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Discourses on Algebra - 02 edition
Summary: The classic geometry of Euclid has attracted many for its beauty, elegance, and logical cohesion. In this book, the leading Russian algebraist I.R. Shafarevich argues with examples that algebra is no less beautiful, elegant, and logically cohesive than geometry. It contains an exposition of some rudiments of algebra, number theory, set theory and probability presupposing very limited knowledge of mathematics. I.R. Shafarevich is known to be one of the leading mathematicians of the 20...show moreth century, as well as one of the best mathematical writers. TOC:Integers.- Simplest Properties of Polynomials.- Finite Sets.- Prime Numbers.- Real Numbers and Polynomials.- Infinite Sets.- Power Series ...show less
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Mathematics
Algebra and Geometry
Algebra I
This is a comprehensive course in which students master manipulatives to gain an understanding of abstract concepts. Those who successfully complete this course enroll in Algebra II/Geometry, Year One the following year.
Algebra IB
This is a course in which students finish mastering multiple methods to gain an understanding of abstract concepts. Those who successfully complete this course enroll in Algebra II/Geometry, Year One the following year.
Algebra II/Geometry, Year One
This course introduces and integrates concepts of geometry and intermediate algebra emphasizing an inductive approach. Geometer's Sketchpad and Fathom computer programs, a graphing calculator, and manipulative tools such as patty paper, compass and straightedge are used to help students discover fundamental geometrical and algebraic relationships. Topics include properties of parallel and perpendicular lines, triangle, polygon, and circle properties, right triangle trigonometry, transformations, linear and quadratic functions, arithmetic sequences, variation, proportion, and similarity. Coordinate geometry is emphasized throughout. If time allows, students will also study some elementary statistics, including measures of central tendency and fitting data to a line. Prerequisite: Algebra I or the equivalent.
Accelerated Algebra II/Geometry, Year One (Honors Level)
This course will cover all of the topics of Algebra II/Geometry, Year One, at an accelerated pace and a greater level of depth. We will place extra emphasis on deductive reasoning and the role of proof in mathematics. Additional topics may be included. Prerequisite: Algebra I or the equivalent; consent of the instructor and the department chair.
Algebra II/Geometry, Year Two
This course is the second in a two-year sequence and continues to integrate geometry and intermediate algebra concepts, but now emphasizing deductive reasoning. Students write various forms of formal proofs in order to establish many of the geometrical and algebraic conjectures they formed in the previous course, as well as additional principles. New topics include congruent triangles, inequalities in triangles, solid geometry, real number exponents, inverse functions, higher degree polynomial functions, exponential and logarithmic functions, complex numbers, Pythagorean proofs, rational functions, and coordinate geometry proofs. Prerequisite: Algebra II/Geometry, Year One, or the equivalent.
Accelerated Algebra II/Geometry, Year Two (Honors Level)
This course will cover all of the topics of Algebra II/Geometry, Year Two, at an accelerated pace and a greater level of depth. Additional topics may be included. Prerequisite: Algebra II/Geometry, Year One, or the equivalent; consent of the instructor and the department chair.
Intermediate Electives
One intermediate elective is offered each year. The prerequisite for all intermediate electives is completion of Algebra II/Geometry, Year Two, or the equivalent.
Functions, Statistics, and Trigonometry
This year-long course provides instruction on functions, statistics, probability, and trigonometry for the general college preparatory student. Emphasis is placed on polynomial, exponential, logarithmic, and rational functions, and the development and use of the trigonometric functions on the unit circle (including the study of right and oblique triangle applications). It also includes a component on the gathering and use of data to address real-world issues, statistical influence, and probability.
Do you play games? Ever wonder if you're using "the right" strategy? What makes one strategy better than another? In this course, we'll explore a branch of mathematics known as game theory, which answers these questions and many more. Game theory is widely applicable in the real world as we face dilemmas and challenges every day, most of which we can mathematically treat as games! We will consider significant global events like the Cuban Missile Crisis, Mandela's rise in South Africa, or the rise of Nobel Peace Prize winner Sirleaf in Liberia from a math perspective. Specific mathematical ideas we'll discuss include two person zero sum games, utility theory, two person non-zero sum games, multi-player games, game trees, matrix algebra, linear optimization, and applications of game theory techniques to a plethora of real world problems. (Prerequisite: Comfortable with Algebra) Note: This is an online course.
Statistics 1 (Fall 2014)
This course will cover gathering, describing, and displaying data, and topics in probability. Students will learn how to gather data by conducting censuses, surveys, and experiments around their school. We will also cover topics including, but not limited to, boxplots, the Normal model, and linear regression. We will always strive to connect the statistical material learned in class with real world applications to economics, elections, weather, and other themes. The semester will culminate with a unit on probability in which students will calculate the expected value of casino games
Statistics 2 (Spring 2015)
This course will cover how to analyze data using statistical methods. Students will study confidence intervals and tests of inference including, but not limited to, hypothesis tests for proportions and means and the Chi-squared test. With the tools from this course, students will be able to form educated opinions from data on questions ranging from, "Is global temperature increasing?" to "Do SAT scores predict success later in life?" We will always strive to connect the statistical material learned in class with real world applications to economics, elections, weather, and other themes Statistics 1 is a useful, but not mandatory, prerequisite.
Advanced Electives
Precalculus
A short review of the concepts of functions and their properties is followed by a thorough study of circular and triangular trigonometry. Students study conic sections, logarithmic and exponential functions, the graphs of rational functions, Binomial Theorem, arithmetic and geometric series and sequences, polar coordinates, 2-D vectors, polynomial graphs and functions, and parametric equations. Students use paper, pencil, and graphing calculators. Completion of this course prepares students to take Honors Statistics and/or Honors Calculus I. Prerequisite: Algebra II/Geometry, Year Two, or the equivalent.
Accelerated Precalculus (Honors Level)
Topics covered include all of those listed for Precalculus. In addition, Accelerated Precalculus includes three-dimensional vectors, DeMoivre's Theorem, and mathematical induction. This course is for students who have a strong interest in mathematics and want to pursue advanced topics in great depth. Students are prepared to take Statistics and/or Calculus I upon successful completion of this course. Prerequisite: Algebra II/Geometry, Year Two, or the equivalent.
Calculus
This course will introduce students to the basics of differential and integral calculus. Concepts of the derivative as a slope and the integral as area will be explored using real-world examples as well as from a numerical, algebraic, visual, and verbal perspective. Activities using technology (Geometer's Sketchpad, Mathematica, Desmos, etc.) will be utilized to help students understand concepts. Introductory rules for finding derivatives and integrals will be mastered and applied. This course is for students who want an introduction to calculus, but without the rigor required of preparing for an AP level exam.
Honors Calculus I (Honors Level)
Students enrolling in this course are assumed to have strong fundamental algebra and precalculus skills. Topics include limits, continuity, derivatives, integrals and their applications, slope fields, and separable differential equations. Concepts are approached through a three-step process: graphically, numerically, and analytically. Graphical analysis plays a major part in the development of many concepts. Students are prepared to take the Advanced Placement Calculus AB exam in May. Prerequisite: Precalculus or Accelerated Precalculus.
Honors Calculus II (Honors Level)
This course is a continuation of Calculus I and includes infinite sequences and series; parametric, polar, and vector function calculus; slope fields; Euler's method; L'Hôpital's rule; improper integrals; integration techniques; and an introduction to differential equations. If time permits, multivariable calculus is introduced. Students are prepared to take the Advanced Placement Calculus BC exam in May. Prerequisite: Calculus I or the equivalent.
In this course, students will explore vector algebra and functions, matrices, curves in space, arc length and curvature, and velocity and acceleration. Further topics include partial differentiation, local extrema, exact differentials, the chain rule, directional derivatives, gradients, double and triple integration, line integrals, and volume. Students must have access to a computerized 3-D graphing utility, such as Grapher (a standard utility on Mac computers) or Autograph, and must be comfortable using learning to use new technology independently. Prerequisite: Calculus I. Note: This is an online course.
Honors Statistics (Honors Level)
This course begins with an in-depth study of descriptive statistics, variation, and probability, which leads into the study of inferential statistics. Topics include the concepts of statistical models and use of samples, variation, statistical measures, sampling distributions, probability theory, tests of significance, one-way and factorial analysis of variance and covariance and elementary experimental design, multiple linear regression and correlational design, and chi-square. If time permits, a few of the following topics will be presented based on student interests: Continuous random variables, Monte Carlo Methods, nonparametric statistical methods, multivariate analysis of variance and covariance, hierarchical linear modeling, and exploratory factor analysis. In addition, students will learn how to critically analyze quantitative research, evaluate the evidence on which generalizations are made, and write a quantitative methods paper.
This course is designed to help students discover the power, diversity, and broad applicability of statistics. Students will learn a variety of data analysis techniques, such as multiple regression, simulation studies, and survival analysis, with an emphasis on showing how these methods have revolutionized the use of statistics in fields such as engineering, environmental studies, economics, and medicine. Within each unit, guided activities assist students in working through the entire process of a real-world case study. The course uses an inquiry-based approach that teaches advanced statistical techniques through group work and hands-on exploration of current research questions. By researching the literature, planning and carrying out experiments, and presenting their results, students in this course will experience data analysis as it is actually practiced. Note: Students should have taken at least one semester or equivalent of an introductory statistics course. *Students taking this course are eligible to receive transferable Grinnell College credit.
Teaching Assistants
Math Teaching Assistants
Teaching assistants are vital contributors to our algebra and geometry classes. TAs attend class each day, help students with practice problems and resolve homework difficulties, answer questions, and grade daily homework. In addition, they run review and extra-help sessions. As the year progresses, TAs plan and teach full lessons to the class. Upon completion of the year, students will receive one math credit. Prerequisite: Invitation of the department. |
Algebraic Structures Using Natural Class of Intervals
In this book the authors introduce a new class of intervals called the natural class of intervals.
