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MyMathLab Instructions
1. Click on the MyMathLab tab on the left side of the course homepage.
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PRECALCULUS 1 Advice
Showing 1 to 3 of 13
I would recommend this course if you are a person who wants to get ahead in their classes.
Course highlights:
The highlight of the course was the math. I enjoyed learning this difficult subject just because my teacher made it so easy to understand.
Hours per week:
6-8 hours
Advice for students:
In order to succeed in this course is just do your homework and to take good notes and pay attention. Its that easy.
Course Term:Fall 2016
Professor:steven king
Course Tags:Great Intro to the SubjectMany Small AssignmentsGreat Discussions
Mar 21, 2017
| Would highly recommend.
Not too easy. Not too difficult.
Course Overview:
All though it is math at a more difficult stage, the projects done when taking this course was so much fun! You would think, "how can I have fun in this class? It'll be boring." No, this course is nothing like that. Mrs. Ahmuada always makes sure you're: learning, on task, and having fun!
Course highlights:
I learned the most I could. When not understanding, she goes one-on-one, making it easier to understand. One highlight was she never let one student fail; moreover, she always tried to push people to do better. I learned logarithmic, basic algebra, linear equations, quadratic functions; everything involving pre-cal!
Hours per week:
3-5 hours
Advice for students:
Take it, but with her! You will never regret it. She is an amazing teacher, and person overall. She isn't lenient, she will prepare you, and she will push you to succeed.
Course Term:Fall 2016
Professor:Ahmuada, Wendy
Course Required?Yes
Course Tags:Math-heavyGroup ProjectsParticipation Counts
Feb 10, 2017
| Would recommend.
Not too easy. Not too difficult.
Course Overview:
I would recommend this class as learning is never a "bad thing", so to speak. We all constantly use math and learning more of it can be extremely helpful.
Course highlights:
Highlights of the course was my colleagues and I competing for the best score. This counts for any math course but the best highlight for myself is when the problem in front of me suddenly clicks and i feel as if i have a new understanding of it.
Hours per week:
6-8 hours
Advice for students:
Do not procrastinate as the work begins to pile quickly. If you take an online course as i did, have someone who is proficient in math so that they can help you if nobody else is there. Do not be afraid to mail your instructor for help. Use the textbook for guidance, i did not use the book for the first semester and it was painful trying to figure it out myself. | 677.169 | 1 |
GED Math Chapter 10: Systems and Basic Matrix Operations
Understanding systems and the methods to solve them are vital in Algebra. This chapter introduces/reviews techniques to solve linear systems. Lastly, the topic of matrices will be introduced. Students will understand the "real world" applications of matrices and basic matrix operations. | 677.169 | 1 |
Showing 1 to 8 of 8
MTHSC 360 Working with Polynomials
January 15, 2008
1
Three ways to compute a straight line.
In High School Algebra, we learned that the equation for a straight line was given by the expression y = mx + (1) where m is the slope (the rise over th
MTHSC 360 Taylor's Theorem
February 27, 2008
1
Taylor's Theorem with Remainder
Let f (x) be a function defined for x in an interval containing the point a. If the first derivative of f is also defined and continuous on this interval, then the Fun
MTHSC 360 Three Linked Bungee Jumpers
January 25, 2008
1
The Basic Problem
Three Bungee jumpers - Alex, Barry, and Carol - plan to form a single long bungee cord by tying themselves together with three short bungee cords and then jump off a bridg
Numerical Methods with MATLAB
Spring 2008 Professor Warner
4
4.1
Least Squares
The Best Constant
In this section we investigate how to fit simple mathematical models to experimental data. Let's start by considering the data displayed in the follow
MTHSC 360 Introduction to Interpolation
January 16, 2008
1
A Basic Example
Suppose that we have an empirical function. We often encounter such functions in books or papers reporting an experiment that measures some physical property. Table 1 list
MTHSC 360 - Numerical Integration
March 10, 2008
The Potential Energy behind a Dam
Assume that we have a small dam and that we are interested in the amount of energy stored in the water behind the dam. Call the part of the dam that contacts the wate
6.2
Now that we have seen an example showing the significance of the eigenvalues and eigenvectors in understanding the behavior of the solutions to a linear system of differential equations, let's systematically explore the 2 2 systems. Let A= Then | 677.169 | 1 |
The Official SAT Question of the Day
Thursday, September 22, 2011
Solving Systems with Matrices and All Things Linear
From Pearson Education
Algebra II will be putting algebra basics behind them and moving on to linear equations with a coordinate geometry twist and an introduction to the concept function. The goal of this week is to recall all you have learned about linear equations and really push your understanding of linearity to the limit. Please find the Pearson PowerPoint slides below, a collection of videos on lines, the homework, and a linear equations reference sheet! | 677.169 | 1 |
Grab this great STRIVE 4 A FIVE, STUFF YOU MUST KNOW COLD handout. It is an adaptation from Sean Bird's material at Covenant Chrisitan. There are six pages of everything important for the AP CALCULUS AB STUDENT to know backwards and forwards. It's a handy reference sheet.
AP Calculus Resources: Handouts from various AP Calculus workshops and institutes & Articles that may be of interest to calculus teachers. Includes a break down of topics and which AP free response questions have targeted those topics.
Do Tornadoes Really Twist Task Cards
This engaging interactive activity is perfect for an end of course review for AP Calculus AB or College Calculus 1. Check what your students remember and have mastered. Great fun! You don't need Google Classroom, but you and your students must have access to the internet and have individual FREE Google Drive Accounts to use this resource.
Calculus Big Bundle of Foldable Organizers plus more
Engage your Calculus students with these one of a kind organizers. They will love you for it! AP Calculus AB and BC, Calculus Honors and College Calculus 1 students use these as study aids and reviews. The Growing bundle includes over fourteen foldable organizers. Some even have quizzes, HW and task cards included for you as a bonus. Easy to make paper savers, no scissors, no glue! | 677.169 | 1 |
Authors: Klein, Felix First English translation of the classic volume on precision mathematics and approximation mathematics Invaluable treatise for any mathematics educator Exhibits the connections between geometry and more formalistic mathematics | 677.169 | 1 |
Menu
New BuzzMath Document – Introduction to Slope
(Algebra > Relations & Functions > Functions)
One of the more difficult concepts for teachers to teach and for students to grasp is linear equations. To begin, students must understand slope. Since most students already understand "steepness" you can stress that slope is the measure of the steepness of a line. You can later discuss rate of change, after they get the basic meaning of slope.
Take some time to make sure students understand that the slope is the ratio of the vertical distance to the horizontal distance. Some students may find it easier to remember the ratio as "rise over run." As students complete subsequent pages, watch out for the common error of using the ratio in the wrong order. You may notice that this introductory document consists of problems with positive slopes only. Negative, zero, and undefined slopes, as well as finding slopes using coordinates are covered in other documents. | 677.169 | 1 |
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racines carrees simplification | 677.169 | 1 |
Sarah Miller
EdTech Memory – Graphing Calculators
Graphing calculatorAs a high school student, my math teacher kept a set of TI-82 graphing calculators at the ready in his classroom. He taught us how to use them and opened us up to a world of straight lines and smooth curves. It was a much less messy and much more efficient way to graph equations and study graphs in my algebra classes.
There is value in learning to draw graphs by hand and we did that, first; we were often required to hand-draw graphs on tests. It is a skill that can serve you well as a math tutor, teacher or if you simply want to take more math classes down the line.
The TI-82 graphing calculator could slice and dice; it could help us find the intercepts of a graph that we had plotted. It could perform analyses, like fitting a regression line to a series of points that we had entered in the calculator and plotted.
As a tutor, now, I would probably use the graphing calculator more than drawing graphs, again for the efficiency factor – students want information so quickly, now. I might even bust out the SpaceTime app on my iPod.
My TI-89 graphing calculator and I were attached at the hip up through my graduation from college in 2003. The major improvements in that calculator for me were that it was able to graph in three dimensions and it had a much sleeker look than it's predecessors. It also had a more intuitive input-output system. | 677.169 | 1 |
Interactive graphs and formulas make things move, adding a new depth of meaning for key ideas. MathWorlds uses the familiar and flexible structure of computer documents and menus connected to the curr... More: lessons, discussions, ratings, reviews,...
Students can use the GeoBoard App to experience the power of geometric concepts electronically. In addition to rotating, reflecting and translating objects, it enables you to measure line segments, ar... More: lessons, discussions, ratings, reviews,...
This is the junior version of Geom-e-Tree. It enables the manipulation of geometric trees with two or three branches. Change angle between branches and change common ratio. Selectable themes draw ... More: lessons, discussions, ratings, reviews,...
Size Wise uses "forced perspective" photography to invite users to reason proportionally--if they want to make something appear half as big on the screen, they need to place it twice as far away. Meas... More: lessons, discussions, ratings, reviews,...
The user reviews definitions of important algebra terms. After viewing further explanations and some examples, users can interactively test their understanding of the definitions of important algebra... More: lessons, discussions, ratings, reviews,...
Using this virtual manipulative you may: graph a function; trace a point along the graph; dynamically vary function parameters; change the range of values displayed in the graph; graph multiple functi... More: lessons, discussions, ratings, reviews,...
Tutorial fee-based software for PCs that must be downloaded to the user's computer. It covers topics from pre-algebra through pre-calculus, including trigonometry and some statistics. The software pos... More: lessons, discussions, ratings, reviews,...
Algebra Concepts is an interactive learning system designed to provide instruction in mathematics at the 7th grade enrichment through adult levels. The instructional goals for Algebra Concepts include | 677.169 | 1 |
Pages
Thursday, August 16, 2012
Life of Fred Beginning Algebra
This was the book that started it all for us. We had been using another algebra book that I just wasn't happy with because I didn't feel like it covered enough algebra topics. I went to a homeschooling conference and heard the author, Stan Schmidt, give a talk about what math should be like and I was sold.
Much to the horror of my eldest daughter, I came home with the Beginning Algebra book and presented it to her as her next math book. "You mean I have to do algebra over again?" she asked. "Yes," I replied, "but this time you'll actually learn it.
After I explained the concept of Fred to the kids, they all wanted to get their hands on the book to read the story and see what it was all about. My daughter dove into the book and finished it before the end of the school year. Ever since then this has been our "go-to" algebra book.
Beginning Algebra is the first book to come with a Home Companion. This is definitely worth getting as it breaks down the main book into 188 lessons. Not only does it give the day-to-day break down, it also gives additional problems for the student to work on.
All of this is covered in a day in the life of Fred, a five year old math professor at KITTENS University in Kansas. His tone is very conversational, which makes learning the math a lot more enjoyable. For example we learn about linear equations in the context of Fred helping a chaplain write a sermon about ten young girls waiting at night to meet an important dignitary :)
I have been very please with this set of algebra books as I believe it to be a very thorough coverage of beginning algebra. If you would like to read more about Fred or to order any of the Fred books, you can go to my website.
Bern... I looked into what you were talking about and then talked to my 16 year old daughter who finished the geometry book in May. She said that Fred has a crush on a little girl his age and then later finds out it is his sister (long story :) Anyhow, she said it was totally innocent and besides, when you're old enough to be doing geometry, that little bit of the story is totally understandable and not a big deal. Other than that possibility, we have not had ANY issues at all with any of the books. Hope that helps. | 677.169 | 1 |
Solving Multi-Step Inequalities Partner Match-Up {Algebra 1]
Be sure that you have an application to open
this file type before downloading and/or purchasing.
1 MB|5 pages
Product Description
Students will solve 11 problems and compare answers with their partner to determine the answer to the riddle. (What is the best time to go to the dentist?) Students will get matching inequality symbols and numerical answers (variables may be different) on each set to help them determine what letter goes in what numbered box.
The skills required are:
*Solving Inequalities with variables on one side
*Solving Inequalities with variables on both sides
*Solving Multi-Step Inequalities (distributing more than once) | 677.169 | 1 |
Jovial John and Rate of Change
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this file type before downloading and/or purchasing.
768 KB
Product Description
Here is an activity that Jovial John takes students on a journey that utilizes the various parts of the rate of change in conceptual problem situations. Students are given the opportunity to analyze graphs to identify the domain and range, to find the rate of change and y-intercept; to find the rate of change from a table, a problem situation; to write the function, to compute a value using the formulated linear function. This activity is rich in conceptual problem situations and provides with a solid foundation and understanding of how to evaluate the slope (rate of change) in multiple real life applications. | 677.169 | 1 |
Mathematics
Overview
A-Level Mathematics is a very enjoyable and demanding subject which requires disciplined study to master. It is vital that students enter year 12 with a fluent understanding of algebra and are prepared to work enthusiastically and diligently from the very beginning of the course. Students who have achieved an A or A* grade at GCSE and who have self-studied the Certificate in Further Maths in year 11 are best placed to both love the subject and succeed in the assessments. We expect students to find the content stretching and as a result we are determined to offer strong support every step of the journey towards success.
Course Outline
A-level Maths is made up of four core and two applied modules. Students study Core 1, Core 2 and Statistics in year 12 and Core 3, Core 4 and Mechanics in year 13. Each module has a distinct exam but the skills, knowledge and understanding build up from Core 1 to Core 4 so that real mathematical fluency is necessary for students to achieve highly in Core 3 and Core 4.
Assessment
There is no coursework for Maths. Exams count for 100% of the final grade. Each module has a 90 minute exam which is sat in the summer exam season (May to June). Students can still sit AS modules at the end of Y12 and end their qualification there if required. To achieve a full A-level, students will sit an exam in all six modules which are equally weighted towards the final award. Only Core 1 is a non-calculator paper.
Examining Board
AQA
Career Opportunities
An A-Level in Maths is well respected by Universities and Employers. Students who go on to study most disciplines including Business, Accountancy, Engineering, Medicine, Architecture or any of the Sciences, will benefit from the subject. Students who study Maths degrees have many very well paid and well respected career choices at their fingertips.
Teaching Methods
Students will study Maths for an average of four hours per week in year 12 and 5 hours per week in year 13. Homework will be set after each lesson and will mostly involve the completion of work started in class as well as past exam papers and problem-style questions. Assessments will take place at the end of each topic and results from these will be used to set intervention work or to raise action plans to inform students and parents of any current issues that need to be addressed.
Other information
A Scientific Calculator is compulsory for the study of Maths. We recommend the Casio Fx85GT (or Fx85GT-Plus) which will cost between £5 and £10 on amazon (often these calculators are for sale for less in ASDA).
Further Maths is a distinct A-level. For information see the Further Maths page on the web-site | 677.169 | 1 |
Be sure that you have an application to open
this file type before downloading and/or purchasing.
24 MB|59 pages
Product Description
This product includes foldables with suggested notes, worksheets, vocab diagrams, a practice test, and a test covering linear and nonlinear functions. They are designed to align with the common core eighth grade math standards. You save 20% by purchasing the foldables and assessments together!
In my class, I use the left hand side of the notebook for guided notes with foldables, while the right-hand side is reserved for individual practice work. Every stick-n-solve foldable has suggested notes to go along with it. For each topic there At the end of each unit, my students always complete essential vocabulary diagrams and a practice test booklet to include in their interactive notebooksThis Bundle focuses on linear & nonlinear functions and includes 9 Stick-n-Solve Foldables. For each foldable, you will see two pictures. You will see a draft picture of notes for the topic, and a picture of the solutions on the inside of the foldable:
The bundle also includes 9 formative assessments (each is a one-sided worksheet), a practice test booklet, vocabulary diagrams, and summative assessment (unit test). ALL of these include answer keys. Here they are as they align to the common core standards.
In your zip file, each foldable is paired with a corresponding homework assignment. In addition, you will find a file for the vocab diagrams, one for the practice test, and finally, the test.
For almost every topic covered, I've made a foldable and an assessment. In total I have created 50 Stick-n-Solve Foldables and coordinating assessments for 8th grade common core math and organized them into the following bundles:
These activities can be found in many different bundles, including my ENTIRE 8th Grade Math Curriculum! Check out my store for all of your options!
**Leave Feedback after your purchase to earn TpT credits!!**
Common Core:
CCSS.MATH.CONTENT.8.F.A.1
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.1
CCSS.MATH.CONTENT.8.F.A.2
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.
