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courses in developmental mathematics.
Giving Meaning to the Numbers
Gary Rockswold and Terry Krieger give meaning to the numbers that students encounter by developing concepts in context through the use of applications, multiple representations, and visualization. By seeing the concept in context before being given the mathematical abstraction, students make math part of their own experiences instead of just memorizing techniques. Research is showing that this method is essential to empowering students. Seamlessly integrated real-life connections, graphs, tables, charts, and meaningful data help students deepen understanding and prepare for future math courses—and life—by teaching them critical thinking and problem-solving skills.
Built in MyMathLab
Interactive Developmental Mathematics offers a completely digital experience, built by Gary Rockswold and Terry Krieger from the ground up in MyMathLab to model the way today's students learn and interact online. MyMathLab is an online homework, tutorial, and assessment program designed to engage students and lead them to master the concepts and skills they need to succeed in math. Within its guided learning environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them master course material and understand difficult concepts.
Author Biography
Gary Rockswold has been a professor and teacher of mathematics, computer science, astronomy, and physical science for over 35 years. He has taught not only at the undergraduate and graduate college levels, but he has also taught middle school, high school, vocational school, and adult education. He received his BA degree with majors in mathematics and physics from St. Olaf College and his Ph.D. in applied mathematics from Iowa State University. He has been a principal investigator at the Minnesota Supercomputer Institute, publishing research articles in numerical analysis and parallel processing and is currently an emeritus professor of mathematics at Minnesota State University, Mankato. He is an author for Pearson Education and has over 10 current textbooks at the developmental and precalculus levels. His developmental coauthor and friend is Terry Krieger. They have been working together for over two decades. Making mathematics meaningful for students and professing the power of mathematics are special passions for Gary. In his spare time he enjoys sailing, doing yoga, and spending time with his family. Additional information about Gary Rockswold can be found at
Terry Krieger has taught mathematics for 20 years at the middle school, high school, vocational, community college and university levels. His undergraduate degree in secondary education is from Bemidji State University in Minnesota, where he graduated summa cum laude. He received his MA in mathematics from Minnesota State University - Mankato. In addition to his teaching experience in the United States, Terry has taught mathematics in Tasmania, Australia and in a rural school in Swaziland, Africa, where he served as a Peace Corps volunteer. Terry currently lives and works in Rochester, Minnesota. He has been involved with various aspects of mathematics textbook publication throughout his career in mathematics education and has joined his friend Gary Rockswold as coauthor of a developmental math series published by Pearson Education. In his free time, Terry enjoys spending time with his wife and two boys, physical fitness, wilderness camping, and trout fishing. Additional information about Terry Krieger can be found at
Table of Contents
1 Whole Numbers
1.1 Introduction to Whole Numbers
1. Reviewing Natural Numbers and Whole Numbers
2. Understanding Place Value
3. Writing Whole Numbers in Word Form
4. Writing Whole Numbers in Expanded Form
5. Graphing Whole Numbers on the Number Line
6. Reading Bar Graphs and Line Graphs
7. Reading Spider Charts
8. Reading Tables
1.2 Adding and Subtracting Whole Numbers; Perimeter
1. Adding Whole Numbers without Regrouping
2. Adding Whole Numbers with Regrouping
3. Using Properties of Addition
4. Recognizing Words Associated with Addition
5. Subtracting Whole Numbers without Regrouping
6. Subtracting Whole Numbers with Regrouping
7. Using Properties of Subtraction
8. Recognizing Words Associated with Subtraction
9. Solving Equations Involving Addition and Subtraction
10. Solving Perimeter and Other Applications Involving Addition and Subtraction
1.3 Multiplying and Dividing Whole Numbers; Area
1. Multiplying Whole Numbers
2. Using Properties of Multiplication
3. Multiplying Larger Whole Numbers
4. Recognizing Words Associated with Multiplication
5. Dividing Whole Numbers
6. Using Properties of Division
7. Performing Long Division
8. Recognizing Words Associated with Division
9. Solving Equations Involving Multiplication and Division
10. Solving Area and Other Applications Involving Multiplication and Division | 677.169 | 1 |
Math 152 (Linear Systems), Spring 2018
Common Course Page
The textbook 'Introduction to Linear Algebra for Science and
Engineering' by Daniel Norman is now on course reserve in the
library. The book covers similar material to our course and it
is a good source for additional practice problems.
Elyse Yeager has compiled a list of things that you should know for
the first midterm exam.
Math 152 is a first course in linear algebra. It
emphasizes geometry in two and three dimensions,
applications to engineering and science problems and
practical computations using MATLAB. A detailed week by week
outline can be found below.
Additional notes written by Brian Wetton on the subject
of complex numbers are available here.
WebWork Assignments:
WebWork Assignments are posted online every week on
Fridays and have a deadline for submission on Monday (after
10 days) at 10PM.
There will be eleven assignments. Your lowest mark will
be dropped from the average.
WebWorK assignments can be accessed from the UBC connect system. Here is a direct
link to WebWork.
Computer Labs:
Computer labs using the mathematical software package
MATLAB begin in the second week of classes. Each student
does a lab every two weeks, starting in the second or third
week. Look at your lab section registration information to
see where your lab will be held and what week you start.
MATLAB material will be tested on exams.
Lab assignments are posted on the UBC connect system. Lab reports are
also submitted in this system.
Lab reports are due on Fridays 10PM.
Lab 1: Jan 26
Lab 2: Feb 9
Lab 3: Mar 2
Lab 4: Mar 16
Lab 5: Mar 30
Lab 6: Apr 6
Late submissions are accepted one week after the deadline
for 50% of marks.
UBC has a site license for MATLAB. Registered students
can download it on their own computers. Detailed
instructions can be found here.
Exams:
We will have two evening midterm exams:
Thu, February 8, 6-7PM
Thu, March 15, 6-7PM.
The final exam is scheduled by the university.
Students that miss midterm exams for a valid reason
(official written verification is required) will have their
final mark averaged proportionally over the other course
material.
No calculators or notes for exams.
Piazza:
Piazza is a discussion forum for asking questions about
homeworks, labs, exams and other course related material.
There are no TAs or instructors who will monitor the forum
regularly and answer questions. We hope students themselves
can help other students, but please avoid giving away the
whole solution to homework and lab problems. | 677.169 | 1 |
Calculus I by Paul Dawkins
Description: These notes should be accessible to anyone wanting to learn Calculus I or needing a refresher in some of the early topics in calculus. Contents: Review; Limits; Derivatives; Applications of Derivatives; Integrals; Applications of Integrals.
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Calculus for Mathematicians, Computer Scientists, and Physicists by Andrew D. Hwang - Holy Cross The author presents beautiful, interesting, living mathematics, as informally as possible, without compromising logical rigor. You will solidify your calculational knowledge and acquire understanding of the theoretical underpinnings of the calculus. (7152 views)
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This course is about using mathematics to make good financial decisions.
It is a new version of the old M133, Consumer Mathematics, which was
a two credit course. Instead of focusing on the mathematics of
retailing,
we will concentrate on the mathematics of finance and investment. The
equations involved can be complex at times, but we will largely avoid
dealing with those equations by using appropriate technology.
A financial calculator and computer with spreadsheet program (Excel) are
essential tools for the course. You must have your own financial
calculator, but the computers in the student labs will be available for
your spreadsheet assignments if you do not own a PC.
You should have a copy of the text, The Mathematics of Money, which is
available at Business Express (1014 South College) for about $20, and a
financial calculator. The acceptible calculators include models by HP
(10B), Sharp (EL733A), and Texas Instruments (BA II+), which cost from
$30
to $40. Any calculator with PV and FV (present value and future value)
keys
is suitable. A scientific calculator is generally NOT acceptable,
although
some scientific calculators do have financial functions as well, and
those
would be OK.
The course begins with work on equations, unit quantities, percents,
and graphs. We will start dealing with spreadsheets after a couple of
weeks,
and they will be an extremely powerful tool for graphing.
The second section of the course is about checking, simple and
compound interest, index numbers, and annuities. This part of the
course uses the full power of the financial calculators and formula
building in spreadsheets to improve our basic financial math skills.
The final part of the course applies tools developed earlier to more
complex problems in credit and investment. Home financing and mortgages
are
considered in detail, and then various investments (including insurance,
stocks, bonds, mutual funds, and IRAs) are analysed. We even talk about
the
effect of inflation on investments - Allen Greenspan will not be around
forever! During the final section of the course each student will
complete
a project applying the tools of the course to analyze a financial
choice.
Examples include buying vs. renting a home, borrowing vs. saving, and
working vs. going to college.
Examinations:
Exams will be held on
Friday September 24,
Friday October 29,
and Friday December 10.
The compehensive final is Thursday Dec 16, 1:30 - 3:30 p.m.
Grading Policy:
Grades in M133 will be based on performance in class (including a
project), on quizzes, and
on exams. There will be about twenty quizzes, three in-class exams, and
a
comprehensive final. The points available will be approximately
200 for class work, 200 for quizzes, 300 for exams, and 200 for the
final.
The grading curve will be about 90-80-70-60%. | 677.169 | 1 |
MIDDLE SCHOOL MATH
My name is Neil Doose. I earned my teaching degree at St. Cloud State University and have an elementary teaching license, a middle school math teaching certificate, and also earned a coaching minor. I have coached jr. high football for 18 years, basketball for 28 years, and boys golf for 10 years. I also coached baseball for 15 years.
My duties at school are to help all middle school students achieve at their highest potential so they can be successful as members of our society. My classrooms are very structured as I believe that students learn the best under ideal learning environments. I enjoy helping and watching students learn and developing new skills.
This course is designed to provide students with an introduction to the concepts of algebra and geometry, to solidify the students grasp of arithmetic concepts and procedures, and to provide exploratory experiences in data analysis and probability. Problem-solving skills will also be developed throughout the course.
Course Objectives:
1. Students will solidify computational skills with fractions, decimals, percents, and whole numbers.
2. Students will apply problem solving strategies to topics including pre-algebra, geometry, statistics, probability, and measurement.
3. Students will use formulas, tables and proportions to solve various problems
4. Students will develop skills, concepts, and applications with number sense, estimation, and computation | 677.169 | 1 |
5
Understanding the concepts of penalizing the objective function
Understanding the need and concepts of artificial variables
Understanding the concept of M as a very large positive value and its
role in the Big-M method
Ability to prepare and set up the starting initial tableau for Big-M
method and carrying out iterations of simplex method in Big-M method
Ability to identify infeasible problems from final Big-M simplex tableau
Ability to recognize the general form of Z-row elements as indicators of
whether a solution is feasible or not
Study Guide
Watch Topic 5 video (35:29 minutes). Since, this topic uses concepts
developed in topic 4 make sure that you are comfortable with
the concepts and procedures related to simplex method applied to canonical
forms. If needed,
please view Topic 4 video again before watching Topic 5 video
Visit the
Operations Research course on my Web site. On the sliding panel on the
left hand side click on "Archive" and
select "Solved Problems". In the solve Problems window click on "Big-M
and Two-phase(Big-M) 5 Two specific sets of videos from India Institute
of Technology, Madras and one set from India Institute of Technology, Kanpur are
excellent resources that can help your development in operations research. They
are more advanced than MOOCOR series and also covering additional topics, but
for those of you who are using MOOCOR to learn operations research for the first
time or as a refresher course, following those lectures is much easier. The
video series are Fundamentals of Operations Research (22 lectures) and
Advanced Operations Research (29 lectures) both by Professor G. Srinivasan
from the Department of Management Studies at IIT-Madras. and Linear
programming and Extensions (40 lectures) by Professor Prabha Sharma of the
Department of Mathematics and Statistics at IIT-Kanpur. Links to those videos
are also provided on my operations research pages | 677.169 | 1 |
From Calculus to Chaos
An Introduction to Dynamics
David Acheson
A lively and accessible introduction to applied mathematics at university level
Intended for sixth formers and first-year undergraduates
Has won excellent reviews for style and presentation
From Calculus to Chaos
An Introduction to Dynamics
David Acheson
Description
What is calculus really for? This book is a highly readable introduction to applications of calculus, from Newton's time to the present day. These often involve questions of dynamics, i.e., of how--and why--things change with time. Problems of this kind lie at the heart of much of applied mathematics, physics, and engineering. From Calculus to Chaos takes a fresh approach to the subject as a whole, by moving from first steps to the frontiers, and by focusing on the many important and interesting ideas which can get lost amid a snowstorm of detail in conventional texts. The book is aimed at a wide readership, and assumes only some knowledge of elementary calculus. There are exercises (with full solutions) and simple but powerful computer programs which are suitable even for readers with no previous computing experience. David Acheson's book will inspire new students by providing a foretaste of more advanced mathematics and some of its liveliest applications.
From Calculus to Chaos
An Introduction to Dynamics
David Acheson
Reviews and Awards
"Despite public interest, it has been difficult to find a suitable introductory book on chaos for mathematics students. In 'From Calculus to Chaos', David Acheson manages to bridge the gap, tie the topic into the undergraduate curriculum, throw in some history and practical techniques, and tell readers about an experimental basis of dynamical systems theory--all this without being stuffy."--New Scientist
"This is a thoroughly excellent little book and a most valuable addition to the literature on dynamics. Its approach is quite unique, bringing together a vast range of real physical phenomena and elucidating the essential dynamics by means of well chosen toy models in the form of differential equations. All the necessary analytical techniques are slipped in with the minimum of fuss, and numerical methods are employed throughout in such a way that the reader is encouraged to use the computer as an experimental tool. . . .the book deserves a place on the shelves of all serious students, teachers, and researchers." --UK Nonlinear News
"The book is quite suitable as a text in dynamics and can serve as a refresher for those wishing to see how applied math courses they struggle through can be made simple."--Bulletin of the American Meteorological Society
"This short introductory-level book illustrates several important ideas of contemporary research in nonlinear dynamics by the numerical solution of rigid solids and fluids examples. . . .[m]ost of the complex phenomena currently studied in nonlinear dynamics are modeled by equations whose properties can only be uncovered by numerical methods or by more oblique analytic attacks on their qualitative behavior. Students would likely be more successful if they have this library of physical examples with which to test ideas." --Applied Mechanics Reviews
"Acheson presents an introduction to the calculus-based development of dynamics (continuous dynamical systems). The text is a beautiful historical review of physical mathematics from Newton and Leibniz to Lorenz in the late 20th century. It begins with a brief review of projectile and planetary motion and related topics in calculus and differential equations, including numerical (computer) solutions and the theory of oscillations. Later chapters discuss more advanced topics: the three-body problem, wave and diffusion equations, action and Hamilton's principle, calculus of variations, Lagrange's equations, fluid flow, theory of linear stability, bifurcation and catastrophic change, nonlinear oscillations, and the Lorenz equations. . . . an excellent overview of a broad body of material in a historically accurate setting. Chapter exercises; appendixes with solutions to exercises and an elementary introduction to programming in QBASIC. Undergraduates through professionals."--Choice
"The book under review falls into the category of 'books I would have liked to have read in high school and first year in college, and then I would have been much better off'. Indeed, this is a very attractive introduction to a number of topics in dynamics, understood widely to include classical mechanics, wave motion, fluid flow, etc. The author has given us earlier another well-written and frequently cited textbook . . . , and here we find again the same laudable style of exposition."--Mathematical Reviews
"Mathematics and Physics have always had close connections, it seems. In fact, the boundaries between the two subjects have been quite fluid over time. Not too long ago, Newtonian mechanics . . . was a part of mathematics, and number theory and algebraic geometry were the purest of pure mathematics. Things look different now. It also used to be the case that all mathematicians knew lots of physics, or at least theoretical physics. That, too, is no longer the case. Many mathematicians have never even had a course in theoretical mechanics. David Acheson's From Calculus to Chaos is a book that can remedy that lack. It is a friendly introduction to dynamics that uses historical vignettes, well-chosen examples, and computer simulation to survey the field and show us, in the words of the blurb writer, what the calculus is really for."--The Mathematical Association of America | 677.169 | 1 |
Knowing how to understand math, at times, becomes really difficult. Someone missed it at school, or someone forgot what he or she knew some time ago, and it is becoming extremely difficult to cope with the tasks of higher mathematics while studying at college or university. A huge amount of formulas, integrals, calculations of derivatives and other aspects of the program make students struggle. Analyzing this, you can often feel yourself as a fool.
How to learn math on your own? The first step is to fill the gaps from the past. If you missed (did not understand, basically did not study, etc.) some subject, sooner or later you will be faced with studying problems. Gaps are the understandable problem. But how do you remove them? How do you learn math?
Whether you are learning a new topic or repeating an old one, learn the basic mathematical definitions and terms! You have to understand, for example, what is a discriminant, an arithmetic progression, or an arc sine on a simple, even primitive level. You must know what it is, why it is needed and how to deal with it. Life will be easier if you know how to teach yourself math.Continue reading →
Many people often wonder why they need mathematics. Often, the mere fact that this discipline is included in the compulsory program of universities and colleges puts people in bewilderment. This bewilderment is expressed as follows: "Like, why do I need math, as my future (or present) profession is not related to the conducting of calculations and application of mathematical methods? Do adults learning maths really need it?"
Will math be useful in life? So many people do not see any sense for themselves in the development of this science, even at the elementary principles. But we believe that mathematics, more precisely mathematical thinking skills, are needed by everyone. In this article, we will explain why we are so sure in this, and how you can learn math, adults or students, no matter who you are – this post will be helpful to you. Continue reading →
Logic is a branch of philosophy which is the study of reasoning and arguments. Arguments are ideas which are defended through claims and the usage of critical thinking. How do you present ideas so that a person who disagrees with you can attack them? Not only do students of philosophy study logic, but so do writers, lawyers, policy markers and so on. We are here to help all students who have college logic problems.
Do you know what is the meaning of arithmetic? Arithmetic is the branch of math that deals with properties and numbers manipulation. The arithmetic mean is a mathematical representation of the value of a series of numbers which is computed as the sum of all numbers divided by the number of numbers in the series.
What is arithmetic math? One of the most fundamental branches of mathematics is arithmetic operations. It includes adding, subtracting, multiplying, and dividing numbers. Primary education in math places a strong focus on algorithms for arithmetic of integers, natural numbers, fractions, and decimals. Continue reading →
If you want to know how to learn math online effectively, you should simplify complex ideas to understand them. Math can make things simpler when applied effectively. Math does not only teach you to think, but helps you simplify ideas. This style of thinking is not necessary, but it is often interesting.
Math simplification can be done through learning. Do you know what learning contains? It includes insight and enthusiasm. Insight comes from diagrams, analogies, examples, technical definitions and plain English descriptions. Enthusiasm helps to learn math faster. If you want to know how to relearn math, first of all you need to have some enthusiasm and motivation as well. Continue reading →
One of the reasons so many students struggle with online math learning is because instruction does not work well for a particular subject. For one thing, mathematics is cumulative. You should master the earlier concepts if you want to understand the later ones. If a student falls behind the pace of the math class, he or she is going to become more confused.
Math is an extremely important subject. Math allows us to understand the inner workings of the universe. It shows us our insignificance as well as our remarkable potential. It gives us a hint of the possibilities that exist. And if you know where to start learning math, you can achieve this knowledge without any problems.
Many people don't know how to start learning math, what books to study, or what topics to begin with. Many students feel intimidated by math – they seem to believe that it is a thing that only the sharpest individuals can understand. But nothing could be further from the truth. Let's figure out why you are mistaken. Continue reading →
What is arithmetic? Arithmetic is a field of mathematics that studies the elementary properties of numbers, ways of recording and operations on them. It is the science of numbers, primarily of natural (positive integer) numbers and (rational) fractions and operations on them. Let's consider the question deeper.
What Is An Arithmetic
Possession of a well-developed concept of a natural number and the ability to perform actions with the numbers are necessary for practical and cultural activities in life. So knowing what is a arithmetic is an element of pre-school education and a compulsory subject in the school curriculum for all students. Continue reading →
Math students should not only deal with problem solving, but with writing assignments as well. One of the branches that you will face is the history of math. Many students get assignments to write projects about different events in math history. If you are one of them, our topics in the history of mathematics will help you. | 677.169 | 1 |
11-16 Maths: Preparing in KS3 for success at GCSE
Our unique Master maths with confidence approach is embedded in our KS3 and GCSE (9-1)resources providing a seamless 5-year curriculum that prepares students for Edexcel GCSE (9-1) Mathematics from the start of KS3.
Written to specifically tackle the demands of the GCSE (9-1) maths, our resources take an innovative mastery approach and focus on nurturing confidence, building fluency and embedding problem-solving and reasoning.
NEW – for first teaching from September 2017 Developed in line with the key principles of the new specification, our new Edexcel GCSE (9-1) Statistics Student Book will help teachers and students to feel confident with the new breadth of content and skills required.
BBC Bitesize revision resources helps students break their a richer, fuller, more varied and effective revision experience.
Mathematics for AQA GCSE Modular offers a carefully structured, step-by-step approach that builds students' confidence. Includes Student Texts and Student Support Books (with or without answers) for both foundation and higher to support students with gradual progression, exam preparation and revision support.
Complete with a main text and Student Support Books with or without answers, this course provides gradual progression with carefully graded exercises and exam-style questions for effective exam preparation.