Using these intervals, algebraic structures are defined.
Over 200 problems are given, of which some of them are at the research level.
Category:Algebra |
Britannica Guide to Algebra and Trigonometry
Essential to further mathematical and scientific study, both algebra and trigonometry provide crucial tools in managing variables and understanding the relationships between them. This volume presents the fundamentals of these fascinating areas of mathematics while chronicling their respective histories. |
Precalculus
9780073312637
ISBN:
0073312630
Edition: 6 Pub Date: 2007 Publisher: McGraw-Hill College
Summary: The Barnett, Ziegler, Byleen College Algebra series is designed to be user friendly and to maximize student comprehension. The goal of this series is to emphasize computational skills, ideas, and problem solving rather than mathematical theory. Precalculus introduces a unit circle approach to trigonometry and can be used in one or two semester college algebra with trig or precalculus courses. The large number of peda...gogical devices employed in this text will guide a student through the course. Integrated throughout the text, students and instructors will find Explore-Discuss boxes which encourage students to think critically about mathematical concepts. In each section, the worked examples are followed by matched problems that reinforce the concept being taught. In addition, the text contains an abundance of exercises and applications that will convince students that math is useful. A Smart CD is packaged with the seventh edition of the book. This CD reinforces important concepts, and provides students with extra practice problems.
Barnett, Raymond A. is the author of Precalculus, published 2007 under ISBN 9780073312637 and 0073312630. Thirty two Precalculus textbooks are available for sale on ValoreBooks.com, seventeen used from the cheapest price of $67.67, or buy new starting at $120.1412637-4-0-3 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:97800733126 |
The ATETV project delivers web-based videos to connect students to careers in advanced technology. In this episode of ATETV, lasers and photonics technology, wind energy technology and the importance of mathematics are...
This online exercise lets students practice vector addition. They choose the precision of the test by selecting a target size, then estimate the sum of the two vectors by dragging and dropping a third arrow. Points are...
Applied Mathematics is a lesson plan which will help students gain proficiency in applied mathematics. After completing this module, students should be able to demonstrate the ability to perform various mathematical...
The ATETV project delivers web-based videos to connect students to careers in advanced technology. This episode of ATETV looks at Water Management and Biotechnology programs, as well as the emphasis one needs in... |
Concepts of Modern Mathematics
stud...more students, and parents. Since then, the negative aspects of "new math" have been eliminated and its positive elements assimilated into classroom instruction. In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts underlying "new math": groups, sets, subsets, topology, Boolean algebra, and more. According to Professor Stewart, an understanding of these concepts offers the best route to grasping the true nature of mathematics, in particular the power, beauty, and utility of pure mathematics. No advanced mathematical background is needed (a smattering of algebra, geometry, and trigonometry is helpful) to follow the author's lucid and thought-provoking discussions of such topics as functions, symmetry, axiomatics, counting, topology, hyperspace, linear algebra, real analysis, probability, computers, applications of modern mathematics, and much more. By the time readers have finished this book, they'll have a much clearer grasp of how modern mathematicians look at figures, functions, and formulas and how a firm grasp of the ideas underlying "new math" leads toward a genuine comprehension of the nature of mathematics itself.(less)
Paperback, 352 pages
Published
February 1st 1995
by Dover Publications
(first published 1975)
Community Reviews
i...moreian to what it is that mathematicians do.(less)
...more it to someone who's mathematically competent and isn't intimidated by a lot of numbers.
I, on the other hand, am much more comfortable with words than with numbers. Whenever Stewart EXPLAINS a theorem, I understood it without a problem. Unfortunately, this was rare - he spends most of time proving or disproving concepts through demonstrations that were too much for me to handle. Also, he doesn't delve enough into the history behind these mathematical ideas, so it all felt a bit cold to me. I need a human face behind a theorem (this why I love Dantzig's Number: The Language of Science, which does a BRILLIANT job of this).
Well, I got through a good amount of the book. At least I feel like I understand the bare basics of set theory, graph theory, and topology (I had to skip most of the section on how symmetry and group theory relate, which I still fail to understand).(less)
r...more relevant and illuminating. Individual topics are only investigated to the depth that we can see patterns emerge. Simple examples demonstrate why these topics are useful. Subsequent topics will usually refer back to elaborate on how everything is (surprisingly!) interwoven.
I can't recommend this book enough, many thanks to my family for picking it up for me. This book would work best, IMO, if you read it during the summer in between high school and college. I imagine that if I had read this book, specifically the chapters on "Short Cuts in the Higher Arithmetic" and "The Language of Sets", before I took CS 666 (Cryptography) @ Stevens-Tech, then I probably would've done much better in that course... I felt comfortable w/ the author because I had read one of his previous works, The Annotated Flatland. (less)
Good general introduction to give you a feel for some diverse areas of modern mathematics. However, the explanations are glossed over too quickly and I found it very difficult to follow some of the details even with a mathematical background. Will still give you the broad ideas but for a more thorough and complete introduction to the topics, topic specific books will be needed.
Read back in high school just as I was getting into calculus (and beginning to think that a Comparative Literature degree might not, after all, be in my future). Gentle introductions to all kinds of things (vector calculus, topology, group theory etc) but lacking either the detail to make any real sense of them, or the historical data to bring them to life.
great intro for me to a wide range of mathematics. a huge boost up. great translation from hard-core math land to non mathematicians. a good balance between oversimplifying one the one hand and overwhelm with symbols on the other.
Ian Stewart is an Emeritus Professor and Digital Media Fellow in the Mathematics Department at Warwick University, with special responsibility for public awareness of mathematics and science. He is best known for his popular science writing on mathematical themes. --from the author's website
Librarian Note: There is more than one author in the GoodReads database with this name. See other authors wit...moreIan Stewart is an Emeritus Professor and Digital Media Fellow in the Mathematics Department at Warwick University, with special responsibility for public awareness of mathematics and science. He is best known for his popular science writing on mathematical themes. --from the author's website |
Description of Intro To Geometry, Grades 5-8 by Frank Schaffer
This revised edition of Intro to Geometry links all the activities to the NCTM Standards. The activities were designed to provide students with practice in the skill areas required to understand basic geometry concepts. Activities that focus on congruence |
Tough Test Questions? Missed Lectures? Not Enough Time?
Fortunately, there's Schaum's. This all-in-one-package includes more than 600 fully solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 20 detailed videos featuring Math instructors who explain how to solve the most commonly... more...
This book on symmetric geometric patterns of Islamic art has educational, aesthetic, cultural and practical purposes. Its central purpose is to bring to the attention of the world in general, and the people of Islamic culture in particular, the potential of the art for providing a unified experience of science and art in the context of mathematical... more...
Boost Your grades with this illustrated quick-study guide. You will use it from high school all the way to graduate school and beyond. Clear and concise explanations. Difficult concepts are explained in simple terms. Illustrated with graphs and diagrams. Search for the words or phrases. Access the guide anytime, anywhere - at home, on the train, in... more...
From the pyramids and the Parthenon to the Sydney Opera House and the Bilbao Guggenheim, this book takes readers on an eye-opening tour of the mathematics behind some of the world's most spectacular buildings. Beautifully illustrated, the book explores the milestones in elementary mathematics that enliven the understanding of these buildings and combines... more...
500 Ways to Achieve Your Best Grades
We want you to succeed on your college algebra and trigonometry midterm and final exams. That's why we've selected these 500 questions to help you study more effectively, use your preparation time wisely, and get
your best grades. These questions and answers are similar to the ones you'll find on a typical... more...
Karl Gustafson is the creater of the theory of antieigenvalue analysis. Its applications spread through fields as diverse as numerical analysis, wavelets, statistics, quantum mechanics, and finance. Antieigenvalue analysis, with its operator trigonometry, is a unifying language which enables new and deeper geometrical understanding of essentially every... more...
Spherical trigonometry was at the heart of astronomy and ocean-going navigation for two millennia. The discipline was a mainstay of mathematics education for centuries, and it was a standard subject in high schools until the 1950s. Today, however, it is rarely taught. Heavenly Mathematics traces the rich history of this forgotten art, revealing... more... |
A-Plus Notes for Beginning Algebra: Pre-Algebra and Algebra 1
Book Description: It provides a clear summary and outline in algebra. Each topic begins with concepts, formulas, and problem-solving steps, followed by well-designed examples. There are 18,000 examples and exercises in this book-7,000 are real-life word problems modeled after typical questions on standardized tests that are given across the United States |
...In addition, as a math and physics major, I have regularly been using concepts from linear algebra in many different contexts and courses. As a math major I have taken many courses which involve logic and also courses just on mathematical logic. I have also taken philosophy classes on logic as well. |
This field guide contains a quick look at the functions commonly encountered in single variable calculus, with exercises for each topic: linear, polynomial, power, rational, exponential, logarithmic, trigonometric, and...
Linked essay sketching trigonometry from its beginnings out of the early correspondence between astronomy and mathematics through the 18th century, with 17 references (books/articles). Influential thinkers addressed...
An introduction and a guide to trigonometry, with hints and answers to exercises, and Java applets as illustrations. Contents include applications of trigonometry, angle measurement, chords, sines, cosines, tangents and...
A brief introduction to the field of continued fractions, including some basic theory about the subject; the history of continued fractions, tracing some of the major developments in the field in the past 2500 years;...