CCSS.MATH.CONTENT.8.F.A.3
Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
CCSS.MATH.CONTENT.8.F.B.5
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | 677.169 | 1 |
This workshop is an introduction to typesetting math using LaTeX. Attendees will learn how to create various environments for equations and formulas; subscripting and superscripting; Greek letters; and other commonly used syntax for math. The workshop will be taught using Overleaf, a collaborative, subscription-based tool being piloted by the library. This is a hands-on workshop - please bring a laptop (the library can provide one if you don't have a laptop). | 677.169 | 1 |
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2Learning Objectives for Lecture 1. Motivate Study of Systems of Equations and particularly Systems of Linear Equations2. Review steps of Gaussian Elimination3. Examine how roundoff error can enter andbe magnified in Gaussian Elimination4. Introduce Pivoting and Scaling as defenses against roundoff.5. Consider what an engineer can do to generate well formulated problems.E. T. S. I. Caminos, Canales y Puertos
3Systems of EquationsIn Part 2 we have tried to determine the value x, satisfying f(x)=0. In this part we try to obtain the values x1,x2, xn, satisfying the system of equations:These systems can be linear or nonlinear, but in this part we deal with linear systems:E. T. S. I. Caminos, Canales y Puertos
4Systems of Equationswhere a and b are constant coefficients, and n is the number of equations.Many of the engineering fundamental equations are based on conservation laws. In mathematical terms, these principles lead to balance or continuity equations relating the system behavior with respect to the amount of the magnitude being modelled and the extrenal stimuli acting on the system.E. T. S. I. Caminos, Canales y Puertos
5Systems of Equations Column 3 Row 2 Matrices are rectangular sets of elements represented by a single symbol. If the set if horizontal it is called row, and if it is vertical, it is called column.Column 3Row 2ColumnvectorRow vectorE. T. S. I. Caminos, Canales y Puertos
7Lower triangular matrix Systems of EquationsLower triangular matrixBanded matrixHalf band widthAll elements are null with the exception of thoise in a band centered around the main diagonal. This matrix has a band width of 3 and has the name of tridiagonal.E. T. S. I. Caminos, Canales y Puertos
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12Systems of EquationsCompatible and determined system. Linearly independent vectors. Nonnull determinant of A, but close to zero. There exists a solution but it is difficult to find precisely. It is an ill conditioned system leading to numerical errors.E. T. S. I. Caminos, Canales y Puertos
13Gauss eliminationNaive Gauss elimination method: The Gauss' method has two phases: Forward elimination and backsustitution. In the first, the system is reduced to an upper triangular system:First, the unknown x1 is eliminated. To this end, the first row is multiplied by -a21/a11 and added to the second row. The same is done with all other succesive rows (n-1 times) until only the first equation contains the first unknown x1.PivotequationsubstractpivotE. T. S. I. Caminos, Canales y Puertos
14Gauss eliminationThis operation is repeated with all variables xi, until an upper triangular matrix is obtained.Next, the system is solved by backsustitution.The number of operations (FLOPS) used in the Gauss method is:Pass 1Pass 2E. T. S. I. Caminos, Canales y Puertos
18Gauss elimination (example) Start with the augmented matrix:Multiply the first row by –1/50and add to second row.Multiply the first row by –2/50and add to third row:Multiply the second row by –6/40E. T. S. I. Caminos, Canales y Puertos
21Gauss elimination (example) WHAT HAPPENED?When we used 50 x1 + 1 x2 + 2 x3 = 1 to solve for x1, there was little change in other equations.When we used 2 x1 + 6 x x3 = 3 to solve for x1 it made BIG changes in the other equations. Some coefficients for other equations were lost!The second equation has little to do with x1.It has mainly to do with x3.As a result we obtained LARGE numbers in the table, significant roundoff error occurred and information was lost.Things didn't go well!If scaling factors | aji / aii | are 1 then the effect of roundoff errors is diminished.E. T. S. I. Caminos, Canales y Puertos
27Gauss elimination (scaling) A. Express all equations (and variables) in comparable units so all elements of [A] are about the same size.B. If that fails, and maxj |aij| varies widely across the rows, replace each row i by:aij This makes the largest coefficient |aij| of each equation equal to 1 and the largest element of [A] equal to 1 or -1NOTE: Routines generally do not scale automatically; scaling can cause round-off error too!SOLUTIONS• Don't actually scale, but use hypothetical scaling factors to determine what pivoting is necessary.• Scale only by powers of 2: no roundoff or division required.E. T. S. I. Caminos, Canales y Puertos
28Gauss elimination (scaling) How to fool scaling:A poor choice of units can undermine the value of scaling.Begin with our original example:If the units of x1 were expressed in µg instead of mg the matrix might read:Scaling then yields:Which equation is used to determine x1 ? Why bother to scale ?E. T. S. I. Caminos, Canales y Puertos
45LU decompositionLU decomposition - The LU decomposition is a method that uses the elimination techniques to transform the matrix A in a product of triangular matrices. This is specially useful to solve systems with different vectors b, because the same decomposition of matrix A can be used to evaluate in an efficient form, by forward and backward sustitution, all cases.E. T. S. I. Caminos, Canales y Puertos
47LU decompositionLU decomposition is very much related to Gauss method, because the upper triangular matrix is also looked for in the LU decomposition. Thus, only the lower triangular matrix is needed.Surprisingly, during the Gauss elimination procedure, this matrix L is obtained, but one is not aware of this fact. The factors we use to get zeroes below the main diagonal are the elements of this matrix L.SubstractE. T. S. I. Caminos, Canales y Puertos
51LU decomposition LU Decomposition Variations Doolittle [L1][U] General [A]Crout [L][U1] General [A]Cholesky [L][L] T Pos. Def. Symmetric [A]Cholesky works only for Positive Definite Symmetric matricesDoolittle versus Crout:• Doolittle just stores Gaussian elimination factors where Crout uses a different series of calculations (see C&C ).• Both decompose [A] into [L] and [U] in n3/3 FLOPS• Different location of diagonal of 1's• Crout uses each element of [A] only once so the same array can be used for [A] and [L\U] saving computer memory!E. T. S. I. Caminos, Canales y Puertos
55Errors in Solutions to Systems of Linear Equations System of EquationsErrors in Solutions to Systems of Linear EquationsObjective: Solve [A]{x} = {b}Problem:Round-off errors may accumulate and even be exaggerated by the solution procedure. Errors are often exaggerated if the system is ill-conditionedPossible remedies to minimize this effect:1. Partial or complete pivoting2. Work in double precision3. Transform the problem into an equivalent system of linear equations by scaling or equilibratingE. T. S. I. Caminos, Canales y Puertos
56Errors in Solutions to Systems of Linear Equations Ill-conditioningA system of equations is singular if det|A| = 0If a system of equations is nearly singular it is ill-conditioned.Systems which are ill-conditioned are extremely sensitive to small changes in coefficients of [A] and {b}. These systems are inherently sensitive to round-off errors.Question:Can we develop a means for detecting these situations?E. T. S. I. Caminos, Canales y Puertos
58Errors in Solutions to Systems of Linear Equations Ill-conditioning of [A]{x} = {b}:Consider the graphical interpretation for a 2-equation system:We can plot the two linear equations on a graph of x1 vs. x2.x1x1x2x2Uncertaintyin x2Uncertaintyin x2Well-conditionedIll-conditionedE. T. S. I. Caminos, Canales y Puertos
59Errors in Solutions to Systems of Linear Equations Ways to detect ill-conditioning:1. Calculate {x}, make small change in [A] or {b} and determine change in solution {x}.2. After forward elimination, examine diagonal of upper triangular matrix. If aii << ajj, i.e. there is a relatively small value on diagonal, then this may indicate ill-conditioning.3. Compare {x}single with {x}double4. Estimate "condition number" for A.Substituting the calculated {x} into [A]{x} and checking this against {b} will not always work!!!E. T. S. I. Caminos, Canales y Puertos
60Errors in Solutions to Systems of Linear Equations Ways to detect ill-conditioning:If det|A| = 0 the matrix is singular==> the determinant may be an indicator of conditioningIf det|A| is near zero is the matrix ill-conditioned?Consider:After scaling:==> det|A| will provide an estimate of conditioning if it is normalized by the "magnitude" of the matrix.E. T. S. I. Caminos, Canales y Puertos
61Norms Norms and the Condition Number We need a quantitative measure of ill-conditioning.This measure will then directly reflect the possible magnitude of round off effects.To do this we need to understand norms:Norm: Scalar measure of the magnitude of a matrix or vector ("how big" a vector is).Not to be confused with the dimension of a matrix.E. T. S. I. Caminos, Canales y Puertos
62Vector Norms Vector Norms: Scalar measure of the magnitude of a vector Here are some vector norms for n x 1 vectors {x} with typical elements xi.Each is in the general form of a p norm defined by the general relationship:1. Sum of the magnitudes:2. Magnitude of largest element:(infinity norm)3. Length or Euclidean norm:E. T. S. I. Caminos, Canales y Puertos
65Matrix norms 3. Spectral norm: ||A|| 2 = (µmax)1/2 where µmax is the largest eigenvalue of [A]T[A]If [A] is symmetric, (µmax)1/2 = max , is the largest eigenvalue of [A].(Note: this is not the same as the Euclidean or Frobenius norm, seldom used:E. T. S. I. Caminos, Canales y Puertos
67Error AnalysisForward and backward error analysis can estimate the effect of truncation and roundoff errors on the precision of a result. The two approaches are alternative views:Forward (a priori) error analysis tries to trace the accumulation of error through each process of the algorithm, comparing the calculated and exact values at every stage.Backward (a posteriori) error analysis views the final solution as the exact solution to a perturbed problem. One can consider how different the perturbed problem is from the original problem.Here we use the condition number of a matrix [A] to specify the amount by which relative errors in [A] and/or {b} due to input, truncation, and rounding can be amplified by the linear system in the computation of {x}.E. T. S. I. Caminos, Canales y Puertos
73Error Analysis Estimate of Loss of Significance: Consider the possible impact of errors [dA] on the precision of {x}.implies that ifOr, taking log of both sides: s > p - log10()log10() is the loss in decimal precision; i.e., we start with p decimal figures and end-up with s decimal figures.It is not always necessary to find [A]-1 to estimate k = cond[A]. Instead, use an estimate based upon iteration of inverse matrix using LU decomposition.E. T. S. I. Caminos, Canales y Puertos
74Iterative Solution Methods Impetus for Iterative Schemes:1. May be more rapid if coefficient matrix is "sparse"2. May be more economical with respect to memory3. May also be applied to solve nonlinear systemsDisadvantages:1. May not converge or may converge slowly2. Not appropriate for all systemsError bounds apply to solutions obtained by direct and iterative methods because they address the specification of [dA] and {db}.E. T. S. I. Caminos, Canales y Puertos
79Iterative Solution Methods -- Gauss-Seidel In most cases using the newest values within the right-hand side equations will provide better estimates of the next value. If this is done, then we are using the Gauss-Seidel Method:( [Lo]+[D] ){x}j+1 = {b} – [Uo] {x}jor explicitly:If this is done, then we are using the Gauss-Seidel MethodE. T. S. I. Caminos, Canales y Puertos
80Iterative Solution Methods -- Gauss-Seidel If either method is going to converge,Gauss-Seidel will convergefaster than Jacobi.Why use Jacobi at all?Because you can separate the n-equations into n independent tasks, it is very well suited computers with parallel processors.E. T. S. I. Caminos, Canales y Puertos
82Convergence of Iterative Solution Methods Iterative methods will not converge for all systems of equations, nor for all possible rearrangements.If the system is diagonally dominant,i.e., | aii | > | aij | where i j thenwith all < 1.0, i.e., small slopes.E. T. S. I. Caminos, Canales y Puertos
83Convergence of Iterative Solution Methods A sufficient condition for convergence exists:Notes:1. If the above does not hold, still may converge.2. This looks similar to infinity norm of [A]E. T. S. I. Caminos, Canales y Puertos
84Improving Rate of Convergence of G-S Iteration Relaxation Schemes:where < l 2.0(Usually the value of l is close to 1)Underrelaxation ( 0.0 < l < 1.0 )More weight is placed on the previous value. Often used to:- make non-convergent system convergent or- to expedite convergence by damping out oscillations.Overrelaxation ( 1.0 < l 2.0 )More weight is placed on the new value. Assumes that the new value is heading in right direction, and hence pushes new value close to true solution.The choice of l is highly problem-dependent and is empirical, so relaxation is usually only used for often repeated calculations of a particular class.E. T. S. I. Caminos, Canales y Puertos | 677.169 | 1 |
MAS3105-review1-fall10 - MAS 3105 Review Exam 1 When in...
MAS 3105 Review - Exam 1 September 16, 2010 When: September 23, 2010, in class What Material: Sections 1.1-1.4, 1.6-1.7, 2.1, 2.3-2.4, 2.7-2.8. Procedure: The exam will be closed book. You will be allowed one sheet of notes, 8-1/2 by 11 inches, front and back. You may not use any graphing calculators of any kind. You may bring in a basic calculator if you want. How to Study: The exam will have straightforward computation questions (find the inverse of a matrix, solve a system of equations, determine if a vector is in the span of a set, etc) and the exam will have "understanding" questions. These are questions that test whether or not you understand the definitions and theorems from the class. All the problems from the homework that were at the end of a section – those were "understanding" questions. You WILL be expected to show your work on all problems. That means you need to show all steps in a Gaussian elimination. You should run through all of the True/False questions. These really help you with definitions and theorems. Computations are straightforward so far, and everything boils down to finding linear combinations and/or performing Gaussian elimination. Make sure you can do both tasks
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Reference
Computing
Computer Algebra Systems
Maple is a proprietary closed source system develped
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Numerical Linear Algebra Software
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It's Windows centric, but runs on *nix.
Octave is an open source (GNU licence) Matlab clone.
It's *nix centric, but runs on Windows.
Scilab is an open source platform for numerical linear
algebra developed in Europe at INRIA.
Free scientific portal for MATLAB/MIDEVA m-files and toolboxes, and Excel/Java/Fortran/C++ resources and links | 677.169 | 1 |
College Geometry A Unified Development
ISBN-10: 1439819114
ISBN-13: 9781439819111 a unified treatment of the three classical geometries: Euclidean, hyperbolic, and spherical (elliptic). This unique approach of combining all three geometries simultaneously using twelve concise axioms has never appeared in book form before at this level. The text introduces each axiom, including its reasons for use and implications, and then explains it in detail. In addition to numerous figures, examples, and exercises, the book includes Geometer's Sketchpad to help students build and investigate math models, objects, figures, and graphs. The author provides programs for students to use on a supporting website. A solutions manual is available for qualifying instructors | 677.169 | 1 |
Chaos Theory Simply Explained (Basic Fractals/Chaos Series)
This is a concise article detailing mathematical equations showing when and where chaos occurs in linear algebraic equations and systems of linear simultaneous algebraic equations. The approach used is very simple and easy to understand by students. More
This is a concise article detailing mathematical equations showing when and where chaos occurs in linear algebraic equations and systems of linear simultaneous algebraic equations. The approach used is very simple and easy to understand by students. Instead of using quadratic equations like the logistic equation to study chaos theory, we use simple linear equations for this purpose. The article starts with a single simple linear equation and ends with a system of two simultaneous linear equations. The conditions under which chaos occurs in linear equations are precisely investigated using several examples. The derivation of all necessary equations is shown in great detail. This article is aimed at the novice reader who is just starting his or her study of chaos and chaos theory. The reader is expected to know the basics of algebra at an elementary level. | 677.169 | 1 |
Description
Please note that all questions are now being checked for the second time. Some questions are intended to be difficult or trick-questions, but we are aware that there are some errors in the app and will be issuing updates to address this.
The app incorporates most topics from the major exam boards and is a fantastic way to revise for your exams, tests or just to brush up on one's mathematical skills. The GCSE is a UK degree for secondary school students aged about 15 and the app therefore covers all the basics.
Features include:
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Circle Theorem 1
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Collecting Like Terms
Conversion of Fractions + Decimals
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Estimation
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Integers
Length, Area + Volume
Linear Equations
Linear Equations (Fractions)
Linear Inequalities
Linear Simultaneous Equations
Mean (Raw Data)
Multiplying Out
Ordering Numbers
Percentage (Increase + Decrease)
Percentage (of)
Polygons
Powers
Probability
Proportion
Pythagoras
Quadratic Factorising
Quadratic Formula
Quadratic Inequalities
Quadratic Simultaneous Equations
Ratio
Rearranging
Recurring Decimals
Roots (Surds)
Sequences
Sequences (Recurrence)
Similarity
Simple Factorising
Simplifying Expressions
Simplifying Fractions
Simplifying Powers
SOHCAHTOA
Solving Equations from Graphs
Standard form
Straight Line Graphs
Straight Lines (Gradients + Equations)
Straight Lines (Gradients + Points)
Straight LInes (Intercepts)
Substitution
Symmetry
Trigonometric Equations
Trigonometry Equivalences
Volume
If you are having problems with your 'd' button, please ensure you have the latest update. You can contact us at: info@educationapps.co.uk | 677.169 | 1 |
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Product Description
I designed these lessons to teach my students about geometric figures (the 8th in a series of 9). This lesson can be purchased as a complete bundled unit at a discounted price under the listing Features of Functions Complete Bundled Unit.
This lesson focuses on: given a set of coordinate points--determining if the set is a function and then listing the domain and range, given an equation, a graph and a table of values--determining the domain and range, given a real world description and determining if the description can be represented as a function, and given a graph--determining domain and range, maximum and minimum, intervals of increasing and decreasing. | 677.169 | 1 |
Maths Terms Mathematics is the study of quantity, structure, space, and change
Calculus Quick Reference Calculus Quick Reference lists down all the important formulas and evaluation techniques used in calculus which makes it easier for you to memorize and apply them in solving problems
Distancia It calculates the distance among two geographical coordinate
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GCSE Edexcel Maths
Description
Edexcel is the most popular examining group for GCSE Maths, with over 300,000 candidates taking Edexcel Specification A exams. "Revision Guide GCSE Edexcel Maths" provides the most comprehensive approach to that specification, with its unique combination of study support and exam practice. "Revision Guide GCSE Edexcel Maths" has been designed to make revision as active and effective as possible. Short 20-minute 'revision sessions' break down content into manageable chunks and maximise students' concentration. An exam practice chapter devised specifically for the Edexcel Maths specification provides detailed guidance on exam technique and makes sure students are fully prepared for the big day. This book provides: short revision sessions on every topic to prepare for the Edexcel GCSE Maths exam; worked examples to show how to tackle every aspect of Maths; hint boxes for extra guidance and support; intermediate and Higher Level content clearly indicated; and check yourself questions to test understanding.show more | 677.169 | 1 |
Math @ Williston
All about math department projects and events.Tue, 23 May 2017 18:21:41 +0000en-UShourly1 AP Calculus BC Free Response Questions & Answers!
23 May 2017 17:55:07 +0000 reading 2017 AP Calculus BC Free Response Questions & Answers!→]]>A few days after each AP Calculus BC exam, the College Board releases the free response questions from the exam. They don't release their very succinct answer keys for a few more weeks… so… I had my students make their own answer keys as well as screen recordings of their solutions!
All 2017 released free response questions and answer keys are online right here. Questions and answers for past years can be found right here.
As we prepare for the AP statistics exam, we need to review several terms and concepts. One way we can do this is with BINGO. Students complete their grids with a list of terms, in an arbitrary (not random) order. Then they are given definitions and examples. They must match the definitions and examples with the core correct terms in order to win. It is very exciting!
]]> math!
19 Apr 2017 16:40:15 +0000 reading Sidewalk math!→]]>With awesome weather all around, we just had to work on math outside, in chalk, on sidewalks around campus!
From Mrs. Baldwin:
The Trig/Prob/Stats class learned about describing data with numerical summaries and graphical displays. We took our work outside to practice these skills. We studied a data set of travel times to work for 20 NYC residents. We found that the median travel time was 22.5 minutes, the minimum was 5 minutes and the maximum was 85 minutes. Students also learned to use a new measure of spread called the interquartile range. This measures the range of the middle half of observations. We found that the middle half of travel times for these New Yorkers vary from 15 minutes to 42.5 minutes. Working outside in the chalk brought a kinesthetic element to our learning that was fun and engaging.
Mr. Matthias: The loved the level of engagement my Engineering & Robotics students showed during the last Trimester. Students asked many questions and demonstrated success with the last set of Challenges. I will certainly miss each one of them!
Ms. Baldwin: Three students wanted some extra help before their final assessment for the Winter term. We were not able to meet in person, but planned a time to meet using Skype for Business. We spent about an hour the night before the test going over problems and addressing their questions about all that we have been studying in probability. They were able to share their screens with me and with other members of the group and I did the same with them. Our time together was extremely productive and it was so convenient to meet in this way. We got a lot of good studying done and had a few laughs at the same time. It's good to have one more way to connect with kids and support their learning.
Mrs. Whipple: One of my students, who works really hard, was discouraged that they were not getting the grades they would have liked on every test. We worked all trimester on their strategy and their confidence when approaching the material and by the final assessment they received a near perfect score!
Ms. Schneider: One of my favorite memories from class this past trimester was when one of my students became the teacher for part of the period. We often begin class by reviewing what we have learned in our previous lessons leading up to that day. This frequently includes discussing the homework assignment. At times the students get into small groups to review; however, on this day one student came to the front and lead the class throughout this activity. She walked the class through each problem, and kept every student engaged. Not only did her classmates gain valuable insight through her explanations and leading questions, but this student, who actually is considering a career in teaching herself, showed excellent leadership skills!
Mrs. Conroy: My Geometry assessment consisted of two parts, a group portion and an individual portion. The group portion of the assessment required students to stretch their problems solving abilities while doing geometry in a collaborative setting. As I described it to the students, "There is little you can do to prepare for this section. It will challenge you. Embrace the challenge." The first question on the group portion was particularly challenging and involved proving triangles congruent after creating a diagram from specific instructions. Each group had the correct diagram but then the problem became interesting. Not a single group earning full credit on the problem but what I witnessed in the classroom during that question was the best math we had done this year. Students were questioning each other, everyone was participating and incredible thoughts were being debated. I was thrilled to sit back, listen and watch young minds at work. Well done my Geometry students. I am proud of your fighting spirit!
Mrs. Hill: I found a stats textbook that used a real trial from 1964 to illustrate the problems of assuming independence to calculate probabilities. A woman had been mugged in CA, and the prosecutor used the assumed probabilities of a man "driving a yellow car," and being "over 6 feet tall," and "having a beard," etc to calculate that the odds of the defendant NOT committing the crime were less than one in a million. Unfortunately though, as the appeals court later determined, the prosecutor was wrongly assuming independence of events when, in fact, there was no way to be sure of that fact. It was a real life example of issues of conditional probability we had been discussing in class. Moreover, we also got the chance to discuss how, in modern times, DNA evidence is based heavily on probabilities. We were not all in agreement as to the legitimacy of that approach.
Mr. Seamon: The math team has been enjoying a very active and successful year! In additions to competing in the 6 rounds of the New England Math League, returning to the Harvard Math Competition, as well as participating in the AMC8/10/12 competitions, the team has also added in the Middle School NEML competition as well as heading to Yale for their spring HS competition. Not only is the team competing in more competitions than ever, the team is scoring as well as ever currently holding strong at 28th our of 140 teams in NEML, scoring in the top 1/3 of teams at the HMMT, and also qualifying a student for the American Invitational Mathematics Exam!
Mrs. King: I have a student who has been away at ski school during the entire second trimester and will return next Monday. Before she left her family and I had a discussion about what math class she should take, an Algebra 1 class at ski school or work with a tutor to complete our curriculum. Wanting to come back fully prepared for the third trimester she chose to work with a tutor and complete our notes, homework, quizzes and tests. I set up One Note Notebooks for both her and the tutor. After a little bit of a slow start she was off and running. The tutor and I communicated each week about what was due, what was coming up or any questions or concerns that we had. The tutor was wonderful and read all of the notes and assisted Arden after she did her assignments. Arden did a great job! It was great that she was willing to take on extra work so that she would be able to transition back into class next week. I can't wait to have her back in class.
Ms. Smith: At the end of our unit on transformations of functions, my Pre-calculus students spent a class period designing a mathematical roller coaster. That is, using their knowledge of the parent functions and transformations, they created one continuous, piecewise-defined function that traced the vertical height of the roller coaster with respect to horizontal distance travelled. As students discovered, the trickiest part was ensuring that the functions linked up, that is, there were no unplanned gaps in the track. However, after a period of work there was a wide range of functions (or should I say roller coasters). Highlights included underground tunnels, death drops, and even a loop-the-loop made using logarithmic, exponential and even elliptic functions.