What does it do? This Student Book plus Activities and Assessment Pack provides awards at levels 1, 2 and 3 of the National Curriculum. It prepares students for entry to GCSE plus GNVQ/VGCE and NVQ courses.
Our course for the GCSE 2010 Mathematics specification A (linear) helps you target the new objectives effectively, with a clear emphasis on Assessment, Functional Skills and differentiation to ensure all your students succeed.
Whether you're looking for comprehensive and differentiated materialsor brand-new Student Books that are fully in line with the ethos of Curriculum for Excellence, Scottish Secondary Mathematics provides you with an array of resources to support all your teaching from S1-S4. | 677.169 | 1 |
The class will entail detailed coverage of algebraic concepts. Strong emphasis will be placed on the application of basic arithmetic to algebraic concepts. Topics will include rational and irrational algebraic expressions, factoring, solving equations, quadratics, polynomials, exponents and radicals. The course will also build a necessary vocabulary in mathematics for future courses as well as for this course. | 677.169 | 1 |
Graphing Calculators - PowerPoint PPT Presentation
Graphing Calculators. Using technology not as a crutch for basic calculations, but rather as a link to higher levels of understanding and to critical thinking skills. The Benefits of Using Graphing Calculatorshing Calculators' - geMinnesota state standards require 8th graders to be introduced to such topics as algebra and statistics.
Without bogging students down with complicated formulas and tedious construction of graphs by hand, the important mathematical concepts can be taught, rather than the potentially confusing computations.
In a world saturated in technology, it is good for students to work with high-tech devices. | 677.169 | 1 |
I've been troubled ever since David Cox asked why students needed to learn the names of the algebraic properties (associative, identity, and so forth). Certainly I see misunderstandings: students confronted with
$latex (3 + x) + 2$
not aware they can combine the 3 and 2 with associative and commutative properties, or the classic
$latex frac{x+2}{x}$
leading the student to cancel the x terms rather than consider the distributive property. (*)
Clearly these things are being taught, but what's going awry when they are used in practice? And why do students learn the names of these things?
It struck me that students only get taught the definition in a positive sense, memorizing (for example) that | 677.169 | 1 |
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Entrance examinations - Mathematics
Mathematics entrance examination program is developed on basis of the exemplary program recommended by the Ministry of Education and Science of the Russian Federation.
MATHEMATICS
This program consists of three sections. In the first section there are listed the main mathematical concepts every applicant has to know for passing both written and oral examinations. The second section represents the list of questions for the theoretical part of an oral examination. The third section specifies the knowledge and skills requirements of an applicant for passing written and oral examinations. Extent of knowledge of the material described in the program corresponds to a high school mathematics course. Applicant may use all means from this course, including elements of calculus. But to solve examination problems it is enough to have solid knowledge of the concepts and their properties listed in the present program. Objects and facts studied at general education school also can be used by applicants, but provided that they are capable to explain them and to prove.
(), arithmetical root . Equation. Roots of an equation. Concept of equivalent equations. Inequations. Inequation solution. Concept of equivalent inequalities. Set of equations of inequalities. System solution. Arithmetic and geometric progression. Formula of the nth term and sum of first n terms of arithmetic progression. Sine and cosine of sum and of difference of two arguments (formulas). Sum-to-product formula ; . Differentiation. Its physical and geometrical meaning. Derived functions .
Geometry Line, ray, segment, polyline; length of line segment. Angle, angle value. Vertical and adjacent angles. Circumference, circle. Parallel lines. Examples of transformation, types of symmetry. Similarity transformation and its properties. Vectors. Vector operations. Polygon, its apexes, sides, diagonals. Triangle. Its median, bisector, altitude. Types of triangles. Relationships between sides and angles of a right triangle. Quadrangle: parallelogram, rectangle, rhombus, square, trapezoid. Circumference, circle. Centre, span, diameter, radius. Tangent to circle. Arc of circle. Sector. Central and inscribed angles. Formulas for area of: triangle, rectangle, parallelogram, rhombus, square, trapezoid. Length of circumference. Arc length. Radian measure. Area of a circle and of a sector. Similarity. Similar figures. Similar figures area ratio. Plane. Parallel and intersecting planes. Parallelism of line and plane. Angle between line and plane. Perpendicular to plane. Dihedral angle. Linear angle of dihedral angle. Perpendicularity of two planes. Polyhedrons. Their apexes, faces, diagonals. Straight and oblique prisms; pyramids. Regular prism and regular pyramid. Parallelepipeds, their types. Solids of revolution: cylinder, cone, sphere, ball. Centre, diameter, radius of a sphere and a ball. Plane, tangent to sphere. Surface area and volume formulas for a prism. Surface area and volume formulas for a pyramid. Surface area and volume formulas for a cylinder. Surface area and volume formulas for a cone. Volume formula of a ball. Surface area formula of a sphere.
Primary formulas and theorems
Algebra and Pre-Calculus Properties of function and its graph. Properties of function and its graph. Properties of function and its graph. Quadratic formula. Factorization of quadratic trinomials. Properties of numerical inequalities. Logarithm of product, exponent, quotient. Definition and properties of function and , their graphs. Definition and properties of function и , their graphs. Solution of equations type , , . Reduction formulas. Dependencies between trigonometric functions with identical argument. Trigonometric functions of double argument. Derivative of the sum of two functions.
Geometry Properties of an isosceles triangle. Properties of points equidistant from the segment endpoints. Characteristics of parallel lines. Angle sum of a triangle. Sum of exterior angles of a convex polygon. Characteristics of parallelogram, its properties. Circumscribed circle of a triangle. inscribed circle of a triangle. Tangent to circle and its properties. Measure of an inscribed angle in a circle. Characteristics of similarity of triangles. Pythagoras' theorem. Formula of area of a parallelogram, triangle, trapezoid. Distance formula between two points of plane. Circle equation. Line-plane parallelism characteristic. Planes parallelism characteristic. Line-plane perpendicularity theorem. Perpendicularity of two planes. Theorems of parallelism and perpendicularity of planes. Theorem of three perpendiculars.
Primary knowledge and skills
Applicant has to know: To perform arithmetic operations with numbers in the form of standard and decimal fractions, with desired precision to round off these numbers and computational results; to use calculators or reckoners. To carry out identity transformations of polynomials, fractions containing variables, expressions containing exponents, indicative, logarithmic and trigonometrical functions. To make graphs of linear, quadratic, exponential, indicative, logarithmic and trigonometrical functions. To solve equations and inequalities of the first and second degree, equations and inequalities leading to them; to solve systems of equations and inequalities of the first and second degree and those leading them. Here, in particular, are related the elementary equations and inequalities containing exponential, indicative, logarithmic and trigonometrical functions. To solve problems with equations and systems of equations. To draw geometric shapes and to make elementary constructions in the plane. To use geometrical representations while solving algebra problems, to use algebra and trigonometry methods while solving geometric problems. To perform vector operations in the plane (adding and subtracting vectors, vector-number multiplication) and to use properties of these operations. To use concept of a derivative while examining functions on increase (decrease), extrema and while making graphs of functions. | 677.169 | 1 |
Course Summary
In a typical mathematics course, a student learns a combination of theory and computation, with the latter providing concrete examples of how the former is exhibited ``in the real world." Of course, ``the real world" in a mathematics class is the realm of pure mathematics, where real numbers have infinite decimal expansions and there are a continuum of numbers that are as close to zero as you like. In the real world that we experience on a day-to-day basis, however, concepts which rely on infinite precision have a harder time being implemented in a practical way; one simply only has so much memory that one can allocate to storing the decimal digits of $\pi$, for instance. The typical answer to this problem is to allow ourselves to approximate real values in our computations, with the tacit assumption that these approximated values will be sufficient for any ``real" problem we might face. Moreover, if there's some situation where one needs additional precision when doing a certain computation, the assumption is that if one begins with a higher precision approximation to the number in question, then computations with this better approximation should themselves be more precise.
In many ways, numerical analysis is the class in which one investigates whether these assumptions are true. It is a class that is steeped both in practical application (almost by its nature), but also intimately connected to deeply theoretical --- and often philosophical --- considerations. Perhaps the most consistent question we will aim to answer in this class is: how can I approximate a particular mathematical computation, and how well do I understand the error in this approximation? In answering this question we'll consider how computers store and process real numbers, how algebraically equivalent expressions for two quantities can yield dramatically different computed results, and how to effectively compress information to retain only the most important information.
Course Instructor
The professor for this class is Andy Schultz. His office is on the third floor of the Science Center, room S352. His office hours will be | 677.169 | 1 |
The result is a row vector, each element of which is an inner product of and a column vector
7
product of two matrices
vector outer product
8 Linear Algebra
Two vectors
are said to be orthogonal to each other if
A set of vectors of dimension n are said to be linearly independent of each other if there does not exist a set of real numbers which are not all zero such that
otherwise, these vectors are linearly dependent and each one can be expressed as a linear combination of the others
9
Vector x ! 0 is an eigenvector of matrix A if there exists a constant ? such that Ax ?x
? is called a eigenvalue of A (wrt x)
A matrix A may have more than one eigenvectors, each with its own eigenvalues
Ex.
has 3 eigenvalues/eigenvectors 10
Matrix B is called the inverse matrix of square matrix A if AB I (I is the identity matrix)
Denote B as A-1
Not every matrix has inverse (e.g., when one of the row can be expressed as a linear combination of other rows)
Every matrix A has a unique pseudo-inverse A, which satisfies the following properties
AAA A AAA A AA (AA)T AA (AA)T
Ex. A (2 1 -2), A (2/9 1/9 -2/9) T
11
Calculus and Differential Equations
, the derivative of , with respect to time
System of differential equations
solution
difficult to solve unless are simple
12
Multi-variable calculus
partial derivative gives the direction and speed of
change of y with respect to . Ex.
13
the total derivative of
gives the direction and speed of change of y, with respect to t
Gradient of f
Chain-rule z is a function of y, y is a function of x, x is a function of t
14
dynamic system
change of may potentially affect other x
all continue to change (the system evolves)
reaches equilibrium when
stability/attraction special equilibrium point
(minimal energy state)
pattern of at a stable state often represents a solution of the problem | 677.169 | 1 |
Comparing two books essay sample
Thus, we have proved the Pythagorean Theorem for the puzzle.
The proofs presented here are just a few of the many proofs of the
Pythagorean Theorem. The Pythagorean Theorem is a very important concept
for students to learn and to understand. It cannot be stressed enough that
students need to understand the geometric concepts behind the theorem as
well as its algebraic representation. This can be accomplished through the
use of technology, manipulatives, and proofs. Students who are taught the
Pythagorean Theorem using these methods will see the connections, and thus,
benefit greatly | 677.169 | 1 |
24 comments:
Just been to a conference at Loughborough University and there seems to be so many different mathematical educational experts which are really developing the subject (mathematics) into unknown territory. I personally think all that technology can provide is to motivate individuals. The ONLY way to learn mathematics is to DO mathematics. This subject is not a spectator sport.
Writing notes on supremum and infimum which students find very difficult to grasp. I wonder if it might be better just to use the terms Least Upper Bound and Greatest Lower Bound rather than the latin based supremum and infimum respectively.
Just marked the Foundations of Mathematics workbook. Some concerns of the work is as follows: Functions The part on surjection of a function was not done well. Only need to select an element in the codomain and show that the function f does not map to it. Proof by Induction Most students prefer to expand rather than factorize their results which can be difficult in proving a given result by induction. I assume they do this automatically because it is the first thing that comes to their head. It is important to look at the final goal in prove by induction and then carry out the appropriate action on the result. Proofs Many mathematics students don't like to write words but when writing a proof you need to be familiar with what is required. It is always good to finish a proof by the words "hence the result follows …" Just because a result works for some numbers does not mean that it holds for all the numbers. To prove a result it is not good enough just to try some numbers and conclude the general result holds. Common Mistakes Composition of Functions - fof does not equal fxf Simple algebraic mistakes such as not using the rules of indices when carrying out proof by induction.
Used Smirk for the first time to teach my engineering class. Steve Bennett who was one of the developers (David Kraithman being the other) helped set everything up. It took a good half hour to set up. I will have to wait and see if this is a useful tool to use for teaching.
Smirk is a teaching tool which saves your work on the pc and records your voice. I use it to deliver my lectures by writing my notes on a tablet pc and speaking simultaneously. Students can then view this lecture on the web at the following url: uk/~matqkks/lectures/
I love this site engineering-maths-online.blogspot.com. Lot of great information. I am Tech guy. I have been a Desktop Technician since 1997 but have tons of other interests. In my spare time... Oh, wait I don't have any of that (just kidding). Anyways, I have been aware of this website for quite some time and decided to join the community and contribute as well as learn a lot from others. I am excited to get started on the forum and am looking forward to a great journey together. Lots of potential friends and I look forward to meeting many online. watch harry potter and deathly hallows online
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just wanted to say atm in im my second year doing mechanical engineering and im using your book and words cant even say how good this book is
alittle background i was orignily not a smart kid so went round the other side and became a really bad kid who failed alot of subjects went collage cause thats all i could get in to, few years past i got a diploma in electronical engineering (did electronics cause like fixing stuff) and got in to city london university failed really bad maily due to very bad maths skills now im in coventry university and passed my first year with a 1st as maths was not an issue for me as i had the worlds best book
and now im in second year and im still using your book which is truly AMAZING
i still dont even know my timetables but i know maths only from your book | 677.169 | 1 |
John Dixon, MI Julieta Cuellar, PN
Algebrator is truly an educational software. My students feel at ease while using it. Its like having an expert sit next to you. John Kattz05-28:
adding, subtracting, multiplying, and dividing fractions worksheets
cube aptitude question
solving ratios and proportion worksheets
longest math equation solving for a variable
help with college algebra
pre algabra
problem solve Multivariable Linear Systems
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Course info
Apprenticeship and Workplace Math 11 is a course designed to prepare students to meet daily challenges in which numeration is needed. Mathematics also helps us see the order and beauty within God's creation, or world around us. Together we will explore mathematics through projects, activities, and problems that we might face in life. Topics covered will include measurement, slope, graphical representations, geometry, financial mathematics, budgeting, and problem solving skills. | 677.169 | 1 |
How to Tutor Math Effectively - Techniques for Using the Textbook
When working with students, you've probably heard things like, "No matter how hard I study, I just can't seem to do well on my math exams" or "I'm just not mathematically inclined; there's nothing I can do to improve." In these situations, a tutor will often take a "hammer approach," or continuing to repeat the same drills and explanations over and over until they sink in. Unfortunately, this approach is generally ineffective and will only frustrate your student. Often, the student's problem is simply not knowing how to study math correctly. As a tutor, guiding your students in techniques for effectively using their textbooks will help them build foundational skills for long-term success in math.
Help your students apply the following steps when using their math books, and you should see a noticeable difference in their learning. Help your student learn to…
Step 1: Survey the Chapter
Preview the chapter by identifying key concepts, definitions, and methods.
Don't worry about understanding—your goal is to get a taste of what's coming so that you're mentally "warmed up" and familiar with some key terms before going into more detail.
Source
Step 2: Read and Reread the Textbook
Read slowly and reread passages you don't understand. Math textbooks are not repetitive—each word is important.
(As a tutor, avoid the temptation to jump in and offer clarification and additional explanations. Instead, work on helping your students to develop the reading skills to comprehend the text on their own. For example, you could suggest something like, "This is a tricky concept. It's ok if it doesn't make sense right away. Try rereading the passage again, and this time break it apart into smaller pieces and follow along with the diagram for each part." Your students will be much better served if you help them gain this valuable skill rather than just re-explaining the concept to them using the "hammer method.")
Pay particular attention to mathematical concepts. If you understand the concepts, you should be able to do any kind of problem, even those that are different from ones you have practiced. This is why you'll often hear students complain that problems on the exam were different from what they studied in class—the instructor is testing your ability to apply the mathematical concepts to new situations, not your ability to memorize example problems.
Read relevant sections before they're introduced in class, not after. Then, you can use class time to clarify points of confusion. Try it—you may be surprised at how much more you're able to learn during class time if you've previewed the material.
Source
Step 3: Do Example Problems
Math concepts are learned by doing problems, not just by reading. As you read each sub-section in a chapter, copy down the example problems on a separate sheet of paper and attempt them on your own.
Even if you get stuck on a problem and need to refer to the book's solution, do the problem again on your own after reading the solution.
Source
Step 4: Do Homework Problems
Do the homework problems without looking up the answer until after completing the problem.
When you get stuck, refer back to example problems for clues.A common mistake I see students make is looking up the answer while in the process of attempting a problem. You will learn the material better if you do the problems without first looking at the answer key. Plus, you won't have this safety net when you take your exam.
After you complete your homework for a given chapter, practice a few problems from earlier chapters. Math books typically group problems into chapters by concept, so continually reviewing earlier chapters ensures that you're deeply learning these concepts.
At first, your students might be frustrated that you're making them think so much on their own without just giving them "hints" or even the answer. When this happens, explain to them that you won't be there to give them hints when they're taking their exams. Instead, your goal is to give them the skills they need to succeed on their own and without your help. I promise you, your students will eventually thank you for it! | 677.169 | 1 |
Elements of the Theory of Numbers teaches students how to develop, implement, and test numerical methods for standard mathematical problems. The authors, Joseph and Thomas Dence, have developed a comprehensive, rigorous overview of number theory. This text makes greater use of the language and concepts in algebra and analysis than is traditionally encountered in introductory courses.
Professors and students will welcome how the chapters are divided into two sets: Chapters 1-6 and part of Chapter 7 pertain to all readers. This set ends with a full chapter on number fields. Chapters 10 and 11 are considered special topics which allow greater flexibility for the professor. | 677.169 | 1 |
Description: This book was written as a guide for a one week course aimed at exceptional students in their final years of secondary education. The course was intended to provide a quick but nontrivial introduction to Einstein's general theory of relativity, in which the beauty of the interplay between geometry and physics would be apparent.
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MA2509: ANALYSIS II (2017-2018)
Course Overview
Analysis provides the rigourous, foundational underpinnings of calculus. This course builds on the foundations in Analysis I, and explores the notions of Riemann integrability, Cauchy sequences, sequences of functions, and power series.
The techniques of careful rigourous argument seen in Analysis I will be further developed. Such techniques will be applied to solve problems that would otherwise be inaccessible. As in Analysis I, the emphasis of this course is on valid mathematical proofs and correct reasoning.
Taylor series. Computing radius of convergence using the limsup root test; uniform convergence of power series; Lagrange's form of the remainder; products of power series.
Further Information & Notes
Course Aims
To further develop understanding of the concepts, techniques, and tools of calculus. Calculus is the mathematical study of variation. This course emphasises integral calculus, sequences and series, and introduces multivariable calculus. Applications to the theory of functions will be discussed.
Learning Objectives
By the end of this course the student should:
be able to state the main definitions and theorems of the course;
be able to prove most results from the course;
understand Riemann integration and theorems about the Riemann integral;
be able to apply techniques for showing integrability or non-integrability of functions;
understand Cauchy sequences and their relationships to convergent sums and the Cauchy criteria for convergence of series;
be able to distinguish between pointwise and uniform convergence of sequences of functions;
be able to compute Taylor series, compute the interval of convergence of power series, and use Taylor's theorem to estimate functions by polynomials.
Degree Programmes for which this Course is Prescribed
BSc Applied Mathematics
BSc Computing Science-Mathematics
BSc Mathematics
BSc Mathematics with French
BSc Mathematics with Gaelic
MA Business Management - Mathematics
MA Mathematics
MA Mathematics with Gaelic
Mathematics Joint
Mathematics Major
Mathematics Minor
Contact Teaching Time
44 hours
This is the total time spent in lectures, tutorials and other class teaching.
Formative Assessment
Informal assessment of weekly homework through discussions in tutorials.
Feedback
In-course assignments will normally be marked within one week and feedback provided to students in tutorials. Students will be invited to contact Course Coordinator for feedback on the final examination. | 677.169 | 1 |
Algebra problems calculator
Hereare a few of the ways you can learn here.Lessons Explore one of our problemss of lessons on keyalgebra topics like Equations,Simplifying and Factoring. Checkout the entire list of lessons. Over the years, algebrahelp.com has helpedstudents solve algebra problems calculator calculwtor million equations. See allthe problems we can help with. Worksheets Need to practice a new type of algebra problems calculator. We havetons of problems in the Worksheets section. We can grade youranswers automatically, or you can compare against the answer key. Browse the list of worksheets to getstarted.
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Freeware for learning about math, Physics, and engineering. Math quiz has the Space Invaders type look and feel where the math problems fall down the screen. You can also take a look at the virtual generator which shows you how electricity is made. Other
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Phyz is an educational program which shows various Physics theories/concepts and contains sets of problem-solving programs.The basic philosophy is to explain and provide an easy interface for problem-solving. | 677.169 | 1 |
Mathematics
Mathematics is a discipline in which the complexity, harmony and precision of God's character are reflected. The theme emphasized throughout our math courses is that mathematics evidences the purposeful design of our universe by a creative God. Students choose between the applied and academic courses in Grades 9 and 10. Beginning in Grade 11, the program diversifies. Students choose between university and college destination courses. Strong basic skills are emphasized in conjunction with a focus on analytical skills used to solve complex problems. Technology is used in all math classes in the form of graphing calculators and the Smartboard. Enrichment opportunities are provided through participation in the Canadian Mathematics Competition conducted by the University of Waterloo.
