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Course Description:A study of
geometric concepts and measurement using nonstandard, English, and metric
units.Coordinate geometry, inductive
and deductive reasoning, and concepts related to two- and three-dimensional
objects including similarity, congruence, and transformations are explored.
Prerequisites:Admission to
Teacher Education
Objectives
The
purpose of this course is for you to:
·Develop
mathematical content knowledge in the areas of geometry and measurement
§You will be
provided with scissors, ruler, protractor, and compass for classroom use.You will need to have your own supplies for
out-of-class use.
§You will need
access to Geometer's Sketchpad.On
campus you will find this program in the Mathematics and Computer Science
folder of the Campus Software folder.I
recommend that you purchase the student edition of GSP to install on your
personal computer.It can be ordered
from Key Curriculum Press at may be several copies for purchase in
the ASU bookstore.)
§TI-83 or TI-84
graphing calculator
PARTIAL COURSE REQUIREMENTS
·Reflective
Journal:A component of effective teaching is reflection
on practice.The NCTM Principles and
Standards for School Mathematics stress that teachers must have
opportunities to reflect on and refine instructional practice –during class and
outside class, alone and with others.As
a part of this course, you are expected to maintain a reflective journal.This journal is a log of your experiences within the course.It should include thoughts about new skills
and accomplishments that you acquire; critical incidents that occur; and your
thoughts and feelings about content (mathematics/geometry investigations) and
technology.Please see me if you are
having difficulty keeping a journal so that I can make some suggestions.
Please
write the date prior to each entry.You
may type or write in long hand (as long as it is neatly done).Do not write on the back.Keep your journal in a folder with a 3-hole
punch.These will be collected every 2
weeks for me to see the progress you are making.I will read them and make comments but no
grade will be assigned.You will receive
credit for the assignment if you submit the journal when it is due and if you
submit an entry that shows you are reflecting on your experiences.
·Electronic
Portfolio of Write-ups:Each person will develop a personal Web Page
for the course. There will be a set of at least 10 "Write-up"
projects.Each Write-up will be prepared
as an HTML document (i.e. a Web Page document) and linked to your personal web
page.
What is
a write-up?
The "write-ups" represent your synthesis
and presentation of a mathematics investigation you have done --usually under
the direction of one of the assignments. The major point is that it
convincingly communicates what you have found to be important from the
investigation. A write-up should communicate the essential material you have
synthesized from your investigation. The format could be entirely in a
word-processing document. After all, an HTML document is basically a word
processing document with links. The HTML format, however, can combine
narrative, pictures, and program applications in a dynamic document. Write-ups
should be posted to your personal Web Page. If you work with a classmate on an
investigation, you should still do your own write-up so that you explain your
thinking and what you learned.You
should also acknowledge the collaborative effort.Criteria for assessment will include correct
mathematics and how well you communicate."Solution" might be another word for "Write-up."
·Reaction
papers:You will have 4 one to two page reaction
papers to write.The papers will be your
reaction to articles you will read related to teaching and learning geometry in
the middle school. The Rubric for Reaction Papers will be used to evaluate your
writing.
·Working
Portfolio/Notebook:You should organize all materials (handouts,
classnotes, homework, readings, writings, tests) in a 3-ring binder, writing
the date on each.This notebook will be
a record of your work in the course and will also serve as a tool for
reflection.You will need this notebook
to help you prepare for tests and to help you develop your final reflective
portfolio.It will also be a valuable
resource to you when you begin teaching.
·Final
Reflective Portfolio:This assignment is designed for you to reflect over
the activities of the course to determine what kind and how much progress you have
made in your understanding of geometry concepts so that you will be able to
teach geometry meaningfully to middle school students.The directions for this assignment will be
given later.For now, you need to be
sure you are keeping a well-organized notebook.
** name is first initial plus last name, e.g. Linda
Crawford "lcrawford"
The
percentages to determine your course grade
Reflective Journal
5%
Daily class participation
5%
Other written or presented
assignments
13%
Reaction Papers
7%
Write-ups posted to
webpage
25%
Midterm exam
20%
Final exam
25%
Class Policies
§Attendance and participation are required in this
class, both for you to learn and for others to benefit from your input.Much of the learning in the course takes
place by participating, sharing, and interacting with others; this cannot take
place if you are absent so regular attendance and punctuality are
expected.Frequently, ideas that we
introduce in one class are expanded upon and developed more fully in later
classes.Thus, every class is
important.However, if you have to
miss class for good reasons, you should contact me as much in advance as
possible.Any student who is absent
more than 10% of the class time (3 class periods) may be dropped with a
WF.Excused absences will count toward
the 10%.If you are absent, you are
responsible for the assignment as well as any announcements made in class.
§Out-of-class assignments are due at the beginning of
class—place them on my desk when you arrive for class.If you are absent, your assignment is still
due so you will have to make arrangements to get it to me.Late assignments are accepted at my
discretion but will be assessed a penalty of 10% for each day (not class period)
the assignment is late.
§No eating or drinking in the classroom—this is a
policy of Allgood Hall.Bottles and cups
should be capped and put away.
§Visitors, including children, are not permitted
without my prior permission.
Academic honesty:Cheating
will not be tolerated.Although you
may collaborate on outside assignments, your write-up should be your
own.Any student who is caught
cheating will face serious consequences.You should read ASU's statement on academic honesty in the catalog.
Professional Organizations
You
are encouraged to join the following professional organizations:
·Georgia Council
of Teachers of Mathematics (GCTM) at
(this membership is free so I will see that you join this organization)
·National Council
of Teachers of Mathematics (NCTM) at
($38 student membership includes your choice of journal—Mathematics Teaching
in the Middle School is recommended for middle grades teachers.) |
MATH 190 - Real-World Mathematics: A Service-Learning Math Course (4)
Contemporary society is filled with political, economic and cultural issues that arise from mathematical ideas. This service-learning Core mathematics course will engage students in using mathematics as a tool for understanding their world with a focus on the connection between quantitative literacy and social justice.Topics covered will include financial mathematics, voting theory, data representation and statistics. |
History of Mathematics
9780130190741
ISBN:
0130190748
Pub Date: 2001 Publisher: Prentice Hall
Summary: For junior and senior level undergraduate courses, this text attempts to blend relevant mathematics and relevant history of mathematics, giving not only a description of the mathematics, but also explaining how it has been practiced through time.
May include moderately worn cover, writing, markings or slight discoloration. SKU:9780130190741-4-0-3 Orders ship the same or next business day. Expedited shipping within U.S. [more]
May include moderately worn cover, writing, markings or slight discoloration. SKU:97801301907Blending relevant mathematics and history, this book immerses readers in the full, rich detail of mathematics. It provides a description of mathematics and shows how mathemat [more]
Blending relevant mathematics and history, this book immerses readers in the full, rich detail of mathematics. It provides a description of mathematics and shows how mathematics was actually practiced throughout the millennia by p.[less] |
Part of the ST(P) graded series in mathematics, this book is for use in the third year of secondary schools and is intended to enable pupils to reach about Level 6 of the National Curriculum in mathematics for Key Stage 3. Some of the work goes beyond Level 6, in preparation for Key Stage 4.
Top page
Complete description
Part of the ST(P) graded series in mathematics, this book is for use in the third year of secondary schools and is intended to enable pupils to reach about Level 6 of the National Curriculum in Mathematics for Key Stage 3. To allow for flexibility, many of the topics which appear in Books 1B and 2B are included here, and also some of the work goes beyond Level 6, in preparation for Key Stage 4 at the age of 16+. This answer book includes some mental tests which are graded to correspond to the order of work in the text book.
Top page |
This article provides a status report on discrete mathematics in America's
schools, including an overview of publications and programs that have had major
impact. It discusses why discrete mathematics should be introduced in the
schools and the authors' efforts to advocate, facilitate, and support the
adoption of discrete mathematics topics in the schools. Their perspective is
that discrete mathematics should be viewed not only as a collection of new and
interesting mathematical topics, but, more importantly, as a vehicle for
providing teachers with a new way to think about traditional mathematical topics
and new strategies for engaging their students in the study of mathematics.
It has been suggested that activities in discrete mathematics allow a kind of
new beginning for students and teachers. Students who have been "turned off" by
traditional school mathematics, and teachers who have long ago routinized their
instruction, can find in the domain of discrete mathematics opportunities for
mathematical discovery and interesting, non-routine problem solving. Sometimes
formerly low-achieving students demonstrate mathematical abilities their
teachers did not know they had. To take maximum advantage of these
possibilities, it is important to know what kinds of thinking during problem
solving can be naturally evoked by discrete mathematical situations—so that in
developing a curriculum, the objectives can include pathways to desired
mathematical reasoning processes. This article discusses some of these ways of
thinking, with special attention to the idea of "modeling the general on the
particular." Some comments are also offered about students' possible affective
pathways and structures.
Experimental
Mathematics and Proofs in the Classroom
(Ulrich Kortenkamp, Berlin)
Experimental mathematics is a serious branch of mathematics that starts gaining
attention both in mathematics education and research. We give examples of using
experimental techniques (not only) in the classroom. At first sight it seems
that introducing experiments will weaken the formal rules and the abstractness
of mathematics that are considered a valuable contribution to education as a
whole. By putting proof and experiment side by side we show how this can be
avoided. We also highlight consequences of experimentation for educational
computer software.
Learning to prove: using structured templates for
multi-step calculations as an introduction to local deduction
(Tony Gardiner, Birmingham (Great Britain))
It is generally accepted that proof is central to mathematics. There is less
agreement about how proof should be introduced at school level. We propose an
approach - based on the systematic exploitation of structured calculation -
which builds the notion of objective mathematical proof into the curriculum for
all pupils from the earliest years. To underline the urgent need for such a
change we analyse the current situation in England - including explicit evidence
of the extent to which current instruction fails even the best students.
About traveling salesmen and telephone networks –
combinatorial optimization
problems at high school (Andreas Schuster, Würzburg)
This article introduces an investigation dealing with the question of what role
the mathematical discipline "combinatorial optimization" can play in mathematics
and computer science education at high school. Combinatorial optimization is a
lively field of applied mathematics and computer science that has developed very
fast through the last decades. |
The first is Cohen's Precalculus. If you don't remember things like the quadratic formula and trigonometry, then this will cover it all. The new edition seems to have typos, so you might want to look around for an older edition on Amazon. Otherwise, you can't go wrong with Sullivan
, which I have not used but heard good things about. Either one of these is better than Larson that's used in most high schools.
Then for calculus, I recommend Anton's Calculus Early Transcendentals. You may opt to skip chapter 0 if you do all of Cohen. If you still remember things like the quadratic formula, how to factor, distribute, etc., then you can skip Cohen and read the trigonometry review in Anton.
I came to this board looking for the same answer to the exact same question. I'm dropping out of comm to follow my hopeless dream of taking physics! Need to rebuild a solid math foundation to have any hope in hell at getting through four years of calculus and physics classes. I'll take your recommendations. Thanks a lot.
I recommended a few going from basic math to vector calculus (namely, Cohen/Sullivan and Anton). For linear algebra, you can go with Leon (which I've used and found boring, but it gets the job done) or Lay (which I've never used but heard other people say good things about).
One of my friends is a graphics researcher who self-studied from Leon, so it will definitely prepare you even if it's not the most fun book in the world.
I don't know of a single book but if you have a university nearby there is likely some kind of non-university bookstore which does buyback. You can probably find old editions of textbooks to guide you along the way. Pre-algebra and college algebra should be good enough. I'm assuming the college algebra book will include trigonometry, if not then make sure you get a trig book. You can probably skip geometry if you are familiar with areas and volumes of common figures. |
The dialect of mathematics employed at this site is a subset of the Haskell
programming language. Beginning problems require direct translations of
algebraic expressions into Haskell. More advanced problems require the use
of higher order functions and infinite sequences.
Haskell is not a popular language. We chose it because of its similarity
to the language of mathematics--not because we want to train programmers.
Proficiency in the language of mathematics requires learning to think in
terms of increasingly abstract functions and hence the title of our site.
Our belief is that most people have trouble with math because they
study individual problems and don't understand the underlying theory. Without
the theory, each problem must stand alone in their minds and so when they see a
slightly disquised version of a problem they are clueless. Understanding
the underlying theory is impossible unless one is fluent in the language
used to explain that theory.
As
with any language, one doesn't become fluent in the language of mathematics
by learning a few words and memorizing a bit of grammar. One must practice
speaking it. Function Fluency provides that kind of practice and does so
with graduated difficulty.
Although training programmers is not our goal, these exercises can provide a
good grounding for the beginning programmer who will later be dealing
with complex algorithms.
The ability to understand mathematics is related to the ability to speak
the language of mathematics.
This site enables you to work
towards fluency by providing feedback when you "speak" in a dialect
of mathematics to our web server.
Click on
on the `about` button
for more information or to contact the developers.
Click on
the `sign up` button if you would to save your work so you can come back to it later.
This site is under development and may be shut down
for improvements on Saturday mornings. Check back every month for new
problems.
These elementary problems require you to translate algebraic expressions
into Haskell.
Algebraic expressions are only useful when values are plugged into them.
If we are to make many of them work together we need to be able to talk
about how values are plugged into them. The concept of a function can
be viewed as a way to do this.
These problems involve composition of functions, that is putting
functions together so that the result of one function is passed
to another function.
In Haskell, new functions can be built this with with a "dot"
operator. For example, f.g can be that function which evaluates
f (g x) for any suitable x.
Numbers seldom exist in isolation. Sequences of them are basic to
mathematics. Calculus, for example, wouldn't exist without such
sequences.
In Haskell sequences of numbers are called lists. You can experiment with
them here. Also you can practice writing functions which apply themselves
to each element of a sequence. Functions which can apply themselve to
achieve repetition are called recursive.
You have seen how Haskell can choose which one of many definitions of a function
f to apply. In this section you will look at a general way to choose what to
calculate next within one definition.
A major Haskell construct for branching is if...then...else.... The
concept is
rather simple but the
choices that can be made can be rather complex because they depend on
something called boolean algebra.
Boolean algebra is an algebra not of
numbers but of the values True and False.
These problems ask you to write recursive functions. Recursive functions
are functions that appear in their own definition.
This category of problems is conceptually more difficult than the others.
We intend to create additional problems to bridge the difficulty gap. Check
back every month or so to see what we've added.
Metafunctions (sometimes called higher-level functions) are functions whose parameters or return values are also
functions.
In these
problems you are asked to define or use such functions. |
Mathematics at St. Olaf
Practical - Popular - Visible - Active - Useful - Fun
Mathematics is all of those things--and more--at St. Olaf, where the mathematics program is recognized nationally for innovative and effective teaching. Our program was cited as an example of a successful undergraduate mathematics program by the Mathematical Association of America (Models That Work, Case Studies in Effective undergraduate Mathematics Programs) and St. Olaf ranks sixth in the nation as a producer of students who went on to complete Ph.D.'s in the mathematical sciences (Report on Undergraduate Origins of Recent [1991-95] Science and Engineering Doctorate Recipients).
One department, three programs
The St. Olaf Department of Mathematics, Statistics, and Computer Science houses three programs, described briefly below. Click the links for further information and details.
This concentration enables students to pursue statistics either as a primary interest or as a supplement to some other major. The statistics concentration - including course work in both theoretical and applied statistics - may be attached to any major. Typically, about 12-15 students complete a statistics concentration each year.
A computer science major was begun recently; the first graduates completed the program in 2005. (A computer science concentration was offered for many years previously.)
Areas of emphasis
Mathematics students choose various areas of emphasis:
Preparation for Graduate School Advanced courses provide breadth and depth for students intending to pursue graduate degrees in the mathematical sciences. Seminars and independent study provide opportunities for research-like experiences.
Applied Mathematics Courses offered in applied mathematics include statistics, computer science, differential equations, and optimization. The Mathematics Practicum has student teams working to solve real problems in industry and business.
Secondary School Teaching Students planning to teach secondary school mathematics complete a standard mathematics major (with certain courses prescribed by state certification requirements). In addition, they take several courses in the Department of Education and devote part of one senior semester to student teaching. In recent years, St. Olaf has averaged 10-12 students each year who receive certification in teaching high school mathematics. |
Microsoft Mathematics is easy to use software to solve math equation from basic math, algebra, trigonometry, calculus (differential and integral) and more. This software also provides graphing capabilities in Cartesian, parametric and polar and more. This is a great tool for student and teacher. Since Microsoft mathematics version 4.0 this software released as freeware.
The best from Microsoft mathematics, this provides step-by-step instructions the math equation problem solving and explains fundamental concepts. Microsoft Mathematics is standalone software but also can be integrated with Microsoft word using add-ins. |
Algebra and Trigonometry, CourseSmart eTextbook, 4th Edition
Description
Beecher, Penna, and Bittinger's Algebra and Trigonometry is known for enabling students to "see the math" through its focus on visualization and early introduction to functions. With the Fourth Edition, the authors continue to innovate by incorporating more ongoing review to help students develop their understanding and study effectively.
Mid-chapter Mixed Review exercise sets have been added to give students practice in synthesizing the concepts, and new Study Guide summaries provide built-in tools to help them prepare for tests. MyMathLab has been expanded so that the online content is even more integrated with the text's approach, with the addition of Vocabulary, Synthesis, and Mid-chapter Mixed Review exercises from the text, as well as example-based videos created by the authors.
Table of Contents
R. Basic Concepts of Algebra
R.1 The Real-Number Systemeal Numbers
R.2 Integer Exponents, Scientific Notation, and Order of Operations
R.3 Addition, Subtraction, and Multiplication of Polynomials
R.4 Factoring Terms with Common Factors
R.5 The Basics of Equation Solving
R.6 Rational Expressions
R.7 Radical Notation and Rational Exponents
Study Guide
Review Exercises
Chapter Test
¿
1. Graphs; Linear Functions and Models
1.1 Introduction to Graphing
Visualizing the Graph
1.2 Functions and Graphs
1.3 Linear Functions, Slope, and Applications
Visualizing the Graph
Mid-Chapter Mixed Review
1.4 Equations of Lines and Modeling
1.5 Linear Equations, Functions, Zeros, and Applications
1.6 Solving Linear Inequalities
Study Guide
Review Exercises
Chapter Test
¿
2. More on Functions
2.1 Increasing, Decreasing, and Piecewise Functions; Applications
2.2 The Algebra of Functions
2.3 The Composition of Functions
Mid-Chapter Mixed Review
2.4 Symmetry and Transformations
Visualizing the Graph
2.5 Variation and Applications
Study Guide
Review Exercises
Chapter Test
¿
3. Quadratic Functions and Equations; Inequalities
3.1 The Complex Numbers
3.2 Quadratic Equations, Functions, Zeros, and Models
3.3 Analyzing Graphs of Quadratic Functions
Visualizing the Graph
Mid-Chapter Mixed Review
3.4 Solving Rational Equations and Radical Equations
3.5 Solving Linear Inequalities
Study Guide
Review Exercises
Chapter Test
¿
4. Polynomial and Rational Functions
4.1 Polynomial Functions and Modeling
4.2 Graphing Polynomial Functions
Visualizing the Graph
4.3 Polynomial Division; The Remainder and Factor Theorems
Mid-Chapter Mixed Review
4.4 Theorems about Zeros of Polynomial Functions
4.5 Rational Functions
Visualizing the Graph
4.6 Polynomial and Rational Inequalities
Study Guide
Review Exercises
Chapter Test
¿
5. Exponential and Logarithmic Functions
5.1 Inverse Functions
5.2 Exponential Functions and Graphs
5.3 Logarithmic Functions and Graphs
Mid-Chapter Mixed Review
5.4 Properties of Logarithmic Functions
5.5 Solving Exponential Equations and Logarithmic Equations
5.6 Applications and Models: Growth and Decay; Compound Interest
Study Guide
Review Exercises
Chapter Test
¿
6. The Trigonometric Functions
6.1 Trigonometric Functions of Acute Angles
6.2 Applications of Right Triangles
6.3 Trigonometric Functions of Any Angle
¿ Mid-Chapter Mixed Review
6.4 Radians, Arc Length, and Angular Speed
6.5 Circular Functions: Graphs and Properties
6.6 Graphs of Transformed Sine and Cosine Functions
Visualizing the Graph
Study Guide
Review Exercises
Chapter Test
¿
7. Trigonometric Identities, Inverse Functions, and Equations
7.1 Identities: Pythagorean and Sum and Difference
7.2 Identities: Cofunction, Double-Angle, and Half-Angle
7.3 Proving Trigonometric Identities
Mid-Chapter Mixed Review
7.4 Inverses of the Trigonometric Functions
7.5 Solving Trigonometric Equations
Visualizing the Graph
Study Guide
Review Exercises
Chapter Test
¿
8. Applications of Trigonometry
8.1 The Law of Sines
8.2 The Law of Cosines
8.3 Complex Numbers: Trigonometric Form
Mid-Chapter Mixed Review
8.4 Polar Coordinates and Graphs
Visualizing the Graph
8.5 Vectors and Applications
8.6 Vector Operations
Study Guide
Review Exercises
Chapter Test
¿
9. Systems of Equations and Matrices
9.1 Systems of Equations in Two Variables
Visualizing the Graph
9.2 Systems of Equations in Three Variables
9.3 Matrices and Systems of Equations
9.4 Matrix Operations
9.5 Inverses of Matrices
9.6 Determinants and Cramer's Rule
9.7 Systems of Inequalities and Linear Programming
9.8 Partial Fractions
Study Guide
Review Exercises
Chapter Test
¿
10. Analytic Geometry Topics
10.1 The Parabola
10.2 The Circle and the Ellipse
10.3 The Hyperbola
10.4 Nonlinear Systems of Equations and Inequalities
Visualizing the Graph
Mid-Chapter Mixed Review
10.5 Rotation of Axes
10.6 Polar Equations of Conics
10.7 Parametric Equations
Study Guide
Review Exercises
Chapter Test
¿
11. Sequences, Series, and Combinatorics
11.1 Sequences and Series
11.2 Arithmetic Sequences and Series
11.3 geometric Sequences and Series
Visualizing the Graph
11.4 Mathematical Induction
Mid-Chapter Mixed Review
11.5 Combinatorics: Permutations
11.6 Combinatorics: Combinations
11.7 The Binomial Theorem
11.8 Probability
Study Guide
Review Exercises
Chapter Test
¿
Photo Credits
Answers
Index
Index of Applications |
Students are asked to predict what an absolute value graph will look like with given parameters. Then they can use a graphing utility that is on the same page to test their predictions. Feedback is g... More: lessons, discussions, ratings, reviews,...
An interactive applet and associated web page that demonstrate the area of an ellipse.
The major and minor axes can be dragged and the area is continuously recalculated.
The ellipse has a g... More: lessons, discussions, ratings, reviews,...
Students learn about fractions between 0 and 1 by repeatedly deleting portions of a line segment, also learning about properties of fractal objects. Parameter: fraction of the segment to be deletedThis applet does symbolic calculation of complex numbers. This means that you can enter integers and fractions for the component values of a complex number (real and imaginary). Values with numbers th... More: lessons, discussions, ratings, reviews,...
This activity allows the user to manipulate the graphs of the conic sections by changing the constants in their respective equations. The equation and variable values are displayed and change as the u... More: lessons, discussions, ratings, reviews,...
