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Fibonacci and Catalan Numbers: An Introduction
Discover the properties and real-world applications of the
Fibonacci and the Catalan numbers
With clear explanations and easy-to-follow examples, Fibonacci
and Catalan Numbers: An Introduction offers a fascinating overview
of these topics that is accessible to a broad range of readers.
Beginning with a historical development of each topic, the book
guides readers through the essential properties of the Fibonacci
numbers, offering many introductory-level examples. The author
explains the relationship of the Fibonacci numbers to compositions
and palindromes, tilings, graph theory, and the Lucas numbers.
The book proceeds to explore the Catalan numbers, with the
author drawing from their history to provide a solid foundation of
the underlying properties. The relationship of the Catalan numbers
to various concepts is then presented in examples dealing with
partial orders, total orders, topological sorting, graph theory,
rooted-ordered binary trees, pattern avoidance, and the Narayana
numbers.
The book features various aids and insights that allow readers
to develop a complete understanding of the presented topics,
including:
Real-world examples that demonstrate the application of the
Fibonacci and the Catalan numbers to such fields as sports, botany,
chemistry, physics, and computer science
More than 300 exercises that enable readers to explore many of
the presented examples in greater depth
Illustrations that clarify and simplify the concepts
Fibonacci and Catalan Numbers is an excellent book for courses
on discrete mathematics, combinatorics, and number theory,
especially at the undergraduate level. Undergraduates will find the
book to be an excellent source for independent study, as well as a
source of topics for research. Further, a great deal of the
material can also be used for enrichment in high school
courses.
RALPH P. GRIMALDI, PhD, is Professor of Mathematics at Rose-Hulman Institute of Technology. With more than forty years of experience in academia, Dr. Grimaldi has published numerous articles in discrete mathematics, combinatorics, and graph theory. Over the past twenty years, he has developed and led mini-courses and workshops examining the Fibonacci and the Catalan numbers | 677.169 | 1 |
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Be sure that you have an application to open this file type before downloading and/or purchasing.
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PRODUCT DESCRIPTION
Special Education Algebra 2. Factoring quadratics in Special Education. These reference posters cover trinomial factoring where A=1. They are for students just learning how to factor, students having trouble factoring or Special Education Algebra and Algebra 2 students. I post these for my self-contained Special Education Algebra 2 students.
There are 2 process posters and 2 example posters. The first process poster shows the 2 scenarios for factoring when C is positive. A second process poster outlines factoring when C is negative. You can see all posters in the preview.
Two example posters give examples for when C is positive (and B is -) and when C is negative (and B is also -). These two scenarios are trickiest for my students to remember without a reference.
Also included is a student handout that walks students through the process of factoring a trinomial in all scenarios | 677.169 | 1 |
Algebra 1
Algebra 1 is a branch of mathematics in which we represent the components of a specified set or the numbers by use of symbols, alphabetical letters to express general relationship between the components of set. Algebra is a way of simplifying Math through the use of variables, formulas or equations.
This topic contains greatest common factor, factorizing of trinomials $(ax^{2} + bx + c)$ by splitting middle term or by the method of perfect square.
Statistics:
It is another branch of algebra 1 which includes introductory matrices, measure of variation, making of histograms, sampling and bias.
Probability:
Probability contains possibility of occurring of an event from a group of events under (distributional, conditional, binomial etc.). It also contains Permutation $(^{n}P_{r})$ and Combination $(^{n}C_{r})$.Solving System of Linear Equation and Inequalities:
Linear equations of one and two variables, and the method of solving them by substitution, elimination, completing square method, solving by graphical method comes under the branch of algebra 1.
Algebra 1 Topics
Algebra is a vast branch of mathematics. There are several topics that comes under Algebra 1 and here are few of them:
Polynomials:
In simple words, polynomial means, 'many terms'. They are the expression which include monomials, binomials, trinomial and also the higher order of polynomials. There are different types of polynomials and they are classified on the bases of number of the terms and the degree. Given below are the different types of Polynomials:
1) Monic Polynomial:
If an expression is having a leading co-efficient of $1$, then such expressions are called as monic polynomials.
The general expression of cubic expression of cubic polynomial is $ax^{3} + bx^{2} + cx + d, a \neq 0$
4) Prime Polynomial:
A polynomial which cannot be factorized into the product of the two polynomials is called as prime polynomial.
Ex: $x^{2} + x + 1$
Radical Expression
An expression containing a square root is called as radical expression. These expressions can be easily solved by performing squaring operation.
Rational Expression An expression where the numerator and denominator or both of them are polynomials are called as rational expressions. By simplifying the rational expression, we can reduce the expression into the lowest form.
Analyzing Linear Equations
A linear equation is an equation of a line, which contains two different variables and is easily transferred into graphical representation. The general form of linear equation is $ax + by + c$ = $0$, where $x$ and $y$ are variables, $a$ and $b$ are co-efficients of $x$ and $y$ and $c$ is constant.
Solving Linear Inequalities
Linear inequality is the comparison of two values. We can add, subtract, multiply and divide the inequalities to solve the linear inequalities. The concept of solving the linear inequalities is the same as solving the linear equation. Linear inequality has its own properties and they are as given below:
1) Transitive Property
When $a, b$ and $c$ are real numbers, then
If $a < b$ and $b < c$, then $a < c$
2) Addition Property:
If $a < b$, then $a + c < b + c$
3) Subtraction Property:
If $a < b$, then $a - c < b - c$
4) Multiplication Property:
• If $a < b$ and $c$ is positive $c \times a < c \times b$
• If $a < b$ and $c$ is negative - $c \times a > - c \times b$
Quadratic Equation
A polynomial with a second degree is called as quadratic equation. When the discriminant is zero, then such quadratic equation is called as perfect square, i.e. $b^{2} - 4ac$ = $0$. When a discriminant is greater than $1$ then the roots of the equation are real and if it is lesser than $1$, at that point the roots of the equation are imaginary. The general form of quadratic equation is $ax^{2} + bx + c$ = $0$. And, the formula of quadratic equation is as follows:
$x$ = $\frac{-b\ \pm\ \sqrt{b^{2}\ -\ 4ac}}{2a}$
Simultaneous Equation
A set of two equations with two unknown variables are called as simultaneous equations. Solving simultaneous equations involves finding the values of the variables that will satisfy the equation.
There are two methods of solving the simultaneous equations:
1) Substitution Method: Here, we first solve one of the equation for one of the unknowns and then, substitute the answer into the other equation.
2) Elimination Method: In this method, first make the co-efficient of one of the variables to the same value in both the equations. Then, add or subtract an equation from the other to form a new equation that contains one variable. | 677.169 | 1 |
Oval Track and Other Permutation Puzzles: And Just Enough Group Theory to Solve Them
Paperback
Temporarily Out of Stock Online
Overview is also an accompanying CD that can be used to reduce the need for carrying out long calculations and memorising difficult sequences of moves. This book will prove useful as supplemental material for students taking abstract algebra courses. It provides a real application of the theory and methods of permutation groups, one of the standard topics. It will also be of interest to anyone with an interest in puzzles and a basic grounding in mathematics. The author has provided plenty of exercises and examples to aid study.
Related Subjects
Table of Contents
1. An overview of oval tracks; 2. The transpose puzzle: an introductory tour; 3. The slide puzzle: an introductory tour; 4. The Hungarian puzzle: an introductory tour; 5. Permutation groups: just enough definitions and notation; 6. Permutation groups: just enough theory; 7. Cycles and transpositions; 8. The parity theorem; 9. The role of conjugates; 10. The role of commutators; 11. Mastering the oval track puzzle; 12. Transferring knowledge between puzzles; 13. What a difference a disk makes!: changing the number of disks, and using Maple or GAP; 14. Mastering the slide puzzle; 15. Mastering the Hungarian rings with numbers; 16. Mastering the Hungarian rings with colours; 17. Advanced challenges. | 677.169 | 1 |
Sixth Form Pure Mathematics: Volume 1
Sixth Form Pure Mathematics, Volume 1, Second Edition, is the first of a series of volumes on Pure Mathematics and Theoretical Mechanics for Sixth Form students whose aim is entrance into British and Commonwealth Universities or Technical Colleges. A knowledge of Pure Mathematics up to G.C.E. O-level is assumed and the subject is developed by a concentric treatment in which each new topic is used to illustrate ideas already treated. The major topics of Algebra, Calculus, Coordinate Geometry, and Trigonometry are developed together. This volume covers most of the Pure Mathematics required for the single subject Mathematics at Advanced Level. Early and rapid progress in calculus is made at the beginning of this volume in order to facilitate the student's progress along the most satisfactory lines in Pure Mathematics, in Theoretical Mechanics and in Physics. The worked examples are an essential feature of this book and they are followed by routine exercises within the text of each chapter, associated closely with the work on which they are dependent. The exercises at the end of each chapter collectively embody all the topics of that chapter and, where possible, the preceding chapters also | 677.169 | 1 |
MAT 132: CALCULUS WITH ANALYTIC GEOMETRY I Page 1 of 8 CHAPTER 1: PRELIMINARIES 1.1 Real Numbers and the Real Line Real Numbers Much of calculus is based on properties of the real number system. Real numbers are numbers that can be expressed as decimals. Rules for Inequalities If a, b and c are real numbers, then: 1. c b c a b a + < + ⇒ < 2. c b c a b a-<-⇒ < 3. b a < and bc ac0 c < ⇒ 4. b a < and ac bc0 c < ⇒ < Special case: a b b a-<-⇒ < 5.0 a 10 a ⇒ 6. If a and b are both positive or both negative, then a 1 b 1 b a < ⇒ < Intervals A subset of the real line is called an interval if it contains at least two numbers and contains all the real numbers lying between any two of its elements. Types of intervals Notation Set description Type Finite: ) b , a ( { } b x a x < < Open [ ] b , a { } b x a x ≤ ≤ Closed [ ) b , a { } b x a x < ≤ Half-open ] b , a ( { } b x a x ≤ < Half-open
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MAT 132: CALCULUS WITH ANALYTIC GEOMETRY I Page 2 of 8 Infinite: ) , a ( ∞ { } a x x Open [ ) , a ∞ { } a x x ≥ Closed ) b , (-∞ { } b x x < Open ] b , (-∞ { } b x x ≤ Closed ) , ( ∞-∞ ℜ (set of all real numbers) Example: Attend lecture. Absolute Value The absolute value of a number x, denoted by x , is defined by the formula <-≥ =0 x , x0 x , x x Absolute Values and Intervals If a is any positive number, then 1. a x = if and only if a x ± = 2. a x < if and only if a x a < <-3. a x if and only if a x or a x-< 4. a x ≤ if and only if a x a ≤ ≤-5. a x ≥ if and only if a x ≥ or a x-≤ Example: Attend lecture.
MAT 132: CALCULUS WITH ANALYTIC GEOMETRY I Page 3 of 8 PROBLEM SET 1.1 Inequalities Solve the following inequalities. 1.
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The Routledge International Handbook of Dyscalculia and Mathematical Learning Difficulties
Mathematics plays an important part in every person's life, so why isn't everyone good at it? The Routledge International Handbook of Dyscalculia and Mathematical Learning Difficulties brings together commissioned pieces by a range of hand-picked influential, international authors from a variety of disciplines, all of whom share a high public profile. More than fifty experts write about mathematics learning difficulties and disabilities from a range of perspectives and answer questions such as:
What are mathematics learning difficulties and disabilities?
What are the key skills and concepts for learning mathematics?
How will IT help, now and in the future?
What is the role of language and vocabulary?
How should we teach mathematics?
By posing notoriously difficult questions such as these and studying the answers The Routledge International Handbook of Dyscalculia and Mathematical Learning Difficulties is the authoritative volume and is essential reading for academics in the field of mathematics. It is an incredibly important contribution to the study of dyscalculia and mathematical difficulties in children and young | 677.169 | 1 |
2nd Quarter, Math Level 1 (9th grade math)
00.00 Start Here (Math Level 1)
Course Description
The fundamental purpose of Mathematics I is to formalize and extend the mathematics that students learned in 8th grade. Students will focus on linear expressions, equations, and functions but also be introduced to exponential functions. They will solve systems of equations and inequalities. They will review learn the basic terms of geometry and solve problems involving angles, triangles, parallel lines, perimeter and area. In addition, they will use the Pythagorean Theorem to solve problems and find the distance and midpoint between two points. They will review transformations and use this knowledge to understand triangle congruence. Finally, they will study the statitistical concepts of spread, frequency tables, histograms, box plots. scatter plots, correlation and causation, and standard deviation. Students should experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.
Class Overview
This integrated Secondary Mathematics I course is based on the New Utah State Standards Initiative.
Credit
This course is worth .25 credits, or nine weeks of Mathematics I. There are four Mathematics II quarter classes available. Taking all four will add up to one credit or one year of Mathematics I. In order to earn credit for each quarter, you must commit to following the EHS Honor Code: "As a student of the Electronic High School, I agree to turn in my assignments in a timely manner, do my own work, not share my work with others, and treat all students, teachers, and staff with respect."This course is for ninth grade students. After completing the work for the class, students must pass a proctored final exam to earn credit. There is not a paper-based textbook assigned for this course. If you find that having a textbook is useful, you can check out a textbook from most local libraries. You can also search for topics on the Internet to find many useful resources.
Prerequisites
You should have successfully completed 8th grade math.
Supplies needed
Graph paper (this can also be downloaded)
Scientific or Graphing Calculator (You can download scientific and graphing calculator simulators or find online versions, but as you will need a graphing calculator for the rest of your high school career, you may consider buying one now.)
Access to a printer to print the daily assignments is vital. Most assignments are NOT interactive and must be printed out to complete.
Ability to scan or photograph a completed assignment to submit electronically.
Organization of Secondary Math Level 1
Units: There are 10 units for the full credit of Secondary Math 2.
Quarter 1 has two units.
Quarter 2 has two unit.
Quarter 3 has three units.
Quarter 4 has three units.
Schedule: When you enroll in a quarter class, you are given 10 weeks to finish all the requirements needed to earn the credit for a quarter. There are no "required" due dates for the assignments in this course. However, there is a pacing guide provided for you that will help you stay on track to being successful and finishing the course within the 10 week time frame. The pacing guide is located in the Syllabus in Module 1. Before you begin, go over the pacing guide to help you set up your own due dates for the assignments. Give your parents permission to nag you about it. You don't want to be one of those students who does a whole lot of work, but never finishes the course.
This Quarter Class
The units in this class have lessons, assignments, quizzes and a unit test.
Lessons: Each lesson provides instruction on a given topic. Many include instructional videos (hosted on YouTube) and one or more assignments for independent practice.
Assignments: Print, then complete the practice worksheet, showing Assignments are submitted by uploading the digital assignment through the course website by following the instructions within each assignment. Under some circumstances, you may snail-mail a hard copy of the assignment to the instructor. If you choose this option, be sure to make a copy for yourself, as the instructor will NOT return your assignment. Also, please send the instructor an e-mail if you must mail an assignment.
Quizzes: Some quizzes are taken online. Others are more like the assignments. Print, then complete the quiz, showing all of your work as to Quizzes are submitted by uploading the digital assignment through the course website by following the instructions within each quiz.
Proctored Final
Each quarter class has a proctored final exam and is worth 25% of the final grade.
Information about the Final Exam
You must get approval from your teacher before you are allowed to take the final exam.
You must complete every assignment and have an overall grade of C in the course to be approved to take the final exam.
The final exam is a comprehensive exam that must be taken with an approved proctor.
You are allowed to have a page of notes. You also will need a calculator and scratch paper.
You must pass the final exam with a 60% in order to pass the class.
The final exam is worth 25% of your final grade.
The exam is timed. You will have 2.0 hours to complete the exam. You must finish it in one attempt.
Final Grade
Assignments and quizzes are worth 75% of the final grade. The proctored final test is worth 25% of the final grade.
Grading Scale
You earn a grade based on a modified total points percentage method. This means that the total number of points you earned is divided by the total number of points possible, times 100%. That will make up 75% of your final grade. The final exam is the remaining 25%. These scores are combined for a total percentage of the class. This percentage is translated into a grade based on this standard scale:
00.02 About Me (Math Level 1)
teacher-scored 10 points possible 10 minutes
About Me Assignment: This assignment gives me, as your teacher, a chance to get to know you better! To complete and submit this assignment copy the material between the asterisks into a blank word-processing document. Answer the questions using complete sentences, appropriate punctuation and sentence structure. Please write your answers in either BOLD or a . Save the document. Finally, select all, copy, then paste the entire document into the box that opens when you click to submit this assignment.
1. What is your full name, what name do you prefer to go by, your parent's/guardian's names, and contact information for both you and your parents? (email addresses and phone numbers.)
2. What high school do you attend and what grade are you in? What is the name of the last math class you completed?
3. Why have you chosen to take this math class with EHS?
4. What is your counselor's full name and contact information?
5. Have you read the EHS Honor Code and do you commit to following it? EHS Honor Code "As a student of the Electronic High School, I agree to turn in my assignments in a timely manner, do my own work, not share my work with others, and treat all students, teachers, and staff with respect."
6. Are you committed to finishing the class within the 10 week time frame, completing your final exam in week 9?
7. Now tell me about you! What are your likes/dislikes etc. Please be sure to include anything you think I need to know as your teacher.
Pacing: complete this by the end of Week 1 of your enrollment date for this class.
00.03 Basic Skills (Math Level 1)
Just like learning to use the English or Spanish language, you learn the language of mathematics by acquiring its vocabulary and grammar and by practicing until you can "think" fluently in the language.
This pre-requisite lesson helps you verify you have a basic understanding of integers, fractions, and simplifying expressions, some of the basic building blocks of the "mathematics language."
00.03.01 Basic Skills - Integers (Math Level 1)
If you don't pass the quiz on the first attempt, search the internet for adding, subtracting, multiplying and dividing integers. Review the material and try again.
Pacing: complete this by the end of Week 1 of your enrollment date for this class.
00.03.02 Basic Skills - Fractions (Math Level 1)
computer-scored 20 points possible 20 minutes
Activity for this lesson
Take the quiz listed as 00.03.02 Basic Skills - Fractions Quiz
If you don't pass the quiz on the first attempt, search the internet for adding, subtracting, multiplying and dividing fractions. Review the material and try again.
Pacing: complete this by the end of Week 1 of your enrollment date for this class.
00.03.03 Basic Skills - Simplifying Expressions (Math Level 1)
computer-scored 20 points possible 20 minutes
Activity for this lesson
Take the quiz 00.03.03 Basic Skills - Simplifying Expressions Quiz
If you don't pass the quiz on the first attempt, search the internet for simplifying expressions. Review the material and try again.
Pacing: complete this by the end of Week 1 of your enrollment date for this class.
03.00 Functions Overview (Math Level 1)
In earlier grades, students define, evaluate, and compare functions, and use them to model relationships between quantities. In this unit, students learn function notation and develop the concepts of domain and range. They move beyond viewing functions as processes that take inputs and yield outputs and start viewing functions as objects in their own right. They explore many examples of functions, including sequences; they interpret functions given graphically, numerically, symbolically, and verbally, translate between representations, and understand the limitations of various representations. They work with functions given by graphs and tables, keeping in mind that, depending upon the context, these representations are likely to be approximate and incomplete. Student work includes functions that can be described or approximated by formulas as well as those that cannot. When functions describe relationships between quantities arising from a context, students reason with the units in which those quantities are measured. By the end of the unit, students will be able to:
Understand the definition of a function and identify its parts and write a relation in function notation.
I highly recommend that you click on the links above before continuing.
You can watch the videos by clicking on the PRESENTATION tab or work through all sections.
Guided Practice
After watching the video try these problems. The worked solutions follow.
Identify 3 points and graph them. Make a table and record the coordinates of each point. Write the domain and range of the set of points.
Example 1:
f(x) = x - 4
Example 2:
f(x) = -3x + 5
Example 3: Fill in the following table given the function and domain
Function
Domain
Range
Ordered Pairs
f(x) = 3 – 4x
–3, 0, 5
f(x) = x –
2, –4, 3
f(x) = –5x
–2, –1, 0Answers
Identify 3 points and graph them. Make a table and record the coordinates of each point. Write the domain and range of the set of points.
Example 1:
f(x) = x - 4
x
f(x)
-3
-6
0
-4
3
-2
Domain: {-3, 0, 3} if you just use the points or all real numbers if you consider all points.
Range: {-6, -4, -2} if you just use the points or all real numbers if you consider all points.
Example 2:
f(x) = -3x + 5
x
f(x)
-2
11
0
5
-2
-1
D: {-2, 0, 2} if you just use the points or all real numbers if you consider all points.
R: {11, 5, -} if you just use the points or all real numbers if you consider all points.
Example 3: Fill in the following table given the function and domain.
Function
Domain
Range
Ordered Pairs
{-3 ,0, 5}
{15, 3, -17}
(-3,15), (3, 0), (5, -17)
{2, -4, 3}
{-2, -1, 0}
{10, 5, 0}
(-2,10), (5, -1), (0,0)Pacing: complete this by the end of Week 3 of your enrollment date for this class.
03.04 Graphing Linear Functions (Math Level 1)
Graph linear functions using input/output pairs.
Something to Ponder
How does the graph of a linear function relate to its input/output pairs?