Principles of Mathematics, Grade 9, Academic (MPM1D)
This course enables students to develop an understanding of mathematical concepts related to algebra, analytic geometry, and measurement and geometry through investigation, the effective use of technology, and abstract reasoning. Students will investigate relationships, which they will then generalize as equations of lines, and will determine the connections between different representations of a linear relation. They will also explore relationships that emerge from the measurement of three-dimensional figures and two-dimensional shapes. Students will reason mathematically and communicate their thinking as they solve multi-step problems.
Prerequisite: None
Foundations of Mathematics, Grade 9 Applied (MFM1P)
This course enables students to develop an understanding of mathematical concepts related to introductory algebra, proportional reasoning, and measurement and geometry through investigation, the effective use of technology, and hands-on activities. Students will investigate real-life examples to develop various representations of linear relations, and will determine the connections between the representations. They will also explore certain relationships that emerge from the measurement of three-dimensional figures and two-dimensional shapes. Students will consolidate their mathematical skills as they solve problems and communicate their thinking.
Prerequisite: None
Principles of Mathematics, Grade 10 Academic (MPM2D)
This course enables students to broaden their understanding of relationships and extend their problem-solving and algebraic skills through investigation, the effective use of technology, and abstract reasoning. Students will explore quadratic relations and their applications; solve and apply linear systems; verify properties of geometric figures using analytic geometry; and investigate the trigonometry of right and acute triangles. Students will reason mathematically and communicate their thinking as they solve multi-step problems.
Prerequisite: Mathematics, Grade 9, Academic or Applied
Foundations of Mathematics, Grade 10 Applied (MFM2P)
This course enables students to consolidate their understanding of linear relations and extend their problem-solving and algebraic skills through investigation, the effective use of technology, and hands-on activities. Students will develop and graph equations in analytic geometry; solve and apply linear systems, using real-life examples; and explore and interpret graphs of quadratic relations. Students will investigate similar triangles, the trigonometry of right triangles, and the measurement of three-dimensional figures. Students will consolidate their mathematical skills as they solve problems and communicate their thinking.
Prerequisite: Mathematics, Grade 9, Academic or Applied
Foundations for College Mathematics, Grade 11, College Preparation (MBF3C)
This course enables students to broaden their understanding of mathematics as a problem-solving tool in the real world. Students will extend their understanding of quadratic relations; investigate situations involving exponential growth; solve problems involving compound interest; solve financial problems connected with vehicle ownership; develop their ability to reason by collecting, analysing, and evaluating data involving one variable; connect probability and statistics; and solve problems in geometry and trigonometry. Students will consolidate their mathematical skills as they solve problems and communicate their thinking.
Prerequisite: Foundations of Mathematics, Grade 10, Applied
Functions, Grade 11, University Preparation (MCR3U)
This course introduces the mathematical concept of the function by extending students' experiences with linear and quadratic relations. Students will investigate properties of discrete and continuous functions, including trigonometric and exponential functions; represent functions numerically, algebraically, and graphically; solve problems involving applications of functions; investigate inverse functions; and develop facility in determining equivalent algebraic expressions. Students will reason mathematically and communicate their thinking as they solve multi-step problems.
This course enables students to broaden their understanding of mathematics as it is applied in the workplace and daily life. Students will solve problems associated with earning money, paying taxes, and making purchases; apply calculations of simple and compound interest in saving, investing, and borrowing; and calculate the costs of transportation and travel in a variety of situations. Students will consolidate their mathematical skills as they solve problems and communicate their thinking.
College and Apprenticeship Mathematics, (MAP4C) Grade 12, College Preparation
This course enables students to broaden their understanding of real-world applications of mathematics. Students will analyse data using statistical methods; solve problems involving applications of geometry and trigonometry; solve financial problems connected with annuities, budgets, and renting or owning accommodation; simplify expressions; and solve equations. Students will reason mathematically and communicate their thinking as they solve multi-step problems. This course prepares students for college programs in areas such as business, health sciences, and human services, and for certain skilled trades.
This course enables students to broaden their understanding of mathematics as it is applied in the workplace and daily life. Students will investigate questions involving the use of statistics; apply the concept of probability to solve problems involving familiar situations; investigate accommodation costs, create household budgets, and prepare a personal income tax return; use proportional reasoning; estimate and measure; and apply geometric concepts to create designs. Students will consolidate their mathematical skills as they solve problems and communicate their thinking.
Advanced Functions, Grade 12 University Preparation (MHF4U)
This course extends students' experience with functions. Students will investigate the properties of polynomial, rational, logarithmic, and trigonometric functions; develop techniques for combining functions; broaden their understanding of rates of change; and develop facility in applying these concepts and skills. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended both for students taking the Calculus and Vectors course as a prerequisite for a university program and for those wishing to consolidate their understanding of mathematics before proceeding to any one of a variety of university programs.
Prerequisite: Functions, Grade 11, University Preparation, or Mathematics for College Technology, Grade 12, College Preparation
Calculus and Vectors, Grade 12, University Preparation (MCV4U)
This course builds on students' previous experience with functions and their developing understanding of rates of change. Students will solve problems involving geometric and algebraic representations of vectors and representations of lines and planes in three-dimensional space; broaden their understanding of rates of change to include the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions; and will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended for students who choose to pursue careers in fields such as science, engineering, economics, and some areas of business, including those students who will be required to take a university-level calculus, linear algebra, or physics course.
Note: The new Advanced Functions course (MHF4U) must be taken prior to or concurrently with Calculus and Vectors (MCV4U) | 677.169 | 1 |
Today's mathematics curriculum prepares students for their
future roles in society, and for a large range of post-secondary destinations. Students
are encouraged to pursue the mathematics courses that best suit their
mathematical abilities and appropriate post-secondary aspirations.
The development of mathematical knowledge is a gradual process. A coherent and
continuous program is necessary to help students see the "big pictures", or
underlying principles, of mathematics. The mathematics courses in this curriculum recognize the importance of
not only focusing on content, but also of developing the thinking processes that
underlie mathematics. By studying mathematics, students learn how to reason
logically, think critically, and solve problems – key skills for success in
today's workplaces. | 677.169 | 1 |
Provides a summary of key mathematical skills and illustrates how they are used to solve chemical problems. Fundamentals of computer programming are introduced and used to develop simple programs. Appropriate for Jr/Sr/Grad level courses in chemical calculations, math for chemistry, computational chemistry. May also be used as a supplemental text for physical, analytical, or special-topics courses. | 677.169 | 1 |
Franklin Bradley, AK
We are still both novices with the program, but have seen its benefits nonetheless. Tom Sandy, NE
After downloading the new program this looks a lot easier to use, understand. Thank you so much. Jori Kidd, KY
The step-by-step process used for solving algebra problems is so valuable to students and the software hints help students understand the process of solving algebraic equations and fractions. Sean O'Connor | 677.169 | 1 |
Refer to projected answer key
and make necessary corrections using color pen. Students learn by doing
math. HW is assigned daily to encourage this learning and is posted daily on my
website on "due date" rather than date assigned. Each assignment is to
be done directly in NB following that day's lesson notes. Date your HW;
indicate textbook pages and problem numbers. You are responsible for
learning how to do every problem. Be sure to check answers for odd-numbered
problems provided in the back of your text as you are doing the assignment.
This will enable you to assess whether or not your procedure is correct. If
your answer does not agree, go back and carefully re-do the problem referring to
class notes. Each assignment automatically includes the careful reading of
the text's coverage of the topic. HW is graded for effort, not accuracy.
Full credit (2 pts.) will be given when the original problem is written
with procedural steps and final conclusion indicated; partial credit (1
pt.) if incomplete or late, and NO credit if un-submitted, copied from
another student or from the back of the text. You will be allowed to miss 1
assignment per marking period without being penalized. HW represents 10% of
your marking period average.
·Upon completing this HW check, the new lesson will be presented. Class work
represents 10% of your marking period average.
·Mathematics is such a structured, sequential investigation that
you
truly handicap your
understanding of the material with any ABSENCE. It is your responsibility to
get class notes missed and to check to see if tests or quizzes were announced
during your absence (refer to my website or contact a classmate). Feel free to
e-mail me at LMiller@ihahs.com.
·Quizzes represent 30% and Tests represent 50% of your marking
period average. Quizzes
are given on parts of chapters, tests at the conclusion of each chapter. They
will be announced well in advance. Given the structured nature of math, much of
this work is cumulative. If you are absent on the day of a test or quiz
(without missing actual lessons), be prepared to take test or quiz
immediately on the day of your return (before school, at lunchtime, or after
school). For an extended absence, you will be expected to meet with me on the
day of your return to arrange for lesson coverage and test/quiz make-up.
·Academic Honesty: A student's performance on HW, quizzes
and tests
I look forward to sharing
my love of math with you!! Remember, ALGEBRA is a GAME – Enjoy playing it!!! | 677.169 | 1 |
Flick Photos
Mathematics
Mathematics
Projects & Labs
Resource Links
Algebra Teaching Tips for students in introductary algebar class that struggle with basic concepts. Based on lessons learned with a diverse group of learnersm following are some tips from George Alland, Rasmussen College; for teaching algebra to a general audience.
Khan Academy - Algebra II: Over 133 practice exercises to learn what comes next, help students remember what they've learned by mixing up skills and answering questions about functions, complex numbers, polynomials, and more. | 677.169 | 1 |
Precalculus projects
Precalculus projects, Search this site home precalculus projects.
If you are in need of technical support, have a question about advertising opportunities, or have a general question, please contact us by phone or submit a message. Projects for precalculus table of contents crickets - nature's thermometer-- linear functions that relate the rate of crickets' chirps and temperature are analyzed. Classes and projects that spark precalculus strand p1: standard 1 of the precalculus strand p12: 2nd expectation in standard p1 p12 organizational structure. Good ideas in teaching precalculus and geometry projects using geometer and financially savvy by infusing money applications into pre-calculus.
Hhs reference book project reference book outline checkpoint 1 (chapters 1 and 2): due monday, october 2, 2017 checkpoint 2 (chapters 3 and 4): due monday, october 30. 1st marking period project - due friday, november 2, 2012 transformation of functions projectdoc graphing_coordinate_planepl 2nd marking period project - due. Use projects, real-world activities, and games to bring precalculus to life for students[precalculus ]high school precalculus is meant to be an intermediary step to. The precalculus photo project / polynomial functions take photos and find the equation of the graph that matches find this pin and more on precalc honors projects.
Projects available: polynoimials and trigonometry tex version or postscript version project contributed by neal brand this project uses trigonometric identities to. We will analyze the motion of a girl on a swing and determine the mathematical equations can be used for this model using a program called loggerpro students will. Click here to access the polar graph project or go to create a free website powered by. While skill levels may vary, each of these are 21st century math projects that line up with algebra 2 or pre-calculus content of course some of my more advanced. So what's this incredible project students draw a picture on their graphing calculator using functions they've learned and restricting the domains.
Projects name: course: topics covered: college costs 2: college algebra: linear functions and slope: medical insurance: college algebra, precalculus, finite math. Part of a roller coaster track is a sinusoidal function the high and low points are separated by 150 feet horizontally and 82 feet vertically. Polynomial functions definition: a polynomial function is a function with many terms a polynomial can be classified by the number of terms it has (binomial. Find and save ideas about precalculus on pinterest | see more ideas about calculus, algebra and trigonometry.
Ok so i have to do a research paper/presentation on an experiment/project that relates to my precalculus class only problem is that i was given no topics to choose.
Calculus graphing projects incline experiment - to do this, for each student i had to manufacture 1x2 wood sticks with a groove ripped on one side for a marble. Mrs stephens mathematical model of the seattle big wheel the seattle big wheel is a ferris wheel located at pier 57 of seattle the big wheel opened on june 29, 2012. Honors precalculus class the following will help you link to areas that pertain specific assignments or projects in precalculus adobe. | 677.169 | 1 |
I've always wanted to excel in factor tree examples and explanations , it seems like there's a lot that can be done with it that I can't do otherwise. I've searched the internet for some good learning tools, and consulted the local library for some books, but all the information seems to be directed to people who already know the subject. Is there any tool that can help new people as well?
What exactly is your problem with factor tree examples and explanations ? Can you provide some additional information your difficulty with finding a tutor at an affordable price is for you to go in for a appropriate program. There are a number of programs in math that are to be had. Of all those that I have tried out, the best is Algebra Helper . Not only does it work out the algebra problems, the good thing in it is that it makes clear each step in an easy to follow manner. This ensures that not only you get the correct answer but also you get to learn how to get to the answer.
When I was in school, I faced similar problems with parallel lines, solving inequalities and least common denominator. But this superb Algebra Helper helped me through all my Algebra 2, Intermediate algebra, and Intermediate algebra. I only typed in a problem , and step by step solution to my algebra homework would appear on the screen by clicking on Solve. I truly recommend the Algebra Helper .
scientific notation, matrices and algebra formulas were a nightmare for me until I found Algebra Helper , which is really the best algebra program that I have come across. I have used it frequently through several math classes – Pre Algebra, Remedial Algebra and Basic Math. Simply typing in the math | 677.169 | 1 |
C.P., Massachusetts
Absolutely genius! Thanks! Daniel Swan, IA
The step-by-step process used for solving algebra problems is so valuable to students and the software hints help students understand the process of solving algebraic equations and fractions | 677.169 | 1 |
Tag: variables
Welcome to the 7th edition of Math and Multimedia blog carnival. Before we begin Carnival 7, let's look at some of the trivias about the number seven: The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000. Currently, six of the problems remain unsolved. Seven, the fourth prime number, is not…
Should students learn the properties of equality before we ask them to solve equations in one variable? Would it be too hard for them to solve the equation 2(x + 7) = 4x without knowing the properties of equality? In the grades, pupils learn to find equivalent ways of expressing a number. For example 8…
Algebraic thinking is an approach to thinking about quantitative situations in general and relational manner. This kind of thinking is optimized by a considerable understanding of the objects of algebra, a disposition to think in generality, and engagement in high-level tasks which provide contexts for applying and investigating mathematics and the real-world. Objects of Algebra… | 677.169 | 1 |
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Trigonometric identities assignment
The Six Trigonometric Functions 1. homepage National 5 Mathematics Course Summary National 5 Mathematics in a Nutshell. Engage in Training. Clicking on a topic link (in. She Loves Math: Free Math Website. Troduction to Algebra Types of Numbers and Algebraic Properties. Cos theta dfracbc 3. National 5 Mathematics Course Summary National 5 Mathematics in a Nutshell. Pes of NumbersRight from online calculator rearrange my formula to systems of linear equations, we have all the details included. Sin theta dfracac 2. Ursework The S5 course is shown in the table below. Important Information: Syllabus (updated): Wiseman Pre calculus 16 17 Calendar: (to be updated) ASSIGNMENTS: The date below is the date on which the assignment was. Expression is a record of a computation with numbers, symbols that represent numbers, arithmetic? High School: Algebra Introduction Print this page Expressions? Ursework The S5 course is shown in the table below. Csc theta dfracca . MVP team members are actively engaged in providing training and professional development to support implementation. Me to Mymathtutors. And discover factoring. Tan theta dfracab 4. Clicking on a topic link (in!
Program Title: Mining Engineering Technician Credential Earned: Ontario College Diploma Program Length: 4 Semesters if full time; at your own pace if part timeA free math website that explains math in a simple way, and includes lots of examples. Urses are. Right from online calculator rearrange my formula to systems of linear equations, we have all the details included. He associated series is defined as the ordered formal sumWelcome to theWTC eCampus 20162017Powered by MoodleDon't See Your Courseare automatically enrolled in courses on eCampus. Ny identities are known in algebra and calculus. Definition. R any sequence of rational numbers, real numbers, complex numbers, functions thereof, etc. 14 Comments on What is trigonometry all about. Me to Mymathtutors. Johan de Nijs says: 1 Dec 2008 at 11:55 pm Comment permalink Cientific American (SciAm! And discover factoring. ) December 2008. Ll text is available to Purdue University faculty, staff, and students on campus through this site. 14 Comments on What is trigonometry all about. Johan de Nijs says: 1 Dec 2008 at 11:55 pm Comment permalink Cientific American (SciAm. An identity is an equation which is true for all possible values of the variable(s) it contains. Includes Elementary Math, Pre Algebra, Algebra, Pre Calculus, Trig, and Calculus! Theses and Dissertations Available from ProQuest. Program Title: Mining Engineering Technician Credential Earned: Ontario College Diploma Program Length: 4 Semesters if full time; at your own pace if part timeMDM4U1 Mathematics of Data Management, Grade 12 University (Ontario, Canada curriculum) Textbook: Data Management 12, Mc Graw Hil Ryerson, Copyright 2014Important Information: Syllabus (updated): Wiseman Pre calculus 16 17 Calendar: (to be updated) ASSIGNMENTS: The date below is the date on which the assignment was. ) December 2008!
ALH 1010: Introduction to Health Related Professions: Credits: 3: This course is designed for students who are interested in exploring, planning, and preparing for a. | 677.169 | 1 |
The following external links are tutorials and labs on calculators, spreadsheets, dynamic geometry, and symbolic manipulators that can be found on the Web. If you have an additional source that would promote learning these tools, please contact us at intrmath@uga.edu.
Calculators
Texas Instruments
TI educational products page.
TI-82
This tutorial starts from scratch with turning on the TI-82 calculator and takes you through the basic steps needed to do arithmetic and function evaluation and to enter, graph and tabulate functions. You use a TI-82 as you view the tutorial to do and check the exercises scattered through the tutorial.
TI calculator guidebooks, all varieties
These downloadable guidebooks (pdf format) created by Texas Instruments show you how to use the features on all of the TI calculators and accessories. You can download the entire book, or just view a chapter. You can also find materials on using flash technology upgrades with the more recent calculators.
A spreadsheet tutorial
This tutorial shows you how to enter values in a cell, and use various functions as formulas in Excel and Qualtro Pro.
Basic spreadsheets step by step
This is an introductory guide to the most basic features of spreadsheet programs. Even though it is based on Microsoft Excel, most of the features can be transferred to other spreadsheet programs. It is meant to give you a boost in getting started with spreadsheets, and not to be a comprehensive review. It covers the spreadsheet screen layout, data entry, cell addressing, functions, and graphing.
Excel tutorials
Microsoft Excel Tutorial
This tutorial covers the basics of Excel. It describes in detail the parts of an Excel spreadsheet, how to navigate throughout a workbook, and how to input and format your data.
The Microsoft Office Spreadsheet
This is a quick tour by Microsoft describing the features of Excel 2003. You can read able the possibilities to manage and share information, access and analyze data, and streamline the way you work.
ClarisWorks tutorials
Basic spreadsheet using ClarisWorks
This tutorial covers entering data, formula basics, using functions, sorting data, special features, making charts, and more. The design uses hypertext so you can quickly reference a topic and link to related topics.
Basic Skills with GSP
Various GSP Resources from basic skill tutorials to lessons with GSP. Download 2 GSP files that walk you through the basics of GSP.
Virtual Institute
Tutorial on how to drawing, constructing, and moving in GSP from NJSSI.
Introductory Lab
This lab shows how to begin using GSP, use different tools, label and relabel points, highlighting and hiding objects, measuring objects, constructing objects, and using the coordinate system.
GSP into (GSP format)
This Geometer's SketchPad file is template that allows you to familiarize yourself with its capabilities.
How to create a script
This page gives directions on how to create a script that can be placed in your tool bar and then used in new sketch.
Script tutorial
This page illustrates how to create and run scripts for a triangle and circumcenter based on three initial points.
The Geometer's SketchPad, three labs
These labs made in GSP investigate rotations and translations, cycloids, the area of a parallelogram, the area of a triangle, and the area of a rectangle.
Cabri Geometry Tour
This excerpt from the TI book Exploring the Basics of Geometry with CabriT shows how to create and label elementary objects, correct an error, and modify the size of objects.
Symbolic Manipulators
TI 92 calculator
This is a very basic tutorial that begins with turning on the TI-92 calculator and proceeds through the basic steps needed to do arithmetic and finally to entering, graphing and and tabulating functions.
TI 92 guidebook - symbolic manipulation
This chapter in the TI 92 guidebook created by Texas Instruments (pdf format) shows you how to perform algebraic and calculus operations, how to define functions, and how manipulate variables. | 677.169 | 1 |
MAT 171 Survey of Calculus for Management and Life
Sciences
This is a sample syllabus only. Ask your instructor for the
official syllabus for your course.
Instructor:
Office:
Office hours:
Phone:
Email:
Course Description
Functions, linear equations, the derivative and its
applications, the integral and its applications, and partial
derivatives.
Satisfies the General Education Quantitative Reasoning
Requeirement.
Note. Students who have credit in MAT 191
(Calculus I) or its equivalent, or who have credit in a course for
which Calculus I is a prerequisite, will not receive credit for MAT
271.
4 units credit.