Mrs. McCullagh: We finished the winter trimester with a project in Calculus. The assignment was for each student, or student pair, to decide what they wanted to hang and from where and then find the minimum amount of wire needed to hang their object. They needed to decide how far apart their two attachments should be and how far down they wanted the object suspended. They needed to find, using calculus, the minimum amount of wire needed for their own scenario. It is a challenging calculus problem for students as they are learning how to solve maximizing/minimizing problems. Then they needed to present their findings with all calculations clearly shown and diagrams labeled with the minimum and extremes. They also needed to produce a model made to scale. The projects were outstanding! We had a target hung from a tree, donuts hung for a birthday party, a chair hung is a bedroom, a rubber ducky hung (just because), as well as a number of others. The students all reported that they learned a lot from the project. It is great to have their work on display!
]]> Mathematics Students of the Trimester – Fall 2016
01 Mar 2017 19:50:34 +0000 reading US Mathematics Students of the Trimester – Fall 2016→]]> Fall 2016.
Andy Cao – Andy's in depth thought, attention to detail and willingness to tackle the most difficult problems has made him an excellent Geometry student. He has shown a genuine interest in all of the material. His approach to class has helped push his classmates to excel along side of him.
Julia Cavanaugh – I chose Julia as my student of the trimester for her work inside and outside of the classroom. Outside of the classroom she is a dedicated student who does her very best every class to prepare herself for our upcoming lesson. During class she is always focused, eager to participate, and extremely willing to help her peers out with their own work. She is a is truly a model student!
Arvin Fieldman – Many students work hard to find success. Arvin finds success and then some. He is not satiated with even strong understanding of material. He must dominate each topic. His work ethic and abilities have shown through in his careful yet creative group work as well as his ridiculously high and consistent quiz and test scores. Bravo Arvin.
Kyle Grabowski – Kyle had a remarkable first trimester at Williston in geometry. His work is neat, thorough and incredibly accurate. He has a strong natural aptitude for mathematics and he thrives on the most demanding questions given both in class and on tests. On more than one occasion this fall, Kyle was the only student in two sections of geometry to get a challenge question correct. His inductive reasoning skills are impressive!
Simon Kim – Simon has great energy in class everyday. He is always prepared and willing to help those around him. He is quick to answer questions and come up to the board. Simon is an all around great student who raises the bar everyday.
Sarah Marion – Sarah is one of the most enthusiastic, most energetic students I have ever met. She is always the first student to ask a question; she stays after class to go over any concept she had difficulty with; and she is always prepared for class with her books and homework out in front of her almost as soon as she gets in the room. She has had a ton of success in Topics, mostly because of her diligent, conscientious approach to the material. It has been such a pleasure working with her this year!
Soma Mizobuchi – Soma's work shows that he has set high standards for his academic performance. His Engineering Notebook is extremely complete and serves as a fine reference for his Engineering Labs and his code development. In writing programs, his code, and its logic, is always well thought-out and his program documentation is outstanding. Congratulations to Soma for a very impressive trimester!
Gabby Monaco – Gabby has taken on a great challenge this year moving into AP Statistics from TPS. She is one of the most persistent students and works very hard to understand difficult concepts. She is not discouraged by setbacks, but resolves to work harder on the next challenge. I am hopeful that, with this continued level of effort, she will make great progress this year and continue to model strong study habits and the kind of determination that leads to success and innovation in the field of statistics.
Gabby Record – Gabby did an outstanding job this fall in Calculus. She was always prepared and engaged in class. Her positive attitude along with interesting questions brought great energy to the class. I'm looking forward to her continued great work.
Andrew Spiegel – Andrew is a talented programmer who accepted the challenge of applying is already significant background and skill to a new context, game design. Rather than executing a safe or simple final project, Andrew pushed himself to attempt a highly challenging game that relies on random room generation. The result was an amazingly polished and enjoyable project that I hope he will continue to build upon!
Xavier Thibault – Xavier has been an extremely strong AP Calculus student. He has very good insights into the material which he is always willing to share with the class. He learns material very quickly and is able to apply his knowledge well. He helps keep our class moving forward as he is always willing to participate in our discussions.
Molly Zawacki – Molly has been a phenomenal addition to our Discrete math course. She has shown leadership in the class, whether it is stepping up to present a hard solution or explaining her thinking to her peers. I can count on Molly to go out on a "mathematical limb" and offer new ideas, even if she is not sure they are correct. Mathematically, she has developed into a beautiful proof writing; creating clear and easy to read explanations for her work. All in all, she has really embraced the core goals of the course; to explore, conjecture and prove.
Topics in Discrete Mathematics students got to review some lessons from geometry when they learned how to construct the Steiner Point of a triangle. The Steiner Point in a triangle is the point from which three branches lead out to the triangle's vertices at perfect 120° angles. (See diagram below.) This Steiner Point has important modern day applications for creating the shortest (and therefore cheapest) possible fiber optic network between any three locations. If a triangle's angle measures are all less than 120°, then the Steiner Point can be found inside the triangle using a geometric construction first developed by Italian mathematician Evangelista Torricelli in the early 1600's. Torricelli (most famous for his work in physics but also an accomplished mathematician) was a protégé of Galileo, and in 1641 succeeded Galileo as the court mathematician to Grand Duke Ferdinand II of Tuscany.
Figure 2
Torricelli's method for finding the Steiner Point in a triangle requires only the use of the traditional geometric construction tools – straightedge and compass. Using properties of equilateral triangles and inscribed angles from elementary Euclidean Geometry, the basics of the construction are shown below in Figure 1 (a,b,c). The students in Topics further learned how the Steiner Point was used in 1989 to connect Hawaii, Japan, and Guam via the Third Trans-Pacific Cable (TPC-3). Also below, Figure 2 shows a stamp issued by the Japanese Postal Service to commemorate the completion of TCP-3. As one can see from the picture, the three undersea cables meet at 120° angles under the western Pacific Ocean.
Teaching Calculus to seniors and a few juniors, I feel an obligation to help move them toward independence and self-sufficiency in their learning. I want them to learn to support themselves as learners and know how to reach out for assistance. I use two primary methods to this end.
First, I provide full solutions for all homework. Students are expected to use these solutions to check their work as they complete each problem to be sure they not only have the correct answer, but more importantly, that they have supported their work appropriately. The other way they can use these solutions is as a hint on how to start a problem if they just need a little help. No one should come to class with a blank homework saying they did not know how to do the work. With this, they know when they need help and are expected to ask for it. My second strategy for student increased independence is to have all students at the boards at the same time to do problems together. By being visible, at the boards, they can and should look to others around them to confirm they are headed in the right direction. Each student becomes a source of information for everyone else. Students who might not take the lead sitting at their desks are now asked for help by their peers. Again, no one is left unable to start a problem. Help is all around.
Ms. Evelti: I had a student who came into my Video Game class reluctantly, unsure if she would be interested in the work. She ended up really excelling in the class both in the technical and creative aspects of the work. She brought humor and visual interest to the stories behind her games while challenging herself to include difficult interactive elements in her projects that extended and deepened her understanding of the topics we covered in class.
Mr. Seamon: As we moved into a different system for graphing (polar coordinates), I worried about the transition. It's a reorientation of how to look at the basic space we've been working in and it's been a challenge in the past to communicate the new "up" and "down". This year I tried bringing in a scene from a science fiction classic (Ender's Game) and it went over quite well, even though most of the students hadn't read the book! Having a concrete picture of our new space for differentiation and integration has translated into a deeper understanding on the part of the students which has been expressed through impressive board work and high quiz scores.
Ms. Schneider: One of my favorite things to do in class is play a review game. Although I made up the game myself, it is similar to jeopardy where the students pick questions of different difficulty within a topic. The students are split up into teams, and if one group answers a question incorrectly other groups have an opportunity to steal the question. I absolutely love this game because the students work so well together in their groups and are extremely invested in each problem. They have smiles on their faces the entire time as well as they work meticulously to complete the problem within the time frame. The pure exhilaration of getting a question correct or having the opportunity to steal a question brings such a positive energy to the classroom. Every test that we have my students get excited because they know that means we get to play the "review game" the lesson beforehand.
Mrs. Conroy: It has been a treat to return to the Geometry classroom. The biggest change in this class over the past three years has been the use of technology. Now that each student in the class has their own surface loaded with the geometer's sketchpad software, the variety of classroom activities available to the class are remarkable. Each day feels different. We are discovering geometry through investigations, constructions and traditional class framework notes. My ability to project figures from a variety of sources has led to a much more efficient classroom. Students can see examples in one note as well as on the board and we are able to spend so much more classroom time doing problems. This has not gone unnoticed by my students. They enter class wondering what will we be doing today. Some things never change. Students love to find the missing angles but proofs remain a challenge!
Mrs. Hill: My Topics class can be a bit of a raucous group. The students are all seniors who, for the most part, have not all had great success in mathematics. In this course, however, we are focusing on political and societal applications of mathematics, and the "math" kind of sneaks in under the radar. A young woman in that class has struggled in past math courses at the school, but has had tremendous results in this one due to her intense work ethic and willingness to participate. She talks about how she really understands the relevance of this course and can appreciate how math is used in the "real world." It is so wonderful to see a person who, before now, has not seen a use for mathematics discovering how it can be relevant to her life.
Mrs. Whipple: During a recent lesson on proving congruent triangles, students in my geometry honors class where given a new type of problem using overlapping triangles. They were put into groups and sent to the white boards to work together to come up with the most efficient ways to prove that certain triangles were congruent. Afterwards, we talked about all the strategies that each group used in tackling the problem and which worked best. After sharing all their ideas and observations, they were given another extremely hard proof to work on together. Not only did they use the strategies that we talked about but the majority of the groups commented on how "this problem was much easier", when it was actually much more challenging.
Ms. Briedis: In a recent class we were beginning a lesson on composite trig functions. The lesson started with absolute value functions and the students were amazed by how the absolute value of a trig function changed the way the graph looked. We began playing with trig functions such as f(x)=(x^2+1)sin(2pix), and they thought the graph was the incredible. The amazement on their faces was exactly what teachers thrive on. We began playing with different functions on Desmos.com, and each student began creating their own functions and then would share them with the class. We would then work on what the two functions would be that the overall function oscillated between. It was a really fun lesson that the students connected with. They were engaged and excited about the different functions they were creating and seeing from others. It was an overall thrilling time to see them so inspired about graphing.
Mrs. Baldwin: Our class has been investigating random phenomena through use of examples and simulations. The students are doing a great job figuring out what makes a process truly random as opposed to arbitrary or haphazard. We have been noticing that the word "random" is used often in a casual sense in everyday language and have begun to recognize cases where the word is used inappropriately. Students did a great job with a recent project in which they found a probability estimate through a little research and conducted a simulation in which they used a random number generator (or table) to conduct repeated trials. One example involved estimating the number of attempts needed to catch a toy in the claw machine when there is an 8% chance of grabbing the toy on any single attempt. The student discovered, through 20+ repeated trials of this simulation that it took about 12 attempts on average. This corresponded with the estimate published on the website. We will next investigate the theory behind these random phenomena and connect the underlying principles to our observations. It has been great working with these students who bring enthusiasm and a lot of creativity to class.
Mr. Matthias: Each year when the class starts Engineering & Robotics, they aren't quite sure what they will be facing. There is some concern as we begin with a survey of Engineering and the Engineering process. Then, as we start ROBOTC programming, the class begins to feel more comfortable and confident about the material. We practice our programming with robots in "Engineering Labs" designed to give students practical experience with programming the movement of their robot to achieve certain goals. The Engineering Labs soon become one of the favorite activities of the class and students regularly ask if we are doing one in the day's class. As a teacher, I am so thrilled that the class looks forward to this engaging hands-on learning activity.
Mrs. McCullagh: Looking back at trimester 1, I am particularly pleased with how the students adjusted to the abstract nature of Calculus. In this course they are asked to use the skills they have built in Algebra, Geometry, and Pre-Calculus. To that we add the concepts of Calculus. While challenging, the students did really well in working with limits and longer problems than they had seen in the past. We spent a block of classes exploring the definition of the derivative. The students have a very good intuitive understanding of what we mean by derivative being the instantaneous rate of change.
Ms. Smith and the math department want student ideas for what to put up on the walls of the math department stairwell. Send your submissions to Ms. Smith (msmith@williston.com) by Friday, 12/16. You can also drop off physical submission in the box in the math office, located in Schoolhouse 21.
Hello, I am Ms. Smith and I am one of the teachers in the math department. But today, I am not here to talk about math. I'm here to talk about math and art, like the mathematical murals projected behind me.
You may think that math is restricted to the realm of numbers and equations. While it is certainly true that numbers and equations form the building blocks of mathematics, they also give rise to things that look a lot like art.
Those equations give rise to parabolas, ellipses, circles, shapes that are found throughout the artistic world. Infinite repetition and self-similarity give rise to fractals, like the dragon curve. Computer programs can even give rise to art. They can generate, random, yet strangely structured images.
Math can give rise to art. And art can give rise to math.
So here's where you come in. The brick stairwell to the math classrooms is empty. We want to fill it with math and art. We want your designs for the space, whether it's math, art, or something in between. Until winter break, the Math Department will be collecting designs and ideas for the stairwell. You can submit your designs to the box in the math office or to msmith@williston.com.
Thank you and happy sketching!
]]> Math Teacher to Present at Math Conference
12 Nov 2016 19:51:21 +0000 reading Williston Math Teacher to Present at Math Conference→]]>Williston math teacher Mia Smith will be traveling to Atlanta this January to present a paper at the Joint Mathematics Meetings, the largest mathematics meeting in the world.
Smith authored the paper "Colorful Graph Associahedra" with Professor Satyan Devadoss while at Williams. From the abstract:
Mia Smith
"Given a graph G, there exists a simple convex polytope called the graph associahedron whose face poset is based on the connected subgraphs of G. Motivated by ideas in algebraic topology and computational geometry, we define the colorful graph associahedron based on an assignment of a color parameter. We show it to be a simple abstract polytope, provide its construction based on the classical permutohedron and prove various combinatorial and topological properties." | 677.169 | 1 |
You know mathematics. You know how to write mathematics. But do you know how to produce clean, clear, well-formatted manuscripts for publication? Do you speak the language of publishers, typesetters, graphics designers, and copy editors? Your page design-the style and format of theorems and equations, running heads and section headings, page breaks,... more...
Mathematical models are used to simulate complex real-world phenomena in many areas of science and technology. Large complex models typically require inputs whose values are not known with certainty. Uncertainty analysis aims to quantify the overall uncertainty within a model, in order to support problem owners in model-based decision-making. In recent... more...
This volume contains a systematic discussion of wavelet-type inversion formulae based on group representations, and their close connection to the Plancherel formula for locally compact groups. The connection is demonstrated by the discussion of a toy example, and then employed for two purposes: Mathematically, it serves as a powerful tool, yielding... more...
Get ready to master the unknown number! Master Math: Solving Word Problems is a comprehensive reference guide that explains and clarifies the difficulties people often face with word problems, in a simple, easy-to-follow style and format. Beginning with the most basic types of word problems and progressing through to the more advanced, Solving Word... more... | 677.169 | 1 |
People who would like direct experience with basic Mathematica 6 features.
Objective
To provide direct experience with all of the basic features of Mathematica 6 as well as a foundation for developing advanced applications of the system.
Course Content
You will receive hands-on instruction in performing basic operations, building up computations, and navigating the user interface. The course will also cover an introduction to the Mathematica programming language emphasizing familiar programming tasks using procedural, functional, and rule- based programming; visualization and graphics including creation of dynamic and interactive graphics; importing and exporting data and files, file formats, file paths, working with data collections, visualization of large data sets25 AM.
If you have a question, problem or suggestion please open a
Service Desk Ticket. | 677.169 | 1 |
Four challenging exam-like questions with fully worked out solutions for A level and IB students who want to test their knowledge of volumes of revolution (C4 Integration).In each question, a solid of revolution has to be subtracted from or added to the integral. The curve in one question is described by parametric equations. Another question uses trigonometric functions. The problem of finding the radius and height of cone/cylinder, is addressed in the solutions.
A pair of presentations that explain what Implicit and Parametric functions are and how you can differentiate them. Presentations have detailed explanations and clear worked examples of exam style questions**All questions are completely new and have not been previously published, therefore students will not be able to have access to mark schemes or have seen them before.**A C4 worksheet mark scheme with examination style questions on the topic Integration. Each question has the value of marks it is worth on the right hand side. The worksheet can be used as homework, in-class or even an assessment.
**All questions are completely new and have not been previously published, therefore students will not be able to have access to mark schemes or have seen them before.**A C4 exam paper mark scheme which has very similar questions to a real C4 exam.
**All questions are completely new and have not been previously published, therefore students will not be able to have access to mark schemes or have seen them before.**A C4 worksheet mark scheme with examination style questions on the topic Parametric Equations. Each question has the value of marks it is worth on the right hand side. The worksheet can be used as homework, in-class or even an assessment.
This is a PDF outlining all the different areas of differentiation and integration in Core 3 and Core 4. It is modelled from the Edexcel specification but is suitable for all exam boards. There's also some rules for differentiation and integration methods (chain rule, integration by parts, etc.) I hope you find it useful!
This is a simple PDF outlining all the standard results that are given in the formula book and a few results that are not given in the formula book, but may be examined on.This document also includes some extra things like general patterns to look out for in integration and what you need to do when faced with a substitution question (hint: hyperbolic and trigonometric substitutions can be tricky!).This is designed as a 'cheat sheet' as opposed to a full revision guide.
These are an attempt to break from the monotony of past papers in the run up to exam season. I have taken 2 or 4 (depending on whether they will fit on a page!)
These were born from a HoDs meeting where we were asked to evidence progress and student response to teacher guidance.I have to thank and for their excellent websites. It was here where i got my inspiration (and most of my resources too).My plan is to give these to students as the course begins and we refer to their learning schedule either directly following a lesson or on a weekly basis. Homework will be set at the appropriate times and when the work is handed back to students, i will give them sufficient time to digest and glean the key areas/tips needed for improvement. We then, as a class, will discuss when we will re-visit the questions they need to look at again (for me this will be on a the same day each fortnight). My vision is that students will know to get these folders out and use THEIR notes in order to make and evidence their progress. These questions will be marked in class (self/peer).If you need specific sheets, please DM me via twitter, @billyads_47, and i will gladly share. Equally, if you do use these with your classes I'd be interested to see how it went and what can be changed to improve for future years.
I use these as a break from the "past paper drudgery" in the run up to exams. The questions are taken from past papers (amended in some cases). The idea is to answer each question fully then scan the QR code linked to the correct answer to form a code. Each QR code (correct or incorrect to avoid "cheating") scans to a song or artist that contains a number or colour, so this generates the code.
Tough C4 maths question on parametric equations. Students complete the question STEP-BY-STEP - use the link below to try it as a starter in class or send the link to students to do it themselves!
Tarsia hexagonal jigsaw for Core 4 Edexcel (6666) questions involving rearranging parametric equations into the equivalent Cartesian equation.To open the file you need to download the file and then open the file from Tarsia as unfortunately it will not open tarsia correctly.
A mat to summarise key concepts from the C4 topic Parametric Equations (Edexcel). I also include a suggestion for how the mat could be filled out. I usually use it as a plenary – ask the pupils for the key ideas from the lesson and collectively fill in sections over a sequence of lessons. At the end of a topic they have a topic mat from which to revise from. I also photocopy them on different coloured paper so they act as dividers in students' folders.I am creating these resources as part of an action research project at my school looking at preparation for improving students retention across a two year linear course and trying to bring the science of memory into the classroom. If you have used these resources and have any comments/feedback/ideas please comment or contact me - thanks!
**All questions are completely new and have not been previously published, therefore students will not be able to have access to mark schemes or have seen them before.**A C4 exam paper which has very similar questions to a real C4 exam.Answers can be found here:
Have written this in preparation to use with my year 13s as they begin their past paper revision. I always like to condense the pertinent notes onto one side of A4. By making it a word they can remember, i hope this helps students recreate the poster for themselves, hence acquiring the correct techniques for their exam. Quite tempted to make a Gryffindor revision poster for Core 3 now ...This has not been used as yet so i would appreciate ANY feedback ...
