to other coursework and real-world problems3.4
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This is a great introductory course for anyone who has been out of touch with math and algebra and would like some short reminders. My math knowledge is like swiss cheese and I decided that I will get back into it as a hobby.
If you are trying to restart that frozen brain of yours start with this course. | 677.169 | 1 |
Mathematics For Physicists - u-course.com
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Free Download Fundamentals of Mathematics, Enhanced Edition PDF
James Van DykeJune 29, 2009
Cengage Learning
English - book pages - ISBN-10: 9781111788261 - ISBN-13: 111178826X
1/5 by 85 votes
The FUNDAMENTALS OF MATHEMATICS, 9th Edition offers a comprehensive review of all basic mathematics concepts and prepares students for further coursework. The clear exposition and the consistency of presentation make learning arithmetic accessible for all. Key concepts are presented in section objectives and further defined within the context of How and Why; providing a strong foundation for learning. The predominant emphasis of the book focuses on problem-solving, skills, concepts, and applications based on real world data, with some introductory algebra integrated throughout. The authors feel strongly about making the connection between mathematics and the modern, day-to-day activities of students. This textbook is suitable for individual study or for a variety of course formats: lab, self-paced, lecture, group or combined formats. Though the mathematical content of FUNDAMENTALS OF MATHEMATICS is elementary, students using this textbook are often mature adults, bringing with them adult attitudes and experiences and a broad range of abilities. Teaching elementary content to these students, therefore, is effective when it accounts for their distinct and diverse adult needs. Using Fundamentals of Math meets three needs of students which are: students must establish good study habits and overcome math anxiety; students must see connections between mathematics and the modern day-to-day world of adult activities; and students must be paced and challenged according to their individual level of understanding.Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version | 677.169 | 1 |
Description: The purpose of these notes is to introduce the reader to the algebraic theory of systems of partial differential equations on a complex analytic manifold. We start by explaining how to switch from the classical point of view to the point of view of algebraic analysis. Then, we perform a detailed study of the ring of differential operators and its modules.
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This easy-to-use guide identifies and addresses the areas where most students need help with basic mathematical problems that occur in everyday life and academic study and provides straightforward, practical tips and solutions that will enable you to assess and then improve your performance | 677.169 | 1 |
Algorithmics and Optimization
Algorithmics and Optimization
Book Details:
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Year:
2015
Publisher:
University of Applied Sciences of Hagen
Pages:
123 pages
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english
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01/12/2015
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Pending review
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Why mathematics in a book about algorithmics? Algorithms are, in essence, applied mathematics. Even if they deal with apparently "unmathematical" subjects such as manipulating strings or searching objects, mathematics is the basis. To mention just a few examples: the classical algorithmic concept of recursion is very closely related to the principle of mathematical induction; rigorous proofs are needed for establishing the correctness of given algorithms; running times have to be computed.
The contents of these lecture notes spread a wide range. On the one hand they try to give the basic knowledge about algorithmics, such that you will learn the following questions: What is an algorithm and what are its building blocks? How can an algorithm be analyzed? How do standard well-known algorithms work? On the other hand, these lecture notes introduce into the wide and important field of optimization. Optimization is a basic principle of human activity and thinking, it is involved in the sciences and in practice. It mainly deals with the question: How can a solution to a given problem under certain constraints be achieved with a minimum cost, be it time, money, or machine capacity? Optimization is a highly economical principle. However, any solution of an optimization problem is a list of instructions, such as "do this, then do that, but only under the condition that . . . ," i.e., an algorithm — the circle is closed.
So we think optimization to be one of the basic subjects for you as a student of business information systems, for it will be one of your main business activities in the future. Surely, no lecture can give an answer to all problems which you will be challenged, but we think that it is important to understand that any optimization problem has a basic structure — it is the structure of a given optimization problem that you should understand, because then you may solve it in a more efficient way (you see, another optimization problem). | 677.169 | 1 |
Algebra Linear or Exponential?