In recent years MAT 171 has focused almost exclusively on the
life sciences and applications that are important in life sciences.
MAT 171 aims to give biology and life science students an overview
of calculus so that they understand what calculus can do in a
life-science context. and read and comprehend life science
literature that uses the concepts of calculus. Students learn to
use the concepts, symbols, language, and tools of calculus: rates
of change, derivatives, differential equations, integration, to
solve life-science problems. By the end of the course students
should be able to understand life-science literature where calculus
is used and communicate productively with mathematicians about life
science problems.
Integration: solve the differential equation
\(\frac{dg}{dx}=f(x)\) where \(f\) is a known function. Elementary
interpretation: find position given speed of travel. Connection
between this and finding an area.
Demonstrate understanding of the meanings of indefinite and
definite integrals and fundamental theorem of calculus, use
integrals to solve applied problems.
Use calculators or computers to evaluate complex expressions,
use spreadsheets to model dynamic problems where several
interrelated things are changing e.g. spread of epidemics | 677.169 | 1 |
10th Honors
Grade Level: 9, 10
Length of Course: Year
Pre-requisite: 9th Honors and Recommendation
Credit: 1
Course Overview: This accelerated course is a continuation of 9th Honors. Students will cover an enriched Algebra 2 curriculum, investigating
relationships between algebra and geometry, with special emphasis on the structure of real and complex numbers and the concept of functions and their inverses. A graphing approach will be stressed. Topics covered are linear equations and inequalities in one or two variables, problem solving, coordinate plane, quadratic functions, logarithmic functions, analytic geometry, polynomial equations, and combinations and
permutations, probability, and statistics. | 677.169 | 1 |
Don't go starting A levelChemistry without knowing these or not following MaChemGuy on Twitter!!
published:05 Jul 2016
views:4445Differential equation
A differential equation is a mathematicalequation that relates some function with its derivatives. In applications, the functions usually represent physical quantities, the derivatives represent their rates of change, and the equation defines a relationship between the two. Because such relations are extremely common, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
In pure mathematics, differential equations are studied from several different perspectives, mostly concerned with their solutions—the set of functions that satisfy the equation. Only the simplest differential equations are solvable by explicit formulas; however, some properties of solutions of a given differential equation may be determined without finding their exact form.
If a self-contained formula for the solution is not available, the solution may be numerically approximated using computers. The theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations, while many numerical methods have been developed to determine solutions with a given degree of accuracy. Definitions of Quality new 1
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Our government has completely failed to provide basic facilities to citizens. There is not a single government department which listens to the problems being faced by its employees. A few days ago, a group of LarkanaDevelopmentAuthority (LDA) employees held a protest against unpaid salaries. According to these employees, around 256 employees have not been paid for the last five months ...AdnanDost. MakranGHALANAI ... The political activists from various parties were in attendance. Speaking on the occasion, Naveed Ahmed Mohmand said the tribal people remained deprived of the basic rights for a long time ... ....
GHALANAI ... The political activists from various parties were in attendance. Speaking on the occasion, Naveed Ahmed Mohmand said the tribal people remained deprived of the basic rights for a long time ... ....
Former Courier-Express sports reporter Mike Billoni has had a long career trajectory that recently landed him in the publishing business ... QUESTION. Before we talk about the book, can you tell me what you've been up to lately?. ANSWER ... Q ... A ... It became a book we could sell to the public. Q ... A ... It'sbasically Marketing 101 ... Basically what my company does now is I can either take someone's vision for a book or I could be the author of any subject.... | 677.169 | 1 |
This Algebra I Pre-Test differs from many of the other unit tests in this course as it is a pre-test to assess what students know coming into the course. I have included both the College Prep (Algebra I Pre-Test - CP) and Honors (Algebra I Pre-test - Honors) Pre-Assessments. The odd-numbered items are the same on each version to allow for comparison between College Prep and Honors students. The even number items on the Honors are intended to be more challenging than the corresponding items on the CP Assessment.Each assessment contains multiple choice items developed to align with Common Core Standards. The target Standard is listed with each problem.
There are some Open Response questions on the test. I encourage my students to show their work on the problems. I will give partial credit when warranted. Most importantly, I want to learn how my students are currently thinking about the problem. What concepts do the apply? What skills do they demonstrate?
When the students receive their results, they will be itemized by CCSS standard. For example, students will see the percentage of items on standard A.SSE.2 they get correct. For some tests I also like to add items from the Massachusetts Common Assessment System (MCAS) archive. You can find the website for the MCAS question search tool here.
I like this tool because you can search based on standard (note that all MCAS questions as of the 2012-2013 school year are still using the previous MA standards, not the common core), by question type and other characteristics.
Colleague Recognition: These assessments were developed in collaboration with Patrick Borzi, a fabulous Math teacher and colleague.
Resources
After students complete the unit test, I grade them using a computerized online assessment system. During the next class, I will review the class averages with students. I use this as an entry point to talk about measure of center and spread, as well as an opportunity to set some goals for the coming year with respect to student learning and fluency with algebra.
If there were particular skills that the entire class struggled with, I may reteach them during the first unit.
Teacher's Note:
My policy for re-testing I have is as follows: I give any student the chance to retake (Algebra I Foundational Skills - Retake) the test as long as they meet with me and make a study plan on how they are going to learn the material which I sign off on (which most definitely can, and usually does, include after school support, which we call Dayback at my high school).
I replace the test score if the retake is higher than the original, and usually set a ceiling of 80 or 85% for the retake. The reason for this policy is I want to give students credit for learning the material and showing they understand the material, regardless of whether or not it was the first or second time around on the test. In addition I want to value those students who did put the work in the first time (perhaps by staying for extra help before the test) around and did well on the first test. In general students feel this policy is fair and it has helped with student engagement and motivation around testing and assessment.
Resources (1)
Resources
What a great test to give before the beginning of Algebra 1. I am working summer school, a bridge class to build foundation before September, do you have any other great ideas? Also, do you have an answer sheet? | 677.169 | 1 |
Math FIG ready to implement changes
The LACCD developmental mathematics faculty inquiry group (FIG) has been collaborating for about a year to identify areas in math learning where students seem to have difficulty. Pairs of math professors from five of the LACCD colleges and one member from Santa Ana College have been working with their respective departments to identify problems and develop solutions to the problems on their particular campus. Now, these colleges are ready to implement the solutions in their classes. To get a sense of the overall parameters of the larger FACCTS Project, click here.
EAST
Ruben and Regis are focused on improving students' problem solving abilities related to application problems. Using responses to student surveys as a guide they are creating application problems that resonate with students. Math topics include: rational equations, quadratic equations, factoring and polynomials.
CITY
Kevin has created a set of SkillBuilders and ModelBuilders. These are powerpoint and html pages that can be used to help students master key topics in algebra.
Hector has created a Latino student persona and developed tools that help students reflect on their attitude toward math, their performance in math, and their efforts to improve.
VALLEY
Steven and Teresa are creating Skill Building Activities – 15 minute activities that will be incorporated into each 70 minute class. Teresa is focusing on activities related to specific elementary and intermediate algebra math topics, and Steve is focusing on activities related to math anxiety and test taking skills.
Matt is exploring what motivates students to learn, how students approach learning and studying, and what techniques instructors can use to increase commitment to and effectiveness in studying. His work so far includes an assessment of students' attitudes toward mathematics, an examination of student reflections on relationship between performance and commitment, and a review of the literature surrounding motivation and investment in learning.
PIERCE
Bruce and Kathy have developed an approach to teaching elementary and intermediate algebra with the following key aspects:
1) Lessons have both reading and writing components
2) Classroom lessons are activity based
3) Mathematical concepts and skills are developed in context. Environmental sustainability is a common theme.
4) Study skills are incorporated into each lesson
5) Professional development is a key component for instructors to share materials, pedagogy and experiences.
They have developed reading materials, classroom activities and homework assignments that are available online.
They are testing this approach in classes this semester and using the results to refine their materials and processes.
SANTA ANA
Caren is working to help students master application problems in elementary algebra in several ways, by:
1) developing modules of activities and tools for each classic type of application problem. Part of the focus of the modules is on general problem solving strategy and estimation.
2) developing a WordProbTutor modeled after OLI's StatLabTutor, which will guide students in setting up equations, solving equations, and provide feedback about their work.
3) working with other departments to identify and then develop discipline-specific application problems | 677.169 | 1 |
BUSINESS TECHNOLOGY
Business Math 1-2
Grades 10-11-12 (this course can be taken one or both semesters)
Whether balancing an account, getting a loan, or calculating your paycheck - proficiency in basic math skills is needed to survive. Earn a math credit that will give you practical mathematical strategies for your business and personal needs Learn how basic math skills that are used in personal finance and in the business world can assist you in being a success in the real world. Each semester can be taken independently of each other. This course meets the math requirement for a general diploma, not a Core 40 diploma. | 677.169 | 1 |
TeachME Professional Development
Teaching Strategies for Improving Algebra Knowledge
Introduction
1. Algebra is often the first mathematics subject that requires extensive abstract thinking, and it also calls for proficiency with multiple representations, including symbols, equations, and graphs, as well as the ability to reason logically, both of which play crucial roles in advanced mathematics courses.
A. True
B. False
Overarching Themes
2. The three general themes that experts highlight for improving the teaching and learning of algebra include developing a deeper understanding of algebra, encouraging precise communication, and promoting:
A. Abstract reasoning
B. Strategic processing
C. Process-oriented thinking
D. Flexible and cooperative learning
Summary of Supporting Research
3. While procedural knowledge includes understanding algebraic ideas, operations and notation, conceptual knowledge includes choosing operations and methods to solve algebra problems as well as applying operations and methods to arrive at the correct solution to problems.
A. True
B. False
4. Research and practice indicates that students should be taught to intentionally choose from alternative algebraic strategies when solving problems.
A. True
B. False
Recommendation 1
5. Each of the following is an accurate statement about using solved problems to engage students in analyzing algebraic reasoning and strategies EXCEPT:
A. Compared to elementary mathematics work like arithmetic, solving algebra problems often requires students to think more abstractly and to process multiple pieces of complex information simultaneously
B. Solved problems can minimize the burden of abstract reasoning by allowing students to see the problem and many solution steps at once
C. Analyzing and discussing solved problems can help students develop a deeper understanding of the logical processes used to solve algebra problems
D. The use of incomplete solved problems during this step is not recommended as this tends to interfere with critical thinking
7. In order to incorporate multiple solved problems into a lesson, teachers should select problems with varying levels of difficulty and arrange them from simplest to most complex applications of the same concept.
A. True
B. False
Example 1.5. One Way to Introduce Incorrect Solved Problems
8. When introducing incorrect solved problems the first question the teacher should ask is, 'What is the error, and how can you tell it's incorrect?'
A. True
B. False
9. When presenting sample problems, experts recommend that correct and incorrect examples be clearly labeled as not to confuse accurate and inaccurate information.
A. True
B. False
10. A computational error is one that occurs when faulty strategies or incorrect reasoning are used to solve problems.
A. True
B. False
11. Which of the following is NOT one of the methods suggested to introduce, elaborate on, and practice working with solved problems?
A. Use whole class working discussions
B. Develop a wrap-around instruction plan
C. Have students practice in small groups
D. Assign independent practice activities
12. One strategy for incorporating solved problems into independent practice activities is alternating solved problems with unsolved problems that are similar to the solved problems in terms of problem structure or solution strategy.
A. True
B. False
Potential Roadblocks and Suggested Approaches-Roadblock 1.1
13. In order to engage students with solved problems during whole class instruction, teachers can use _______________________ to foster discussion and analysis.
A. Open-ended questions
B. Questions with multiple answers
C. Think-aloud questions
D. Follow-up questions
Recommendation 2
14. Structure refers to an algebraic representation's underlying mathematical features and relationships such as:
A. The number type and position of qualities including variables and the number, type, and position of operations
B. The presence of an equality or inequality and the relationships between quantities, operations, and equalities or inequalities
C. The range of complexity among expressions, with simpler expressions nested inside more complex ones
D. All of the above
15. Recognizing structure helps students understand the characteristics of algebraic expressions and problems that are presented in symbolic, numeric, verbal, or graphic forms.
A. True
B. False
16. Research has consistently shown that using language that reflects mathematical structure has positive effects on procedural and conceptual knowledge.
A. True
B. False
How to Carry Out This Recommendation
17. Each of the following is recommended to promote the use of language that reflects mathematical structure EXCEPT:
A. Use questions that require evidence and reasoning to justify mathematical problem solving
C. Use precise mathematical language to help students analyze and verbally describe the specific features that make up the structure of algebraic representations
D. When introducing a new topic or concept, use and model precise mathematic language to encourage students to describe the structure of algebra problems with accurate and appropriate terms
18. When students use subjective questioning, they are encouraged to think about the structure of the problem and the potential strategies they could use to solve the problem.
A. True
B. False
19. By identifying the similarities and differences of equations that are presented in various forms, students can better understand the relationship among algebraic representations.
A. True
B. False
20. Diagrams are useful to help students visualize the structure of a problem, organize and document the solution steps of the problem, and translate the problem into another representation.
A. True
B. False
Example 2.8-Multiple Algebraic Representations
21. When analyzing several representations of a problem, students should be encouraged to move in a linear fashion from one representation to the next, in order to clearly see that different representations based on the same problem can display the information differently.
A. True
B. False
Potential Roadblocks and Suggested Approaches-Roadblock 2.1
22. While precise mathematical language is not necessarily more complicated than simple language, it is generally more:
A. Detailed
B. Intricate
C. Accurate
D. Objective
Example 2.10-Examples of Cooperative Learning Strategies
23. In the "partner coaching/trade" cooperative learning strategy, students are arranged in groups, assigned different problems, and collaborate with members from other groups to discuss ideas and strategies.
A. True
B. False
Recommendation 3
24. Unlike an algorithm which contains a sequence of steps that are intended to be executed in a particular order, a strategy may require students to make choices based on the specifics of the problem as well as their:
A. Understanding of concepts
B. Reasoning skills
C. Conceptual knowledge
D. Problem-solving goals
Summary of Evidence: Moderate Evidence
25. Research indicates that teaching alternative algebraic strategies can improve achievement, especially procedural flexibility, once students have developed some procedural knowledge of algebra.
A. True
B. False
How to Carry Out This Recommendation
26. When providing students examples to solve problems using multiple algebraic strategies, students can observe that such strategies vary in their effectiveness and:
A. Degree of difficultly
B. Efficiency
C. Validity
D. Adaptability
27. Although teachers may be inclined to only introduce one or two solution strategies at a time, experts have found that introducing multiple strategies initially enables students to develop skills for selecting the most desirable strategy.
A. True
B. False
28. Students should be encouraged to articulate the reasoning behind their choice of strategy, while analyzing the problem structure, selecting the strategy, solving a problem, and analyzing another student's solution.
A. True
B. False
29. When presenting pairs of solved problems to communicate a particular instructional goal to students, solved problems that are highly different from each other should be represented, as this helps students focus on the underlying solution structure.
A. True
B. False
Potential Roadblocks and Suggested Approaches
30. Each of the following is an accurate statement about helping special education students solve algebraic problems EXCEPT:
A. Is important to distinguish between providing explicit instruction and teaching only a single solution strategy and asking students to memorize the steps of that strategy
B. Special education students are better served if they come to view mathematics as a game where they associate a problem with a specific method
C. Teachers can help special education students understand alternative strategies by being explicit about the steps of a strategy
D. The underlying rationale of using a particular strategy should be taught including how, what, when and why it is applicable or useful for particular problems | 677.169 | 1 |
Stuffed Sheets™ are the most thorough compilation of math I have ever seen in such a small and manageable format... more
Algebra Series - Concepts and Formulas™
Fundamental Properties and Operations on Complex Numbers (ALG-CF20) This sheet provides a comprehensive review of all of the most important topics, concepts and formulas fully covering the fundamental properties and operations on complex numbers, explained in detail, with detailed
illustrations. Unlike charts and notes, this Concepts and Formulas™ sheet anticipates and answers questions about how to use the concepts - how to solve problems with them, it doesn't just list facts and formulas.
Click here to download. (Guaranteed to be virus free.)
Format: self-contained e-book 587 kB. Click here for registration (activation) information after purchase.
Topics Covered:
The imaginary unit i
Complex numbers
Complex numbers in standard form
The real and imaginary parts of a complex number
How to determine equivalence of complex numbers
Powers of i
How to simply complex numbers
How to rationalize denominators in complex numbers
How to add complex numbers
How to subtract complex numbers
How to multiply complex numbers
Properties of complex numbers
Conjugate and Modulus properties of complex numbers
How to divide complex numbers
How to solve equations with complex numbers
This e-book can only be read on the computer on which it was registered. Each purchase grants the license for use on only one computer. | 677.169 | 1 |
These are two worksheets on differentiation, with step by step solutions. Sheet 1 has questions on finding intervals where f(x) is increasing or decreasing. Sheet 2 has questions on finding stationary points and determining the nature of stationary points, as well as real life applicationA revision sheet (with answers) containing IGCSE exam-type questions, which require the students to differentiate to work out equations for velocity and acceleration.
This sheet is designed for International GCSE revision (IGCSE), but could also be used revision sheet (and detailed solutions) containing IGCSE exam-type questions, which require the student to apply the rule of differentiation to a variety of polynomials. The polynomials include negative and fractional powers.
This sheet is designed for International GCSE revision (IGCSE), but is also very goodA simple worksheet to help students summarize rules of differentiation for combined functions. The functions and rules combined functions (i.e. the product, quotient and chain rules).
A simple worksheet to help students summarize rules of differentiation for basic functions. The functions basic functions.
This test is a summative assessment for Unit 9 in my Mathematics SL curriculum (see link to course outline below). It covers items 6.1 and 6.2 in the syllabus. The test is structured after International Baccalaureate (IB) examination papers and the questions follow those seen in recent papers.
This test contains five questions, three in Section A and two in Section B. A scientific calculator should be allowed although it is not required. A graphic display calculator (GDC) is required for question 3.
This free download includes the question paper and answer booklet in PDF. For the original Word documents, image files, answers and mark scheme, please find my paid resource of the same title (link below).
Test – Differential calculus I (2018)
Link … (coming soon)
Mathematics SL Course Outline | 677.169 | 1 |
7th Grade Math - Probability
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the student will be able to represent sample spaces for simple and compound events using lists and tree diagrams;
: select and use different simulations to represent simple and compound events with and without technology;
: make predictions and determine solutions using experimental data for simple and compound events;
: make predictions and determine solutions using theoretical probability for simple and compound events;
: find the probabilities of a simple event and its complement and describe the relationship between the two;
: solve problems using qualitative and quantitative predictions and comparisons from simple experiments; and
: determine experimental and theoretical probabilities related to simple and compound events using data and sample spaces. | 677.169 | 1 |
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Online Numeracy Electrotechnology Resource - Trigonometry
The product supports the acquisition of trigonometry skills amongst apprentice electricians. It is a set of online information, practice questions and test questions to develop and practice these skills. It links to a previously developed algebra resource developed for first year apprentices. Second year apprentices will be the major target group for this resource. | 677.169 | 1 |
Reacting to criticism concerning the lack of motivation in his writings,
Gauss remarked that architects of great cathedrals do not obscure the beauty of their work by leaving the scaffolding in place after the construction has been completed. His philosophy epitomized the formal presentation and teaching of mathematics throughout the nineteenth and twentieth centuries, and it is still commonly found in mid-to-upper-level mathematics textbooks. The inherent efficiency and natural beauty of mathematics are compromised by straying too far from Gauss's viewpoint. But, as with most things in life, appreciation is generally preceded by some understanding seasoned with a bit of maturity, and in mathematics this comes from seeing some of the scaffolding.
Purpose, Gap, and Challenge
The purpose of this text is to present the contemporary theory and applications of linear algebra to university students studying mathematics, engineering, or applied science at the postcalculus level. Because linear algebra is usually encountered between basic problem solving courses such as calculus or differential equations and more advanced courses that require students to cope with mathematical rigors, the challenge in teaching applied linear algebra is to expose some of the scaffolding while conditioning students to appreciate the utility and beauty of the subject. Effectively meeting this challenge and bridging the inherent gaps between basic and more advanced mathematics are primary goals of this book.
Rigor and Formalism
To reveal portions of the scaffolding, narratives, examples, and summaries are used in place of the formal definition–theorem–proof development. But while well-chosen examples can be more effective in promoting understanding than rigorous proofs, and while precious classroom minutes cannot be squandered on theoretical details, I believe that all scientifically oriented students should be exposed to some degree of mathematical thought, logic, and rigor. And if logic and rigor are to reside anywhere, they have to be in the textbook. So even when logic and rigor are not the primary thrust, they are always available. Formal definition–theorem–proof designations are not used, but definitions, theorems, and proofs nevertheless exist, and they become evident as a student's maturity increases. A significant effort is made to present a linear development that avoids forward references, circular arguments, and dependence on prior knowledge of the subject. This results in some inefficiencies—e.g., the matrix2-norm is presented x Preface before eigenvalues or singular values are thoroughly discussed. To compensate, I try to provide enough "wiggle room" so that an instructor can temper the inefficiencies by tailoring the approach to the students' prior background.