**All questions are completely new and have not been previously published, therefore students will not be able to have access to mark schemes or have seen them before.**A C4 worksheet with examination style questions on the topic Parametric Equations. Each question has the value of marks it is worth on the right hand side. The worksheet can be used as homework, in-class or even an assessment.Answers can be found here:
**All questions are completely new and have not been previously published, therefore students will not be able to have access to mark schemes or have seen them before.**A C4 worksheet with examination style questions on the topic Integration. Each question has the value of marks it is worth on the right hand side. The worksheet can be used as homework, in-class or even an assessment.Answers can be found here: | 677.169 | 1 |
Solving Equations Flip Book (Foldable)
Be sure that you have an application to open
this file type before downloading and/or purchasing.
507 KB|13 pages
Product Description
Solving Equations - Flip Book Notes Activity
This is a great way to introduce solving equations or to use as a refresher activity. I have included combining like terms, variables on one side, and variables one both sides of the equation sign. All components have step by step guidelines to solve equations, as well as three examples.
This product fits perfectly into an interactive notebook, but would also work well as a stand alone piece. It is designed to be printed front and back, so only two pieces of paper are needed per student!
Try out these other activities that will help your students master solving equations. | 677.169 | 1 |
Review the syllabus.
Talk about the course.
Introduce the Mathematical Concepts/Applications website.
Introduce GDT::Resource::Math.
Introduction to exponents.
Introduction to the base-10 number system.
Assignment(s): Read the syllabus. And
First Assessment on ExponentsHandouts:MAT102 Syllabus
and About the Course | 677.169 | 1 |
The Mathematics department commits to provide students with strong foundation in Mathematics needed in their respective field of specialization through improved classroom instructions and augmentation programs.
Goals and Objectives
Mathematics department is a service oriented department whose primary objective is to deliver Math-related services through classroom-based and computer aided instructions. With its supervision of the BS Mathematics program, the department faces the challenge of developing the potentials of the young who have shown passion and skill in Math problem solving and Math research.
Being a service department, Mathematics department aims to:
1. Develop students who can make decisions which are Mathematically based;
2. Make students appreciate the importance of Mathematics in their day-to-day routines;
3. Enhance their creative, logical, analytical and critical thinking thereby making them competitive, more confident and well-respected individuals. | 677.169 | 1 |
Questions about the course
What is the focus of this course?
AP Calculus AB covers differential and integral calculus, including concepts and skills of limits, derivatives, definite integrals, and the Fundamental Theorem of Calculus. Students learn to approach calculus concepts and problems when they are represented graphically, numerically, analytically, and verbally, and to make connections among these representations. For more details go to the two-page Course Overview (.pdf/977.3MB).
What has changed in the AP Calculus AB course?
Only minor changes have been made. The updated course is defined in a new curriculum framework that ties course content and mathematical practices to clearly stated learning objectives, giving teachers greater transparency into course and exam expectations. For more specific information go to Key Changes to AP Calculus. You can also watch this narrated presentation.
What is the difference between AP Calculus AB and AP Calculus BC?
AP Calculus BC is an extension of AP Calculus AB: the difference between them is scope, not level of difficulty. AP Calculus AB includes techniques and applications of the derivative, the definite integral, and the Fundamental Theorem of Calculus. It is equivalent to a semester of calculus at most colleges and universities. AP Calculus BC includes all topics in AP Calculus AB, plus others such as parametric, polar, and vector functions, and series. It is equivalent to one year of calculus at most colleges and universities.
What is the equivalent college-level course?
AP Calculus AB is roughly equivalent to a first semester college calculus course devoted to topics in differential and integral calculus.
Are there any student prerequisites?
Before studying calculus, all students should complete four years of secondary mathematics designed for college-bound students: courses in which they study algebra, geometry, trigonometry, analytic geometry, and elementary functions.
What's the best way to identify students who should take this course?
Any motivated student should be given the chance to benefit from an AP course. If your school offers the PSAT/NMSQT®, use AP Potential™. This free online tool allows you to identify students who are likely to succeed in AP based on their PSAT/NMSQT or SAT® scores. Such scores have proved to be stronger predictors of AP success than have high school grades or GPA.
Which textbooks does the College Board recommend?
The College Board does not recommend specific textbooks. However, a list of textbooks appropriate for the course appears on the AP Course Audit.
How can I prepare myself to teach this course?
Teaching and Assessing AP Calculus is an online professional development resource that features videos of master teachers modeling key instructional strategies for challenging skills and content. It also gives you resources to help you implement these strategies in your classroom. Log in or learn more.
Our school has block scheduling. Can we teach AP Calculus?
Yes. AP Calculus AB and AP Calculus BC were designed to represent yearlong college-level courses, so it's important that a block arrangement encompass a full year of instruction. Some schools extend each course over two blocks to give students the hours they need to complete a full year of classesWhat resources are available to support the course authorization processQuestions about the exam
How can I prepare my students for the exam?
These resources will help:
A full practice exam, including sample student responses, is available by logging in to your AP Course Audit account and others can be purchased on the College Board store.
When is the AP Calculus AB Exam administered?
The exam is given each year in early May. Go to the Exam Calendar for the most current exam dates.
How much of the exam requires a calculator?
A calculator is required for Section I, Part B of the exam (15 multiple-choice questions) and for Section II, Part B of the exam (2 free-response questions). View our calculator policy for more information.
What brand of calculator does the College Board recommend?
The College Board does not recommend brands, but we do maintain a list of approved graphing calculators – make sure you and your students know the calculator policy for the exam.
What score do students need to get on the AP Exam to receive credit or advanced placement?
That depends on the college. Some require higher scores than others. Tell your students to use the AP Credit Policy Info tool to verify the credit/placement policies at the schools they are considering. | 677.169 | 1 |
Exploration 3: Introduction to Definite Integrals
In this integral instructional activity, students estimate the definite integral and find the derivative of functions. They graph functions and determine the range of the velocity. This three-page instructional activity contains approximately 40 problems. | 677.169 | 1 |
Each student's studies will be individualized. students will use a combination of written and computerized materials and programs during the course. specific goals must be accomplished and a final test passed to receive credit. emphasis is on numeric skills, number sense, estimation, problem solving, and basic algebraic equations. students will strengthen their problem solving skills with and without the aid of calculators.
307 Algebra A (two semester course) (9-10-11-12)
(teacher recommendation)
This course is first half of a two year algebra course the second course is algebra 1b. Algebra 1b covers the essential tools of general math, algebra terminology, properties, and classifications, solving, graphing, and analyzing linear equations, the real number system, absolute value and inequality equations, probability, and statistics
This class deals with problem solving, the rules of algebra, the use of variables, solving equations, graphing, introduction to data analysis and concept of function. Students are required to use cognitive tutor computer program and to participate in small group activities
310c Algebra 1b (10-11-12) (two semester course)
Two-semester course.
Prerequisite: Successful completion of Algebra A.
This course is first half of a two year algebra course the second course is algebra 1b. Algebra b cover lines of best fit, solving systems of equations by graphing, substitution, and elimination, non-linear functions, quadratics, factoring polynomials, and simplifying expressions.
This course is a review and reinforcement of concepts dealt with in algebra 1, building a firmer foundation leading to greater success in algebra 2. Concepts covered in geometry are also introduced with special emphasis placed on the correlations between algebraic processes and their applications in geometry.
320 Geometry (9-10-11-12)
(two semester course) (NCAA)
Two-semester course.
Prerequisite for grade 9: C or better in High School Algebra I and teacher's recommendation & satisfactory score on Alg 1 final.
Prerequisite for grade 10, 11, or 12: teacher recommendation and completion of Algebra 1 with grade of C or better.
Geometry is a study of line, angle, polygons and polygon relationships, circles and other plane figures. Emphasis is placed on discovering the fundamental properties and becoming actively involved in the learning process. Students explore geometric relationships with a wide variety of tools; they perform investigations and constructions, measure figures, observe patterns and discuss their finding to discover geometric ideas,write definitions and formulate their on conjectures. Students are presented with formal proofs after they have discovered and mastered the conceptual basis of the theorems they are to prove. All topics from a more traditional geometry courses and covered, but in a manner that students passive to active participants.
325 Algebra 2 (10-11-12) (two course semester) (NCAA)
Two-semester course.
Prerequisite: Successful completion of Geometry and Algebra I or Trag with B or better in each course.
This course is a continuation of algebra 1 providing a more in depth study of 1st degree equations, quadratics, conic, complex numbers, exponents and logarithms, matrices, problem solving, and a continuation of data analysis and function.
335 Math Analysis/Trig (PreCalculus) (11-12) (NCAA)
Two-semester course.
Prerequisite: Successful completion of Geometry and a B or better in Algebra II.
This course is a prerequisite for calculus. It focuses on algebraic and geometric representations of problem situations that can be modeled using functions. The extensive use of graphing calculator helps to clarify the connections between past mathematics topics and the new. Linear, polynomial, rational, exponential, logarithmic and trigonometric functions are analyzed throughout the course. Approximately half the year is devoted to an in depth study of trigonometry. Ownership of a TI 82 or 83 calculator is highly recommended.
345 AP Calculus (12) (NCAA)
Two-semester course.
Prerequisite: Successful completion of Math Analysis with B or better and teacher recommendation.
AP calculus develops the student's understanding of the concept of calculus (functions, graphs, limits, derivatives and integrals) and provides experience with its methods and application. The course encourages the geometric, numerical, analytical, and verbal expression of concepts, results, and problems. Appropriate technology, from manipulative to
calculators and applications software will be used regularly for instruction and assessment.
350 Statistics (11-12) (NCAA)
Two-semester course.
Prerequisite: Geometry or with teacher consent.
Students will be able to learn statistical concepts and apply statistical reasoning through learner-centered activities based on real information and data from a wide variety of fields such as sports, entertainment, business, education, experimentation, probability and simulations, statistical inference.
347 AP Statistics (11-12) (NCAA)
Two-semester course.
Prerequisite: Successful completion of Algebra 2 with a grade of B or better.
The Advanced Placement Statistics course focuses on four major themes. Exploring Data: Describing patterns and departures from patterns. Sampling and Experimentation: Planning and conducting a study. Anticipating Patterns: Exploring random phenomena using probability and simulation. Statistical Inference: Estimating population parameters and testing hypotheses. Course is based on College Board AP Statistics guidelines.
804 Personal Finance (taught by business dept.) (10-11-12) (one or two semester course)
(NCAA)
One or Two semester course. Either semester may be taken independently.
Prerequisite: Algebra I.
Refer to Personal Finance course listed under career-technical. Math credit or elective credit may be given. | 677.169 | 1 |
I covered the basics of these topics about 3 years ago, and have done virtually no maths studying since then, so i only have vague memories :(
Can anyone reccomend a decent book that covers these topics, and contains solid self practice exercises.
This is knowledge which im supposed to have as a prerequisite for a masters degree, so i really just want to brush up on it to a point where i know what im talking about to pass an interview and not struggle with the more advanced use of the mathematics which might come up in the degree (computing). | 677.169 | 1 |
Run a Quick Search on "The Ultimate Math Refresher for the GRE, GMAT, and SAT" by Lighthouse Review Inc to Browse Related Products:
Short Desription
A comprehensive math review for the GRE, GMAT, and SAT. This math refresher workbook is designed to clearly and concisely state the basic math rules and principles of arithmetic, algebra, and geometry which a student needs to master. This is accomplished through a series of carefully sequenced practice sets designed to build a student's math skills step-by-step. The workbook emphasizes basic concepts and problem solving skills. Strategies for specific question types on the GRE, GMAT, and SAT are the focus of the Lighthouse Review self study programs.
If You Enjoy "The Ultimate Math Refresher for the GRE, GMAT, and SAT (Paperback)", May We Also Recommend: | 677.169 | 1 |
Project Maths - Ordinary Level Free Course
Description
Outcome
Certification
This course is for students interested in studying the Project Maths Ordinary Level Course in its entirety. This free online course provides students with videos on all the Ordinary Level, Algebra, Functions and Calculus.
Having completed this course students will be able to:
Describe the concepts of probability
Understand outcomes of random processes
Describe statistical reasoning with an aim to becoming a statistically aware consumer
Find, collect and organise data
Represent data graphically and numerically
Analyse, interpret and draw inferences from data
Develop synthesis and problem-solving skills
Determine the slope of a line passing through two given points
Find the equation of a line passing through two given points
Find the equation of a line perpendicular to a given line and passing through a given point
Determine the equation of a circle having a given centre and radius
Find the equation of a tangent to a given circle at a specified point
Find distance and angle using Sine and Cosine Rules
Find length of an arc and area of a sector using circular measure
Determine the area of a triangle given the lengths of two sides and the included angle
Determine the sum of an arithmetic series
Determine the sum of a geometric series
Work out the profit made on a sale
Work out the income tax paid on the gross pay
Multiply and divide complex numbers
Work out the areas and volumes of well known shapes and solids
Solve linear simultaneous equations with 2 unknowns
Factorise expressions of order 2
Form quadratic equations with given roots
Solve one linear equation and one equation of order 2 with two unknowns | 677.169 | 1 |
Eighth grade mathematics is about (1) formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; (2) grasping the concept of a function and using functions to describe quantitative relationships; (3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.
Key Areas of Focus for Grade 8: Linear algebra
For more information on the NYS Common Core Standards for Mathematics Grade 8, please see:
Select topics from the NYS Common Core Algebra Curriculum will be explored. Students will NOT sit for the Algebra I Regents Examination in June 2016. For more information on Algebra 1 Standards, please see: | 677.169 | 1 |
Discrete Mathematics and Its Applications is intended for one or two term introductory Discrete Mathematics courses taken by students from a wide variety of majors, including Computer Science, Mathematics, and Engineering. This renowned best-selling text, which has been used at over 500 institutions around the world, gives a focused introduction to the primary themes in a Discrete Mathematics course and demonstrates the relevance and practicality of Discrete Mathematics to a wide variety of real-world applications?from Computer Science to Data Networking, to Psychology, to Chemistry, to Engineering, to Linguistics, to Biology, to Business, and many other important fields"synopsis" may belong to another edition of this title.
Product Description:
We are pleased to present this "Global Edition" "Global Edition" has been adapted to meet the needs of courses outside of the United States and does not align with the instructor and student resources available with the US edition.
Product Description:
…from computer science to data networking, to psychology, to chemistry, to engineering, to linguistics, to biology, to business, and to many other important fields. Book Condition: New. Publisher/Verlag: McGraw-Hill Higher Education | Global Edition |This Global Edition includes:An entire new chapter on Algebraic Structures and Coding Theory New and expanded sections within chapters covering Foundations, Basic Structures, and Advanced Counting Techniques Special online only chapters on Boolean Algebra and Modeling Computation New and revised problems for the international student integrating alternative methods and solutions. This Global Edition has been adapted to meet the needs of courses outside of the United States and does not align with the instructor and student resources available with the US edition. | Chapter 1: The Foundations: Logic and Proofs Chapter 2: Basic Structures: Sets, Functions, Sequences, Sums, and Matrices Chapter 3: Algorithms Chapter 4: Number Theory and Cryptography Chapter 5: Induction and Recursion Chapter 6: Counting Chapter 7: Discrete Probability Chapter 8: Advanced Counting Techniques Chapter 9: Relations Chapter 10: Graphs Chapter 11: Trees Chapter 12: Algebraic Structures and Coding Theory Appendices | Format: Paperback | Language/Sprache: english | 1885 gr | 261x218x34 mm | 1024 pp. Bookseller Inventory # K978 | 677.169 | 1 |
Registration
Algebra I Prep- This Pre-Algebra camp will focus on concepts and skills which provide a firm basis for entering Algebra I. It will include a review of fractions, decimals and percent relationships & operations, equation solving, ratios, integers, squares and roots, graphing and an introduction to linear functions. This camp is for those students in middle school who need to review or practice basic Algebra strategies to support assure continuing success inAlgebra I. | 677.169 | 1 |
Crossing the River with Dogs: Problem Solving for College Students, 2nd Edition
Crossing the River with Dogs: Problem Solving for College
Students, 2nd edition promotes
the philosophy that students learn best by working in groups and
the skills required for real workplace problem solving are those
skills of collaboration. The text aims to improve students'
writing, oral communication, and collaboration skills while
teaching mathematical problem-solving
strategies. Focusing entirely on
problem solving and using issues relevant to college students
for examples, the authors continue their approach of
explaining classic as well as non-traditional strategies through
dialogs among fictitious students. This text is appropriate
for a problem solving, quantitative reasoning, liberal arts
mathematics, mathematics for elementary teachers, or developmental
mathematics course | 677.169 | 1 |
Saxon Algebra 1/2, Revised Home Kit
Algebra 1/2 Home Study Kit includes the hardcover student text, softcover answer key and softcover test booklet. Containing 123 lessons, this text is the culmination of prealgebra mathematics, a full pre-algebra course and an introduction to geometry and discrete mathematics. Some topics covered include Prime and Composite numbers; fractions & decimals; order of operations, coordinates, exponents, square roots, ratios, algebraic phrases, probability, the Pythagorean Theorem and more. Utilizing an incremental approach to math, your students will learn in small doses at their own pace, increasing retention of knowledge and satisfaction!
Saxon Algebra 1/2 Kit & DIVE CD-Rom, 3rd Edition
Boost your students understanding of Saxon Math 1/2 kit with DIVE's easy-to-understand lectures! Each lesson in Saxon Math's textbook is taught step-by-step on a digital whiteboard, averaging about 10-15 minutes in length; and because each lesson is stored separately, you can easily move about from lesson-to-lesson as well as maneuver within the lesson you're watching. Taught from a Christian worldview, Dr. David Shormann also provides a weekly syllabus to help students stay on track with the lessons.
Algebra 1/2 covers pre-algebra mathematics and skills, and includes review of fractions, decimals, percents and graphing. For use with 3rd Edition.
Saxon Teacher for Algebra .5, Third Edition on CD-ROM
Help your students transition to pre-algebraic topics such as fractions, decimals, percents, ratios, unit conversions, and graphing; and provides introductions to geometry and discrete mathematics with Saxon Algebra =! Comprehensive lesson instructions feature complete solutions to every practice problem, problem set, and test problem with step-by-step explanations and helpful hints. These user-friendly CD-ROMs contain hundreds of hours of instruction, allowing students to see and hear actual textbook problems being worked on a computer whiteboard. A slider button allows students to skip problems they don't need help on, or rewind, pause, or fast-forward to get to the sections they'd like to access. Problem set questions can be watched individually after the being worked by the student; the practice set is one continuous video that allows for easy solution review. For use with the 3rd Edition. Four Lesson CDs and 1 Test Solutions CD is included.
Pre-Algebra Grade 8 Homeschool Kit (Second Edition) Problem solving and real life uses of math are featured in each chapter. Dominion mathematics can be used to manage God's creation to His glory. 2nd Edition.
This kit includes:
Pre-Algebra Student Book
Pre-Algebra Teacher's Edition
Pre-Algebra Test Pack
Pre-Algebra Test Pack Answer Key
Pre-Algebra Student Activity Manual
Pre-Algebra Student Activities Answer Key
This resource is also known as Bob Jones Pre-Algebra Grade 8 Homeschool Kit, 2nd Edition.
Teaching Textbooks Pre-Algebra Kit, Version 2.0
Created for the independent, homeschooling student, Teaching Textbooks has helped thousands of high schoolers gain a firm foundation in upper-level math without constant parental or teacher involvement.
Extraordinarily clear illustrations, examples, and graphs have a non-threatening, hand-drawn look, and engaging real life questions make learning pre-algebra practical and applicable. Textbook examples are clear while the audiovisual support includes lecture, practice and solution CDs for every chapter, homework, and test problem. The review-method structure helps students build problem solving skills as they practice core concepts and rote techniques.
Teaching Textbooks' new Pre-Algebra Version 2.0 edition now includes automated grading! Students watch the lesson on the computer, work a problem in the consumable workbook, and type their answer into the computer; the computer will then grade the problem. If students choose to view the solution, they can see a step-by-step audiovisual solution.
Teaching Textbooks Pre Algebra 2.0 includes the following new features:
Automated grading
A digital gradebook that can manage multiple student accounts and be easily edited by a parent.