With this applet, students study the extrema of the function A cos^2 (t) + B cos(t) + C. A parabola is drawn with student-supplied coefficients and constant, and the unit circle is drawn below, so th... More: lessons, discussions, ratings, reviews,...
The applet manipulates an apparatus that draws a parabola from its definition that the distance from a fixed point called the focus is equivalent to the distance from a fixed line called the directri... More: lessons, discussions, ratings, reviews,...
An interactive applet and associated web page that show the definition and properties of an ellipse.
The applet has a draggable point that shows that the sum of the distances to the foci is a co... More: lessons, discussions, ratings, reviews,...
An interactive applet and associated web page that show the major and minor axes of an ellipse.
The applet has an ellipse whose major and minor axis endpoints can be dragged. As they are dragge |
This book reminds students in junior, senior and graduate level courses in physics, chemistry and engineering of the math they may have forgotten (or learned imperfectly), which is needed to succeed in science courses.
Algebra is the language of modern mathematics. This course introduces students to that language through a study of groups, group actions, vector spaces, linear algebra, and the theory of fields. The recorded lectures are from the Harvard Faculty of Arts and Sciences course Mathematics 122, which was offered as an online course at the Extension School.
Just-In-Time Math is a concise review and summary of the mathematical principles needed by all engineering professionals. Topics covered include differential calculus, integral calculus, complex numbers, differential equations, engineering statistics, and partial derivatives. Numerous example engineering problems are included to show readers how to apply mathematical techniques to a wide range of engineering situations. This is the perfect mathematics refresher for engineering professionals who use such math-intensive techniques as digital signal processing.
Learn how to create a full-length, interactive math lesson with a glossary, equations, illustrative charts and graphs, and a section that tests your students on what they've learned. This course builds on the lessons in iBooks Author for Teachers: Fundamentals and shows teachers how to leverage their existing math material and present it in an engaging digital way. Author Mike Rankin shows you how to import text from Microsoft Word, format your pages, add images and hyperlinks, and even add a useful calculator widget so students can perform calculations right inside the lesson.
Would you be interested in learning how to directly solve even the difficult math questions (in just one step). Learn the handy tricks to verify (double-check) your answer so that you can avoid making those silly calculation errors (thus get that 100% score in your math test) In short, would you like to discover the fastest and easiest way to master maths (from basic to advanced level)?
Number puzzles, spatial/visual puzzles, cryptograms, Sudoku, Kokuro, logic puzzles, and word games like Frame Games are all a great way to teach math and problem-solving skills to elementary and middle school students. In these two new collections, puzzle master Terry Stickels provides puzzles and brain games that range from simple to challenging and are organized by grade level and National Council of Teachers of Mathematics (NCTM) content areas. Each book offers over 300 brain games that will help students learn core math concepts and develop critical thinking skills. The books include a wide range of puzzle types and cover a variety of math topics, from fractions and geometry to probability and algebra. |
If by algebra you mean pre-calculus algebra (vs abstract algebra) then I personally don't see the point of really separating arithmetic and algebra. The two have an enormous amount of overlap. – EuYuNov 26 '12 at 9:41
As much beauty as there is in mathematics, I don't know that I would say it, "is never a messy subject to study." – JeremyNov 26 '12 at 9:43
@EuYu Yeah, I agree with you. But this is an application designed for secondary school students (grade 7 to grade 10) and they are just starting to learning about rational number, prime number, ratio, etc so it would be better to separate arithmetic and algebra. – user38927Nov 26 '12 at 9:47
1 Answer
In lower level mathematics, I normally take algebra to mean the study of relationships between functions and equations, and arithmetic to mean the study of the operations, such as addition, subtraction, multiplication, division.
I guess the main question then becomes, do we lump exponentiation and logarithms into arithmetic, or say that it belongs under algebra? My personal view is that, if we really have to draw the line somewhere (of course, the distinctions are terribly arbitrary), then logarithms and exponents should belong under algebra. The primary reason for this is that we are typically not interested in actually calculating exponents and logarithms; I think of elementary school arithmetic as the set of skills that students need to calculate quantities throughout their lives. One cannot, for example, calculate $\log{5}$ or $e^{2}$, in their heads, except through very rough approximation. Usually, it is the properties of logarithms that we are interested in studying, because they allow us to solve certain equations or rewrite certain functions, just as you have mentioned, and I believe this squarely makes the study of logarithms part of secondary school algebra. |
Costs
Course Cost:
$299.00
Materials Cost:
None
Total Cost:
$299Students do best when they have an understanding of the conceptual underpinnings of calculus. This course stresses the dual concepts of conceptual understanding of calculus and fluency in the procedures that accompany those concepts. If students can grasp the reasons for an idea or theorem, they can usually figure out how to apply it to the problem at hand. We will study the following major ideas during the year: limits, derivatives, indefinite integrals, Taylor series, parametric functions, polar functions and vector-valued functions. Students practice the skills of calculus while they solve real-world problems with calculus concepts. |
This book and the accompanying CD-ROM address the problem of computing and visualizing the standard special functions. Although the most important formulas are presented, this book complements rather than replaces standard works like ``The Handbook of Mathematical Functions'' edited by Abramowitz and Stegun and nearly one third of the material in this book is pictorial. Programs for computing the functions are available on the CD-ROM both in Fortran 90 and Mathematica. The same book but with the programs in C instead of Fortran 90 has been reviewed in [1997, Zbl 0873.68100]. [G.Gripenberg (Helsinki)] |
The course content of 6th
grade math focuses on continuing the mastering of many skills started in
earlier grades and the introduction of many new concepts and skills. Skills,
concepts, topics covered in 6th grade math include: addition,
subtraction, multiplication, and division with whole numbers, fractions, and
decimals; estimating answers and mental solutions to problems; numeration to
the hundred-thousandths place; rounding off; prime and composite numbers;
geometry of quadrilaterals, triangles, circles and rectangular prisms with
respect to perimeter, circumference, area and volume; metric and customary
units of measurement; ratios and percents; probability; adding and
subtracting of integers, and the graphing of ordered pairs of numbers. Tests
at the end of each chapter are cumulative, covering all work from the
beginning of the sixth grade.
Sixth grade math classes
are heterogeneously grouped and do exactly the same work. However, based on
6th grade class grades, national standardized test results, and
teacher recommendations, students will be placed in a 7th grade
on level math class or in a 7th grade advanced class.
Activities consist of
laboratory experiments and classroom discussion. In the laboratory students
learn to work cooperatively, perform experiments, use laboratory equipment
properly and safely, and reason scientifically. Students are required to
submit a project each quarter.
General Math-8th Grade
This course covers
typical grade 8 topics required by the State Education Department. Grade 7
topics are reviewed and expanded. New topics include: the Pythagorean Rule,
the use of sine, cosine, and tangent, relations, functions, and graphing,
transformations and constructions. Special attention is placed on problem
solving. The course culminates in a Grade 8 State Math exam. |
Algebra 2 Team
Students continue their study of advanced concepts including functions, polynomials, rational expressions, systems of equations and inequalities, matrices and complex numbers. Emphasis is placed on practical applications and modeling. Topics in this course will enable you to become critical thinkers, increase your knowledge in the subject area and enhance your natural curiosity. You will be able to use the appropriate math language to communicate effectively. You will also learn how to work together collaboratively, and become a reflective and principled learner. The areas of interaction will allow you to make connections between math and real-life.
At the completion of this course, you should able to recognize patterns, understand, demonstrate and use appropriate mathematical concepts and skills to solve problems and apply them to real-life context.
The TI-graphing calculator is used on a regular basis in this course. Oftentimes it is needed to complete homework assignments. If you need to purchase one, please check with me so that I can recommend one that is user-friendly and can be used on tests.
Students continue their study of advanced concepts including functions, polynomials, rational expressions, systems of equations and inequalities, matrices and complex numbers. Emphasis is placed on practical applications and modeling. The TI-graphing calculator is used on a regular basis in this course. Oftentimes it is needed to complete homework assignments. If you need to purchase one, please consider checking with me so that I can recommend one that is user-friendly and can be used on tests. |
Probability Textbooks
Probability textbooks explore the chance of an event occurring by using mathematics. In addition to exploring core concepts such as probability distribution and probability and statistics, probability textbooks also have subcategories of more specific subjects such as probability theory. A probability textbook could also focus on practical applications of probability math, such as risk assessment. Probability textbooks often include probability examples to help students learn how to calculate probability and memorize different probability formulas. Textbooks.com offers a wide variety of new and used textbooks so you can find the probability |
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Abstract
We investigated how students interpret linear and quadratic graphs on a graphics calculator screen. Clinical interviews were conducted with 25 Grade 10–11 students as they used graphics calculators to study graphs of straight lines and parabolas. Student errors were attributable to four main causes: a tendency to accept the graphic image uncritically, without attempting to relate it to other symbolic or numerical information; a poor understanding of the concept of scale; an inadequate grasp of accuracy and approximation; and a limited grasp of the processes used by the calculator to display graphs. Implications for teaching are discussed |
Although the classroom is not the heart and soul of The World of Math, it is a stalwart and
trustworthy guide through much of the principles used on examinations and competitions.
It is a repository of knowledge, and, although it is not meant as a replacement for four
years of high school math it can prove useful to consult in times of need.
The fundamental building block of all that is to come. Through the arithmetic and problem solving skills built in the following lessons, we will eventually construct feats of awesome complexity. But first we have to start small. Although these few lessons should already be familiar to the vast majority of you, their importance cannot be overstated. Careful study now we reap great rewards later on.
Hopefully, if you're reading this you have a basic understanding of the foundation of algebra. You understand the four most basic operations of arithmetic: addition, subtraction, multiplication, and division. You should know most of the basic properties of these operations. You should understand about variable substitution and how to solve for a variable in basic equalities. If all of the above made sense, prepare yourself for an overview of more advanced algebra topics. The following lessons are designed to impart a greater understanding of the principles of algebra, and to increase the depth and experience of students.
Geometry cannot truly be taught via the Internet. However well written the following lessons may be, they will not impart the understanding of geometric concepts that can only come with careful experimentation. The compass is a very important part of geometry; if you do not own one, you should consider buying or borrowing this surprisingly useful mathematical tool. Hopefully, your geometry teachers will be able to show you how to use a compass and how it relates to the theorems discussed in your classes. This review of geometry cannot be more than a review. It can aid your understanding or remind you of theorems that you have forgotten but it will not teach you geometry by itself. Its purpose is to impart the most basic levels of geometry to you and to immerse students in the proper terminology and mindset for more advanced studies.
By now, you should have an understanding of the fundamental principles that compose algebra. In this unit, we will build upon those principles to review the more complex aspects of high school math. Although it is impossible to learn advanced algebra from a web page alone, we hope that this abstract will prove a useful summary for the algebra student. |
Find an Annandale, VA MathKnowledge of numbers is extended to include not only integers and rational numbers, but irrational, real, transcendental and complex numbers and operations involving them. Knowledge of functions is extended to include solving linear functions using matrices; exploring not only quadratic function... |
Book Description: Provides the user with a step-by-step introduction to Fortran 77, BLAS, LINPACK, and MATLAB. It is a reference that spans several levels of practical matrix computations with a strong emphasis on examples and 'hands on' experience. |
Book Description: The premiere text for the emerging Quantitative Reasoning/Quantitative Literacy Course offers an innovative approach for Liberal Arts/Survey Math. It provides a legitimate alternative to algebra and math appreciation courses for non-quantitative majors, helping to reduce math anxiety, emphasizing practicality, and focusing on the use of mathematics in college, career and life. |
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This mini-unit involves the learning of quadratic functions. Students will work on an egg launch activity.Title: 5 Day Mini-Unit-QuadraticsAuthor: Jennifer CrawfordSubject area: Algebra ITopic:…Continue
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This mini-unit involves the learning of quadratic functions. Students will work on an egg launch activity.Title: 5 Day Mini-Unit-QuadraticsAuthor: Jennifer CrawfordSubject area: Algebra ITopic: Quadratic FunctionsMMC:A2.6.1A2.6.2A2.1.3 See More
"I plan to use many of the activities from the modules in the upcoming school year. I plan to start the year off with the shapes of algebra activity so that students see there are different functions and that they can be represented in…"
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I really haven't had any exposure to the TI-84 graphing calculators and wanted to have some training. I was hoping to get some training through this class too, although the calculator tutorials have been helpful. I…"
"I am excited to begin the school year so I can incorporate all that I have learned through the AfA online class. One thing I will be doing is having the students work in groups. I'm hoping this will increase the communication among…"
"I started reading this book earlier this year, but just wasn't able to finish due to time! I have it on my summer reading list- my principal said it's wonderful! I saw you are presenting in July. If there is anything you…"
"I'm excited to use this mini unit in the upcoming school year. At the moment I do not have a smart board or document camera so I may need to revamp these areas, but this is definitely a great resource for me to use. I think the…"
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examine common algebra-related misconceptions and errors of middle school students. In recent years, success in Algebra I is often considered the mathematics gateway to graduation from high school and success |
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Short description With a focus on one central theme (the Impossibility Theorem) throughout, this highly accessible introduction to Galois theory presents a classical treatment of the topic and poses questions related to the solvability of polynomial equations by radicals. Modern points of view are also discussed in contrast to the historical development and context. With exercises for each chapter, as well as useful appendices, this guide is ideal for anyone wanting a deeper appreciation of the origins of Galois theory, its fundamental concepts, and applications. |
DescriptionWFMath is a math library that focus on geometric objects. Thus, it includes several shapes (boxes, balls, lines), in addition to the basic math objects that are used to build these shapes (points, vectors, and matrices).
Math Objects is a math template library written in C++ using generic programming techniques. In order to use the "Math Objects" library, the user only has to include the header files he needs (e.g. Matrix.h, Polynomial.h etc.). |
An Arithmetic for Upper Grades, while intended chiefly
for pupils of the last two years of the elementary school,
has been arranged to include the work of the sixth grade.
The seventh year portion comprises a simple, but system-
atic, treatment of commercial arithmetic, including per-
centage with its several applications, and" elementary
exercises involving the employment of common business
forms. This is preceded by reviews of fractions and deci-
mals, and is followed by miscellaneous problems, oral and
written.
The eighth year section contains the remaining topics
of the ordinary course, prefaced by a review of compound
denominate numbers and simple measurements. The mis-
cellaneous problems that immediately follow are limited
to the subjects treated in this portion, so as to be available
for use in such schools as teach the seventh and eighth
grades in combined classes alternating the work of each
year.
A scientific treatment of numbers and processes is next
presented, which may be taken up at any stage. The mis-
cellaneous reviews that follow cover all the ground previ-
ously studied.
In many schools whose courses of study require an ad-
vanced text-book in the sixth year, it is customary to begin
the arithmetic work of this grade with the development of
formal definitions, principles, rules, etc. In this case, the
section on numbers and processes should first be taken up,
then the fraction and decimal reviews; followed by the
reviews of compound numbers and measurements.
Areas of Plane Surfaces ; Area of a Polygon ; Area of a
Regular Hexagon ; United States Public Lands ; Circum-
ference and Area of a Circle ; Prisms ; Cylinders ; Pyramids
and Cones ; The Sphere ; Miscellaneous Problems.
1. As a preliminary to the regular percentage work of
the seventh year, it will often be found profitable to give a
short time to the review of fractions, common and decimal.
At intervals throughout the year, a few minutes of an arith-
metic period should be spent in rapid oral reviews, employ-
ing the drills and the sight exercises of this chapter.
Drill Exercises.
Note. The fractions in the answers should be given in their low-
est terms.
2. Add:
1.
l
3
2.
2.
5
3.
4
9
4.
2
5
5.
2
9
6.
4
9
1
3
1
1
9
2
2
9
4
9
7.
2
3
8.
3
5
9.
5
9
10.
1
3
11.
4
5
12.
8
9
1
3
5"
4
9
2
3
•
3
5
5
9
3.
31
14.
41
15.
U 9
16.
H
17.
61
18.
8±
°9
1
• "3
1
5
1
9
1
2
9
4
9
.9.
°3
20.
6f
21.
QA
J 9
22.
6^
u 3
23.
64
5
24.
13|
1
3
2
~5
4
9
2
3
3
5
3
9
2 . - Arithmetic
Add:
'
25.
4!
^3
26.
H
27.
^9
28.
H
29.
8^-
°9
30.
U 9
^3
H
2*
H
n
94
J 9
31.
42
^3
32.
n
33.
»f
34.
^3
35.
n
36.
2*
3 1
^3
H
41
* 9
8f
64
3f
37.
1
4
38.
H
39.
5
8
40.
5 T V
41.
3
8
42.
^4
°9
1
4
1
6
^1
^8
9- 1 -
^12
3
8
2
9
43.
3
1
44.
^12
45.
7
8
46.
Q8
°9
47.
7
1
48.
^T2
°1
Q 5
°T2"
5
8
7
9
Q_9_
°l
71i
' 12
3. Subtract;
13
19
25.
•
4
5
JL
5
2.
7
9
5
9
3.
6f
2
5
4.
8^-
°9
4
9
5.
74
'"5
2!
6.
•
8
8.
6
9.
7
10.
4
11.
6
12.
8
1
1
2
5
5
9
Q2
^3
5*
7^-
1 9
.
8
14.
6
15.
7
16.
9
17.
'6
18.
8
H
H
1^
Q2
H
95
~9
H
20.
H
21.
71
4 9
22.
91
,; 3
23.
6*
24.
8^
°9
if
H
1^
3|
4f
Z 9
.
5
6
26.
7
8
27.
7
9
28.
ItV
29.
9|
30.
8^-
°9
1
6
5
8
4
9
5
1 2
1
8
2
9
4.
Multiply
:
•
l.
ix
2
2.
3x
1
4
3.
iof
4
4.
5
x*
5.
*X
9
6.
17 x
1
8
7.
iof 23
8.
31
x tV
9.
|x
2
10.
3x
2
7
11.
f of
5
12.
7xf
Review of Fractions
Multiply :
13.
H
14. 51
15.
n
16.
9 1
17. 84
2
3
4
5
6
18.
92
2
19. 5f
3
20.
7^
' 8
5
21.
Q2
8
22. 91
7
23.
i°f
2
24.
3
x«
25.
i
8
X 4
26.
6xi
27.
iof
4
28.
6
xi
29.
i
8
Xl6
30.
27xi
31.
lof
6
32.
9
xi
33.
l
8
x20
34.
33 x i
35.
fof
2
36.
3
x|
37.
•5
6
x 3
38.
7x1
39.
f of 15
40.
24
x|
41.
5
8
xl2
42.
3xi
43.
2
44. 51
4
45.
61
u 8
2
46. 7f
3
47- 8,A
6
48.
6
49. 8J
9
50.
Q2
3
51. 4|
4
52. 6|
5
5.
Divide :
l.
2)4 fifths
2.
3)6
sevenths
3
. 4)8 ninths
Note. In dividing i by 2, the pupil may think 2 into 4 fifths, or
i of 4 fifths, or 4 fifths divided by 2. These and the following ex-
amples are placed in the short-division form to lead pupils to refrain,
at times, in written work from changing the mixed number in the
dividend to an improper fraction when the divisor is a whole number.
4.
<)ii
5.
W
6.
m
7.
6)ff
8.
2)44
9.
3)6f
10.
■±M
11.
5)5}
12.
2 )A
13.
31i
14.
4 )i
15.
%
16.
2)12i
17.
3)91
18.
4)161
19.
5)151
Arithmetic
Divide :
20. 6 )181
24. 5)|
28. 4)2j
32. 2)191
36. 2)j
40. 2 )171
44. 6 )431
21. 7 )211
25. 5)21
29. 5)3f
33. 4 )26f
37. 2)11
41. 3 )161
45. 7 )4Qi
22. 8)401
26.
2)1
30.
'6)3*
34.
5)28|
38.
31i
42.
4)191
46.
8)411
23. 9 )631
27. 2)11
31. 7)4j
35. 6 )33f
39. 3)11
43. 5)42|
47. 9 )461
6. Preliminary Exercises.
1. How many baseballs at $ i each can be purchased
for$i? For$l? For $11?
2. 1)1 3. 1)1 4. 1)11 5. 1)2
7. 1)8 8. 1)20 9. 1)6 10. 1)12
How is the quotient obtained in each case ?
12. f)i 13. 11)11 14. f)| 15. 11)3 16. 1#6
Multiply the divisor and the dividend in each of the five preceding
examples by 2 :
6- i]2J
11. 1)12
17. 3)3 18. 3)3 19. 3)6 20. 3)6
How do the quotients compare in each case ?
21.
)12
7. 1. Divide 12 by If
Proof.
1|)12
x2 x2
3 ^24
8 Ans.
l|x 8 = 12.
2. Divide 21 by f.
Proof.
f)21
x4 x4
28
3)84
28 Ans
x | = 21.
Review of Fractions 5
Note. In mental work it is often convenient to change a fractional
divisor to a whole number by multiplying the divisor by the denomi-
nator of the fraction, the dividend being multiplied by the same num-
ber. Divide the new dividend by the new divisor.
8. Drill Exercises,
Divide :
1. 11)9
6. 21)15
11.
2. 11)15
7. 31)21
12.
3. 11)18
8. 21)27
13.
4. 11)15
9. 31)26
14.
5. 11)20
10. 1|)15
15.
f)12 16. li]7J 21. J)2i
f]12 17. H)8| 22. |)2£
4)12 18. 11)9! 23. |)4J
f)10 19. 1£7J 24. f)5f
|)14 20. 1 1)16| 25. f)6*
9. Oral Problems.
1. A farmer sold 151 cords of wood in January and 10^
cords in February. How many cords did he sell in all ?
2. From a piece of cloth containing 30 yards, 121 yards
are sold. How many yards remain ?
3. A rectangular field is 121 rods long and 1\ rods wide.
How many rods of fence will be needed to inclose it ?
4. How many i-pound packages will 24J pounds of
candv make ?
5. A traveler w r alked 60J miles in 3 days. How many
miles a day did he average ?
6. How many square rods are there in a field 20^ rods
long and 10 rods wide ?
7. Mr. Yates pays % 171 for carpet and $ 201 for furni-
ture. What is the amount of his bill ?
8. How many minutes are there in 1 of a day ?
9. At 60 pounds per bushel, what will J bushel weigh ?
10. How many yards of cloth at $ 11 per yard can be
bought for $12?
6 Arithmetic
10. Written Problems.
1. A boy sold. 16| dozen eggs at one time and 20f dozen
at another time. How many eggs did he sell ?
2. Fin'd the sum of four numbers, two of which are 15 T 4 -
and 19 T 7 5, respectively, the third being equal to the sum of
these two, and the fourth being equal to their difference.
3. Two trains start from the same point and move in
opposite directions, each at the rate of 32i miles per hour.
How far apart are they in 4 hours ? .
4. What is the total weight of 16 barrels of sugar,
averaging 310 J pounds each ?
5. A crop of wheat averaged 121 bushels per acre.
How many acres were required to produce 500 bushels ?
6. How many square rods are there in a rectangular field
160 J- rods by 84 rods ?
7. A train starting at 10.45 a.m. reaches a town 140
miles distant at 2.15 p.m. How many miles per hour does
it average ?
8. If 3 eighths of a number is 147, what is 1 eighth of
the number ? What is the number ?