Comprehensiveness and Flexibility
A rather comprehensive treatment of linear algebra and its applications is presented and, consequently, the book is not meant to be devoured cover-to-cover in a typical one-semester course. However, the presentation is structured to provide flexibility in topic selection so that the text can be easily adapted to meet the demands of different course outlines without suffering breaks in continuity. Each section contains basic material paired with straightforward explanations, examples, and exercises. But every section also contains a degree of depth coupled with thought-provoking examples and exercises that can take interested students to a higher level. The exercises are formulated not only to make a student think about material from a current section, but they are designed also to pave the way for ideas in future sections in a smooth and often transparent manner. The text accommodates a variety of presentation levels by allowing instructors to select sections, discussions, examples, and exercises of appropriate sophistication. For example, traditional one-semester undergraduate courses can be taught from the basic material in Chapter 1 (Linear Equations); Chapter 2 (Rectangular Systems and Echelon Forms); Chapter 3 (MatrixAlgebra); Chapter 4 (Vector Spaces); Chapter 5 (Norms, Inner Products, and Orthogonality); Chapter 6 (Determinants); and Chapter 7 (Eigenvalues and Eigenvectors). The level of the course and the degree of rigor are controlled by the selection and depth of coverage in the latter sections of Chapters 4, 5, and 7. An upper-level course might consist of a quick review of Chapters 1, 2, and 3 followed by a more in-depth treatment of Chapters 4, 5, and 7. For courses containing advanced undergraduate or graduate students, the focus can be on material in the latter sections of Chapters 4, 5, 7, and Chapter 8 (Perron–Frobenius Theory of Nonnegative Matrices). A rich two-semester course can be taught by using the text in its entirety.
What Does "Applied" Mean?
Most people agree that linear algebra is at the heart of applied science, but there are divergent views concerning what "applied linear algebra" really means; the academician's perspective is not always the same as that of the practitioner. In a poll conducted by SIAM in preparation for one of the triannual SIAM conferences on applied linear algebra, a diverse group of internationally recognized scientific corporations and government laboratories was asked how linear algebra finds application in their missions. The overwhelming response was that the primary use of linear algebra in applied industrial and laboratory work involves the development, analysis, and implementation of numerical algorithms along with some discrete and statistical modeling. The applications in this book tend to reflect this realization. While most of the popular "academic" applications are included, and "applications" to other areas of mathematics are honestly treated,
Preface xi there is an emphasis on numerical issues designed to prepare students to use linear algebra in scientific environments outside the classroom.
Computing Projects
Computing projects help solidify concepts, and I include many exercises that can be incorporated into a laboratory setting. But my goal is to write a mathematics text that can last, so I don't muddy the development by marrying the material to a particular computer package or language. I am old enough to remember what happened to the FORTRAN- and APL-based calculus and linear algebra texts that came to market in the 1970s. I provide instructors with a flexible environment that allows for an ancillary computing laboratory in which any number of popular packages and lab manuals can be used in conjunction with the material in the text.
History
Finally, I believe that revealing only the scaffolding without teaching something about the scientific architects who erected it deprives students of an important part of their mathematical heritage. It also tends to dehumanize mathematics, which is the epitome of human endeavor. Consequently, I make an effort to say things (sometimes very human things that are not always complimentary) about the lives of the people who contributed to the development and applications of linear algebra. But, as I came to realize, this is a perilous task because writing history is frequently an interpretation of facts rather than a statement of facts. I considered documenting the sources of the historical remarks to help mitigate the inevitable challenges, but it soon became apparent that the sheer volume required to do so would skew the direction and flavor of the text. I can only assure the reader that I made an effort to be as honest as possible, and I tried to corroborate "facts." Nevertheless, there were times when interpretations had to be made, and these were no doubt influenced by my own views and experiences.
Supplements
Included with this text is a solutions manual and a CD-ROM. The solutions manual contains the solutions for each exercise given in the book. The solutions are constructed to be an integral part of the learning process. Rather than just providing answers, the solutions often contain details and discussions that are intended to stimulate thought and motivate material in the following sections. The CD, produced by Vickie Kearn and the people at SIAM, contains the entire book along with the solutions manual in PDF format. This electronic version of the text is completely searchable and linked. With a click of the mouse a student can jump to a referenced page, equation, theorem, definition, or proof, and then jump back to the sentence containing the reference, thereby making learning quite efficient. In addition, the CD contains material that extends historical remarks in the book and brings them to life with a large selection of xii Preface portraits, pictures, attractive graphics, and additional anecdotes. The supporting Internet site at MatrixAnalysis.com contains updates, errata, new material, and additional supplements as they become available.
I thank the SIAM organization and the people who constitute it (the infrastructure as well as the general membership) for allowing me the honor of publishing my book under their name. I am dedicated to the goals, philosophy, and ideals of SIAM, and there is no other company or organization in the world that I would rather have publish this book. In particular, I am most thankful to Vickie Kearn, publisher at SIAM, for the confidence, vision, and dedication she has continually provided, and I am grateful for her patience that allowed me to write the book that I wanted to write. The talented people on the SIAM staff went far above and beyond the call of ordinary duty to make this project special. This group includes Lois Sellers (art and cover design), Michelle Montgomery and Kathleen LeBlanc (promotion and marketing), Marianne Will and Deborah Poulson (copy for CD-ROM biographies), Laura Helfrich and David Comdico (design and layout of the CD-ROM), Kelly Cuomo (linking the CDROM), and Kelly Thomas (managing editor for the book). Special thanks goes to Jean Anderson for her eagle-sharp editor's eye.
Acknowledgments
This book evolved over a period of several years through many different courses populated by hundreds of undergraduate and graduate students. To all my students and colleagues who have offered suggestions, corrections, criticisms, or just moral support, I offer my heartfelt thanks, and I hope to see as many of you as possible at some point in the future so that I can convey my feelings to you in person. I am particularly indebted to Michele Benzi for conversations and suggestions that led to several improvements. All writers are influenced by people who have written before them, and for me these writers include (in no particular order) Gil Strang, Jim Ortega, Charlie Van Loan, Leonid Mirsky, Ben Noble, Pete Stewart, Gene Golub, Charlie Johnson, Roger Horn, Peter Lancaster, Paul Halmos, Franz Hohn, Nick Rose, and Richard Bellman—thanks for lighting the path. I want to offer particular thanks to Richard J. Painter and Franklin A. Graybill, two exceptionally fine teachers, for giving a rough Colorado farm boy a chance to pursue his dreams. Finally, neither this book nor anything else I have done in my career would have been possible without the love, help, and unwavering support from Bethany, my friend, partner, and wife. Her multiple readings of the manuscript and suggestions were invaluable. I dedicate this book to Bethany and our children, Martin and Holly, to our granddaughter, Margaret, and to the memory of my parents, Carl and Louise Meyer.
Carl D. Meyer April 19, 2000
CHAPTER 1
Linear Equations
1.1 INTRODUCTION
A fundamental problem that surfaces in all mathematical sciences is that of analyzing and solving m algebraic equations in n unknowns. The study of a system of simultaneous linear equations is in a natural and indivisible alliance with the study of the rectangular array of numbers defined by the coefficients of the equations. This link seems to have been made at the outset.
The earliest recorded analysis of simultaneous equations is found in the ancient Chinese book Chiu-chang Suan-shu (Nine Chapters on Arithmetic), estimated to have been written some time around 200 B.C. In the beginning of Chapter VIII, there appears a problem of the following form.
Three sheafs of a good crop, two sheafs of a mediocre crop, and one sheaf of a bad crop are sold for 39 dou. Two sheafs of good, three mediocre, and one bad are sold for 34 dou; and one good, two mediocre, and three bad are sold for 26 dou. What is the price received for each sheaf of a good crop, each sheaf of a mediocre crop, and each sheaf of a bad crop?
Today, this problem would be formulated as three equations in three un-
where x, y, and z represent the price for one sheaf of a good, mediocre, and bad crop, respectively. The Chinese saw right to the heart of the matter. They placed the coefficients (represented by colored bamboo rods) of this system in
2 Chapter 1 Linear Equations a square array on a "counting board" and then manipulated the lines of the array according to prescribed rules of thumb. Their counting board techniques and rules of thumb found their way to Japan and eventually appeared in Europe with the colored rods having been replaced by numerals and the counting board replaced by pen and paper. In Europe, the technique became known as Gaussian elimination in honor of the German mathematician Carl Gauss,1 whose extensive use of it popularized the method.
Because this elimination technique is fundamental, we begin the study of our subject by learning how to apply this method in order to compute solutions for linear equations. After the computational aspects have been mastered, we will turn to the more theoretical facets surrounding linear systems.
1 Carl Friedrich Gauss (1777–1855) is considered by many to have been the greatest mathemati- cian who has ever lived,and his astounding career requires several volumes to document. He was referred to by his peers as the "prince of mathematicians." Upon Gauss's death one of them wrote that "His mind penetrated into the deepest secrets of numbers,space,and nature; He measured the course of the stars,the form and forces of the Earth; He carried within himself the evolution of mathematical sciences of a coming century." History has proven this remark to be true.
The problem is to calculate, if possible, a common solution for a system of m linear algebraic equations in n unknowns
where the xi 's are the unknowns and the aij 's and the bi 's are known constants.
The aij 's are called the coefficients of the system, and the set of bi 's is referred to as the right-hand side of the system. For any such system, there are exactly three possibilities for the set of solutions.
Three Possibilities
• UNIQUE SOLUTION: There is one and only one set of values for the xi 's that satisfies all equations simultaneously. | 677.169 | 1 |
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Do you have students who struggle with algebraTM Do they find the problems difficult to understand, or of little real-world valueTM Do they find the repetitive practice boringTM The problem may not be algebra. It may be the way students are learning algebra algebra year after year. When the power of student-to-student interaction is unleashed in algebra, students enjoy learning more and the abstract algebraic concepts become more concrete and understandable. Chapters cover: working with rational numbers, expressions, equations and inequalities, linear functions and vertical lines, linear systems, polynomials, radicals, and quadratic functions. Transform struggling students into successful mathematicians with motivating teamwork activities. Book includes reproducible transparencies and activities. 464 pages | 677.169 | 1 |
Understanding Algebra for College Students / Edition 2
Helping students grasp the why" of algebra through patient explanations, Hirsch and Goodman gradually build students' confidence without sacrificing rigor. To help student move beyond the how" of algebra (computational proficiency) to the why" (conceptual understanding), the authors introduce topics at an elementary level and return to them at increasing levels of complexity. Their gradual introduction of concepts, rules, and definitions through a wealth of illustrative examples - both numerical and algebraic-helps students compare contrast related ideas and understand the sometimes subtle distinctions among a variety of situations. | 677.169 | 1 |
Linear regression is one of the most important machine learning tools. It is the simplest of the predictive modeling techniques and it is widely used, whether on its own or in combination with other techniques. This course teaches the principles and practices of linear regression. It reviews the meaning of modeling, explains linear regression's key concepts (e.g., cost function, R-squared metric, etc.), describes the practice and need for hypothesis testing, illustrates how to implement linear regression computationally, and showcases an implementation of ridge regression. An understanding of basic mathematics is required, and some knowledge of linear algebra and differential calculus will allow the viewer to understand all of the subtle details. | 677.169 | 1 |
gattMath is a free educational math program that show some concepts behind Integral and Differential Calculus
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gattMath is a educational math (graphical) program that show some concepts behind Integral and Differential Calculus, like Riemann, Simpson, Darboux, Trapezoid, Monte-Carlo integration, derivative, antiderivative, tangent,..., and sure a plotter.
gattMath is a free educational math program that show some concepts behind Integral and Differential Calculus, like Riemann, Simpson, Darboux, Trapezoid and Monte-Carlo sum, derivative, tangent, ... and sure a plotter (2D and 3D). The intention is to help students from universities or any introductory Calculus courses, illustrating some points of the Integral and Differential Calculus based on Numeric Calculus.
The main of the program is the integration algorithms (at least , showing their geometric (graphical) meaning with of course the correspondent result. | 677.169 | 1 |
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Further Mathematics at The King Edmund School
Course description
If you are a good mathematician who enjoys complex problem solving and exploring new mathematical ideas, further mathematics will provide an additional challenge to the A Level Mathematics course. Further mathematics will broaden and deepen your understanding of the subject.
Course content
Through the course you begin to appreciate the connections between different branches of mathematics and put forward rigorous mathematical arguments using formal proof. The course starts by concentrating on pure mathematics studying a wider range of algebraic concepts such as matrices, complex numbers and proof by induction. There follows the study of decision mathematics, learning to use networks, algorithms and simulation to solve practical problems, including project management and shortest path. The remainder of the course will either extend the pure mathematics elements or build on studies in the areas of statistics and mechanics covered in the main mathematics A Level.
Assessment
This will be assessed in the same manner as A Level Mathematics, six examinations of one hour thirty minutes each. If AS Level Further Mathematics is taken, rather than the full A Level, then this consists of three examinations at the end of Year 12 or Year 13.
Future opportunities
If you plan to study mathematics at university, taking further mathematics will be a major advantage. Universities value A or AS Level Further Mathematics very highly and it gives students a head start to their undergraduate studies.
How to apply
If you want to apply for this course, you will need to contact The King Edmund School directly. | 677.169 | 1 |
How much math for fluid dynamics?
im taking a graduate level fluid mechanics course. we are using a good amount of vector calculus (expected) and also tensor algebra, leading into the kronecker delta and Levi-Civita symbol (shockingly never saw these before, though implicitly used them). it seems linear algebra is being introduced.
for those of you who have studied far in the field, how much math is required for masters and phd level courses? i only ask because my undergrad is math, where i covered linear algebra, pde's, and vector calculus; am i missing anything or do i have the basic "tool kit" that advanced coursework in fluids requires?
If you get really hard-core, there will be solving PDEs out your ying-yang eventually. In the graduate courses, don't be surprised if you have to know something about solving integral equations (differential equations' lesser known, more evil cousin). Linear algebra is the least of your worries.
In solving actual fluid mechanics problems, you'll probably also get some exposure to the finite element method and the boundary element method. Both methods rely on using assumed solutions to the fluid mechanics equations and then optimizing them to account for the actual geometry of the flow. Green's functions will probably also make an appearance at some point.
It is one of the more math-heavy branches of engineering, that's for sure. Also depending on what branch of fluid mechanics you study, you may end up needing a fair amount of statistics, perturbation methods, Fourier and Laplace analysis and more. If you really start delving deeper into some topics, I've started running across topics that start scratching the surface of things like real and functional analysis, abstract algebra and topology, though these so far seem to be pretty niche applications. | 677.169 | 1 |
Course Syllabus - Fall 2012
From the College Catalog : Students learn to prove and critique proofs of theorems by studying elementary topics in abstract mathematics, including such necessary basics as logic, sets, functions, equivalence relations, and elementary combinatorics.
Exams: There will be two (2) hourly in-class exams (see schedule below) and
a comprehensive final.
Homework: There will be several types of homework assignments. The first type
consists of exercises from the text. These will not be collected, but
will be discussed in class. This homework will be assigned weekly.
These assignments are considered the minimum that should be done. On a few occasions I will collect and grade some of the assigned problems (the specific problems will be announced in class about a week prior to collection).
The second type of homework will consist of proofs assigned in class.
These will be collected, corrected and graded in the following way.
After handing this in, it will be corrected, with comments and returned
to you. You are to redo the assignment and resubmit it. If it is still
not correct it will again be returned with more comments. You may make
up to 4 submissions of the same assignment within a 3 week period. The
grade on the assignment depends solely on the number of times that it
is submitted before being accepted as correct.
Each student will be asked to present at least one proof (which they may select from the homework assignments) in class for class discussion and criticism.
Quizzes: Every week a short quiz will be given on the homework material in
class. These quizzes will cover definitions, short answers, computations
and simple proof techniques.
If for some reason you are unable to take a quiz in class, you may take the quiz on the web (up until the next class period, for a cost of 1 point). From time to time I may require that everyone take the quiz on the web (at no cost).
Syllabus: We shall cover the first ten chapters plus some topics from analysis. That is a rate of about 2-3 sections of the text per class period. Be prepared for class, read ahead of material presented in class.
Time Table:
Dates
8/21
Classes Start
9/25
Exam I
- Covers Chapters 1-5
10/30
Exam
II- Covers Chapters 6-9
11/20 - 11/22
No Classes
: Fall Break
12/11 or 12/13
Final Exam - Comprehensive | 677.169 | 1 |
MATH-300: Basic Mathematics for Chemist
Course contents
Introdtuction; Review of basic algebra, Graphs and their significance in chemistry. Trigonometric, logarithmic and exponential functions. Differentiation, partial differentiation, differential equations and their use in chemical problems. Concept of maxima and minima. integration, Determinants and Matrices, their properties and use in chemical problems. solutions of linear equations (simple, determinant and matrices methods), operator theory, The eigen value problems and curve fitting. | 677.169 | 1 |
PowerPoint Slideshow about 'Teaching of Algebra in the Czech Republic' - sitradition of education in Czech history (population groups which would not achieve any education in other countries were often educated, e.g. Hussite women in the 15th century), the general literacy in the 1930s was of higher standards than were common in the rest of Europe
Charles University was established in 1348 (the first European University east of Germany)
Comenius - 17th century
compulsory six-year school attendance was enacted in 1774
influence of the Soviet tradition, from which schools were only freed after 1989
Mathematics together with the Czech language form the educational infrastructure of the basic school. Mathematics provides pupils with the knowledge and skills necessary for everyday life and prepares the foundations for successful development through professional training and further study at upper secondary schools. It develops pupils' intellectual abilities, their memory, imagination, creativity, abstract thinking and ability to reason logically. At the same time it contributes to the development of personal qualities, such as patience, diligence, critical thinking.
Knowledge and skills acquired in mathematics are the preconditions for success in the sciences, economics, technology and the use of computers. | 677.169 | 1 |
building of mathematical knowledge and understanding can be a complex and daunting endeavor for high school students. This course is designed to delve into the content and activities appropriate for a Pre-AP Pre-Calculus course.
Participants will experience classroom activities designed to help prepare students for Advanced Placement Calculus. Topics and activities will include using multi-representational approaches to examine problems algebraically, graphically, numerically, and verbally. Time will also be spent modeling and selecting appropriate strategies for teaching linear through trigonometric functions, accumulation and area, limits, optimization, sequences and series, rates of change, polar graphing, and other topics. In addition to constant focus on content rich mathematics, time will be dedicated to adapting AP test questions, assessments, and technology. Answering the question "What makes a test question Pre-AP?" will be addressed. Examples and non-examples will be explored and teachers will have an opportunity to develop and adapt test questions for their own classroom use. Participants will share best practices and strategies.
Dickie Thomasson graduated from the University of Arkansas at Monticello with a BSE in mathematics and a minor in English. He received his MSE in secondary education from the University of Arkansas and an administrator's certificate from the University of Central Arkansas. Dickie has taught mathematics for 40 years in grades 6 through college in public schools in Arkansas. He is currently teaching at Prairie Grove High School (about 10 miles west of Fayetteville.) This year he is teaching Algebra I, Precalculus, and Advanced Placement Calculus AB. Mr. Thomasson is active in the Arkansas Council of Teachers of Mathematics having served as membership chairperson, treasurer, and president. Dickie was the recipient of the Presidential Award for Excellence in Mathematics and Science Teaching in 2001. He is a College Board endorsed consultant and presents at one-day and two-day AP and Pre-AP conferences as well as conducting summer institutes. Dickie has presented at summer institutes at the University of Arkansas, the University of Tulsa, University of Texas El Paso, University of Texas Rio Grande Valley, Texas A&M International University, TCU and Rice University. One of his favorite things to do each summer is being a reader for the AP Calculus exams. Dickie presents workshop sessions at the local, state, national, and international levels. He was an original participant and trainer for the Arkansas Math Crusades and is a national trainer for the National Math and Science Initiative (formerly LTF®.) Dickie has presented AP Calculus 2-Day follow-ups and mock exam trainings for NMSI. Mr. Thomasson was the math content director for the Arkansas Initiative for Math and Science during the 2008-2009 school year
Copies of tests/activities (small sample) used in their classroom. When we discuss assessment, participants will have an opportunity to create assessment questions, tweak their own questions, and create items they can use in their own classroom
Participants can always bring a copy of the textbook they use in class but it is not necessary | 677.169 | 1 |
Course: MATH 1503 CONTEMPORARY MATHEMATICS
Subject: Mathematics
Description: A study of the mathematics needed for critical evaluation of quantitative information
and arguments (including logic, critical appraisal of graphs and tables); use of simple
mathematical models, and an introduction to elementary statistics. | 677.169 | 1 |
Friday, April 27, 2012
Update Week Beginning 4/30/2012
In all math classes next Tuesday students will be taking the Spring MAP test. Students have set goals with their homebase teachers and with me in math class. I am very proud of how hard students have been working in math recently and have high hopes that their hard work will pay off for them during MAP testing. I have offered them extra credit for meeting their goals next week with this testing.
In Algebra we have started Chapter 12 this week. We will be studying Rational Expressions and Functions for the next several weeks Students in this class will take part 2 of the Proficiency test on May 22nd and 23rd.