Over a dozen more lessons and hundreds of new problems and solutions
Interactive lectures
Hints and second chance options for many problems
Animated buddies to cheer the student on
Reference numbers for each problem so students and parents can see where a problem was first introduced
Walch Science Literacy Series: Physics, Student Text
The high-interest, easy-to-understand materials in this engaging series will make science relevant to your daily life. You will find a host of hands-on activities, stimulating reading selections, and clear illustrations that make science - and scientific thinking, come alive. All activities have been designed to address current national science standards; all materials also help you develop the critical science-literacy skills you need in today's world.
Physics takes you on a voyage to Mars, analyzes the effects of music, describes threats posed by electromagnetic radiation, debates the pros and cons of nuclear power, and explores future technologies - along with other chapters that illustrate key scientific concepts. Grades 6-8. 58 pages. This may not cover 1 full year. | 677.169 | 1 |
Do professors have
a sense of humor? Listen to Calvin professor Robert Keeley (left) describe
the writing of his latest textbook.
"Sitting in an
office with no windows all summer writing a math book is not as much
fun as it sounds," he says with a wry smile.
Which is why it's
no surprise that the precalculus textbook Keeley wrote during that summer
of 1997 (with Hope professors Todd Swanson and Janet Anderson) is filled
with real-life examples and, yes, even humor, despite the humorless
title "Precalculus: A Study of Functions and Their Applications."
The new text's
point of departure from other precalculus books is its treatment of
mathematical functions.
"We didn't want
series of disconnected functions," said Keeley.
"Precalculus: A
Study of Functions and Their Applications" begins by explaining all
of the basic functions and their relationships to each another. Once
the students have these functions on their mathematical palettes, they
are free to play and have fun with the material -- an attitude that
the authors hope will be felt by the students who use the book.
"We wanted a text,"
says Keeley, "that students could actually read."
The real hook,
though, is the text's true-to-life study problems. For instance, they
used Swanson's actual utility bills for certain problems and utilized
linear function to find the dimensions of a life-sized Barbie doll --
focusing on the head and feet, of course.
The book was based
on a previous award-winning workbook, published in 1997, called "Projects
for Precalculus." Anderson, Keeley and Swanson wrote the 1997 text after
receiving a $150,000 grant from the National Science Foundation.
"Projects for Precalculus"
went on to win an award at the Innovative Programs Using Technology
competition and also earned a feature "Exemplary Programs in Introductory
College Mathematics," published by the Mathematical Association of America.
Harcourt College
Publishers then approached the team about expanding their effort into
a full-sized text, which led to marathon writing sessions to complete
a much larger book in less time than it took to write the original shorter
"Projects for Precalculus." Keeley refers to their latest work as "how
I spent my vacations for the last two years."
Keeley dabbles
in both music and drama in addition to teaching courses in educational
psychology and the teaching of religion in elementary schools as a member
of the Calvin Education Department. He wrote two
Christmas plays for children with his wife. The plays are meant to teach
kids about Christmas is a way that is light-hearted but also gives them
(and adults) something to think about. Keeley plays guitar and leads
worship in his church in Holland and, occasionally, for Calvin's Chapel
services.
Before coming to
Calvin he taught middle and high school math for 20 years, most recently
at Holland Christian High School. In
fact, it was his teaching at Holland Christian which led to his 1991
meeting with the two Hope professors. They formed a team that has now
published two innovative works together and has plans for a third. | 677.169 | 1 |
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this file type before downloading and/or purchasing.
236 KB|16 pages
Product Description
This is an animated powerpoint presentation that I made to use in my Algebra class. It worked out much better than what I did last year so I thought others might find it helpful.
The slideshow takes students through several examples of how to factor monomials and animates the process to show what is happening. I also included a notes sheet that has the problems from the presentation all on one sheet which can be printed and given to students. This saves a lot of time since I don't have to wait for students to write down each problem every time I change slides.
I tried to make the slides easy to understand, but it would be a good idea to run through all the animations at least once before using it in your class. The nature of how powerpoint does its animations may mean that some of the slides will look messed up when you view them outside of a slideshow. But everything looks correct when you're presenting it to your class. I believe you should be able to check out the preview file to get an idea of what it will look like when you use it in your class.
If you have any questions or comments, please let me know. I've got a lot of other presentations along these lines that I use in my class; I just haven't had the time to clean them up and put them online. | 677.169 | 1 |
...
Show More Modules for Interactive Learning Using MapleA (R) has been carefully designed to help students develop their geometric intuition and deepen their understanding of linear algebra concepts and methods. These modules support both individual work and interactive collaboration. They can be used as a supplement in a traditional lecture course, or in a lab-only format. Due to their versatility, they can be easily adapted to a variety of curricula, institutions, and styles of teaching. Goals of the Modules 1. To help students develop their geometric intuition about the concepts of linear algebra; 2. To deepen students' understanding of the algebraic formulation of these concepts and to strengthen their ability to manipulate concepts; 3. To help students gain an appreciation of how the concepts and methods of linear algebra are applied.Structure of the Modules Each module is divided into two main parts, the Tutorial and the Problems: The Tutorial is further divided into sections and consists of an interlaced text (usually brief), examples and demonstrations, and exercises (with answers provided in closed sections). The Problems are all intended to be fairly substantial, as they provide the work on which students will be graded. They include explorations, applications, constructions (e.g., of specified types of matrices or specified pictures or animations), counter-examples, short essays, proofs, true/false questions, and many challenging computations. Each module is a Maple worksheet that is to be used in conjunction with Release 5 of Maple V A (R | 677.169 | 1 |
Mathematical Sciences
Submitted by nkmazano on July 25, 2013 - 1:01pm
Mathematics is one of the oldest and most fundamental sciences. Mathematics is the science of quantitative relationships using numbers and symbols. Mathematicians use mathematical theory, computational techniques, algorithms and the latest computer technology to solve economic, scientific, engineering, physics and business problems. Mathematics is usually referred to as pure (theoretical and abstract) or applied (practical problem solving). Mathematics includes the following specialty areas: algebra, geometry, trigonometry, calculus, probability, and statistics.
Actuarial science deals with the analysis of financial consequences of risk. Actuaries are highly trained professionals who are well versed in mathematical, statistical and economic techniques that enable them to evaluate financial risk of uncertain future events, especially those pertaining to health care, insurance and pension plans.
*PUL = Principles of Undergraduate Learning define a set of abilities and skills that undergraduate students are expected to master. They reflect the expertise that graduate and professional schools and the workforce are seeking.
The college graduate with a bachelor's degree in mathematics can qualify for a broad range of highly paid positions in business, government and secondary education. Banks, insurance companies, oil companies and companies in the computer and communication industries employ many mathematicians, as do almost every bureau and branch of the federal government. A bachelor's degree in mathematics can also lead to graduate study in mathematics or in a variety of other fields such as economics, computer science, medicine, engineering, business and law.
Actuarial Science: Actuaries find employment with insurance companies, government, hospitals, banks and accounting firms. This concentration aims to prepare students for the first three actuarial examinations administered by the professional actuarial organizations.
Applied Mathematics: Students with training in applied mathematics are employed in business, industry and government. This option is also good preparation for graduate study in fields closely related to mathematics such as computer science, statistics and engineering.
Pure Mathematics: Students will be well prepared for a variety of careers in the mathematical sciences as well as for graduate work in mathematics. Pure math students succeed in computer science, economics, law, engineering, medicine and business.
Mathematics Education:Students will be prepared to become secondary education (middle school and high school) and other careers related as well as prepared for M.S. Mathematics with concentration in Mathematics Education.
Employers of IUPUI Math Graduates
Employment for mathematicians is expected to grow much faster than the average compared to all other occupations for the 2008-2018 decade, however, keen competition for jobs is expected. Employment of mathematicians is projected to increase by 22% partly due to advancement in technology.
Salaries earned by mathematicians are dependent on degree level and whether they are employed by industry, government, or academia. According to the most recent data from the United States Bureau of Labor Statistics, the median annual wages for mathematicians was $95,150.
Employment of actuaries is expected to grow by 27 percent between 2010 and 2020. Students with internship experience who have passed at least one actuarial exam while in school should have the best prospects for entry-level positions. The 2010 median pay for actuaries was $87,650 per year. | 677.169 | 1 |
03872017Integers, Polynomials, and Rings: A Course in Algebra (Undergraduate Texts in Mathematics)
This book began life as a set of notes that I developed for a course at the University of Washington entitled Introduction to Modern Algebra for Tea- ers. Originally conceived as a text for future secondary-school mathematics teachers, it has developed into a book that could serve well as a text in an - dergraduatecourseinabstractalgebraoracoursedesignedasanintroduction to higher mathematics. This book di?ers from many undergraduate algebra texts in fundamental ways; the reasons lie in the book s origin and the goals I set for the course. The course is a two-quarter sequence required of students intending to f- ?ll the requirements of the teacher preparation option for our B.A. degree in mathematics, or of the teacher preparation minor. It is required as well of those intending to matriculate in our university s Master s in Teaching p- gram for secondary mathematics teachers. This is the principal course they take involving abstraction and proof, and they come to it with perhaps as little background as a year of calculus and a quarter of linear algebra. The mathematical ability of the students varies widely, as does their level of ma- ematical interest | 677.169 | 1 |
MELISSA GONZALEZ
Assignment quiz16.6 due 06/20/2016 at 11:59pm AST
MATE 3063 Arturo Portnoy
2. (1 point)
Calculate Tu , Tv , and n(u, v) for the parametrized surface at
the given point.
Then find the equation of the tangent plane to the surface at that
po
MATE 3063 Advice
Showing 1 to 1 of 1
It's a hard class (I mean, it's math) but if you practice a lot from the book you'll succeed in the test. The class consists of the professor giving lectures and examples. The tests are usually around 7 exercises; they are doable but tricky at times. It's necessary to put in the extra work so if one doesn't practice, they will fail. The course is only evaluated by the exams; so it can be hard to pull ones grade up sometimes. I don't recommend taking this course with several other hard and/or demanding classes in the semester.
Course highlights:
The course is really focused on double or triple integration as well as partial derivatives; the latter being the best part of the course as it was the easiest. A lot of times the concepts were a bit confusing until one actually started applying the theorems and such. That led to much independent study which I think is what I mainly gained from this course; the discipline to apply myself as necessary to study outside of lecture hours.
Hours per week:
6-8 hours
Advice for students:
If you're taking this course, it's probably because it's mandatory for you. So take it with this professor; he's great. The people that complain about him are just doing so because they expect 'good professor' to equal 'easy A' which is very far from the truth. | 677.169 | 1 |
- A program features tasks of different complexity and complete solutions with answers to every task. - For: high school students of final years of study. - Develops analytical skills and non-standard approach to math. - Adaptive solutions. The most complex issues are marked as optional commentaries, so that the students who don't want it too complex can read the necessary and the most easy part while still getting an understanding. - Topics: Numbers, Calculus, Geometry, Algebra, Probability theory. - Checks answers which are entered by the user and gives final number of points collected. - The task bank is updated regularly. - The program is available in English and Russian. - Private tutorship and consultancy over all topics are possible via skype with the author of the appplication.
A Grades part of our Education and have average installs from 10 to 50.
Last Update May 24, 2014. Google play rating is 60.0. Current verison is 1.0. Actual size 3.4 MB. | 677.169 | 1 |
Section 8 Linear Functions Lesson #1 Introduction to Linear Functions | 677.169 | 1 |
If you can describe the term, read on to the next one; if you cannot, then look it up in the text (the section number is shown in brackets).
IMPORTANT IDEAS
Can you explain each of these important ideas in your own words? Guidelines for Problem Solving[1.1]
Order of Operations [1.2]
Euler Circles [1.2]
Extended Order of Operations [1.3]
Laws of Exponents [1.3]
Inductive vs Deductive Reasoning [1.3]
Next, make sure you understand the types of problems in Chapter 1.
TYPES OF PROBLEMS Use Polya's method to solve a problem. [1.1]
Use Pascal's triangle as an aid to problem solving. [1.1]
Answer questions by using inductive reasoning. [1.2]
Simplify an expression using the order of operations. [1.2, 1.3]
Distinguish inductive from deductive reasoning. [1.2]
Use Euler circles to determine the validity of a syllogism [1.2]
Write out exponential numbers without using exponents. [1.3]
Write a large or small number in scientific notation. [1.3]
Use a calculator to answer numerical questions. [1.3]
Estimate answers to numerical questions. [1.3]
Simplify numerical problems by using the laws of exponents. [1.3]
Describe the relative sizes of large and small numbers. [1.3]
Once again, see if you can verbalize (to yourself) how to do each of the listed types of problems. Work all of Chapter 1 Review Questions (whether they are assigned or not).
Work through all of the problems before looking at the answers, and then correct each of the problems. The entire solution is shown in the answer section at the back of the text.
If you worked the problem correctly, move on to the next problem,but if you did not work it correctly (or you did not know what to do), look back in the chapter to study the procedure, or ask your instructor. Finally, go back over the homework problems you have been assigned. If you worked a problem correctly, move on the next problem, but if you missed it on your homework, then you should look back in the text or talk to your instructor about how to work the problem. If you follow these steps, you should be successful with your review of this chapter.
We give all of the answers to the Chapter Review questions (not just the odd-numbered questions), so be sure to check your work with the answers as you prepare for an examination. | 677.169 | 1 |
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this file type before downloading and/or purchasing.
22 KB
Product Description
Guided notes teaching students how to pull out important information from word problems to evaluate functions written in function notation. Multiple word problems with values in the domain filled in to solve for the range, and values of the range filled in to find the domain, as well as problems with functions not written in sentence form. I also have a corresponding assignment of the same name. | 677.169 | 1 |
The Miller/O'Neill/Hyde author team continues to offer an enlightened approach grounded in the fundamentals of classroom experience in Intermediate Algebra 3e. The practice of many instructors in the classroom is to present examples and have their students solve similar problems. This is realized through the Skill Practice Exercises that directly follow the examples in the textbook. Throughout the text, the authors have integrated many Study Tips and Avoiding Mistakes hints, which are reflective of the comments and instruction presented to students in the classroom. In this way, the text communicates to students the very points their instructors are likely to make during lecture, and this helps to reinforce the concepts and provide instruction that leads students to mastery and success. The authors included in this edition Problem-Recognition Exercises, that many instructors will likely identify to be similar to worksheets they have personally developed for distribution to students. The intent of the Problem-Recognition exercises is to help students overcome what is sometimes a natural inclination toward applying problem-solving algorithms that may not always be appropriate. In addition, the exercise sets have been revised to include even more core exercises than were present in the previous edition. This permits instructors to choose from a wealth of problems, allowing ample opportunity for students to practice what they learn in lecture to hone their skills and develop the knowledge they need to make a successful transition into College Algebra. In this way, the book perfectly complements any learning platform, whether traditional lecture or distance-learning; its instruction is so reflective of what comes from lecture, that students will feel as comfortable outside of class as they do inside class with their instructor. For even more support, students have access to a wealth of supplements, including McGraw-Hill's online homework management system, MathZone.
"synopsis" may belong to another edition of this title.
About the Author:
Julie Miller is from Daytona State College, where she has taught developmental and upper-level mathematics courses for 20 years. Prior to her work at Daytona State College, she worked as a software engineer for General Electric in the area of flight and radar simulation. Julie earned a bachelor of science in applied mathematics from Union College in Schenectady, New York, and a master of science in mathematics from the University of Florida. In addition to this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus, as well as several short works of fiction and nonfiction for young readers. My father is a medical researcher, and I got hooked on math and science when I was young and would visit his laboratory. I can remember using graph paper to plot data points for his experiments and doing simple calculations. He would then tell me what the peaks and features in the graph meant in the context of his experiment. I think that applications and hands-on experience made math come alive for me and I'd like to see math come alive for my students I grew up in Brevard County, Florida, where my father worked at Cape Canaveral. I was always excited by mathematics and physics in relation to the space program. As I studied higher levels of mathematics I became more intrigued by its abstract nature and infinite possibilities. It is enjoyable and rewarding to convey this perspective to students while helping them to understand mathematics.
Molly ONeill is from Daytona State College, where she has taught for 22 years in the School of Mathematics. She has taught a variety of courses from developmental mathematics to calculus. Before she came to Florida, Molly taught as an adjunct instructor at the University of Michigan-Dearborn, Eastern Michigan University, Wayne State University, and Oakland Community College. Molly earned a bachelor of science in mathematics and a master of arts and teaching from Western Michigan University in Kalamazoo, Michigan. Besides this textbook, she has authored several course supplements for college algebra, trigonometry, and precalculus and has reviewed texts for developmental mathematics. I differ from many of my colleagues in that math was not always easy for me. But in seventh grade I had a teacher who taught me that if I follow the rules of mathematics, even I could solve math problems. Once I understood this, I enjoyed math to the point of choosing it for my career. I now have the greatest job because I get to do math every day and I have the opportunity to influence my students just as I was influenced. Authoring these texts has given me another avenue to reach even more students.
About the Author:
Julie Miller has been on the faculty in the School of Mathematics at Daytona State College for 20 years, where she has taught developmental and upper-level courses. Prior to her work at DSC, she worked as a Software Engineer for General Electric in the area of Flight and Radar simulation. Julie earned a Bachelor of Science in Applied Mathematics from Union College in Schenectady, New York, and a Master of Science in Mathematics from the University of Florida. In addition to this textbook, she has authored several course supplements for College Algebra, Trigonometry, and Precalculus, as well as several short works of fiction and nonfiction for young readers.
Molly O'Neill is also from Daytona State College, where she has taught for 22 years in the School of Mathematics. She has taught a variety of courses from Developmental Mathamatics to Calculus. Before she came to Florida, Molly taught as an adjunct instructor at the University of Michigan-Dearborn, Eastern Michigan University, Wayne State University, and Oakland Community College. Molly earned a Bachelor of Science in Mathematics and a Master of Arts in Teaching from Western Michigan University in Kalamazoo, Michigan. Besides this textbook, she has authored several course supplements for College Algebra, Trigonometry, and Precalculus and has reviewed texts for Developmental Mathematics | 677.169 | 1 |
A few comments on LaTeX
LaTeX has been the industry standard in mathematical typesetting for
years and, with use on sites sites like
Math.SE
and other web sites via
MathJax,
it only becoming more ubiquitous. As a user, you simply type
specialized, mathematical markup into your text document and the
output as processed by LaTeX is beautiful typeset mathematics. For example,
to include something like $f(x)=x^2-x-1 \implies f'(x)=2x-2$ in your page,
you just type the following:
$f(x)=x^2-x-1 \implies f'(x)=2x-2$
The single dollar signs indicate that the expression should be typeset inline.
Sometimes, you want the expression to be displayed on it's own and with more
spacious spacing, like so:
$$\int_{-\infty}^{\infty} e^{-x^2} dx = \frac{\pi^2}{6}$$
In this case, just use double dollar delimiters:
$$\int_{-\infty}^{\infty} e^{-x^2} dx = \frac{\pi^2}{6}$$
You might notice, by the way, that those statements are both false. The point:
LaTeX is a typesetter, not a mathchecker!
To put this all within a document, you might have a look at the first couple of
handouts on our main class page. As far as LaTeX
implementations go, I'd recommend | 677.169 | 1 |
Algebra Explained provides motivation to all learners by tracking their overall progress at the bottom of each screen. The ultimate goal is to earn your diploma! However, it takes consistent practice to earn that diploma. The learner must earn a graduation cap for each lesson by completing each practice set. To complete a practice set the learner must get all of the answers correct in a 5 problem practice set. Because the first 5 questions are generally warm-up problems the learner only earns their cap on the second or subsequent practice set. If you miss a problem or two just keep trying additional practice sets until you get 5 out of 5. To complete the practice set for the chapter test the student must get 10 correct answers. In addition to counting the number of completed lessons (caps), the tracking display also shows the number of correct answers (stars) and the percentage of correct answers.
Once you earn your diploma you can click the diploma button on the home screen. Then simply email it to yourself and you can print it out. Once you earn your diploma you may also request membership in our Hall of Fame.