Mathematics Vocabulary
Linear Function: a function that satisfies the following two properties:
Input/Output Pair: the input and output of a function is an "ordered pair", such as (4,16). This pair is an "ordered pair" because the input always comes first, and the output second. So (4,16) means that the function takes in "4" and gives out "16."
Learning these concepts
Click the mathematician image to launch the video to help you better understand this "mathematical language."
Pacing: complete this by the end of Week 4 of your enrollment date for this class.
03.08 Writing Functions from Graphs (Math Level 1)
Write linear functions in function notation to describe what is happening in a graph.
Something to Ponder
How would you describe the process for writing a linear function rule from a graph?
Mathematics Vocabulary
Function notation: A function with domain X and codomain Y is commonly denoted by
or
The elements of x are called arguments of . For each argument x, the corresponding unique y in the codomain is called the function value at x or the image of x under . It is written as f(x). One says that associates y with x or maps x to y. This is abbreviated by
Pacing: complete this by the end of Week 6 of your enrollment date for this class.
04.00 Exponential Functions Overview (Math Level 1)
Students build on and informally extend their understanding of integer exponents to consider exponential functions. They compare and contrast linear and exponential functions, distinguishing between additive and multiplicative change. They interpret arithmetic sequences as linear functions and geometric sequences as exponential functions. By the end of the unit, students will be able to:
Pacing: complete this by the end of Week 7 of your enrollment date for this class.
04.03 Graphing Exponential Functions (Math Level 1)
Graph exponential functions using input-output pairs.
Something to Ponder
How would you describe an exponential function and how it relates to a table, equation and graph?
Mathematics Vocabulary
Exponential: change by a given proportion over a set interval. An example of exponential behavior is a medical isotope decaying to half the previous amount every twenty minutes and a bacteria culture tripling every day each, because, in a given set amount of time (in these examples - twenty minutes or one day), the quantity has changed by a constant proportion (one-half as much and three times as much.
Exponential function graph: points on a graph are either too close to one fixed value or else to too large to be conveniently graphed. There will generally be only a few points that are "reasonable" to use for drawing the curve; picking sensible points require that a good grasp of the general behavior of an exponential, so the curve can be approximated.[defintion derived from ]
Learning these concepts
Click each mathematician image OR click the link below to launch the video to help you better understand this "mathematical language." | 677.169 | 1 |
question
Course 02: Discrete Mathematics (Arsdigita University)
This course covers the mathematical topics most directly related to computer science. Topics include: logic, relations, functions, basic set theory, countability and counting arguments, proof techniques, mathematical induction, graph theory, combinatorics, discrete probability, recursion, recurrence relations, and number theory. Emphasis is placed on providing a context for the application of the mathematics within computer science. The analysis of algorithms requires the ability to count the number of operations in an algorithm. Recursive algorithms in particular depend on the solution to a recurrence equation, and a proof of correctness by mathematical induction. The design of a digital circuit requires the knowledge of Boolean algebra. Software engineering uses sets, graphs, trees and other data structures. Number theory is at the heart of secure messaging systems and cryptography. Logic is used in AI research in theorem proving and in database query systems. Proofs by induction and the more general notions of mathematical proof are ubiquitous in theory of computation, compiler design and formal grammars. Probabilistic notions crop up in architectural trade-offs in hardware design.
Instructor: Shai Simonson
Text: Discrete Mathematics and its Applications, Rosen.
Reference: Concrete Mathematics, Graham, Knuth and Patashnik
Requirements: Four exams, seven problem sets, one research problem set.
I found a truth table tester that may help you train the concepts from lecture 1. It is in German but that shouldnt matter for that topic.
Here is the url .
Reviewer:sivam.iitm -
favoritefavoritefavoritefavorite -
August 23, 2007 Subject:
its a greeeeeeeeeeeeet work | 677.169 | 1 |
...
Show More rigour. Dr Steven Cook, University of Wales Swansea Essential Mathematics for Economic Analysis provides an invaluable introduction to mathematical analysis and linear algebra for economists. Its main purpose is to help students acquire the mathematical skills they need in order to read the less technical literature associated with economic problems. The coverage is comprehensive, ranging from elementary algebra to more advanced material, whilst focusing on all the core topics usually taught in undergraduate courses on mathematics for economists | 677.169 | 1 |
Staff: Mentor
AP practice thread
Here's an idea that might work. Create a thread in the appropriate Homework Help forum (title it "AP Calc practice problems", if you like) where people can take turns posting their favorite (or trickiest) AP-like problems along with their solution or attempted solution. Then others can chime in with corrections or tips. Then someone else can post a different problem. And so on...
What would not be acceptable is to just post a problem for someone else to answer--that's against our rules. (Please review our posting rules, which are linked at the top of every page, and the Homework Help FAQ.) | 677.169 | 1 |
Welcome to Calculus! Join me on this journey through one of the great triumphs of human thought.
2 videos, 2 readings
WEEK 2
Functions and Limits
Functions are the main star of our journey. Calculus isn't numbers: it's relationships between things, and how one thing changing affects something else.
13 videos, 5 readings
Calificado: Functions and Limits
WEEK 3
The End of Limits
People have thought about infinity for thousands of years; limits provide one way to make such ponderings precise. Continuity makes precise the idea that small changes in the input don't affect the output much.
15 videos, 4 readings
Calificado: The End of Limits
WEEK 4
The Beginning of Derivatives
It is time to change topics, or rather, to study change itself! When we wiggle the input, the output value changes, and that ratio of output change to input change is the derivative.
13 videos, 4 readings
Calificado: The Beginning of Derivatives
WEEK 5
Techniques of Differentiation
With the product rule and the quotient rule, we can differentiate products and quotients. And since the derivative is a function, we can differentiate the derivative to get the second derivative.
14 videos, 5 readings
Calificado: Techniques of Differentiation
WEEK 6
Chain Rule
The chain rule lets us differentiate the composition of two functions. The chain rule can be used to compute the derivative of inverse functions, too.
13 videos, 5 readings
Calificado: Chain Rule
WEEK 7
Derivatives of Transcendental (Trigonometric) Functions
So far, we can differentiate polynomials, exponential functions, and logarithms. Let's learn how to differentiate trigonometric functions.
14 videos, 5 readings
Calificado: Derivatives of Transcendental (Trigonometric) Functions
WEEK 8
Derivatives in the Real World
Derivatives can be used to calculate limits via l'Hôpital's rule. Given a real-world equation involving two changing quantities, differentiating yields "related rates."
11 videos, 3 readings
Calificado: Derivatives in the Real World
WEEK 9
Optimization
In the real world, we must makes choices, and wouldn't it be great if we could make the best choice? Such optimization is made possible with calculus.
12 videos, 4 readings
Calificado: Optimization
WEEK 10
Linear Approximation
Replacing the curved graph by a straight line approximation helps us to estimate values and roots.
13 videos, 5 readings
Calificado: Linear Approximation
WEEK 11
Antidifferentiation
Antidifferentiation is the process of untaking derivatives, of finding a function whose derivatives is a given function. Since it involves working backwards, antidifferentiation feels like "unbreaking a vase" and can be just as challenging.
14 videos, 4 readings
Calificado: Antidifferentiation
WEEK 12
Integration
By cutting up a curved region into thin rectangles and taking a limit of the sum of the areas of those rectangles, we compute (define!) the area of a curved region.
14 videos, 6 readings
Calificado: Integration
WEEK 13
Fundamental Theorem of Calculus
Armed with the Fundamental Theorem of Calculus, evaluating a definite integral amounts to finding an antiderivative.
13 videos, 4 readings
Calificado: Fundamental Theorem of Calculus
WEEK 14
Substitution Rule
Substitution systematizes the process of using the chain rule in reverse. Considering how often we used the chain rule when differentiating, we will often want to use it in reverse to antidifferentiate.
12 videos, 3 readings
Calificado: Substitution Rule
WEEK 15
Techniques of Integration
Integration by parts is the product rule in reverse. Integrals of powers of trigonometric functions can be evaluated.
10 videos, 4 readings
Calificado: Techniques of Integration
WEEK 16
Applications of Integration
We have already used integrals to compute area; integration can also be used to compute volumes.
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Calificaciones y revisiones
Calificado 4.8 de 5 3,342 calificaciones
JL
the best presentation I have ever seen
Extreme Good Teaching Method!
AR
Great energy in the course. A lot of fun to work on.
TL
I really enjoyed this course but week 9 was extremely ridiculous. I had a hard time relating the examples to the quiz and, when i finally figured it out, the answers were huge and complex numbers. Other then that though, i do recommend this course. | 677.169 | 1 |
Mathematics
Pre-Algebra is extremely important for students to master because having a foundation in algebra is essential to doing well in trigonometry, geometry, calculus and beyond. This series will build students skills in this critical area, which will ultimately help in all math courses that follow.
THE GEOMETRY TUTOR - LEARNING BY EXAMPLE Geometry is frequently challenging for students because every problem involves a figure that students must use to solve the problem. It is very important early on to master the art of reading the geometric figures properly in order to do well in this subject. The best way to do this is to introduce the definitions early on and solve problems involving diagrams to give students the much needed practice. The Geometry Tutor series is geared towards students who have been exposed to Algebra 1 and are ready to tackle geometry.
The Basic Math Word Problem Tutor teaches students how to easily tackle basic math word problems. After students learn a math skill such as multiplication or division, many are frequently confused on how to apply these skills to solve word problems. Word problems present the problem to be solved in sentence form and in these types of problems students must pull the information out of the problem and decide the best way to solve it.
The Basic Math Tutor series is focused on building skills at the first through seventh grade level. Building an understanding of fundamental Math concepts is essential for students to move on and conquer more advanced math and science such as Pre-Algebra and Algebra. Topics include addition, subtraction, multiplication, division, fractions, decimals, percents and more!
A 30 volume series covering basic math problems from addition, subtraction, multiplication and division of whole numbers, fractions, decimals and intergers to percentages, ratios and proportions, as well as exponents, powers, intro to geometry, graphing number theory and patterns, problem solving, statistics and simple equations.
When will I ever use algebra? That's a question you will never ask after you see concrete examples and practical applications to show how a mastery of fundamental algebraic concepts is the key to success in today's technologically advanced world. In this 30 volume series a variety of new perspectives on teaching and learning algebra are combined to produce a rewarding learning experience for you.
Now you can brush up your Algebra skills in this easy to understand refresher course. The Algebra Tutor is designed to help you with the basic concepts of Algebra in a clearly demonstrated and well-paced manner.
The best kept-secret in high school is that when it's taught the right way, GEOMETRY IS GORGEOUS! These videos will guide you through the mysteries of lines, planes, angles, inductive and deductive reasoning, planning proofs, parallel lines and planes, triangles and polygons.
Rapmatics is an exciting video created for modern High School students. The often daunting subject of Algebra is woven into an entertaining narrative music video with a two-fold educational intention; to increase students interest and confidence in the subject matter and to introduce complex mathematical concepts using popular rap music.
Calculus essentially takes the fundamentals of algebra and extends them to include rates of change between quantities. Calculus is extremely powerful and very useful in the study of Science and Engineering, motion of bodies, fluid mechanics, electricity, magnetism, and is the foundation for nearly all branches of science.
Trigonometry and PreCalculus are essential topics in mathematics that are needed to bridge the gap between Algebra and Calculus.† Attempting to tackle calculus without a mastery of Trigonometry will almost certainly lead to frustration. This series covers essential subjects in Trigonometry and PreCalculus with exceptional clarity so that students will feel well prepared to move onto Calculus and Physics.
The Algebra 2 Tutor teaches students the core topics of Algebra 2 and bridges the gap between Algebra 1 and Trigonometry. It contains essential material to help students do well in advanced mathematics. Many of the topics in this series are used in other Math courses, such as writing equations of lines, graphing equations and solving systems of equations. These skills are used time and time again in more advanced courses such as Physics and Calculus. | 677.169 | 1 |
Functions in R and C, including the theory of Fourier series, Fourier integrals and part of that of holomorphic functions, form the focal topic of these two volumes. Based on a course given by the author to large audiences at Paris VII University for many years, the exposition proceeds somewhat nonlinearly, blending rigorous mathematics skilfully with didactical and historical considerations. It sets out to illustrate the variety of possible approaches to the main results, in order to initiate the reader to methods, the underlying reasoning, and fundamental ideas. It is suitable for both teaching and self-study. In his familiar, personal style, the author emphasizes ideas over calculations and, avoiding the condensed style frequently found in textbooks, explains these ideas without parsimony of words. The French edition in four volumes, published from 1998, has met with resounding success: the first two volumes are now available in English | 677.169 | 1 |
[center]
Practice Makes Perfect has established itself as a reliable practical workbook series in the language-learning category. Now, with Practice Makes Perfect: Calculus, students will enjoy the same clear, concise approach and extensive exercises to key fields they've come to expect from the series--but now within mathematics. Practice Makes Perfect: Calculus is not focused on any particular test or exam, but complementary to most calculus curricula. Because of this approach, the book can be used by struggling students needing extra help, readers who need to firm up skills for an exam, or those who are returning to the subject years after they first studied it.
[center] | 677.169 | 1 |
PDF (Acrobat) Document File
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0.06 MB | 2 pages
PRODUCT DESCRIPTION
This quiz is created to follow the Power Point, Using Algebraic Properties to Simplify Expressions. It includes a quiz (2 to a page) and a retake version (also 2 to a page).
It assesses whether students can recognize the properties in use as well as whether students can use the properties to simplify an algebraic expression | 677.169 | 1 |
Euclidean Geometry and Transform good textbook."--Mathematical Gazette This introduction to Euclidean geometry emphasizes both the theory and the practical application of isometries and similarities to geometric transformations. Each chapter begins with an optional commentaryMore...
"A good textbook."--Mathematical Gazette This introduction to Euclidean geometry emphasizes both the theory and the practical application of isometries and similarities to geometric transformations. Each chapter begins with an optional commentary on the history of geometry. Contents include modern elementary geometry, isometries and similarities in the plane, vectors and complex numbers in geometry, inversion, and isometries in space. Numerous exercises appear throughout the text, many of which have corresponding answers and hints at the back of the book. Prerequisites for this text, which is suitable for undergraduate courses, include high school algebra, geometry, and elementary trigonometry. 1972 ed | 677.169 | 1 |
How can technology bring substantive algebra content to students traditionally excluded from algebra? Such "low achieving" students do not lack ability, motivation, or dedication when presented with appropriate and challenging material. Their talents can be enhanced with new content and instruction in all mathematics courses through the exploitation in all mathematics courses through the exploitation of computer and calculator technologies. A decade ago, we were challenged to use technology to "move our subject away from the routine and toward the content and processes that will give the class of 2000 originality, insight, judgment, initiative, and understanding" (McConnell 1988). Our use of technology transforms our sequence of courses for low-achieving students so that the "modified" algebra they get is no longer weakened and diluted but rather is modified for power, applications, and depth (PAD). | 677.169 | 1 |
Calculus: Locally Linear - Linear Models for Functions at a Point
PDF (Acrobat) Document File
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0.09 MB | 6 pages
PRODUCT DESCRIPTION
Introduce calculus students that it is possible to write a linear model for a function at a point by zooming in or refining a table until the function appears linear. The model they will write is actually the tangent line to the function at the given point.
Students can be writing tangent lines (or linear models) before they know formally how to find a derivative. This is a great lead in to using derivatives | 677.169 | 1 |
Completing the Square Notes
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0.46 MB | 2 pages
PRODUCT DESCRIPTION
This is a one-sided notes page intended for the beginner over completing the square.
The notes begin by explaining the purpose of the completing the square technique. Then a schematic shows the equation of a quadratic from standard form to vertex form.
Next, a worked out example is shown including steps. The second example includes the steps and has the student fill in parts of the process. Finally, the third example repeats the same steps, but has the student do all of the work.
The three examples also include identifying the vertex once the completing the square process is completed. All examples have "a" as 1 and "b" as an even number. Key | 677.169 | 1 |
Math Calculator
You can use this math calculator to calculate expression, solve equation, find extremum, calculate derivative and integral.
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Math Calculator is an expression calculator
You can input an expression including variable x, for example, log(x), then input a value of x; You can also input an expression such as log(20) directly. Math Calculator is an equation solver
Math Calculator can be used to solve equations with one variable, for example, sin(x)=0. Math Calculator is a function analyzer
Math Calculator has the abilities of finding maximum and minimum. Math Calculator is a derivative calculator and calculus calculator
You can use this program to calculate derivative and 2 level derivate of a given function. Math Calculator is an integral calculator
Math Calculator has the ability of calculating definite integral.
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Stretch Introduction to Algebra A
Stretch Introduction to Algebra A covers the same topics as Introduction to Algebra A, but at a more methodical pace (22 two-hour classes versus 16 ninety-minute classes). Topics covered include exponents and radicals, linear equations and inequalities, ratio and proportion, systems of linear equations, factoring quadratics, complex numbers, completing the square, and the quadratic formula.
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AoPS Holidays
There are no classes May 29, July 4, September 4, November 18 - 26, and December 21 - January 3.
Who Should Take?
Students are ready for this class if they have mastered arithmetic with fractions,
decimals, percents, negative numbers, and integer exponents. Most students who
have completed a typical Prealgebra course are ready for this course.
Our Stretch Introduction to Algebra A course covers the same syllabus as
our Introduction to Algebra A course.
AoPS Stretch courses are designed for high-performing students who seek
a more gradual pace than our regular courses offer.
Our Stretch Introduction to Algebra A consists of
22 two-hour classes, compared to 16 ninety-minute classes
in Introduction to Algebra A.
Each Stretch class features an instructor-led component that
highlights the week's central concepts, followed by a student-led session in which
students apply these concepts to more challenging problems.
Please note: Our Algebra sequence will likely not match up exactly with your school's.
Most students who have completed a Prealgebra course are ready for this course.
This course covers much of the algebra of a typical honors Algebra 1 course, some of the content of an honors
Algebra 2 course,
and some additional material not taught in most standard curricula.
Visit our Recommendations page for help in choosing the right class.
This course has given me a confidence in math that I have never before had in my life. While I do have to admit that I have been pushed over and over again to the peak of my mathematical ability, I have also begun to see math, particularly geometry, as more of an art that I have begun to enjoy more and more. | 677.169 | 1 |
MATH ASSIGNMENT HELP
Math assignment help
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Fundamentals of Automobile Engineering
Enjoy learning the working of Cars right from basics and make it stick in your brain for ever with the Fundamentals of Automobile Engineering. You don't need to have a de...
Become an Academic Writing Ninja with this Step-by-Step Guide to Writing Excellent Academic Essays.
Easy Steps to Write Better Essays is a step-by-step guide to writing outstanding academic essays for all type...
Write your first novel, novella or short story using this inspirational guide to writing for beginners.
Learn the Components of Successful Storytelling; Plot, character, and place and how to juggle them all li...
Discover all of the universes unique mysteries with expert Neil deGrasse Tyson.
Central to The Inexplicable Universe is the way it takes you deep into hidden layers of the universe in a manner that is extremel...
This workshop is designed to help you make sense of basic probability and statistics.
The Probability and Statistics Course includes simple explanations of all the subject's most important concepts. Whether yo...
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Barron's SAT Subject Test Math Level 1
Overview a section covering the most important tactics for succeeding on the test. Separate chapters review basic arithmetic, fractions and decimals, ratios and proportions, basic algebra, plane geometry, solid and coordinate geometry trigonometry, functions, statistics, and miscellaneous math topics. Three full-length model tests are presented with complete solutions for every problem. Test-taking strategies that make the difference between good scores and great scores; An overview of the SAT Math Level 1 test; Three full-length model tests to boost your confidence; Thorough review of all test topics; All material updated to reflect the most recent SAT Math 1 tests; Hyperlinks that allow students to click between questions and answer explanations. | 677.169 | 1 |
PDF (Acrobat) Document File
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1.56 MB
PRODUCT DESCRIPTION
This graphic organizer can be used as a foldable for your interactive notebook or it can just be printed on both sides as a four part graphic organizer. It can also be used as a review guide before a test or it could be used instead of notes; students actually prefer this type of note taking format.
The topics included in these notes are the following:
• Defining monomials, degree of a monomial, polynomial, degree of a polynomial, lead coefficient
• Defining the standard form of a polynomial
• Classifying polynomials by number of terms and degree
• End behavior of polynomial graphs
I hope this organizer is helpful to you and your students; I would love to hear back from you and see how it helped | 677.169 | 1 |
Categories
Mathematics Class VIII (English)(Paperback, R. D. Sharma)
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Description
The present Revised edition of the book has been written strictly according to the latest syllabus prescribed by the NCERT.
Keeping in mind the mental level of a child, every effort has been made to introduce new concepts in a simple language, so that the child understands them easily. Basic concepts have been explained through attractive illustrations relating to our day-to-day life experiences.
The book is divided into 27 chapters. The text is written in a lucid and easy to understand language. The difficulty level of the problems has been reduced and mathematical concepts have been explained in the simplest possible way. Each chapter contains a large number of illustrative examples to understand the applications of concepts. In each section, illustrative examples are followed by an exercise containing an adequate number of unsolved problems. The level of the problems in exercises has been kept such as to encourage the student to practice, so that the student becomes more confident in solving them.