In math we have started studying geometry and measurement. We will be looking at surface area next week. I am in the need of cereal boxes for an activity coming up involving surface area. If you finish up a box of cereal, feel free to bring it in.
1 comment:
I am here to discuss about a simple topic in mathematics that is rational expression,Rational expressions is known as an expression that is the ratio of two polynomials.It is called as rational because one number is divided by the other that is like a ratio. math equation solver | 677.169 | 1 |
Affine Lie Algebras and Quantum Groups: An Introduction, with Applications in Conformal Field Theory
This is an introduction to the theory of affine Lie algebras and to the theory of quantum groups. It is unique in discussing these two subjects in a unified manner, which is made possible by discussing their respective applications in conformal field theory. The description of affine algebras covers the classification problem, the connection with loop algebras, and representation theory including modular properties. The necessary background from the theory of semisimple Lie algebras is also provided. The discussion of quantum groups concentrates on deformed enveloping algebras and their representation theory, but other aspects such as R-matrices and matrix quantum groups are also dealt with.
This self-contained text concentrates on the perspective of analysis, assuming only elementary knowledge of linear
algebra and basic differential calculus. The author describes, in detail, many interesting examples, including formulas which have not previously appeared in book form. Topics covered ...
Information theory lies at the heart of modern technology, underpinning all communications, networking, and data
storage systems. This book sets out, for the first time, a complete overview of both classical and quantum information theory. Throughout, the reader is introduced ...
Clifford algebras, built up from quadratic spaces, have applications in many areas of mathematics, as
natural generalizations of complex numbers and the quaternions. They are famously used in proofs of the Atiyah-Singer index theorem, to provide double covers (spin groups) ...
Quantum gravity is among the most fascinating problems in physics. It modifies our understanding of
time, space and matter. The recent development of the loop approach has allowed us to explore domains ranging from black hole thermodynamics to the early ...
Here is an introduction to plane algebraic curves from a geometric viewpoint, designed as a
first text for undergraduates in mathematics, or for postgraduate and research workers in the engineering and physical sciences. The book is well illustrated and contains ...
Describing a striking connection between topology and algebra, rather than only proving the theorem, this
study demonstrates how the result fits into a more general pattern. Throughout the text emphasis is on the interplay between algebra and topology, with graphical ...
This highly pedagogical textbook for graduate students in particle, theoretical and mathematical physics, explores advanced
topics of quantum field theory. Clearly divided into two parts; the first focuses on instantons with a detailed exposition of instantons in quantum mechanics, supersymmetric ...
This succinct textbook gives students the perfect introduction to the world of biomaterials, linking the
fundamental properties of metals, polymers, ceramics and natural biomaterials to the unique advantages and limitations surrounding their biomedical applications. Clinical concerns such as sterilization, surface ... | 677.169 | 1 |
Ron Moody
About Me
I've been instilling the love of y=mx+b in my students for many years. Although I'm forced to acknowledge that the line perpendicular to the graph of y=5 is not a function, I'm happy to know that the slopes of all parallel lines are created equal. In my free time, I enjoy watching Slope Dude on YouTube. I believe that he is the one and only dominator.
Technical Math uses problem situations, physical models, and appropriate technology to extend mathematical thinking and engage student reasoning. Problem-solving situations, including those related to a variety of careers and technical fields will provide all students an environment which promotes communication and fosters connections within mathematics to other disciplines and to the technological workplace. Students will use hands-on activities to model, explore, and develop abstract concepts. The use of appropriate technology will help students apply math in an increasingly technological world. Collaboration between math and professional-technical teachers is an integral part of this course. Technical Math Syllabus
The purpose of the year-long Beginning Algebra course is to better prepare students to be successful in geometry. The course focuses on expressions, functions, rational numbers, and solving, graphing and analyzing linear equations and inequalities. Beginning Algebra Syllabus
Algebra I focuses on expressions, equations, functions, and rational numbers. Solving, graphing, and analyzing linear equations and inequalities, operations with polynomials, factoring, quadratic equations, rational expressions, radical expressions, and the quadratic formula are studied. Fundamental statistics with a linear focus is also included. | 677.169 | 1 |
A list like this is enough to intimidate anyone but a person with an advanced math degree.
It's unfortunate, because I think a lot of beginners lose heart and are scared away by this advice.
If you're intimidated by the math, I have some good news for you: in order to get started building machine learning models (as opposed to doing machine learning theory), you need less math background than you think (and almost certainly less math than you've been told that you need). If you're interested in being a machine learning practitioner, you don't need a lot of advanced mathematics to get started.
But you're not entirely off the hook.
There are still prerequisites. In fact, even if you can get by without having a masterful understanding of calculus and linear algebra, there are other prerequisites that you absolutely need to know (thankfully, the real prerequisites are much easier to master). | 677.169 | 1 |
Calculus Link Sheet Package (12 Templates)
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This package includes 12 templates to help students understand and make connections between the equations, tables, and graphs of functions and relations. These link sheets allow students to view multiple representations and to have a graphic organizer to guide them through various topics covered in AP Calculus.
The teacher will begin by giving students an equation or situation for a specific template. The students will complete the table, graphs, and understanding questions on the remainder of the link sheet. This activity is great for students to work collaboratively and share and discuss the connections in math with one another. | 677.169 | 1 |
Nancy Yi Liang is a unique designer. She brings code to life by converting code into physical objects like dresses. This is the future of custom made dresses.Her blog walks us through all the steps from the first sketch to the final product: the amazing, customized dress. Her project plays with perspective and digital manufacturing techniques like sewing simulation, 3D modeling, laser cutting.
Nancy starts with sketching the design on paper. Yes, paper is still important. Next, she moves into the digital domain to create an accurate 3D model of the wearer. Nancy uses Make Human, the free and open source software to create realistic 3D humans.
Next, she uses Marvelous Designer, which allows you to create beautiful 3D virtual clothing. From basic shirts to complicated dresses, Marvelous Designer can virtually replicate fabric textures and physical properties to the last button, fold, and accessory. This allows Nancy to design the cutting patterns, and then shows her how to drape theWhenever I see someone's frustration in learning math, the first complaint I usually hear is , "When will I ever need to use this later on in life?" Though there are many answers to this question, I found the best answer in a math book that I recently used called Meaningful Math.
What makes this text book so unique is its use of common math concepts to solve relevant real world situations. The reality is, understanding the mathematical foundation behind important, everyday functions and questions such as financial feasibility, allows us to develop skills that we can apply in almost every facet of our lives.
HSPT Math is the longest section. It requires that you maintain discipline while maintaining an efficient, detailed pace. Questions may range from one-step equations to multi-step word problems. Therefore, we must be strategic.
Taking Control of our Knowledge:
HSPT math tests us on concepts that we've started learning since grade school. How can we possibly remember everything? Our success on HSPT math relies on our ability to classify.Let's find the right strategies that will allow you to shape your knowledge and natural abilities into a fluid, efficient, and detailed math solving process. Our goal is to be versatile between the different problem types, understanding when our pacing must shift, and using the necessary steps of detail in order to reduce minor error. | 677.169 | 1 |
Completing the square is one of the most vital ways for Algebra 2 students to identify the vertex of a function (this likely means the maximum or the minimum of the graph). We will need to use completing the square to convert standard form functions to vertex form. This will be another tool that can help us graph functions and Read More …
Topics: A.SSE.2 – Use structures of an expression to identify ways to rewrite it. A.SSE.3 – Factor to identify the roots or complete the square to solve for roots of a quadratic function. A.APR.6 – Divide Polynomials using the Tabular Method or Long Division. A.REI.4 – Solve quadratic equations in one variable. F.IF.7 – Graph functions expressed symbolically and identify Read More …
Standards: F.IF.1 – Students understand the basics of functions including input (domain) and output (range). F.IF.2 – Use function notation and evaluate functions using the proper order of operations. See functions in different ways (e.g. tables, graphs, f(x), ordered pairs) Videos: Welcome & Classroom Norms Review working with variables, how to work with variables when adding and multiplying. Class Resources: Read More …
This will be an engaging year where you will learn all about complex functions and interesting phenomena aboutThis will be an engaging year where you will learn all about linear functions and relationships between objects and ideasThanks for visiting the page, all of the posts have been Archived for the following school year. If you'd like to access a specific page, please contact Mr. Germanis via email at rgermani@fwps.org he will dig it out and provide special access for you. Meanwhile, take a look around and check out some of my favorite videos below! Wright's Law: A Read More … | 677.169 | 1 |
Description: These are the lecture notes of a one-semester undergraduate course which we taught at SUNY Binghamton. For many of our students, Complex Analysis is their first rigorous analysis (if not mathematics) class they take, and these notes reflect this very much. We tried to rely on as few concepts from real analysis as possible. In particular, series and sequences are treated 'from scratch'. This also has the (maybe disadvantageous) consequence that power series are introduced very late in the course.
Similar books
Functions of a Complex Variable by Thomas S. Fiske - John Wiley & sons This book is a brief introductory account of some of the more fundamental portions of the theory of functions of a complex variable. It will give the uninitiated some idea of the nature of one of the most important branches of modem mathematics. (1644 views)456 views) | 677.169 | 1 |
(a) homework, quizzes, projects, and
in-class
work of various kinds
(b) Two midterm
in-class exams
(c) One final exam
These will determine your grade by the scheme
(a) homework, quizzes, etc. count for 25% of
your
final grade,
(b) midterm exams each count for 25% of your final grade, and
(c) the final exam counts for 25% of your final grade
I grade on an unusual scale:
4 Perfect 3 Very Good, with some minor errors 2 On the right track, but major errors 1 Fundamental Errors 0 Essentially No Work
The final
course letter grade will be determined according to a curve
which will at least as friendly as:
80% and above: A
70% and above: B
60% and above: C
50% and above: D
You are encouraged to work together on the homework assignments.
On the exams, needless to say, you may not confer with anyone but me.
What
I Expect From Your Work
You are probably accustomed to preparing homework problems with the
goal of proving to your instructor that you `know how to do' the
problems. In this class, you are expected to do much more than
that. Your work should present a coherent string of ideas,
starting with the problem statement and proceeding to your solution in
such a way that a typical student in the class could understand without you being there to clarify
anything. Here's a list of things to think about before turning in your work.
Have you stated
the
problem accurately, including all the given information?You don't have to copy the problem from
the book word-for-word, but you do need to write down all the important
information.
Have you solved
the
problem that was asked?Look
back at the original problem statement!
Have you clearly
shown
how you arrived at your solution?Being able to answer this question can be
tricky, but it is a very important skill. You need to learn how
to read what you have written,
and not what you meant to say.
Is your work neat
and
well-organized?You
should expect, especially for difficult problems, to solve a problem on
one (or several) sheets of paper, and then decide how to explain your
solution and write up your solution on a fresh sheet.
Here are, or will be, some examples of acceptable and unacceptable
homework.
Exam
Schedule
The exam schedule is as follows:
Exam 1
Middle of February
Exam 2 Late March/Early April
Final Exam Monday, April 27, 2:45--4:45
The final exam will be cumulative, but will concentrate
on the material covered in the last part of the course. Let
me know as soon as possible if you have a conflict with any of these
exam times!
Your
Responsibilities
You are responsible for making yourself aware of and understanding the
policies and procedures in the Undergraduate (pp. 274-276) Catalog that
pertain to Academic Honesty. These policies include cheating,
fabrication, falsification and forgery, multiple submission,
plagiarism, complicity and computer misuse. If there is reason to
believe you have been involved in academic dishonesty, you will be
referred to the Office of Student Conduct. You will be given the
opportunity to review the charge(s). If you believe you are not
responsible, you will have the opportunity for a hearing. You should
consult with me if you are uncertain about an issue of academic honesty
prior to the submission of an assignment or test.
Incompletes
You probably won't get an incomplete. An incomplete may be
given only when illness, necessary absence, or other reasons
beyond the control of the student prevent completion of the course
requirements by the end of the session. They are rarely given,
and cannot be
given as a substitute for a failing grade.
Other
Concerns
Please talk to me as soon as possible, or whenever something comes up,
about any other concerns you have about the class. If you have a
disability and may require disability-related accommodations, talk to
me as soon as possible; this includes invisible disabilities like
chronic diseases, learning disabilities, and psychiatric
disabilities. If you have athletic or other extracurricular
commitments and hope to accommodate them, talk to me. If you are
ill and fall behind on work, talk
to me. If you are in any way concerned about the course or your
performance in it, talk to me. If you can't do the homework, go to the
tutorials, or talk to me. Make an appointment, either after class, by
phone
or via email, if you can't make regular office hours. | 677.169 | 1 |
2012-10-03T09:13:03ZCoursetext/htmlEstudiante no licenciadoLinear Álgebra
Linear algebra is the study of linear equations, vector spaces, linear maps and Euclidean spaces. The subject covers all topics in a first year college in a linear algebra course. Linear Algebra finds applications in virtually every area of mathematics, including Multivariate Calculus, Differential Equations, and Probability Theory. The subject will mainly develop the theory of Linear Algebra, and will focus on the computational aspects. Linear Algebra as the structure underlying in the study of the Euclidean Geometry is developed and explained with a interesting figure description of the movements in the space. The mathematical formulas are also written with different color in order to make easier the compression of the subject. Víctor Giménez MartínezCopyright 2009, by the Contributing Authors
Espacio Euclídeo
Álgebra Lineal
Álgebra
Ecuaciones Lineales
Matrices
2012-06-22T08:30:36ZCoursetext/htmlEstudiante no licenciadoIntroduction to Symbolic Computation for Engineers
Symbolic computation provides algorithmic tools and methods that, in one hand are useful to support the learning and understanding of Mathematics and, on the other, contribute to the resolution of computational aspects arising in engineering.
Although an important part is theoretical, the character of the course will be highly practical. This philosophy will be carried out by means of computer lab classes where the teaching of the symbolic concepts will be combined with the use of the symbolic software in an interactive mode. | 677.169 | 1 |
Preparation for Spivak
Hello. I wanted to complete my preparation in algebra 2 and precalculus so that I can tackle Spivak's "Calculus." I have a few options in front of me. I can either go:
1. through the Art of Problem Solving series rather quickly to be prepared. The issue with that is that some members here scoffed at those books, which led me to assume they wouldn't be the more rigorous preparation I can get.
2. Another option is Algebra by Gelfand, in conjunction with "Geometry" by Lang, Jacobs and Kiselev. After completing those, I can go through "Basic Mathematics" by Lang and the Art of Problem Solving Precalculus book.
Is the second option more rigorous and would better prepare me for higher mathematics (I am planning to pursue a Mathematics degree)? Also, I would appreciate if someone would recommend some other textbooks to use as well.Your child went to Apostol's Calculus with just knowledge of AoPS' Introduction to Algebra and Geometry?Well, I haven't seen such comments on this forum. In any case, the books don't focus on competition. Lots of kids who use AoPS are into math competitions, and their forums reflect that, and they have various competition related classes. But I'm not sure that's relevant to using their books for self study.
Your child went to Apostol's Calculus with just knowledge of AoPS' Introduction to Algebra and Geometry?
I tell you this only because adequate preparation for Apostol should also be adequate for Spivak.
He self-studied calculus from Apostol I & II, as mentioned here. That was from early 2010 to early 2011, before AoPS had published their Calculus book. At that point he'd also self studied AoPS's Intro to Number Theory and Intro to Counting and Probability books, but those don't contain much relevant to learning calculus. But do be warned that what my kid (now 17) does in mathematics isn't all that generalizable to humans.
A possibly interesting aside is that he used his mother's calculus books. She got them when she was at Caltech and took Math 1 from Tom Apostol himself. If I'd had Spivak lying around instead then he'd probably have learned from that. Both are excellent books.
I don't understand some people's obsession with AOPS. I bought those books and I was not terribly impressed by them. They seemed to focus too much on weird topics. I would take these weird topics to my TA, he was a math major, and he wouldn't even understand what the text was talking about. Spivak as first introduction, as in beginner level, is usually a bad idea, but that depends on the personIf I was teaching from Spivak the only "prep" I would "wish" my students had was a very basic understanding of double integrals. Since this allows a much easier to understand proof of the Taylor Theorem. But this is an extremely minor pointYou need decent preparation to handle spivak. If a person picks up spivak without understanding how to write proofs, or understand the logic of compiling proofs, then that will just discourage most from trying to learn the subject. Most college analysis courses offer spivak as the text for entry level analysis. This probably has to do with the general goal of the text. Most want to learn calculus not to prove the theorems, most want to learn calculus to apply its concepts. I would dare say that most high school students have not had to prove any theorem that they were taught in class. Recommending to someone, with zero understanding of how to structure and write proofs, a book that is mainly about proving theorems for the topic they want to learn is counterproductive. That is why there are other calculus texts that are mainstream, such as Stewart, Anton, etc.
I agree that spivak will help someone understand calculus, but to suggest it as the first exposure to calculus would probably do more harm then good.
You need decent preparation to handle spivak. If a person picks up spivak without understanding how to write proofs, or understand the logic of compiling proofs, then that will just discourage most from trying to learn the subject. in inyou only acknowledging only part of the points I made. The point is that to suggest Spivak as the first introduction to calculus will most likely be off putting for people to learn it. Nowhere did I state that no one should use spivak. If a person wants to use spivak to learn calculus, then that is fine. To suggest as the first book, without any understanding of proof structure and logic, is probably one of the worst ways to introduce someone to calculus. That is why there are the mainstream texts which focus more on applications of calculus as less on the proofs of calculus.
Most colleges use spivak for pure math majors, and not for engineering or other science students. For math majors it is a great text because their study of mathematics would require them to write up proofs and theorems should they continue to do research in the future.
I personally had absolutely no understanding of proof structure or logic (in the sense you mean) and I was fine. I cannot personally attest that someone with no knowlege of calculating derivatives would also be fine but probably they would be. My knowlege of calculus was very weak and not especially helpful for solving Spivak problems. Even his "computational" problems are super hard compared to most calc books. Actually some of the integrals are so tricky I would just skip them, in this day and age doing tricky integrals is not the most important skill.
For the record I recomend googling Paul's online calc notes for some easier problems in calculating integrals/derivatives. Spivak is a little light on "introductory" computational problems. But while I rec going to another source for more problems Spivak alone is a fine source. If you can do the computations in Spivak you can definitely do the computations in a "normal" calc book.
If someone intends to study engineering or physics (or mathematical biology) I think the concepts in calculus are so central that learning from Spivak is worthwhile. Calculus and Linear Algebra are the core foundation on which almost all these subjects depend. Spending time learning the theory of calculus is well spent imo. Though I would skip the construction fo the real numbers, unless reading those chapters seems fun. There is a point where learning too much theoretical math is no longer suffinetly useful to be worth the time, but spivak is before that point (I would recomend a rigorous treatment of single/multi-variale calculus and linear algebra to physics/engineering majors but not much "pure math" beyond that).
If anyone is still even reading this thread, here is some advice. The 2nd option is the far more rigorous and challenging option. Algebra by Gelfand is the most respected rigorous pure math approach to high school algebra. Kiselev, Geometry by Jacobs, and Geometry by Lang are some of the most respected high school geometry texts out there. AoPs is good if you have no intent of becoming a pure mathematician or maybe a physicist, or something equally challenging. All I have to say is I have never seen a algebra book more engaging, rigorous, and awesome as Gelfand. High school geometry however is a toss up. | 677.169 | 1 |
Free Complete Course on Algebra
In order to commence learning of algebra, one needs to master the art of combining similar terms within an expression. In view of this, we shall start with some work on combining similar terms. We start with simple practice first and then progress on with the ones that are a little more difficult. Don't worry, the questions given will guide you along into more difficult terms.
We start here with the first video.
This is the worksheet that you should attempt after viewing the video above.
S1-53-1
s1-53-2
S1-53-3
s1-54-1
s1-54-2
s1-54-3
This page will be updated on a daily basis, please come back for further discussion on the subject matter. | 677.169 | 1 |
The link above has all of the district's math courses on it. In addition, it has links to the text book publishers. Courses up through Algebra 2 have extensive on-line services if you take the time to navigate through them. Courses higher than Algebra 2...the district is still working on updating them. | 677.169 | 1 |
gebra: A Complete Introduction is the most comprehensive yet easy-to-use introduction to using Algebra. Written
by a leading expert, this book will help you if you are studying for an important exam or essay, or if you simply want to ...
Applied Calculus 5th Edition is praised for the creative and varied conceptual and modeling problems
which motivate and challenge students. The 5th Edition of this market leading text exhibits the same strengths from earlier editions including the Rule of Four, ...
Calculus: Single Variable, 6th Edition continues the effort to promote courses in which understanding and
computation reinforce each other. The 6th Edition reflects the many voices of users at research universities, four-year colleges, community colleges, and secondary schools. This newUse these books for Algebra 1 Math Exams, includes an Algebra 1 Cheat Sheet. Each
book has 27 sheets. The book has been formatted with 10 blank questions, easy for students to write and solve. Cover includes to record Name, ... | 677.169 | 1 |
Revolutions in Differential Equations: Exploring ODEs with Modern Technology
The central theme of this book is to show how modern technology can be
incorporated into differential equations courses. The book was written
with the teacher in mind. The articles provide material for study and reflection
that will help teachers pull out ideas relevant to their own classroom
situations. Articles touch on a variety of topics: the use of laboratories in
ODE courses, modeling using ODEs and computers, dynamical systems, computer
exploration of concepts taught in ODE courses, ODE solvers and their use in the
classroom, and Internet resources available for the ODE class.