9. A rectangular lot is 120 feet long. Its width is T 9 7
of its length. How many running feet of fence will be
required to inclose it ? (Make a diagram.)
10. How many gallons are there in 1J barrels of 31^ gal-
lons each ?
11. Sight Exercises.
Note. To accustom the pupils to avoid unnecessary figures, fre-
quent drills in sight and blackboard exercises are important. Pupils
should give orally the answers to the following examples, or should
promptly write the answer to each at a signal, the pupil being ex-
pected to know the answer before beginning to write.
Review of Fractions 7
Add
1. 241 4. 172 7 . 48 5
Q3 Kl Ql
°¥ °4 ^3
2. 42f 5. 8 J- 8. 84|f
8i 36f 9i
3. 931 6. 3f 9. 46f
7| 91* 71
12. Blackboard Exercises.
Note. Pupils are expected to write only the answers to the follow-
ing examples, but time should be allowed them to write the total of
each column as they obtain it. These exercises are designed to show
pupils that it is not always necessary to rewrite the fractions with a
common denominator.
Add :
1. 241 4. 401 7. 471
6} 281 7|
59\ 51 59^
8. 461
81
39 1
2. 47|
5.
48^
181
321
H
7|
3. 841
6.
9Q1
10|
4of
°T<T
.
»i
13. Sight Exercises.
Subtract :
1. 18}
3.
721
H
21
w 6
2. 541
4.
9T1
^' 2
H
6f
401
_ii
801
71
4 3
8
Arithmetic
Subtract :
7.
36i
8.
62 T V
8*
9.
931.
10i
14. Blackboard Exercises,
Subtract :
1. 841
4.
401
7.
631
29£
16#
27|
2. 90 T V
5.
60f
8.
52 T V
261
23|
341
3. 78^
6.
45- 7 -
^1
9.
93|
39f
18f
471
15. Sight Exercises.
Multiply :
i. m
4.
16
7.
101
8
41
12
2. 20|
5.
24 *
8.
12f
9
_?i
7
3. 21f
6.
48
9.
40f
4
«
Ji
_9^
16. Blackboard Exercises.
Multiply :
1. 1241
4.
304£
7.
251^
7
5.
12
8.
10
2. 320f
423f
9<>9 3
8
6.
2
9.
13
3. 621f
516f
2011
5
5
14
Review of Fractions 9
17. Sight Exercises.
Divide :
1. 2 )261 4. 7 )781 7. 6 )67j
2. 3 )39| 5. 8 )17f 8. 5 )51$
3. 4 )36f 6. 9)36-^ 9. 4 )27f
18. Blackboard Exercises.
Divide :
1. 2 )2461 4. 5 )8491 7. 8)6491
2. 3)4591 5. 6 )2731 8. 9 )833|
3. 4 )7231 6. 7 )723f 9. 1 0)537f
19. Written Exercises.
Note. Determine the common denominator by inspection.
Find results :
1. 8i + 7L-fl3f + 42f 3. 28f + 45i + 83| + 96i
2. 26J + 30f + 471 + 56| 4. 351 + 56^ + 971 + 4811
5. 19if + 12| + 24|| + 87|
6. 910f-316 T i- 9. 862|-258f
7. 862|-258| 10. 683^-42311
8. 200-V - 103 T V 11. 7091-357^
To multiply two mixed numbers, reduce them to improper
fractions, multiply the numerators together and the denomina-
tors together, and reduce the resulting fraction, if possible.
In each of these examples the price per yard is obtained by dividing
the total cost by the number of yards: 24^ -r- 2, 30 p -*■ 2^, 6^-e-^,
9?-=-f.
21. Oral Problems.
Note. In solving each of the following problems, the pupils should
first state whether it is an example in multiplication or in division.
They may easily determine this by mentally substituting a whole
number for the traction.
1. A 24-acre field is divided into plots of § acre each.
How many plots are there ?
2. At $J per bushel, find the cost of 56 bushels of
wheat.
3. How many cords of wood in 32 piles containing J
cord each?
Review — Type Problems n
4. If a train goes f mile in a minute, how many minutes
will it take to go 60 miles?
5. A dealer's profit is \ of the cost. What is the cost,
if his profit is $24?
6. How many f-pound packages can be filled from a
36-pound box of tea ?
7. A drover sells § of his herd of 120 cattle. How
many does he sell ?
8. Nine tenths of the pupils of a certain class are pres-
ent. There are 27 present. How many pupils belong to
the class ?
9. If a man can do two fifths of a piece of work in a
day, how long will it take him to do the whole work ?
Number of days = 1 work -f- f work = \ work -f- f work = 5 -f- 2.
10. How long will it take a pipe discharging f gallon per
second to empty a tank containing 60 gallons ?
22. Written Problems.
Note. Before solving the following problems, the required opera-
tion should be indicated in each case by the use of the proper sign.
1. Into how many building sites of f acre each can a
farm of 192 acres be divided ?
Number of sites = 192 A. -=- 1 A.
2. Find the cost of 784 bushels of wheat at $ }f per
bushel.
Cost = $ i| x 784.
3. How many loads, each containing -J cord, are there in
336 cords of wood ?
4. What time will it take a train to go 195 miles at the
rate of f mile a minute ?
5. At 95^ per bushel, how many bushels of wheat can
be bought for $ 142.50 ?
12 Arithmetic
6. How many bushels of wheat at $ i| per bushel can
be bought for $ 1421 ?
7. If it takes J yard of material to make an apron, how
many yards will be required to make 144 aprons ?
8. How many vests can be made from 144 yards of
cloth, if J yard is needed for each ?
9. If three men working together can do ^ + 2*5 + ^V
of a piece of work in a day, how long will they require to
do the whole work ?
10. Find the cost of if acre of land at $ 256 per acre.
11. If a horse eats § bale of hay in a week, how long
will a bale last ? 32 bales ?
12. A farmer sold his farm for f of its cost, which was
14800. What did he receive for it ?
13. A can do J as much work in a day as B. How many
days would he require to do a piece of work that B could
finish in 105 days ?
14. A and B together can do ^- as much work as B alone.
How many days would both working together require to do
a piece of work which B can do in 105 days ?
15. A dealer's profits average ^^ of the cost of the goods
sold. How much does he gain on goods costing $ 275 ?
16. If the weight of roasted coffee is JJ of the weight of
unroasted coffee, how many pounds of the latter will be re-
quired to make 221 pounds of roasted coffee ?
Suggestion. In this problem and in the remaining four, the pupil
may use x as follows : |
Mathematics in Action empowers students to develop mathematical literacy in the real world and is a solid foundation for future study in mathematics and other disciplines. This first book, of a two book series, supports the need for mathematics through real life applications that are relevant to students. It is filled with real world situations in which the crucial need for mathematics arises. |
Prealgebra and Introductory Prealgebra (Basic Math with very early Algebra) and Introductory Algebra (or Beginning Algebra). This engaging prepa... MOREration My Math Lab. Elayn Martin-Gay believes "every" student can succeed and that is the motivating force behind her best-selling texts and acclaimed video program. With Martin-Gay you get 100% consistency in voice from text to video! "Prealgebra and Introductory Algebra 2e "is appropriate for a 2-sem sequence of Prealgebra (Basic Math with very early introduction to algebra) and Introductory Algebra (aka Elementary Algebra). This text was written to help students effectively make the transition from arithmetic to algebra and provide a strong foundation for success in their next, intermediate algebra course. To reach this goal, Martin-Gay introduces algebraic concepts early and repeats them as she treats traditional arithmetic topics, and then further develops their exposure to elementary-level algebra topics." "The material from this text is also available split out into two separate textbooks, "Prealgebra 5e" and "Introductory Algebra 3e, "if you prefer to use split textbooks, rather than one combined textbook for your 2-sem sequence.
Whole Numbers and Introduction to Algebra Tips for Success in Mathematics |
MAED 5030: GEOMETRY AND MEASUREMENTS
An investigative approach to the study of Euclidean, Non- Euclidean and transformation geometry that enriches students knowledge of the concepts, principles and process as it relates to the school curriculum. Students will make conjectures, test and verify properties of geometric figures in the physical world using such tools as the Geometer's Sketchpad. Proof as it relates to geometric concepts and principles will be constructed.... more »
Credits:3
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Thanks, enjoy the course! Come back and let us know how you like it by writing a review. |
This is the first of two courses designed to emphasize topics which are fundamental to the study of calculus. Emphasis is placed on equations and inequalities, functions (linear, polynomial, rational), systems of equations and inequalities, and parametric equations. Upon completion, students should be able to solve practical problems and use appropriate models for analysis and predictions.
This course has been approved to satisfy the Comprehensive Articulation Agreement general education core requirement in natural sciences/mathematics. |
These challenging books are designed for students with significant mathematical backgrounds, yet it can be appreciated by non-mathematicians; there are no maths formulae. As well as exploring the concepts of transformation and deformation, they introduce the idea of surfaces without thickness or boundary.
Waves, Diffusion and Variational Principles (MS324)
Variational Principles
Four books focus on three areas of applied mathematics. The first explores wave motion using vibrating strings and sound waves as examples. The second describes heat flow and the flow of particles which follow random walks. The third area introduces variational principles and calculus through simple problems.
In recent decades, mathematicians have increasingly employed computer- assisted algebra packages in their calculations. Maple is one of the more popular packages, used to expand functions as series, evaluate sums and integrals, solve differential equations and plot the results of calculations. Books and a CD-ROM introduce computer-assisted algebra techniques using Maple. |
The course will focus on the mathematical aspects of public-key
cryptography, the modern science of creating secret ciphers (codes), which
is largely based on number theory. Additional topics will be taken from
cryptanalysis (the science of breaking secret ciphers) and from
contributions that mathematics can make to data security and privacy.
4-dimensional geometry
Math 53 - Visualizing the Fourth Dimension(Fall).
This course investigates the idea of higher dimensions and some of the
ways of understanding them. The classic novel, Flatland, will serve
as the starting point, and through discussions, writing, projects and
interactive computer graphics, we will extrapolate ideas from two and
three dimensions to their analogues in four dimensions and higher.
Ancient Greek mathematicians invented the notion of abstraction (in
mathematics and other fields), absolute precision, and proof. The
approach to mathematics that we take today can be traced back to these
Greek mathematicians. After examining some pre-Greek mathematical
traditions, we study Greek mathematics, beginning with Thales and
Pythagoras. Topics include the intellectual crisis caused by the discovery
that not all magnitudes are commensurable; Plato and his academy; Euclid
and his Elements; the three special construction problems (trisecting an
angle, squaring a circle, doubling a cube); and the greatest of the Greek
mathematicians, Archimedes.
history of mathematics
Math 56 - History of Mathematics(Spring).
Traces the development of mathematical ideas and methods in literate
cultures from ancient Egypt and Mesopotamia, to Hellenistic Greece and
medieval China, India and the Islamic world, up through the dawn of
calculus at the start of the Scientific Revolution in early modern Europe.
philosophy, literature, linguistics, the humanities, psychology
Math 57 - Game Theory and its Applications in the Humanities and
Social Sciences(not offered 2012-13).
Completely self-contained introduction to the mathematical theory of
conflict, including parlor games, auctions, games from the Bible and games
commenting on the existence of superior beings, game-theoretic analyses in
literature, philosophical questions and paradoxes arising from game theory,
and game theoretic models of international conflict.
economics, management or
a course that will help prepare you for calculus
Differential and integral calculus with applications in the social
sciences. Not open to students who have passed a college calculus course;
students who wish to continue the calculus should enroll in Math 112.
Prerequisite: Math 58.
political science
Math 60 - Topics in Mathematical Political Science(Winter). (Same as Political Science 123)
A mathematical treatment (not involving calculus or statistics) of
political power, social choice, and international conflict. No previous
study of political science is necessary, but PS 111 or 112 would be
relevant.
public policy
Math 61 - Math in the Public Interest(not offered 2012-13).
Explores key mathematical topics including statistics, probability,
exponential and logarithmic functions, and visual/graphical representation
of numbers, in the context of contemporary public policy issues such as the
2008 financial crisis, gaming institutions, population demographics, and
climate change.
public policy
Math 64 - Statistical Thinking(Fall).
Seeks to provide the conceptual foundation and analytical skills required
to understand a complex, data-rich and uncertain (stochastic) world from a
stochastic versus deterministic perpective, and to navigate through the
daily bombardment of data from all sides. |
Discrete Mathematical Structures - 6th edition
Summary: Key Message: Discrete Mathematical Structures Sixth Edition offers a clear and concise presentation of the fundamental concepts of discrete mathematics. This introductory book contains more genuine computer science applications than any other text in the field and will be especially helpful for readers interested in computer science. This book is written at an appropriate level for a wide variety of readers and assumes a college algebra course as the only prerequisite. Key Topics: Fu...show morendamentals; Logic; Counting; Relations and Digraphs; Functions; Order Relations and Structures; Trees; Topics in Graph Theory; Semigroups and Groups; Languages and Finite-State Machines; Groups and Coding Market: For all readers interested in discrete mathematics |
High
school graduation requirements are becoming more and more challenging
for today's students. The real challenge for
schools is reaching those students who need to see the "real
world" relevance of the math before they can learn it and be
successful. Now into a brand new third edition, CORD's Algebra
1 : Learning In Context, Third Edition, remains the primary
tool for the contextual teaching approach. By combining new rigorous
math content and a hands-on approach through real-world applications,
you reach more students and more students succeed.
NEW!
Common Core Standard Supplements
-Makes All CORD textbooks Common Core compliant
- Available on-line and new book reprints!
• Workplace Applications, real-world examples,
labs and activities fit perfectly with the Common Core Standards mission
statement of: " The standards are designed to be robust and
relevant to the real world, reflecting the knowledge and skills that
our young people need for success in college and careers."
Report
Errata CORD Communications strives to produce
error-free materials. However, mistakes do happen. If you find errors
in the textbook, please click the link above. Tell us which book,
page number and problem number. Provide a brief description of the
error. We will look into the error and post any corrections needed
to the website. |
Gateways:
Mathematics
The Mathematics curriculum is traditional, although many of the best reform ideas (technology, group projects, writing mathematics, etc.) are being incorporated where appropriate to enhance the traditional topics.
The following list of courses represents current or recent course offerings. See the course catalog for updated information.
52-001 SELECTED TOPICS
May be repeated with change in topic.
52-002 SELECTED TOPICS
May be repeated with change in topic.
52-003 SELECTED TOPICS
May be repeated with change in topic.
52-004 SELECTED TOPICS
May be repeated with change in topic.
52-104 MATHEMATICAL CONCEPTS
An introduction to some of the important ideas in mathematics illustrating the scope and spirit of mathematics and emphasizing the role that mathematics plays in society from a historical point of view. Topics include number systems, algebra, geometry and measurement. This course is designed for tho...
52-114 INTRODUCTION TO STATISTICS
Designed to provide students in the social and biological sciences with the skills necessary to perform elementary statistical analysis. Descriptive measures, probability, sampling theory, random variables, binomial and normal distributions, estimation and hypothesis testing, analysis of variance, r...
52-124 ELEMENTARY FUNCTION THEORY
Relations, functions and general properties of functions. Some of the elementary functions considered are polynomials, rational functions, exponentials, logarithms and trigonometric functions. An objective of this course is to prepare students for Calculus I. May not be used for Mathematics major or...
52-154 CALCULUS I
Functions and graphs, derivatives, and applications of differentiation. Exponential, logarithmic and trigonometric functions, integration, and applications of integration. The course includes a laboratory component designed to explore applications and to enhance conceptualization. Prerequisite: Mast...
52-204 TOPICS IN MATHEMATICS
May be repeated with change in topic. (NS)
52-254 CALCULUS II
Numerical integration, methods of integration, applications of the definite integral, improper integrals, and sequences and series, Taylor's Formula and approximation, polar coordinates and an introduction to differential equations. The course includes a laboratory component designed to explore ap...
52-291 PUTNAM POWER HOUR
This course is designed to sharpen problem solving abilities. Students will tackle challenging problems from the William Lowell Putnam Competitions of previous years and study some of the published solutions. Students enrolled in this course will be encouraged to compete in the Putnam Competition in...
52-301 SELECTED TOPICS
May be repeated with change in topic. Prerequisite: Permission of instructor.
52-302 SELECTED TOPICS
May be repeated with change in topic. Prerequisite: Permission of instructor.
52-303 SELECTED TOPICS
May be repeated with change in topic. Prerequisite: Permission of instructor.
52-304 SELECTED TOPICS
May be repeated with change in topic. Prerequisite: Permission of instructor.
Emphasizes the derivations and applications of numerical techniques most frequently used by scientists: interpolation, approximation, numerical differentiation and integration, zeroes of functions and solution of linear systems. Also Computer Science 54-524. Prerequisites: Mathematics 52-674, and Co...
A limited enrollment seminar in a major area of mathematics not generally covered in other courses. Topics may include but are not limited to advanced analysis, combinatorics, and logic and history of mathematics. May be repeated for credit as topics vary. Prerequisite: Three courses at the 200 leve...
52-854 REAL ANALYSIS I
Topics include completeness, topology of the reals, sequences, limits and continuity, differentiation, the Mean-Value Theorem, Taylor's Theorem and infinite series. May also include sequences and series of functions. A rigorous approach to learning and writing proofs is emphasized. Prerequisite: M...
52-864 REAL ANALYSIS II
Topics vary but may include the theory of Riemann integration, Lebesgue integration, sequences and series of functions, Fourier analysis, function spaces. Prerequisite: Mathematics 52-854 or permission of instructor. (Spring, even years) (NS)
This course will fulfill the capstone requirement in Mathematics. Since it serves as a culmination of the student's undergraduate mathematical experience, a balance is sought between application and theory. Topics may include linear and non-linear differential and difference equations and stochast... |
Introducing Expanded Step-by-step Math Solutions
Step-by-step solutions, one of the most popular features for mathematics in Wolfram|Alpha, has just received a dramatic expansion in its functionality! With our new interface, you now have the ability to walk through all of our Step-by-step solutions at your own pace, revealing only one step at a time. Some of our programs will offer to guide you with hints when walking through solutions. And for common math problems, we can even show multiple ways to find the solutions. We are also very excited to introduce three new math content areas that now have Step-by-step solutions: solving equations, rational arithmetic, and verifying trigonometric identities. When you're signed into Wolfram|Alpha, you can use this new feature three times a day. Or, when you upgrade to Wolfram|Alpha Pro, you can use it as many times as you like!
Let's look at a new Step-by-step solution for an integral (one of the more popular math queries we receive). We'll type "integrate cos^2(x)" into Wolfram|Alpha and then click the Step-by-step solution button in the top right of the results page.
To walk through the problem one step at a time, you can click the Next step button, as we have done above. Or if you'd rather see everything at once, click the Show all steps button:
Now let's look at the input (8 * 11) / 3 + 4, which features a Step-by-step solution from one of our brand-new programs. In this walkthrough, you will have the option to use hints to help guide you through the problem:
As you walk through the problem, hints will give you an idea of what comes next. If you'd rather not use the hints, you can click the Hide hints button in the top right. And of course, if you'd like to see all of the steps at once, we can click "Show all steps," as we did in our first example.
The top-right corner of the Step-by-step solutions window has a drop-down menu to let us choose how to solve the problem: use the factor method, complete the square, or use the quadratic formula. Let's try all three and compare:
Again, we see that we have the option to walk through the steps one at a time (using hints if we'd like) or to show all steps at once.
In addition to offering hints and multiple methods to solve a problem, we can now solve equations over the real numbers or over the complex numbers! Let's see this in action by asking Wolfram|Alpha to find the roots of (e^x + 2)(x – 1). When solving over the real numbers, Wolfram|Alpha will show us that (e^x + 2)(x – 1) has only one root; over the complex numbers, Wolfram|Alpha will find the complex roots of this expression.
To see even more of our brand-new functionality, let's ask Wolfram|Alpha to verify a trigonometric identity. To do this, we simply type the identity we wish to prove into Wolfram|Alpha, and it will walk us through our proof one step at a time. For example, let's try the identity (sin(x) – tan(x))(cos(x) – cot(x)) = (sin(x) – 1)(cos(x) – 1):
Here are some more examples for you to explore the scope of Step-by-step solutions.
This gives you a brief overview of what you can do with our new Step-by-step solutions. When you're signed into Wolfram|Alpha, you can use this new feature three times a day. Wolfram|Alpha Pro users receive unlimited access to Step-by-step solutions.
With Wolfram|Alpha's Step-by-step Solutions feature, you can be guided—at your own pace—through a broad range of math problems, from arithmetic and equation solving all the way through integrals and ordinary differential equations. We look forward to expanding our Step-by-step solutions to more areas—please let us know if there are new solutions that you'd like to see! |
Mathematics Galore!: Masterclasses, Workshops and Team Projects in Mathematics and its Applications for an Amazon.co.uk gift card of up to £5.50, which you can then spend on millions of items across the site. Trade-in values may vary (terms apply). Learn more
Book Description23.74,"ASIN":"0198507704","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":28.49,"ASIN":"019851493X","isPreorder":0}],"shippingId":"0198507704::%2Furz7jdpMAs1PR1%2Bzz5jp0PoURa9j8I4WLLSYl5ouatzhHn96VGWrRUPZw54E5P%2BJFJSiB%2FikSY2tAFVm7gVThrZ0KDaSqei,019851493X::voWwo%2FFiokqwWC7yCEI80O1J%2FTsCeCGeCxibEZS1vs9hQc%2BL%2BzoWw565FCcIzYYpSR0KedcTmkCSEOPlN205WsbcXKzM%2BQ book that meets not only the needs of teachers who are involved in the delivery of enrichment material whether it be in the classroom or on a Saturday morning, but also the cravings of those occasional students whose appetite for mathematics is insatiable. (The Mathematical Gazette )
Resources like this deserve a prominent place on the shelf of any mathematics department that is on the look out for ways to enthuse, educate, inspire and challenge. (The Mathematical Gazette )
The main ideas are accessible to children from the age of eleven, while some parts of the book should interest and challenge older school and university students, as well as their teachers and parents. (EMS )
What a good read for anyone interested in mathematics ... historical stories link beautifully to work involving different bases and give good introductory stories for lessons in number work ... Whether you are a teacher in a junior or secondary school this book offers some interesting starting points in areas of mathematics not normally covered in the standard school curriculum ... the author's style is very engaging. (Mathematics TODAY )
"As Obi-Wan Kenobi said about the Light Sabre in Star Wars, a slide-rule is an ancient weapon from a more civilised age" State Budd and Sangwin in their book Mathematics Galore ... placed in the right hands [the book] is a powerful weapon. May the force be strong with readers. was there ever a more civilised age when mathematics was taught as eclectically as this? (Plus Online Magazine )
This is a book which anyone with an interest in mathematics should enjoy, particulary those looking for innovative teaching ideas. (Education in Chemistry )
First Sentence
Unlike most other mathematical problems, the study of mazes and labyrinths takes us into the dark territory of murder, suicide, adultery, passion, intrigue, religion, and conquest. Read the first page |
Forms Pro is the most in-depth and comprehensive math program ever. (This may get kind of long, so for a quick overview, just read the last two words). With 100+ formulas it is undoubtedly the best math program ever. FormsPro contains everything from a 2-5 VARUABLE EQUATION SOLVER to just about every AREA, LATERAL AREA, SURFACE AREA, VOLUME and PERIMETER formulas that their are. FormsPro also contains many helpful triangle formulas such as the SSS,SAS,SAA,SSA and ASA. Also solves for any side of the PYTHAGOREAN THEROM. Forms Pro has a very neat SLOPES EQUATION for just about everything including being able to find a parrallel and perpendicular line. Also included is a very good X=GRAPHER that solves for all X= equations. FormsPro also has some very helpful conversions, like STANDARD->SLOPE, and SLOPE->STANDARD. New and improved, and it's still ONE PROGRAM, so you don't need to worry about a whole bunch of programes to unarchive and archive. All this and much, much more in a program that is (needless to say) Simply Amazing. |
Prerequisite: acceptable placement score (or ACT math score of at least 28), or at least 3 years of high school algebra and trigonometry with at least a B average, or a grade of C or better in MATH 180. General Education course: G9.