Algebra Explained also offers the unique ability to add multiple learners and track their progress from one centralized reporting screen that allows the
teacher to view progress in the following 3 ways:
Three Report Types
Learner by Learner
Day by Day
Lesson by Lesson
*Please note that for data privacy reasons only the teacher account can view progress of other learners. All other learners can only view their own progress. The teacher account is always the first account created and does not necessarily have to have the user name of "Teacher." | 677.169 | 1 |
Final Exam Practice 6
In this instructional activity, young mathematicians test their understanding of some of the basic concepts of algebra by completing 33 various types of problems. This is a nice overview of different algebra problems, unfortunately, no answers are provided. | 677.169 | 1 |
Showing 1 to 30 of 54
Binary Integer Programming
The California Manufacturing Co. is
considering expansion by building a new
factory in either Los Angeles or SanFrancisco, or perhaps even in both cities.
It is also considering building at most one
new warehouse but the choice
Climate in the Calculus Classroom
Thomas J. Pfaff
Ithaca College
[email protected]
There is a great need for scientific research on climate instability and the related energy issues,
and the mathematics community can and should be involved. But we also ne
Chapter
2
INVERSE TRIGONOMETRIC
FUNCTIONS
v Mathematics, in general, is fundamentally the science of
self-evident things. FELIX KLEIN v
2.1 Introduction
In Chapter 1, we have studied that the inverse of a function
f, denoted by f 1, exists if f is one-one
Lecture 7: Relations
1
Relation
Relation between two objects signify some connection between them. For example,
relation of one person being biological parent of another. If we take any two
people at random, say persons X and Y , then either X is a parent
Lecture 5: Functions : Images, Compositions,
Inverses
1
Functions
We have all seen some form of functions in high school. For example, we have
seen polynomial, exponential, logarithmic, trigonometric functions in calculus.
These functions map real numbers
Lecture 9: Principle of Mathematical Induction
1
Properties of Natural Numbers
Most fundamental property of natural numbers is ability to do proof by induction.
The set of natural numbers is denoted by the set N. The set N consists of a distinguished elem
Lecture 8: Equivalence Relations
1
Equivalence Relations
Next interesting relation we will study is equivalence relation.
Definition 1.1 (Equivalence Relation). Let A be a set and let be a relation
on A. The relation is an equivalence relation if it is re
Lecture 6: Functions : Injectivity, Surjectivity, and
Bijectivity
1
Injectivity, Surjectivity, Bijectivity
We are interested in finding out the conditions for a function to have a left inverse,
or right inverse, or both.
Definition 1.1. Let f : A B be a f
Lecture 2: Strategies for Proofs
1
Introduction
Thales of Miletus of sixth century BC is credited with introducing the concepts of
logical proof for abstract propositions. Euclid popularized the axiomatic system
of proofs in his book The elements, written
Lecture 17: Continuous Functions
1
Continuous Functions
Let (X, TX ) and (Y, TY ) be topological spaces.
Definition 1.1 (Continuous Function). A function f : X Y is said to be
continuous if the inverse image of every open subset of Y is open in X. In othe
Lecture 13: Basis for a Topology
1
Basis for a Topology
Lemma 1.1. Let (X, T) be a topological space. Suppose that C is a collection of
open sets of X such that for each open set U of X and each x in U , there is an
element C C such that x C U . Then C is
QAM-I Assignment (2014-15)
The Cutting Stock Problem
A company manufactures electrical transformers. Transformer core contains a number of metal rods of
a specified length, which varies for different models of transformers depending on the specifications.
Paper Recycling
A paper recycling plant processes box board, tissue paper, newsprint,
and book paper into pulp that can be used to produce three grades of
recycled paper. The prices per ton and the pulp contents of the four
inputs are shown in the Table b
Queuing Models
The single server waiting line system
Undefined and constant service time.
Finite Queue length.
Finite calling population
The multiple server waiting line.
Single Server waiting line System
The queue discipline: In what order the customers
Goal Programming
Multiple Objectives
The organization instead of single goal, decides
on a list of specific, operationally defined goals
that it wishes to achieve.
The list is arranged from the most important
goal to the goal with the lowest priority.
Pr
Result
Two equivalent system of linear equations have the same set of
solutions.
Result
Two equivalent system of linear equations have the same set of
solutions.
Gaussian Elimination Method: Use the following steps to
solve a system of equations Ax = b.
11. Let A be an n n matrix such that the system of equations Ax = 0 has a non-trivial solution. Is it
possible that the syste
DEPARTMENT OF MATHEMATICS, IIT GUWAHATI
MA101: Mathematics I
Mid Semester Exam (Maximum Marks: 30)
Date: September 20, 2011
Time: 2 pm - 4 pm
1. (a) Prove or disprove: If A and B are two matrices of the same size such that the linear system
of equations AModel Solutions
1. Let A be an n n matrix such that the system of equations Ax = 0 has a non-trivial solution. Is it possibl
Lecture 15: The subspace topology, Closed sets
1
The Subspace Topology
Definition 1.1. Let (X, T) be a topological space with topology T. If Y is a
subset of X, the collection
TY = cfw_Y U |U T
is a topology on Y , called the subspace topology. With this
Lecture 11 : Cardinality of Sets
1
Cardinality
We are interested in knowing sizes of sets. Finite sets are usually well behaved.
The difficulty starts in trying to understand infinite sets. Infinite sets have been
notoriously difficult to understand. In f
Lecture 20: Compactness
Parimal Parag
1
Compact spaces
Definition 1.1. A collection A of subsets of a space X is said to cover X, or to
be a covering of X, if the union of the elements of A is equal to X. It is called
an open covering of X if its elements | 677.169 | 1 |
Learn about this topic in these articles:
discussed in biography
...opened in 1794, he became, with Gaspard Monge, its leading professor of mathematics. His lectures were published as
Théorie des fonctions analytiques (1797; "
Theory of Analytic Functions") and
Leçons sur le calcul des fonctions (1804; "Lessons on the Calculus of Functions") and were the first textbooks on...
history of mathematics
...time to place the calculus on a sound basis, and Lagrange used the occasion to develop his ideas for an algebraic foundation of the subject. The lectures were published in 1797 under the title
Théorie des fonctions analytiques ("Theory of Analytical Functions"), a treatise whose contents were summarized in its longer title, "Containing the Principles of the... | 677.169 | 1 |
Product Overview
Subtitle: Designed as an Introduction to Peirce''s Course of Pure Mathematics, and as a Sequel to the Arithmetics Used in the High Schools of New England General Books publication date: 2009 Original publication date: 1845 Original Publisher: James Munroe Subjects: Arithmetic Education / Teaching Methods | 677.169 | 1 |
The number of high school students choosing the right level of mathematics to prepare for university mathematics and science courses continues to decline, so universities have been employing new and inspiring methods to get students up to speed in mathematics.
"It's really important for lecturers from different universities to share tactics for dealing with students who start university without enough of a background in mathematics to cope with their mathematics and science courses," said Associate Professor Manju Sharma, Director of the Institute for Innovation in Science and Mathematics Education.
"If we work together, we can have systematic improvement rather than forever reinventing the wheel," said Associate Professor Sharma.
"The problem of students not choosing high enough level mathematics or even choosing not to study senior mathematics at all at high school is widespread and increasing. There are a number of reasons for this trend, including there not being enough adequately trained maths teachers in high schools, and more maths teachers retiring than new maths teachers entering the system."
Australia needs increasing numbers of graduates with mathematical skills and a greater number of university courses require quantitative skills, so the decreasing numbers of students choosing high level mathematics courses in senior high school is a worrying trend.
Associate Professor Leon Poladian, Convenor of the Forum on 15 February and an award winning lecturer in the School of Mathematics and Statistics at the University of Sydney, said, "Regardless of students' initial state of preparedness in mathematics, we ensure our science students become mathematically literate by making first year mathematics compulsory at the University of Sydney."
"To make this work, we run bridging courses and offer our first year mathematics at five levels: introductory, fundamental, normal, advanced and special studies program for gifted students."
The forum will allow academics from around Australia from at least 15 different universities to share current practice and openly and frankly discuss problems and common issues.
"Sharing information is part of the standard process of scientific research, so it's appropriate that we apply this method to our teaching practice too. By overtly examining which methods are successful in combating this issue, we avoid making decisions on the basis of passing fads, short term fiscal constraints or the whims of senior administrators," said Associate Professor Poladian.
Professor Jacqui Ramagge, from the University of Wollongong, will present the keynote address on current patterns of mathematics study in Australian high schools. Dr Shaun Belward, from James Cook University, will follow, presenting on quantitative skills in science and curriculum models for the future.
The Forum will include snapshot presentations from 16 Australian universities and workshops on key issues and strategies.
Associate Professor Manju Sharma said, "It's so important that we get this right across Australia to combat falling numeracy skills. Mathematical literacy is required for all modern citizens - it helps us understand matters to do with health, education and decisions about climate change." | 677.169 | 1 |
This book presents an introduction to linear algebra and to some of its significant applications. It covers the essentials of linear algebra (including Eigenvalues and Eigenvectors) and shows how the computer is used for applications. Emphasizing the computational and geometrical aspects of the subject, this popular book covers the following topics comprehensively but not exhaustively: linear equations and matrices and their applications; determinants; vectors and linear transformations; real vector spaces; eigenvalues, eigenvectors, and diagonalization; linear programming; and MATLAB for linear algebra. Its useful and comprehensive appendices make this an excellent desk reference for anyone involved in mathematics and computer applications.
"synopsis" may belong to another edition of this title.
Product Description:
This text provides an introduction to the basic ideas, computational techniques, and applications of linear algebra. The most applied of our basic texts in this market, this text has a superb range of problem sets. Also, this book is extremely technology-friendly, integrating optional CAS and a robust website. Topics covered include wavelets; the Leslie Population Model; fractals; dynamical systems; linear equations and matrices; determinants; vectors; eigenvalues and eigenvectors; linear transformations and matrices; linear programming; and more. Ideal as an introduction to Linear Algebra.
From the Back Cover:
This book provides an introduction to the basic ideas, computational techniques, and applications of linear algebra. Introductory Linear Algebra with Applications Sixth Edition emphasizes the computational and geometrical aspects of linear algebra, while keeping abstraction to a minimum and illustrating every idea with examples. It provides three different types of exercises. Exercises contains routine exercises. Theoretical Exercises includes exercises that fill in gaps in some of the proofs and can be used to challenge the more capable and interested reader. The third class consists of MATLAB exercises connected to the available MATLAB disk. In addition, the end of every chapter contains a summary of Key Ideas for Review, a set of Supplementary Exercises, and a Chapter Test. The sixth edition of Introductory Linear Algebra with Applications has been revised to incorporate recommendations from The Linear Algebra Curriculum Study Group on developing ways to improve instruction in linear algebra. A valuable reference book on the basic of linear algebra and its applications for any reader seeking information on the subject. | 677.169 | 1 |
Precalculus: With Limits, First Edition
The new 1st edition of Cynthia Young's Precalculus helps to bridge the gap between in-class work and homework by helping students overcome common learning barriers and build confidence in their ability to do mathematics. The text features unique, strong pedagogy and is written in a clear, single voice that speaks directly to students and mirrors how instructors communicate in lectures. In this text, Young enables students to become independent, successful learners by including multiple exercise types, more opportunities to use technology, and a themed modeling project that empowers students to apply what they have learned in the classroom to the world outside the classroom. The seamlessly integrated digital and print resources to accompany Precalculus offer additional tools for both instructors and students in order to help students experience success.
Precalculus is suited for a 1 or 2 semester course and will focus on different learning styles. There will also be an emphasis on more challenging problems as well as streamlined prose to quicken the pace of the book | 677.169 | 1 |
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write an equation of the line containing the given point and parallel to the given line | 677.169 | 1 |
Key Message: A History of Mathematics, Third Edition, provides a solid background in the history of mathematics, helping readers gain a deeper understanding of mathematical concepts in their historical context. This book's global perspective covers how contributions from Chinese, Indian, and Islamic mathematicians shaped our modern understanding of mathematics. This book also includes discussions of important historical textbooks and primary sources to help readers further understand the development of modern mathematics. Key Topics: Ancient Mathematics: Egypt and Mesopotamia, The Beginnings of Mathematics in Greece, Euclid, Archimedes and Apollonius, Mathematical Methods in Hellenistic Times, The Final Chapter of Greek Mathematics; Medieval Mathematics: Ancient and Medieval China, Ancient and Medieval India, The Mathematics of Islam, Medieval Europe, Mathematics Elsewhere; Early Modern Mathematics: Algebra in the Renaissance, Mathematical Methods in the Renaissance, Geometry, Algebra and Probability in the Seventeenth Century, The Beginnings of Calculus, Newton and Leibniz; Modern Mathematics: Analysis in the Eighteenth Century, Probability and Statistics in the Eighteenth Century, Algebra and Number Theory in the Eighteenth Century, Geometry in the Eighteenth Century, Algebra and Number Theory in the Nineteenth Century, Analysis in the Nineteenth Century, Probability and Statistics in the Nineteenth Century, Geometry in the Nineteenth Century, Aspects of the Twentieth Century Market: For all readers interested in the history of mathematics. A History of Mathematics: An Introduction Katz, Victor J., Addison Wesley Longman Victor J. Katz, Books, Science and Nature, A History of Mathematics Books>Science and Nature, Pearson Education
Katz, Victor J.
A History of Mathematics: An Introduction | 677.169 | 1 |
What is calculus about? by W. W Sawyer(
Book
) 58
editions published
between
1961
and
2015
in
7
languages
and held by
1,560 WorldCat member
libraries
worldwide
"In this book, the author tells what calculus is about in simple nontechnical language, understandable to any interested reader."--Back
cover
Mathematician's delight by W. W Sawyer(
Book
) 120
editions published
between
1943
and
2012
in
9
languages
and held by
1,152 WorldCat member
libraries
worldwide
Recommended with confidence" by The Times Literary Supplement, this lively survey starts with arithmetic and algebra and gradually
proceeds to trigonometry and calculus. The author, who is internationally renowned for his innovative teaching methods, offers
insights into the pleasures of mathematics that will appeal to readers of all backgrounds. 1943 edition
Prelude to mathematics by W. W Sawyer(
Book
) 83
editions published
between
1955
and
2012
in
9
languages
and held by
997 WorldCat member
libraries
worldwide
This lively, stimulating account of non-Euclidean geometry by a noted mathematician covers matrices, determinants, group theory,
and many other related topics, with an emphasis on the subject's novel, striking aspects
Vision in elementary mathematics by W. W Sawyer(
Book
) 31
editions published
between
1964
and
2012
in
4
languages
and held by
456 WorldCat member
libraries
worldwide
As the title suggests, this technique employs visual elements in its exploration of the most graphic and least "forbidding"
aspects of mathematics. The author observes that most people possess a direct vision that permits them to "see" only the smaller
numbers. In addressing this difficulty, both for those who like recreational mathematics and for those who teach, he suggests
a variety of methods: techniques of visualizing, dramatizing, and analyzing numbers that attract and retain the attention
and understanding. Topics range from basic multiplication and division to algebra, encompassing word problems, graphs, negative
numbers, fractions, and many other practical applications of elementary mathematics. 1964 ed. Answers to Problems
A path to modern mathematics by W. W Sawyer(
Book
) 35
editions published
between
1965
and
1974
in
5
languages
and held by
376 WorldCat member
libraries
worldwide
The search for pattern by W. W Sawyer(
Book
) 15
editions published
between
1970
and
1988
in
English and Polish
and held by
359 WorldCat member
libraries
worldwide | 677.169 | 1 |
GCSE Mathematics Higher Tier
Course introduction
The Higher Tier GCSE Mathematics is aimed at students who already have a grade C at GCSE Mathematics. The aim of the course is for students who wish to improve on their existing GCSE Mathematics grade. This is a one year top up course.
The course is split into 3 units which are assessed in November, March and June and follows the AQA Modular B Mathematics 2010 specification.
Course structure
A varitey of techniques are used to aid learners who have different learning styles. So activities are aimed at kinaesthetic, auditory and visual learners. Some activities are aided with the use of ICT and Tarsia decision making cards. You will be expected to back up the work covered in college by completing homework and self study at home.
Minimum entry requirements
Minimum GCSE grade required: C
How will I be assessed?
The GCSE Mathematics course comprises of 3 modules:
• Unit 1H Statistics and Number
• Unit 2H Number and Algebra
• Unit 3H Geometry and Algebra
Information & support
Students are required to pay a course fee of £5 which covers the cost of a substantial amount of photocopied past papers, personalised geometry sets for the year, when appropriate, a calculator for use in the classroom and in the exam so that you do not need to purchase one and the use of GCSE course text books.
What can I do with this qualification?
Successful students can if they so wish: • Enrol on the Uses of Mathematics A level the next year • Aid their application for a more prestigious University (some University courses require a GCSE Mathematics grade B or better)
I've been part of the Academy for two years and absolutely loved it! It's encouraged me to become more confident and I have enjoyed my overall college experience because of netball. It's allowed me to improve my netball and fitness skills and I have found it a great way to take a break from college work. | 677.169 | 1 |
OCR (Oxford, Cambridge and RSA Examinations) is a unitary awarding body, established by the University of Cambridge Local Examinations Syndicate and the RSA Examinations Board in January 1998. OCR provides a full range of GCSE, A level, GNVQ, Key Skills and other qualifications for schools and colleges in the United Kingdom, including those previously provided by MEG and OCEAC. It is also responsible for developing new syllabuses to meet national requirements and the needs of students and teachers. This mark scheme is published as an aid to teachers and students, to indicate the requirements of the examination. It shows the basis on which marks were awarded by Examiners. It does not indicate the details of the discussions which took place at an Examiners& meeting before marking commenced.
This is the end of the preview. Sign up
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This note was uploaded on 04/01/2012 for the course MATH 1016 taught by Professor Rotar during the Spring '12 term at Central Lancashire. | 677.169 | 1 |
Everything found in MathXL but on CD. MathXL offers unlimited self-paced tutorials, guided mathematical instructions, and multimedia learning aids. MathXL allows students to learn and practice the concepts so they will succeed. MathXL also creates personalized study plans based on the student's test results and offers unlimited (algorithmically generated) practice exercises correlated directly to the exercises in the textbook.
"synopsis" may belong to another edition of this title.
From the Back Cover:
Real-life applications— unparalleled in terms of quantity, quality, degree of integration, nontrivial use of real data, variety of fields, and level of interest, and many based on real data from a variety of fields— highlight the relevance of math to various careers. The Whole Numbers, Multiplying and Dividing Fraction, Adding and Subtracting Fractions, Decimals, Ratio and Proportion, Percent, Statistics and Probability, Measurement, Geometry, The Real Numbers, Introduction to Algebra. Includes approximately 550 worked examples, and 4000 exercises. For a variety of business, science, math, and technology careers.
About the Author:
K. Elayn Martin-Gay has taught mathematics at the University of New Orleans for more than 20 years and has received numerous teaching awards including the local University Alumni Association's Award for Excellence in Teaching.
Over the years, Elayn has developed a videotaped lecture series to help her students understand algebra better. This highly successful video material is the basis for her books: Basic College Mathematics, Second Edition; Prealgebra, Third Edition; Introductory Algebra, Second Edition; Intermediate Algebra, Second Edition; Algebra A Combined Approach, Second Edition; and her hardback series: Beginning Algebra, Third Edition; Intermediate Algebra, Third Edition; Beginning and Intermediate Algebra, Second Edition; and Intermediate Algebra: A Graphing Approach, Second Edition3004ZS9 | 677.169 | 1 |
Summary of How Not to Be Wrong by Jordan Ellenberg | Includes Analysis
How Not to Be Wrong by Jordan Ellenberg attempts to demonstrate real-life applications of mathematics. In schools, students learn math principles in abstract contexts. Math in the real world is used to make accurate predictions, measure impact, evaluate the best choice when a trade-off is needed, and gauge complicated facts. Mathematical understanding gives individuals the ability to determine when unsound logic has been used to arrive at a factually inaccurate conclusion, and how to correct that logic in order "not to be wrong".
Inferences require a strong understanding of the implications of certain mathematical tools. Linear projections are one common pitfall: observations tend to regress back to the mean of a set of observations, but people tend to draw linear conclusions, even when a curve better describes and predicts the data.
Observed data can also be manipulated, because there is always a chance that false positives will give the impression of an effect where none exists....
Please Note: This is key takeaways and analysis of the book and not the original book. | 677.169 | 1 |
Dalton Mervold
Administrator
Instructional DesignerLearning Technologies Saskatchewan Polytechnic
Course Description
Applied Trade Math MOOC will provide students the opportunity to review and improve their math skills. In this course students will review concepts related to addition, subtraction, multiplication, division, fractions, decimals, percentages, measuring, algebra, geometry, and working with money. The course focusses on concepts most commonly used in workplace, apprenticeship and trades environments. | 677.169 | 1 |
PRODUCT DESCRIPTION
Students are given real world problems that require identifying independent and dependent variables, using input output tables to show variable relationships, and writing function equations.