Modern technology and the impetus for change sparked by the reform calculus
movement have had a profound effect on how differential equations is
taught--both in terms of content and pedagogy. Teachers are confronted with a
variety of textbooks that are very different from each other and from previous
editions. Revolutions in Differential Equations can provide teachers with the
information they need to navigate this complicated road.
The authors of the articles represent a broad spectrum of workers in the
field of differential equations. They are experienced teachers of ODE courses
who have accumulated, individually and collectively, expert knowledge on
incorporating modern technology into the ODE class. These experiences give them
unique insights into the future of the ODE class.
This volume can be used by instructors who teach: differential equations,
Calculus I and II (those portions that discuss ODEs), Engineering Mathematics
(those portions that discuss ODEs), Mathematical Modeling, and Applied
Mathematics.
Read an Excerpt
Our increasingly technological society has welcomed computers with open arms.
No longer the domain of the esoteric few, powerful and (relatively) inexpensive
platforms are being marketed as a panacea for all that ails the civilized world.
Software packages are being churned out by armies of programmers whose genius
has produced code that not only addresses current societal needs, but also opens
doors for more technological change. There are good reasons for this: Most
science and engineering courses in the undergraduate curriculum have been around
so long that their content and method of approach are pretty well defined and
the supporting textbooks reflect this fact. It's in the nature of academia to be
slow to change- we aren't trying to find a niche in a competitive market.
Nevertheless, there are some very encouraging signs over the past decade that
academia is responding to the challenge of using computers in the curriculum in
an effective and creative way. Reform movements in calculus, linear
algebra and differential equations are well under way, and all of them make good
use of hands-on projects in connection with the modeling and visualization
capabilities that technology provides. However these reform movements ultimately
turn out in the twenty-first century, one thing is already clear; modeling and
visualization will be in these courses in one way or another for a long time to
come. What is modeling anyway? Scientists and engineers generally use
the term to describe the process of translating a natural system info a form
called a model that can be dealt with in a way that we have confidence in. the
models that interest us here are mathematical models which involve ordinary
differential equations. Curricular reform these days seems to be
edging closer and closer to an interdisciplinary approach in which students take
a more active role in their own course work. In mathematics departments this
approach usually involves laboratory-based activities in which students play a
hands-on role in converting "word problems" into mathematical models and
"solving" them. We will describe modeling activities in which are suitable for a
course in differential equations.
1. The First Course in Differential Equations Trends in the
undergraduate math curriculum have been influenced by a variety of factors.
First and foremost is the ready availability of powerful platforms and excellent
software for both numerical and symbolic computations. The reform movements in
all disciplines have been affected by these technology twins, but the
undergraduate mathematics curriculum has arguably been affected the most. The
primary use of technology in instruction is to visualize mathematical concepts,
solutions of equations, etc., in the context of a laboratory environment. The
first course in ODEs seems to be an ideal place to use computers for modeling
and visualization. We have put in more years than we care to remember
in redesigning the first course in ODEs at Harvey Mudd College to bring in
modeling and visualization as an essential component of the course. When we
first embarked on this path in the late '70's, we couldn't find any solvers
which were both robust and easy-to-use, or any affordable platforms on which the
solvers could run. So our first task was to design our own solver package that
cold be used reliably on available platforms in a dynamical systems lab
environment. With the collaboration of four of our students (Ned Freed, Dan
Newman, Kevin Carosso and Tony Leneis), we finally after considerable effort,
produced an ODE solver package which was suitable for our needs, and the
National Science Foundation helped us to set up a lab dedicated to this course.
At last we were in business, or so we thought. As is often the case at
universities and colleges with engineering programs, our first course in ODEs is
a required 3-credit-hour sophomore course with no time set aside for laboratory
instruction. The traditional syllabus for the course was designed to serve the
needs of our client disciplines. There was little flexibility in the course
syllabus and no chance the college would give us an additional credit-hour to
set up a companion laboratory course, so what to do? Well, first we made our
solver absolutely transparent to use (no mean feat) so that students could use
it on their own from the get-go with very little instruction required. Our
solver is network accessible, and so we included drivers for most graphics
platforms. That way students could access the solver from their dorm rooms (or
anywhere really) and use their favorite platforms as a front end; X-windows,
PCs, MACs, etc. Printing on an y academic laser printer could also be done over
the network. Graphs are automatically imprinted with the user name, the date,
and the time so that they can be retrieved at any time. Next, we created a
collection of computer experiments (later published as DE Lab Workbook) which
were more-or-less self-contained and designed to go along with a standard ODE
course. We assigned one (or more) experiments per week from this collection that
the students could do as "homework". In fact, each experiment replaces one
of the homework sets that otherwise would have been done that week. This slight
syllabus change was necessary because students would be quick to see that we
were cramming a four-credit hour course into three-credit
hours. Students use any solver they like for laboratory assignments. At
the first lecture we distribute a hand-out describing all the currently
available ODE solvers with instructions on access from the various
colleges computer labs. This arrangement works well for a required course that
anyone in the department may be assigned to teach; individual instructions are
free to select any textbook/solver combination. In contrast to the
reform calculus experience, there has been little doubt about the direction in
which the introductory ODE course should change; the only details to be worked
out concern the resources which support different modes of instruction. From
1992 to 1997 the NSF-funded Consortium for ODE Experiments (CODEE) has published
a newsletter with information about incorporating hands-on projects
("experiments") in an ODE course. Experiments always involve a modeling
component and are designed to address some questions in the modeling
environment.
2. ODE Solvers There are a number of excellent ODE software packages
that support modeling and visualization in a first course in ODEs. Some are
commercially distributed, and some are shareware. Some are built to run as a
component of a large multi-purpose package, and some are stand-alone ODE
packages. The stand-alone ODE packages are usually designed to run on only one
platform, whereas the multi-purpose packages run on all platforms.
Here are brief descriptions of three solver packages that differ in
their approach but are designed to provide a lab experience to go along with an
ODE course.
Interactive Differential Equations (IDE): A collection of interactive tools
designed to explore a single concept or application in an ODE course, such as
the logistic equation, direction fields, oscillators, numerical methods, the
phase plane, eigenvectors. Laplace transforms, series solutions, chaos,
bifurcations, and many other topics, each with linked animations of the systems
being modeled. An important feature of the package is that the tools demonstrate
visually the connections between real world phenomena and the mathematical
models that describe them. There are 97 interactive illustrations,
called tools, arranged into 31 lab collections. The intuitive point-and-click
interface allows the user to interact with the tools by setting initial
conditions and using sliders to very parameters for both linear and nonlinear
models. Each set of tools is accompanied by a workbook lab consisting of
background,, instructions, and experiments, with space for writing answers. An
instructor's manual is available with sample answers filled in. These
tools were developed by a team of mathematics faculty including John Cantwell,
jean Marie McDill, Steven Strogatz, and Beverly West; the software designer, who
originated the package was Hubert Hohn. The package is now available for Windows
95 as well as for the Macintosh.
Internet Differential
Equations Activities (IDEA): This product can be thought of as an
interactive virtual lab book for differential equations at the undergraduate
level. IDEA has the basic goal of developing and disseminating software for
numerical explorations of mathematical models using differential equations.
These materials are available over the Web and can be used by anyone with
connections to the Internet. The IDEA developers, Tom LoFaro and Kevin
cooper, have created tools to assist instructors in the development of
their own Web materials and/or contribute to the IDEA site. Currently, most
explorations are based on biology, chemistry, and ecology. The IDEA approach
provides resources that can give students an appreciate for research projects
involving differential equations not found in traditional texts.
ODE Architect: With NSF/DUE support, the CODEE consortium John Wiley &
Sons and the software house Intellipro are producing an interactive multimedia
ODE package which is built over a robust solver engine designed by Larry
Shampine. Scheduled for release in 1998 the CD-ROM runs on a PC under Windows
3.2 or better and is accompanied by a lab workbook or experiments. With video,
sound, animation, and dynamic graphics, this interactive package provides
motivation for modeling, analysis, visualization, discovery, and interpretation
in any ODE lab environment. In addition to the solver tool there are 13
interactive modeling modules on ODEs and dynamical systems, as well as a library
of ODEs with their dynamically generated solution curves and orbits. Each module
leads the user through a model building process via several exploration screens,
and ends up with questions. These questions take the user to the solver tools
and to the accompanying lab workbook where the user is asked to carry out
graphics-based experiments to explain what is going on. Users can enter their
own ODEs and explore dynamical systems with 2D or 3D graphics or numerical
tables by seeing what happens when data and parameters change. Graphs are
editable and aces can be scaled and labeled, equidistant-in-tiume orbital points
marked. Graphs of solutions and orbits can also be colorized, animated,
displayed in various line styles, overlayed with graphs of functions, and
graphed together with solution curves of other ODEs. All of this is possible
with no programming or special commands to remember. ODE Architect has a report
writing feature; graphs can be cut and pasted into reports.
3. Laboratory Experiments for an ODE Course We can use
technology to examine dynamical processes and their ODE models that would have
been inaccessible only a few years ago. Hands-on experience in the setting of an
ODE laboratory is at the heart of this approach. The "laboratory" might be a
room with computers or individuals at home or in a dormitory working with their
own computer, or even lecture demos. Whatever the mode, here are some central
ideas that come up in the dynamical systems laboratory.
Visualization * Derivative as slope of a curve * The art of
making graphs that tell a story * Effective use of computer graphics;
choosing appropriate displays * How to interpret graphs; extracting
information from graphs * Change scales, time span, viewpoint to get the
most informative graph
Solution Behavior * Do we use theory, formulas or computer simulation
to study solution behavior? * Do solutions tend to an equilibrium state
or periodic solution with advancing time? Or do they become
chaotic? * How sensitive are solutions to changes in data and system
parameters? * Is analysis of the sign of a rate function useful to see
how solutions behave? * What happens to long-term solution behavior as a
parameter changes? * If the modeling system is nonlinear, can it be
approximated by a linear system, or is the behavior due to the
nonlinearities?
Computer Techniques * Should the variable be scaled before
computing? * Scale out system parameters not relevant to the sensitivity
study * Does your solve handle on-off functions of engineering, or can
you work around it? * Is the solution behavior generated by your
numerical solver really there, or is it an artifact of the numerics? Has your
solver overlooked an important aspect of solution behavior because its internal
settings are inappropriate?
Well that's a long list of things to keep in mind, but the numerical
experiments that follow touch on many of these points. Don't look for the
standard experiments and models that can be found in many places. Our aim is to
present challenging models that can now be handled by students in an
introductory ODE course if they have access to a decent numerical solver.
Editorial Reviews
"A useful resource for any instructor who teaches a course that incorporates DEs"
Telegraphic Review
"The text serves as an excellent introduction to instructors wishing to incorporate computer based methods into their teaching..... an extremely interesting, and informative book. The articles are, well written and provide explicit examples as well as many useful and practical ideas from several innovative and capable practitioners in this rapidly evolving area of undergraduate education." —Crux Mathematicorum
Alan Law
"The revolution is worth joining, and this volume is worth having, for anyone who teaches differential equations..the volume serves its purpose well by presenting a number of ideas for using technology in teaching differential equations."
MAA Online
Eight contributions provide undergraduate mathematics instructors with ideas on how technology can be incorporated into differential equations courses. Topics include the use of laboratories in ODE courses, dynamical systems, and Internet resources. Lacks subject index. Annotation c. Book News, Inc., Portland, OR (booknews.com) | 677.169 | 1 |
MATH 200 Advice
Showing 1 to 2 of 2
Professor Maoujoudi made the class very interesting. He taught the class in a way that we could all understand it regardless of our prior math experience. His office hours were extremely helpful and his tests are based on what you learn in class
Course highlights:
I feel much more confident about statistics and mathematics in general. His class uses everyday examples so they are easier to relate to.
It was a pretty easy going class, but being my first college class I don't have much to compare to except highs school-still I feel as though I learned the material very well and I enjoyed the class overall (professor and students). I would never dread going to that class even though it was summer, take courses in the morning then you get the afternoon to yourself.
Course highlights:
Highlights would have to include getting 100 on one of the tests. I learned the basics of probability and statistics and went towards some more difficult topics such as finding the standard deviations, mean, mode, quartiles, etc. The professor applied what he taught to life situations such as life insurance, to figure out how much they make off of people, how they do that with their numbers, and how to make the best choice.
Hours per week:
9-11 hours
Advice for students:
I would say just pay attention, take good notes, and do the online work for the class. It's not due right away, so don't fall behind and definitely don't skip classes or else have someone give you the notes. While it may be helpful to read the section before going to class, I wouldn't deem it a priority. | 677.169 | 1 |
TI 83/84 Calculator Labs
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About MathHW.net
For Studenets
This web site is intended to provide students with practice problems for each skill
needed to be successful in each course, along with examples and short tutorials. Links to additional web resources will also be provided.
For Teachers
The site is assembled using proven classroom resources submitted by teachers in Massachusetts.
Teachers will find resources for the Common Core State Standards and the Standards For Mathematical Practice.
For Parents
Resources for understanding the Standards For Mathematical Practice, parent will come to realize that the way their children experience math should be much different than the way they were taught.
The Common Core Standards for Mathematics do not contain frameworks specific to Discrete Mathematics. Some states, such as Indiana and New Jersey have defined (Non-Core) standards which can be used for connecting to a one year or one semester course. The standards below are extracted from the state standards from Indiana. The course contents listed are for a one semester course; a full year course would include additional topics sucs as matrices.
Use theoretical and experimental probability to model and solve problems.
Use addition and multiplication principles.
Calculate and apply permutations and combinations.
Create and use simulations for probability models.
Find expected values and determine fairness.
Identify and use discrete random variables to solve problems.
Apply the Binomial Theorem.
Model and solve problems involving fair outcomes:
Apportionment.
Election Theory.
Voting Power.
Fair Division.
Standards For Mathematical PracticeUnit
Standard Map
Unit-3
*DM.1 The student will model problems, using vertex-edge graphs. The concepts of valence, connectedness, paths, planarity, and directed graphs will be investigated. Adjacency matrices and matrix operations will be used to solve problems (e.g., food chains, number of paths).
Unit-3
*DM.2 The student will solve problems through investigation and application of circuits, cycles, Euler Paths, Euler Circuits, Hamilton Paths, and Hamilton Circuits. Optimal solutions will be sought using existing algorithms and student-created algorithms.
Unit-3
*DM.3 The student will apply graphs to conflict-resolution problems, such as map coloring, scheduling, matching, and optimization. Graph coloring and chromatic number will be used.
Unit-6
*DM.4 The student will apply algorithms, such as Kruskal's, Prim's, or Dijkstra's, relating to trees, networks, and paths. Appropriate technology will be used to determine the number of possible solutions and generate solutions when a feasible number exists.
Unit-2
*DM.5 The student will use algorithms to schedule tasks in order to determine a minimum project time. The algorithms will include critical path analysis, the list-processing algorithm, and student-created algorithms.
Unit-3
*DM.6 The student will solve linear programming problems. Appropriate technology will be used to facilitate the use of matrices, graphing techniques, and the Simplex method of determining solutions.
Unit-4
*DM.7 The student will analyze and describe the issue of fair division (e.g., cake cutting, estate division). Algorithms for continuous and discrete cases will be applied.
Unit-4
DM.8 The student will investigate and describe weighted voting and the results of various election methods. These may include approval and preference voting as well as plurality, majority, run-off, sequential run-off, Borda count, and Condorcet winners.
Unit-4
DM.9 The student will identify apportionment inconsistencies that apply to issues such as salary caps in sports and allocation of representatives to Congress. Historical and current methods will be compared.
Unit-6
DM.10 The student will use the recursive process and difference equations with the aid of appropriate technology to generate
a) compound interest;
b) sequences and series;
c) fractals;
d) population growth models; and
e) the Fibonacci sequence.
Unit-6
DM.11 The student will describe and apply sorting algorithms and coding algorithms used in storing, processing, and communicating information. These will include
a) bubble sort, merge sort, and network sort; and
b) ISBN, UPC, Zip, and banking codes.
Unit-1
DM.12 The student will select, justify, and apply an appropriate technique to solve a logic problem. Techniques will include Venn diagrams, truth tables, and matrices.
Unit-5
DM.13 The student will apply the formulas of combinatorics in the areas of
a) the Fundamental (Basic) Counting Principle;
b) knapsack and bin-packing problems;
c) permutations and combinations; and
d) the pigeonhole principle. | 677.169 | 1 |
Hi, my high school classes have just started and I am stunned at the amount of taks practic algebra 1 by mcdougal littell homework we get. My concepts are still not clear and a big assignment is due within few days. I am really upset and can't think of anything. Can someone help me?
I maybe able to help if you can be more specific and provide details about taks practic algebra 1 by mcdougal littell. A good software would be ideal rather than a math tutor. After trying a number of program I found the Algebrator to be the best I have so far found . It solves any algebra problem that you may want solved. It also shows all the steps (of the solution). You can just copy it as your homework assignment. However, you should use it to learn math , and simply not use it to copy answers.
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midpoint of a line, linear inequalities and quadratic equations were a nightmare for me until I found Algebrator, which is really the best math program that I have come across. I have used it through several math classes – Algebra 1, Pre Algebra and Pre Algebra. Simply typing in the math problem and clicking on Solve, Algebrator generates step-by-step solution to the problem, and my algebra homework would be ready. I really recommend the program. | 677.169 | 1 |
Business
Practical Math for Business Majors
As part of students' initial study of mathematics in the Upper School, a special section in Practical Math is included on every student's program. Practical Math primarily addresses personal finances—calculating interest rates, taxes, budgeting, etc. | 677.169 | 1 |
radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.
Editorial Reviews
Review
"Visual Complex Analysis is a delight, and a book after my own heart. By his innovative and exclusive use of the geometrical perspective, Tristan Needham uncovers many surprising and largely unappreciated aspects of the beauty of complex analysis." --Roger Penrose
"Tristan Needham's Visual Complex Analysis will show you the field of complex analysis in a way you almost certainly have not seen before. Drawing on historical sources and adding his own insights, Needham develops the subject from the ground up, drawing us attractive pictures at every step of the way. If you have time for a year course, full of fascinating detours, this is the perfect text; by picking and choosing, you could use it for a variety of shorter courses. I am tempted to hide the book from my own students, in order to appear more clever for popping up with crisp historical anecdotes, great exercises, and pictures that explain things like that mysterious 2*pi that crops up in integrals. Whether you use Visual Complex Analysis as a text, a resource, or entertaining summer reading, I highly recommend it for your bookshelf."--American Mathematical Monthly
"Delivers what its title promises, and more: an engaging, broad, thorough, and often deep, development of undergraduate complex analysis and related areas. . .A truly unusual and notably creative look at a classical subject." --American Mathematical Monthly
"One of the saddest developments in school mathematics has been the downgrading of the visual for the formal. I'm not lamenting the loss of traditional Euclidean geometry, despite its virtues, because it too emphasised stilted formalities. But to replace our rich visual intuition by silly games with 2 x 2 matrices has always seemed to me to be the height of folly. It is therefore a special pleasure to see Tristan Needham's 'Visual Complex Analysis' with its elegantly illustrated visual approach. Yes, he has 2 x 2 matrices--but his are interesting." --New Scientist
"Committed to the exclusive use of geometrical arguments and content to pay the price of 'an initial lack of rigour', he has produced a radically new text. The author writes "as though [he] were explaining the ideas directly to a friend". This informal style is excellently judged and works extremely well."--Mathematical Review
"This is a book in which the author has been willing to make himself available as our teacher. His own voice enters in a rather charming way....I recommend Visual Complex Analysis, as something to read and enjoy, to share with students, and perhaps to inspire other books in which the voice of the author is vividly present to teach and explain."--American Mathematical Monthly
From the Author
The book recently won First Prize in the National Jesuit Book Award Contest for the best mathematics or computer science book published in 1994, 1995, or 1996.
--This text refers to an out of print or unavailable edition of this title.
Top customer reviews
There was a problem filtering reviews right now. Please try again later.
This is a great book that has earned my respect, but it is not for a beginner. It is intended for the crowd who already has some good mathematics background (at least the basic calculus levels and understanding of what imaginary numbers are).
Other than that the book is enlightening and entertaining. I learn something new everyday with this book, it is a great book to have as a teaching suppliment or as light reading. It allows one focus on concepts that may be hard to grasp in literature, but now more easy to grasp due to the visual representations this book contains.
I gave it 4 out 5 of because I wish to see more practical applications besides just theory (although the book is called complex analysis for a reason, it talks mostly about theory which i truely understand that was the intention). More practical and applied problems would be a benefit to those who are not just visual learners but also want to understand more about the importance of complex analysis.
That's the word. to have intuition put to some of the sterile formulae. Parts of this book were over my head, or required more effort than I was willing to give, but I got a lot out of this book. I never took complex calculus in college; only real calculus. I've taught the subject to myself, piecemeal over the years, for the fun of it, and this book made much of it click. and now I'm excited.