About the Author:-
Dr. R.D. Sharma is currently working as Head of Deptt. (Science and Humanities) under the Directorate of Technical Education, Delhi. A Ph.D in Mathematics, he is a double gold medalist, ranking first in the order of merit in both B.Sc (Hons.) and M.Sc Examinations from the University of Rajasthan, Jaipur. He has undergone rigorous training from IIT, Kharagpur in computer-oriented mathematical methods and has a long experience of teaching post-graduate, graduate and engineering students | 677.169 | 1 |
Operations on Complex Numbers
PDF (Acrobat) Document File
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0.43 MB | 4 pages
PRODUCT DESCRIPTION
This packet contains an activity, a two-tier worksheet, answer keys, and access to online MATHguide lessons, videos, and interactive quizzes.
Students first work on algebra skills when simplifying operations on expressions containing 'i.' Next, students are told that i-squared is -1. They then clean up their expressions to gain final solutions.
The breaking up of the process by allowing students to work on algebra and then i-squared substitution helps slower learners lighten the burden of the assignment. This addresses differentiated | 677.169 | 1 |
Welcome to the website for a Numerical Methods
course for engineering undergraduates. It is dedicated to reaching a
large audience of undergraduate students through its holistic but
customized approach.
Holistically,
the resources review background information; present numerical methods
through notes, presentations, simulations and assessments; show how what
they learned is applied in real life; tell stories to illustrate special
topics and pitfalls; and give historical perspectives.
From a customized perspective,
the user can choose a computational language of choice - Maple, MathCAD,
MATHEMATICA or MATLAB. Electrical Engineering one of the
seven
engineering majors one can choose to illustrate the numerical methods. | 677.169 | 1 |
Mathematics & Further Mathematics
Mathematics is universally recognised as a key qualification providing evidence of a student's ability to process information logically, demonstrate skills in problem solving and work creatively.
It is one of the top three A level subject choices at St Gabriel's with currently almost one third of the girls choosing to take Mathematics. Further Mathematics is becoming increasingly popular and the department has links with the Further Mathematics Network with all the extra support this involvement brings.
Many girls have gone on to study Mathematics at university. We also prepare students for Oxbridge entrance tests such as MAT, STEP and AEA | 677.169 | 1 |
Calculus Early Transcendent and Concise. Varberg focuses on the most critical concepts. This popular calculus text remains the shortest mainstream calculus book available -- yet covers "all" relevant material needed by, and appropriate to, the study of calculus at thisMore...
Clear and Concise. Varberg focuses on the most critical concepts. This popular calculus text remains the shortest mainstream calculus book available -- yet covers "all" relevant material needed by, and appropriate to, the study of calculus at this level. It' s conciseness and clarity helps you focus on, and understand, critical concepts in calculus without them getting bogged down and lost in excessive and unnecessary detail. It is accurate, without being excessively rigorous, up-to-date without being faddish.
Preface
Preliminaries
Real Numbers, Estimation, and Logic
Inequalities and Absolute Values
The Rectangular Coordinate System
Graphs of Equations
Functions and Their Graphs
Operations on Functions
Exponential and Logarithmic Functions
The Trigonometric Functions
The Inverse Trigonometric Functions
Chapter Review
Review and Preview Problems
Limits
Introduction to Limits
Rigorous Study of Limits
Limit Theorems
Limits at Infinity; Infinite Limits
Limits Involving Trigonometric Functions
Natural Exponential, Natural Log, and Hyperbolic Functions
Continuity of Functions
Chapter Review
Review and Preview Problems
The Derivative
Two Problems with One Theme
The Derivative
Rules for Finding Derivatives
Derivatives of Trigonometric Functions
The Chain Rule
Higher-Order Derivatives
Implicit Differentiation
Related Rates
Derivatives of Exponential and Logarithmic Functions
Derivatives of Hyperbolic and Inverse Trigonometric Functions
Differentials and Approximations
Chapter Review
Review and Preview Problems
Applications of the Derivative
Maxima and Minima
Monotonicity and Concavity
Local Extrema and Extrema on Open Intervals
Practical Problems
Graphing Functions Using Calculus
The Mean Value Theorem for Derivatives
Solving Equations Numerically
Antiderivatives
Introduction to Differential Equations
Exponential Growth and Decay
Chapter Review
Review and Preview Problems
The Definite Integral
Introduction to Area
The Definite Integral
The First Fundamental Theorem of Calculus
The Second Fundamental Theorem of Calculus and the Method of Substitution | 677.169 | 1 |
Welcome to Machine Learning! In this module, we introduce the core idea of teaching a computer to learn concepts using data—without being explicitly programmed. The Course Wiki is under construction. Please visit the resources tab for the most complete and up-...
4 videos, 10 readings
Calificado: Introduction
Linear Regression with One Variable
Linear regression predicts a real-valued output based on an input value. We discuss the application of linear regression to housing price prediction, present the notion of a cost function, and introduce the gradient descent method for learning.
7 videos, 8 readings
Calificado: Linear Regression with One Variable
Linear Algebra Review
This optional module provides a refresher on linear algebra concepts. Basic understanding of linear algebra is necessary for the rest of the course, especially as we begin to cover models with multiple variables.
6 videos, 1 reading, 1 reading
WEEK 2
Linear Regression with Multiple Variables
What if your input has more than one value? In this module, we show how linear regression can be extended to accommodate multiple input features. We also discuss best practices for implementing linear regression.
8 videos, 16 readings
Calificado: Linear Regression with Multiple Variables
Octave/Matlab Tutorial
This course includes programming assignments designed to help you understand how to implement the learning algorithms in practice. To complete the programming assignments, you will need to use Octave or MATLAB. This module introduces Octave/Matlab and shows yo...
6 videos, 1 reading
Calificado: Octave/Matlab Tutorial
WEEK 3
Logistic Regression
Logistic regression is a method for classifying data into discrete outcomes. For example, we might use logistic regression to classify an email as spam or not spam. In this module, we introduce the notion of classification, the cost function for logistic regr...
7 videos, 8 readings
Calificado: Logistic Regression
Regularization
Machine learning models need to generalize well to new examples that the model has not seen in practice. In this module, we introduce regularization, which helps prevent models from overfitting the training data.
4 videos, 5 readings
Calificado: Regularization
WEEK 4
Neural Networks: Representation
Neural networks is a model inspired by how the brain works. It is widely used today in many applications: when your phone interprets and understand your voice commands, it is likely that a neural network is helping to understand your speech; when you cash a ch...
7 videos, 6 readings
Calificado: Neural Networks: Representation
WEEK 5
Neural Networks: Learning
In this module, we introduce the backpropagation algorithm that is used to help learn parameters for a neural network. At the end of this module, you will be implementing your own neural network for digit recognition.
8 videos, 8 readings
Calificado: Neural Networks: Learning
WEEK 6
Advice for Applying Machine Learning
Applying machine learning in practice is not always straightforward. In this module, we share best practices for applying machine learning in practice, and discuss the best ways to evaluate performance of the learned models.
7 videos, 7 readings
Calificado: Advice for Applying Machine Learning
Machine Learning System Design
To optimize a machine learning algorithm, you'll need to first understand where the biggest improvements can be made. In this module, we discuss how to understand the performance of a machine learning system with multiple parts, and also how to deal with skewe...
5 videos, 3 readings
Calificado: Machine Learning System Design
WEEK 7
Support Vector Machines
Support vector machines, or SVMs, is a machine learning algorithm for classification. We introduce the idea and intuitions behind SVMs and discuss how to use it in practice.
6 videos, 1 reading
Calificado: Support Vector Machines
WEEK 8
Unsupervised Learning
We use unsupervised learning to build models that help us understand our data better. We discuss the k-Means algorithm for clustering that enable us to learn groupings of unlabeled data points.
5 videos, 1 reading
Calificado: Unsupervised Learning
Dimensionality Reduction
In this module, we introduce Principal Components Analysis, and show how it can be used for data compression to speed up learning algorithms as well as for visualizations of complex datasets.
7 videos, 1 reading
Calificado: Principal Component Analysis
WEEK 9
Anomaly Detection
Given a large number of data points, we may sometimes want to figure out which ones vary significantly from the average. For example, in manufacturing, we may want to detect defects or anomalies. We show how a dataset can be modeled using a Gaussian distributi...
8 videos, 1 reading
Calificado: Anomaly Detection
Recommender Systems
When you buy a product online, most websites automatically recommend other products that you may like. Recommender systems look at patterns of activities between different users and different products to produce these recommendations. In this module, we introd...
6 videos, 1 reading
Calificado: Recommender Systems
WEEK 10
Large Scale Machine Learning
Machine learning works best when there is an abundance of data to leverage for training. In this module, we discuss how to apply the machine learning algorithms with large datasets.
6 videos, 1 reading
Calificado: Large Scale Machine Learning
WEEK 11
Application Example: Photo OCR
Identifying and recognizing objects, words, and digits in an image is a challenging task. We discuss how a pipeline can be built to tackle this problem and how to analyze and improve the performance of such a system.
Calificaciones y revisiones
Calificado 4.9 de 5 31,240 calificaciones
GS
This course is fantastic . It gives insights into various machine learning techniques its applications and implementation. Thoroughly enjoyed the course
马
完美的课程,深入浅出,对我的各个方面都有提升吗,很有意义的学习体验!
UP
The course is very interesting. The explanations are clear, exercises are very useful to apply and understand better what is explained in the class. I really recommend this course to anybody who wants a good introduction to machine learning. | 677.169 | 1 |
Algebra: Solving Linear Equations - Part 2: Applications (Sample 1)
[NOTE: This video is only the first 20 minutes of the full lesson] This lesson consists of providing you with a Self-Tutorial on how to solve typical linear word problems (story problems or applied problems). The tutor shows you how to solve for a specific variable in formulas. He also discusses how to covert a repeating decimal into a fraction (which was skipped in Basic Math: Lesson 6 -"Fractions") and will teach you how to convert units of measurement. | 677.169 | 1 |
<P>Accessible to all students with a sound background in high school mathematics, <STRONG>A Concise Introduction to Pure Mathematics, Fourth Edition</STRONG> presents some of the most fundamental and beautiful ideas in pure mathematics. It ...
ISBN: 9781498722933
Binding: Kobo eBook
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<P>Accessible to all students with a sound background in high school mathematics, <STRONG>A Concise Introduction to Pure Mathematics, Third Edition</STRONG> presents some of the most fundamental and beautiful ideas in pure mathematics. It covers
ISBN: 9781439888926
Binding: Kobo eBook
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$86.50
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<P><STRONG>Algebra & Geometry: An Introduction to University Mathematics</STRONG> provides a bridge between high school and undergraduate mathematics courses on algebra and geometry. The author shows students how mathematics is more than a ...
ISBN: 9781482246490
Binding: Kobo eBook
eBook
$86.37
$77.79
P>Fuzzy social choice theory is useful for modeling the uncertainty and imprecision prevalent in social life yet it has been scarcely applied and studied in the social sciences. Filling this gap, <STRONG>Application of Fuzzy Logic to Social ...
ISBN: 9781482250992
Binding: Kobo eBook
eBook
$157.33
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The development of the theory of fuzzy sets was motivated largely by the need for a computational framework for dealing with systems in which human judgement, behavior and emotions play a dominant role. Although there are very few papers on ...
ISBN: 9781483294360
Binding: Kobo eBook
eBook
$97.01
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This book lays the foundations for an exciting new area of research in descriptive set theory. It develops a robust connection between two active topics: forcing and analytic equivalence relations. This in turn allows the authors to develop a ...
ISBN: 9781107424234
Binding: Kobo eBook
eBook
$73.00
$62.09
<P>Combinatory logic is one of the most versatile areas within logic that is tied to parts of philosophical, mathematical, and computational logic. Functioning as a comprehensive source for current developments of combinatory logic, this book is
ISBN: 9781439800010
Binding: Kobo eBook
eBook
$166.16
$132.99
<P>This book provides a one-semester undergraduate introduction to counterexamples in calculus and analysis. It helps engineering, natural sciences, and mathematics students tackle commonly made erroneous conjectures. The book encourages ...
ISBN: 9781482246681
Binding: Kobo eBook
eBook
$91.75
$73.39
<P>For many years, this classroom-tested, best-selling text has guided mathematics students to more advanced studies in topology, abstract algebra, and real analysis. <STRONG>Elements of Advanced Mathematics, Third Edition</STRONG> retains the ...
ISBN: 9781439898352
Binding: Kobo eBook
eBook
$134.24
$107.39
Ordered sets are ubiquitous in mathematics and have significant applications in computer science, statistics, biology and the social sciences. As the first book to deal exclusively with finite ordered sets, this book will be welcomed by graduate
ISBN: 9781107086777
Binding: Kobo eBook
eBook
$91.00
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<P>Applicable to any problem that requires a finite number of solutions, finite state-based models (also called finite state machines or finite state automata) have found wide use in various areas of computer science and engineering. ...
ISBN: 9781439846193
Binding: Kobo eBook
eBook
$79.79
$63.89
Successful development of effective computational systems is a challenge for IT developers across sectors due to uncertainty issues that are inherently present within computational problems. Soft computing proposes one such solution to the ...
ISBN: 9781466698000
Binding: Kobo eBook
eBook
$498.67
$448.89
This Handbook is an introduction to set-theoretic topology for students in the field and for researchers in other areas for whom results in set-theoretic topology may be relevant. The aim of the editors has been to make it as self-contained as ...
ISBN: 9781483295152
Binding: Kobo eBook
eBook
$306.52
$245.29
Intermediate Logic is an ideal text for anyone who has taken a first course in logic and is progressing to further study. It examines logical theory, rather than the applications of logic, and does not assume any specific technical grounding. ...
ISBN: 9780191037221
Binding: Kobo eBook
eBook
$66.48
$59.89
Introduction to Fuzzy Systems provides students with a self-contained introduction that requires no preliminary knowledge of fuzzy mathematics and fuzzy control systems theory. Simplified and readily accessible, it encourages both classroom and ...
$107.49
<P><STRONG>Introduction to Mathematical Proofs</STRONG> helps students develop the necessary skills to write clear, correct, and concise proofs.</P> <P>Unlike similar textbooks, this one begins with logic since it is the underlying language of ... | 677.169 | 1 |
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Modular Math
Modular Math is an accelerated study of mathematics. These courses provide students
with the opportunity to progress through multiple developmental math courses in one
semester.
There are modular sections of math available to students who are enrolling in Math
20, Math 40 or Math 110. Students enrolled in these courses will work at their own
pace with the aid of ALEKS software, e-books, and a math instructor present at each
class session.
How does it work?
In this class, students will have the opportunity to advance through as many levels
of algebra as they can master in one be given an assessment using the computer software
ALEKS. Upon completion of the assessment, ALEKS will indicate which learning objectives
have already been mastered and those which need to be completed and the student will
be given an individualized study plan. After the assessment, a student will begin
working on the areas that have not yet been mastered. Students may work at their own
pace. Study plans with suggested dates are discussed with the instructor on an individual
basis. A student may work faster or slower depending on their own approach. After
completion of the assigned units, students will test over that material. There will
be periodic tests and a comprehensive final exam in each math class. If a student
completes the requirements for the course they are enrolled in before the end of the
semester, that student will be given the opportunity to proceed to the next course
in the developmental sequence. (I.e. completion of Math 40, start of Math 110 or completion
of Math 20, start of Math 40) Students can complete as many levels of math as they
can master during one semester. All modular math courses are taught in a "hybrid"
fashion. This means half time in the classroom and half time completed by the student
away from class.
Who will benefit from it?
Self motivated students wishing to devote themselves to the math curriculum so that
they may finish more than one level of math during a semester
Students who may have been away from Math for a while and may need only to review
portions of a particular class curriculum to become proficient
Students who can be successful at self study (one on one tutoring from the instructor
is available during class sessions)
Student with minimum of 7-8 hours outside of the classroom to devote to course work
close window
Modular Math Courses
Summer 2015Fall 2015Spring 2016
Accelerated English
Accelerated English 30 is a 3-credit course designed to help students understand and
more effectively use the conventions of Standard American English and to write focused,
adequately supported, and mechanically sound paragraphs and essays.
This specialized course is designed to provide motivated students the opportunity
to progress through both English 30 and English 101 in a single semester. Students,
therefore, must be enrolled in both Accelerated English 30 and English 101 at the
same time.
How does it work?
First, it is best to understand that Accelerated English 30 is not a remedial writing
course. It differs from a regular English 30 course in the following several ways:
1. The class is coupled with an English 101 course and the student will be completing
all the assignments of the English 101 class; 2. The class size is smaller and more
intimate; 3. The course can be structured to meet the writing needs of individual
students; 4. More time is allotted for revision—either individually or through peer
review sessions/writers' workshops; 5. More time is available for student/instructor
conferences.
Who might most benefit from Accelerated English 30?
Students who are self-disciplined and motivated tend to be most successful. The course
requires attention to detail in one's writing as well as participation in significant
revision activities. Ideal candidates for this course will be prepared to engage in
an in-depth inquiry into their own writing and thinking. For more information, students
are encouraged to contact the instructors listed below.
close window
Accelerated English Courses
Summer 2015Fall 2015Spring 2016
Service Learning Courses
Service-learning is a form of experiential learning that aims to build knowledge,
character, and civic skills in students by combining service to the local and/or global
community with academic learning.
By directly linking service to the academic curriculum, service-learning creates a
place for service that is integrated into a school's core mission: education. By requiring
student reflection as part of the process, the course content and service experience
are connected. (Derived from: Students in Service to America: A Guidebook for Engaging
America's Students in a Lifelong Habit of Service.) | 677.169 | 1 |
The fascinating world of graph theory goes back several centuries and revolves around the study of graphs-mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics-and some of its most famous problems. For example, what is the shortest route for a traveling salesman seeking to visit a number of cities in one trip? What is the least number of colors needed to fill in any map so that neighboring regions are always colored differently? Requiring readers to have a math background only up to high school algebra, this book explores the questions and puzzles that have been studied, and often solved, through graph theory. In doing so, the book looks at graph theory's development and the vibrant individuals responsible for the field's growth. Introducing graph theory's fundamental concepts, the authors explore a diverse plethora of classic problems such as the Lights Out Puzzle, the Minimum Spanning Tree Problem, the Konigsberg Bridge Problem, the Chinese Postman Problem, a Knight's Tour, and the Road Coloring Problem. They present every type of graph imaginable, such as bipartite graphs, Eulerian graphs, the Petersen graph, and trees. Each chapter contains math exercises and problems for readers to savor. An eye-opening journey into the world of graphs, this book offers exciting problem-solving possibilities for mathematics and beyond.
" The Fascinating World of Graph Theory is readable and 'student-friendly'--more so than the typical math textbook . . ." --Robert Schaefer, New York Journal of Books
"[The authors] have set out to make graph theory not only accessible to people with a limited mathematics background, but also to make it interesting. They have--by virtue of very clear writing, combined with a greater-than-usual emphasis on the historical and personal side of the subject--succeeded admirably." --Mark Hunacek, MAA Reviews
"The book is written masterfully; the narrative in each chapter flows naturally, engagingly. . . . [I]t's a popular but also comprehensive introduction into graph theory." --Alexander Bogomolny, Cut the Knot blog
L'autore:
Arthur Benjamin is professor of mathematics at Harvey Mudd College. His books include Secrets of Mental Math and Proofs That Really Count. Gary Chartrand is professor emeritus of mathematics at Western Michigan University. Ping Zhang is professor of mathematics at Western Michigan University. Chartrand and Zhang are the coauthors of several books, including A First Course in Graph Theory and Discrete Mathematics. | 677.169 | 1 |
Saxon Math Course 2 Teacher Manual Volume 2
Saxon Math Courses 1, 2, and 3 integrate and distribute traditional units, giving students time to learn and practice skills throughout the year, master content, and develop algebraic thinking for mastery of the Common Core State Standards | 677.169 | 1 |
Books Similar to :
Business Mathematics
Book Summary of Business Mathematics
Paper Back
Description Business Mathematics focuses on transforming learning andteaching math into its simplest form by adopting "learning byapplication" approach. The book is refreshingly different in itsapproach, and endeavors to motivate student to learn the conceptand apply them in real-life situations. It is purposely designedfor the undergraduate students of management and commerce andcovers wide range of syllabuses of different universities offeringthis course.
Each topic explained in the simplest manner with the help of step-by-step illustration and solved example.
Chapters include:
More than 900 solved problems
More than 2300 unsolved problems
Graphical presentations and figures to support argument, reinforce logic and to boost up visual memory.
Similar concepts and chapters grouped together to ensure clarity in understanding.
Surds
Indices and Logarithm
Quadratic Equation
Complex numbers
Set, Relations and Function
Profit?Loss, Discount, Commission and Brokerage
Simple Interest, Average Due Dates and Rebate on Bills Discounted
Compound Interest and Depression
Annuity
Limit and Continuity
Different Calculus (Derivative)
Integral Calculus (Indefinite and Definite Integration)
Application of Calculus
Point
Straight Line
Straight lines
Circle
Parabola
Ellipse
Hyperbola
Determination
Matrix Algebra
Permutation?Combination
Binominal Expansion
Principle of Mathematical Induction
Sequence and Series
Mr. Kashyap Trivedi is a senior professor at ArihantInstitute Private Ltd, Ahmedabad and visiting faculty to some otherinstitutes. Dr Chirag Trivedi teaches at R.J.Tibrewal Commerce College, University of Gujarat, Ahmedabad
Details Of Book :
Business Mathematics
Book:
Business Mathematics
Author:
Kashyap TrivediChirag Trivedi
ISBN:
8131732185
ISBN-13:
9788131732182
Binding:
Paper Back
Publishing Date:
2011
Publisher:
Pearson Education Limited
Number of Pages:
728 | 677.169 | 1 |
Interactive
Info
Functions - Grade 8 - 8.F.A.1 | Tennessee Department of Education
Help students understand that a function is a rule that assigns exactly one output to each input. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. This interactive outlines Common Core State Standard 8.F.A.1 | 677.169 | 1 |
Introduction to Vector Addition and Scalar Multiplication
In the strictly mathematical definition of a vector, the only operations
that vectors are required to possess are those of addition and scalar
multiplication. (Compare this with the operations allowed on ordinary real
numbers, or scalars, in which we are given addition, subtraction,
multiplication, and division). For instance, in a raw vector space there is no
obvious way to multiply two vectors together to get a third vector--even though
we will define a couple of ways of performing vector multiplication in
Vector Multiplication.