These lessons are leveled to ensure students demonstrate learning in a variety of ways which better prepares them for standardized testing.
Each worksheet comes with a stated LO (learning objective) and guided lessons (simple step by step notes) on the left column. Students can easily reference these notes while working. The two additional columns of problems provide ample opportunities for guided and independent practice. Two DOL (demonstration of learning) problems at the end provide the teacher with an opportunity to assess learning and take grades as needed.
A second worksheet provides homework review that aligns directly to the lesson. Additional mixed review worksheets provide the essential review and reteach that is needed to ensure mastery.
note: I am continually additional lessons and expect to have additional levels of mini lessons available this year.
Using this instructional format has engaged my struggling learners and allowed them to demonstrate consistent growth.
These materials have proven to be an effective tool when modifying lessons for remedial students and providing mandated IEP modifications as it provides comprehensive and sequential remediation of skills, concepts, and problem solving applications.
Also available for purchase separately are:
* Independent and Dependent Variable Task Cards. With the problem on the front and the answer with explanations on the back of each card, students are able to practice their problem solving skills independently.
note: I have received great feedback from parents that felt these
cards provided them with an effective structured approach
to home study.3.50. | 677.169 | 1 |
Mathematics
No one expects you to be a mathematician or to know all the intricacies of
statistics. However, having a basic command of the terminology and processes
really helps when it comes to styling mathematical information. This section
will give you some background on mathematical terms and some guidelines to help
you style variables and equations.
Basic Information
The minus sign symbol is always indicated by the
«minus» code (to avoid any confusion of the
«minus» sign with a hyphen, en-dash, or em-dash).
The following table shows commonly encountered mathematical symbols, how they
can be written out, and some information regarding the specific mathematical
process. Words should not be changed to math signs if the meaning becomes less
clear by doing so.
Symbol
Written Out Version
Notes
Symbols that can be changed to words in text
+
plus
Addition
«minus»
minus
Subtraction
×
times
Multiplication
•
times
Multiplication
*
times
Multiplication (change to × or •)
÷
divided by
Division
/
divided by
Division
=
equals
~
approximately, about
≈
approximately equal to
<
less than
>
greater than
≤
less than or equal to
≥
greater than or equal to
Symbols that should not be written out
≡
is defined as
The exact mathematic definition
≠
does not equal
±
plus or minus
Statistical deviation
√
square root of
Square root function
|…|
absolute value of
Absolute value
∞
infinity
∩
intersection
Σ
sum of
Sum of the values of the following formula
∫
integral of
Integral of the following formula
∆
change in
Change in the following variable (over time)
∂
derivative
dt
derivative
e
exponent
exp
exponent
f
function
Insert spaces between numbers if the following mathematical symbols are used:
≈, ≡, <, >, =, +, «minus», ×, and ÷. Do not insert spaces between these symbols:
/, |…|, ~, and %.
Do not use two math symbols before a number. Change the first symbol to its
written out form and bump the second to the number. Two consecutive math signs
are only acceptable if one of them is the equal sign (=).
Ranges and symbols used with negative numbers can be especially difficult to
decipher. For example, does «minus»5-10 mean
that the range was between «minus»5 to
«minus»10 or from
«minus»5 to (+)10? If this occurs, rephrase the range so that it goes
"from" one value "to" the second, e.g., "The nerve was stimulated a voltage
range from «minus»5 to
«minus»10 mV." This does, of course,
necessitate a query to the author to verify the values. | 677.169 | 1 |
Now available in paperback! An introduction to the calculus, with an excellent balance between theory and technique. Integration is treated before differentiation–this is a departure from most modern texts, but it is historically correct, and it is the best way to establish the true connection between the integral and the derivative.
A 2-in-1 value: Thinkwell's Pre-Calculus combines the course materials from Algebra 2 with Trigonometry. It has hundreds of video tutorials and thousands of automatically graded exercises, so your students have all of the pre-calculus math help they need to prepare for Calculus.Thinkwell's Pre-Calculus video tutorials feature award-winning teacher Edward Burger, who has an amazing ability to break down concepts and explain examples step by step. He gives your students all they need to succeed in calculus.
The biggest stars of gypsy jazz guitar heirs of Django Reinhardt counted on the fingers of one hand. With this new album Complicity, Angelo Debarre wanted to compose four hands with violin virtuoso Marius Apostol. Beyond the obvious technique, the works? Reach heights of lyricism proving if necessary talents of composers of these two musicians. | 677.169 | 1 |
Galois Theory for Beginners A Historical Perspective
ISBN-10: 0821838172
ISBN-13: 9780821838174 Galois theory is the culmination of a centuries-long search for a solution to the classical problem of solving algebraic equations by radicals. In this book, Bewersdorff follows the historical development of the theory, emphasizing concrete examples along the way. As a result, many mathematical abstractions are now seen as the natural consequence of particular investigations. Few prerequisites are needed beyond general college mathematics, since the necessary ideas and properties of groups and fields are provided as needed. Results in Galois theory are formulated first in a concrete, elementary way, then in the modern form. Each chapter begins with a simple question that gives the reader an idea of the nature and difficulty of what lies ahead. The applications of the theory to geometric constructions, including the ancient problems of squaring the circle, duplicating the cube, and trisecting an angle, and the construction of regularn$-gons are also presented. This book is suitable for undergraduates and beginning graduate | 677.169 | 1 |
Illustrative Examples of Units of
Practice
Deltalyzers - An intuitive approach to finite differences
Snapshot
This short activity uses
Apple Works 5.0 spreadsheets to provide a concrete, visual, goal driven exploration
that bridges the gap between number patterns and the technique of finite differences.
Subject: Math
Learning Levels: Grades 10-12
Author(s): Terry Thorsen
Invitation
Students are lead to develop their own algorithm for finding
the equation for a table of values. Their explorations provide motivation and
develop understandings for finite differences.
A series of 10 spreadsheets (Deltalyzers) require students
to guess the equation for a table of values. They accomplish this by comparing
the tables and graphs of the given data with those of their guessed equation.
Eventually, students will develop their own algorithm. This can lead to a good
discussion prior to the introduction of #5 below.
Outcomes
Students will develop skills and ideas concerned with:
Using spreadsheets.
Guess and check.
Successive approximation.
Visualization of lines, quadratics and cubics.
Connections between tables, equations and graphs.
The leading coefficient determines the shape.
The constant term is the y intercept.
An algorithmic approach to finding the equation is possible.
Situations
The method of finite differences is developed in the following
way:
Number patterns arise naturally in many areas.
Calculating successive differences (delta y's) is
a valuable technique for analyzing these patterns.
Polynomial equations of degree n have constant nth differences.
Deltalyzers.
The usual technique of finite differences involves building
a table of values with algebraic expressions as y values, and then comparing
the original table with the algebraic table. This sets up a system of n equations
in the coefficients a, b, c ... that is easily solved.
Students will have considered realistic problems involving
number patterns as well as items 1 through 3.
As an introductory experience, Deltalyzers shouldn't
take more than half a period. If one gets involved with writing up their discoveries,
extended discussion, formal evaluation, mastery learning or one of the extensions
it takes two or three periods.
Tasks
4 Deltalyzers: Have the students try each spreadsheet in
turn. Students should focus not only on getting the equation but on describing
their method. If they develop a purely visual technique (using only the graphs),
then shrink the window and have them focus on the tables. Conclude by having
students share their algorithms.
This activity can be extended in a number of ways:
Students bring in their own data for others to guess
the equation.
Students formalize their ideas as spreadsheet formulas.
Students can guess equations by acting out their algorithm
using pencil and paper. This can be computationally intensive so keep the
tables simple.
Students build or customize the deltalyzer template.
This technique can be extended to data tables with errors
in the y values (just use the average of the nth differences to calculate
the leading coefficient and subtract to produce a data table of degree n-1
and repeat). Doing this will provide an understandable alternative to polynomial
regression using least squares.
Interactions
The critical issue is
that if students develop a purely visual technique (using only the graphs), then
respond by shrinking the window and have them focus on the tables. The teacher
will have to watch for this.
Assessment
This activity is self checking and provides the student
with a fair bit of feedback. Remembering that this activity is more of an introductory
exploration, the teacher can evaluate student understandings by:
Tools
Projects
The files are currently locked so that student changes are not saved. You can
unlock them and change them however you want.
If you create your own data tables or translate the spreadsheets onto another
program or version of Apple Works, submit your own unit of practice. To help
others to find it, include "Deltalyzer" as a keyword. | 677.169 | 1 |
Mathematical Applications in Agriculture, 2nd Edition
Get the specialized math skills you need to be successful in today's farming industry with MATHEMATICAL APPLICATIONS IN AGRICULTURE, 2nd Edition. Invaluable in any area of agriculture-from livestock and dairy production to horticulture and agronomy--this easy to follow book gives you steps by step instructions on how to address problems in the field using math and logic skills. Clearly written and thoughtfully organized, the stand-alone chapters on mathematics involved in crop production, livestock production, and financial management allow you to focus on those topics specific to your area while useful graphics, case studies, examples, and sample problems to help you hone your critical thinking skills and master the concepts. | 677.169 | 1 |
'...even at this early stage (only a week in) I have been really impressed with the scheme so far. Our NQTs love the lesson plans and say they really help with ideas and with them finding out what sort of level to teach a topic.
The lower set pupils love the workbooks, and they have been a great motivator. The books are clear and easy to read and are excellent practise for filling in SATs papers. Our only problem is that we struggle to get them to stop working and move on to their next lesson!
We had a very heated discussion with one Year 9 boy who was insisting that he took his book home to carry on, and was very angry when we said he couldn't take it home! These pupils who are usually fairly unmotivated are working through at a real pace.'
Cass Jackson, Barr Beacon Language College
Book Description:
Full of functional maths, covering the new framework for Year 8 pupils working at level 6-7
Book Description HarperCollins Publishers, United Kingdom, 2008. Paperback. Book Condition: New. Second Edition, Second edition. 278 x 218 mm. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. Aimed at effectively delivering the 2008 framework, the Pupil Books are packed with functional maths questions and spreads and ensure progression by providing differentiated material for each level. Year 8 Pupil Book 3 is fully levelled with built-in progression helping students to progress with confidence from level 6 to level 7. This Pupil Book: * Guarantees progression with colour-coded levelling and level boosters to help pupils work at the right level and progress with ease. * Enables pupils to develop vital functional skills and put maths into context with the help of the integrated functional maths questions and exciting real-world spreads. * Promotes personalised learning and self assessment using pupil-friendly learning objectives for every chapter. * Eases the class into understanding new concepts with worked examples. * Stretches and challenges the knowledge and skills of pupils using extension activities. * Provides rigorous maths practice with the hundreds of levelled questions. * Captures pupils attention using the colourful design. * See the Teacher s Pack for more support and answers. Bookseller Inventory # APE9780007267965
Book Description Harpercollins Publishers, 2008. Book Condition: New. Designed to enable progression and encourage enjoyment of maths, the Pupil Books offer completely differentiated material matched to the new specification and packed full of functional maths questions and spreads. Year 8 Pupil Book 3 is fully-levelle . . . Bookseller Inventory # 1510080 | 677.169 | 1 |
The Math
This section provides several perspectives on the mathematics that is developed in Connected Mathematics including a detailed description of the development of the mathematics within each strand and of the unifying mathematical themes across the curriculum. It also includes the mathematics, goals, and the correlations to the CCSSM for each unit. | 677.169 | 1 |
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JEE Advanced Syllabus 2016 for Maths
JEE ADVANCED 2016 Syllabus:
Jee Advanced Syllabus covers all the topics required to be studied by aspirants who wish to avail admissions in IIT's via the Jee Advanced 2016 Examination. Students will have to study topics as prescribed for Mathematics in the Jee Advanced 2016.
harmonic means, sums of finite arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n natural numbers.
Logarithms and their properties.
Matrices as a rectangular array of real numbers, equality of matrices, addition,
multiplication by a scalar
2. Trigonometry:
Trigonometric functions, their periodicity and graphs, addition and subtraction
Relations between sides and angles of a triangle, sine rule, cosine rule, halfangle
formula and the area of a triangle, inverse trigonometric functions (principal value only).
3. Analytical geometry
Two dimensions: Cartesian coordinates, distance between two points, section
formulae, shift of origin.
Equation of a straight line in various forms, angle between two lines, distance
of a point from a line; Lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines, concurrency of lines; Centroid, orthocentre, incentre and circumcentre of a triangle.
Equation of a circle in various forms, equations of tangent, normal and chord.
Parametric equations of a circle, intersection of a circle with a straight line or a circle, equation of a circle through the points of intersection of two circles and those of a circle and a straight line.
Equations of a parabola, ellipse and hyperbola in standard form, their foci,
directrices and eccentricity, parametric equations, equations of tangent and normal.
Locus problems.
Three dimensions: Direction cosines and direction ratios, equation of a straight | 677.169 | 1 |
A Level Mathematics solving, data handling and mathematical modelling. What will I study? Students study Pure Mathematics and its applications. Pure Mathematics is an extension of the skills covered at GCSE including algebra, trigonometry, graphs and a new area of study called calculus. Statistics extends the work done at GCSE to cover areas such as data presentation, probability and correlation. Mechanics, which is studied by those taking Physics, covers such areas as Newton's laws of motion and forces. By the end of the course you will have gained confidence and proficiency in a wide variety of mathematical concepts and methods and in their application. Huish Extra All students will be able to use the Mathematics workshop which is an excellent provision enabling students to work with other like-minded students and staff. Students can also participate in the Senior Mathematics challenge leading to the British Mathematical Olympiad. so | 677.169 | 1 |
MATLAB and Its Applications in Engineering, published by Dorling Kindersley, is a comprehensive book on various MATLAB concepts and the latest features, for students who are taking undergraduate and graduate courses in MATLAB. The book comprises of a number of examples for better understanding of the topics. Some of the subjects covered in the book are Script M-Files, Function M-Files, Multidimensional Arrays, Character Strings, Control Flow, Matrix Algebra, File and Directory Management, Data Analysis, Data Interpolation, Polynomials, Optimization, Handle Graphics, Using Colour and Light and Differential equations among a lot others. The book is essential for students for a wider knowledge of MATLAB. This is an essential book for students of both theory and laboratory MATLAB courses. The book is compiled by Raj Kumar Bansal, Ashok Kumar Goel and Manoj Kumar Sharma.
About Dorling Kindersley
Dorling Kindersley is a British multinational publishing company which is known for creating and publishing high quality, illustrated books and also numerous online resources. It is based in London and was found in the year 1974. DK is a part of the Penguin Random House Group and is spread across in many major cities in different continents, including New Delhi, India. They publish books of all genres. Some of the most popular books produced by DK in India are Encyclopaedia of Plants and Flowers, The Motorbike Book, Natural History, Eyewitness Dinosaur and Where to Go When, among many other works. | 677.169 | 1 |
Forum for Science, Industry and Business
The Aftermath of Calculator Use in College Classrooms
13.11.2012
Students may rely on calculators to bypass a more holistic understanding of mathematics, says Pitt researcher
Math instructors promoting calculator usage in college classrooms may want to rethink their teaching strategies, says Samuel King, postdoctoral student in the University of Pittsburgh's Learning Research & Development Center.
King has proposed the need for further research regarding calculators' role in the classroom after conducting a limited study with undergraduate engineering students published in the British Journal of Educational Technology.
"We really can't assume that calculators are helping students," said King. "The goal is to understand the core concepts during the lecture. What we found is that use of calculators isn't necessarily helping in that regard."
Together with Carol Robinson, coauthor and director of the Mathematics Education Centre at Loughborough University in England, King examined whether the inherent characteristics of the mathematics questions presented to students facilitated a deep or surface approach to learning. Using a limited sample size, they interviewed 10 second-year undergraduate students enrolled in a competitive engineering program. The students were given a number of mathematical questions related to sine waves—a mathematical function that describes a smooth repetitive oscillation—and were allowed to use calculators to answer them. More than half of the students adopted the option of using the calculators to solve the problem.
"Instead of being able to accurately represent or visualize a sine wave, these students adopted a trial-and-error method by entering values into a calculator to determine which of the four answers provided was correct," said King. "It was apparent that the students who adopted this approach had limited understanding of the concept, as none of them attempted to sketch the sine wave after they worked out one or two values."
After completing the problems, the students were interviewed about their process. A student who had used a calculator noted that she struggled with the answer because she couldn't remember the "rules" regarding sine and it was "easier" to use a calculator. In contrast, a student who did not use a calculator was asked why someone might have a problem answering this question. The student said he didn't see a reason for a problem. However, he noted that one may have trouble visualizing a sine wave if he/she is told not to use a calculator.
"The limited evidence we collected about the largely procedural use of calculators as a substitute for the mathematical thinking presented indicates that there might be a need to rethink how and when calculators may be used in classes—especially at the undergraduate level," said King. "Are these tools really helping to prepare students or are the students using the tools as a way to bypass information that is difficult to understand? Our evidence suggests the latter, and we encourage more research be done in this area."
King also suggests that relevant research should be done investigating the correlation between how and why students use calculators to evaluate the types of learning approaches that students adopt toward problem solving in | 677.169 | 1 |
Lesson content has been expanded and includes more video instruction for each lesson. In addition to the video examples each lesson includes interactive practice problems, challenge questions, and worksheets.
WRITE_EXTERNAL_STORAGE permission has been enabled to accommodate the download of PDF worksheets.
Description
Need more than free videos to learn math? YourTeacher's Algebra app is like having a personal math tutor in your pocket.
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"It's like a private school math classroom, but you are the only student."
John
"I just love YourTeacher and the way you explain things. I felt like I was in a classroom instead of just looking at examples."
Diane
"My daughter is doing Algebra 1 in 8th Grade. She had been getting really low grades because they are moving through the material so quickly. She had a test 3 days after we bought your program and she got 94% (the highest score in the class) because we had her work through the modules over and. She really enjoys the program and her motivation is good again."
Melanie
CHAPTER 4: INEQUALITIES, ABSOLUTE VALUE, FUNCTIONS, GRAPHING
Solving and Graphing Inequalities
Combined Inequalities
The Coordinate System
Domain and Range
Definition of a Function
Function and Arrow Notation
Graphing within a Given Domain
Graphing Lines
The Intercept Method
Graphing Inequalities in Two Variables
CHAPTER 5: LINEAR EQUATIONS
Patterns and Table Building
Word Problems and Table Building
Slope as a Rate of Change
Using the Graph of a Line to Find Slope
Using Slope to Graph a Line
Using Coordinates to Find Slope (Graphs and Tables)
Using Coordinates to Find Slope
Using Slope to Find Missing Coordinates
Using Slope-Intercept Form to Graph a Line
Converting to Slope-Intercept Form and Graphing
Linear Parent Graph and Transformations
Using Graphs and Slope-Intercept Form
Using Tables and Slope-Intercept Form
Direct Variation
Applications of Direct Variation and Linear Functions
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Flag Sticker also has a Transparency Adjustment feature for fast and convenient adjustment of how much your flag can cover your screen, and a handy "How Much do you Love your Countr… | 677.169 | 1 |
Approximation Algorithms, 6 points, period 1-2, 10/11
The goal of the course is to learn the underlying techniques used
when designing approximation algorithms, by study famous applications
from the literature. Starting with basic techniques such as "greedy
algorithms" and then moving on to more powerful paradigms including the
use and analysis of linear/semidefinite programs. The exact topics to
be covered will depend on our interests and any suggestions are very
welcomed. For inspiration I have prepared a list of
possible topics that I find interesting (see here).
News
Thanks for a great course that I have really enjoyed teaching. A summary of the course evaluations is available here .
Sixth and final set of homeworks due December 21 is available, see below.
Lecturer
Ola Svensson, is responsible for
all aspects of this course. Tobias Mömke,
helped out by giving 1.5 lectures and homework 5 on iterative rounding. Cenny
Wenner and Lukas Polacek helped out by giving one lecture each on Semidefinite
programming and homework 6. Lectures will be given in English.
Course requirements
Course requirements are given by biweekly assignments. Students may
also choose to complement (or replace) some of the assignments with a
project work.