Teacher2Teacher is "a peer-mentored question-and-answer service" and intended to serve as "a resource for teachers and parents who have questions about teaching mathematics." Visitors to the website can search or browse... |
11.5 Probability with the Fundamental Counting principle, Permutations, and Combinations
11.6 Events Involving Not and Or; Odds
11.7 Events Involving And; Conditional Probability
11.8 Expected Value
12. Statistics
12.1 Sampling, Frequency Distributions, and Graphs
12.2 Measures of Central Tendency
12.3 Measures of Dispersion
12.4 The Normal Distribution
12.5 Problem Solving with the Normal Distribution
12.6 Scatter Plots, Correlation, and Regression Lines
13. Mathematical Systems
13.1 Mathematical Systems
13.2 Rotational Symmetry, Groups, and Clock Arithmetic
14. Voting and Apportionment
14.1 Voting Methods
14.2 Flaws of Voting Methods
14.3 Apportionment Methods
14.4 Flaws of Apportionment Methods
15. Graph Theory
15.5 Graphs, Paths, and Circuits
15.2 Euler Paths and Euler Circuits
15.3 Hamilton Paths and Hamilton Circuits
15.4 Trees166 |
Mathematics
Mathematics is best described as the study of patterns. In that sense, everybody is a mathematician. Mathematics as an academic discipline simply carries the study of patterns to a greater depth. Geometry concerns patterns of shape. Arithmetic concerns patterns of number. Calculus concerns patterns of continuous change. Statistics concerns patterns of chance. The department offers courses serving majors, minors, the Central Curriculum and other disciplines.
Mathematics – Secondary Education combines a regular mathematics major with the Education Department's program for certification for secondary school teaching. |
Featured Research
from universities, journals, and other organizations
Math goes viral in the classroom
Date:
December 14, 2009
Source:
University of Alberta
Summary:
At least a dozen Alberta high-school calculus classrooms were exposed to the West Nile virus recently. Luckily, it wasn't literally the illness. Educators used the virus as a theoretical tool when they designed materials for use in an advanced high-school math course.
Share This
At least a dozen Alberta high-school calculus classrooms were exposed to the West Nile virus recently.
Luckily, however, it wasn't literally the illness. University of Alberta education professor Stephen Norris and mathematics professor Gerda de Vries used the virus as a theoretical tool when they designed materials for use in an advanced high-school math course. The materials allow students to use mathematical concepts learned in their curriculum to determine the disease's reproductive number, which determines the likelihood of a disease spreading.
The approach is a marriage of science and math, subjects the researchers say seem to exist in separate worlds at a secondary-school level, but that when brought together can effectively bring real-world scenarios into the classroom to enhance learning and understanding.
Not to mention answering that ages old high-school student question: "why do I need to know this?"
"This piece was designed to satisfy an optional unit in Math 31 (Calculus), for which there are no materials, so we said, 'let's fill the gap,'" said Norris. "These materials show a real application of mathematics in the biology curriculum for high-school students."
Norris and de Vries chose a published academic math paper on the transmission of the West Nile virus and modified it -keeping the science intact, but making it readable and practical for high-school calculus students.
The information and equations in the original paper dealing with disease transmission were then used as the basis for calculus math problems to be solved by the students. Students were presented with a variety of materials that covered topics and concepts such as rate of change, exponential growth-decay models, and models for the carriers of the virus, including mosquitoes and infectious and susceptible birds. The students' mathematical skills were then put to use in determining the spread of the disease using various parameters, which included variables such as biting rate and the probability of infection.
Norris underlines that the project challenged the students to see and understand science in a different fashion from what they learn inside the science curricula. He points out that high-school classroom scientific experiments are "proven" science and have been around for at least 300 years, in many cases. For the students to discover that real scientists often work with some assumptions that they know to be false in order to reach their conclusions was certainly an eye-opening realization for them, he says.
"There's no way out of the fact that the knowledge you gain from science is imperfect; it's tentative and subject to change," said Norris. "I think that's what struck the students between the eyes."
Both researchers agree that this form of collaborative, interdisciplinary learning can take place across all subject areas. De Vries and Norris are currently working on another project that focuses on population genetics that will fit into Grade 12 biology and math courses.
"It's mathematics in the real world. Kids are always asking, 'why am I learning this,'" she said. "All of a sudden the mathematics that kids have learned comes together in a project likeOct. 11, 2013 — Writing instruction in US classrooms is "abysmal" and the Common Core State Standards don't go far enough to address glaring gaps for students and teachers, an education scholarApr. 20, 2009 — More challenging middle-school math classes and increased access to advanced courses in predominantly black urban high schools may be the key to closing the racial academic achievement gap, according ... full story
ScienceDaily features breaking news and videos about the latest discoveries in health, technology, the environment, and more -- from major news services and leading universities, scientific journals, and research organizations. |
In this section
Intermediate 2 Mathematics
The Intermediate 1 Course builds on the content of previous mathematical learning and develops further skills in arithmetic, algebra, geometry and trigonometry. For those choosing the Applications of Mathematics unit, there is further work on calculations relating to earnings, logic diagrams and formulae and a statistical assignment appropriate to this level.
The Intermediate 2 Mathematics Course is at SCQF level 5.
For more information on SCQF levels and how Intermediate 2 fits in to the Scottish Credit and Qualifications Framework, visit our SCQF section.
The Mathematics page on Education Scotland's site provides support materials and external web links for teaching and learning as well as news, events and feature articles to assist with professional development. |
Indefinite Integrals : learn how to solve them 2.3 Full Screenshot
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Learn-How-To-Cook-Like-A-Chef is an ideal E-book for you whether you are a new cook, or a seasoned kitchen veteran, there are some simple tricks that you can use to improve the quality of your meals. Free Download |
Know the basic function library. Knowing the basic properties of common will save you a lot of time in your calculus studies. Basic functions include trigonometry functions, exponential function, polynomials, and many more. |
Product Information
ISBN: 1592578659 ISBN-13: 9781592578658 Availability: Usually ships in 24-48 hours. Series:Humongous Book of
Publisher's Description
A brain explains...
Most math and science study guides are dry and difficult, but this is the exception. Following the successful The Humongous Books in calculus and algebra, bestselling author Mike Kelley takes a typical statistics workbook, full of solved problems, and writes notes in the margins, adding missing steps and simplifying concepts and solutions. By learning how to interpret and solve problems as they are presented in statistics courses, students prepare to solve those difficult problems that were never discussed in class but are always on exams.
•With annotated notes and explanations of missing steps throughout, like no other statistics workbook on the market
• An award-winning former math teacher whose website (calculus-help. com) reaches thousands every month, providing exposure for all his books
Author Bio
Michael Kelley is a former award-winning math teacher and the author of seven math books, including five from Alpha. He won Maryland's Outstanding High School Mathematics Teacher and "Most Popular Teacher" in his home school for four years. Mr. Kelley is also the founder and editor of calculus-help.com, which helps thousands of students every month. |
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19901990 Hardcover Good in good dust jacket. Our goal with every sale is customer satisfaction, so please buy with confidence. All orders are shipped the same day or the next day. ...This is a used book in good condition and may show some signs of use or wear.Read moreShow Less
Dust Cover Missing. Book shows minor use. Cover and Binding have minimal wear and the pages have only minimal creases.A tradition of southern quality and service. All books ...guaranteed at the Atlanta Book Company. Our mailers are 100% recyclable. Read moreShow Less
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the real world. Just as there are many approaches to learning, there are many ways to solve mathematical problems. The authors zero in on each reader's math anxiety and offer alternative ways to conceptualize and compute, clarifying along the way such confusing concepts as proportions and percentages. No matter how "anti-numbers" you think you are, Rudey and Nirenberg can remove the obstacles to math proficiency and help you build confidence through a variety of exercises and workable |
With more than 100 built-in functions, forms to enter matrix and list data, SCalc calculates matrix inversions, LU (QR) decompositions, definite integrals, derivatives and zeros of simple functions. Solve a system of linear equations using QRS operation. Draw 15 graphs/plots, compute 10 commands. Switch to increasingly complex layouts, solve equations and compute special functions. Draw parametric, cartesian and polar graphs. Zoom in and zoom out with a display of scale and zoom level used. Track graph functions. Stretch and compact graphs along the y-axis. Compute commands like integrations, derivatives, maxima and minima along with drawings of results on the graphics screen. Also obtain samples of x-y data of graphs or functions. Using x-y data, curve-fit and plot. Use 3 choice backgrounds and draw with a selection of colors. Compute list functions, exponential functions, statistical, and various special functions. Define your own functions and variables, store them on external SD card and reload them back into internal memory. Do multiple conversions between primary units. Compute properties of simple geometric figures. Install or move the application to an SD card. Choose any previous command from a history list. Read the built-in function list -- upon long pressing the result -- and the helpful summary information to bring the function into input. Use help to determine valid values for the parameters for built-in functions. With recent improvements, swipe left and swipe right on the special function keys to find the keys you want easily. Position the coordinate lines precisely with left and right arrow controls on the graph screen. Find the scale and zoom level upon touch in a floating window display. Pinch with two fingers to zoom in and zoom out of the graphs. To find zero, repeatedly touch the result (R button) on graphics screen. If possible, you can find different zeros each time within a given range. With SCalc , you do not need to visit a help website or usage manual as plenty of easy to read instructions are provided with every step of calculation. These help messages can be turned off once you are familiar with the usage. When there is an error in the input, SCalc highlights the exact location of error in the input. Care has been taken in the design of the interface, so users with or without a keyboard can get the same functionality and ease of use. To use international versions, set the input language for on screen keyboard to beGraphite Pro is the FREE professional scientific graphing calculator, with support for parsing advanced mathematical expressions including parentheses. Command history is kept to allow easy reproducibility of previous calculationsMore from developer
With more than 100 built-in functions, special functions, and forms to enter matrix and list data, ZCalc calculates matrix inversions, LU decompositions, definite integrals, derivatives and zeros of simple functions. Switch to increasingly complex layouts, solve equations, compute statistical and list functions. To use international versions, set the input language for onscreen keyboard to be English.
Draw 15 graphs including parametric and polar functions. Compute 9 commands like integrals, derivatives, zeros, min and max values of cartesian functions. See the results graphically on the screen. Track x-y values. Zoom in and zoom out. Users can input data in separate files and export to the graphing engine. Graph images can be saved as .png files with white background for easier printing. With more than 150 builtin function library, it is easier to draw graphs of curve fitted data, including polynomial best fit. Draw scatter plots with standard deviations. Choose various colors for the graphs and a choice of three background colors.