It makes sense, then, to begin studying vectors with an investigation of the
operations of vector addition and scalar multiplication. This section will be
entirely devoted to explaining addition and scalar multiplication of two- and
three-dimensional vectors. This explanation will involve two different, yet
equivalent, methods: the component
method and the graphical
method. | 677.169 | 1 |
<P>A Concise Introduction to Languages, Machines and Logic provides an accessible introduction to three key topics within computer science: formal languages, abstract machines and formal logic. Written in an easy-to-read, informal style, this ...
ISBN: 9781848001213
Binding: Kobo eBook
eBook
$39.92
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Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of ...
ISBN: 9781139636568
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$96.00
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This monograph focuses on the numerical methods needed in the context of developing a reliable simulation tool to promote the use of renewable energy. One very promising source of energy is the heat stored in the Earth's crust, which is ...
ISBN: 9783319170794
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$111.16
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<p>This is the first work on Discrepancy Theory to show the present variety of points of view and applications covering the areas Classical and Geometric Discrepancy Theory, Combinatorial Discrepancy Theory and Applications and Constructions. ...
ISBN: 9783319046969
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$118.57
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<P>Linear models courses are often presented as either theoretical or applied. Consequently, students may find themselves either proving theorems or using high-level procedures like PROC GLM to analyze data. There exists a gap between the ...
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The main purpose of this book is to provide a simple and accessible introduction to the mixed finite element method as a fundamental tool to numerically solve a wide class of boundary value problems arising in physics and engineering sciences. ...
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<p>This volume contains contributions from the Gulf International Conference in Applied Mathematics, held at the Gulf University for Science & Technology. The proceedings reflects the three major themes of the conference. The first of these was ...
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This book gathers selected contributions on emerging research work presented at the International Conference eXtended Discretization MethodS (X-DMS), held in Ferrara in September 2015. It highlights the most relevant advances made at the ...
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This book focuses on the approximation of nonlinear equations using iterative methods. Nine contributions are presented on the construction and analysis of these methods, the coverage encompassing convergence, efficiency, robustness, dynamics, ...
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Current research results in stochastic and deterministic global optimization including single and multiple objectives are explored and presented in this book by leading specialists from various fields. Contributions include applications to ...
ISBN: 9783319299754
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<p>This edited monograph provides a compelling analysis of the interplay between neuroscience and aesthetics. The book broaches a wide spectrum of topics including, but not limited to, mathematics and creator algorithms, neurosciences of ...
ISBN: 9783319462332
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<p>This book gives an overview of affine diffusions, from Ornstein-Uhlenbeck processes to Wishart processes and it considers some related diffusions such as Wright-Fisher processes. It focuses on different simulation schemes for these processes,
ISBN: 9783319052212
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<p>Algorithms play an increasingly important role in nearly all fields of mathematics. This book allows readers to develop basic mathematical abilities, in particular those concerning the design and analysis of algorithms as well as their ...
ISBN: 9783319395586
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Taken literally, the title "All of Statistics" is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who ...
ISBN: 9780387217369
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Examining the basic principles in real analysis and their applications, this text provides a self-contained resource for graduate and advanced undergraduate courses. It contains independent chapters aimed at various fields of ...
ISBN: 9783319124810
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<p>This book introduces a variety of neural network methods for solving differential equations arising in science and engineering. The emphasis is placed on a deep understanding of the neural network techniques, which has been presented in a ...
ISBN: 9789401798167
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Numerical analysis provides the theoretical foundation for the numerical algorithms we rely on to solve a multitude of computational problems in science. Based on a successful course at Oxford University, this book covers a wide range of such ...
ISBN: 9781139636902
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<p>Developed during ten years of teaching experience, this book serves as a set of lecture notes for an introductory course on numerical computation, at the senior undergraduate level. These notes contain the material that can be covered in a ...
ISBN: 9789814730099
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This is the first comprehensive introduction to the powerful moment approach for solving global optimization problems (and some related problems) described by polynomials (and even semi-algebraic functions). In particular, the author explains ...
ISBN: 9781316234723
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This is the second, completely revised and expanded edition of the author's first book, covering numerous new topics and recent developments in ultrametric summability theory. Ultrametric analysis has emerged as an important branch of ... | 677.169 | 1 |
gives an introduction to functional analysis for graduate students pursuing research involving numerical analysis. The text covers basic results of functional analysis as well as additional topics needed in theoretical numerical analysis.
This outstanding text by two well-known authors treats numerical analysis with mathematical rigor, but presents relatively few theorems and proofs. Oriented toward computer solutions of problems, it stresses errors in methods and computational efficiency, and it compares different solutions to the same problem.
This introductory book directs the reader to a selection of useful elementary numerical algorithms on a reasonably sound theoretical basis, built up within the text. The primary aim is to develop algorithmic thinking-emphasizing long-living computational concepts over fast changing software issues.
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. | 677.169 | 1 |
Saturday, 3 September 2016
CBSE Class 11 Syllabus
CBSE Class 11 Syllabus 2017: Check out the new changes made in CBSE Class 11 Syllabus this year. Students who are studying in CBSE Class 11 they can check CBSE Class 11 Exam Syllabus for Commerce, Arts & Science Stream from this page. Here on this page you can find Exam Syllabus subject wise as English, Math, Physics etc and course structure in Detail. Central board Secondary education conducts Class 11 exams every year and no. of contenders appears in it. So, all contestants who are preparing for Class 11th exams they can get the CBSE Class 11 Syllabus PDF and CBSE Class 11 Exam Pattern in detail from below section.
CBSE Class 11 Syllabus
Sets and their representations. Empty set. Finite and Infinite sets. Equal sets. Subsets. Subsets of a set of real numbers especially intervals (with notations). Power set. Universal set. Venn diagrams. Union and Intersection of sets. Difference of sets. Complement of a set. Properties of Complement Sets. Practical Problems based on sets.
2. Relations & Functions
Ordered pairs, Cartesian product of sets. Number of elements in the cartesian product of two finite sets. Cartesian product of the sets of real (upto R x R). Definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Function as a special kind of relation from one set to another. Pictorial representation of a function, domain, co-domain and range of a function. Real valued functions, domain and range of these functions: constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic and greatest integer functions, with their graphs. Sum, difference, product and quotients of functions.
3. Trigonometric Functions
Positive and negative angles. Measuring angles in radians and in degrees and conversion of one into other. Definition of trigonometric functions with the help of unit circle. Truth of the sin2x+cos2x=1, for all x. Signs of trigonometric functions. Domain and range of trignometric functions and their graphs. Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple application.
Unit-II: Algebra
1. Principle of Mathematical Induction
Process of the proof by induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers. The principle of mathematical induction and simple applications.
2. Complex Numbers and Quadratic Equations
Need for complex numbers, especially √1, to be motivated by inability to solve some of the quardratic equations. Algebraic properties of complex numbers. Argand plane and polar representation of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex number system. Square root of a complex number.
3. Linear Inequalities
Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables. Graphical solution of system of linear inequalities in two variables.
History, statement and proof of the binomial theorem for positive integral indices. Pascal's triangle, General and middle term in binomial expansion, simple applications.
6. Sequence and Series
Sequence and Series. Arithmetic Progression (A.P.). Arithmetic Mean (A.M.) Geometric Progression (G.P.), general term of a G.P., sum of n terms of a G.P., Arithmetic and Geometric series infinite G.P. and its sum, geometric mean (G.M.), relation between A.M. and G.M.
Unit-III: Coordinate Geometry
1. Straight Lines
Brief recall of two dimensional geometry from earlier classes Shifting of origin. Slope of a line and angle between two lines. Various forms of equations of a line: parallel to axis, point-slope form, slope-intercept form, two-point form, intercept form and normal form. General equation of a line. Equation of family of lines passing through the point of intersection of two lines. Distance of a point from a line.
2. Conic Sections
Sections of a cone: circles, ellipse, parabola, hyperbola; a point, a straight line and a pair of intersecting lines as a degenerated case of a conic section. Standard equations and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle.
3. Introduction to Three–dimensional Geometry
Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula.
Unit-IV: Calculus
1. Limits and Derivatives
Derivative introduced as rate of change both as that of distance function and geometrically. Intutive idea of limit. Limits of polynomials and rational functions, trignometric, exponential and logarithmic functions. Definition of derivative, relate it to slope of tangent of a curve, derivative of sum, difference, product and quotient of functions. The derivative of polynomial and trignometric functions.
Unit-VI: Statistics and Probability
1. Statistics
Measures of dispersion; Range, mean deviation, variance and standard deviation of ungrouped/grouped data. Analysis of frequency distributions with equal means but different variances. | 677.169 | 1 |
Learning SciPy for Numerical and Scientific Computing
Book Description
For solving complex problems in mathematics, science, or engineering, SciPy is the solution. Building on your basic knowledge of Python, and using a wealth of examples from many scientific fields, this book is your expert tutor.
Perform complex operations with large matrices, including eigenvalue problems, matrix decompositions, or solution to large systems of equations
Step-by-step examples to easily implement statistical analysis and data mining that rivals in performance any of the costly specialized software suites
Plenty of examples of state-of-the-art research problems from all disciplines of science, that prove how simple, yet effective, is to provide solutions based on SciPy
In Detail
It's essential to incorporate workflow data and code from various sources in order to create fast and effective algorithms to solve complex problems in science and engineering. Data is coming at us faster, dirtier, and at an ever increasing rate. There is no need to employ difficult-to-maintain code, or expensive mathematical engines to solve your numerical computations anymore. SciPy guarantees fast, accurate, and easy-to-code solutions to your numerical and scientific computing applications.
"Learning SciPy for Numerical and Scientific Computing" unveils secrets to some of the most critical mathematical and scientific computing problems and will play an instrumental role in supporting your research. The book will teach you how to quickly and efficiently use different modules and routines from the SciPy library to cover the vast scope of numerical mathematics with its simplistic practical approach that's easy to follow.
The book starts with a brief description of the SciPy libraries, showing practical demonstrations for acquiring and installing them on your system. This is followed by the second chapter which is a fun and fast-paced primer to array creation, manipulation, and problem-solving based on these techniques.
The rest of the chapters describe the use of all different modules and routines from the SciPy libraries, through the scope of different branches of numerical mathematics. Each big field is represented: numerical analysis, linear algebra, statistics, signal processing, and computational geometry. And for each of these fields all possibilities are illustrated with clear syntax, and plenty of examples. The book then presents combinations of all these techniques to the solution of research problems in real-life scenarios for different sciences or engineering — from image compression, biological classification of species, control theory, design of wings, to structural analysis of oxides. | 677.169 | 1 |
Quadratic Equations Project (with FREE printables!)
One of the best ways to really learn something so that it sticks with you is to teach it to someone else. Giving students a project that gets them thinking through a mathematical process and allows them to express their creative side is always a win-win! The following example involves solving quadratic equations. A skill in Algebra that, while important, can very easily become boring and meaningless. And while I believe it is always helpful for students to have multiple options and methods to use for solving problems, I have seen that it can become easy for them to confuse and mix together different strategies.
This project attempts to help students look at multiple approaches to solving quadratic equations, helping them to study for a test, better understand what all the pieces are and how they fit together, as well as internalize the information by learning it well enough to explain to someone else.
I used the R.A.F.T approach, which stands for Role, Audience, Format, Topic. This is a quick and helpful way to bring focus to a project on virtually any topic. This specific project uses the role of Mathematician (the student), an audience of Algebra students, a "How To" book as the format and (obviously) quadratic equations as the topic of interest. The object, then, of your students is to design a clear and concise "how to" book of explanations for solving quadratic equations. Even though I usually only taught 2 or 3 methods for solving during our classroom instruction, I required students to include 4 or 5 methods in their booklet. This required them to do some research on their own, and compare other methods to what they already knew.
Included in the download below are some tips for using this in your class, an explanation handout for your students and a sample grading rubric. If you prefer different requirements, feel free to use your own rubric, or you can use the one I have included.
And remember, the R.A.F.T. model is easily adapted to use with other topics or formats, so if you would like your students to explore some other math topic in greater depth, simply create your own! Or, give them a few different formats to choose from (just be sure to give clear guidelines for your expectations for each). | 677.169 | 1 |
The Bittinger Graphs and Models Series helps readers learn algebra by making connections between mathematical concepts and their real-world applications. Abundant applications, many of which use real data, offer students a context for learning the math.
There has been an increasing interest in multi-disciplinary research on multisensor attitude estimation technology driven by its versatility and diverse areas of application, such as sensor networks, robotics, navigation, video, biomedicine, etc. | 677.169 | 1 |
PDF (Acrobat) Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
6.69 MB | 82 pages
PRODUCT DESCRIPTION
Use task-based learning to keep your students engaged! They will stay focused simply because the material is so interesting.
This unit provides Secondary Math One students with a complete and thorough understanding of what an inequality represents, including inequalities in the abstract (with variables). This unit will teach students how to write, solve, and graph inequalities, including systems of inequalities and inequalities in context.
This bundle includes:
*Developing Tasks with complete keys and teacher notes
*Solidifying Notes with complete keys and teacher notes
*Activities to help students practice the concepts
*Homework and Worksheets with complete keys
*Assessments with complete keys and rubrics | 677.169 | 1 |
Bundle: Introductory Algebra, 4th + Student Solutions Manual
Algebra can be like a foreign language. But one text delivers an interpretation you can fully understand. Building a conceptual foundation in the "language of algebra," INTRODUCTORY ALGEBRA, Fourth Edition, provides an integrated learning process that helps you expand your reasoning abilities as it teaches you how to read, write, and think mathematically. Packed with real-life applications of math, it blends instructional approaches that include vocabulary, practice, and well-defined pedagogy with an emphasis on reasoning, modeling, communication, and technology skills. The authors' five-step problem-solving approach makes learning easy. More student-friendly than ever, the text offers a rich collection of student learning tools, including the Enhanced WebAssign online learning system. With INTRODUCTORY ALGEBRA, Fourth Edition, algebra makes sense! | 677.169 | 1 |
The Barnett, Ziegler, Byleen College Algebra/Precalculus series is designed to be user friendly and to maximize student comprehension. The goal of this series is to emphasize computational skills, ideas, and problem solving rather than mathematical theory. Precalculus, 5/e, introduces a unit circle approach to trigonometry and can be used in one or two semester college algebra with trigonometry or precalculus courses. The large number of pedagogical devices employed in this text will guide a student through the course. Integrated throughout the text, the students and instructors will find Explore-Discuss boxes which encourage students to think critically about mathematical concepts. In each section, the worked examples are followed by matched problems that reinforce the concept that is being taught. In addition, the text contains an abundance of exercises and applications that will convince students that math is useful. A Smart CD is packaged with the seventh edition of the book. The CD tutorial reinforces important concepts, and provides students with extra practice problems.
"synopsis" may belong to another edition of this title.
Book Description:
Mathematical reform is the driving force behind the organization and development of this new precalculus text. The use of technology, primarily graphing utilities, is assumed throughout the text. The development of each topic proceeds from the concrete to the abstract and takes full advantage of technology, wherever appropriate. The first major objective of this book is to encourage students to investigate mathematical ideas and processes graphically and numerically, as well as algebraically. Proceeding in this way, students gain a broader, deeper, and more useful understanding of a concept or process. Even though concept development and technology are emphasized, manipulative skills are not ignored, and plenty of opportunities to practice basic skills are present. A brief look at the table of contents will reveal the importance of the function concept as a unifying theme. The second major objective of this book is the development of a library of elementary functions, including their important properties and uses. Having this library of elementary functions as a basic working tool in their mathematical tool boxes, students will be able to move into calculus with greater confidence and understanding. In addition, a concise review of basic algebraic concepts is included in Appendix A for easy reference, or systematic review. The third major objective of this book is to give the student substantial experience in solving and modeling real world problems. Enough applications are included to convince even the most skeptical student that mathematics is really useful. Most of the applications are simplified versions of actual real-world problems taken from professional journals and professional books. No specialized experience is required to solve any of the applications | 677.169 | 1 |
6
Calculations of dot product and cross product of vectors Calculations of dot product and cross product of vectors
7
Special definition of matrix elements as a function of row-column number M i,j =f(i,j) Special definition of matrix elements as a function of row-column number M i,j =f(i,j) –E.g. Value of element is equal to product of column and row number MathCAD – vectors and matrix Constrain: function arguments have to be integer
24
The system of linear equations The system of linear equations –Solving on the base of matrix toolbar: »Prepare square matrix of equations coefficients (A) and vector of free terms (B) »Do the operation x:=A -1 B and show result: x= Or »Use the procedure LSOLVE: lsolve(A,B)= MathCAD, the system of equations solving
26
The system of nonlinear equation The system of nonlinear equation –Can be solved using given-find method »Assign starting values to variables »Type Given »Type the equations using = sign (bold) »Type Find(var1, var2,...)= MathCAD, the system of equations solving
29
Ordinary differential equations solving Numerical methods principle Numerical methods principle –Calculation involve bounded range of independent variable only –Every point is being calculated on the base of one or few points calculated before or given starting points. –Independent variable is calculated using step: x i+1 = x i + h = x i + x –Dependent value is calculated according to the method y i+1 = y i + y= y i +K i
30
Ordinary differential equations solving Runge-Kutta 4 th order method principles: Runge-Kutta 4 th order method principles: –New point of the integral is calculated on the base of one point (given/calculated earlier) and 4 intermediate values
34
System of first order differential equations System of first order differential equations 1.Assign the vector of initial conditions of dependent variables (starting vector) 2.Define the vector function of derivatives (right-hand sides of equations) 3.Assign to the variable function rkfixed: R:=rkfixed(init_vect, low_bound, up_bound, num_seg, function) MathCAD differential equations
37
Single second order equation Single second order equation 1.Transform the second order equation to the system of two first order equations: Initial condition MathCAD differential equations
38
Example: Example: Solve the second order differential equation (calculate: values of function and its first derivatives) given by equation: While y=10 and y=-1 for x=0 In the range of x= In the range of x= | 677.169 | 1 |
Product Description:
Williams offers a refreshing and innovative approach to college algebra, motivating the topics with a variety of applications and thoroughly integrating the graphing calculator. Written in a clear and friendly voice that speaks to students with weak algebra skills, this text teaches students to look at math from both algebraic and geometric viewpoints. Williams focuses on the underlying concepts, introducing and using the graphing calculator as an integral means, not an end. New applications examples and exercises from a variety of fields motivate the key ideas and show students why math is useful and powerful. Packaged free with every new copy of the text, an ELECTRONIC COMPANION TO COLLEGE ALGEBRA CD-ROM is a dynamic and interactive college algebra tutorial. It covers key concepts through multiple representations: graphic, numerical, algebraic, and verbal. "Review Topics" boxes present the main ideas of the course and "Test Yourself" problems test student understanding. A workbook of additional examples and exercises is built into the CD-ROM.
REVIEWS for Applied College Algebra | 677.169 | 1 |
We are here for Bliss. Lifes very purpose is for each and everyone to be Blissful. When we are Blissful the entire creation is dancing with us. Life becomes a great song. We act for the care and love for all.The Natural Calculator is an elementary book on mental mathematics. Each of the nine chapters covers one of the Vedic Mathematics formulae. The main theme is mental multiplication but addition, subtraction and division are also included. Indian Mathematics belongs not only to an hoary antiquity but is a living discipline with a potential for manifold modern applications. Vedic Mathematics was rediscovered from ancient Sanskrit texts earlier this century by Bharati Krsna Tirthaji (1884-1960....Three Volumes with CD's which...
This Manual is the secondThis Manual is the first...
This Manual is the second of three (elementary, intermediate and advanced) ManualsThe set consists of 3 books....
Vedic Mathematics for School offers a fresh and easy approach to learning mathematics. The system was reconstructed from ancient Vedic sources by the late Bharati Krsna Tirthaji earlier this century and is based on a small collection of sutras. Each sutra briefly encapsulates a rule of mental working, a principle or guiding maxim. Through simple practice of these methods all may become adept and efficient at mathematics. Book I of the series is intended for primary schools in which many of the...