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Students examine linear and exponential rules, tables, graphs, and situations. They sort them by linear, exponential growth, and exponential decay. Students will summarize the key features of each function. | 677.169 | 1 |
Calculators/Policies
In addition to general purpose calculators, there are those designed for specific markets; for example, there are scientific calculators which include trigonometric and statistical calculations. Some calculators even have the ability to do computer algebra. Graphing calculators can be used to graph functions defined on the real line, or higher-dimensional Euclidean space. Currently, basic calculators are inexpensive, but the scientific and graphing models tend to be higher priced.
In 1986, calculators still represented an estimated 41% of the world's general-purpose hardware capacity to compute information. This diminished to less than 0.05% by 2007. | 677.169 | 1 |
Mathematical Methods Units 3 and 4
Overview
Mathematical Methods covers four broad areas – Functions and graphs, Calculus, Algebra, Probability and statistics. Unit 3 begins with graphs of different functions, how to sketch them and find their equations. We also explore how to transform the functions graphically and algebraically.
The functions we cover are varied: polynomials (parabolas, cubics and so on); logarithmic, exponential and trig. functions (sine, cos and tan).
In Calculus we look at the rates of change in these functions. We use algebraic skills and graphs to analyse how rates of change affect each function. Calculus continues from Unit 3 into Unit 4, where we study integration – how to find the area under the curve of a graphed function.
Many of the functions are applied to practical problems. Things like tide movements, growth in population, or temperature fluctuations, are some of the examples where functions and calculus are applied.
The final topic is Probability and statistics. Describing the outcomes of chance, working out probabilities and analysing statistical data are the main areas of this topic.
Algebra occurs throughout each topic. We use algebra to complete tasks in most weeks. Algebraic skills include simplifying expressions, setting up equations, identifying key information and interpreting answers.
Technology plays a role as well. Students use their CAS calculator to check their answers, graph and interpret information, and to investigate mathematical problems.
Who is it for?
Mathematical Methods CAS is central to many areas of science and technology. Mathematical Methods CAS provides background in mathematics for students to better understand the world around them and for further study. It provides a foundation for study in various fields, ranging from medical technology and engineering to economic predictions and statistical modelling.
Many students are interested in Mathematical Methods CAS as a prerequisite for their pathway plan. While it is certainly helpful for students to be good at maths, with revision and extra study, an interested student can still achieve in the subject. The key is to allocate regular study time and develop consistent study habits.
What do you do?
In graphing, students explore the effects of transformations of a graph interactively. They study how the equation of the graph changes when it is transformed.
In calculus, students explore the relationship between a graph and the way its gradient changes interactively. They develop algebraic skills to describe relationships and apply them in practical problems.
Students also use their CAS calculator throughout to check answers and complete calculations.
What skills do you need?
Mathematical Methods assumes some background skills: knowing how to graph straight lines and parabolas, factorise quadratics and find trig. ratios (sine, cos and tan). Algebraic skills such as substituting values into algebraic expressions and solving equations are an important part of the course.
While we provide revision of many of these skills, a general review of algebra, graphing and trigonometry from Year 10 and Year 11 Maths is recommended.
What skills do you develop?
Mathematical Methods develops several skills:
being able to sketch graphs of functions
applying graph sketching to solve problems
developing skills in manipulating equations
solving equations of various functions, including trig. functions
interpreting answers to practical problems
using a CAS calculator efficiently to solve problems, check graphs and equations.
Requirements
You must have access to the internet in order to access this course. Weekly work will be submitted online.
The purchase of the following textbook will also be required: Maths Quest 12, Mathematical Methods, published by Jacaranda. Students have the option of either purchasing the textbook or the eBook.
The purchase of the following textbook is recommended: Checkpoints 2018, VCE Mathematical Methods Units 3 and 4.
CAS calculator
For this study, students need access to a VCAA-approved CAS calculator. DECV course notes are written using the TI-Nspire CAS and students are highly recommended to get one, if they are going to buy a new calculator. The Maths Quest 12 textbook includes instructions for both TI-Nspire CAS and Casio ClassPad calculators. However, any of the VCAA-approved CAS calculators can be used. | 677.169 | 1 |
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