To enter input in international versions, set the input language for onscreen keyboard to be english. |
Summary: Provides completely worked-out solutions to all odd-numbered exercises within the text, giving you a way to check your answers and ensure that you took the correct steps to arrive at an answer.4962.2170.00 +$3.99 s/h
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Mathematics - Algebra (529Bertrand Russell was a British logician, nobleman, historian, social critic, philosopher, and mathematician. Known as one of the founders of analytic philosophy, Russell was considered the premier logician of the 20th century and widely admired and respected for his academic work. In his lifetime, Russell published dozens of books in wildly varying fields: philosophy, politics, logic, science, religion, and psychology, among which The Principles of Mathematics was one of the first published and remains one of the more widely known. Although remembered most prominently as a philosopher, he identified as a mathematician and a logician at heart, admitting in his own biography that his love of mathematics as a child kept him going through some of his darkest moments and gave him the will to live. With his book The Principles of Mathematics, Russell aims to instill the same deep seated passion for mathematics and logic that he has carefully cultivated in the reader. He adeptly explores mathematical problems in a logical context, and attempts to prove that the study of mathematics holds critical importance to philosophy and philosophers. Russell utilizes the text to explore the some of the most fundamental concepts of mathematics, and expounds on how these building blocks can easily be applied to philosophy. In the second part of the book, Bertrand addresses mathematicians directly, discussing arithmetic and geometry principles through the lens of logic, offering yet another unique and groundbreaking interpretation of a field long before considered static. This book affords new insight and application for many basic mathematical concepts, both in roots of and application to other fields of scholarly pursuit. Russell uses his book to establish a baseline of mathematical understanding and then expands upon that baseline to establish larger and more complex ideas about the world of mathematics and its connections to other fields of personal interest. The Principles of Mathematics is a very captivating glimpse into the logic and rational of one of history's greatest thinkers. Whether you're a mathematician at heart, a logician, or someone interested in the life and thoughts of Bertrand Russell, this book is for you. With an incredible amount of information on mathematics, philosophy, and logic, this text inspires the reader to learn more and discover the ways in which these very disparate fields can interconnect and create new possibilities at their intersections.
Isaac Todhunter's Algebra for Beginners: With Numerous Examples is a mathematics textbook intended for the neophyte, an excellent addition to the library of math instructionals for beginners. Todhunter's textbook has been divided into 44 chapters. Early chapters highlight the most basic principles of mathematics, including sections on the principal signs, brackets, addition, subtraction, multiplication, division, and other topics that form the foundation of algebra. Simple equations make up the large majority of the material covered in this textbook. Later chapters do introduce quadratics, as well as other more advanced subjects such as arithmetical progression and scales of notation. It is important to note that Todhunter sticks very much to the basics of algebra. The content of this book lives up to its title, as this is very much mathematics for beginners. The content is provided in an easy to follow manner. This book could thus be used for independent learning as well as by a teacher. A great deal of focus has clearly been given to providing examples. Each concept is accompanied by numerous sample questions, with answers provided in the final chapter of the book. The example questions are every bit as important as the explanations, as one cannot begin to grasp mathematical concepts without having the opportunity to put them into practice. The basics of algebra are explained in an easy to follow manner, and the examples provided are clear and help to expand the knowledge of the learner. If given a chance, Isaac Todhunter's Algebra for Beginners: With Numerous Examples can be a valuable addition to your library of mathematics textbooks.
Florian Cajori's A History of Mathematics is a seminal work in American mathematics. The book is a summary of the study of mathematics from antiquity through World War I, exploring the evolution of advanced mathematics. As the first history of mathematics published in the United States, it has an important place in the libraries of scholars and universities. A History of Mathematics is a history of mathematics, mathematicians, equations and theories; it is not a textbook, and the early chapters do not demand a thorough understanding of mathematical concepts. The book starts with the use of mathematics in antiquity, including contributions by the Babylonians, Egyptians, Greeks and Romans. The sections on the Greek schools of thought are very readable for anyone who wants to know more about Greek arithmetic and geometry. Cajori explains the advances by Indians and Arabs during the Middle Ages, explaining how those regions were the custodians of mathematics while Europe was in the intellectual dark ages. Many interesting mathematicians and their discoveries and theories are discussed, with the text becoming more technical as it moves through Modern Europe, which encompasses discussion of the Renaissance, Descartes, Newton, Euler, LaGrange and Laplace. The final section of the book covers developments in the late 19th and early 20th Centuries. Cajori describes the state of synthetic geometry, analytic geometry, algebra, analytics and applied mathematics. Readers who are not mathematicians can learn much from this book, but the advanced chapters may be easier to understand if one has background in the subject matter. Readers will want to have A History of Mathematics on their bookshelves differentThis text is prepared to meet the needs of the student who will continue his mathematics as far as the calculus, and is written in the spirit of applied mathematics. This does not imply that algebra for the engineer is a different subject from algebra for the college man or for the secondary student who is prepared to take such a course. In fact, the topics Avhich the engineer must emphasize, such as numerical com)utations, checks, graphical methods, use of tables, and the solution of specific problems, are among the most vital features of the subject for any student. But important as these topics are, they do not comprise the substance of algebra, which enables it to serve as part of the foundation for future work. Rather they furnish an atmosphere in which that foundation may be well and intelligently laid. The concise review contained in the first chapter covers the topics which have direct bearing on the work which follows. No attempt is made to repeat all of the definitions of elementary algebra. It is assumed that the student retains a certain residue from his earlier study of the subject. The quadratic equation is treated with unusual care and thoroughness. This is done not only for the purpose of review, but because a mastery of the theory of this equation is absolutely necessary for effective work in analytical geometry and calculus. Furthermore, a student who is well grounded in this particular is in a position to appreciate the methods and results of the theory of the general equation with a minimum of eii ort. The theory of equations forms the keystone of most courses in higher algebra. The chapter on this subject is developed gradually, and yet with pointed directness, in the hope that the processes which students often perform in a perfunctory manner will take on additional life and interest.
The present work is intended as a sequel to our Elementary Algebra for Schools. The first few chapters are devoted to a fuller discussion of Ratio, Proportion, Variation, and the Progressions, which in the former work were treated in an elementary manner; and we have here introduced theorems and examples which are unsuitable for a first course of reading.<br><br>From this point the work covers ground for the most part new to the student, and enters upon subjects of special importance: these we have endeavoured to treat minutely and thoroughly, discussing both bookwork and examples with that fulness which we have always found necessary in our experience as teachers.<br><br>It has been our aim to discuss all the essential parts as completely as possible within the limits of a single volume, but in a few of the later chapters it has been impossible to find room for more than an introductory sketch; in all such cases our object has been to map out a suitable first course of reading, referring the student to special treatises for fuller information.<br><br>In the chapter on Permutations and Combinations we are much indebted to the Rev. W. A. Whitworth for permission to make use of some of the proofs given in his Choice and Chance.
The present work contains a full and complete treatment of the topics usually included in an Elementary Algebra. The author has endeavored to prepare a course sufficiently advanced for the best High Schools and Academies, and at the same time adapted to the requirements of those who are preparing for admission to college.<br><br>Particular attention has been given to the selection of examples and problems, a sufficient number of which have been given to afford ample practice in the ordinary processes of Algebra, especially in such as are most likely to be met with in the higher branches of mathematics. Problems of a character too difficult for the average student have been purposely excluded, and great care has been taken to obtain accuracy in the answers.<br><br>The author acknowledges his obligations to the elementary text-books of Todhunter and Hamblin Smith, from which much material and many of the examples and problems have been derived. He also desires to express his thanks for the assistance which he has received from experienced teachers, in the way of suggestions of practical value.
Already Published Anthropology By R.R. Makett An Introduction To Science By J.Arthuk Tnousos Evolution By J, Abthuk Thohson am The Animal World By F.W. Gakele Introduction To Mathe-Matics By A.N. Whitehead Astronomy By A. R.Hinks Psychical Research. By W.F. Eabbett The Evolution Of Plants By D.H. Scott Crime And Insanity. By C.A. Mebcieb Matter And Energy. By F.Sodd Psychology By W.McDouoau. Principles Of Physiology By J.G. McKendrick The Making Of The Earth By J.W. Gregoev Electricity By Gisbest Kapp The Human Body By A.Kiitb Future Issues Chemistry By R.Meldola The Mineral World. By SiT.
The Directly Useful Technical Series requires a few words by way of introduction. Technical books of the past have arranged themselves largely under two sections: the theoretical and the practical. Theoretical books have been written more for the training of college students than for the supply of information to men in practice, and have been greatly filled with problems of an academic character. Practical books have often sought the other extreme, omitting the scientific basis upon which all good practice is built, whether discernible or not. The present series is intended to occupy a midway position. The information, the problems, and the exercises are to be of a directly useful character, but must at the same time be wedded to that proper amount of scientific explanation which alone will satisfy the inquiring mind. We shall thus appeal to all technical people throughout the land, either students or those in actual practiceJr il 4 eU-- 2.The Mathematical Repository. Mathematical Questions. To he answered in Number XIV. Lquestion 33 t, ly Mr. John Hyices, Dublin. To find any number of squares whose sum and product are equal. IL Question 33 fl, by Mr. John Hynes. To find two fractions such, that the sum and sura of their squares shall both be rational squares; and either of them being added to the square of the other shall make the same square. III. Question 333, iy Junius. Required the general value of xin the equation a?23)211 ?Iv. Question 334. by Mr. W.Callow. There are two such quantities that the sum of their squares Vexceeds their sum by a, and that the sum of their fourth powers together with their sum, exceeds twice the sum of their cubes by: It is required to find them without resolving any equation higher than a quadratic? cV. Question 335, hy Mr. Callow. Having given y--qy + ry -s:=.Oy andy (x+ wi)= 0 :It is required to assign such a value tow, as will enable us to Qdetermine xand yand thus to resolve a general biquadratic, supposing the solution of a general cubic to be known? VI. Question 336. by Aieyoyo. Demonstrate the following Theorems: 1.If three circles be situated any how in a plane, and through the centres of every two a circle be described to touch the remaining one, the lines joining the centre of each of the circles with the point in which the circles passing through it meet each other intersect in the same point.s. If there be three circles situated any how in a plane, and if through the centre of each, a circle be similarly described to touch the other two, then lines joining the centre of each of the circles with the intersection of those two which touch it, (taking always the corresponding intersections) will meet in the same point.3.