Vedic Mathematics for Schools, Book 2 is intended as a first year textbook for senior schools or for children aiming for examination at 11+. It is based on the fundamental principles of Vedic mathematics which were reconstructed earlier this century by Sri Sankaracarya Bharati Krsna Tirthaji. Although the sutras may well be very ancient, practice and experience have shown that they are highly relevant and useful to the modern-day teaching of mathematics. They are entirely applicable to modern... | 677.169 | 1 |
Number Theory: An Introduction to Mathematics
Paperback | August 12, 2009 first course on the subject. Part B delves into more advanced topics and an exploration of related mathematics. Part B contains, for example, complete proofs of the Hasse-Minkowski theorem and the prime number theorem, as well as self-contained accounts of the character theory of finite groups and the theory of elliptic functions.The prerequisites for this self-contained text are elements from linear algebra. Valuable references for the reader are collected at the end of each chapter. It is suitable as an introduction to higher level mathematics for undergraduates, or for self-study. From the reviews:"This is a book which many mathematicians could enjoy browsing, and one which a good undergraduate could be encouraged to read to learn something of the interconnections, which exist between apparently disparate parts of mathematics."--Canadian Mathematical Society"As a source for information on the 'reach' of number theory into other areas of mathematics, it is an excellent work."--Mathematical Association of America
Pricing and Purchase Info f...
From the Jacket
"Number Theory" is more than a comprehensive treatment of the subject. It is an introduction to topics in higher level mathematics, and unique in its scope; topics from analysis, modern algebra, and discrete mathematics are all included. The book is divided into two parts. Part A covers key concepts of number theory and could serve.- The Expanding Universe of Numbers.- Divisibility.- More on Divisibility.- Continued Fractions and their Uses.- Hadamard's Determinant Problem.- Hensel's P-Adic Numbers.- Notations.- Axioms.- The Arithmetic of Quadratic Forms.- The Geometry of Numbers.- The Number of Prime Numbers.- A Character Study.- Uniform Distribution and Ergodic Theory.- Elliptic Functions.- Connections with Number Theory.- Notations.- Axioms.- Index. | 677.169 | 1 |
Properties of Quadratics Digital Task Cards with GOOGLE Slides
PDF (Acrobat) Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
2.54 MB | 26 pages
PRODUCT DESCRIPTION
Properties of Quadratics Digital Task Cards with Google® Slides, Paperless and NO Prep for you.
In the this fun Teach Interactive™ activity students determine the vertex, axis of symmetry, y - intercepts, x - intercepts, maximums, minimums, concave up or down, and matching a graph of a quadratic to an equation.
The backgrounds of the slides are famous architectural landmarks who shapes are or appear to be parabolic. This activity is appropriate for Algebra 1, Algebra 2, PreCalculus, and College Algebra.
Task Cards really do work! They get the students engaged and keep them motivated to go through all of the problems, more so than a simple worksheet.
This resource includes 20 digital task cards plus a digital answer sheet. A printable answer sheet is also included should you want a blended activity. Your students can also make notes on the slides and do as many as you assign. As with other traditional task cards, students can work alone or in groups. This activity can also be used for HW or an assessment.
Detailed illustrated instructions on accessing and sharing this resource your students are included as well as the link to the product. An answer key is included.
New innovative resources which you and your students access through the free Google file sharing system, Google Drive®. Students can interact, edit, and if desired, print files from any computer or tablet. They explore math interactively whileClick on the green star next to my name to follow me and be the first hear of new, engaging resources for all of your classes.
This purchase is for one teacher only. Additional teachers must purchase their own license. You may not upload this resource to the internet in any form. If you are a coach, principal or district interested in purchasing several licenses, please contact me for a multi-user | 677.169 | 1 |
Name:
Principles of Engineering
Date:
Final Exam Practice Problems
Period:
1. An insulator has _ electrons in its valance shell.
2. In a _ circuit, there is only one path for current to flow.
3. The total resistance for the circuit pictured is _.
4. In a
CHAPTER 27
Empire and Expansion, 1890-1909
V. SINGLE-ANSWER MULTIPLE CHOICE.
Mark the one best answer for each of the following questions.
1. In his book Our Country: Its Possible Future and Its Present Crisis, the Reverend Josiah Strong
advocated America
AP Calculus AB Advice
Showing 1 to 1 of 1
Mrs. Nawrocki is an incredible teacher. She encourages collaboration unlike many other math teachers. For example, her classroom is constantly filled with the sounds of thought and understanding as opposed to the telling silence of most math rooms. This, to me, is a very important aspect of teaching
Course highlights:
I think very spatially, so when we began to evaluate the areas of functions being rotated around axes via the the washer and shell method, I began to really enjoy myself in the class. This material is so interesting! Even the most gifted of mathematicians will have pause when considering one of these integral-problems.
Hours per week:
9-11 hours
Advice for students:
Do not think you are above studying. This class will push you to your limits and require you to step out of your intellectual comfort zone. Study! | 677.169 | 1 |
Product Description:
Hailed by The American Mathematical Monthly as "a rigorous and lively introduction," this text explores a topic of perennial interest in mathematics. The author, a distinguished mathematician and formulator of the Hurewicz theorem, presents a clear and lucid treatment that emphasizes geometric methods. Topics include first-order scalar and vector equations, basic properties of linear vector equations, and two-dimensional nonlinear autonomous systems. Suitable for senior mathematics students, the text begins with an examination of differential equations of the first order in one unknown function. Subsequent chapters address systems of differential equations, linear systems of differential equations, singularities of an autonomous system, and solutions of an autonomous system in the large.
REVIEWS for Lectures on Ordinary | 677.169 | 1 |
This test includes a good mix of both mastery questions and questions that test conceptual understanding. The mastery questions are fairly straight forward. In this narrative, I am going to discuss the conceptual questions and the rationale behind them:
Question #6: This an interesting take on a traditional question. Students need to realize that allowing x to be three of the given choices would cause the relation to no longer be a function. Only one of the choices (d) will make the relation a function.
Question #7: Requires students to make meaning around a function in context. Students need to examine the inputs and outputs to find to correct series of values for the given function.
Question #13: This question asks students to build a function that could model a given situation.
Question #14: This question will assess if students understand the domain of a function as the inputs and the range as the outputs in an abstract scenario.
Question #21: This question requires students to build a linear function based on a given context.
Question #22: Students need to critique the reasoning of two students to determine who has written the correct function to transform the original function three units to the left. The students also need to explain why the student they chose is correct.
Question #23: Students will need to model a scenario graphically. Student's labels on the axes will also so whether they are understanding the relationship between the independent and dependent variable. | 677.169 | 1 |
Reviewed OER Library
Secondary Two Mathematics: An Integrated Approach
Note that this resource was reviewed during the Spring 2014 review period. The resource may or may not have been updated since the review. Check with the content creator to see if there is a more recent version available.
License
Format and Features
Common Core
Professional development
Mathematics Vision Project (MVP) provides both professional development and ancillary support material customized to the needs of the school or district and provided on site. MVP also provides regional conferences in various locations throughout the country where teachers can attend to receive professional development. See The production of answer keys and sample assessments is underway. This ancillary resource is available for purchase
Additional Information
Professional development pricing is dependent on the service contract. Contact Mathematics Vision Project team at mathematicsvisionproject@gmail.com to get more information.
Review
Background from OER Project Review Team
The Mathematics Vision Project has partnered with Utah State Office of Education on this open textbook focused on an integrated model of the Common Core State Standards. The book is designed around the Comprehensive Mathematics Instruction (CMI) model. The CMI framework is an integral part of the materials. Knowing and understanding the framework is essential to facilitation of a successful implementation and professional development with this resource is highly suggested. Both teacher and student versions are available. Additional support materials (answer keys and sample assessments) are available to teachers for a small fee. This should factor into the viewer's analysis of the review results.
Amount of work required to bring into CCSS alignment (average score): Minor (1.8)
Ideal Use/Comments
This curriculum is very good in my eyes. I like the launch/explore/discuss protocol. These are clearly outlined in the lesson plans for the instructor. They are thorough and well planned. This protocol meets the "Practice-Content Connections" with in the HSPC document section 5. The amount of practice is nicely suited for the majority of students. The CCSS instructor document is great.
Very strong in "Interpreting Functions" F-IF #1-#9. I like the linear flow and layout, very few "horizontal" dives where a student with a device could get lost. No distractions and useless added material. In unit 6.8, I like the simple connection between the factored form, x-intercepts, y-intercepts. Students have difficulty with this topic making the connections between factoring and the "information" it lends about the graph of a parabola. Well done here.
Overall, this review was very intriguing for me. I liked the curriculum and will be using some of these units in my personal class. I see a novice teacher up to a veteran teacher being comfortable in teaching this curriculum. It is very close to being textbook adoptable in my eyes. This curriculum could be used in a one to one device audience or printed and bound as a textbook. I like that it is available in "ibooks", very nice for students and teacher navigation who use iPad devices.
Challenges:
The main weakness is the lack of embedded technology and manipulatives with in the curriculum.
I am very concerned with the lack of example exercises for students. Research has demonstrated that the visual process of students "seeing" a worked exercise is critical to learning content.
Need for continued scrolling through past lessons if a student is using a device.
The lack of assessments and embedded mini-quizzes with in the curriculum.
Suggestions:
I would recommend spending the time adding hyper-links from the CCSS standards to the unit level of the modules. Teachers would use this feature when planning.
I firmly believe sine and cosine MUST be connected to the coordinate plane when introducing the subject; this makes a very simple connection for the student to x and y graphing on a Cartesian Plane. In the developers presentation of sine and cosine (for the first time for the algebra student) the student only observes side ratios of on a right triangle. Which is ok but a possible overlay of these triangles onto a coordinate axis would be superb.
Ideal Use/Comments
I was impressed with this curriculum; however, the lack of answer keys and rubrics for student performance is a glaring deficiency. Practice standards need to be specifically addressed as well. The ideal use for this resource is for a classroom in which the teacher has a deep understanding of the CCSS content standards, shifts, and practice standards. The students should all show mastery of learning from previous grades (6-8). This is NOT suited for ELL students. Although this material could be handled by a newer teacher, a veteran would be more successful.
Challenges:
Lack of answer keys/rubrics for student performance
Limited support for struggling/ELL students
No technology/media
No specific reference to the math practices in the lessons (or the correlation documents)
Suggestions:
Provide a supplemental document with such answer keys/rubrics.
Provide a supplemental document with "Skill Builder"/Review lessons and answers.
Specifically identify these practice standards in a line or two after the content standards in the teaching hints for each lesson.
Challenges:
Assessment needs work - missing rubrics, answer keys, and ability for students to check their own work
Missing technology
Suggestions:
Complete an answer guide with scoring rubrics
Include a student driven/initiated learning experience away from the necessary directions listed in the teacher notes. More individual learning opportunities
Ideal Use/Comments
This could be used as a classroom text for an Integrated Math 2 course. Experienced teachers would find this user-friendly. A beginning teacher would find the lesson notes quite helpful, but would need to have answer keys for all the in-class activities as well as the Ready-Set-Go assignments. Also, modules could be used to replace units in a teacher's current textbook.
Challenges:
No clear identification of the Standards for Mathematical Practice. The only mention of the Standards for Mathematical Practice is in the overview of the materials.
No Answer Keys provided for student work. No assessment materials or suggestions included.
Addresses standards not in the PARCC Model Content Framework and leaves out some the standards included in the framework.
Suggestions:
Provide guidance in the lesson notes to teachers regarding which practices to focus on and how to engage students in those practices.
Include answer keys for student work. Include sample student answers showing expected depth/detail of work. Include rubrics to help teachers evaluate student work.
Provide suggestions to teachers about what to assess and how. Better yet, provide assessments that teachers can use - both formative and summative. Ensure there is a variety of assessment methods included.
Consider providing a modified version that doesn't include standards not in Math 2, and that does include AL. | 677.169 | 1 |
Product Description:
This support text provides a more thorough presentation of mathematical aspects of meteorology including equations. Except for Chapters 1 and 19, the chapters directly coincide with METEOROLOGY TODAY, FIFTH EDITION by Ahrens. The first chapter provides the mathematical and physical background for subsequent chapters. A background in high school algebra, geometry, and trigonometry is assumed. No calculus is used, and finite differential equations are substituted in place of differential equations where appropriate. Most problems and exercises can be easily solved using hand calculators; some, however, require more extensive computations using computer spreadsheets. This book is intended for courses requiring more quantitative material than is currently offered in either text by Ahrens.
REVIEWS for Meteorology Today for Scientists and Engineers | 677.169 | 1 |
...
Show More Crossroads standards of the American Mathematical Association of Two Year Colleges, as well as the standards of the National Council of Teachers of Mathematics and the Mathematical Association of America. Symbols, Real Numbers, and Problem Solving; Variables, Polynomials, Solving Linear Equations and Inequalities; Relations, Functions, and the Cartesian Plane; Linear Systems, Graphical Solutions of Linear Equations and Inequalities; Multiplication and Division of Polynomials; Factoring and Solving Equations by Factoring; Rational Expressions and Equations; Roots and Radical Equations; Arithmetic Review For all readers interested in introductory | 677.169 | 1 |
Key Design Features of Intensified Algebra
The Intensified Algebra program is built around rigorous, but accessible, treatment of those topics that are most critical for success in a first algebra course and in future mathematics courses. Supporting this core is an integrated set of tools and structures that support student success.
Supports for teachers
A key challenge for all teachers is enacting "high cognitive demand" tasks for struggling learners so that a high level of cognitive demand is maintained. In an extended-time algebra class, teachers are also challenged with keeping students motivated throughout the longer period. Intensified Algebra helps teachers with these challenges by providing structures and routines designed to maintain student motivation and engagement, as well as detailed, daily advice for teachers to support task enactments, including debriefing strategies, scaffolding questions, probes, and key discussion questions.
Efficient review/repair
Connecting new learning with prior knowledge involves engaging students in tasks and activities that help them access relevant prior knowledge when they need it and repairing misconceptions they might have related to that knowledge. Intensified Algebra takes a "just in time" approach to review and repair; based upon research with struggling learners, review tasks are strategically placed to help students access prerequisite knowledge, preview upcoming content in the algebra core, or repair common misconceptions.
Ongoing distributed practice
Struggling students need extra practice opportunities to develop mathematical proficiency. Our approach is based upon long-standing research that supports the use of distributed practice in mathematics.
Literacy & language supports
Researchers have begun to understand how literacy and language issues affect learning in mathematics and science classes, particularly with struggling learners, and how to support content learning through the use of simple strategies and tools for language and literacy development. The Intensified Algebra program helps students build essential academic vocabulary, comprehend and analyze key elements of mathematics problems, explicitly connect different representations of mathematical situations, and reflect upon and communicate their understandings.
Shaping attitudes toward learning
Drawing on the latest advances in developmental and social psychology, Intensified Algebra helps shape students' motivation, confidence, and ultimate success as learners.
Assessment strategies
Intensified Algebra contains a comprehensive set of assessment activities and tools that provide struggling learners and their teachers with regular and targeted feedback to help them monitor progress, address sources of confusion, and build on the strengths in students' mathematical knowledge to move them toward more advanced thinking and toward regulation of their own learning.
Tools to organize learning
Struggling learners have difficulty organizing and interpreting information and complex processes, thereby increasing the challenges they face when attempting to access new mathematical learning. Thus, a key feature of Intensified Algebra is the inclusion of well-defined routines and supports that help students make connections within algebra, organize information, and make their mathematical thinking "visible" to them and to their teachers.
People are talking about Intensified Algebra
I am finding that I want students to use several different methods to solve a problem. I'm teaching them to become problem solvers rather than problem doers. | 677.169 | 1 |
This book provides an original introduction to the geometry of Minkowski space-time. A hundred years after the space-time formulation of special relativity by Hermann Minkowski, it is shown that the kinematical consequences of special relativity are merely a manifestation of space-time geometry.The book is written with the intention of providing students (and teachers) of the first years of University courses with a tool which is easy to be applied and allows the solution of any problem of relativistic kinematics at the same time. The book treats in a rigorous way, but using a non-sophisticated mathematics, the Kinematics of Special Relativity. As an example, the famous 'Twin Paradox' is completely solved for all kinds of motions.The novelty of the presentation in this book consists in the extensive use of hyperbolic numbers, the simplest extension of complex numbers, for a complete formalization of the kinematics in the Minkowski space-time.Moreover, from this formalization the understanding of gravity comes as a manifestation of curvature of space-time, suggesting new research fields. | 677.169 | 1 |
Many physical problems are most naturally described by systems of differential and algebraic equations. This book describes some of the places where differential-algebraic equations (DAE's) occur. The basic mathematical theory for these equations is developed and numerical methods are presented and analyzed. Examples drawn from a variety of applications are used to motivate and illustrate the concepts and techniques. This classic edition, originally published in 1989, is the only general DAE book available. It not only develops guidelines for choosing different numerical methods, it is the first book to discuss DAE codes, including the popular DASSL code. An extensive discussion of backward differentiation formulas details why they have emerged as the most popular and best understood class of linear multistep methods for general DAE's. New to this edition is a chapter that brings the discussion of DAE software up to date. | 677.169 | 1 |
GCSE Subjects
What is Maths?
Maths is a core subject and a grade C is often an essential qualification for progression to the next stage of your education. If you want to study Maths at A level you must complete the GCSE at Higher level and aim for at least an A.
You will be taught to solve problems in a systematic way by teachers who are patient and sympathetic and very familiar with the difficulties faced by students.
What will I study?
Some of the major topics are: trigonometry, areas and volumes, simplifying and factorising algebraic expressions, ratios, percentages and statistics.
The above topics will be covered in more depth at the Higher level and the specification will also include many algebraic topics not dealt with at the Foundation level.
Why should I study Maths?
A grade C in GCSE Maths is a minimum requirement for entry to university in any course. In addition, Mathematics today is a diverse discipline that deals with data, measurements and observations from science, inference, deduction, proofs as well as with mathematical models of natural phenomena, human behaviour and social systems: you will certainly come across applications of mathematics at some stage in your future careers.
How is it assessed?
The first examination session for the new specification in GCSE Mathematics (9-1) will be available in May/June 2017 and will be assessed through three equally-weighted written examination papers at either Foundation tier or Higher tier. Paper 1 is a non-calculator paper and each paper is 1.30 hour long. The grading is 9 to 1 overall with grade 8 and 9 corresponding to A* and grade 4 corresponding to C. The assessment objectives are: using and applying standard techniques; reasoning, interpretation and communicating; solving non-routine problems in mathematical and non-mathematical contexts.
Exam Board: ED
What do I need?
If you have found Maths difficult in the past we can help you approach the subject with confidence. Equally, if you are good at Maths you will be stretched to achieve your best possible result.
We ask however that you be focussed whilst in class – be organised, follow instructions and practise outside class. There is no reason why students who work consistently hard using techniques taught by their teachers cannot do well in the exam. | 677.169 | 1 |
Middle School
CHHS has adopted a Middle School Philosophy in recent years with respect to its grade 7 and 8 students. In an effort to reduce the number of teachers our Middle School students see on a daily basis, courses like Math and Science have been podded together—meaning students have one teacher that teaches them both Math and Science.
Senior High
The Grades 10-12 Mathematics Program of Studies includes a combined Grade 10 course, Mathematics 10C, that is the starting point for the -1 and -2 course sequences. This will allow Mathematics 10C students to delay choosing a mathematics course sequence until Grade 11. Upon successful completion of 10C students will choose a path of 20-1 or 20-2 depending on their post secondary aspirations. The other Grade 10 mathematics course available is Mathematics 10-3 (Apprenticeship & Workplace) for students planning to enter a trade or the workforce. Students who have successfully completed Math 10-3 may move on to Math 20-3 or to Math 10C.
Senior High - Course Offerings and Descriptions (2013-2014 School Year)
MATHEMATICS 9
The Math curriculum is made up of 4 major strands [big ideas] with 2 or 3 substrands [smaller ideas] under each strand. A scientific calculator is needed for this course. The strands and substrands are as follows:
This course sequence is designed to provide students with the mathematical understandings and critical-thinking skills identified for entry into post-secondary programs that require the study of calculus.
Topics in this sequence include sequences and series, trigonometry, quadratics, absolute values and radicals, inequalities, systems of equations inequalities and rational expressions and equations post-secondary studies in programs that do not require the study of calculus.
Topics in this sequence include measurement, statistics, reasoning, quadratics, radicals and geometry entry into post-secondary programs that require the study of calculus.
Topics in this sequence include trigonometry, relations and functions, permutations, combinations and the binomial theoremThis course sequence is designed to provide students with the mathematical understandings and critical-thinking skills identified for post-secondary studies in programs that do not require the study of calculus.
Topics in this sequence include logical reasoning, probability, relations and functions, and a mathematical reasoning projectMath 31 is an introductory course in the study of Calculus. The suggested prerequisite is a mark of 60% in Math 30-1. Students can take Math 31 concurrently with Math 30-1 with the instructor's approval.
Calculus has two branches of study: differential calculus and integral calculus. Differential calculus deals with instantaneous rates of change. Integral calculus is concerned with finding a quality by knowing the rate of change.
Students who are considering further studies in the Sciences, Engineering, or Commerce and Economics should consider taking this course. | 677.169 | 1 |
Mathematical functions
This book is intended primarily for students on economics, business studies and management
courses. It assumes very little prerequisite knowledge, so it can be read by students who have
not undertaken a mathematics course for some time. The style is informal and the book contains
a large number of worked examples. Students are encouraged to tackle problems for
themselves as they read through each section. Detailed solutions are provided so that all
answers can be checked.