3. Life Values: Students analyze, evaluate and respond to ethical issues from informed personal, professional, and social value systems.
(a) Develops an appreciation for the intellectual honesty of deductive reasoning.
(b) Understands the need to do one's own work, to honestly challenge oneself to master the material.
4. Cultural Skills: Students understand their own and other cultural traditions and respect the diversity of the human experience.
(a) Develops and appreciation of the history of calculus and the role it has played in mathematics and in other disciplines.
(b) Learns to use the symbolic notation correctly and appropriately.
NCTM Goals: The NCTM (National Council of Teachers of Mathematics) gives the following set of overall goals for mathematics education in general, which are worth including here, since I think they are such fundamental reasons for studying mathematics.
1. Learn to value mathematics.
2. Learn to reason mathematically.
3. Learn to communicate mathematically.
4. Become confident in your mathematical ability.
5. Become problem solvers and posers.
Course Goals:
1. Students shall develop a solid foundation in the basic concepts and methods of Differential Calculus.
2. Students shall develop problem solving skills.
3. Students shall understand the appropriate use of technological tools in their mathematical work.
Outcomes: This is a list of more specific mathematical outcomes this course should provide. The student shall...
Content:
1. ... demonstrate the knowledge of the theory and methods of Differential Calculus, specifically, limits, derivatives by definition, differentiation formulas, and applications of the derivative.
Problem-Solving:
2. …demonstrate the ability to apply appropriate mathematical tools and methods of novel or non-routine problems.
3. …demonstrate the ability to use various approaches in problem solving situations, and to see connections between these varied mathematical areas.
Technology:
4. …demonstrate the basic ability to perform computational and algebraic procedures using a calculator or computer.
5. …demonstrate the ability to efficiently and accurately graph functions using a calculator or computer.
6. …demonstrate the knowledge of the limitations of technological tools.
7. …demonstrate the ability to work effectively with a CAS, such as DERIVE, to do a variety of mathematical work.
Communication:
8. …use the language of mathematics accurately and appropriately.
9. …present mathematical content and argument in written form.
COURSE POLICIES AND PROCEDURES:
Probably the best single piece of wisdom I can pass on to you as you begin this course is: "Mathematics is not a spectator sport!" You need to view yourself as the LEARNER – and "learn" is an active verb, not a passive verb. I will do what I can to help structure things so that you have an appropriate sequence of topics and a useful collection of problems, but it is up to YOU to DO the problems and to READ the book and THINK ABOUT the topics.
You must develop a system that works for you, but let me suggest that it might include finding a study group or coming to me with your questions or going to tutoring sessions in the learning center. In any case you should expect to spend at least the traditional expectation of 2 hours outside of class for each hour in class – this is important! Class time is for exploring the topics and answering questions you might have, but you simply can't master the material without putting in the time alone to really engage in the mathematics.
We are in the process of phasing in a new textbook and more than ever it is important that you actually READ the BOOK! The authors attempt to force the reader to think about the material and to develop an intuitive sense of what is going on; there is much emphasis on solving problems and much reliance on graphing technology as well as on symbolic manipulation.
HOMEWORK: In a nutshell, working problems is one of the key ways you will learn Calculus. Attending class is important, of course, but without doing problems you will not develop a solid foundation in the material. I will give you daily assignments and will expect that you will do as many as time allows (which I take to be roughly 2 hours per class period). I will not generally collect these assignments but I do see them as testing your understanding and as raising questions for you to ask in class.
LABS: Throughout the course there will be an occasional "lab", a problem set you will work on
EXAMS: There will be exams after each of the 4 chapters we will cover – these will be in two parts, a group practice problem set worth 20 points and then an individual exam worth 80 points, 100 points in total. The final exam will be cumulative and worth 150 points (25 on the group part, 125 on the individual part). By the way, I do not expect you to memorize the various formulas – you are allowed a page of notes for each exam, and you can bring all four pages in for the final exam.
GRADING POLICY: In general I use the rather traditional 90% of possible points for an "A", 80% for a "B", 70% for a "C", and 60% for a "D". I will try to make enough points available in non-test situations that "test-anxiety" should not entirely kill your chances for success, but I am a very firm believer in putting students through the exam experience so that I can see whether you, not your study group, understand the material.
AMERICANS WITH DISABILITIES ACT |
Let's Review Integrated Algebra
Using many step-by-step demonstration examples, helpful diagrams, informative "Math Fact" summaries, and graphing calculator approaches, this book presents:A clearly organized chapter-by-chapter review of all New York State Regents Integrated Algebra topicsExercise sections within each chapter with a large sampling of Regents-type multiple-choice and extended-response questionsRecent New York State Regents Integrated Algebra ExamAnswers are provided for all questions in the exercise sections and all questions on the Regents exam.
show more show less
Preface
Sets, Operations, and Algebraic Language
Numbers, Variables, and Symbols
Classifying Real Numbers
Learning More About Sets
Operations with Signed Numbers
Properties of Real Numbers
Exponents and Scientific Notation
Order of Operations
Translating Between English and Algebra
Linear Equations and Inequalities
Solving One-Step Equations
Solving Multistep Equations
Solving Equations with Like Terms
Algebraic Modeling
Literal Equations and Formulas
One-Variable Linear Inequalities
Problem Solving and Technology
Problem Solving Strategies
Using a Graphing Calculator
Comparing Mathematical Models
Ratios, Rates, and Proportions
Ratios and Rates
Proportions
Solving Motion Problems
Solving Percent Problems
Probability Ratios
Polynomial Arithmetic and Factoring
Combining Polynomials
Multipying and Dividing Polynomials
Factoring Polynomials
Multiplying and Factoring Special Binomial Pairs
Factoring Quadratic Trinomials
Solving Quadratic Equations by Factoring
Solving Word Problems with Quadratic Equations
Rational Expressions and Equations
Simplifying Rational Expressions
Multiplying and Dividing Rational Expressions
Combining Rational Expressions
Rational Equations and Inequalities
Radicals and Right Triangles
Square and Cube Roots
Operations with Radicals
Combining Radicals
The Pythagorean Theorem
General Methods for Solving Quadratic Equations
Similar Triangles and Trigonometry
Trigonometric Ratios
Solving Problems Using Trigonometry
Area and Volume
Areas of Parallelograms and Triangles
Area of a Trapezoid
Circumference and Area of a Circle
Areas of Overlapping Figures
Surface Area and Volume
Graphing and Writing Equations of Lines
Slope of a Line
Slope-Intercept Form of a Linear Equation
Slopes of Parallel Lines
Graphing Linear Equations
Direct Variation
Point-Slope Form of a Linear Equation
Functions, Graphs, and Models
Function Concepts
Function Graphs as Models
The Absolute Value Function
Creating a Scatter Plot
Finding a Line of Best Fit
Systems of Linear Equations and Inequalities
Solving Linear Systems Graphically
Solving Linear Systems By Substitution
Solving Linear Systems By Combining Equations
Graphing Systems of Linear Inequalities
Quadratic and Exponential Functions
Graphing a Quadratic Function
Solving Quadratic Equations Graphically
Solving a Linear-Quadratic System
Exponential Growth and Decay
Statistics and Visual Representations of Data
Measures of Central Tendency
Box-and-Whisker Plots
Histograms
Cumulative Frequency Histograms
Counting and Probability of Compound Events
Counting Using Permutations
Probability of Compound Events
Probability Formulas for Compound Events
Answers and Solution Hints to Practice Exercises
Glossary of Integrated Algebra Terms
The Integrated Algebra Regents Examination
June 2011 Regents Examination
Answers
June 2012 Regents Examination
Answers
Index
List price:
$16.99
Edition:
2nd (Revised)
Publisher:
Barron's Educational Series, Incorporated
Binding:
Trade Paper
Pages:
544
Size:
6.00" wide x 9 |
How it works
Algebra.com is an interactive website. Our solvers generate
formulae "on the fly". It is also a "people's math" website, where tutors who know math share their
knowledge by writing lessons, solvers, and tutor children on homework problems.
Besides that, our needs require a capacity of our software not only
to draw, but also ot "understand" expressions. That's needed for the
universal simplifier, as well as for plotting graphs.
All of that requires a simple way of potting dynamically generated
formulae, graphs, number lines, and geometric diagrams. That's what my
system does. A formula or a drawing can be described in a format that
everyone could understand. There is much less (in a normal case, none)
learning that's involved compared to TeX.
How it works
A tutor writes a solution, a lesson or a solver. He types in (or
has his/her solver generate) a formula, and marks it using a {{{ }}}
notation. Example:
As you know, a proportion is a relation such as {{{x/a=c/d}}}, where x is the unknown and a, c and d are constants.
My system would notice the curly brackets and replace the text between them with a call to a script
to plot the formula.
The script would do the following
Check to see if the result is already available in the cache
If not, parse the formula and understand what it means
Determine the size of the formula and of each of its components
Plot the formula. if graphs or animations are requested, draw them
Return the generated image to the browser.
The result would be seen as
As you know, a proportion is a relation such as , where x is the unknown and a, c and d are constants. |
Mathematical concepts such as probability, statistics, geometric constructions, measurement, ratio and proportion, pre-algebra, and basic tests and measurements concepts including interpretation of data. Use of manipulatives in learning mathematical concepts. Only applicable to graduation requirements of elementary education students. |
Bridging courses for Statistics are run by the Mathematics Learning Centre. Details about the 2012 statistics bridging courses follow.
To find out more about a course programme, the number of spaces available, and to enrol contact the Maths Learning Centre.
Bridging Courses for Statistics — February 2013
Early in 2013 the Mathematics Learning Centre will offer short bridging courses for students planning to undertake programmes which require the study of statistics, such as Statistics and Research Methods for Psychology, and degrees/diplomas in Public Health or other postgraduate degrees.
These courses are designed for people who lack confidence when faced with mathematical tasks or as a refresher for people who want to brush up on basic mathematical skills. They may also be useful for students who have not studied Mathematics (2 Unit) at school. They are not appropriate for students who have at any time completed the higher levels of mathematics for the Higher School Certificate.
The courses aim to review the basic mathematics needs of students in a statistics course and to develop an intuitive understanding of some fundamental statistical concepts.
The program includes:
use of a scientific calculator, including the use of statistical functions
algebra, including the use of formulae and the solution of simple linear equations
introduction to concepts in probability by means of practical activities
Enquiries/Enrolments: Please call us for advice before enrolment on 9351 4061. An enrolment form is available below.
email: mlc.enquiries[at]sydney.edu.au
Class sizes will be limited to 24 students, to ensure individual help is available. For this reason, numbers may have to be restricted, so early enrolment is recommended. If there are insufficient enrolments for any course, the University reserves the right to offer students the choice of an alternative arrangement or a refund of fees paid.
Calculators
Students will need a scientific calculator with statistical functions.
Recommended models are the Casio fx 82 AU PLUS or Casio fx 82 AU. Some other models in the fx82 and fx100 series may also be suitable.
If you already have a scientific calculator, check with the teachers in the course first before buying a new one. |
My Research Question: Does an introductory biomathematics course increase the ability to connect biological scenarios and mathematical models?
The Problem
Many modern characterizations of biological systems have reached an unparalleled level of detail. Mathematics is playing an important role by allowing scientists to organize this information and arrive at a better fundamental understanding of life processes. In fact, mathematical modeling of biological systems is evolving into a partner of experimental work. Not only for the statistical analysis of experimental data but also in deterministic models predicting future outcomes.
Introducing biology students to mathematics early provides the biology department with the ability to expand the level of quantitative emphasis in their courses and their research labs. As a result, students will be better prepared for the growing job market in the biological sciences.
Fulfilling a need
Biology major is the largest major on campus. A large number of undergraduates participate in research projects in the biological and chemical sciences.
In the past three years, there have been at least 36 freshman declaring a biology major with AP Calculus or Statistics credit. However, only one math course is required for most biology concentrations. Most biology majors take elementary statistics.
Methodologies & Types of Evidence of Student Learning Gathered
I administered two surveys to the class at the beginning of the semester. The first survey solicits studentís opinions about math and its relevance to their future careers. The second survey measures studentís connection of biological scenarios with the mathematical graphs modeling those scenarios. I distributed the second survey again during week 7 and week 14 of the semester.
When a disease spreads through a small population, the number of new infections in a week is directly proportional to the product of the number of infected people with the rest of the population. Which of the following graphs would describe the number of infected people (horiz. axis) vs. new infections in a week (vertical axis)
Project Summary
The University of Wisconsin - La Crosse is currently developing a biomathematics course, BioMath, introducing biology majors (with no calculus pre-requisite) to calculus and statistics-based mathematical modeling in biology. Unlike a traditional calculus course for the life sciences, BioMath takes the perspective of a biologist trying to set up a mathematical model based upon experimental observations. Students are asked analyze data, provided in part by the biology faculty, drawing sound conclusions about the underlying processes using their developing knowledge of calculus and statistics.
My project measures the students' connections of biological scenarios and mathematical models during the course of the semester.
Learning Outcomes
Students will
have an enhanced knowledge and understanding of mathematical modeling and statistical methods in the study of biological systems;
be better able to assess biological inferences that rest on mathematical and statistical arguments;
be able to analyze data from experiments and draw sound conclusions about the underlying processes using their understanding of mathematics and statistics.
BioMath I Outline
1. Functions and mathematical models
2. Discrete-time dynamical systems
3. Limits and the derivative
4. Differential equations
5. Integration
6. Probability
Example Application: Spread of a disease
*Students are first introduced to the model for the spread of an infectious disease when learning about functions and variable relationships.
1. Quadratic Model
The number of new infections N in a week is proportional to the product of the size of the infected population I with the size of the healthy population,
N = r I (Total - I), r = parameter
*We revisit the model three more times; each time using our previous work to increase the complexity.
2. Discrete-time Dynamical System
The future size of the infected population is equal to the current size plus the number of new infections in a week.
3. Differential Equations
We use the graph of the equation from the quadratic model to sketch the solutions to the differential equation.
4. Two Compartment Models(infectious and recovered populations)
We increased the complexity of the model by studying the effects of transmission and recovery rates on equilibrium solutions.
* Question 5 was designed as a control.
Preliminary Findings, Results, Conclusions, & Implications
Fall Semester 2007. Each of the question topics except Respiration was discussed in class within the first seven weeks. The number of correct answers increased (up 20.6%) or remained the same on all questions from week 1 to week 7. However, at the end of the semester the number of correct answers decreased (down 16.8%) suggesting that the students did not retain the connection throughout the semester.
Spring Semester 2008. I will introduce simple versions of the model early in the semester and increase the complexity and realism as the course progresses. By building upon the foundations established in the first half of the semester, students will use their new mathematical tools to revisit and modify the simple models. Since each topic will be covered in more depth (see Example Application), I think they are more likely to retain the material. I will use homework and exam problems to assess their ability to apply the same modeling skills to biological processes not discussed in class.
Career Relevance & Impact
I would like to acknowledge and thank my fellow Wisconsin Teaching Fellows and Scholars for their assistance in focusing my SoTL question. You can view their KEEP Gallery. I acknowledge the support and encouragement from the UW-L mathematics and biology department.
I presented the results of this work at the national Mathematical Association of America-American Mathematical Society Joint Mathematics Meetings in San Diego, CA on January 8th, 2008. |
Cofactor Expansions
In this lesson our instructor talks about cofactor expansions. First, he talks about cofactor expansions and their application. Then he discusses evaluation of determinants by cofactor, inverse of a matrix by cofactor, and list of non-singular equivalences. He ends the lesson by talking about Cramer's Rule.
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Cofactor Expansions |
2.3 Transformations of graphs: translations; stretches; reflections in the axes The graph of y = f^(-1) (x) as the reflection in the line y = x of the graph of y = f(x) The graph of 1/f(x) from y = f(x) The graphs of y = |f(x)| and y = f(|x|)
7.3 Local maximum and minimum points Use of the first and second derivative in optimization problems
7.4 Indefinite integration as anti-differentiation Indefinite integral of x^n (n ≠ -1), sinx, cosx, e^x, 1/x The composites of any of these with the linear function ax + b
7.5 Anti-differentiation with a boundary condition to determine the constant term Definite integrals Area between a curve and the x-axis or y-axis in a given interval, areas between curves Volumes of revolution
7.7 Graphical behaviour of functions: tangents and normals, behaviour for large |x|; asymptotes The significance of the second derivative; distinction between maximum and minimum points Points of inflexion with zero and non-zero gradients
7.8 Implicit differentiation
7.9 Further integration: integration by substitution; integration by parts
7.10 Solution of first order differential equations by separation of variables
Option
Option A: Statistics and probability
A1 Expectation algebra Linear transformation of a single random variable Mean and variance of linear combinations of two independent random variables Extension to linear combinations of n independent random variables
A3 Distribution of the sample mean The distribution of linear combinations of independent normal random variables The central limit theorem The approximate normality of the proportion of successes in a large sample
A4 Finding confidence intervals for the mean of a population Finding confidence intervals for the proportion of successes in a population
B6 The identity element e The inverse a^(−1) of an element a Proof that left-cancellation and right-cancellation by an element a hold, provided that a has an inverse Proofs of the uniqueness of the identity and inverse elements
B7 The axioms of a group {G, *} Abelian groups
B8 R, Q, Z, C under addition; matrices of the same order under addition; invertible matrices under multiplication; symmetries of a triangle, rectangle; invertible functions under composition of functions; permutations under composition of permutations
B9 Finite and infinite groups The order of a group element and the order of a group
B10 Cyclic groups Proof that all cyclic groups are Abelian
B11 Subgroups, proper subgroups Use and proof of subgroup tests Lagrange's theorem Use and proof of the result that the order of a finite group is divisible by the order of any element (Corollary to Lagrange's theorem)
B12 Isomorphism of groups Proof of isomorphism properties for identities and inverses
Option C: Series and differential equations
C1 Infinite sequences of real numbers Limit theorems as n approaches infinity Limit of a sequence Improper integrals The integral as a limit of a sum; lower sum and upper sum
C2 Convergence of infinite series Partial fractions and telescoping series (method of differences) Tests for convergence: comparison test; limit comparison test; ratio test; integral test The p-series Use of integrals to estimate sums of series
C3 Series that converge absolutely Series that converge conditionally Alternating series
C4 Power series: radius of convergence and interval of convergence Determination of the radius of convergence by the ratio test
C5 Taylor polynomials and series, including the error term Maclaurin series for e^x, sinx, cosx, arctanx, ln(1 + x), (1 + x)^p Use of substitution to obtain other series The evaluation of limits using l'Hôpital's Rule and/or the Taylor series
D1 Division and Euclidean algorithms The greatest common divisor, gcd(a, b), and the least common multiple, lcm(a, b), of integers a and b Relatively prime numbers; prime numbers and the fundamental theorem of arithmetic |
Curriki launches free, project-based algebra course online
Curriki, a global K-12 community for creating, sharing, and finding open learning resources, has launched a free Algebra 1 course aligned with the Common Core State Standards. Available online, this project-based modular course engages students through real-world examples, projects, interactive web 2.0 tools, videos, and targeted feedback, Curriki says. Read more with registration. |
Understand Algebra: A Teach Yourself 60 million Teach Yourself products sold worldwide! A helpful guide for students struggling with algebraUnderstand Algebraprovides everything you need to broaden your skills and gain confidence. Assuming only a basic level of arithmetic, this carefully graded and progressive book guides them through the basic principles of the subject with the help of exercises and fully worked examples.Includes: One, five and ten-minute introductions to key principles to get you started Lots of instant help with common problems and quick tips for succ... MOREess, based on the author's many years of experience Tests in the book to keep track of your progress Exercises and examples with full answers allow you to practice your new skills progressivelyTopics include: The meaning of algebra; Elementary operations in algebra; Brackets and operations with them; Positive and negative numbers; Expressions and equations; Linear equations; Formulae; Simultaneous equations; Linear inequalities; Graphical representation of quantities; Straight line graphs; coordinates; Using inequalities to define regions; Multiplying algebraicalalgebraics; Factors; Fractions; Graphs of quadratic functions; Quadratic equations; Indices; Logarithms; Ratio and proportion; Variation; The determination of laws; Rational and irrational numbers; Arithmetical and geometrical sequences |
Humble CalBioStatistics is extremely similar to other statistics courses. The calculations are the same. The statistical and probability interpretations are the sameWe are now able to solve a variety analytical geometry problems which we could not solve with trigonometry and algebra alone. Prealgebra covers factoring and how to solve for the unknown variable for basic equations. It also makes sure that the student has a thorough understanding of fractions. |
MathOdes: Etching Math in Memory: Algebra 1 And 2
MathOdes is a math study aid designed to help students remember math concepts and formulas in the form of poetry and illustrations. Each "ode" details a particular math concept such as polynomials, matrices, and conics. A portion of the proceeds will go to the MathOdes Scholarship fund to assist qualified students in their educational pursuits.
show more show less
List price:
$29.99
Edition:
N/A
Publisher:
CreateSpace Independent Publishing Platform
Binding:
Trade Paper
Pages:
108
Size:
6.00" wide x 9.00" long x 0.26 |
GCSE Maths P/T (57917)
What topics are covered by the course?
What you will study
You will study topics on statistics, number, algebra and geometry. The course focuses on how these areas of mathematics are connected and how the skills acquired can be applied in functional situations.
Your Course Structure
The course is divided into 3 units. Unit 1 covers statistics and numerical work using a calculator. Unit 2 covers numerical work without a calculator and algebra. Unit 3 covers all of the geometry material and some further algebra.
Who should attend?
Entry Requirements
You will require a GCSE grade D for this course or, if you have been out of education for some time, be prepared to undertake an initial interview and numeracy assessment.
What will I be able to do on completion?
Further study
Many jobs require GCSE Mathematics as a basic requirement as do Higher Education courses. Wakefield College also offers a range of courses for which GCSE Mathematics is either a requirement or very useful.
Career opportunities
You will need GCSE Mathematics as a basic requirement for many jobs, particularly for courses leading to careers in Nursing, Business, Engineering and Teaching.
How will I be assessed?
The three units are assessed at the end of the session; Unit 1 is worth 26.7%, Unit 2 33.3% and Unit 3 40% of the overall mark. There is no assessed coursework element for this course. |
TA:
Course Description
The first part of the course covers vector calculus and applications. This includes
directional derivatives, vector fields, gradient, divergence, and curl, as well as
line, volume, and surface integrals. Emphasis will be on effective use of these
concepts to solve problems. In the second part of the course we move to the
complex plane. There we will study more about how to compute integrals using
residues and the Cauchy integral formula, as well as Taylor and Laurent series.