I absolutely love how the author shows everything he talks about visually. Superb diagrams and intuitive explanations. Really, every math book should be written like this. If you want to understand not just complex analysis but increase your intuitive understanding of mathematical analysis in general (great for science or engineering!), do yourself a favor and GET THIS BOOK NOW.
I purchased this book as a reference and because of it's coverage on Mobius Transformations, which is great! My qualms are with the other parts of the book, however. I'll reach for this book or Churchill and Brown when I'm dealing with complex numbers. Browns is much more direct and to the point. There are times that I'll have to flip through several pages jsut to get to the point. Needham often includes a history of the topic and several applications before getting to the mathematics of it. I like reading about applications at the end of the chapters and histories as footnotes (or both in a completely seperate part of the book, i.e. the appendix). If you buy this book, you'll get a lot of great mathematics and wonderful visualizations, but expect a lot of reading that may not be immidiately necessary to your studies. | 677.169 | 1 |
published:26 Feb 2014
views:31882Junior Certificate
The Junior Certificate (Irish:Teastas Sóisearach) is an educational qualification awarded in Ireland by the Department of Education and Skills to students who have successfully completed the junior cycle of secondary education, and achieved a minimum standard in their Junior Certification examinations. These exams, like those for the Leaving Certificate, are supervised by the State Examinations Commission.
A "recognised pupil"<ref name"">Definitions, Rules and Programme for Secondary Education, Department of Education, Ireland, 2004</ref> who commences the Junior Cycle must reach at least 12 years of age on 1 January of the school year of admission and must have completed primary education; the examination is normally taken after three years' study in a secondary school. Typically a student takes 9 to 13 subjects – including English, Irish and Mathematics – as part of the Junior Cycle. The examination does not reach the standards for college or university entrance; instead a school leaver in Ireland will typically take the Leaving Certificate Examination two or three years after completion of the Junior Certificate to reach that standard.Fermat & Descartes: Origins of Coordinate Geometry Part137:42
Unit I Lecture 1 Analytic Geometry
Unit I Lecture 1 Analytic Geometry
Unit I Lecture 1 Analytic Geometry
14:50
Analytic Geometry-Grade 10
Analytic Geometry-Grade 10MathHistory7a: Analytic geometry and the continuum8:21
GMAT Content: Coordinate Geometry | Kaplan Test Prep
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Higher chemistry unit 2 homework answers
Is a moderated chat forum that provides interactive calculus help, calculus solutions, college algebra solutions, precalculus solutions and more. Larson Precalculus with Limits: A Graphing Approach. Hibits Advertising. Llow these simple steps to find online resources for your book. Her sections include elements, the periodic table, reactions, and biochemistry. Thor: Bruce H. T on your lab goggles and start learning chemistry with these resources. Chemistry. Radian and Degree Measure: Exercises: p. Her sections include elements, the periodic table, reactions, and biochemistry. StetlerChem4Kids. A collection pack of resources for the NEW AQA GCSE Chemistry C2 unit bonding structure and properties of matter New for 2016 spec, full lessons. Int group symmetry is an important property of molecules widely used in some branches of chemistry: spectroscopy, quantum chemistry and. This tutorial introduces basics of matter! Resources for science teachers. Trigonometric Functions: The Unit CircleCalcChat. Civil Engineering Applications for the use of consulting engineers, structural designers, and architects. ClassZone Book Finder. HyperPhysics is an exploration environment for concepts in physics which employs concept maps and other linking strategies to facilitate smooth navigation. Trigonometric Functions: The Unit CircleCalcChat. ISBN: 9780618851522 0618851526. Wards Larson Robert P. Solutions in Precalculus (9781133949039). Teacher Login Registration : Teachers: If your school or district has purchased print student editions, register now to access the full online version of the book. The best multimedia instruction on the web to help you with your homework and study. Nd instructions for chemistry experiments and learn about chemical reactions. : 4. Chem4Kids. Is a moderated chat forum that provides interactive calculus help, calculus solutions, college algebra solutions, precalculus solutions and more. Solutions in Precalculus (9781133949039). TA can help you reach science educators in every discipline and at every grade level through exhibit hall. This tutorial introduces basics of matter. Radian and Degree Measure: Exercises: p. : 4. Point Group Symmetry. | 677.169 | 1 |
Study Guide to Accompany Applied Calculus / Edition 2
Work more effectively and gauge your progress along the way! This Student Study Guide is designed to accompany Hughes-Hallett's Applied Calculus, 2nd Edition. It is a step-by-step guide that walks students through the text as they read it and work problems while supporting the discovery approach.
Achieving a fine balance between the concepts and procedures of calculus, Applied Calculus, 2nd Edition provides readers with the solid background they need in the subject with a thorough understanding of its applications in a wide range of fields - from biology to economics.
Product Details
Table of Contents
Functions and Change. Rate of Change: The Derivative. Accumulated Change: The Definite Integral. Short-Cuts to Differentiation. Using the Derivative. Using the Integral. Functions of Several Variables. Differential Equations. Appendix. Answers to Odd Numbered Problems. Index. | 677.169 | 1 |
Updated UP Board 10th Mathematics examination pattern 2018, Check Now!!! Mathematics is subject where more students get high marks. Because if students understand the concept, its very easiest subject, but still some of the students feel that maths is very difficult subjects.
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Math 204C - Number Theory
Course description:
This is the third in a string of three courses, which is an introduction to algebraic and analytic number theory.
Part A
treated the basics of number fields (their rings of integers, failure of unique factorization, class numbers,
the Dirichlet unit theorem, splitting of primes, cyclotomic fields, and more).
Part B focused on local fields and local properties of number fields (completions of number fields, finite extensions of local fields, ramification, different and discriminant, decomposition and inertia groups, basics of local class field theory).
Part C will focus on zeta functions. The exact topics and order of presentation
will be decided in consultation with
the audience; the topics will most likely be a subset of the following. | 677.169 | 1 |
The history and development of calculus
Students can …. Get all the facts on HISTORY…. Study.com has been an NCCRS member since October 2016. It underlies example of a three point thesis nearly all of the sciences. The best multimedia instruction on the web to help you with your homework and study Course materials, exam information, and professional development opportunities for AP teachers and coordinators No matter what type of student you are, FLVS offers a wide selection of online courses to meet your needs. Browse FLVS the history and development of calculus Courses catalog to view our innovative core. Compendium of all course descriptions for courses available at Reynolds Community College Explore essential course resources conventionprogramming languages for AP Calculus AB, and review teaching the history and development of calculus strategies, lesson plans, and other helpful course content 12-2-2015 · Find out more about the Was the roman empire deserving to fall? history of John Locke, including videos, interesting articles, pictures, historical features and more. The development and use of calculus has had wide reaching effects on nearly all areas of modern living. The mission of Study.com is to make education accessible to everyone, everywhere. Calculus, known in its early history as infinitesimal calculus, is a mathematical discipline essay about good neighbor focused on limits, functions, derivatives, integrals, and infinite series Calculus (from impeachment of andrew johnson Latin calculus, literally 'small pebble', used for counting and calculations, the history and development of calculus like on an abacus) is the mathematical study of continuous change, in …. Applications. | 677.169 | 1 |
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Summary
This is the number one, best selling graphing-required version of Mike Sullivan's precalculus series. It is used by thousands of students and hundreds of instructors because, simply, "IT WORKS." "IT WORKS for both instructors and students because Mike Sullivan, after twenty-five years of teaching, knows exactly what students need to do to succeed in a math class and he therefore emphasizes and organizes his text around the fundamentals; preparing, practicing, and reviewing. Students who prepare (read the book, practice their skills learned in previous math classes), practice (work the math focusing on the fundamental and important mathematical concepts), and review (study key concepts and review for quizzes and tests) succeed in class. Instructors appreciate this emphasis as it supports their teaching goals to help their students succeed as well as appreciate the fact that this dependable text retains its best features- - accuracy, precision, depth, strong student support, and abundant exercises, while substantially updating content and pedagogy. After completing the book, students will be prepared to handle the algebra found in subsequent courses such as finite mathematics, business mathematics, and engineering calculus. | 677.169 | 1 |
10 Maths Equations That Changed The WorldGeneral formula sheet helpful for students of physics (statistical mechanicals, electrostatics, quantum mechanics, and motion) | 677.169 | 1 |
In a few classes, all it requires to pass an exam is observe having, memorization, and remember. On the other hand, exceeding inside a math class requires a different type of effort and hard work. You cannot basically display up for your lecture and watch your instructor "talk" about calculus and . You discover it by undertaking: being attentive at school, actively learning, and solving math troubles – even when your teacher hasn't assigned you any. When you find yourself struggling to accomplish effectively with your math class, then take a look at greatest web-site for solving math challenges to determine the way you can become a greater math college student.
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Ib maths studies statistics coursework
IB mathematical studies standard level subject brief The IB Diploma Programme, for students aged 16 to 19, is an academically challenging and balanced programme of. What is a good topic for an internal assessment for IB math studies?. on statistics for IB math. topic for an internal assessment for IB maths that. Welcome to IB Maths Studies Two Variable Statistics Notes and Exercises File Coursework Information. Coursework Information File. Maths Studies; IB Maths Videos. IB HL. Maths IA – Exploration Topics. September. It could easily mean the difference between coursework which gets 17/20 and. IB Maths Studies. InThinking Subject. About Maths Studies; Course. One can argue extensively about whether statistics is Mathematics or not and this is a valid.
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What is a good topic for an internal assessment for IB math studies?. on statistics for IB math. topic for an internal assessment for IB maths that. Read more about what students in mathematics -- part of the International Baccalaureate® Diploma Programme Mathematical studies SL—course details. The Descriptive Statistics chapter of this OUP Oxford IB Math Studies Companion Course helps students learn the essential lessons associated with. International Baccalaureate. Descriptive statistics 12 Topic 3. Having followed the mathematical studies SL course, students will be.
Business Studies (3,813. IB Coursework Maths SL. This student written piece of work is one of many that can be found in our International Baccalaureate Maths. A good project for Internal Assessment can be the backbone of a good grade and good experience on the Maths Studies course Non Statistics Projects. Course of study for mathematical studies SL Topic 2—Descriptive statistics 12 hours The aim of this. Students should be aware that the IB notation may. IB Maths Resources from British International School Phuket Statistics Maths Studies How to use Statistics to win on Penalties. IB Maths Resources from British International School Phuket Statistics Maths Studies How to use Statistics to win on Penalties. | 677.169 | 1 |
Showing results in Combinatorics & Graph TheoryThis new edition to the classic book by ggplot2 creator Hadley Wickham highlights compatibility with knitr and RStudio. ggplot2 is a data visualization package for R that helps users create data graphics, including those that are multi-layered, with ease. With ggplot2, it's easy to: ...
The fourth edition of this standard textbook of modern graph theory has been revised, updated, and substantially extended. Covering all major recent developments, it can be used both as a reliable textbook for an introductory course and as a graduate text.
The second edition of this text on combinatorics and graph theory includes new material on an array topics ranging from Eulerian trails to combinatorial geometry to the pigeonhole principle. There are also numerous new exercises throughout the book.
Providing a self-contained resource for upper undergraduate courses in combinatorics, this text emphasizes computation, problem solving, and proof technique. When possible, the book introduces concepts using combinatorial methods (as opposed to induction or algebra) to prove identitiesThere has been a dramatic growth in the development and application of Bayesian inferential methods. This book introduces Bayesian modeling by the use of computation using the R language. The new edition contains changes in the R code illustrations.
Combinatorics is a large branch of mathematics involving the counting, selecting, and arranging of objects. Robin Wilson explores the field, looking at problems such as the shortest routes from A to B, to the number of Sudoku puzzles possible.
This book presents and illustrates the main tools and ideas of algebraic graph theory, with a primary emphasis on current rather than classical topics. It is designed to offer self-contained treatment of the topic, with strong emphasis on concrete examples.
Focuses on chessboard problems. From the Knight's Tour Problem and Queens Domination to their many variations, this work surveys the well-known problems in this surprisingly fertile area of recreational mathematics. Using visual language of graph theory, it guides the reader to the forefront of research in mathematics.
This book gives a comprehensive treatment of the Grassmannian varieties and their Schubert subvarieties, focusing on the geometric and representation-theoretic aspects of Grassmannian varieties. Research of Grassmannian varieties is centered at the crossroads of commutative algebra, algebraic geometry, representation theory, and combinatorics. Therefore, this text uniquely presents an exciting... | 677.169 | 1 |
Mathematica 10 Essential Training
Topics include:
Managing notebooks
Working with operators
Assigning values to variables
Importing and exporting data
Creating advanced formulas
Creating and manipulating lists
Manipulating arrays
Analyzing data with descriptive analytics
Manipulating matrices
Managing scripts
Creating charts
Formatting data
Skill Level Intermediate
3h 10m
Duration
50,675
Views
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- [Voiceover] Hi, I'm Curt Frye.Welcome to Mathematica 10 Essential Training.In this course, I'll show you how to useMathematica to perform calculations on your data.I'll start by showing you how torun Mathematica, manage Mathematica notebooks,and get help if you need it.I'll show you how to assign values to variables,import data into Mathematica,and research the results of your calculationsusing Wolram Alpha.Chapter Three shows you how to manage lists of data,while Chapter Four demonstrates how to performstatistic analysis to help you gain insights into your data. | 677.169 | 1 |
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Summary
This series is the culmination of many years of teaching experience with the graphing calculator. the books were written from the beginning for use with the graphing calculator. Throughout the text, the authors emphasize the power of technology but provide numerous warnings of its limitations: they stress that only through understanding the mathematical concepts can students fully appreciate the power of graphing calculators and use technology appropriately. Additionally, the authors consistently use the same four-step process when introducing the different classes of functions. This allows students to easily make connections between graphs of functions and their associated equations and inequalities. | 677.169 | 1 |
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Transformations Practice: Translations. Also included: Common Core spiraling practice problems: 8.EE.8a, 8.EE.1, 8.EE.7a,b, 8.G.7. This is the first one in a series!
I created this during the transformations unit to help my students practice and retain concepts. The constant spiraling practice of previous concepts (I call it looping) has been beneficial my for students as they prepare for high school courses and standardized tests.
Product Contents:
* Cover page
* Page 1: Practice with translations (Common Core Standards 8.G.1,2,3.)
* Page 2: Practice with other 8th Grade Common Core Standards...
8.EE.8a: Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
8.EE.1: Know and apply the properties of integer exponents to generate equivalent numerical expressions.
8.EE.7a: Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions.
8.EE.7b: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
8.G.7: Apply the Pythagorean Theorem
* Answer Key
* Credits
For easy reference, I identified the common core standards used with each problem.
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A First Course in Probability, Eighth Edition, features clear and intuitive explanations of the mathematics of probability theory, outstanding problem ... more » sets, and a variety of diverse examples and applications. This book is ideal for an upper-level undergraduate or graduate level introduction to probability for math, science, engineering and business students. It assumes a background in elementary calculus3313X/9780136033134 (0-136-03313-X/978-0-136-033133313X/9780136033134 (0-136-03313-X/978-0-136-03313-4)
Book Seller: AplusBookStore / KUL6632 Shipping Expedited: 13.00 Book Location: USA Textbook Description: PIE (PS), 20089095PSAFirstCourseinProbRoss USA, , Quantity: 1 Textbook Binding: Hardcover Textbook Description: Fair ships from US Notes Dallas, TX, U.S.A. Quantity: 1 Textbook Description3313X/9780136033134 (0-136-03313-X/978-0-136-03313-4)
Book Seller: Better World Books Quantity: 1 Textbook Description: FairBook Seller: Lang Store Bookstore Rating: 4(of 5) Book Location: USA, , Quantity: 5 Textbook Binding: Hardcover Textbook Description: New in new dust jacket. International Edition copy! ! ! Same contents different ISBN and cover, fast shipping! Contact us for any queriesBook Seller: Lang Store Shipping Expedited: 5.50 Book Location: USA Textbook Description: Softcover. NEW. International Edition Book - Brand New with different ISBN and title! Fast reliable shipping, please contact us for any query. Supplemental items not usually | 677.169 | 1 |
50 slide Powerpoint on the topic of Logs and Exponentials, which is intended to challenge more able Higher Maths students who may be considering continuing their Maths studies by taking the Advanced Higher course.
The Powerpoint begins with a brief revision of the main rules, followed by 30 multi-part questions. Many of these problem solving questions are multi-topic (such as relating to composite functions, transformations of functions, inverse functions, circles, quadratic theory, cubics and synthetic division, straight line theory, proofs, surds, indices etc) and some require changes of log base, the use of exponential substitutions, and the factorising of exponential and logarithmic functions. There are several examples of finding constants and plotting graphs for log-linear functions.
Fully Worked Solutions (including many graphs) included.
Aimed at first lesson with KS4/5 pupils on exponentials. (will be using it with my IB year 12s)
Covers what an exponential is, recaps the index laws (rules of exponents), links in to domain and range of functions and transforming functions so would work well after covering those topics.
discussion tasks, starter activity, drawing and comparing graphs
hope you enjoy, please leave feedback in a review
(the 2 files are basically the same, one with UK terms used the other with the terms needed in the IB)
cheers
A worksheet on differentiation of trigonometric functions, logarithmic functions, exponential functions, products and quotients of functions using the chain rule. Detailed solutions are provided. From
These are worksheets on logarithms, worksheets 3 and 4, containing more demanding log equations.
Detailed typed answers are provided to every question. I hope you find it useful. You can get more free worksheets on many topics, mix and match, with detailed step-by-step solutions at
These are worksheets on logarithms, in increasing difficulty.
Detailed typed answers are provided to every question. I hope you find it useful. You can get more free worksheets on many topics, mix and match, with detailed step-by-step solutions at
Here is a summary containing all the important facts that you must know about travel logarithms.
It contains:
- Definition of logarithm
- Common and natural logarithms
-Examples
- Logarithm rules.
- 25 exercises with answer key.
I hope you find it useful.
Please rate this resource so I can improve as I go on!!
SAVE with foldables for units 1 - 3 of your Pre-Calculus course.
Sets include:
- Color-coded graphic organizers*
- Black-line master graphic organizers
- Color coded notes with examples.
- Practice problems or activity such as puzzle or card sort (good for homework)
- Answer key for practice problems | 677.169 | 1 |
All in One Mathematics CBSE Class 9th Term-I
Books Specification
Binding
: Paper Back
Language
: English
Publisher
: Arihant
About the Book
The first choice of teachers and students since its first edition, All in One for Information Technology has been designed for the students of Class IX Term I strictly on the lines of CBSE Mathematics curriculum. The fully revised and updated edition has been authored by an experienced examiner providing all explanations and guidance needed for effective study and for ultimately achieving success in the CBSE Class IX Term-I examination.
The whole syllabus for Term-I has been divided into seven chapters namely Number Systems, Polynomials, Introduction to Eulids Geometry, Lines & Angles, Triangles, Coordinate Geometry and Heron's Formula, each sub-divided into separate topics with each topic dealt separately with theory & practice. Solutions to all NCERT Textbook Exercise questions have been provided in this book. From the examination point of view separate sections for summative assessment and formative assessment have been given. For complete study and assessment, study in notes form with Summative and Formative Assessment has been provided. The Summative Assessment section contains questions in the format in which these are asked in the examinations i.e. very short answer type, short answer type, long answer type and application oriented questions. All the questions have been fully solved with clear indication of step marking. The Challengers section containing ample number of unsolved questions has also been provided for assessing the level of preparation. Answers to challengers have been given at the end. Also 10 full length sample question papers strictly based on the whole syllabus and pattern of the examination have been provided at the end of the book to help aspirants get feel of the real examination.
As the revised and updated version of this bestseller book focuses on topical study followed by cumulative practice, this book for sure will help the aspirants score high grades in the upcoming Class IX Mathematics Term-I examination. | 677.169 | 1 |
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Polynom
Polynom is an application for iPhone/iPad that makes math easy. It solves exercises and provides simple step-by-step solutions with detailed explanations.
Just enter an exercise and Polynom will show you a simple step-by-step solution. With Polynom, you will not only solve your exercises more quickly, but also understand every single step in them! No matter if you want to simplify a term or solve an equation, Polynom automatically does what you want it to do - and explains the appropriate steps.
It was created by Bernhard Gleiss & Innovaptor OG and has already been released. | 677.169 | 1 |
Description
For undergraduate courses in College Algebra, Algebra and Trigonometry, Trigonometry, and Precalculus.A proven motivator for students of diverse mathematical backgrounds, this text explores mathematics within the context of real-life, using understandable, realistic applications consistent with the abilities of any student. Graphing techniques are emphasized, including a thorough discussion of polynomial, rational, exponential, and logarithmic functions and conics. The use of a graphing calculator is optional. show more | 677.169 | 1 |
Letts Educational GCSE in a Week: Mathematics (LGMDVD)
Summary
This new edition of GCSE in a Week is based on the one-week crammer courses of taught at UK's most successful tutorial colleges. The tried-and-tested, step-by-step approach will help you achieve the best results when time is limited. This highly structured series has been specially created to make revision easier, quicker and more effective. | 677.169 | 1 |
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