This book is based onmy notes fromlectures to students of electrical, elec-
tronic, and computer engineering at South Bank University. It presents
a first year degree/diploma course in engineering mathematics with an
emphasis on important concepts, such as algebraic structure, symme-
tries, linearity, and inverse problems, clearly presented in an accessible
style. It encompasses the requirements, not only of students with a good
maths grounding, but also of those who, with enthusiasm and motiva-
tion, can make up the necessary knowledge.
This book contains some of the contributions, divided into five main sections, that have been carefully selected and peer-reviewed, which were presented at the International Symposium MME06 Mathematical Methods in Engineering, held in Cankaya University, Ankara, April 27—29, 2006.
The Symposium provided a setting for discussing recent developments in Fractional Mathematics, Neutrices and Generalized Functions, Boundary Value Problems, Applications of Wavelets, Dynamical Systems and Control Theory....
n this book you find the basic mathematics that is needed by computer scientists. The author will help you to understand the meaning and function of mathematical concepts. The best way to learn it, is by doing it, the exercises in this book will help you do just that.
Topics as Elementary logic, factorization, plotting functions and matrices are explained.
Robotics and computer vision are interdisciplinary subjects at the intersection of engineering and computer science. By their nature, they deal with both computers and the physical world. Although the former are in the latter, the workings of computers are best described in the black-and-white vocabulary of discrete mathematics, which is foreign to most classical models of reality, quantum physics notwithstanding. This class surveys some of the key tools of applied math to be used at the interface of continuous and discrete. It is not on robotics or computer vision.
Mathematics in Action: Algebraic, Graphical, and Trigonometric Problem Solving, Fourth
Edition, is intended to help college mathematics students gain mathematical literacy in the
real world and simultaneously help them build a solid foundation for future study in mathematics
and other disciplines.
Our team of fourteen faculty, primarily from the State University of New York and the City
University of New York systems, used the AMATYC Crossroads standards to develop this threebook
series to serve a very large population of college students at the pre-precalculus level.
The Project Gutenberg EBook of On Riemann's Theory of Algebraic Functions and their Integrals, by Felix Klein On Riemann's Theory of Algebraic Functions and their Integrals A Supplement to the Usual Treatises Author: Felix Klein Translator: Frances Hardcastle Release Date: August 3, 2011...
Rediscovering Mathematics is an eclectic collection
of mathematical topics and puzzles aimed at
talented youngsters and inquisitive adults who
want to expand their view of mathematics. By
focusing on problem solving, and discouraging
rote memorization, the book shows how to learn
and teach mathematics through investigation,
experimentation, and discovery. Rediscovering
Mathematics is also an excellent text for training
math teachers at all levels
In this article we study several homology theories of the algebra E ∞ (X) of Whitney functions over a subanalytic set X ⊂ Rn with a view towards noncommutative geometry. Using a localization method going back to Teleman we prove a Hochschild-Kostant-Rosenberg type theorem for E ∞ (X), when X is a regular subset of Rn having regularly situated diagonals. This includes the case of subanalytic X. We also compute the Hochschild cohomology of E ∞ (X) for a regular set with regularly situated diagonals and derive the cyclic and periodic cyclic theories. ...
The Institute for Mathematical Sciences at the National University of
Singapore was established on 1 July 2000 with funding from the Ministry
of Education and the University. Its mission is to provide an international
center of excellence in mathematical research and, in particular, to promote
within Singapore and the region active research in the mathematical
sciences and their applications. It seeks to serve as a focal point for scientists
of diverse backgrounds to interact and collaborate in research through
tutorials, workshops, seminars and informal discussions....
In this paper we solve the subconvexity problem for Rankin-Selberg L-functions L(f ⊗ g, s) where f and g are two cuspidal automorphic forms over Q, g being fixed and f having large level and nontrivial nebentypus. We use this subconvexity bound to prove an equidistribution property for incomplete orbits of Heegner points over definite Shimura curves. L(f, s),
The divisibility properties of Dirichlet L-functions in infinite families of characters have been studied by Iwasawa, Ferrero and Washington. The families considered by them are obtained by twisting an arbitrary Dirichlet character with all characters of p-power conductor for some prime p. One has to distinguish divisibility by p (the case considered by Iwasawa and FerreroWashington [FeW]) and by a prime = p (considered by Washington [W1], [W2]). Ferrero and Washington proved the vanishing of the Iwasawa µ-invariant of any branch of the Kubota-Leopoldt p-adic L-function. ...
If α is an irrational number, Yoccoz defined the Brjuno function Φ by
Φ(α) =n≥0
α0α1 · · · αn−1 log
1
αn
,
where α0 is the fractional part of α and αn+1 is the fractional part of 1/αn.
The numbers α such that Φ(α)
We study the problem of conformally deforming a metric to a prescribed symmetric function of the eigenvalues of the Ricci tensor. We prove an existence theorem for a wide class of symmetric functions on manifolds with positive Ricci curvature, provided the conformal class admits an admissible metric. 1. Introduction Let (M n , g) be a smooth, closed Riemannian manifold of dimension n.
An important chapter in the theory of distribution of zeros of entire functions pertains to the study of linear operators acting on entire functions. This dissertation presents new results involving not only linear, but also some non-linear operators. | 677.169 | 1 |
Calculus: Related Rates Sort & Match Activity
PDF (Acrobat) Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
1.85 MB | 10 + key pages
PRODUCT DESCRIPTION
If you like group activities, here's a fun RELATED RATES MATCH UP. Eight task cards contain a rate problem to be solved. Calculus students match the question card with the correct equation card and then the proper derivative card. For an extension to the activity, students state the unknowns and givens, then finally solve each problem. There is an answer key for both parts.
My students love to work cooperatively. Yours will, too! Let me know how it works | 677.169 | 1 |
Holt Algebra Chapter 3 "Inequalities" Review Worksheet (DOC & PDF)
Compressed Zip File
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0.07 MB | 2 pages
PRODUCT DESCRIPTION
This r squared creation document is a review of the topics that will be covered on the Chapter 3 Test. The materials covered in the review are standards based and are aligned to Chapter 3 of the Holt Algebra textbook. Concepts covered are how to graph and write linear inequalities, how to solve one-step linear inequalities using addition and subtraction, how to solve one-step linear inequalities using multiplication and division, how to solve multi-step linear inequalities by having to distribute and/or combine like terms, how to solve multi-step linear inequalities involving variables on both sides, how to write, graph, and solve linear compound inequalities that are "And" statements, and how to write, graph, and solve linear compound inequalities that are "Or" statements, how to solve absolute value inequalities that are "And" statements, and how to solve absolute value inequalities that are "Or" statements.
The zip file contains the worksheet | 677.169 | 1 |
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SYLLABUS OF AIEEE MATHEMATICS
UNIT 1: SETS, RELATIONS AND FUNCTIONS: Sets: COMPLEX NUMBERS AND QUADRATIC EQUATIONS: Complex numbers as ordered pairs of reals, Representation of complex numbers in the form a+ib and their representation in a plane, Argand diagram, algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a complex number, triangle inequality, Quadratic equations in real and complex number system and their solutions. Relation between roots and co-efficients, nature of roots, formation of quadratic equations with given roots.
UNIT 3: MATRICES AND DETERMINANTS: Mat
equations in two or three variables using determinants and matrices. UNIT 4: PERMUTATIONS AND COMBINATIONS: Fundamental principle of counting, permutation as an arrangement and combination as selection, Meaning of P (n,r) and C (n,r), simple applications. UNIT 5: MATHEMATICAL INDUCTION: Principle of Mathematical Induction and its simple applications. UNIT 6: BINOMIAL THEOREM AND ITS SIMPLE APPLICATIONS: Binomial theorem for a positive integral index, general term and middle term, properties of Binomial coefficients and simple applications. UNIT 7: SEQUENCES AND SERIES: Arithmetic and Geometric progressions, insertion of arithmetic, geometric means between two given numbers. Relation between A.M. and G.M. Sum upto n terms of special series: Sn, Sn2, Sn3. Arithmetico Geometric progression. UNIT 8: LIMIT, CONTINUITY AND DIFFERENTIABILITY: Real - valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions. Graphs of simple functions. Limits, continuity and differentiability. Differentiation of the sum, difference, product and quotient of two functions. Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order upto two. Rolle's and Lagrange's Mean Value Theorems. Applications of derivatives: Rate of change of quantities, monotonic - increasing and decreasing functions, Maxima and minima of functions of one variable, tangents and normals.
Cartesian system of rectangular co-ordinates in a plane, distance formula, section formula, locus and its equation, translation of axes, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes. Straight lines Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, distanceCir UNIT 12: THREE DIMENSIONAL GEOMETRY: Coordinates of a point in space, distance between two points, section formula, direction ratios and direction cosines, angle between two intersecting lines. Skew lines, the shortest distance between them and its equation. Equations of a line and a plane in different forms, intersection of a line and a plane, coplanar lines. UNIT 13: VECTOR ALGEBRA: Vectors and scalars, addition of vectors, components of a vector in two dimensions and three dimensional space, scalar and vector products, scalar and vector triple product. | 677.169 | 1 |
Find an Arlington, VA Algebra 2Having a firm grasp of polynomial operations, graphs, systems of equations and inequalities, matrix operations, logs and exponents, conic sections, and complex numbers is essential for succeeding at linear algebra, calculus, and advanced statistics. It is also essential to fields like science, e... | 677.169 | 1 |
Executive Summary
The research and designs presented in this project
fall under five major themes: usability, graphing, simplification,
learning, and form. The number of features supported by the calculator
was cut in half to create a less intimidating interface and contextually-relevant
menus replaced stagnant ones to improve overall usability. The graphing
interface was streamlined by removing the link between Stat Plot
and Lists, letting users adjust a graph's equation in real-time,
and providing hard buttons for Zoom and Pan. The calculator was
simplifed by removing features that made concepts unnecessarily
complex such as supporting multiple lists and a 2ND button. Some
exploration into using the calcaulator as a learning tool was made
by user testing applications such as factoring and symbol manipulation.
Several forms were iterated upon and user tested, resulting in the
sliding form factor illustrated in this report. | 677.169 | 1 |
This concise and clear introduction to the topic requires only basic knowledge of calculus and linear algebra - all other concepts and ideas are developed in the course of the book. Lucidly written so as to appeal to undergraduates and practitioners alike, it enables readers to set up simple mathematical models on their own and to interpret their results and those of others critically. To achieve this, many examples have been chosen from various fields, such as biology, ecology, economics, medicine, agricultural, chemical, electrical, mechanical and process engineering, which are subsequently discussed in detail. Based on the author's modeling and simulation experience in science and engineering and as a consultant, the book answers such basic questions as: What is a mathematical model? What types of models do exist? Which model is appropriate for a particular problem? What are simulation, parameter estimation, and validation? The book relies exclusively upon open-source software which is available to everybody free of charge.
The entire book software - including 3D CFD and structural mechanics simulation software - can be used based on a free CAELinux-Live-DVD that is available in the Internet (works on most machines and operating systems).
Author Biography - Kai Velten
Kai Velten is a professor of mathematics at the University of Applied Sciences, Wiesbaden, Germany, and a modeling and simulation consultant. Having studied mathematics, physics and economics at the Universities of Gottingen and Bonn, he worked at Braunschweig Technical University (Institute of Geoecology, 1990-93) and at Erlangen University (Institute of Applied Mathematics, 1994-95). From 1996-2000, he held a post as project manager and group leader at the Fraunhofer-ITWM in Kaiserslautern (consultant projects for the industry). His research emphasizes differential equation models and is documented in 34 scientific publications and one patent. | 677.169 | 1 |
Text meeting the need for a compact introduction to Mathematica for students enrolled in various standard mathematics courses using Mathematica. Presents concepts in an order closely following a standard mathematics curriculum, rather than along the features of the software. Provides a brief introduction to those aspects of the program most usefulto students. Includes a brief introduction to Versions 3 and 4, followed by discussions of functions and graphs, algebra, calculus, multivariate calculus, and linear algebra. Can be used as a supplementary text or as a tutorial introduction to Mathematica. | 677.169 | 1 |
About this product
Description
Description
Teach yourself the math you need. This title includes: down-to-earth explanations; easy-to-remember tips and tricks; formulas and calculations for construction, carpentry, plumbing, electrical, HVAC, roofing, and more; packed with examples; and, metric conversion tables.Get the math you need for framing a wall, spacing beams, figuring water flow, sizing wiring, mixing concrete, preparing estimates, determining loan costs - just about any calculation in the building trades. A complete, compact self-study course, Mastering Math for the Building Trades even helps with tools, from steel square and surveyor's transit to calculators and computers. Here to help you meet deadlines, avoid costly and wasteful errors, write better estimates and plans, and have happier customers, this self-teaching tool provides the answers you want, in the office or in the field. This edition includes all new examples and illustrations, self-test Q and A's, HVAC load calculations, thermal performance calculations, fiber optic cabling formulas, and guidance on estimating software.
Author Biography
James Gerhart is experienced in residential construction, working for a number of years as a project coordinator. He built his reputation, however, teaching subjects such as math, estimating, scheduling, blueprint reading, and surveying to vocational and construction management studies students. | 677.169 | 1 |
PDF (Acrobat) Document File
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1.41 MB | 4 pages
PRODUCT DESCRIPTION
I designed these lessons to teach my students about piecewise and absolute value functions (the 7th in a series of 7). This lesson focuses on reviewing drawing basic geometric ideas (lines, rays, bisectors, etc), describe a graph using domain, range, maximum, minimum, intervals of increasing and intervals of decreasing, using a word description to draw a function and then writing the equation of that function, given a function and writing the inverse, and graphing an absolute value function and then writing a piecewise function for the same function | 677.169 | 1 |
Product Description:
The purpose of this book is to present the three basic ideas of geometrical probability, also known as integral geometry, in their natural framework. In this way, the relationship between the subject and enumerative combinatorics is more transparent, and the analogies can be more productively understood. The first of the three ideas is invariant measures on polyconvex sets. The authors then prove the fundamental lemma of integral geometry, namely the kinematic formula. Finally the analogues between invariant measures and finite partially ordered sets are investigated, yielding insights into Hecke algebras, Schubert varieties and the quantum world, as viewed by mathematicians. Geometers and combinatorialists will find this a most stimulating and fruitful story.
REVIEWS for Introduction to Geometric | 677.169 | 1 |
ISBN :
9783540940715
Publisher :
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Author(s) :
Alan F. Karr
Overview
This is a textbook which will provide students with a straightforward introduction to the mathematical theory of probability. It is written with the aim of presenting the central results and techniques of the subject in a complete and self-contained account. As a result, the emphasis is on giving results in simple forms with clear proofs and to eschew more powerful forms of theorems which require technically involved proofs. Any graduate student who has a familiarity with real analysis will be able to use this text - measure theory is used only where necessary and undue abstraction is avoided. Throughout there are a wide variety of exercises to illustrate and to develop ideas in the text. | 677.169 | 1 |
Vedic Maths is a science that connects to the ancient Indian faster calculation methodology.Sri Bharati Krsna Tirthaji rediscovered it after studying the Vedas for years. It is a list of mental calculation techniques based on sixteen Sutras.Learning this ancient high-speed Vedic mathematics will help you calculate much faster than the normal calculation system. Enroll in our Vedic maths courses.
AJTmaths online and maths solutions are designed to help students, teachers, and parents understand a variety of mathematical concepts. This covers Addition, Angle, area, Algebra,Multiplication, Probability, percentage, and lots more! | 677.169 | 1 |
Assuming only calculus and linear algebra, Professor Taylor introduces readers to measure theory and probability, discrete martingales, and weak convergence. This is a technically complete, self-contained and rigorous approach that helps the reader to develop basic skills in analysis and probability.
This book presents the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics in a pedagogical, way and is mainly addressed to non-specialists in the subject. | 677.169 | 1 |
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,...
MathStudio is an open-source program intended to be an easy and powerful symbolic calculator. It differs from other programs of this type both because of the way the user inputs the expression and bec... More: lessons, discussions, ratings, reviews,...
Practice arithmetic and algebraic skills, and investigate the important concept of equivalence. This interactive pan balance allows numeric or algebraic expressions to be entered and compared. You can... More: lessons, discussions, ratings, reviews,...
This program introduces students to fundamental concepts in algebra. Using two or three weighing scales, students must determine the weight of a specific object or group of objects. The program provid... More: lessons, discussions, ratings, reviews,...
This tool arranges the numbers 1 to 64 in an 8x8 grid, then outlines a 3x3 square within that grid. Multiply the diagonal corners, then take the difference of your results. Is that difference the same... More: lessons, discussions, ratings, reviews,...
Slide and jump the frogs to move each group to the opposite side. Can you find a pattern to get them there in the smallest number of moves? Can you predict how many moves it will take different number... More: lessons, discussions, ratings, reviews,...
See how many bounces it takes to get the ball to a pocket on this special snooker table. (Snooker in Britain is similar to pool in America.) Change the size of the table and see what difference it mak... More: lessons, discussions, ratings, reviews,...
This is a quiz on two-step algebraic equations with a focus on algebraic expressions. There are 15 multiple-choice questions with built in answer checking, and some helpful hints from the aliens, miss... More: lessons, discussions, ratings, reviews,...
This tools helps you investigate the pattern of the sums of numbers within a stair shape drawn on a 10x10 grid. What happens if you change the position of the stair? ...the size of the grid? the size ... More: lessons, discussions, ratings, reviews,...
This mathlet allows you to solve simple linear equations through the use of a balance beam. Unit blocks (representing 1s) and X-boxes (for the unknown, X), are placed on the pans of a balance beam | 677.169 | 1 |
Find a Santa WesternTopics include simplifying expressions, evaluating and solving equations and inequalities, and graphing linear and quadratic functions and relations. Real world applications are presented within the course content and a function's approach is emphasized. This course extends the topics first seen in Algebra I and provides advanced skills in algebraic operations | 677.169 | 1 |
High-Performance Matrix Computations --- 2012-13
Prerequisites
Basic knowledge of numerical linear algebra.
Principles of algorithms and programming.
Familiarity with Matlab and C.
Overview
The course centers around the idea of developing efficient numerical algorithms
through a synergy between mathematics and architectures.
We will cover all the following topics.
Please also visit
[HPMC 2011] | 677.169 | 1 |
EDF Documents
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An executive summary provides a quick overview or synopsis of a report,
summarising the essential parts. It outlines the following information:
the purpose of the report
the methods used to conduct the research
the results of the research
the conclusions
SYSTEMS OF LINEAR EQUATIONS
Our object is to solve a system of equations like
2x + y + z + w = 4
4x + y + 3z + 2w = 7
2x + z
w = 9:
Such a system is called linear because each of the equations on the left hand side is a
linear function of the unknown vari
The following example completes our discussion on transformations. Rotations in R3 ; presented
here in raw form, are obviously more complicated than rotations in R2 :
The 3
3 Rotation Matrix
The problem is to nd the matrix of the linear transformation whi
The Cauchy-Schwarz inequality
We are about to to prove the Cauchy-Schwarz inequality which states that for all vectors u; v 2 Rn
e e
we have
u v
e e
Lets take a moment to consider what this means.
u v
e e
Let u = (u1 ; u2 ;
; un ) and v = (v1 ; v2 ;
; vn
Finding inverses
The rst method we will use for nding inverses is the row operations method.
We will see from an example how to implement the method and then we will examine the
theory behind it; that is why it works.
Given an n n matrix A (which may or m
A Proof of the Cauchy Schwarz inequality:
Let u and v be any two vectors in Rn and let x be a real variable.
Let u and v be any two vectors in Rn and let x be a real variable.
Consider the quadratic function q (x) = (u + xv) (u + xv) :
Let u and v be any
DS-303
Practice exam 2
Fall 2009
Name_
1. Florida reappraises real Estate every year, and the county appraisers Web site lists the
current fair market value of each piece of property. Property usually sells for somewhat
more than the appraised market valu
Critique(Liangsquestions)
To what social, cultural, economic,
political, or educational problem is the
curriculum attempting to respond?
In the curriculum, what kinds of content
are most important, and how should the
content be organized for instruction
School Strategic Plan for
The University High School
School Number 8405
2014 -2017
Purpose
A quality strategic plan that engages the whole school community in its development ensures that the school is
united by a common purpose. The plan helps to establi
EDF1303 TUTORIAL WEEK 6
Activity 1:
For three minutes, sit silently on your own, reflecting if you are a reflective learner?
What are reflection strategies you often use to reflect your learning experiences?
(if any mentioned in the lecture?)
What did you
Welcome to EDF 1304
Where you are NOT
another brick in the wall
teachers, learners and creators of new structures
referred to as curriculum for new generational learning and teaching.
You are engineers, participants,
As you enter this lecture theatre you
In the following theorem each of the capital letters A; B; C; D; U etc. denote n n matrices.
Lower case bold face characters b; x; y are vectors in Rn ; which as matrices, are represented by
n 1 column matrices. This means that yT ; for example, is an 1 n
Assignment focus:
mechanics of referencing and using
resources as evidence
monash.ed
u
Today
Mechanics of referencing: in text and in the list
of references (in this ppt)
Referencing a chapter from the textbook
Referencing a secondary source from a cha | 677.169 | 1 |
Hi. I'm taking differential equations using the Boyce Diprima textbook and it's absolutely kicking my ass right now. We cover about a chapter a week, and have a test every two weeks. The professor doesn't really explain the concepts. He gives a general overview. I go to the MIT OCW website and watch the video lectures there, and the lectures are much more helpful and in-depth than what my professor teaches. Often times, it's more effective to not go to class and listen to the MIT lectures.