Textbook
There is no required textbook. We will use Notes from Mark Kot that are available
online:
Notes
References
The mathematics library has a number of Springer ebooks that can be
downloaded and used as textbooks for the complex variables portion of
the course. For examples, please see:
Learning objectives and instructor expectations
Students are expected to gain a good grasp of how to use theorems from vector calculus
and complex analysis to solve a variety of problems.
Schedule and Homework
Follow links in the table below to obtain a copy of the homework in
latex (.tex) or Adobe
Acrobat (.pdf) format. You may also obtain here solutions to some of the
homework and exam problems. An item shown below in plain text is not yet
available.
Class Summaries
Grading
There will be homework assignments, a midterm (tentatively scheduled for Tues., Oct. 23),
and a final. Exams count for 60% of the
final grade. The final counts more than the midterm. Homework counts for 40% of your grade.
You may work together on homework assignments, but each person must write up his/her own
answers to the exercises.
No late homework accepted. I will drop your lowest homework score. |
For computer science students taking the discrete math course. Written specifically for computer science students, this unique textbook directly addresses their needs by providing a foundation in discrete math while using motivating, relevant CS applications. This text takes an active-learning appr...
This text is intended for one semester courses in Logic, it can also be applied to a two semester course, in either Computer Science or Mathematics Departments. Unlike other texts on mathematical logic that are either too advanced, too sparse in examples or exercises, too traditional in coverag... |
Description
A Concrete Approach to Abstract Algebra begins with a concrete and thorough examination of familiar objects like integers, rational numbers, real numbers, complex numbers, complex conjugation and polynomials, in this unique approach, the author builds upon these familar objects and then uses them to introduce and motivate advanced concepts in algebra in a manner that is easier to understand for most students. The text will be of particular interest to teachers and future teachers as it links abstract algebra to many topics wich arise in courses in algebra, geometry, trigonometry, precalculus and calculus. The final four chapters present the more theoretical material needed for graduate study.
Presents a more natural 'rings first' approach to effectively leading the student into the the abstract material of the course by the use of motivating concepts from previous math courses to guide the discussion of abstract algebra
Bridges the gap for students by showing how most of the concepts within an abstract algebra course are actually tools used to solve difficult, but well-known problems
Builds on relatively familiar material (Integers, polynomials) and moves onto more abstract topics, while providing a historical approach of introducing groups first as automorphisms
Exercises provide a balanced blend of difficulty levels, while the quantity allows the instructor a latitude of choices
Recommendations:
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The important ideas of algebra, including patterns, variables, equations, and functions, are the focus of this book. Student activities that introduce and promote familiarity with these ideas include constructing growing patterns using isosceles triangles, analyzing situations with constant or varying rates of change, and observing and representing various patterns in an array. The supplemental CD-ROM features interactive electronic activities, master copies of activity pages for students, and additional readings for teachers. Publisher: NCTM Author: Cuevas, Yeatts Price: $36.95
This book shows how middle school students can use mathematical models and represent and analyze mathematical situations and structures to explore the concept of function. The activities and problems require students to use representations related to work with functions, and they highlight some of the interactions that may occur among these representations. The supplemental CD-ROM features interactive electronic activities, master copies of activity pages for students, and additional readings for teachers. Publisher: NCTM Author: S. Friel,S. Rachlin,D.Doyle Price: $33.95
This book focuses on algebra as a language of process, expands the notion of variable, develops ideas about the representation of functions, and extends students' understanding of algebraic equivalence and change. In the activities, students apply properties of functions by using median salary data, explore the meaning of equivalent equations, and use recursive or iterative forms to represent relationships. The supplemental CD-ROM features interactive electronic activities, master copies of activity pages for students, and additional readings for teachers.
Publisher: NCTM Author: M.Burke, D.Erickson, J. W. Lott, M. Obert Price: $32.95
This book demonstrates how some of the fundamental ideas of algebra can be introduced, developed, and extended. It focuses on repeating and growing patterns, introduces the concepts of variable and equality, and examines relations and functions. Its activities are designed to capture the interest of small children as they investigate growing patterns, use pictures of dogs with varying numbers of spots to solve for missing addends, and use spinners to identify and explore functions. The supplemental CD-ROM features interactive electronic activities, master copies of activity pages for students, and additional readings for teachers. Publisher: NCTM Author: Greenes, M. Cavanagh, L. Dacey, C. Findell, M. Small Price: $35.95 |
Welcome to the Online Math Center
Whatcom Community College's Online Math Center is available to provide free access to a wide range of resources related to mathematics, its application, technology, and mathematics education.
We hope that you find the resources you need to be a successful math student at WCC!
Washington State Community College Math Conference Thursday May 9, 2013 – Saturday May 11, 2013 Official Website
WHATCOM MATH PLACEMENT
Information related to Whatcom's Math Placement Test may be found under Learning Math (then scroll down to WCC Math Placement Info). Questions regarding Math Placement Tests should be directed to the Entry & Advising Center at 360.383.3080 or the Testing Center at 360.383.3052. Prospective Running Start students should contact the Running Start Office at 360.383.3123 or [email protected] for a testing appointment.
MATH LEAGUE CONTEST
The American Mathematical Association of Two-Year Colleges conducts a mathematics contest every year, the AMATYC Student Math League, giving one test in the fall and one in the spring. Any two-year college student, full or part time, who has not earned a two-year college or higher degree is eligible to participate.
The level of the tests is Precalculus mathematics. Questions may involve precalculus algebra, trigonometry, synthetic and analytic geometry, and probability. Questions are short answer or multiple choice. Students are permitted to use any scientific or graphics calculator which does not have a regular computer keyboard (a QWERTY Keyboard).
Dates for the 2012-2013: Round 2: Friday, February 15 through Saturday, March 9, 2013
2012-2014 President of the National Council of Teachers of Mathematics (NCTM), Linda Gojak, has graciously accepted an invitation for an evening presentation at Whatcom in the Winter Quarter 2013. Dates, times, and location will be announced. |
The book is designed for an advanced undergraduate two or three semester course of analysis. The topics of the course are presented relatively briefly, but correctly and rigorously. Some preliminary knowledge of calculus is expected, as well as the motivation of the students, as examples from ``practical life" motivating particular mathematical constructions are quite rare. This enabled to cover a wide range of the subject, from the basic theory of real and complex numbers through functions of a real variable, metric spaces, Lebesgue measure and integration to advanced topics, like function spaces or Fourier series. Mathematical books usually respect the rule that no constructions should be used before they are rigorously explained. This supports the correctness of the text, but often results in an artificial ruptures in its inner logic. A typical example is the integral criterion for the convergence of infinite series. Usually the theory of infinite series preceeds the integrals, so the section on the integral criterion is often included into chapters dealing with integrals. The author breaks this rule by means of dividing the text into essential parts, which are self-contained, and advanced ones, denoted with an asterix, which expect some additional knowledge or present interesting non-trivial ideas. From this point of view the book opens new horizons in the second reading. Each section is divided into subsections and a set of exercises follows each subsection. The exercises are of both routine and theoretical nature.\par The contents of the book is the following: {\it 1. Introduction.} Basic facts on real numbers and operations with them, construction of real numbers by Dedekind cuts. {\it 2. The Real and Complex Numbers.} Infimum and supremum, algebraic properties, decimal expansions, countability. An advanced part on algebraic and transcendental numbers. {\it 3. Real and Complex Sequences.} Basic properties of sequences and limits, extended real line. {\it 4. Series.} Convergence, absolute convergence, series with nonnegative terms, tests for convergence. An advanced part on conditional convergence, alternating series, including Riemann's rearrangement theorem. {\it 5. Power Series.} Radius of convergence, differentiation of power series, operations with power series, Abel's theorem. {\it 6. Metric Spaces.} Metric space, types of its subsets and points. Covering and compactness, Heine-Borel theorem, sequential compactness. An advanced part on the Cantor set. {\it 7. Continuous Functions.} Continuity of mappings between metric spaces, uniform continuity, properties of continuous functions on compact sets. The space of continuous functions on a real interval. Weierstrass polynomial approximation theorem. {\it 8. Calculus.} Differentiation of real- and complex-valued functions, mean value theorems, inverse functions. Riemann integral, its properties, Fundamental theorem of calculus. Taylor's theorem. {\it 9. Some Special Functions.} Complex exponential function, Fundamental Theorem of algebra, infinite products, Euler's formula for sine. {\it 10. Lebesgue Measure on the Line.} Introduction (including the Theorem of Banach and Tarski, proof is in the appendix at the end of the book). Outer measure, measurable sets and their properties. An example of a nonmeasurable set as an advanced section. {\it 11. Lebesgue Integration on the Line.} Measurable functions, Lebesgue integration, properties of the Lebesgue integral. Dominated convergence theorem, monotone convergence theorem, Fatou's Lemma. {\it 12. Integration and Function Spaces.} Null sets, measurability almost everywhere. Connection between Riemann and Lebesgue integrals, Riemann integrability of real functions with null sets of discontinuity points. The spaces $L^1$ and $L^2$. Differentiation of the integral, the Hardy-Littlewood inequality. {\it 13. Fourier Series.} Periodic functions, Fourier coefficients. The Bessel's inequality. Dirichlet's and Fejér's theorems. The Weierstrass approximation theorem, the Riesz-Fischer's theorem. An advanced part on the convolution. {\it 14. Applications of Fourier Series.} The Gibbs phenomenon. An example of a continuous, nowhere differentiable function. The isoperimetric inequality (among curves of a givel length the circle encloses the largest area). Weyl's equidistribution theorem. Applications with partial differential equations. Fast Fourier transform. The Fourier integral. Uncertainity principle. The whole section is an advanced one. {\it 15. Ordinary Differential Equations.} Homogeneous linear equations, first order systems with constant coefficients. Existence and uniqueness, Peano theorem, Banach fixed point theorem, basic numerical methods. [Vladim\'ir Janiš (Banská Bystrica)] |
Standards for Grades 9–12
Students in secondary school face choices and decisions that will determine the
course of their lives. As they approach the end of required schooling,
they must have the opportunity to explore their career interests—which
may change during high school and later—and their options for postsecondary
education. To ensure that students will have a wide range of career and
educational choices, the secondary school mathematics program must be
both broad and deep.
The high school years are a time of major transition. Students enter high school
as young teenagers, grappling with issues of identity and with their own
mental and physical capacities. In grades 9–12, they develop in multiple
ways—becoming more autonomous and yet more able to work with others,
becoming more reflective, and developing the kinds of personal and intellectual
competencies that they will take into the workplace or into postsecondary
education.
These Standards describe an ambitious foundation of mathematical ideas and applications
intended for all students. Through its emphasis on fundamental mathematical
concepts and essential skills, this foundation would give all students
solid preparation for work and citizenship, positive mathematical dispositions,
and the conceptual basis for further study. In grades 9–12, students
should encounter new classes of functions, new geometric perspectives,
and new ways of analyzing data. They should begin to understand aspects
of mathematical form and structure, such as that all quadratic functions
share certain properties, as do all functions of other classes—linear,
periodic, or exponential. Students should see the interplay of algebra,
geometry, statistics, probability, and discrete mathematics and various
ways that mathematical phenomena can be represented. Through their high
school experiences, they stand to develop deeper understandings of the
fundamental mathematical concepts of function and relation, invariance,
and transformation. »
In high school, students should build on their prior knowledge, learning more-varied
and more-sophisticated problem-solving techniques. They should increase
their abilities to visualize, describe, and analyze situations in mathematical
terms. They need to learn to use a wide range of explicitly and recursively
defined functions to model the world around them. Moreover, their understanding
of the properties of those functions will give them insights into the
phenomena being modeled. Their understanding of statistics and probability
could provide them with ways to think about a wide range of issues that
have important social implications, such as the advisability of publicizing
anecdotal evidence that can cause health scares or whether DNA "fingerprinting"
should be considered strong or weak evidence.
Secondary school students need to develop increased abilities in justifying claims,
proving conjectures, and using symbols in reasoning. They can be expected
to learn to provide carefully reasoned arguments in support of their claims.
They can practice making and interpreting oral and written claims so that
they can communicate effectively while working with others and can convey
the results of their work with clarity and power. They should continue
to develop facility with such technological tools as spreadsheets, data-gathering
devices, computer algebra systems, and graphing utilities that enable
them to solve problems that would require large amounts of computational
time if done by hand. Massive amounts of information—the federal
budget, school-board budgets, mutual-fund values, and local used-car prices—are
now available to anyone with access to a networked computer (Steen 1997).
Facility with technological tools helps students analyze these data. A
great deal is demanded of students in the program proposed here, but no
more than is necessary for full quantitative literacy.
All students are expected to study mathematics each of the four years that they
are enrolled in high school, whether they plan to pursue the further study
of mathematics, to enter the workforce, or to pursue other postsecondary
education. The focus on conceptual understanding provides the underpinnings
for a wide range of careers as well as for further study, as Hoachlander
(1997, p. 135) observes:
Most advanced high school mathematics
has rigorous, interesting applications in the work world. For example,
graphic designers routinely use geometry. Carpenters apply the principles
of trigonometry in their work, as do surveyors, navigators, and architects....
Algebra pervades computing and business modeling, from everyday spreadsheets
to sophisticated scheduling systems and financial planning strategies.
Statistics is a mainstay for economists, marketing experts, pharmaceutical
companies, and political advisers.
p.
288
With the experience proposed here in making connections and solving problems
from a wide range of contexts, students will learn to adapt flexibly to
the changing needs of the workplace. The emphasis on facility with technology
will result in students' ability to adapt to the increasingly technological
work environments they will face in the years to come. By learning to
think and communicate effectively in mathematics, students will be better
prepared for changes in the workplace that increasingly demand teamwork,
collaboration, and communication (U.S. Department of Labor 1991; Society
for Industrial and Applied Mathematics 1996). Note that these skills are
also needed increasingly by people who will pursue careers
» in mathematics or science. With its emphasis on fundamental
concepts, thinking and reasoning, modeling, and communicating, the core
is a foundation for the study of more-advanced mathematics. Consider,
for example, the recommendations for precalculus courses generated at
the Preparing for a New Calculus conference (Gordon et al. 1994, p. 56):
Courses designed to prepare students for the new calculus should:
cover
fewer topics ... with more emphasis on fundamental concepts.
place
less emphasis on complex manipulative skills.
teach
students to think and reason mathematically, not just to perform routine
operations....
emphasize
modeling the real world and develop problem-solving skills.
make
use of all appropriate calculator and computer technologies....
promote
experimentation and conjecturing.
provide
a solid foundation in mathematics that prepares students to read and
learn mathematical material at a comparable level on their own.
A central theme of Principles and Standards for School Mathematics
is connections. Students develop a much richer understanding of mathematics
and its applications when they can view the same phenomena from multiple
mathematical perspectives. One way to have students see mathematics in
this way is to use instructional materials that are intentionally designed
to weave together different content strands. Another means of achieving
content integration is to make sure that courses oriented toward any particular
content area (such as algebra or geometry) contain many integrative problems—problems
that draw on a variety of aspects of mathematics, that are solvable using
a variety of methods, and that students can access in different ways.
High school students with particular interests could study mathematics that extends
beyond what is recommended here in various ways. One approach is to include
in the program material that extends these ideas in depth or sophistication.
Students who encounter these kinds of enriched curricula in heterogeneous
classes will tend to seek different levels of understanding. They will,
over time, learn new ways of thinking from their peers. Other approaches
make use of supplementary courses. For instance, students could enroll
in additional courses concurrent with the program. Or the material proposed
in these Standards could be included in a three-year program that allows
students to take supplementary courses in the fourth year. In any of these
approaches, the curriculum can be designed so that students can complete
the foundation proposed here and choose from additional courses such as
computer science, technical mathematics, statistics, and calculus. Whatever
the approach taken, all students learn the same core material while some,
if they wish, can study additional mathematics consistent with their interests
and career directions.
These Standards are demanding. It will take time, patience, and skill to implement
the vision they represent. The content and pedagogical demands of curricula
aligned with these Standards will require extended and sustained professional
development for teachers and a large degree of administrative support.
Such efforts are essential. We owe our children no less than a high degree
of quantitative literacy and mathematical knowledge that prepares them
for citizenship, work, and further study. |
Modern Computer Arithmetic focuses on arbitrary-precision algorithms for efficiently performing arithmetic operations such as addition, multiplication and division, and their connections to topics such as modular arithmetic, greatest common divisors, the Fast Fourier Transform (FFT), and the computation of elementary and special functions. Brent and Zimmermann present algorithms that are ready to implement in your favourite language, while keeping a high-level description and avoiding too low-level or machine-dependent details. The book is intended for anyone interested in the design and implementation of efficient high-precision algorithms for computer arithmetic, and more generally efficient multiple-precision numerical algorithms. It may also be used in a graduate course in mathematics or computer science, for which exercises are included. These vary considerably in difficulty, from easy to small research projects, and expand on topics discussed in the text. Solutions to selected exercises are available from the authors. less |
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Detailed description This book details how applied mathematics involves predictions, interpretations, analysis, and mathematical modeling to solve real-world problems. Due to the broad range of applications, mathematical concepts and techniques and reviewed throughout, especially those in linear algebra, matrix analysis, and differential equations. Some classical definitions and results from analysis are also discussed and used. Some applications (postscript fonts, information retrieval, etc.) are presented at the end of a chapter as an immediate application of the theory just covered, while those applications that are discussed in more detail (ranking web pages, compression, etc.) are presented in dedicated chapters. Acollection of mathematical models of a slightly different nature, such as basic discrete mathematics and optimization, is also provided. Clear proofs of the main theorems ultimately help to make the statements of the theorems more understandable, and a multitude of examples follow important theorems and concepts. In addition, the author builds material from scratch and thoroughly covers the theory needed to explain the applications in full detail, while not overwhelming readers with unneccessary topics or discussions. In terms of exercises, the author continuously refers to the real numbers and results in calculus when introducing a new topic so readers can grasp the concept of the otherwise intimidating expressions. By doing this, the author is able to focus on the concepts rather than the rigor. The quality, quantity, and varying level of difficulty of the exercises provides instructors more classroom flexibility. Topical coverage includes linear algebra; ranking web pages; matrix factorizations; least squares; image compression; ordinary differential equations; dynamical systems; and mathematical models. |
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Careers
In this section you will find information on what mathematics
graduates have gone on to do, the resources and support available to
you whilst an undergraduate with us and examples of events open to our
undergraduate students. Current undergraduates please click here for events and opportunities.
First of all, you can hear from our Careers Consultant Abi Sharma, about what support is available for our mathematical sciences undergraduates.
Mathematics Graduates
Some students entering university know what career
they want to go into but the reality is that many don't, so there's no
need to worry if you're not sure what you want to do. The most
important thing to remember is that when you graduate with your
mathematics degree you'll have a set of skills that employers will find
very desirable. When you graduate with your degree you will have:
Excellent analytical abilities
The ability to work independently
Highly developed numerical skills
Effective communication skills
The ability to apply mathematical modelling to the real world
Practical computational skills.
These skills are in great demand by employers and you will have
the potential for high earnings in the course of your career. The average
starting salary for a mathematics graduate is around £22,000 and is higher than
the average starting salary for all subjects. Unlike graduates in more
vocational disciplines, mathematicians are not limited to one obvious area of
employment. For example, mathematics graduates can be found in
The two guides below have been produced for the benefit of our
students. One looks at the impact of mathematics beyond the subject
itself and provides a clear link from the syllabus to applications in a
range of different industries whilst the other has primarily Queen Mary
mathematics alumni talking about their careers and/or postgraduate
study. You can also find advice from employers in a series of videos to
be found here.
An opportunity for your students to join Quest Overseas
on our summer community projects in Peru and Malawi.
We have teams departing to work on
these projects in July 2012, and
wanted to make your department aware, as they may
be of particular interest to your Mathematics students
interested in overseas travel, volunteering and
international development.
Working in partnership with Joshua Orphan & Community Care,
the aim of this project is to improve the quality of life for some of Malawi's
thousands of orphans. The majority of these children have been orphaned as a
result the HIV/AIDS crisis and each community supports around hundred
vulnerable children, a major strain on local resources. The project work aims
to improve community facilities, e.g. schools and clinics to give these
children a brighter start in life.
The
focus of the work is construction, for example
renovating schools or building a feeding centre. The exact nature of the work
you will be doing depends on what is most needed in the area at the time,
something Joshua work out in consultation with the local community. Aside from
getting hands on with the construction, volunteers also have opportunities to
get more involved with the community, such as working with the local scout
groups and with local kids ‐ on health and hygiene, environment or HIV workshops‐ the options
are endless! Work in local orphan feeding centres, and potentially work with local youth groups on projects
on HIV/AIDS awareness. The project is extremely community based and offers
volunteers a unique insight into the challenges and the warmth of rural
Malawian life.
Volunteers will also have the chance
to visit some of Malawi's best sights, for example kayaking on Lake Malawi,
trekking up Mount Mulanje or spotting wildlife on safari in Liwonde National
Park.
Quest
Overseas has been working with the Inti
Wara Yassi wild animal sanctuaries in Bolivia for the past 9 years,
building the infrastructure, expanding the land of the parks, and working with
the animals. Just over two years ago, the project expanded into its third
location in the Bolivian Amazon, due to the ever increasing flow of animals
arriving at the parks.
Work with the animals is extremely hands on, with each
volunteer taking responsibility for their own animal, whether it be a monkey,
bird or wild cat. Daily tasks will involve cleaning enclosures, feeding your
animal and accompanying them out into the forest. With the monkeys and birds,
it is often a case of working with them while they are getting used to their
natural habitat again (most will have been rescued from the pet or circus
trade) before releasing them back into the wild. With the wild cats, it is more
often a case of making their life as enjoyable as possible as they almost
always cannot be released into the wild - so they get taken for daily
walks!
As well as the work with the animals, our teams also work to
improve the infrastructure of the parks, building enclosures and clearing
trails, for around two and a half weeks of the project. A substantial
proportion of the cost of the project is a donation direct to the sanctuaries,
allowing them to continue their work throughout the year. It is a fantastic
project to be a part of and we are sure your students would benefit immensely
from being part of it
If you would like to find out more about the projects
above, please email [email protected],
phone us on 01273 777206, or chat
to us online. More information about Quest Overseas and how we work can
also be found on our website and
we're more than happy to answer any further questions you may have. |
Online Math Readiness Information
Please review this page for information on this self-paced online course. Registration is free.
You do not have to be a U of S student to register. If you have already registered, you may
log in here.
Course Content
The Math Readiness Course is designed to help students prepare for university-level calculus courses
by refreshing skills from high school mathematics. The families of topics from high school mathematics that are
reviewed in Math Readiness include:
Working with Algebra
Functions and Graphs
Exponential and Logarithmic Functions
Geometry
Trigonometry
More detailed information on the concepts covered in the Math Readiness course is available on the
Course Content page.
Course Versions and Fees
Online Math Readiness is provided free of charge. The University of Saskatchewan also offers a
face-to-face version of the course, which is subject to a tuition fee. For more information about
registration, dates and fees for the face-to-face course, please refer to the
Centre for
Continuing & Distance Education or email [email protected].