Methods for Matrix Inversion and for the Solution of Simultaneous Linear Algebraic Equations was written by J. H. Curtiss. This is a 51 page book, containing 4607 words and 2 pictures. Search Inside is enabled for this title.
I am glad to be permitted to dedicate this Volume to you, because an opportunity is thus given me of publicly expressing the high opinion I entertain of the value of your scientific labours, especially those relating to Terrestrial and Cosmical Magnetism, which I have had peculiar means of appreciating from the use I have made of them in my Theory of Magnetic Force.<br><br>I feel also much gratified by the circumstance that in availing myself of your permission I dedicate the work to the President of the Royal Society. The special object of my theoretical researches has been to arrive at a general physical theory by means of mathematical reasoning employed in accordance with principles and rules laid down in the philosophical works of Newton.
This report was prepared as an account of Government sponsored work. Neither the United States, nor the Commission, nor any person acting on behalf of the Commission:<br><br>A. Makes any warranty or representation, express or implied, with respect to the accuracy, completeness, or usefulness of the information contained in this report, or that the use of any information, apparatus, method, or process disclosed in this report may not infringe privately owned rights; or<br><br>B. Assumes any liabilities with respect to the use of, or for damages resulting from the use of any information, apparatus, method, or process disclosed in this report.<br><br>As used in the above, "person acting on behalf of the Commission" includes any employee or contractor of the Commission to the extent that such employee or contractor prepares, handles or distributes, or provides access to, any information pursuant to his employment or contract with the Commission.
Edward Everett Whitford was bom in Brookfield, N.Y., January 31, 1865;graduated from Brookfield Academy in 1881; received the degree of A.B. from Colgate University in 1886 and of A.M. in 1890. He taught in Colbj Academy, New London, N.H., Keystone Academy, Factorjrville, Pa., Shamokin (Pa.) High School, Commercial High School and Pratt Institute, Brooklyn, N.Y. He was principal of Brookfield High School, 1900-1. He is now instructor in mathematics in the College of the City of New York with which institution he has beei connected since 1905. He has been a graduate student in Coliunbia University since February, 1904, and is a member of the American Mathematical Society. The writer takes this opportunity of expressing hithanks to Professor David Eugene Smith for fruitfnsuggestions and able and helpful criticism.523 West ISIbt Str., New Yobk, December, 1911.
It is the purpose of this work to present a through investigation of the various systems of Symbolic Reasoning allied to ordinary Algebra. The chief examples of such systems are Hamilton's Quaternions, Grassmann's Calculus of Extension and Boole's Symbolic Logic. Such algebras have an intrinsic value for separate detailed study; also they are worthy of a comparative study, for the sake of the light thereby thrown on the general theory of symbolic reasoning, and on algebraic symbolism in particular.<br><br>The comparative study necessarily presupposes some previous separate study, comparison being impossible without knowledge. Accordingly after the general principles of the whole subject have been discussed in Book I. of this volume, the remaining books of the volume are devoted to the separate study of the Algebra of Symbolic Logic, and of Grassmann's Calculus of Extension, and of the ideas involved in them. The idea of a generalized conception of space has been made prominent, in the belief that the properties and operations involved in it can be made to form a uniform method of interpretation of the various algebras.<br><br>Thus it is hoped in this work to exhibit the algebras both as systems of symbolism, and also as engines for the investigation of the possibilities of thought and reasoning connected with the abstract general idea of space. A natural mode of comparison.between the algebras is thus at once provided by the unity of the subject-matters of their interpretation. The detailed comparison of their symbolic structures has been adjourned to the second volume, in which it is intended to deal with Quaternions, Matrices, and the general theory of Linear Algebras. This comparative anatomy of the subject was originated by B. Peirce's paper on Linear Associative Algebra, and has been carried forward by more recent investigations in Germany geometry basedThe object of what are here called mathematical essays is to co-ordinate a pupils knowledge on certain subjects which are not specially dealt with in text-books. The essays, of which outlines are given in the first part of this book, are of the following types: (i) A group of theorems on one subject, the theorems in ordinary text-books being often scattered in one or several volumes (e.g., Essays 19, 26, 70, 91);(ii) A series of questions leading up to the solution of an important problem (e.g., Essays 79, 87, 90, 93);(iii) A collection of different methods of proving the same theorem (e.g., Essays 28, 61, 75, 78);(iv) A series of applications- of the same theorem (e.g., Essays 37, 48, 75); (v)A classification of tests of the same geometrical condition (e.g. Essays 3, 4, 40, 41).The subjects given in the first part (Essays1-100) are, as a rule, of an elementary character. In several of these, a question, which throws light on different subjects, is repeated, Those given in the second part (Essays101-200) are taken from papers set for entrance scholarships in the Trinity and Pembroke groups of Cambridge colleges from 1905 and 1907 respectively. I should be grateful for notices of any errors that may be found in the text or answers, and for any suggestions from teachers for the improvement of the book. Charles Davison. Birmingham, November, 1914.
By Pi-of. J.Sylvester. All the proofs that I am acquainted with (and their name is legion) of the possibility of depriving a quadric, in three or more variables, of its mixed terms by a real orthogonal transformation are made to depend on the theorem that the latent roots of any symmetrical matrix are all real. By the latent roots is understood the roots of the determinant expressed by tacking on a variable Xto each term in the diagonal of symmetry to such matrix. I shall show that the same conclusion may be established hpriori by purely algebraical ratiocination and without constructing any equation, by the method of cumulative variation. The proof I employ is inductive: i.e. if the theorem is true for two or any number of variables I prove that it will be true for one more. To illustrate the method let us begin with two variables. Consider the form ax2+ 2 hxy +by 2. If in any such form b= , then by an obvious orthogonal X XIX - 11 transformation, viz. writing and, :;for xand y, the the form becomes a(x+ y2)+ h(x -y), or (a+ h)x 2 +(a - h)y 2. Vol. XIX.
In preparing this work the author has been prompted by many reasons, the most unportant of which are: The dearth of short but complete books covering the fundamentals of mathematics. The tendency of those elementary books which begin at the beginning to treat the subject in a popular rather than in a scientific manner. Those who have had experience in lecturing to large bodies of men in night classes know that they are composed partly of practical engineers who have had considerable experience in the operation of machinery, but no scientific training whatsoever; partly of men who have devoted some time to study through correspondence schools and similar methods of instruction; partly of men who have had a good education in some non-technical field of work but, feeling a distinct calling to the engineering profession, have sought special training from night lecture courses; partly of commercial engineering salesmen, whose preparation has been non-technical and who realize in this fact a serious handicap whenever an important sale is to be negotiated and they are brought into competition with the skill of trained engineers; and finally, of young men leaving high schools and academies anxious to become engineers but who are unable to attend college for that purpose. Therefore it is apparent that with this wide.
This tract is intended to give an account of the theory of equations according to the ideas of Galois. The conspicuous merit of this method is that it analyses, so far as exact algebraical processes permit, the set of roots possessed by any given numerical equation. To appreciate it properly it is necessary to bear constantly in mind the difference between equalities in value and identities or equivalences in form; I hope that this has been made sufficiently clear in the text. The method of Abel has not been discussed, because it is neither so clear nor so precise as that of Galois, and the space thus gained has been filled up with examples and illustrations.<br><br>More than to any other treatise, I feel indebted to Professor H. Weber's invaluable Algebra, where students who are interested in the arithmetical branch of the subject will find a discussion of various types of equations, which, for lack of space, I have been compelled to omit.<br><br>I am obliged to Mr Morris Owen, a student of the University College of North Wales, for helping me by verifying some long calculations which had to be made in connexion with Art. 52. |
The importance of mathematics competitions has been widely recognized for three reasons: they help to develop imaginative capacity and thinking skills whose value far transcends mathematics they constitute the most effective way of discovering and nurturing mathematical talent and they provide a means to combat the prevalent false image of mathematics held by high school students, as either a fearsomely difficult or a dull and uncreative subject. This book provides a comprehensive training resource for competitions from local and provincial to national Olympiad level, containing hundreds of diagrams, and graced by many light-hearted cartoons. It features a large collection of what mathematicians call "beautiful" problems - non-routine, provocative, fascinating, and challenging problems, often with elegant solutions. It features careful, systematic exposition of a selection of the most important topics encountered in mathematics competitions, assuming little prior knowledge. Geometry, trigonometry, mathematical induction, inequalities, Diophantine equations, number theory, sequences and series, the binomial theorem, and combinatorics - are all developed in a gentle but lively manner, liberally illustrated with examples, and consistently motivated by attractive "appetiser" problems, whose solution appears after the relevant theory has been expounded.