It seems like an awful lot of self-teaching compared to the linear algebra and calc III that I took last semester, where the lectures were more or less similar in depth/breadth to the ones in MIT OCW.
I'm just really scared since I"m only taking 13 credits this semester and only one serious math course but next semester I"m taking 16 credits and two serious math courses (number theory and numerical analysis). Is there something I should study that would help me across most fields of mathematics? like something that would teach me to think more like a mathematician.
I wouldn't say most, but certainly a large amount. The speed of roughly a chapter a week seems typical. Also, it is often a matter of being fortunate when you find professors in upper level math who are competent teachers. Sometimes you get professors who are most useful when you bombard them with questions and interrupt every other step in the lecture. Some professors are just bad.
I'm not familiar with the topic of differential equations, but for most classes I took, even if the professor was brilliant, I had to spent countless hours working on things by myself. That's just how math is.
So yes, you might have a bad professor, but if you're going into upper level math you can't rely on lectures to serve as the brunt of your understanding. If you find it more effective to not go to a particular lecture, then don't. Sometimes it just works better that way.
I"m not surprised at the fact that I have to put in a lot of work, but it just seems like the lectures aren't very helpful. I guess I"m just stuck with a prof that doesn't explain everything and I should learn to cope with that.
Is differential equations an upper level course now? That surprises me. Anyway, the more math you do, the more you need to learn how to study yourself and fill in the gaps. Oftentimes teachers omit details in order for you to question the ideas and see for yourself why they're true.
Calculus? I mean, I can understand that LA/diff eq/multi might be the last courses those folks take, but they surely aren't very advanced, at least in comparison to the rest of an undergrad math degree
As an engineer, Linear Algebra and Differential Equations are typically taken 4th and 5th semester. If you test out of Calc I, then both could be taken sophomore year.
I think for a lot of engineering/science students, they just have no idea how vast math is. It's like they went to the beach on vacation for a few weeks, and now they think they know something about the ocean.
Depending on the level at which it is taught, a course in differential equations can certainly be an extremely advanced. I suppose you're thinking of introductory ODEs, but bifurcation theory, normal form theory, nonlinear PDEs, and many other topics can comprise a very advanced course in differential equations.
Well yes, for sure. Shit, you can devote your whole mathematical life to them. But clearly OP was referring to an intro course, and since you need metric space theory or a lot of LA to prove things like existence and uniqueness, I assume it lacks too much theory. Not saying its a bad course or anything! It was my favorite of all my calculus based classes
ODEs is a relatively straightforward subject. Luckily, it's usually very computational based, and books provide tons of exercises. Just work through those and really think about what you're doing. Following an example it even knowing the answer for the first few is a good way to make sure you are on the right track.
My 'advanced undergrad' diffeq course was similar: the required text was Boyce and DiPrima but the teacher virtually covered nothing the text covers directly: it tried to make the course have a bit more theory. In the end, though, I had to go through the text and cover chapters 1-8 i believe. Not something that was enjoyable at all.
Not to be a dork, but at least you have a professor. I'm at a point in my life where I can't go back to school, which is sad since I discovered what math really is. I've been trying to work through various books by myself (as I have no friends who think anything past geometry is fun) and I end up re-reading pages for hours. And that's before life decides to throw a curve and I need to use all my "sharp" hours doing other things. So then I lose where I am at and need to start over.
I guess I'm just bitching, but I wish I just had a little time every day where I wasn't exhausted and someone to help when I'm stuck. Than again, no one promised me life would be easy except the people on TV and I know they lie.
I'm also curious, OP: are the OCW videos really superior to your professor, or do you just have the advantage of watching them in the comfort of your own room with headphones and a rewind button? Or it may very well be that your professor is going way too fast...
In my experience, it varied from professor to professor and class to class. Some loved to teach and went out of their way to explain concepts in various ways, weave supplemental resources into the curriculum, and demonstrate a real passion for teaching the subject. Others, however, were not good at teaching either because they weren't really teachers at heart or they were unable to relate to undergrads and their needs. Sometimes it wasn't really the fault of the instructor at all, but rather the fact that the class took place in a lecture hall with 90+ students. Sometimes there is a lot of material to push through and instructors can't spend a lot of time, providing examples and fleshing out all of the details.
In short, no, not every math class and every professor is like that, but the math class you are in right now is not atypical either.
I will mention, however, that the professor of my first upper division math course (by upper division, I refer to proof-based math courses), did make it a point to wean us off of having to rely on the professors and aids for all the answers. They made it a point to only give students hints and support rather than load us with a lot of examples of completed proofs because they wanted us to learn how to rely on ourselves and each other. There comes a time in every academic field where students must become independent learners. Becoming an independent learner entails learning how to learn, learning how to ask the big questions, learning how to explore, and learning how to study with other students. This is often a difficult process, especially in mathematics, because students often leave high school ill-equipped for higher-level thinking in math, even those who passed calculus with flying colors.
By the way, is your differentiable equations class a proof-based course? Have you taken an intro-to-proofs course yet? I imagine you should have if you are slated to take number theory and numerical analysis next term.
In my case, number theory and other proof-based math courses differed greatly from the non-proof-based courses such as differential equations. For one, we only covered a few chapters of a textbook that was quite unlike the textbooks you see in diff. equations, linear algebra, calculus, etc.. Classes tended to be much smaller with some exceptions (Abstract Algebra was such an exception simply because all math majors and some non-math majors had to take it. Not all math majors had to take number theory, graph theory, proof theory, math history, etc..). In my proof theory course, we only got through two and half chapters of our text in ten weeks, and the class consisted of 9 undergrads and 1 graduate student.
What are these courses like at your university. Have you ever considered sitting in on a number theory course to see. Have you spoken with other math majors who have taken a lot of upper-division math courses? Every university, every math program, every math department, every math class, and every math professor are different.
Lastly, have you formed a study group yet? If you are going to major in math, you will very likely have to form a study group. Very few students can survive without one. And whether it happens now or later, you will have to learn how to become an independent learner. The fact that you watch other lectures online is a good start. Imagine if you formed a study group and you watched the videos together, discussed them, discussed the underlying theory, practiced problems, came up with your conjectures and problems, etc.. That's how you become a mathematician. Don't just think like one, be like one.
You should keep in mind that some professors just aren't very good teachers, and some are in fact too demanding (these can be correlated). The more advanced the class, the harder you can generally expect it to be, but you can also expect great variation in teaching philosphies, styles and abilities. Coping with a bad teacher is a good skill to have, and it sounds like you've already found some methods, such as seeking out other material. I wouldn't get too discouraged.
A test every two weeks seems like a LOT in any university classroom. In any case, differential equations is not the model of a math course; it's a class in computational techniques with very little theory. An actual upper division math course will not have much in the way of calculation. Also, it's hard to say what covering a chapter a week means except for a particular book. | 677.169 | 1 |
Classes for Students Entering 7th Grade
Summer 2017 Information Coming Soon!
Preparation for 7th Grade Math
Description: This course is for 6th graders entering 7th grade who have been placed in the 7th grade math course. It will review foundation concepts from 6th grade that will be built upon in 7th grade. Course topics will include: fractions and mixed numbers, ratios, expressions and equations, area, surface area, and volume, statistics, and rational numbers in the coordinate plane. | 677.169 | 1 |
Quick Links
Application of Derivatives
Differentiation has applications in nearly all quantitative disciplines. In Physics, the derivative of the displacement of a moving body with respect to time is the velocity of the body. The reaction rate of a chemical reaction is also a derivative. Even Mathematics witnesses its widespread use in areas such as complex analysis, functional analysis, differential geometry, and abstract algebra. This video series is based on Application of Derivatives for class 12 students for board level and IIT JEE Mains.
Audience
These video classes have been designed for Class 12 students (Non-medical students and commerce students with Mathematics), those who are preparing for CBSE and other Board Exams for Intermediate, +2 and IIT JEE entrance exams. These classes will also be helpful for students in preparing them for Competitive Examinations for Engineering Institutes like IIT JEE etc.
Instructor
Ridhi Arora holds a B. Tech Honors - Gold medalist in Computer Science. Ridhi is an ardent
learner, a keen observer and a passionate Mathematics faculty for classes 11,12 and IIT JEE
Mains. She is among the top 10 most viewed writers in Kota, Rajasthan, on Quora.
Ridhi is also associated with Ganit Hub as Algebra HOD and Miracle Live Coaching Private
Limited as a Mathematics faculty. Ridhi is a confident and dynamic trainer with a total teaching
experience of 5+ years. | 677.169 | 1 |
Description
EasyFactor Quadratics is a powerful learning aid to help students master factoring of simple quadratic expressions and solving of quadratic equations (trinomials).
Interactive Coaching Calculators and Guides combine to speed the learning process.
Students develop their skills quickly as they work with the calculator and see each step of a process in detail.
Quadratic binomial expressions such as,
4x² - 2x
9x² - 16
Quadratic trinomial expressions such as,
x² - x - 6
3x² - 3x - 18
with x² coefficients of one at the start or after factoring out the GCF.
Coaching Calculators focus on integer coefficients up to 99.
The in depth Guide is ideal for students as the menu design reinforces each problem solving step and examples highlight and simplify algebra that students find hard.
For convenience, the app also has Coaching Calculators covering many quadratic factoring and solving methods :
- factoring by Guess and Check or Trial and Error method
- factoring by Grid or Box method
- factoring by Grouping or AC method
- solving by quadratic formula
- solving by Completing the Square
Do you know how to install the app?
Download EasyFactor Quadratics | 677.169 | 1 |
learning of slope is important in school algebra, and understanding the concept of slope requires knowledge of proportional reasoning and steepness. This mixed-methods study examines middle school participants'' abilities to solve steepness problems in three different contexts and of varying difficulty levels, the connections between proportionality and steepness that middle school participants exhibit, and the strategies which middle school participants use to solve steepness problems. It was concluded that participants'' abilities to solve steepness problems are related to their abilities to reason proportionally. The findings of this research contribute to literature on early algebraic reasoning that explores ways in which algebraic topics such as slope can be made accessible to students prior to their formal studies of algebra. | 677.169 | 1 |
Byju's provides NCERT solutions for class 9 maths in pdf format. These pdf books are free to download and students can have access to these NCERT solutions anywhere and anytime according to their convenience.
If a student has trouble finding solutions to a difficult problem, they can refer to the these NCERT maths solutions pdf's. NCERT books can very helpful for students in achieving maximum marks in their examinations. Students just need to cover these NCERT books and solve the questions and exercises given in each chapter. Students can be assured of positive results.
Chapter-14: Statistics Exercise 1 Q1) Give 5 scenarios of day to day life from which any type of data can be collected. Solution: Daily life activities from where data can be collected are as follows: (i) Daily household expenditure (ii) Rainfall happening in your area (iii) Electricity bill of monthly (iv) Voting results or […]
Chapter-1: Number systems 1) Prove that zero as a rational number. Write zero in p/q, where p and q are integers and q ≠ 0? Answer: Yes. Zero is a rational number and it can be represented as . 2) In between 3 and 4, find six rational numbers. Answer: There are an infinite number of rational numbers between the numbers […]
Chapter – 8 : Quadrilaterals Q1. The angles of quadrilateral are in the ratio . Find the angles of the quadrilateral. Solution: Let the common ratio between the angles be x. We know that the 'Sum of the interior angles of the quadrilateral' = Now, Therefore the Angles of the quadrilateral are: Q2. […]
Chapter- 3: Coordinate Geometry Exercise 1 Q1. How will you describe the position of a mobile phone kept on the study table to another person? Solution: For describing the position of a mobile phone kept on the study table, we take two lines, a perpendicular and a horizontal line. Considering the table as a […]
Chapter-2 : Polynomials Exercise – 1 Q.1.Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer: (i) Answer: It is a polynomial in one variable. (ii) Answer: It is a polynomial in one variable. (iii) Answer: It is not a polynomial since the […]
Chapter-5: Introduction to Euclid's Geometry Exercise 5:1 Question 1 : State true or false for the following statements mentioned below with the reason: a: Through a single point only one line can be passed. b: Through two distinct lines there are infinite number of lines that can be passed. c: A line that is […]
Chapter-11: Constructions Question-1 Construct an angle of at the initial point of a given ray and justify the construction. Solution: Given a ray OA. Required: To construct an angle of at 0 and justify the construction. Steps of Construction: Taking 0 as centre and some radius, draw an arc of a circle, which intersects OA, […] | 677.169 | 1 |
Daily Math Review Openers for Algebra 1 Semester 2
Compressed Zip File
Be sure that you have an application to open this file type before downloading and/or purchasing. How to unzip files.
18.96 MB | 188 pages
PRODUCT DESCRIPTION
Review past topics and help students perform well on the standardized test and final exam! This is such a simple concept that makes such a huge difference! Replace your regular class openers with this activity. Each day for two weeks, students practice the same five types of problems in order to solidify that standard in their memories. Hand the day's Daily Math Review to your students as they walk in the door. After five to ten minutes, show the answer key (included in your purchase), which shows how to obtain the answer step-by-step. At the end of two weeks, you give a quiz (also included in your purchase) on the five problems. You will be shocked at how well they work on this! I don't even have to grade or collect the reviews because students know they must take it seriously in order to pass the two-sided, ten-question quiz at the end of two weeks. This has been a wonderful way for me to really get students to keep practicing the most important concepts of Algebra 1 so that my test scores are excellent at the end of the year. Try this and become a believer too!
Included in this file:
*88 Daily Math Reviews (two-week sets of 9-10 reviews for 18 weeks!
*1 double-sided Quiz every 2-week set (2-3 versions for each of the 9 sets)
*Answer keys for all reviews and quizzes (the answers are worked out step-by-step and handwritten)
Concepts Covered:
Set #9 and 10
• Graph two lines in slope-intercept form & find the point of intersection
• Graph a line in point-slope form
• Graph a line in standard form
• Solve a standard form equation for y
• Use substitution or elimination to find the solution of the system
Set #10b
• Find the equation of a line through a given point and parallel or perpendicular to a given line
• Determine which points are solutions to a systems of linear inequalities (from a graph)
• Use substitution or elimination to find the solution of the system
• Find the x- and y-intercepts of a line from a standard form equation
• Use substitution or elimination to find the solution of the system in a word problem
Set #11 and 12 x- and y-intercepts of a line from a standard form equation
• Use substitution or elimination to find the solution of the system in a word problem
Set #13 missing side of a right triangle using Pythagorean Theorem
• Use substitution or elimination to find the solution of the system in a word problem
Set #14
• Find the equation of a line through a given point and parallel or perpendicular to a given line
• Graph a line in slope-intercept form
• Solve by factoring (or quadratic formula, if you wish)
• Find the missing side of a right triangle using Pythagorean Theorem in a word problem
• Use substitution or elimination to find the solution of the system in a word problem
Set #15 and 16
• Distribute a monomial through a binomial using laws of exponents
• Graph a parabola
• Solve by using the quadratic formula
• Find the perimeter of a shape (combining like terms with laws of exponents)
• Find the missing side of a right triangle using Pythagorean Theorem in a word problem
You will notice that there is a LOT of repetition of concepts. This is intentional! Your students need to practice difficult concepts repeatedly over a long period of time for it to be cemented permanently into their brains. These Daily Math Reviews do exactly that | 677.169 | 1 |
PDF (Acrobat) Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
0.26 MB | 1 pages
PRODUCT DESCRIPTION
This can be purchased individually or as a complete unit titled Logarithmic and Exponential Functions Complete Unit (at a discounted price).
This quiz is designed to be given after the lesson titled Logarithmic and Exponential Functions Lesson 1 of 5. Given a table of values, come up with the exponential function represented and graphing two exponential | 677.169 | 1 |
Product Description
▼▲
Singapore Math's Primary Mathematics, Standards Edition Workbooks are consumable and should be used in conjunction with the corresponding textbooks; these Standard Edition workbooks are not compatible with other Singapore editions (e.g. U.S. 3rd Ed.). Containing independent student exercises, workbooks provide the practice essential to skill mastery; each chapter in the textbook has corresponding problems in the workbook while review exercises help students to consolidate concepts they've learned previously. A variety of exercises are presented in the concrete>pictorial>abstract approach, covering algebra, fractions & decimals, percentage, ratio & proportion, rate & speed, and more. 112 pages, softcover. Grade 6. | 677.169 | 1 |
Delivery :
This book is an exposition of some fundamental concepts of Fuzzy Algebra, Fuzzy Topology along with applications of Fuzzy Set Theory in diverse field of scientific knowledge. Today in almost all disciplines of science, engineering and technology, the theory of Fuzzy Sets has become an indispensable part of the curriculum. In fact, Fuzzy Set Theory (FST) provides language for almost all disciplines in contemporary mathematics in much the same way as mathematics does for many sciences. The book first provides exposure to the concepts of fuzzy subgroupoids, fuzzy subgroups, fuzzy level subgroups, fuzzy normal subgroups, fuzzy ring, fuzzy ideal, fuzzy field, fuzzy linear spaces, geometrical sets in a linear space, fuzzy module. Secondly, topological & algebraic topological linear spaces has been dealt with. Finally, the applicational aspects of Fuzzy Set Theory (FST) to two different areas of human knowledge such as sports (Cricket scores) and medicine (detection of blood sugar in human beings) are in-corporated. | 677.169 | 1 |
Synopses & Reviews
Publisher CommentsThe concept of turtle geometry grew out of the Logo Group at MIT. Directed by Seymour Papert, author of Mindstorms, this group has done extensive work with preschool children, high school students and university undergraduates. Harold Abelson is an associate professor in the Department of Electrical Engineering and Computer Science at MIT. Andrea diSessa is an associate professor in the Graduate School of Education, University of California, Berkeley.
Review
"Reading this book with the help of a good graphics computer system, you are sure to discover new and interesting math... an excellent textbook or self-study guide." W. Lloyd Milligan , ByteThe MIT Press
Review
"A college-level math text for serious mathematicians and fans of recreational mathematics. This book proves that turtle graphics is not just kid stuff." Popular ComputingThe MIT Press
Synopsis
Turtle Geometry presents an innovative program of mathematical discovery that demonstrates how the effective use of personal computers can profoundly change the nature of a student's contact with mathematics.
Synopsis The concept of turtle geometry grew out of the Logo Group at MIT. Directed by Seymour Papert, author of Mindstorms, this group has done extensive work with preschool children, high school students and university undergraduatesAndrea diSessa is Chancellor's Professor in the Graduate School of Education at the University of California, Berkeley, and a member of the National Academy of Education. He is the coauthor of Turtle Geometry: The Computer as a Medium for Exploring Mathematics (MIT Press, 1981). | 677.169 | 1 |
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HatO'N Maths
HatO'N Maths
HatO'N Maths provide resources for AQA A-Level Maths Modules. Initially for C1 and C2, the resources will grow over the coming year and eventually become a single source for the new A-Level Maths with a first teaching from September 2017.
Most topic packs will include Powerpoints, Workbooks and Homework sheets with answers.
A complete workbook and series of PowerPoint lessons for the Coordinate Geometry topic which forms part of AQA Core 1 Mathematics AS Level.
Individual topics include: Coordinate Geometry Formulae, Gradient, Mid-point, Length of a line, Finding the Equation of a line and Intersecting lines.
Workbook examples are worked through in the PowerPoint with fully animated examples with explanations given every step of the way. Also included in the PowerPoints are answers to the questions from the Exercises.
Can be used in lessons or outside of lessons for students to learn, recap and revise.
A PowerPoint for students to navigate to revise AQA Decision PowerPoint for students to navigate to revise AQA Core 2 complete workbook and series of PowerPoint lessons for the Surds topic which forms part of AQA Core 1 Mathematics AS Level.
Individual topics include: Simplifying and Rationalising Surds.
Workbook examples are worked through in the PowerPoint with animated examples and explanations given every step of the way. Also included in the PowerPoints are answers to the questions from the Exercises.
Can be used in lessons or outside of lessons for students to learn, recap and revise.
A series of homework tasks covering the Coordinate Geometry section of AQA Core 1 Mathematics.
Topics covered are Length, Midpoint, Gradient, Equation of a Line, and Points of Intersection between lines
PDF files for the questions and editable Word documents with printed answers.
A complete workbook and series of Powerpoint lessons for the Quadratics topic which forms part of AQA Core 1 Mathematics AS Level.
Individual topics include: Completed square form, Factorising, Solving quadratic equations, The discriminant, Disguised quadratics, Simultaneous equations, Finding intersections and Types of intersection.
Workbook examples are worked through in the Powerpoint with animated examples and explanations given every step of the way. Also included in the Powerpoints are answers to the questions from the exercises in the workbook.
Can be used in lessons or outside of lessons for students to learn, recap and revise.
*Updated some Powerpoints due to small errors - please let me know if you find any more
A PowerPoint for students to navigate to revise AQA Core series of homework tasks covering the Surds section of AQA Core 1 Mathematics.
Topics covered are Simplifying and Rationalising.
PDF files for the questions and editable Word documents with printed answers.
These worksheets are tests given to new AS Mathematics student during the first week of the college year to assess their skills from GCSE.
Topics include substitution, surds and indices, rearranging formulae, expanding brackets, factorising and solving equations. Topics are split between the A and B test so both need to be sat. Each one is timed at 25 minutes.