Format of the Math Readiness Online Materials
Online Math Readiness is primarily an independent study course - a student will be able to proceed
through the course at his or her own pace. One of the features of Online Math Readiness is that a student
is able to ask fellow students for their thoughts about the course notes and exercises via online discussion
boards and chat. Additional support may be available online on an ad-hoc basis.
Accounts expire after a certain period of time (usually about a year). If you find that your own account has expired
and you would still like access to the course materials, please fill out this registration form again.
Re-establishing your access to the online course should be straightforward.
Contact Information
For further information about the online course, please contact Holly Fraser, University Learning Centre
Math/Stats Help Coordinator, at [email protected].
For more information about the face-to-face version of the Math Readiness Course, email
[email protected]. |
Math Function Mania is a fun multimedia game that teaches functions, algebra and problem solving skills. Functions are very important in math! By mastering them, you will greatly increase your math skills. This game teaches you by the "hands on" ...
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Yacas (Yet Another Computer Algebra System) is an open source general purpose computer algebra system. Its strength is in the language so that you will be able to easily write your own symbolic manipulation algorithms.. Yacas for Macintosh. This site ...
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Mac OS
Our flagship Computer Algebra System product, LiveMath is a computer algebra system. LiveMath Maker is a computer program you use to MAKE (and explore and experiment with and create) LiveMath. Any LiveMath you make with LiveMath Maker may be shared ...
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Mac OS
Ace High School Math Algebra today! Many step by step video examples to learn concepts. Content is based on the latest US math syllabus. Please note that App requires internet connection to stream the videos. Algebra I: Solving Equations with an ...
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Windows 95/98
Algebra Sudoku is a mixture of the classical sudoku and algebra. Instead of numbers you fill in the solutions of mathematical equations. For example, the equation might be "z=2z-2", and you should fill in "z=2". All equations to be ...
OS:
The Personal Algebra Tutor is a comprehensive algebra problem solver for solving algebra problems from basic math through college algebra and preCalculus. The user can enter his/her own problems to get step-by-step solutions. Additional topics generally ...
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Algebra WorkBench (AWB), a mathemathical application, an optimised unification designed to provide users with the most homogenous work environment possible. You can find the fundamental elements of AWB listed in the order in which they appear in the ...
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Prealgebra and Introductory Algebra is an application which enables students to have unlimited practice and homework problems. It also has access to definitions, objectives, and examples like a textbook. The matching table of contents makes it easy to ...
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Grid Algebra is a new visual and kinaesthetic way to learn number concepts and pre-algebra at KS2 and to learn about number and algebra for KS3 and KS4. What is more, it supports more developed algebra ideas as features: - mental arithmetic |
Do you want to further your study of science but worry that you lack confidence in mathematics? Then this course could be for you. Mathematical techniques are explained, and worked examples are included throughout the course, but the main emphasis is on providing examples for you to try for yourself.
ManyMathematical techniques are explained, and worked examples are included throughout the course, but the main emphasis is on providing examples for you to try for yourself. ManyThe course assumes some knowledge of arithmetic, but other topics, such as addition and multiplication of fractions, are revised; while algebraic techniques, such as rearranging and combining equations, are taught from first principles. You will also have an introduction to scientific notation, logarithms, radians, trigonometry, differentiation, and some scientific uses of statistics and probability.
Entry
The course is not meant for absolute beginners in mathematics and is not recommended as your first Open University course. It is only one of a number of Level 1 mathematics courses available to you.
The maths in S151 would be excellent preparation for The physical world (S207) or Astronomy (S282). However, it is not an adequate preparation if you intend to go on to Open University physics courses at Level 3 or mathematics courses at Level 2 or 3.
The course assumes that you can add, subtract, multiply and divide positive and negative numbers and understand the use of brackets in numerical calculations. You should know how to express numbers as fractions and decimals and as simple powers (e.g. know that 1000 can be written as 103). You should be able to measure angles in degrees; plot and read data from straight-line graphs; use symbols to represent quantities and substitute numerical values into simple formulae. You will find the course more straightforward if you know how to add and multiply numerical fractions; rearrange very simple algebraic equations and find the gradient of a straight-line graph. But the course does not assume great confidence in these topics and they are all revised. If you have any doubt about the suitability of the course, please contact our Student Registration & Enquiry Service.
If you would like more information about the range of science short courses available you can visit the science short courses website. This site includes a frequently asked questions section and throughout the year details of special regional events are posted here assessment for the course is delivered online via the course website, so you will have to spend considerable amounts of time using a personal computer and the internet.
IfAdobe Portable Document Format (PDF) versions of printed material are available. Some Adobe PDF components may not be available or fully accessible using a screen reader and scientific or diagrammaticStudy support
You can contact a team of expert science study advisers through an online discussion forum, and they will be able to help you with academic questions to do with the course and the assessment. There will also be an online discussion forum that you can use to get in touch with other students.
How to register
To register a place on this course return to the top of the page and use the Click to register button.
Student Reviews
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"Great module for brushing up your maths. At the end of it I considered doing other modules in maths, I regulations or in policy or of financial or other necessity. |
Course Objectives:† Possessing elementary school certification
in mathematics in the state of Kansas means that you can be called upon to
teach any level of mathematics from first through eighth grade.† This is a large amount of mathematical
material, covering everything from basic arithmetic to algebra and basic
geometry.† The primary purpose of this
course is to give you the mathematical understanding you will need to teach
this material.† The specific course
topics have been chosen to enable you to meet the state guidelines as described
in the Kansas Teacher Licensure Standards.
But learning specific mathematical skills is only
one small part of this course.† Far more
important is learning how a mathematician approaches a problem.† The bulk of the course will emphasize logic
and reasoning rather than the rote memorization of algorithms.† This aspect is, all too often, lost in
traditional classroom presentations of mathematics.† The result is the popular misconception that mathematics is
largely separate from the world at large.†
After all, the amount of numerical computation you are called upon to do
in your day-to-day life is rather small.†
But the reasoning skills you learn in the process of doing mathematics
will serve you well in all aspects of life.
Course Requirements:† Your grade in this course will be
based on several factors.† Homework will
be assigned every other class period and will be collected two class periods
after it is assigned.† Thus, if an
assignment is given on a Monday, it will be collected on Friday.† If it is assigned on Wednesday, it will be
collected the following Monday.† There
will also be two in-class exams during the term, plus a final exam.† It is likely that there will be some quizzes
along the way, but I will never give a pop quiz.† There will also be several writing assignments.† In addition, classroom participation will be
taken into account as well.
Studying Groups:† Most students find it helpful to study with
other class members, and I strongly encourage you to do this.† You are free to work together on homework
assignments, but in the end everyone must hand in his own paper.†
Attendance:† This class moves very quickly, so missing
even one day will entail having to catch up on a substantial amount of
material.† Take this into consideration
if you are considering cutting a particular class period.† Generally, I donít take attendance in a
formal way.† But I will certainly be
aware if you miss a substantial number of class periods and, since class
participation is an important feature of the class, it will adversely affect
your grade.
Textbook Reading:† At the end of each class period I will tell
you the portions of the textbook we will be covering in the next class.† It is expected that you will read the text
before coming to class.† Even if you
find the reading difficult you will be in a much better position to understand
the material in class if you have already seen it once before.† Keep in mind that reading mathematics is
different from reading normal literature.†
Thus, even if the reading assignment is only a few pages long, you might
find that it takes you a substantial amount of time to get through it.† Keep that in mind when you are budgeting
your time.
Final Thoughts:† If you have any special needs, and
medical conditions, etc. that will in any way affect your performance in my
class, let me know as soon as possible.†
Also, if for some reason you will have to be absent for an extended
period of time, again, let me know as soon as possible.† Donít be bashful about coming to office
hours during the term, or talking to me after class.† Ultimately, everything I do at the front of the room is done for
your benefit, so it is important to me that I have your feedback along the way. |
Advanced Functions and Modeling is a course intended to give students experience with applied mathematics.
"When am I ever going to use this?" is the question that this course is intended to answer.
We begin by revisiting some of the mathematical models students learned about in Algebra and Geometry, and almost immediately begin using these tools to represent real world phenomenon.
Worried about being bored by seeing the same old stuff? Not to worry!
We have plenty of "new" stuff to explore as well. Univariate statistics and modeling data sets using distributions, probability of compound events, gaming theory, sequences and series, recursion models, and maybe even a little bit of programming!
Glad to have you with us and here's to a fascinating year!
Visit our Class Edmodo site to find announcements, handouts, and other useful information related to AFM: |
Analytic Trigonometry Lesson 5: The Law of SinesLesson 5 in the unit introduces The Law of Sines, Solving AAS, ASA and SSA (The Ambiguous Case) plus applications. The lesson is complete with a Smart Notebook file, an 8-page graphic organizer in the form of a Dinah Zike style "Bound-book foldable" with directions for creating the handout. There is a *.pdf file of the completed lesson also.
Compressed Zip File
Be sure that you have an application to open this file type before downloading and/or purchasing.
1347.94 |
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
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Math 2326, Test II Name _ 1. a. Find the general solution to the following system, for arbitrary a = 1. x y = 1 1 0 a x yanswer:x y= C1 et1 0+ C2 eat1 a1b. For what values of a is (0, 0) a source? (answer: a > 0) c. For what values of a
Chapter FiveBeams and FramesDr. Cesar CarrascoBeams Beams are some of the most common elements in structures. To design a beam, the engineer needs: Shear and bending-moment diagrams Axial force (usually small in beams) Deflection curve Se
Chapter ThreeStatics of Structures ReactionsDr. Cesar CarrascoReactions Structural systems are designed to support and to transfer all loads to the structural connecting systems. The following steps should be followed to calculate reactions:
Chapter NineDeflections of Beams and FramesDr. Cesar CarrascoDeflection of Beams and Frames When a structure is loaded its elements deform These deformations change the shape of the structure Although deformations are generally small, the desi
Chapter TenWork-Energy Methods for Computing DeflectionsDr. Cesar CarrascoWork-Energy Methods Based on the principle of the conservation of energy The work done by a series of forces applied to a structure equals the strain energy stored in the
Chapter TwelveAnalysis of Indeterminate Beams and Frames by the Slope-Deflection MethodDr. Cesar CarrascoSlope-Deflection Method This is a procedure for analyzing indeterminate beams and frames. This is an important method because it is the bas
Chapter SevenArchesDr. Cesar CarrascoArches Arches make efficient use of material because internal forces are mostly axial. Types of arches: a) Three hinged arch. Stable and determinate. b) Two hinged arch. Stable and indeterminate to the fi
Chapter SixCablesDr. Cesar CarrascoCables Cables are constructed with high-strength steel wires. They have a tensile strength four to five times greater than that of structural steel. Their strength to weight ratio makes them attractive for l
Chapter FourTrussesDr. Cesar CarrascoTrusses A truss is a structure composed of slender interconnected elements that usually form triangular patterns. Although joints are usually welded or bolted to a gusset plate they are idealized as frictio
Chapter ElevenAnalysis of Indeterminate Structures by the Flexibility MethodDr. Cesar CarrascoFlexibility Method Also known as the consistent deformations or superposition method Used for the analysis of linear elastic indeterminate structuresFOREWORDThis volume contains reports from three task forces that were established in 2004 as a first step in a strategic planning process designed to guide the University of Texas at El Paso toward its Centennial celebration in 2014. Each of these
DISTINGUISHED ACHIEVEMENT AWARDSThe University of Texas at El Paso GuidelinesI. IntroductionThe University of Texas at El Paso annually presents awards to faculty and staff in recognition of outstanding achievement in the areas of teaching, resea
SRF 980804-06Measuring The RF Critical Field of Pb, Nb, and Nb3SnThomas Hays and Hasan PadamseeLaboratory of Nuclear Studies,Cornell University Ithaca, NY 14853, USAAbstract High peak pulsed power is used to raise the cavity elds well above the
LHC More than just Discoveries Tilman Plehn WBF and SUSY SUSY parameters Markov chains SUSY mapsLHC More than just DiscoveriesTilman PlehnMPI fur Physik & University of Edinburgh Budapest, 6/2007LHC More than just Discoveries Tilman Plehn
Final Project Report to the NYS IPM Program, Agricultural IPM 2000 2001Title: Expanding the Implementation of Integrated Pest Management and IntegratedCropping Management through the Use of Host Farms (public meetings) and Improved Use of CommuniGENERAL CHEMISTRY:CHAPTER:CHAPTER |
We will also give the properties of radicals. Polynomials We will introduce the basics of polynomials in this section including adding, subtracting and multiplying polynomials. Factoring Polynomials This is the most important section of all the preliminaries. |
You will be graded based on your performance from each chapter. Each chapter's possible points earned will total to 100. We will cover about three chapters each quarter.
Textbook Practice Homework <<< 5 points >>>
Homework will be assigned each night as practice with a focus on the odd numbered exercises so that you may find the answers to the exercises and work toward those solutions. It is expected that you will complete these problems and that you will be prepared to work these problems on the board the following day. Practice problems from the text book will not be collected. If it is obvious that you are not prepared or have not done your homework, you will be deducted homework points for each instance. Keep in mind that as we go over the problems in class, students should be following along and as not to copy work. When people become too focused on copying, your mind becomes too limited in comprehending.
Sign-ups Problems <<< 30 = 5 x 2 x 3 points >>>
For each section there will be 5 sign up problems worth 2 points each that you are to work on with the expectation that you will be prepared to present your solution to the class. You will receive full points for simply signing up for these problems. However, if you sign up for a problem that you are unprepared to do, you will automatically be deducted 1 point for each problem that you signed up for. Once called upon, you will present to the class your method and solution.
Quizzes <<< 30 = 10 x 3 points >>>
For each chapter you will be given three 10 point quizzes to be taken alone based on your preparation from your homework problems. Even though correct answers are important, credit is also given based on your procedure.
Tests <<< 25 Points >>>
At the end of each chapter you will be given a chapter test that is mainly multiple-choice in format. Show as much work as possible so that you can earn partial credit on problems with incorrect solutions.
Application Problem <<< 10 = 5 x 2 Points >>>
For each chapter you will be given two problems that may be a little bit more challenging in nature. You should show neatly on paper how to arrive at you solution and provide a final answer to the problem. |
App provides a way for students to study and learn how to identify the coefficients of a function from a graph. Students can choose linear functions, quadratic functions, and absolute value functCalculate solutions (unique, representation of the infinite solutions, or no solution) for linear systems up to 30x30. In addition, students can: enter symbolic data; save and edit up to five constan... More: lessons, discussions, ratings, reviews,...
A TI-NspireTM file that students can use to reflect on the "Make a Mathematical Model" Activity from the Math Forum's Problem Solving and Communication Activity Series. This is designed to ... More: lessons, discussions, ratings, reviews,...
The main objective of this activity is to find an approximation for the value of the mathematical constant e and to apply it to exponential growth and decay problems. To accomplish this, student... More: lessons, discussions, ratings, reviews,...
This packet contains a copy of the original problem used to create the activity, rationale and explanation behind the "Change the Representation" focal activity, and some thoughts on why this activity... More: lessons, discussions, ratings, reviews,...
This activity is intended to provide students with an opportunity to discover a few interesting properties of an ellipse. The first property students will explore forms the basis of the deᤙIn a beach race, contestants must swim to a point along the beach and then run to reach the finish line. Where should I aim to land on the beach so as to minimize my total time for the race? StuTurn your iPad into a wireless whiteboard. Annotate PDF documents and images live. You can now project PDF documents (such as exported PowerPoint or Keynote decks) to a computer on the same local netw... More: lessons, discussions, ratings, reviews,...
Turn your iPad into a wireless whiteboard. Project live sketches to a local computer. The Free Edition of Air Sketch supports basic diagrams, but runs on the same engine as the Full Edition. You can u |
Discrete Math
Discrete mathematics, broadly speaking, is the "study of discrete objects." As opposed to objects that vary smoothly, such as the real numbers, discrete mathematics has been described as the mathematics of countable sets. Because of the absence of an all-encompassing definition, the best way to understand what discrete mathematics entails is to enumerate some of the topics it covers: graph theory, combinatorics, set theory, logic, discrete probability theory, number theory, certain topics in algebra (numerical semigroups and monoids, for instance), discrete geometry, and several topics in game theory.
Of these topics, Princeton offers separate courses on graph theory, combinatorics, logic, discrete geometry, and game theory. Set theory, number theory, probability, and the "discrete" topics in algebra come up in their own right in various other courses, where they can be studied in more depth.
Finally, it should be stated that discrete mathematics is very closely associated with computer science. As a result, many of the topics can be studied as integral parts of either of the two disciplines. In fact, there are a couple of courses offered by Princeton's COS department which are really discrete mathematics courses in disguise. Students majoring in either of the two also often end up taking courses from the other, and as a result there is constant exchange and collaboration between the two departments.
Discrete Math Courses [Show]Discrete Math Courses [Hide] MAT 375: Introduction to Graph Theory
This course, taught by Professor Seymour, serves as the "standard" Princeton introduction to discrete mathematics. The course covers the fundamental theorems and algorithms used in graph theory. Since there is not enough time to build the deeper results in graph theory, the course is based on breadth rather than depth, and therefore goes through a host of topics. These include connectivity, matching, graph coloring, planarity, the celebrated Four Color Theorem, extremal problems, network flows, and many related algorithms which are often of significance to computer science.
Professor Seymour is one of the greatest graph theorists that the world has ever seen, and the course is designed and taught by him; it is, consequently, a unique experience that not many other universities can provide. He uses his own course notes, which have evolved through the last couple of decades, and are notorious for their terse expositions ("Proof: Trivial.") as well as the large amount of material condensed into them. Professor Seymour also recommends Douglas West's classic graph theory textbook, although he rarely consults it after the first lecture.
The course is meant for a wide range of students. Since it assumes no background except with the basics of mathematical reasoning, it is one of the largest departmental courses offered by Princeton Mathematics. Students taking the course range from the mathematics majors who intend to specialize in graph theory to students who need a "theoretical" requirement for their Princeton academic career. A huge contingent of the class is comprised of computer science majors, who are interested in the connections between graph theory and computer science. It is important to note that the course is cross-listed with COS 342, and is therefore also a computer science departmental.
The class starts slowly, but picks up very fast as it goes into more and more material. Although it is almost universally agreed as a "fun" class, doing well can be challenging, since there is a scramble for the higher grades – the class is notorious for yielding medians of 9.8 out of 10 in its weekly problem sets.
The grade is based on eleven problem sets through the semester, and on a ten-problem take-home final exam. The problem sets are instructive, and often end up teaching new material outside of class. Professor Seymour always goes over all the homework problems every week after they are handed in. Collaboration is allowed, and heavily encouraged.
All in all, the course is well-organized, brilliantly taught, and extremely fun and accessible to students of all levels. However, doing well in the course requires hard work and a somewhat substantial time commitment. Collaboration is encouraged and asking the TAs for help is not at all uncommon. MAT 377: Combinatorial Mathematics
This course is taught by Professor van Zwam, and functions as the standard undergraduate introduction to non-graph-theoretic combinatorics. Combinatorics, the theory of "counting," is an indispensable tool and integral component of many areas of mathematics; but more importantly, it has recently, in light of modern research, grown into a fundamental mathematical discipline in its own right. This modern theory relies on deep, well-developed tools, some of which the course gets into. In essence, the course covers over a dozen virtually independent topics illustrating some of the most powerful theorems of modern combinatorics, such as Ramsey Theory, Turan-type theorems, extremal graph theory, probabilistic combinatorics, algebraic combinatorics, and spectral techniques in graph theory.
This course is meant primarily for mathematics majors looking for an introduction to the theory of combinatorics. The class, therefore, is typically much smaller than its "predecessor," MAT 375. Professor van Zwam uses his own notes and supplements them with some of the classic expository texts in combinatorics, such as Peter Cameron's notes or Richard Stanley's book. Students are highly encouraged to take notes during lectures, since they are usually not put up online. Another useful resource is Jacob Fox's notes from the same course, which was taught by him in earlier years.
There are about six problem sets spread evenly through the semester. Each contains about five or six problems, which get steadily more and more challenging. Collaboration, therefore, is an important part of the course. Students have been known to stay up for several nights working on a couple of seemingly impossible problems towards the end. However, this is an effort to introduce students to basic combinatorics research, and is an important part of the course; solutions are discussed in depth after the problems are handed in.
There is a take-home final with six problems, which collectively involve techniques learned throughout the semester. As a recapitulation of these broad techniques, the final is a brilliant but completely reasonable test of what the students are expected to have taken out of the course. Therefore, it is easy to do well on the course as long as a student has attended the lectures and learned the general principles.
An important part of the course is the last two or three weeks, when it departs from the traditional topics taught in similar courses in other universities, and delves into some of the modern research in combinatorics. In particular, the lectures on spectral graph theory and the basic introduction to matroid theory are extremely rewarding, since Professor van Zwam himself is a matroid theorist. There is usually less homework assigned from this part, but the material is wonderfully presented by Professor van Zwam; these last couple of lectures also serve as sufficient background to the graduate course on matroid theory, MAT 595. MAT 378: Game Theory
Professor van Zwam's course on game theory the only class that the mathematics department offers on the subject (there are other classes on game theory offered by other departments). Game theory is the formal mathematical study of strategic decision-making; consequently it deals with a number of scenarios where one person's success depends on others' choices, and therefore choosing the "right" course of action is a complex calculation. Game theory is not entirely a subset of discrete mathematics, since a lot of the more modern results in it are much more continuous in nature; however, given the large discrete component of the discipline, it deserves mention in this category. MAT 584: Incidence Theorems and their Applications
This is Professor Dvir's graduate course on Incidence Theorems and their applications. The titular theorems are a way of formally describing how discrete shapes such as lines, points and various other geometric objects intersect each other. These theorems have recently risen in importance because of their tremendous applications. The course serves as a rigorous introduction to this vast and wonderful theory, proving some of its major results. The course delves into problems such as Szemeredi-Trotter problems ("How many incidences can a set of lines have with a set of points?"), Kakeya problems ("What are the properties of sets in Euclidean space containing line segments in each direction?"), as well as Sylvester-Gallai problems ("Is it possible to have a non-collinear set of points such that a line through any two of them must go through a third?"). The topics covered in this graduate course have far-reaching consequences in some of the most important areas of modern research, such as additive combinatorics, coding theory and computational complexity.
Professor Dvir follows his own excellent notes, which are available on his website. The same page also details some additional readings for the interested reader. The course is aimed primarily at graduate students, although undergraduates with sufficient background in mathematics and computer science are encouraged to try it as well. As with all mathematics graduate courses, the undergraduates have to solve a few problems in order to pass the course, though typically this is more a formality than a stringent requirement.