Students that are interested in doing a project should
first discuss the topic with me (Ola)!
Course material
The material of the course will be
articles, notes, and parts of the book "Approximation
Algorithms" by V. Vazirani. The book is also available on the web
as a pdf . | 677.169 | 1 |
GraphSight Junior Desciption:
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GraphSight Junior is an easy to use freeware handy 2D math-graphing program. It was originally designed to help students and teachers satisfy their day-after-day math plotting needs. It makes it easy to plot and explore common Y(X) = F(X) Cartesian graphs, set text labels on the coordinate plane, zoom or shift a graph with just a single click & move of mouse. The picture can be than exported to a file or windows clipboard as a bitmap.
Review GraphSight Junior
GraphSight is a feature-rich comprehensive 2D math graphing utility with easy navigation, perfectly suited for use by high-school an college math students. The program is capable of plotting Cartesian, polar, table defined, as well as specialty...
It can compute and plot a very high amount of functions, including many probability functions and is fairly good configurable.
A maximum number of three graphs can be displayed in one image.
Installation
Upload the files to the webserver and point...
Waves Calculator is a useful application that allows you to generate 3D graphs for mathematical functions. The program allows you view the graph and to combine multiple variables such as logarithms.You can use the program to understand the functions...
Mark Jacobs Graph Plotter is an application that allows you to easily build a graph of multiple mathematical functions.You can insert up to 10 functions and the program automatically plots the resulting chart, which you can save in a separate file.
active..., as well...
Complex Grapher is a graphing calculator to create a graph of complex function. 3D function graphs and 2D color maps can be created with this grapher. You can input complex functions in the form of w=f(z) (where z=x+yi) directly before creacting...
Visual Complex is a graph software to create graph of complex function. 3D function graphs and 2D color maps can be created with this grapher. You can input complex functions in the form of w=f(z) (where z=x+yi) directly before creacting graphs. Graphs | 677.169 | 1 |
SectionWILAWhat is Linear Algebra?
We begin our study of linear algebra with an introduction and a motivational example.
SubsectionLALinear + Algebra
The subject of linear algebra can be partially explained by the meaning of the two terms comprising the title. "Linear" is a term you will appreciate better at the end of this course, and indeed, attaining this appreciation could be taken as one of the primary goals of this course. However for now, you can understand it to mean anything that is "straight" or "flat." For example in the $xy$-plane you might be accustomed to describing straight lines (is there any other kind?) as the set of solutions to an equation of the form $y = mx + b$, where the slope $m$ and the $y$-intercept $b$ are constants that together describe the line. If you have studied multivariate calculus, then you will have encountered planes. Living in three dimensions, with coordinates described by triples $(x,\,y,\,z)$, they can be described as the set of solutions to equations of the form $ax+by+cz=d$, where $a,\,b,\,c,\,d$ are constants that together determine the plane. While we might describe planes as "flat," lines in three dimensions might be described as "straight." From a multivariate calculus course you will recall that lines are sets of points described by equations such as $x=3t-4$, $y=-7t+2$, $z=9t$, where $t$ is a parameter that can take on any value.
Another view of this notion of "flatness" is to recognize that the sets of points just described are solutions to equations of a relatively simple form. These equations involve addition and multiplication only. We will have a need for subtraction, and occasionally we will divide, but mostly you can describe "linear" equations as involving only addition and multiplication. Here are some examples of typical equations we will see in the next few sections:
\begin{align*}
2x+3y-4z&=13
&
4x_1+5x_2-x_3+x_4+x_5&=0
&
9a-2b+7c+2d&=-7
\end{align*}
What we will not see are equations like:
\begin{align*}
xy + 5yz&=13
&
x_1 + x_2^3/x_4 - x_3x_4x_5^2&=0
&
\tan(ab)+\log(c-d)&=-7
\end{align*}
The exception will be that we will on occasion need to take a square root.
You have probably heard the word "algebra" frequently in your mathematical preparation for this course. Most likely, you have spent a good ten to fifteen years learning the algebra of the real numbers, along with some introduction to the very similar algebra of complex numbers (see Section CNO). However, there are many new algebras to learn and use, and likely linear algebra will be your second algebra. Like learning a second language, the necessary adjustments can be challenging at times, but the rewards are many. And it will make learning your third and fourth algebras even easier. Perhaps you have heard of "groups" and "rings" (or maybe you have studied them already), which are excellent examples of other algebras with very interesting properties and applications. In any event, prepare yourself to learn a new algebra and realize that some of the old rules you used for the real numbers may no longer apply to this new algebra you will be learning!
The brief discussion above about lines and planes suggests that linear algebra has an inherently geometric nature, and this is true. Examples in two and three dimensions can be used to provide valuable insight into important concepts of this course. However, much of the power of linear algebra will be the ability to work with "flat" or "straight" objects in higher dimensions, without concerning ourselves with visualizing the situation. While much of our intuition will come from examples in two and three dimensions, we will maintain an algebraic approach to the subject, with the geometry being secondary. Others may wish to switch this emphasis around, and that can lead to a very fruitful and beneficial course, but here and now we are laying our bias bare.
SubsectionAAAn Application
We conclude this section with a rather involved example that will highlight some of the power and techniques of linear algebra. Work through all of the details with pencil and paper, until you believe all the assertions made. However, in this introductory example, do not concern yourself with how some of the results are obtained or how you might be expected to solve a similar problem. We will come back to this example later and expose some of the techniques used and properties exploited. For now, use your background in mathematics to convince yourself that everything said here really is correct.
This example is taken from a field of mathematics variously known by names such as operations research, systems science, or management science. More specifically, this is a prototypical example of problems that are solved by the techniques of "linear programming."
There is a lot going on under the hood in this example. The heart of the matter is the solution to systems of linear equations, which is the topic of the next few sections, and a recurrent theme throughout this course. We will return to this example on several occasions to reveal some of the reasons for its behavior. | 677.169 | 1 |
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Mathematics is often portrayed as an 'abstract' cerebral subject, beyond the reach of many. In response, research with digital technology has led to innovative design in which mathematics can be experienced much like everyday phenomena. This lecture examines how careful design can 'phenomenalise' mathematics and support not only engagement but also focus on key ideas. It argues that mathematical knowledge gained in this way prioritises the powerful reasons for doing mathematics, imbuing it with a sort of utility and offering learners hooks on which they can gradually develop fluency and connected understanding. David Pratt illustrates this lecture with examples taken from conventional topics such as number, algebra, geometry and statistics and from novel situations where mathematical methods are juxtaposed with social values. The suggestion that prioritising utility supports a more natural way of learning mathematics emerges directly from constructionist pedagogy and inferentialist philosophy. | 677.169 | 1 |
Lively Math
Scholars realize the importance of reading and correct interpretation when engaging in mathematical problem solving. This begins with the understanding of vocabulary and the translation from numeric to algebraic and algebraic to numeric. | 677.169 | 1 |
CALCULUS
What is CALCULUS and Why we study CALCULUS?
What is CALCULUS:
CALCULUS is a branch of Mathematics in which we study how things change and the rate at which things change. CALCULUS was developed in the later half of 17th century by two great mathematicians, Isaac Newton and Gottfried Leibniz. Now a days, CALCULUS has widespread uses in science, engineering and economics and can solve many problems that elementary algebra alone cannot. CALCULUS deals with the instantaneous rate change of continuously varying quantities, areas under curves, and sequences and series etc. | 677.169 | 1 |
Stephanie Riddle, Math
Welcome Students and Parents!
I am excited to be your teacher for the upcoming 2016-2017 school year.
The following are the supplies I would like students to have for my class, and the course syllabus.
Supply List Algebra I All students need a TI- 83 or TI-84 graphing calculator. (Any version of these two calculators is fine). It is very important that students have their own graphing calculator. Although this is a big expense, these calculator are used throughout high school and college level math, as well as allowed on the ACT and SAT. (I do not recommend the Casio calculators, as they are very difficult to use). Label with your name! A composition notebook, a spiral notebook (any size) for math only, graph paper, pencils (mechanical preferred). | 677.169 | 1 |
FSMQ Level 3 (legacy) Working with algebraic and graphical techniques scheme of work
This FSMQ requires a total of 60 guided learning hours that could be used in a variety of ways, such as 2 hours per week for 30 weeks, 4 hours per week for 15 weeks, or 5 hours per week for 12 weeks. Before starting this course learners should be able to:
use power notation (including positive and negative integers and fractions)
solve quadratic equations by factorising and using the formula (must be memorised).
A suggested work scheme for this unit is given below. It includes some revision of the above as well as the other topics and methods to be covered, but note that you will also need to allow time for students to complete an AQA Coursework Portfolio. The Coursework Portfolio requirements are listed on page 56 of the AQA Advanced FSMQ specification and also on page 101 of the AS Use of Mathematics specification. The assignments below provide some examples of the sort of work your students could include in their portfolios, but if possible you should use work that is more relevant to their other studies or interests..
The following techniques should be introduced as soon as possible and used throughout the course:
using a calculator effectively and efficiently, including the use of memory and function facilities (recording the working as well as the result)
doing calculations without a calculator using written methods and mental techniques
graph plotting using computer software or a graphical calculator, and using trace and zoom facilities to find significant features such as turning points and points of intersection
checking calculations using estimation, inverse operations and different methods.
Topic area
Content
Nuffield resources The links below go to pages from which you can download the resources, some recently revised.
Linear functions
(3 hours)
Revise the main features of graphs of direct proportional (y = mx) and linear (y = mx + c) functions. Fit such functions to real data using gradients and intercepts.
Understand whether it is appropriate or not to use a particular function to model data by consideration of intercepts, long term behaviour (etc.) in real world terms.
Use error bounds to consider a range of possible functions to model data.
Factor cards
Nearly 100 pairs of cards showing a wide variety of quadratic expressions and their factors. Pairing will give students practice in expanding brackets or factorising.
Water flow
Includes data about the velocity of water as it flows along an open channel and sample examination question. Data could also be used to give practice for portfolio requirements or form the basis for an assignment.
Completing the square
Presentation shows how to complete the square and use this form to sketch graphs. Card-matching activity using a selection from 24 sets each of 3 cards showing a quadratic graph, the corresponding function and its completed square form.
Gradients of curves, maxima and minima
(3 hours)
Calculate and understand gradient at a point on a graph using tangents drawn by hand (and also using zoom and trace facilities on a graphic calculator or computer if possible).
Use and understand the correct units for rates of change.
Interpret and understand gradients in terms of their physical significance.
Identify trends of changing gradients and their significance both for known functions and curves drawn to fit data.
Tin can
Students design a tin can, using algebraic and graphical techniques. Optional use of the internet.
Maximum and minimum problems
Presentation and practice questions using a spreadsheet or graphic calculator to solve problems involving maximum and minimum values.
Topic area
Content
Nuffield resources The links below go to pages from which you can download the resources, some recently revised.
Power functions and inverse functions
(3 hours)
Draw graphs of functions of powers of including where is a positive integer, , , and
Learn the general shape and position of such functions.
Find the graph of an inverse function using reflection in the line y = x.
Draw graphs of exponential functions of the form and (m positive or negative) and understand ideas of growth and decay.
Draw graphs of natural logarithmic functions of the form y = a ln(bx) and understand the logarithmic function as the inverse of the exponential function.
Solve exponential equations of the form
Learn and use the laws of logarithms
·
·
·
to convert equations involving powers to logarithmic form and solve them (using both base 10 and natural logarithms).
Growth and decay
Presentation using compound interest and radioactive decay to introduce exponential growth and decay.
Population growth
Students use a given exponential function to model population data, then consider predictions made by the model.
Calculator table
Students use the calculator's table function to complete tables for population models then draw and use the corresponding graphs.
Ozone hole
Data concerning depletion of ozone levels and the increase in the area of the Antarctic ozone hole over the last twenty years. Students investigate possible linear, quadratic and exponential models.
Optional use of spreadsheet.
Climate prediction A and B
Students use an Excel spreadsheet and/or graphic calculator to find polynomial functions to model temperature change and compare with exponential models.
Cup of coffee
Data sheet gives the amount of caffeine remaining in the bodies of a group of people at intervals of 1 hour after they have drunk a cup of coffee or cola. Students are asked to model the data
(exponential and linear functions).
Topic area
Content
Nuffield resources The links below go to pages from which you can download the resources, some recently revised.
Sea defence wall (assignment)
Two versions of an assignment in which students find functions to model the outline of a sea defence wall. The first version encourages students to work independently, the second is more structured for less able students.
Trigonometric Functions
(8 hours)
Draw graphs of
·
·
Learn the general shape and position of trigonometric functions and use the terms amplitude, frequency, wavelength, period and phase shift correctly.
Fit trigonometric functions to real data.
Solve trigonometric equations of the form and
Coughs and sneezes
Includes data about the way in which an outbreak of the common cold spreads. Students are asked to model the data using trigonometric and polynomial functions.
SARS A and B (assignments)
Data set giving the number of deaths from SARS. Students choose, draw and evaluate functions to model the data.
Sunrise and sunset times (assignment)
Students find and evaluate trigonometric functions to model how the amount of daylight varies with the day of the year. Includes data for Adelaide, Brisbane and London.
Tides (assignment)
Data set giving the water depth each hour during a day. Students choose, draw and evaluate functions to model the data.
Topic area
Content
Nuffield resources The links below go to pages from which you can download the resources, some recently revised.
Log graphs - earthquakes
Examples (involving earthquakes and planetary motion) that can be used to introduce log graphs. Ideas of experiments and other situations that can be used for practice. (Includes logs to base 10.)
Gas guzzlers
Slide presentation and activity in which students use a log graph to find an exponential function to model real data.
Smoke strata
Includes data about the height of smoke layers due to a fire in a tall building and sample examination question. Data could also be used to give practice in linearising data. | 677.169 | 1 |
Math 8 Guided Interactive Math Notebook Pages: Solving Equations
Be sure that you have an application to open
this file type before downloading and/or purchasing.
6 MB
Product Description
This is two 8th Grade Common Core guided, color-coded notebook pages for the Interactive Math Notebook on Solving Equations.
Included in the notes are notes on solving basic one-step and two-step equations, solving equations by combining like terms, solving multi-step equations and solving mulit-step equations with fractions.
Blackline masters and color-coded answer keys are | 677.169 | 1 |
This book introduces students to probability, statistics, and
stochastic processes. It can be used by both students and
practitioners in engineering, various sciences, finance, and
other related fields. It provides a clear and intuitive approach
to these topics while maintaining mathematical accuracy.
The book covers:
Basic concepts such as random experiments, probability
axioms, conditional probability, and counting methodsThis well-respected text offers an accessible introduction to
functional programming concepts and techniques for students of
mathematics and computer science. The treatment is as
nontechnical as possible, assuming no prior knowledge of
mathematics or functional programming. Numerous exercises
appear throughout the text, and all problems feature complete
solutions. 1989 edition.
The Eighth Edition of this highly dependable book retains its best features–accuracy, precision, depth, and abundant exercise sets–while substantially updating its content and pedagogy. Striving to teach mathematics as a way of life, Sullivan provides understandable, realistic applications that are consistent with the abilities of most readers. Chapter topics include Graphs; Trigonometric Functions; Exponential and Logarithmic Functions; Analytic... more...
Renowned for its clear prose and no-nonsense emphasis on
core concepts, Statistics covers fundamentals using real
examples to illustrate the techniques.
The Fourth Edition has been carefully revised and updated to
reflect current data.
This textbook provides an introduction to financial mathematics and
financial engineering for undergraduate students who have completed
a three or four semester sequence of calculus courses. It
introduces the theory of interest, random variables and
probability, stochastic processes, arbitrage, option pricing,
hedging, and portfolio optimization. The student progresses from
knowing only elementary calculus to understanding the derivation
and solution... more...
This book studies the foundations of quantum theory through its
relationship to classical physics. This idea goes back to the
Copenhagen Interpretation (in the original version due to Bohr
and Heisenberg), which the author relates to the mathematical
formalism of operator algebras originally created by von Neumann.
The book therefore includes comprehensive appendices on
functional analysis and C*-algebras, as well as a briefer one on... more...
This unique volume returns in its second edition, revised and updated with the latest advances in problem solving research. It is designed to provide readers with skills that will make them better problem solvers and to give up-to-date information about the psychology of problem solving. Professor Hayes provides students and professionals with practical, tested methods of defining, representing, and solving problems. Each discussion of the important... more...
Success in your calculus course starts here! James Stewart's
CALCULUS texts are world-wide best-sellers for a reason: they are
clear, accurate, and filled with relevant, real-world examples.
With CALCULUS, Eighth Edition, Stewart conveys not only the utility
of calculus to help you develop technical competence, but also
gives you an appreciation for the intrinsic beauty of the subject.
His patient examples and built-in learning aids will help you... more... | 677.169 | 1 |
Tag Archives: conceptual understanding
One of the main objectives of mathematics education is for students to acquire mathematical habits of mind. One of the ways of achieving this objective is to engage students in problem solving tasks. What is a problem solving task? And when is a math problem a problem and not an exercise? What is a problem… Read More »
One of the most difficult items for the Philippine sample in the Trends and Issues in Science and Mathematics Education Study (TIMSS) for Advanced Mathematics and Science students conducted in 2008, is about comparing the slopes of the tangent at a point on a curve. The question is constructed so that it assesses not only… Read More » | 677.169 | 1 |
Types of Sequences
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this file type before downloading and/or purchasing.
1 MB|24 pages
Product Description
This is an Algebra 1 Common Core Lesson on Different Types of Sequences. Using knowledge of sequences and linear equations, students will develop equivalent equations to model the sequence. After a few teacher led examples, students will practice on their own or in groups. | 677.169 | 1 |
Visual Mathematics is a highly interactive visualization software (containing -at least- 67 modules) addressed to High school, College and University students. This is a very powerful tool that helps to learn and solve problems by the hundreds in a very short time.
Included areas: Arithmetic, Algebra, Geometry, Trigonometry, Analytic Geometry and miscellaneous.
Visual Mathematics, a member of the Virtual Dynamics Mathematics Virtual Laboratory, is an Intuitively-Easy-To-Use software.
Visual Mathematics modules include the theory necessary to understand every theme, they include very many solved examples. Every student should have this powerful tool at home.
Teachers use Visual Mathematics to prepare homeworks and tests in a short time.
With Visual Mathematics the student solves homework problems while he/she really learns and enjoys mathematics.
Visual Mathematics may be used (1) in the classroom, to very easily make clear the topics the teacher covers, (2) in the school library, as reference to review themes covered in classes (3) at home, for the student to study at his own pace and understand while solving and visualizing hundreds of problems. Teachers may use Visual Mathematics to prepare classes. <>
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This program is designed to help coaches of kids basketball teams to plan their game line-ups throughout the season. A simple GUI allows for easy browsing through games and rosters as well as entering in and editing new rosters. | 677.169 | 1 |
Search for 'math' returned 2503 results
Learn to Program & Simulate a software Robot & learn Maths fundamentals simultaneously !!
This is a very basic STEM (Science Technology Engineering & Mathematics) course introducing you to the wo...Project Management Professional (PMP®) Exam Prep:2 full high real PMP® Exams &How get every math question Correctly.
the content of this course includes but not limited to:
2.How to get every mat... more ››
NO MORE MECHANICAL LEARNING!-help kids learn easy the foundational skills in math even if you are a parent or a teacher
This course is helpful for parents with children between 3 and 7 years old,... more ››
Master All Concepts in GMAT Maths Section to Achieve A High Score In GMAT!
Know what to expect and what topics to prepare for GMAT Math section.
Get an overview of all the topics covered in the GMA... more ››
Lessons and resources to support study for the 11+ Mathematics exam.
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Feel confident for success in the math element of the 11+ exam.
Broaden their understanding of a range of prim... more ››
Master all basic math formulas and solve problems easily
REVIEW THIS COURSE
Master most of the important Math skills
Solve mathematical problems easily and quickly
Know the formulas for calculating ... more ›› | 677.169 | 1 |
Characteristics of Relations and Functions
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this file type before downloading and/or purchasing.
484 KB|18 pages
Product Description
This PowerPoint is intended to help students with defining relations and functions. Students will define and then be given examples of each. Students will also be shown the difference between discrete and continues functions. Students will also be shown how to use the vertical line test to determine if a relation is a function. Student will also be introduced to function notation. | 677.169 | 1 |
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