Each chapter is presented as a "toolchest" of instruments designed for cracking the problems collected at the end of the chapter. Other topics, such as algebra, co-ordinate geometry, functional equations and probability, are introduced and elucidated in the posing and solving of the large collection of miscellaneous problems in the final toolchest |
In precalculus, the student no longer mindlessly follows a set of rules, but must learn to understand the interpret questions and understand the math's meaning. But don't panic. I can explain everything in plain language and analogies (which I make up on-the-fly). And I will show you how to use the knowledge to do your homework. |
A Course in Number Theory
Second Edition
H. E. Rose
A Course in Number Theory
Second Edition
H. E. Rose
Description
Perfect for students approaching the subject for the first time, this book offers a superb overview of number theory. Now in its second edition, it has been thoroughly updated to feature up-to-the-minute treatments of key research, such as the most recent work on Fermat's coast theorem. Topics include divisibility and multiplicative functions, congruences and quadratic resolves, the basics of algebraic numbers and sums of squares, continued fractions, diophantine approximations and transcendence, quadratic forms, partitions, the prime numbers, diophantine equations, and elliptic curves. More advanced subjects such as the Gelfond-Schneider, prime number, and Mordell-Weil theorems are included as well. Each chapter contains numerous problems and solutions.
A Course in Number Theory
Second Edition
H. E. Rose
Reviews and Awards
"This excellent book on number theory is detailed and readable. If the appropriate chapters are selected, it is suitable for upper-undergraduate and graduate levels..... The book contains excellent problems, a bibliography, and many references to computer applications. Rose's second edition can serve as a good textbook or a fine reference book and can be used for independent study by anyone interested in learning number theory." --The Mathematics Teacher
"An extremely demanding text for undergraduates, but well-suited for a mathematician who wants to learn some number theory." --American Mathematical Monthly
"The author shows an impeccable taste in his choice of topics and gives a lot of historical discussion, making this book a pleasant one to browse, and a great text on which to base a first undergraduate number theory course . . . . It should give students a tantalizing glimpse into a beautiful area of number theory, and inspire them to further explore the subject."--Mathematical Reviews |
Mathematics
Software for teaching and learning mathematical proofs
Where most mathematical proof software concentrates on formal logic (or some other specialty area of mathematics), Lurch aims to be truly general-purpose, with an attracitve user interface. |
Math Made Nice - N - Easy, Book #3 - 00 edition
Summary: Almost everyone needs some math in everyday life, at work, in a career, for study, for shopping, for paying bills. dealing with a bank, in sports, using credit cards, etc. This series of books simplifies the learning, understanding, and use of math, making it non-threatening, interesting, and even fun. The series develops math skills in an easy-to-follow sequence ranging from basic arithmetic to pre-algebra and beyond. These books draw on material developed by the U....show moreS. Government for the education of government personnel with limited math and technical backgrounds. Volume III covers factoring, ratios, linear equations, proportions, variations, and functions. |
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...analyze what's needed and then act upon that to answer a series of questions." Mr. Lindsey said it's a new modelformathinstruction. "Math is totally different now," he said. "We're answering the question: 'Why do I have to learn this... |
Precalculus with Unit-Circle Trigonometry - 3rd edition
Summary: This book introduces trigonometry through the unit circle. Cohen emphasizes graphing to explain complex concepts in an uncomplicated style, and provides supplementary graphing-calculator exercises at the end of most sections for additional perspective and reinforcement.
Trigonometric Functions of Real Numbers. Graphs of the Sine and the Cosine Functions. Graphs of y = A sin(Bx-C) and y = A cos(Bx - C). Simple Harmonic Motion. Graphs of the Tangent and the Reciprocal Functions.
Right-Triangle Applications. The Law of Sines and the Law of Cosines. Vectors in the Plane, a Geometric Approach. Vectors in the Plane, an Algebraic Approach. Parametric Equations. Introduction to Polar Coordinates. Curves in Polar Coordinates.
PART X. SYSTEMS OF EQUATIONS.
Systems of Two Linear Equations in Two Unknowns. Gaussian Elimination. Matrices. The Inverse of a Square Matrix. Determinants and Cramer's Rule. Nonlinear Systems of Equations. Systems of Inequalities.
PART XI. ANALYTIC GEOMETRY.
The Basic Equations. The Parabola. Tangents to Parabolas (Optional). The Ellipse. The Hyperbola. The Focus-Directrix Property of Conics. The Conics in Polar Coordinates. Rotation of Axes.
PART XII. ROOTS OF POLYNOMIAL EQUATIONS.
The Complex Number System. Division of Polynomials. Roots of Polynomial Equations : The Remainder Theorem and the Factor Theorem. The Fundamental Theorem of Algebra. Rational and Irrational Roots. Conjugate Roots and Descartes' Rule of Signs. Introduction to Partial Fractions. More About Partial FractionsFollett School Solutions, Inc. Woodridge, IL
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Inglewood GeometryThus, central to linear algebra is the study of matrices and how to perform basic operation such as matrix multiplication. The notion of vector space and subspace becomes important and Eigenvalue problems will be introduced in more advanced linear algebra courses. Quantum physics uses the langu... |
With the new editions, the approachable writing and pedagogy, varied exercise sets, and robust ancillary resources have been updated. A Drawing upon his passion for statistics and teaching, Mike Sullivan addresses the needs of today's students, the challenges teachers face, and changes in the statistics community. With feedback from his own students and classroom experience, Fundamentals of Statistics provides the tools to help students
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if gte mso 9]> Normal 0 false false false MicrosoftInternetExp Books a la Carte are unbound, three-hole-punch versions of the textbook. This lower cost option is easy to transport and comes with same access code or media that would be packaged with the bound book. College Mathematics, Ninth Edition , is designed for students in a broad range of career programs requiring a solid understanding of basic math, elementary algebra, trigonometry, and geometry. The authors introduce topics using a step-by-step
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Directed primarily toward undergraduate Management or Business college/university majors, this text also provides practical content to current and aspiring industry professionals. This bestselling text vividly illustrates management theories by incorporating the perspectives of real-life managers. Throughout this text, readers will see and experience management in action, helping them understand how the concepts they're reading about work in today's business world.</P>
Highlights: 032190107X / 9780321901071 Intermediate Algebra, Books a la Carte Edition Plus MyMathLab -- Access Card Package Package consists of: |
Understanding Algebra is a textbook written by James Brennan of Boise State University. The entire contents of the textbook are located on this site, and a PDF version is also available through the author?s Website. B...
Provided by the University of Vienna?s futureMedia initiative, the Maths Online Gallery consists of a large collection of extremely useful interactive learning units that demonstrate mathematical concepts. A large n...
For students in college-level math courses, revisiting algebra can be a challenge, and learning for it the first time can prove to be tricky as well. This website, created by Professor John Miller of the City College of...
Teaching algebra can be a difficult proposition, and at times, those who have just entered the field of mathematics education can feel a bit overwhelmed. Stepping in to provide a bit of assistance is this series of...
Math Power is a site created by Professor Freedman, a highly acclaimed teacher of basic mathematics. She has several resources to help students of all ages learn pre-algebra and elementary algebra skills. Many sample... |
Survey of Mathmatics With Applications - 9th edition
Summary: In a Liberal Arts Math course, a common question students ask is, ''Why do I have to know this?'' A Survey of Mathematics with Applicationscontinues to be a best-seller because it shows studentshowwe use mathematics in our daily lives andwhythis is important. The Ninth Edition further emphasizes this with the addition of new ''Why This Is Important'' sections throughout the text. Real-life and up-to-date examples motivate the topics throughout, and ...show morea wide range of exercises help students to develop their problem-solving and critical thinking skills.
Angel, Abbott, and Runde present the material in a way that is clear and accessible to non-math majors. The text includes a wide variety of math topics, with contents that are flexible for use in any one- or two-semester Liberal Arts Math90.16 +$3.99 s/h
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MATLAB Fundamentals
This course provides a comprehensive introduction to the MATLAB® technical computing environment. This course is intended for beginning users and those looking for a review. No prior programming experience or knowledge of MATLAB is assumed, and the course is structured to allow thorough assimilation of ideas through hands-on examples and exercises. MATLAB competency is developed in a natural way, with an emphasis on practical application. Themes of data analysis, visualization, modeling, and programming are explored throughout the course. Topics Include: |
The most helpful favourable review
The most helpful critical review
5.0 out of 5 starsVery useful set of questions
These are a great set of books full of useful revision questions (but bear in mind, they are NOT books of revision TIPS)
Published on 20 Dec 2011 by MC
2 of 2 people found the following review helpful
3.0 out of 5 starsan amazing product but has faults...
most people would struggle on.however on the down side, the answers are not explained on how you got to that answer so you do not know where you were at fault also some answers are not accurate.the fact that they made mistakes with the answers was really irritating as i was positive i got the answer right and was not sure how it could be wrong i then had to check with my maths teacher who said i was right. and this was not just with one question i had to check with him with a few and again my maths teacher said i was right and the book was wrong. overall i really like the book and am still using it but the little mistakes are a let down.
This book is highly helpful for the whole set of grade ranges A*-G and will ensure a least a grade higher if used effectively - I'm sure. It is on the whole good and full of practice questions which help for the real papers. A few negatives, such as the spaces given for the answers is small, the marks are a bit uneven - there was a 6 mark question for simply comparing two stem and leaf diagrams - which is highly unlikely and furthermore on one of the questions, the answer in the back of the book was wrong - this was on f(x) functions, and the questions was a co-ordinate change for y=1/2 f(x). In the back it said it stayed the same, but it doesn't. The y is stretched by 1/2. So for (2, 5) it would end up as (2, 2.5). I don't know how it happened. |
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MATLAB Primer
Edition:
7
Publisher:
Chapman & Hall/CRC
Number of Pages:
215
Price:
17.96
ISBN:
1-58488-523-8
MATLAB Primer (7th edition) is a pocket-sized quick reference guide to the popular software package MATLAB, updated to be used with the 7th version of the software. The little book is divided in two parts. The first part consists of 21 chapters where the authors go over different topics (the basics about MATLAB and the desktop; operations with numbers and matrices; functions; control statements; M-files; graphics; polynomials; solving equations; differential equations; calling other programming languages: C, Fortran, Java). The second part of the book is a comprehensive list of commands, followed by a one-line description (the list includes over 1250 commands). Also, the book contains a helpful table of contents and index.