The course is rewarding but challenging, and any undergraduate student planning on taking it is advised to read up as much background material as possible in order to follow the lectures easily. It also helps to be interested in computer science, as then the motivation behind much of the material becomes evident. MAT 595: Topics in Discrete Mathematics
This graduate topics course is usually offered by Professor Seymour (the matroid theory course has also been offered by Professor van Zwam). The course changes from semester to semester, but is usually one of the three following topics. Matroid Theory: This class is offered by either Professor Seymour or Professor van Zwam, and serves as a rigorous introduction to matroids, which are discrete structures similar to graphs that exhibit properties of rank and linear independence. This theory is young and exciting, and the course covers most of its seminal results in addition to going into current research topics. The instructor's notes are usually used in conjunction with Oxley's classic textbook. Structural Graph Theory – Induced Subgraphs: This course is an introduction to the theory of induced subgraphs, building up gradually to the celebrated 2002 proof of the Strong Perfect Graph Theorem (a graph is perfect if and only if it is a Berge graph). Like its counterpart, the Graph Minors course, this course is about structural graph theory, which is traditionally one of the "hardest" branches of combinatorics, and hence students are expected to be comfortable with long proofs and extremely intricate arguments. Structural Graph Theory – Graph Minors: This course is a fast but intensive run through some of the results of the famous Graph Minors Project of Seymour and Robertson. The course builds up a lot of the theory behind containment relations such as minors, subgraphs, immersions and topological containment, and then goes into structure theorems and many forbidden-minor characterizations. Using pathwidth, treewidth and branchwidth, the course then develops most of the necessary tools for attacking Seymour and Robertson's celebrated Graph Minor Theorem (graphs are well-quasi-ordered under minors), and sketches the proof.
The discrete mathematics graduate course is rewarding in the extreme, since it is taught by the best in the world. Any student planning on taking it, however, should be prepared to put in a lot of time for the problem sets. Some of the homework problems, be warned, have been unsolved and are (still) open.
Another point that should be kept in mind is that knowing the material from MAT 375 is really a pre-requisite to taking this course. The first lecture is sometimes a refresher, but unless a student already knows some standard techniques in graph theory beforehand, even the refresher does not help. This should be kept in mind because of the frenetic nature of the course; it delves into quite advanced material from the second lecture onwards. COS 488: Analytic Combinatorics
This course of Professor Sedgewick's serves as an introduction to one of the most powerful recent techniques in algorithm analysis. The discipline of analytic combinatorics represents many decades of collaboration between Professor Sedgewick and Phillipe Flajolet. Essentially, the course is divided into two halves. In the first half, the course covers techniques from classical combinatorics to tackle "hard" approximation problems that come up in computer science (particularly in the analysis of certain recursion-based algorithms), and then in the second half, it goes into deeper mathematics in order to deal with more general classes of problems by using techniques from complex analysis.
This course is very unique, in that it really is a mathematics class; there is next to no coding, and not much mention of computer science. However, unlike most mathematics classes, it switches gears in the middle, and moves from discrete to continuous mathematics, but with the same end in sight. Not much background is required for the class, though some familiarity with algorithm analysis helps distinctly. Furthermore, a student who knows complex analysis is at a great advantage towards the beginning of the second half of the course. Professor Sedgewick encourages collaboration and is one of the most organized lecturers at Princeton, so the course ends up being accessible to anyone interested in taking it. He is also known to be very generous with his final grades.
Although the "discrete" part of this course is confined to the first half, it is a course worth taking. Professor Sedgewick loves teaching the class, and takes great care to ensure that the content is well understood by everyone. Furthermore, it is useful in simplifying a number of problems that come up a lot in "real-life computer science," and solving them with the aid of the beautiful but counter-intuitive approaches arising from mathematics. |
REQUISITES
Prerequisite:
MATH C152 Systems of Linear Equations
1. systems solution
2. Gauss-Jordan and Gaussian elimination
3. applications
B. Matrices
1. matrix algebra
2. properties of matrices
3. inverse of a matrix
4. applications
C. Determinants
1. properties
2. numerical evaluation
3. relationship with matrices
4. systems of equations
D. The Vector Space R
1. vectors
2. subspaces
3. linear combination of vectors
4. linear dependence and independence
5. bases, dimension, and rank.
E. N-Dimensional Euclidean Space
1. dot product, norm, angle, distance
2. orthonormal vectors, projections.
F. General Vector Spaces
1. generalizing the concept of a vector space
2. inner product spaces
3. applications.
G. Linear Transformations
1. matrix transformations, kernel, range
2. transformations and systems of linear equations
3. coordinate vectors
4. matrix representation of linear transformations
5. applications
H. Eigenvalues and Eigenvectors
1. definition of eigenvalues and eigenvectors
2. computation
3. diagonalization of matrices
4. applications (Use for short answer and essay answers exams.)
A. tests on course content, to include solving equations as well as demonstration of specific skills. B. quizzes (in-class and take-home) to include solving equations as well as demonstration of specific skills. C. group work to analyze and solve application problems.
TEXTS, READINGS, AND MATERIALS: Instructional materials may include but are not limited to |
Introduction to Topology and GeometryPresenting upper graduate level material in an accessible way for undergraduates, this Second Edition strikes a welcome balance between academic rigor and accessibility while covering an unparalleled range of topics, including the elements of projective geometry, conics and the applications and properties of conic selections, cross ratio points of infinity and fundamental transformations of projective geometry, the points of a homography/involution, and more. In addition, this comprehensive book includes numerous exercises and historical notes.... MORE
An easily accessible introduction to over three centuries of innovations in geometry
Praise for the First Edition
". . . a welcome alternative to compartmentalized treatments bound to the old thinking. This clearly written, well-illustrated book supplies sufficient background to be self-contained." —CHOICE
This fully revised new edition offers the most comprehensive coverage of modern geometry currently available at an introductory level. The book strikes a welcome balance between academic rigor and accessibility, providing a complete and cohesive picture of the science with an unparalleled range of topics.
Illustrating modern mathematical topics, Introduction to Topology and Geometry, Second Edition discusses introductory topology, algebraic topology, knot theory, the geometry of surfaces, Riemann geometries, fundamental groups, and differential geometry, which opens the doors to a wealth of applications. With its logical, yet flexible, organization, the Second Edition:
• Explores historical notes interspersed throughout the exposition to provide readers with a feel for how the mathematical disciplines and theorems came into being
• Provides exercises ranging from routine to challenging, allowing readers at varying levels of study to master the concepts and methods
• Contains coverage on the elements of polytope theory, which acquaints readers with an exposition of modern theory
Introduction to Topology and Geometry, Second Edition is an excellent introductory text for topology and geometry courses at the upper-undergraduate level. In addition, the book serves as an ideal reference for professionals interested in gaining a deeper understanding of the topic. |
The 2012 Cengage Learning TeamUP Mathematics Conference was held in Atlanta, Georgia, for instructors of mathematics courses from two year and four year programs. Session topics included incorporating study skills, using video games to increases time on task and understanding, the reform of mathematics curriculum over 50 years, using active learning strategies in the math classroom, the relevance of trigonometry and algebra understand in the calculus course and strategies for transforming students into long line learners. The sessions are valuable for current and prospective teachers of mathematics. |
resource book which looks at the design of mechanisms, for example gears and linkages, through the eyes of a mathematician. There are a wide variety of examples including car steering, anglepoise lamps, bicycles, cine cameras, folding push chairs and the design of robots. Readers are encouraged to make models throughout and to look for further examples in everyday life. Suitable for GCSE, A level, and mathematics/technology/engineering courses in Further Education. |
About AppShopper
Graduate Sequence and Set Practice
iOS iPhone
Graduate Sequence and Set Practice provides students with a variety of challenging word problems that will help them develop a solid foundation of math skills. Graduate Sequence and Set Practice will help students prepare for the math portion of standardized tests, such as the SAT (Scholastic Aptitude Test), and will help improve performance on test day.
A few sample questions are shown in the screenshots. Additional sample questions are listed at the end of this description.
For each application, use the Configure button in the help window to turn the sound and timer on or off. The Solution button in the help window offers three options: 1.Select Rules to see the rules for working with each application. 2.Select Show Solution to see the correct answer. 3.Select Analyze to see a detailed explanation of the answer.
The screenshots show some sample questions. A few more are listed here:
1. Set: In a neighborhood, families have dogs or cats. 14 families have dogs, 7 have cats, and 2 have both. How many families are there in the neighborhood?
2. Arithmetic sequence: The first 3 terms of an arithmetic sequence are 37, 34, and 31. Which term is the first negative term?
3. Geometric sequence: If you add a value to each of these numbers (24, 6, -6), the result is a geometric sequence. What is this value?
4. Specific sequence: The first 2 terms of a sequence are 4 and 8. From the second term, the next term equals the current term divided by the previous term. For instance, the third term is 2, which is 8 / 4. What is the fiftieth term?
Disclaimer: SAT is a registered trademark of the College Entrance Examination Board, which does not sponsor or endorse this product. |
Course Overview
Most students who enter this course are used to calculation-based mathematics, such as algebra, trigonometry, and calculus. The purpose of this course is to help you make the transition to the later math courses in which proofs, logic, language, and notation play an integral role. The prerequisites are a logical mind, enjoyment of patterns, and a willingness to work. Usually completion of Calculus II and your interest are enough.
Content Goals:
facility in interpreting and using mathematical language and notation;
a firm background in elementary logic and practice in reasoning;
experience dealing with sets, functions, relations;
improvement of computer skills, particularly Mathematica;
Skills:
asking good questions;
discovering and writing proofs;
evaluating the proofs of others;
knowing when you are correct, when you are on a useful path, and when you're lost;
This year the course becomes 4 credit hours. The content includes material from my own text, Essentials of Mathematics. Most of your time will be spent on digesting the definitions, axioms, and theorems in the book and proving the theorems. In addition, there will be lab problems from various areas of math. These will help you to expand your mathematical horizons, learn to explore, and develop computer skills. I also encourage you to read the recommended book by Ian Stewart, Letters to a Young Mathematician. Other interesting books are found in additional resources.
Grading
Your grade will be based on the following:
homework
15%
labs
10%
3 tests
10% 15% 15%
paper and presentation
10%
final exam
25%
Homework should consume about 8 hours per week outside of class. The first test will occur at the end of Chapter 1, approximately the week of 9/17. Subsequent tests will be announced a week ahead of time. After each test, you will receive an update on your cumulative grade. Shortly after the first test, you will begin work on the paper. Due toward the end of the semester, it will report on an article you have read. Please see the paper and talk guidelines. Thursdays are lab days, meeting in 205E. Lab due dates are announced with each lab. The final exam is Tuesday 12/11, 4-6 pm.
Policies
Becoming a mathematician involves learning new skills and adopting new habits of mind. The purpose of this course is to gently push you in the right directions. Two of the goals, asking your own questions and dealing with the frustration of not knowing answers immediately, are achieved only when the professor takes a step away. Therefore, my teaching style is to let you explore on your own until you're ready for help. I have not abandoned you, I'm simply transferring to you the responsibility of forming the question.
Class work is subject to some rules that both further our goals and assure that the class runs smoothly.
Read your email regularly, as I sometimes send class announcements that way. Upon request, I can also send confidential grade information to you at your Stetson email address or through Blackboard. You can forward your Stetson email or configure Blackboard for another address. IT can provide help (ext. 7217). If you have special needs, don't hesitate to discuss them, either with me or with the Academic Resources Center. I hope you're looking forward to the semester. |
Book Description: Certain contemporary mathematical problems are of particular interest to teachers and students because their origin lies in mathematics covered in the elementary school curriculum and their development can be traced through high school, college, and university level mathematics. This book is intended to provide a source for the mathematics (from beginning to advanced) needed to understand the emergence and evolution of five of these problems: The Four Numbers Problem, Rational Right Triangles, Lattice Point Geometry, Rational Approximation, and Dissection. Each chapter begins with the elementary geometry and number theory at the source of the problem, and proceeds (with the exception of the first problem) to a discussion of important results in current research. The introduction to each chapter summarizes the contents of its various sections, as well as the background required. The book is intended for students and teachers of mathematics from high school through graduate school. It should also be of interest to working mathematicians who are curious about mathematical results in fields other than their own. It can be used by teachers at all of the above mentioned levels for the enhancement of standard curriculum materials or extra-curricular projects. |
What will be studied? Mathematics at AS and Advanced GCE is a course worth studying not only as a supporting subject for the physical and social sciences, but in its own right. It is challenging but interesting. It builds on work you will have met at GCSE, but also involves new ideas produced by some of the greatest minds of the last millennium.
AS level mathematics consists of three modules. Two of these are Core modules and the third is in Statistics.
In module Core 1 we revisit many ideas already met at GCSE but they are extended further. For instance quadratic equations, simultaneous equations and inequalities are all covered again but in greater depth. The geometry of straight lines is taken further and a new approach to mathematical sequences is given. An important branch of mathematics called Calculus is introduced for the first time.
Module Core 2 is an extension of Core 1. GCSE trigonometry is reviewed and then extended further to include solving easy trigonometric equations. Radian measure is introduced. Geometry is now extended to circles. Exponential and logarithmic functions are introduced.
Statistics 1 is an applied mathematics module and some of it will be familiar from the work covered in GCSE mathematics. When you study statistics you will learn how to analyse and summarise numerical data in order to arrive at conclusions about it. You will extend the range of probability problems that you looked at in GCSE using the new mathematical techniques learnt in the pure mathematics units. Many of the ideas in this part of the course have applications in a wide range of other fields, from assessing what your car insurance is going to cost to how likely it is that the Earth will be hit by a comet in the next few years. Many of the techniques are used in sciences and social sciences. Even if you are not going on to study or work in these fields, in today's society we are bombarded with information (or data) and the statistics units will give you useful tools for looking at this information critically and efficiently. Three more modules are studied for A2 Mathematics. Core 3 and Core 4 build upon the ideas already studied in Core 1 and Core 2. However there are several new topics which do not rely on the previous modules. These include Numerical Methods, Parametric Equations and Vectors.
The third module is Mechanics 1, another applied mathematics module. Mechanics deals with the action of forces on objects. It is therefore concerned with many everyday situations, e.g. the motion of cars, the flight of a cricket ball through the air, the stresses in bridges, the motion of the earth around the sun. Such problems have to be simplified or modelled to make them capable of solution using relatively simple mathematics. The study of one or more of the Mechanics units will enable you to use the mathematical techniques which you learn in the Core units to help you to produce solutions to these problems. Many of the ideas you will meet in the course form an almost essential introduction to such important modern fields of study such as cybernetics, robotics, bio-mechanics and sports science, as well as the more traditional areas of engineering and physics.
What assessment is there? Each module is assessed by a one and a half hour written examination. Students may re-sit an examination to try to improve their mark. There is no coursework element.
Where will it take me? Advanced GCE mathematics is a much sought-after qualification for entry to a wide variety of full-time courses in higher education. There are also many areas of employment that see a Mathematics Advanced GCE as an important qualification and it is often a requirement for the vocational qualifications related to these areas. Higher Education courses or careers that either require Advanced GCE mathematics or are strongly related include: economics medicine architecture engineering accountancy teaching psychology physics computing information and communication technology. If you wanted to continue your study of mathematics after Advanced GCE you could follow a course in mathematics at degree level or even continue further as a postgraduate and get involved in mathematical research. People entering today's most lucrative industries such as IT, banking and the stock market need to be confident using mathematics on a daily basis. To be sure of this, many employers still look for a traditional mathematics A-level qualification. Researchers at the London School of Economics have recently found that people who have studied mathematics can expect to earn up to 11% more than their colleagues, even in the same job! Even in areas where pure mathematics isn't required, other mathematics skills learned at AS and A level, such as logical thinking, problem solving and statistical analysis, are often very desirable in the workplace. Mathematics is the new lingua franca of commerce, business and even journalism.
For more information please see Mr J. Thompson in the Maths Department. |
Elementary and Intermediate Algebra (Hardcover), 1st Edition
This book has been designed to present the material, reinforce major concepts, and test student understanding using a variety of instructional methods and features. The authors had seven objectives in writing this text: 1.) To teach students the language of algebra--how to read, write, speak, and think mathematically (Graphics, examples, and Study Sets throughout text emphasize key phrase and translation); 2.) To use a group of fundamental algebraic concepts as the foundation of the text (introduce equations, variables, problem solving, functions, and graphing in Chapter 1) and constantly reinforce those major concepts of algebra throughout the text (Key Concept feature); 3.) To aid student comprehension and confidence by introducing concepts in one context and revisiting throughout the book in other contexts (coverage of problem solving is one good example); 4.) To gain and keep students' attention through creative applications (See any Applications section in Study Sets), an interactive approach to instruction (Self Checks), and a visually appealing design; 5.) To have top-notch problem sets (purposefully named Study Sets, not Problem or Exercise Sets) that break learning into smaller pieces so that students do not become overwhelmed; 6.) To constantly show how the material being studied can be used to solve real-world problems; 7.) To blend traditional and reform instructional approaches--from vocabulary, practice, and well-defined pedagogy to place an emphasis on problem solving, reasoning, communicating, and technology (Study Sets |
College Algebra - 2nd edition
ISBN13:978-0201347111 ISBN10: 0201347113 This edition has also been released as: ISBN13: 978-0201383980 ISBN10: 0201383985
Summary: The Dugopolski Precalculus series for 1999 is technology optional. With this approach, teachers will be able to w...show moreho will study additional mathematics, this text will provide the skills, understanding and insights necessary for success in future courses. For those students who will not pursue further mathematics, the extensive emphasis on applications and modeling will demonstrate the usefulness and applicability of mathematics in today's world. Additionally, the focus on problem solving that is a hallmark of this text provides numerous opportunities for students to reason and think their way through problem situations. The mathematics presented here is interesting, useful, and worth studying. One of the author's principal goals in writing this text was to get students to feel the same way. New! Linking Concepts This new feature is located at the end of nearly every exercise set. It is a multipart exercise or exploration that can be used for individual or group work. The idea of this feature is to use a concept from the current section along with concepts from previous sections, and ask questions that help students see the links among various concepts. Some parts of these questions are open-ended, and require somewhat more thought than standard exercises. Answers to this feature are given only in the Instructor's Solutions Manual.
New! Applications Hundreds of new exercises have been added to the exercise sets, most based on and involving applications of real-world situations. The emphasis of the new exercises is on understanding concepts and relationships.
New! Exercise Sets The exercise sets have been examined carefully to ensure that the exercises range from easy to challenging, and are arranged in order of increasing difficulty. Many new exercises require a graphing calculator.
New! Regression Problems Many new regression problems have been included in the text, so that students can start with real data, and use a calculator to obtain mathematical models of real problem situations.
New! Graphing Calculator Exercises Optional exercises that require a graphing calculator are now located in more natural positions in the exercises rather than at the end of the exercise sets as in first edition. The exercises are optional and are marked with a graphing calculator icon.
New! Graphing Calculator Discussions Optional graphing calculator discussions have been integrated into the text, and are set off with graphing calculator icons so that they can be easily skipped by those not using this technology.
New! Web Site A new Web site has been established that is designed to increase student success in the course by offering section-by-section tutorial help, enhancement of text group projects, downloadable TI programs and author tips. An icon alerts students to when this site would be useful. The site will also be helpful to instructors by providing useful resources for teaching a precalculus course.
Chapter Opener Each chapter begins with a Chapter Opener that discusses a real-world situation in which the mathematics of the chapter is used. Examples and exercises that relate back to the opener are included within the chapter.
Index of Applications The many applications contained within the text are listed in an Index of Applications that immediately follows the Table of Contents. The applications are page referenced and grouped by subject matter.
For Thought Each exercise set begins with a set of true or false questions that review the basic concepts in that section, help check student understanding before beginning the exercises, and offer opportunities for writing and/or discussion.
Highlights This end-of-chapter feature presents an overview of each section of the chapter and is a useful summary of the basic information that students should have mastered in that chapter.
Chapter Review Exercises These exercises are designed to review the chapter, without reference to the individual sections, and prepare students for the Chapter Test.
Chapter Test The problems in the Chapter Test are designed to help students measure their readiness for a classroom test, and instructors may use them as a model for their own end of chapter tests.
Tying It All Together This is a review of selected concepts from the present and prior chapters, and requires students to integrate multiple concepts and skills.
Content Changes
Revised Chapter P This chapter contains prerequisite material on real numbers, rules of exponents, factoring, and simplifying expressions. Basic linear, quadratic, and absolute value equations and inequalities are covered in Chapter 1. Some sections from both of these chapters may be omitted depending on the preparation level of the students.
New! Revised Chapter 3 Quadratic type equations, equations with rational exponents or radicals, and more complicated absolute value equations now occur in Section 3.5, following the theory of polynomial equations, Section 3.4. Because some of these equations are polynomial equations, they will be better understood after the theory of polynomial equations has been studied.
New! Parametric Equations A new section on parametric equations has been added to Chapter 7.
New! Vector Dot Products Material on vector dot products has been added to the coverage of vectors in Chapter 7GreenEarthBooks Portland, OR
CD Missing. Light every |
All our staff are skilled at helping students learn and use maths on their own. We can help you find the key concepts you need to know in order to solve a problem, interpret what your course materials say, and identify any gaps in your assumed knowledge. We are particularly experienced in the concepts in first-year level courses, but can still help in the above ways for courses we are unfamiliar with. Finally, we can also provide useful handouts, offer general advice on study skills, or give you fun activities to try if you are bored.
So the short answer is: "Try us out!"
Statistics relating to a research project:
We are happy to discuss your statistics, but we prefer you email us on [email protected] to make an appointment first, since this is often a complex discussion. Also, it is important to note that we are not professional statisticians, so it can happen that we may not know the correct statistical procedures you need to use, and even if we do we can only give you general advice. |
Help
There is a substantial research literature that suggests learning in mathematics can be achieved by reading worked-out examples. WebGraphing.com goes one step further: it strives to jump-start students to learn mathematics by reading worked-out examples of their own choosing.
Unlike other web sites dedicated to mathematics, WebGraphing.com delivers real-time, step-by-step answers to challenging mathematics problems. There are a number of unique, patented features that make our calculators easier to use and more powerful than other graphing calculators. In comparison, our calculators take more of the grunt work out of demanding computations that contribute very little either to student learning or teacher productivity.
WebGraphing.com began operations in 2003. On average, we receive over 8,000 daily visitors from over 100 countries. We currently have over 150,000 members comprised of students, teachers and parents. This represents a lot of learning of mathematics, checking answers, copying publication-quality graphs, and mathematics exploration.
WebGraphing.com is the brainchild of Barry Cherkas (also known as pskinner on the Forum), a Professor of Mathematics holding a joint faculty appointment with the Department of Mathematics & Statistics at Hunter College and the Ph.D. Program in Urban Education at the City University of New York Graduate Center.
Professor Cherkas has received numerous grants and written many articles in mathematics and mathematics education, including an article related to graphing: "Finding polynomial and rational function turning points in precalculus," which appeared in the International Journal of Computers for Mathematical Learning, Vol. 8, No. 2, 2003, 215-234 Computer Math Snapshots Section. He has also written a book on using technology to learn precalculus: "Precalculus: Anticipating Calculus Using Mathematica® Labs," 2002, Jamaica, New York: Euler Press. More recently, he is a coauthor (with Dr. Rachael Welder) of the chapter Interactive Web-based Tools for Learning Mathematics: Best Practices appearing in the 2011 IGI Global publication, Teaching Mathematics Online: Emergent Technologies and Methodologies (edited by Dr. Angel A. Juan, Maria A. Hertas, Sven Trenholm and Cristina Steegman.)
Professor Cherkas welcomes any feedback and suggestions through the contact form.