A homework is also included for students to complete outside of the lesson with the same topics covered.
It serves to remind students which aspects of their GCSE Mathematics are required for success in A-Level Maths, as well as giving a measure of the students who are undertaking the course.
A 2 page document with hints and tips for completing the January 2010 Core 1 AS Maths exam.
The exam with the worked solutions follows. You can give out just the hints and tips so that students can refer to them if needed as they work through the past paper for revision.
Worked solutions are then attached for the student to look at when they have completed the paper. | 677.169 | 1 |
About this Category Get the CBSE Class 10 NCERT Solutions for all subjects. Download NCERT Solutions for Class 10th for Science, Maths, Biology and other subjects, all for free only on jagranjosh.com, India's No. education website.
NCERT Exemplar (eBook) Problems and Solution for CBSE Class 10 Maths: Chapter 12 – Surface Areas and Volumes is available for download. With this article, students can get the complete PDF of the chapter.
NCERT Exemplar Problems and Solution eBook for CBSE Class 10 Mathematics: Chapter 11 – Area Related to Circles is available for download. With this article, students can get the complete PDF of the chapter.
Get NCERT Exemplar Problems and Solution for CBSE Class 10 Maths: Chapter 8 – Introduction to Trigonometry and its Applications. With this article, students can download the complete PDF of the chapter.
Learn about NCERT Exemplar Problems and Solution for CBSE Class 10 Mathematics: Chapter 4 – Quadratic Equations. With this article, students can download the complete PDF of the chapter freely as per their convenience.
Get NCERT Exemplar Problems and Solution eBook for CBSE Class 10 Mathematics, Chapter 3 – Pair of Linear Equations in Two Variables. With this article, students can download the complete PDF of the chapter.
Get NCERT Exemplar Questions & Answers eBook for CBSE Class 10 Science: Chapter 11 – The Human Eye and the Colourful World. Students can download the complete PDF of this chapter freely as per their convenience. | 677.169 | 1 |
A unique textbook for an undergraduate course on mathematical modeling, Differential Equations with MATLAB: Exploration, Applications, and Theory provides students with an understanding of the practical and theoretical aspects of mathematical models involving ordinary and partial differential equations (ODEs and PDEs). The text presents a unifying picture inherent to the study and analysis of more than 20 distinct models spanning disciplines such as physics, engineering, and finance.
The first part of the book presents systems of linear ODEs. The text develops mathematical models from ten disparate fields, including pharmacokinetics, chemistry, classical mechanics, neural networks, physiology, and electrical circuits. Focusing on linear PDEs, the second part covers PDEs that arise in the mathematical modeling of phenomena in ten other areas, including heat conduction, wave propagation, fluid flow through fissured rocks, pattern formation, and financial mathematics.
The authors engage students by posing questions of all types throughout, including verifying details, proving conjectures of actual results, analyzing broad strokes that occur within the development of the theory, and applying the theory to specific models. The authors' accessible style encourages students to actively work through the material and answer these questions. In addition, the extensive use of MATLAB? GUIs allows students to discover patterns and make conject | 677.169 | 1 |
Mathematics Core 3 C3 and Core 4 C4 LessonsThis is a set of lessons for A2 Core Mathematics. The resources includes Powerpoints.Powerpoint include:Learning objectivesQuestions on the topicImportant information written in red boxes to scaffold learning.Topics:FunctionsTrigonometryExponentials and LogarithmsProduct RuleQuotient RuleDifferentiation and Integration of Trigonometry Roots to equations (staircase and cobweb diagrams)Integration using the chain ruleIntegration using the rule of LogarithmsIntegration by Substitution Integration by PartsMid ordinate rule and Simpsons RuleExpansion formulaAlgebraPartial FractionsApplications of Partial FractionsImplicit differentiation Tangents and normalsParametric Equation and Differentiation Exponential Growth and DecayDifferential EquationsVectorsI hope you enjoy these lessons, they can be used in the following ways:To deliver a course with reduced planning but not reducing quality of the lesson.As a basis for an observation lesson to save time preparing resources.To give to students for out of lesson learning.To support teachers who are new to this topic, again to reduce planning time.As a bases for your own lessons where you can include exam questions to each presentation.As an activity where the questions can be printed and cut out.
A recap of surds and simplifying expressions with surds, then a full presentation of multiplying brackets and surds, including the conjugate of a binomial.simplify and manipulate algebraic expressions (including those involving surds) by: collecting like terms multiplying a single term over a bracket taking out common factors expanding products of two binomials Lots of points to stop for the learner to try three of four examples, and each questions slide followed by the answers slide.Also suitable for A'level revision!
Pupils are tasked with assessing answers given to questions requiring completing the square of quadratics (trinomials).Thank you for looking.Get in touch via @numberloving or numberloving@outlook.com
Here is my power point trying to structure questions for C2 from past papers. I have split the paper into 91 from past papers. I have split the paper into 113 from past papers. I have split the paper into 7 sections and tried to group questions together. All solutions are given at a click. For use by giving to pupils and leaving them to it, or working through topics as a class. Every question from 2006-2014. Also works extremely well on iPads.
The pdf collects together into a single document the 40 investigatory tasks from the popular Risp website created by Jonny Griffiths at These activities are all pure maths ones, and are written for the A Level Maths syllabus. They represent excellent practise on problem-solving. There are 151 pages, and hyperlinks enable easy navigation.
Huge number of posters to help to produce some great maths displays - in particular focused on real life maths, maths in the news and careers using maths. I've also posted a lot of content on ibmathsresources - so if you like all this, check that out as well!
Dividing Polynomials – Circuit TrainingWork out the problem in the cell #1. To advance in the circuit, find your answer and mark that cell #2. Work out that problem and then find your answer again. Continue working in this manner until you complete the circuit.There are 16 problems in this product.My students love doing these activities.Thank you for checking my resources.
This is 7 lessons worth of resources (more than you need) to teach all the basics that are covered in the first chapter for C1. This is not a chapter I ever rush, because it is the foundations for every other chapter, so it vital they are fully secure. 1. Expanding Quadratics2. Factorising Quadratics3. Algebraic Fractions4. Surds - simplifying5. Surds - multiplying6. Surds - rationalising7. Index notation / Indices NOTE: Feel free to browse my shop for more excellent free and premium resources, and as always please rate and feedback, thanks.
This bundle includes 15 different algebra related resources which suit a range of abilities from simplifying expressions to solving linear and quadratic simultaneous equations.
All resources are available separately and will be part of a bundle by activity type, return buyers should check carefully. Contact me if you would like to see resources bundled in a different way.
Differentiated worksheet with increasing difficulty. Students start at Question A , Record their answer on the sheet and work their way through to L.. Suitable for paired work or individually.Most suitable for all sets but particularly the top sets as it has cubic factorisation as well with (common x) and difference of two squares, snap bracket factorisation.Page 1 is the worksheetPage 2 is the solutions.Goes from level 5 till 8Some students should be able to to A-C, Middle of the group should be able to do A-F , and the top of group should be able to do all of them, A-L This can lead into sketching graphs, solving quadratic and cubic equations...great for 9-1 GCSE and for ADDITIONAL Maths work too...
Review prior learning and help plug gaps with factorising. Do students know difference of two squares, and all the other type of factorising...Page 1 . Start at Question A , record answer and continue onwards up to L. Can be paired work or individual ..Answers on Page 2.
This file has in total 347 algebraic expressions with brackets, which need to be expanded and simplified. The questions are organised by type and each of the seven pages have their own heading and as such can be used as an independent worksheet. All worksheets include answers.Because of the range of difficulty levels of the questions in this file, they can be used, selectively, in Key Stage 3, Key Stage 4 and even at the start of the AS-level course, making sure that all students have a sound understanding of how to expand brackets in more difficult expressions. It would also be a very useful resource on a school's VLE where students can use it for independent study.
A large selection of presentations and activities that show the learners how to sketch rational functions. It includes intercepts, asymptotes and also looks at substituting small and large values of x so students can collect all the data needed to sketch the graphs.Also includes finding the min/max point on a graph without using calculusSMART Notebook Express presentations can be used for free by using SMART online or by downloading SMART software, also free, I use it because it allows a more interactive presentation than a powerpoint. Just search 'SMART Notebook Express' and try it with my free SMART resource.
*UPDATED 3RD MARCH NOW INCLUDES NEW TICK OR TRASHES!
Each resource consists of increasingly difficult questions on the topic. Topics included in this bundle are
1. Rationalising the denominator
2. Comparing fractions, decimals and percentages
3. Vectors
4. Evaluating composite functions
5. Finding the gradient
6. Sharing amounts by ratio
7. Comparing data sets
8. Solving inequalities
9. Reciprocals
10. Completing the square
This worksheet is a follow-up of 'Graphs of Quadratic Functions (1). It has 30 quadratic functions of which the graphs need to be drawn on blank coordinate systems, one for each function. The first 18 functions given are in the form y = p(x + q)2 + r ; by applying appropriate transformations their graphs need to be derived from the standard parabola of the function y = x2. The last 12 functions are given in the form y = ax2 + bx + c and in order to draw the graphs of these functions, they need to be written in the form of y = p(x + q)2 + r by completing their square.This worksheet is aimed to give the skill 'Completing the Square' a clear purpose and it also can be used as an introduction to transformations of graphs
This worksheet has 30 parabolas drawn on individual coordinate systems. For each graph, the corresponding quadratic function needs to be found in the form of y = p(x + q)2 + r and then to be written in the form of y = ax2 + bx + c. The idea of this worksheet is to apply one or more transformations to the standard parabola with function y = x2 to find the functions of a range of parabolas. Transformations to be used are: horizontal translations, vertical translations, vertical stretches and reflections in the x-axis.This worksheet is not only useful to introduce transformations of graphs and the effect they have on functions, it also provides practice for expanding brackets and shows the link between the two formats of quadratic functions as a first step towards completing the square. In 'Graphs of Quadratic Functions (2)' this link is further explored | 677.169 | 1 |
Throughout the year, students will relate new vocabulary to familiar words, listen to, read, and discuss familiar and concept ually challenging text and will use new vocabulary that is introduced and taught directly. (LA.910.1.6.1,
6.2, 6.5
and LA.1112.1.6. 1, 6.2, 6.5 )
Students will also use a variety of problem solving strategies and will apply these skills using axioms and theorems in writing proofs.
(MA.912. G.8.1 through 8.6 )
First Quarter
Second
Quarter
Chapter 1
Body of Knowledge: Geometry
Standard 1: Points, Lines, Angles, and Planes
MA.912.G.1.1
MA.912.G.2.1,
2.7
Building Blocks of Geometry
A.
Defining point, line, angle, ray, plane
B.
Segments and their measures
C.
Angles and their measures
D.
Segment and a ngle bisectors
E.
Introduction to p erimeter, circumf erence and a rea
Chapter 2
Body of Knowledge: Discrete Mathematics
Standard 6: Logic
MA.912.D.6.1,
6.2, 6.4
Body of Knowledge: Geometry
Standard 4: Triangles
MA.912.G.4.5
Standard 8: Mathematical Reasoning and Problem Solving
MA.912.G.8.1
through 8.6
(on - going)
Reasoning and Proof In Geometry
A.
Inductive reasoning
B.
Deductive reasoning
C.
Conditional statements
D.
Reasoning with properties of Algebra
E.
Proving theorems
F.
Planning a proof
Chapter 3
Body of Knowledge: Geometry
Standard 1: Points, Lines, Angles, and Planes
MA.912.G.1.2, 1.3
Perpendicular and Parallel Lines
A.
Lines and angles
B.
Parallel and transversals
C.
Proving lines and parallel
D.
Lines in the coordinate plane
Chapter 4
Body of Knowledge: Geometry
Standard 2: Polygons
MA.912.G.2.2, 2.6
Stand ard 4: Triangles
MA.912.G.4.1, 4.3
Congruent Triangles
A.
Triangles and angles
B.
Triangle inequality
C.
Proving triangles are congruent
D.
Applications in the real - world
Chapters 5 and 6
Body of Knowledge: Discrete Mathematics
Standard 6: Logic
MA.912.D.6.3,
6.4
Body of Knowledge: Geometry
Standard 1: Points, Lines, Angles, and Planes
MA.912.G.1.2
Standard 4: Triangles
MA.912.G. 2.3, 4.2,4.3, 4.4, 4.6, 4.7
Properties of triangles
A.
Medians, altitudes midsegment
B.
Perpendiculars and bisectors
C.
Inequalities in triangles
D.
Construction of angles
E.
Inequality theorems
Similarity
A. Use properties of similar triangles
B. Apply segment divided proportionally
theorems
C. Prove triangles are similar
Body of Knowledge: Geometry
Standard 2: Polygons
MA.912.G.2.4, 2.6
Transformations
A.
Transformations
B.
Reflections
C.
Rotations
D.
Translations
Geometry Honors
(High School )
Course 12 06320
Year at a Glance
Holt McDougal
Larson Geometry
Page 2
REV 11/08/12
Course description:
blicPreviewCourse37.aspx
NG SSS:
Third Quarter
Fourth Quarter
Chapter 7
Body of Knowledge: Geometry
Standard 5: Right Triangle
MA.912.G.5.1 through 5.4
Body of Knowledge: Trigonometry
Standard 2:
Trigonometry of Triangles
MA.912.T.2.1
Right Triangles & Trigonometry
A.
Pythagorean theorem and converse
B.
Special right triangles
C.
Similarity in right triangles
D.
Right triangle trig ratios
E.
Law of sines and cosines
F.
Solve real - world problems using trigonometry
Chapter 8
Body of Knowledge: Discrete Mathematics
Standard 6: Logic
MA.912.D.6.2, 6.4
Standard 11: Sequences and Series
MA.912D.11.5
Body of Knowledge: Geometry
Standard 2: Polygons
MA.912.G.2.3, 2.5
Standard 3: Quadrilaterals
MA.912.G.3.1 through 3.4
Quadrilaterals
A.
Polygons
B.
Properties of parallelograms
C.
Proving quadrilaterals are parallelograms
D.
Rhombuses, rectangles and squares
E.
Trapezoids and kites
F.
Proving theorems about quadrilaterals
G.
Special quadrilaterals
H.
Fibonacci sequence and g olden ratio (Ch 6.3)
I.
Similarity (Ch 6.3)
Chapters 10 and 11
Body of Knowledge: Geometry
Standard 7: Polyhedra and Other Solids
MA.912.G.7.4
Standard 6: Circles
MA.912.G.6.1 through 6. 7
Geometry of Circles
A.
Arc lengths and area of sectors
B.
Ratio of area s
C.
Chord properties
D.
Tangent properties
E.
Arc and angle properties
F.
Circumference / diameter ratio
G.
Inscribed angles
H.
Area and circumference
Chapters 11 and 12
Body of Knowledge: Geometry
Standard 2: Polygons
MA.912.G.2.5
Standard 7: Polyhedra and other Solids
MA.912.G.7.1, 7.2, 7.3, 7.5, 7.6, 7.7
Area and Volume
A.
Area of polygons
B.
Prisms and cylinders
C.
Pyramids and cones
D.
Displacement and density
E.
Spheres
F.
Polyhedrons
G.
Cross sections
H.
Total surface area
I.
Similar solids (Ch11.3)
.
Chapter 9
Body of Knowl edge: Geometry
Standard 2: Polygons
MA.912.G.2.6
Standard 4: Triangles
MA.912.G.4.8
Body of Knowledge: Discrete Mathematics
Standard 6: Logic
MA.912.D.6.4
Standard 9: Vectors
MA.912.D.9.3
Coordinate Geometry
A.
Vectors
B.
Midpoint formula(Ch 8)
Geometry Honors
(High School )
Course 12 06320
Year at a Glance
Holt McDougal
Larson Geometry
Page 3
REV 11/08/12
Course description:
blicPreviewCourse37.aspx
NG SSS:
Qtr
1
Qtr 2
Qtr 3
Qtr 4
YEAR LONG
Text Alignment
MA.912.G.8.1
High
Analyze the structure of Euclidean geometry as an axiomatic system. Distinguish between undefined terms, definitions, postulates, and theorems.
MA.912.G.8.2
Moderate
Use a variety o f problem - solving strategies, such as drawing a diagram, making a chart, guess - and - check, solving a simpler problem, writing an equation, and working backwards.
MA.912.G.8.3
Moderate
Determine whether a solution is reasonable in the context of the or iginal situation.
MA.912.G.8.4
High
Make conjectures with justifications about geometric ideas. Distinguish between information that supports a conjecture and the proof of a conjecture.
MA.912.G.8.5
High
Write geometric proofs, including proofs
by contradiction and proofs involving coordinate geometry. Use and compare a variety of ways to present deductive proofs, such as flow charts, paragraphs, two - column, and indirect proofs.
Use properties of congruent and similar triangles to solve problems involving lengths and areas.
MA.912.G.4.6
High
Prove that triangles are congruent
or similar and use the concept of corresponding parts of congruent triangles.
MA.912.G.4.7
Moderate
Apply the inequality theorems: triangle inequality, inequality in one triangle, and the Hinge theorem.
MA.912.G.2.4
High
Apply transformations (tran slations, reflections, rotations, dilations, and scale factors) to polygons. to determine congruence, similarity, and symmetry. Know that images formed by translations, reflections, and rotations are congruent to the original shape. Create and verify tesse llations of the plane using polygons.
MA.912.G.2. 6
High
Use coordinate geometry to prove properties of congruent, regular and similar polygons, and to perform transformations in the plane.
Geometry Honors
(High School )
Course 12 06320
Year at a Glance
Holt McDougal
Larson Geometry
Page 5
REV 11/08/12
Course description:
blicPreviewCourse37.aspx
NG SSS:
Week of Explicit Instruction
Quarter 3
Text Alignment
MA.912.G.5.1
High
Prove and apply the Pythagorean theorem
and its co nverse .
MA.912.G.5.2
Moderate
State and apply the relationships that exist when the altitude
is drawn to the hypotenuse
of a right triangle .
MA.912.G.5.3
Moderate
Use special right triangles
(30° -
60° -
90° and 45° -
45° -
90°) to solve problems.
MA.912.G.5.4
High
Solve real - world problems involving right triangles.
MA.912.T.2.1
Moderate
Define and use the trigonometric ratios (sine, cosine, tangent, cotangent, secant, cosecant) in terms of angles of right triangles.
MA.912.D.6.3
Moderate
Determine whether two propositions are logically equivalent.
MA.912.D.6.4
Moderate
Use methods of direct and indirect proof and determine whether a short proof is logically valid.
MA.912.D.11.5
High
Explore and use other sequences
found in nature such as the fibonacci sequence
and the golden ratio .
MA.912.G.2.3
High
Use properties of congruent and similar polygons to solve mathematical or real - world problems. | 677.169 | 1 |
Advanced Algorithms and Complexity
Advanced Algorithms and Complexity
University of California, San Diego, Higher School of Economics
About this course: You've learned the basic algorithms now and are ready to step into the area of more complex problems and algorithms to solve them. Advanced algorithms build upon basic ones and use new ideas. We will start with networks flows which are used in more typical applications such as optimal matchings, finding disjoint paths and flight scheduling as well as more surprising ones like image segmentation in computer vision. We then proceed to linear programming with applications in optimizing budget allocation, portfolio optimization, finding the cheapest diet satisfying all requirements and many others. Next we discuss inherently hard problems for which no exact good solutions are known (and not likely to be found) and how to solve them in practice. We finish with a soft introduction to streaming algorithms that are heavily used in Big Data processing. Such algorithms are usually designed to be able to process huge datasets without being able even to store a dataset profoundNetwork flows show up in many real world situations in which a good needs to be transported across a network with limited capacity. You can see it when shipping goods across highways and routing packets across the internet. In this unit, we will discuss the ma...
9 videos, 3 readings
Graded: Flow Algorithms
Graded: Programming Assignment 1
WEEK 2
Linear Programming
Linear programming is a very powerful algorithmic tool. Essentially, a linear programming problem asks you to optimize a linear function of real variables constrained by some system of linear inequalities. This is an extremely versatile framework that immediat...
10 videos, 1 reading
Graded: Linear Programming Quiz
Graded: Programming Assignment 2
WEEK 3
NP-complete Problems
Although many of the algorithms you've learned so far are applied in practice a lot, it turns out that the world is dominated by real-world problems without a known provably efficient algorithm. Many of these problems can be reduced to one of the classical pro...
16 videos, 1 reading
Graded: NP-complete Problems
Graded: Programming Assignment 3
WEEK 4
Coping with NP-completeness
After the previous module you might be sad: you've just went through 5 courses in Algorithms only to learn that they are not suitable for most real-world problems. However, don't give up yet! People are creative, and they need to solve these problems anyway, s...
11 videos, 1 reading
Graded: Coping with NP-completeness
Graded: Programming Assignment 4
WEEK 5
Streaming Algorithms (Optional)
In most previous lectures we were interested in designing algorithms with fast (e.g. small polynomial) runtime, and assumed that the algorithm has random access to its input, which is loaded into memory. In many modern applications in big data analysis, howeve...
10 63 ratings
Nice one.
illuminative
N
Loved what I learnt, I also implemented a project using Google MAP API for the organization I'm working at
TS
The problems are really challenging, thank you! However, the instructor is not very active in the discussion forum, which is a pity when you really need help and get stucked in the problem set. | 677.169 | 1 |
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