In the first part of the book, the different features and commands present in MATLAB v7.0 are explained in a brief and concise way, and mostly through examples, so the users/readers can try some spelled-out exercises before trying some examples of their own.
I believe that the beginners and casual users of MATLAB will find the little book very helpful as a companion when trying to run the software. However the "Primer" will probably not be useful to the expert MATLAB user, because each topic is treated quite briefly. The convenient size makes it a nice book to have around, for quick help on usage of a command or a little intro on some new topic. The long (and nicely organized) list of commands in the second part of the book is useful to the reader to find the appropriate command. |
Volume 8, Number 35
1 September 2003 Vol. 8, No. 35
THE MATH FORUM INTERNET NEWS
Dr. Math Gets You Ready for Algebra | Simon Says
Thinking Fountain Shapes Cluster
DR. MATH GETS YOU READY FOR ALGEBRA
by the Math Forum @ Drexel
John Wiley & Sons
ISBN 0-471-22556-8
For almost a decade, kids have been writing to Dr. Math at
the Math Forum Web site with questions about their math
problems. And the math doctors at The Math Forum @ Drexel
have been replying with clear explanations and helpful hints.
"Dr. Math Gets You Ready for Algebra" helps prepare kids
for one of the biggest leaps in their math learning
experience -- the jump from the concrete world of numbers and
real objects to the abstract world of letters and symbols.
The book includes dozens of letters from kids who've had
trouble understanding the basic math concepts used in
algebra, along with answers from trained volunteers drawn
from a pool of college students, mathematicians, teachers,
and professionals from the mathematical community. Topics
covered include fundamental operations, integers, real
numbers, equations with variables, algebra applications,
and much more.
For more information and a link to purchase the book from
Amazon.com, please visit:
The second book, "Dr. Math Explains Algebra," is available
for advance purchase through Amazon.com and will be on
bookstore shelves in November, 2003. The third and fourth
books will cover geometry and will be available in 2004.
We hope the books will find a place in classroom, library,
and home collections. We invite you to display a link from
your school's website to our book information page. Please
use the information given on this page:
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SIMON SAYS...
Jeanne Winters from Princeton Community High School has
designed a WebQuest for her calculus students. The WebQuest
addresses the concepts of integration, elliptical curves,
cylinders and the forces of gravity and lift.
Using the resource links provided, students must design the
hull of a blimp. This requires deriving definite integrals,
and using technology to check work or approximate the
"un-evaluate-able" integrals when necessary.
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THINKING FOUNTAIN SHAPES CLUSTER
The Science Museum of Minnesota offers hands-on experiments
and activities that relate shapes to elementary math,
science, and language arts. Each page lists related
activities or resources, including recommended books.
Other Thinking Fountain clusters include:
- Tropical Rainforest
- Loose Parts
- Tools for Investigation
- Science Props
- Books You Can Use
- Students as Designers
- Journey North
- Air
- Project Galleries |
Find a Hilshire Village, TX Algebra 2 can use symbols to represent not only what certain statements say but also can use other symbols to specify specific meanings, ex, using 'V' to represent an 'OR' situation as in 'it is raining OR is it sunny" After using these symbols, we can then apply the many rules of logic to determine th...
...And I really like using calculus while solving problems. These were some of the founding subjects for my undergraduate degree in physics from UT Austin. It is very interesting to play with geometrical structures and problems, and finding solutions. |
Presented by HippoCampus, a project of the Monterey Institute for Technology and Education, this free online course follows up on a previous course, Algebra 1A, which "develops algebraic fluency by providing students...
This course, designed for Miami Dade Community College, integrates arithmetic and beginning algebra for the undergraduate student. By applying math to real-life situations most students experience during college, the...
This document from SpaceTEC National Aerospace Technical Education Center presents a core readiness course which will serve to prepare individuals entering the aerospace field. The document is 55 pages and contains...
OP-TEC has developed program planning and course materials to support education and training for future and current photonics technicians. Classroom materials include Scientific Notification, Unit Conversion,...
Brought to you by Elizabeth Stapel and purplemath.com, this collection of learning modules contains over 100 mathematics modules designed to teach beginning, intermediate, and advanced algebra concepts. Some algebra... |
Find a Garnet Valley, PAIt takes all the skills learned in Algebra 1&2 to a much deeper level, while at the same time advances several concepts begun in Geometry. The goal of Precalculus is to prepare students for Calculus by exposing them to a variety of graphs and functions which will be used or seen in higher level math. It is a great deal of fun, especially if you like puzzles |
Islamic Societies of the Middle East and North Africa: Religion, History, and Culture Notre Dame OpenCourseware (OCW) offers free educational resources for the course "Islamic Societies of the Middle East and North Africa" in the Program in Arabic and Middle East Studies.This subsequ Author(s): Asma Afsaruddin
Do you own an iPhone? Do you also have toddlers or kids who are about to enter school? Put the iPhone and the kids together with some of the apps listed below to keep the kids busy as they prepare themselves
A=B This book is about identities in general, and hypergeometric identities in particular, with emphasis on computer methods of discovery and proof. The book describes a number of algorithms for doing these tasks. Author(s): No creator set
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9 Putting it all together Questions Different kinds of thinkingBasic Concepts of Mathematics This book helps the student complete the transition from purely manipulative to rigorous mathematics. The clear exposition covers many topics that are assumed by later courses but are often not covered with any depth or organization: basic set theory, induction, quantifiers, functions and relations, equivalence relations, properties of the real numbers (including consequences of the completeness axiom), fields, and basic properties of n-dimensional Euclidean spaces. Author(s): No creator set |
Pre-Algebra, Algebra 1, and Algebra 2 Worksheets
Here is a graphic preview for all of the Algebra Worksheet Sections. You can select different variables to customize these Algebra Worksheets for your needs. The Algebra Worksheets are randomly created and will never repeat so you have an endless supply of quality Algebra Worksheets to use in the classroom or at home. These Algebra Worksheets are divided into three different topic areas, consisting of Pre-Algebra Worksheets, Algebra 1 Worksheets, and Algebra 2 Worksheets to make finding the right worksheet for your needs.
Our Algebra Worksheets are free to download, easy to use, and very flexible.
These Algebra Worksheets are a great resource for children in the 4th Grade, and 5th Grade, 6th Grade, 7th Grade, and 8th Grade.
Quick Link for All Algebra Worksheet Sections
Pre-Algebra Worksheets
This section contains all of the graphic previews for the Pre-Algebra Worksheets. We have six different topics covering Algebraic Expressions, Inequalities, Equations, Linear Functions, Polynomials, and Systems of Equations. These Pre-Algebra worksheets are a good resource for children in the 5th Grade through the 8th Grade.
Algebra 1 Worksheets
This section contains all of the graphic previews for the Algebra 1 Worksheets. We have nine different topics covering Basic Review, Inequalities, Equations, Linear Equations, Systems of Equations, Quadratic Functions, Rational Expressions, Polynomials, and Radical Expressions. These Algebra 1 worksheets are a good resource for children in the 5th Grade through the 9th Grade.
Algebra 2 Worksheets
This section contains all of the graphic previews for the Algebra 2 Worksheets. We have thirteen different topics covering Basic Review, Equations and Inequalities, Linear Relations and Functions, Systems of Equations, Matrices, Complex Numbers, Quadratic Functions, Polynomial Functions, General Functions, Radical Functions, Sequences and Series, Rational Expressions, and Exponential and Logarithmic Functions. These Algebra 2 worksheets are a good resource for children in the 5th Grade through the 9th Grade. |
55Focusing on applications rather than theory, this book elucidates the real-life utilization of mathematical modeling and modern mathematical methods, such as bifurcation analysis, dynamical system theory, nonlinear dynamics, and chaotic dynamics. It provides a practical understanding of how the models are used in current research in the areas of population dynamics, physical science, and engineering, and contains a large number of solved examples, applications, and hints to unsolved problems. The text covers all fundamental concepts and mathematical skills needed to build models and do analyses and also provides an informative overview of known literature. |
Journey into Mathematics: An Introduction to Proofs [NOOK Book] ...
More About
This Book historical and etymological asides. The three-part treatment begins with the mechanics of writing proofs, including some very elementary mathematics--induction, binomial coefficients, and polygonal areas--that allow students to focus on the proofs without the distraction of absorbing unfamiliar ideas at the same time. Once they have acquired some geometric experience with the simpler classical notion of limit, they proceed to considerations of the area and circumference of circles. The text concludes with examinations of complex numbers and their application, via De Moivre's theorem, to real numbers.
Editorial Reviews
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Intended as a textbook for a one-semester course between calculus and the first courses in abstract algebra and real variables. Starts with concepts such as trigonometry and integration that are already to familiar to students at this level, so that they can concentrate on the mechanics of writing proofs. Synthetic geometry is then used as an inroad to introducing convergence of sequences. The text ends with a discussion of complex numbers, De Moivre's Theorem, and irrationalities |
Math Teaching
Mon, 2013-11-11 15:03 -- univcomm
Math Teaching
The mathematics teaching major prepares students to teach mathematics at the secondary level, completing mathematics courses such as Calculus I, II, and III; Linear Algebra; Discrete Mathematical Structures; College Geometry; Abstract Algebra; Real Analysis; Problem Seminar; either Introductory Statistics with Applications or Mathematical Statistics; and either Differential Equations or Mathematical Models. Students must also meet requirements of the School of Education to meet professional teaching requirements. |
Find a Marana MathMy entire Controls and Stability course was involved with MATLAB. Attitude Dynamics was based in MATLAB. I'm an aerospace engineer, every single calculation that is too complex for a calculator, or requires modelling, is done in MATLAB. |
A little algebra
In computer graphics it is crucial that we have knowledge about some
basic mathematics. In this module we will, as in the other mathematics modules,
go straight to the point and treat the mathematics as a tool. We will not worry
about proof or generalization, but focus on the practical issues.