Just like a math textbook, every once in a while we publish an error. If you think you've come across an error, please let us know. We'll get back to you with the correct solution. |
Fundamentals With Elements of Algebra
9780759310001
ISBN:
0759310009
Pub Date: 2002 Publisher: Cengage Learning
Summary: This student-friendly and non-traditional text provides a solid foundation in algebra concepts before introducing signed numbers, helping to build student confidence. Conversational so that students will actually read it, yet mathematically accurate, this text helps students overcome their fear and dislike of mathematics, develops critical thinking and decision-making skills, and prepares them for subsequent courses |
MATH 2500
MATHEMATICAL STRUCTURES (4 cr.)
This course covers the real number system and its operations; patterns and relations, number sense, and number theory; and space and shape, data collection, randomness and uncertainty, with a special emphasis on problem solving and communication. This course is designed to fulfill the Minnesota Board of Teaching's requirements for grades K-5 teachers of mathematics for elementary education majors. Does not fulfill liberal arts core requirement in mathematics/statistics. Offered every winter semester. Also offered in the Weekend Program. Prerequisites: High school higher algebra and appropriate level on mathematics/statistics placement assessment or ACT math score. |
Speaker's Bureau
The Road to Success in College Mathematics: Important Study Skills We Should Teach
Description:
Ninety-five percent of university math students have never been taught techniques of studying mathematics. Learn techniques for teaching your students methods of studying mathematics so that they will be more likely to succeed in their college math courses. |
This course aims to introduce the basic concepts and techniques of calculus, ordinary differential equations and linear algebra to the students who have not studied AS Level Applied Mathematics, or Further Mathematics, or Mathematics and Statistics, or Mathematics with Applications, or Pure Mathematics, or Statistics, or AL Applied Mathematics, or Further Mathematics, or Pure Mathematics in their secondary schools. It trains students skills in logical thinking.
Course Intended Learning Outcomes (CILOs) Upon successful completion of this course, students should be able to:
develop simple mathematical models through single variable calculus and ordinary differential equations, and apply to a range of application problems in finance.
2
5.
the combination of CILOs 1-4
3ILO No.
Hours/week
Learning through teaching is primarily based on lectures.
1--5
26 hours in total
Learning through tutorials is primarily based on interactive problem solving allowing instant feedback.
1
4 hours
2
4 hours
3
3 hours
4
2 hours
Learning through take-home assignments helps students understand basic concepts and techniques of single variable calculus, ordinary differential equations and basic linear algebra, and some applications in finance.
1--5
after-class
Learning through online examples for applications helps students apply mathematical and computational methods to some application problems in finance.
4
after-class
Learning activities in Math Help Centre provides students extra help.
2
70% Examination (Duration: 2hours2
15-30%
Questions are designed for the first part of the course to see how well the students have learned concepts and techniques of single variable calculus.
Hand-in assignments
1--4
0-15%
These are skills based assessment to see whether the students are familiar with concepts and techniques of single variable calculus, ordinary differential equations and basic linear algebra and some applications in finance.
Examination
5
70%
Examination questions are designed to see how far students have achieved their intended learning outcomes. Questions will primarily be skills and understanding based to assess the student's versatility in single variable calculus and basic linear algebra.
Formative take-home assignments
1--4
0%
The assignments provide students chances to demonstrate their achievements on single variable calculus, ordinary differential equations and basic linear algebra and their applications in finance learned in this course.
Grading of Student Achievement: Refer to Grading of Courses in the Academic Regulations |
This playlist is for my students to use on the first day of their introduction to functions week.
All credit is passed on to Melissa Jaeger who posted this at algebra 4 all. Thank you! To download this lesson plan for ...
A-CED.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
This playlist will... |
Biological Sciences
Biology: One Equation at a Time[Full]
John Berges, Associate Professor
Course: BIO SCI 194, SEM 001
Class Number: 26398
Credits: 3 NS
Time: TR 3:00 - 4:00 PM
Place: TBA
Course Description:
Biology has been described as "the ideal major for the scientifically-inclined but mathematically-challenged," but paradoxically, many of the most exciting recent discoveries in biology have relied on application of mathematical techniques. This seminar is intended to develop mathematical literacy among biology students, but also to introduce students of more mathematically-oriented sciences to the important applications of mathematics in biological sciences, ranging from medicine to marine biology. Goals of the seminar include: developing an appreciation of the critical importance of mathematics in all areas of biology, improving understanding of the application of specific mathematical approaches in biology, increasing confidence in quantitative problem-solving skills.
Work Involved:
The seminar explores critical biological questions (chosen by the class) using relatively simple equations. Only basic mathematical skills and biological background are assumed. Our sessions involve in-class experiments, interactive problem-solving (often use computers), group work, and discussion. The course operates in a 'hybrid' format with weekly assignments (generally involving on-line activities) and online discussions. Short field-trips to biology research labs will also be organized. Grading is based on weekly assignments (50%), participation in in-class and on-line discussions (10%), and a final term assignment (40%); there are no formal examinations.
Sample Reading:
Most of the equations are somewhat more advanced than what we will cover in the course, but it captures the flavor.
About the Instructor:
John Berges holds degrees in Marine Biology and Oceanography and has studied marine and freshwater ecosystems ranging from the Canadian High Arctic to the Great Barrier Reef in Australia. In Canada, N. Ireland and the U.S., he has tried to convince biology students that mathematics can be fun; his eight-year old son and his cat remain skeptical. John has mixed mathematical abilities: he does his own taxes and has memorized many biologically-important mathematical constants, but struggles to program his MP3 player and has trouble remembering his cell phone number. |
Dogue PrealgebraPolynomials in the operations are reviewed, with more challenging examples included. Polynomial division (long and synthetic) is covered in Algebra 2. Occasionally, some Algebra 1 classes do cover the long division, in addition to division by a monomialI have taken the following relevant courses in high school and college: European History, Earth Science, U.S. Government, U.S. History, Sociology, Psychology, Human Geography, English Language, English Literature, Spanish 1,2,3,4, and AP, Political Science, International Relations, Microeconomics, and Macroeconomics |
This interactive geometry course is a computer/classroom curriculum that comes with an install CD-ROM, a text in workbook form, a homework helper, and student assignments. It covers all of geometry and early trigonometry--from basic area and perimeter to sine, cosine, tangent, and isometric drawings.
Once you've installed the computer lab on your computer, your child will work on it for typically two days a week, and the program will tailor itself to the student's individual needs. The remainder of the week would be spent on workbook exercises and tests. A very helpful aspect of the curriculum is the Teacher's Toolkit, which provides detailed reports and allows the teacher to track student progress (e.g., the number of hints used and the time involved). In the Text Investigations, the student is required to explain the answers and formulas in complete sentences; and at the end of the week, the student uses a "writing prompt" to produce a written explanation of what was learned in that chapter.
On the negative side, answers are provided only for the weekly tests, not for the assignments and text investigations. In addition, the computer lab numbering does not correspond to that of the student text. Lesson 2.6 in the text is Lesson 11 on the computer.
We feel this program would be best suited for a small cottage school or a homeschool co-op situation where the teacher has an understanding of geometry.
Product review by Colton Dumont, The Old Schoolhouse Magazine, LLC, June 2007 |
Introduction
This book—which can be used alone, in combination with the LearningExpress publication, Practical Math Success in 20 Minutes a Day, or along with another basic math text of your choice—will give you practice in dealing with whole numbers, fractions, decimals, percentages, basic algebra, and basic geometry. It is designed for individuals working on their own, and for teachers or tutors helping students learn the basics. Practice on 1001 math problems should help alleviate math anxiety, too!
A
re you frightened of mathematics? You're not alone. By the time I was nine, I had developed a full-blown phobia. In fact, my most horrible moments in grade school took place right before an arithmetic test. My terror—and avoidance—lasted well into adulthood, until the day I landed a job with a social service agency and was given the task of figuring budgets, which involved knowing how to do percentages. I might just as well have been asked to decipher the strange squiggles incised on the nose-cone of an alien spaceship. I decided I'd better...
[continues] |
Math Competition LinksAmerican Mathematics Contest 8 (Middle School) The AMC 8 is a 25 question, 40 minute multiple choice examination in junior high school (middle school) mathematics designed to promote the development and enhancement of problem solving skills. The examination provides an opportunity to apply the concepts taught at the junior high level to problems that not only range from easy to difficult but also cover a wide range of applications.
American Mathematics Contest 10 (Secondary Grades) The AMC 10 is a 25-question, 75-minute multiple choice examination in secondary school mathematics containing problems which can be understood and solved with pre-calculus concepts. Calculators are allowed. The main purpose of the AMC 10 is to spur interest in mathematics and to develop talent through the excitement of solving challenging problems in a timed multiple-choice format. The problems range from the very easy to the extremely difficult.
American Mathematics Contest 12 (Secondary Grades) The AMC 12 is a 25-question, 75-minute multiple choice examination in secondary school mathematics containing problems which can be understood and solved with pre-calculus concepts. Calculators are allowed. The main purpose of the AMC 12 is to spur interest in mathematics and to develop talent through solving challenging problems in a timed multiple-choice format. Because the AMC 12 covers such a broad spectrum of knowledge and ability there is a wide range of scores. The National Honor Roll cutoff score, 100 out of 150 possible points, is typically attained or surpassed by fewer than 3% of all participants. The AMC 12 is one in a series of examinations (followed in the United States by the American Invitational Examination and the USA Mathematical Olympiad) that culminate in participation in the International Mathematical Olympiad, the most prestigious and difficult secondary mathematics examination in the world.
The Mandelbrot Competition (Secondary Grades) In those ten years the contest has grown to two divisions encompassing students from across the United States as well as from several foreign countries. Nearly half of the competitors in the USA Math Olympiad in the last couple of years have been Mandelbrot competitors. The Mandelbrot Competition is split into two divisions: Division A for more advanced problem solvers and Division B for less experienced students.
Mathcounts (Grades 7-8) Each year, more than 500,000 students participate in MATHCOUNTS at the school level. Those who do tell us that their experience as a "mathlete" is often one of the most memorable and fun experiences of their middle school years.
Math Problems of the Week (Grades K-12) The Problem of the Week is an educational web site that originates at the University of Mississippi. All the prizes are generously donated by CASIO electronics. All contest winners are chosen randomly from the pool of contestants that successfully solve that week's problem. |
Test authoring mathematics software offers 35126 algebraic problems with answers and solutions and easy-to-use test authoring options. Algebra problems from basic to advanced are arranged by complexity and solution methods and correspond to linear, quadratic, cubic, reciprocal, biquadratic and fractional expressions, identities, equations and inequalities. The software enables users to prepare math tests, homeworks, quizzes and exams of varied complexity literally in a minute, and generates three variants around each prepared test. Tests with or without the solutions can be printed out. A number of variant tests are ready for students to review and reinforce their math skills. The software supports bilingual interface and a number of interface styles. Free fully functional trial software version is available
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Sample chapters for download
About the book
Mathematics for Australia 10 has been designed and written for the Australian
Curriculum. The textbook covers all of the content outlined in the Year 10 curriculum.
This textbook is best used in conjunction with the related year levels in our 'Mathematics
for Australia' series.
The textbook and interactive student CD provide an engaging and structured package,
allowing students to explore and develop their confidence in mathematics. The material is presented in a clear, easy-to-follow style, free from unnecessary distractions, while effort
has been made to contextualise questions so that students can relate concepts to everyday
use.
The book contains a variety of exercises, ranging from basic to advanced, to cater for a
range of student abilities and interests. Plenty of lower level questions are included,
allowing students to improve their skills.
Each chapter begins with an Opening Problem, offering an insight into the application of
the mathematics that will be studied in the chapter. Important information and key notes
are highlighted, while worked examples provide step-by-step instructions with concise
and relevant explanations. Discussions, Activities, Investigations, Puzzles, and Research
exercises are used throughout the chapters to develop understanding, problem solving,
and reasoning, within an interactive environment.
Extensive Review Sets are located at the end of each chapter, comprising a range of
question types including short answer, extended response, and multiple choice.
Graphics calculator instructions are provided throughout the book to help students build
an understanding of the technology. Instructions are provided for the Casio fx-9860G
Plus, TI-84 Plus, and TI- spire calculator models.
The accompanying CD contains specially designed SELF TUTOR software. Click on any
worked example throughout the book to activate a teacher's voice which will explain each
step in the worked example. SELF TUTOR is an excellent tool for students who have
been absent from class and for those who need extra revision and practice.
In addition to SELF TUTOR, the interactive CD contains links to geometry software,
statistics packages, demonstrations, calculator instructions, and a range of printable
worksheets, tables, spreadsheets and diagrams, allowing teachers to demonstrate concepts
and students to experiment for themselves.
Using the Interactive CD
The interactive CD is ideal for independent study.
Students can revisit concepts taught in class and undertake their own revision and practice. The CD also has the text of the book, allowing students to leave the textbook at school and keep the CD at home.
By clicking on the relevant icon, a range of new interactive features can be accessed:
Self Tutor
Self Tutor is an exciting feature of this book.
The icon on each worked example denotes an active link on the CD.
Students can revisit concepts taught in class and undertake their own revision and practice. The CD also has the text of the book, allowing students to leave the textbook at school and keep the CD at home.
Simply click on the (or anywhere in the example box) to access the worked example, with a teacher's voice explaining each step necessary to reach the answer.
Play any line as often as you like. See how the basic processes come alive using movement and colour on the screen. Ideal for students who have missed lessons or need extra help. |
work deals with Numerical Algorithms. This unique book provides concepts and background necessary to understand and build algorithms for computing the elementary functions - sine, cosine, tangent, exponentials, and logarithms. The author presents and structures the algorithms, hardware-oriented as well as software-oriented, and also discusses issues related to accurate floating-point implementation. The purpose is not to give "cookbook recipes" that allow one to implement a given function, but rather to provide the reader with tools necessary to build or adapt algorithms for their specific computing environment. This expanded second edition contains a number of revisions and additions, which incorporate numerous new results obtained during the last few years. Graduate and advanced undergraduate students, professionals, and researchers in scientific computing, numerical analysis, software engineering, and computer engineering will find the book a useful reference and resource. less |
Introduction
Arapahoe High School will be offering one section of Algebra 1 next year that will be taught using a "flipped classroom" approach. This class covers the same curriculum and standards as every other Algebra 1 section at AHS, but the way class time and homework are structured will be different. Instead of the more typical math class where the lecture is presented in class and then students do practice for homework, this class will use class time for inquiry and practice and have the students watch the lecture for homework. This is the third year we have offered this class, but since there has been a lot of press around Khan Academy lately (60 Minutes, TED Talk), we wanted to explain what our class looks like (it's similar to Khan Academy in some ways, yet different in some important ways).
In a traditional math classroom approach, a teacher might briefly go over the previous night's homework, lecture for a good part of the class period, and then students would be assigned 15-30 homework problems. Students might have some time to get started on those problems in class, but then the rest would need to be completed as homework. This works very well for many students, but the flipped approach works in a slightly different way.
The idea behind this approach is pretty simple. For some students, listening to a lecture in Algebra class and then doing homework at home is somewhat problematic. If they get home and are struggling with the homework, there is often no one there who can help them. As a result, they can spend a lot of time on the homework, often reinforcing misunderstandings of concepts and frequently getting very frustrated. But now, because of the technology available to us, we can "flip" the traditional classroom model. Students can now watch the lecture at home (typically an 8-10 minute video, one to two videos per week) as homework and do the traditional "homework" at school.
Here are some reasons that some students might find this approach better. First, students have more control over the time and place that they watch the lecture. If watching the lecture right after school when they get home works best for them, great. If watching it at school during an unscheduled hour works for them (with headphones), then do it then. If the best time for a particular student to work on this is at 10:00 pm, then more power to them. They can choose the time and location that works best for them.
Second, students have much more control over the pace of the lecture. They can pause the video at any time to study what's on the screen, and they can replay part or the entire lecture any time they want. So a student that typically "gets it" the first time they hear it can move on to other things and not have to listen to a teacher repeat various parts of the lecture for other students in the class. On the other hand, students that need more time to process, or need multiple repetitions of examples, can control that without the teacher needing to move on to other topics. (Depending on the Algebra topic, your student might be both kinds of students at different times.) And all students can go back to videos they've already watched if they need to review a particular topic.
Third, students are no longer practicing in isolation. They now have the opportunity to do the traditional "homework" practice problems in class, where they have the teacher and other students available to help them. If they don't understand something they no longer have to struggle with it on their own at home and possibly get frustrated because they know they can't get help until the next day (if the teacher has time). Now they are practicing together, in class, with the support of the teacher.
Finally, this approach also frees up class time to not only practice but to explore mathematics. Teachers often feel pressed to cover the Algebra curriculum in the time we have. By shifting the lectures to outside of class, it frees up class time to practice mathematical inquiry. It allows us time to explore, question and investigate the mathematics, which is not only more interesting for students but leads to a deeper understanding.
Inquiry-->Explain-->Apply and Bloom's Taxonomy
This is an attempt to leverage technology to address some of the shortcomings of the traditional approach. For years educators have worked to move students to higher levels of thinking on Bloom's Taxonomy. Here is the revised taxonomy:
Typically students have spent much of class time at the lower levels of Bloom's taxonomy, concentrating on remembering, understanding and perhaps applying. If they ever get the chance to move to the higher levels of analyzing, evaluating and creating, it has been done on their own time. The flipped classroom approach tries to "flip" this as well. We try to leverage the technology to allow students to concentrate on the remembering, understanding and a bit of applying outside of class, and then utilize our time together in class to work more on analyzing, evaluating and creating. (That's not set in stone, though, we do some of each in both settings.)
What It Looks Like in Practice
What we do each day varies, but here's what a typical lesson cycle might look like in this class.
Class typically begins with "openers" – a few problems that review something we've just learned and/or leads into the new topic (example pdf).
Then if it's our first day on a topic, we'd begin with some inquiry around that topic (this is the "inquiry" phase). This might include students doing an experiment, gathering some data and trying to form a conclusion (example pdf), or it might be some guided inquiry around a mathematical idea (example pdf). The initial inquiry portion might last just one class period, or it might last several, but it's designed to have the students begin to develop an intuitive feel for the concept and begin to construct their own understanding of it.
After the initial inquiry phase in class, students then might watch a video at home ("explain" phase). These videos (example) replicate what a typical lecture in class might have looked like several years ago (albeit somewhat shorter). Each video is composed of three parts (often referred to in education as "I do," "we do," and "you do." First is the explanation phase, where I explain the topic step-by-step with examples ("I do"). Second is the guided practice part, where students are guided through several examples to solidify their understanding ("we do"). Finally students do a self-check section ("you do"), where they are given several problems, asked to pause the video and work them out on their own, and then resume the video to see the worked out solutions. All of the videos are available via YouTube or for download.
Students then return to class where we continue to practice and apply the mathematics ("apply" phase). They will also have additional practice opportunities outside of class via various online or print sources should they need it, and they of course can always come in for help or receive help from me electronically (email, Skype, chat, text, etc.).
The Technology We Use
We use a variety of technologies in this class, and each student will use a variety of their own technology. There is no specific hardware requirement for this class (other than a scientific or graphing calculator which is true of every AHS Algebra class), but students must have high-speed access to the Internet at home. It doesn't matter whether they have a PC or a Mac (or other), desktop or laptop, brand new or relatively old computer – as long as it works reasonably well and can access the Internet at reasonable speeds.
For Homework and Pre-Assessments: LPS Moodle (any modern web browser).
Optional: Students can use things like Skype to contact me (webcam, microphone), and if they have a text-capable cell phone we can communicate via text as well.
Moodle
Moodle is an open-source course management system that allows me to "collect" homework from students and to pre-assess them online without having to use valuable class time. While Moodle is very powerful, we use just a small portion of it and it's pretty straightforward for students. Here's a screenshot of the main course page in Moodle to give you an idea of what it looks like (students each have an individual login).
Video Homework
When students watch a video and complete the two or three self-check problems in their notebooks, they then login to the Moodle and simply enter their answers.
This allows me to quickly see that the student is completing the video without using valuable class time. (Since the video completely works out the self-check problems, this is graded on completion only.)
Pre-Assessments
Other than the midterm and the final exam, each assessment in Flipped Algebra is over one concept at a time (this is often referred to as standards-based-grading – see assessment/grading below). At least two class days before each assessment students will take a short online pre-assessment on the Moodle (as a homework assignment). This pre-assessment is typically only two or three questions (just enough to show me if they understand the various nuances of the particular concept). After they submit their answers they will see the problems fully worked out, including steps and explanations.
These pre-assessments are graded on completion only, and students can take the pre-assessment as many times as they like. This gives students a great idea of what they understand – and what they don't – before taking the actual assessment, so it gives them time to get help before taking the graded assessment.
Other
Students will occasionally have other short assignments on the Moodle, sometimes a couple of homework problems or perhaps a reflection or explanation problem.
Class Blog
Everything is organized through the class blog (2011-12 version). Each day class meets a blog entry is posted that summarizes what we did that day (you can subscribe via email or RSS). We have a Smart Board in our classroom so the openers and the lesson we do each day are captured and posted as PDFs. Then whatever homework they might have is listed (could be completing a video, or a pre-assessment, or preparing for an assessment, etc.).
Assessment/Grading
Initial assessment is done in class. Students are assessed over the essential skills in Algebra I. Because Algebra is skill-based, the class uses a modified form of standards-based-grading (modified because there is still an overall grade for the class). Students are assessed frequently with short assessments over discrete standards. Each skills assessment is scored using the following five-point students master the skills as we go along and not get behind. Therefore, if students do not score proficient on the skill (4.5 or 5.0 on the scale), that grade is temporary. They will have multiple opportunities to get help from various sources and then re-assess over that skill, and the improved score replaces the previous score in the grade book. Students may re-assess as often as once per day, by appointment, for the next five school days (for a possible total of up to five re-assessments). Students, however, must do the work necessary to come to those re-assessments prepared. If a student needs help, they can come in, but they can't re-assess that same day (otherwise students can memorize how to do something just long enough to pass the assessment, but perhaps not truly understand it).
If they score a 2.5 or a 3 on the original assessment (given in class) it will not get put in the grade book. Instead, the assessment will show as missing (with the score noted in the comments) until the student comes in at least once and re-assesses. If they should still get a 2.5 or a 3 on a re-assessment, then that will go in the grade book, but they need to make at least one attempt to improve their score (and their understanding) before it goes in the grade book. They can re-assess up to five times, no matter what their original score, until they get at least a 4.5 (preferably a 5).
What Type of Student Will Be Successful in a Flipped Algebra Classroom?
In general, successful students will need to be fairly independent, self-directed learners. This class only works for students if they watch the videos and complete the online pre-assessments outside of class, participate fully in class, ask for help when they need it, and generally take charge of their own learning. While this is true of all classes at Arapahoe, it is even more important in the Flipped Algebra class as the productive use of class time depends on students having watched the videos and completed the online pre-assessments for homework.
Signing Up
If you decide you'd like to enroll in Flipped Algebra, then you'll need to enter in course #354013.4 (1st semester) andcourse #354014.4 (2nd semester) as electives in the online course registration. Please note that the course title will say Extended Algebra I/II on the course request screen (with a note about it being Flipped Algebra in the description field) simply for scheduling reasons, but the course will show as Algebra I on the student's schedule and transcript. Please also note that all students are pre-populated into the traditional Algebra I so you'll see two sets of Algebra courses on there after you add Flipped Algebra as an elective (we'll remove the other one before scheduling). |
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