The advantage is that we quickly can establish the apparatus we need. The disadvantage
is that we may lose the general concepts that could be necessary when we need to study
the mathematics more deeply.
Matrices
Addition
We know that we can add two matrices, or two vectors, if the number
of rows and columns are equal in both.
A=B+C
aij=bij+cij
all rows i and columns j
Multiplication
We know that we can multiply two matrices if the number of columns in the
first matrix equals the number of rows in the second (n). The result matrix
gets the same number of rows, nr, as the first matrix and the same number
of columns, nk, as the second one.
Remember the modules about transformations in the plane and the space.
By inspection we can see that the matrices we use in the expressions
P2=M·P1 are the transposed of the ones we use in
P2=P1·M.
Inverting
Matrix B is said to be the inverted of matrix A if
A·B=I, the identity matrix. Geometrically we
perceive this so that a matrix is the inverted of another if it neutralizes a
transformation, that means, does the opposite. In some cases we can by reasoning find the
inverted of a matrix by using geometrical reasoning.
For example we can assume that the inverse matrix for a rotation around the
z-axis with the angle v is a matrix with the rotation -v.
If we give up geometrical knowledge about the matrices we have to use standard
algorithms to find the inverted of a matrix. We'll not discuss this here,
but algorithms like these can be found in most numerical libraries.
Graphical packages sometimes have use for operating with inverted transformations.
A case could be when we want to interactively point with the mouse
on a part of a model and wish to find what object we pointed at.
If we assume that the model has been transformed
we should be able to transform the mousepoint back into the model by the inverse transformation.
In the MS-Windows API the routines LPtoDP (Logical Point to Device Point) and
DPtoLP (Device Point to Logical Point) handles transformations between model coordinates
and screen coordinates. Here are both model and screen (device) coordinates given in the plane.
We will see in the module: To identify by pointing, that OpenGL
uses another strategy to identify objects that are pointed at in a three dimensional
model.
Vectors
The length of a vector
Assume a vector A. The length of A in n-space is defined to be
This is a generalization of Pythagoras. For n=3, the space,
we can illustrate it like this:
Scalar product
The scalar product of two vectors is a number, a scalar. Assume
two vectors A and B. The scalar product is defined as
where n is the dimension of the vectors.
We set n=3 and describe the vectors A and B as row vectors: A=(2,3,5) and B=(1,-6,2).
The scalar product becomes: A·B=2·1-3·6+5·2=-6
Further we see that
We can for example let A be described by (x,y,z), and we can write
We will use the scalar product to deduce a practical way to find the
angle between to vectors.
Consider the two vectors A and B.
This is interesting and useful because it tells us that if we know two
vectors, we can find the cosine of the angle between them.
and if the vectors are normalized, their length equal 1, we
can write.
cos(v)=AB.
In OpenGL the angle between different directions (vectors) is used,
among other things to calculate reflected light. To make OpenGL act
reasonable, we usually have to state the normal vectors for surfaces
we specify:
glNormal3f(x,y,z)
Internally OpenGL would like to do calculations on these as normalized
vectors. We can avoid the work with normalizing vectors ourselves by turning on
automatic normalization:
glEnable(GL_NORMALIZE)
The cross product
The cross product of two vectors is a new vector, AxB=C.
The vector C is placed in a 90 degrees angle to A and B and
its direction is in a way so that the vectors A, B and C creates a right hand system.
C is the normal of the plane spawned by A and B.
The cross product for two vectors in space is defined as:
C=AxB=(a2b3-a3b2,
a3b1-a1b3, a1b2-a2b1)
This is useful in situations where we are specifying normals for surfaces.
We know that if we know three points (not in line) in a plane we can calculate
the plane's normal.
References and examples:
Source for this material is algebra books.
The most important parts are, as here, summed up in most
computer graphics books |
Book summary
This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra. |
1.1: Trigonometry and Right Angles
This Trigonometry Teaching Tips FlexBook is one of seven Teacher's Edition FlexBooks that accompany the CK-12 Foundation's Trigonometry Student Edition.
To receive information regarding upcoming FlexBooks or to receive the available Assessment and Solution Key FlexBooks for this program please write to us at teacher-requests@ck12.org.
Basic Functions
The Basics of Functions
Some students' eyes may glaze over at the equation used in the "gas mileage" situation, especially if it's been a while since their last algebra class. Watch for students who look confused and walk them through setting up the equation if necessary.
Another way to explain the definition of domain is that it is the set of real values you can plug into the function that will produce a real number as the output. You can show that the domain of is the set of all real numbers because any real number can be multiplied by to get a real number ; then you can show that the domain of is restricted to the nonnegative real numbers by demonstrating that you get a real value for when you plug in a positive or zero value for , but not when you plug in a negative value.
Similarly, you can explain that the range of a function is the set of values that could be the possible outputs of the function given a real number as the input.
The "rounding" example provides a good opportunity to remind students that rounding "up," in the case of a negative number, means rounding toward zero rather than away from zero; since is greater than, should be rounded up to .
Families of Functions
In the "families of functions" table, you may need to clarify what "these functions have a highest exponent of " means—i.e., the highest power that appears anywhere in the equation is 2. (We can also say that the degree of the function is , or that the function is of the "second degree.") The same holds, of course, for "these functions have a highest exponent of 3," but you also may want to clarify "the ends of the graph have opposite behavior": it simply means that one end of the graph goes up while the other goes down. You may also want to graph to show why it has no local maximum or minimum.
And finally, for students who may have forgotten how asymptotes work, it's worth reminding them that the values of the function approach the asymptote but never actually reach it. Specifically, if a function has a horizontal asymptote, it means that y will get closer and closer to that value as approaches infinity, but will never quite reach it; if a function has a vertical asymptote, it means that will get closer and closer to infinity as gets closer to the given value, but the function is undefined when is exactly equal to that value.
A useful way to explain direct and inverse variation is that with direct variation, the dependent variable increases when the independent variable increases, while with inverse variation, the dependent variable decreases when the independent variable increases. This makes the contrast between the two types of function clearer.
You can clarify the definition of a periodic function by explaining that all the values of the function repeat themselves every units. It may be useful to demonstrate with the "weather" example above: in this case is , so you can show that , and so on.
Points to Consider
(You may want to go over these as a group each lesson.)
Using a calculator to graph functions is quicker and more accurate than doing it by hand, but it can be hard to see precisely where the important points on the graph are.
Angles in Triangles
Similar Triangles
It may be useful to note that the proportions that show that the ratios of corresponding sides are equal can be derived directly from the proportions that show that the side ratios within the two triangles are equal. (For example, can be derived directly from .)
If you want to move through example a little more quickly, you can point out that the side lengths in the second triangle are simply half those in the first.
Students may ask whether ASA and SAA are also criteria for determining if two triangles are similar, since criteria like those exist for determining if triangles are congruent. Explain that they are, but for a very simple reason: if two of the angles are congruent, then the third angle must also be congruent, and so the ASA and SAA cases simply reduce to the AAA case.
The HL case, on the other hand, is a special example of SSA: two of the sides are proportional, and an angle that is not between them is congruent. Normally, this would not be enough to determine that two triangles are similar, but what helps us here is that we are dealing with right triangles, which means that we can use two side lengths to determine the third. Once we've found that the other leg is proportional too, then instead of looking at this as a case of SSA, we can see it as a case of SSS: all three pairs of sides are proportional. (Incidentally, we could also see it as a case of SAS: the two legs are proportional, and the angle between them (the right angle) is congruent.)
Points to Consider
The answer to question #1 can be demonstrated in more than one way. First, you can draw two right angles with the included side between them, and show that the other two sides are now parallel, meaning that they can't ever meet to make a triangle.
Second, you can point out that two right angles add up to , and since that is the sum of all three angles of a triangle, that would mean the third angle would have to measure , which is not possible.
Similar reasoning holds for question #2. Drawing two obtuse angles with the included side between them demonstrates even more clearly that the other two sides could never meet, and adding together two angle measures greater than each would give you a sum greater than , which is impossible even before you consider the measure of the third angle.
Question #3 has a different answer depending on what situation you are considering. If you just look at an angle in isolation, then in a sense it cannot have a measure greater than , because an angle of, say, could just as easily be described as an angle of viewed from the other side. However, when you are measuring angles of rotation, as the next lesson will cover, an angle can measure more than 180º or even more than . Mentioning this might be a good segue to the next lesson.
Measuring Rotation
Measuring Angles
Some students may need to see example worked out in more detail. You may need to spell out that the circumference of the smaller wheel is π meters and that of the larger is ; then, rather than simply explaining that the larger wheel rotates once every time the smaller one rotates twice (and therefore rotates twice when the small one rotates four times), you may need to show that the four rotations of the smaller wheel cause its circumference to travel along the larger wheel, and that this is equal to or rotations of the larger wheel.
Angles of Rotation in Standard Position
Students may not have encountered the terms "initial side" and "terminal side" before. Explain, if necessary, that these terms are specific to this particular situation; when we place an angle in standard position, the initial side is just what we call the side we chose to place along the axis, and the terminal side is simply the other side.
Co-terminal Angles
In working through the next example, you may want to take a moment to remind students which quadrant is which (quadrants I through IV proceed counterclockwise starting from the upper right). Knowing the quadrants will be important in upcoming lessons.
Another way to generate the angle , of course, is to subtract from to get . This method can be faster than rotating clockwise, but students should familiarize themselves with both techniques.
Points to Consider
Real-life instances of angles of rotation might include a wheel, a swinging door, a doorknob, or a screw.
Review Questions
You may need to walk students through problem 7. First they must find the total distance the car's inner wheel travels, which is a quarter ( worth) of the circumference of a circle with a radius. Then they must find the number of rotations the inner wheel makes in traveling that distance, which takes two steps: first find the circumference of the wheel based on the given diameter of ., and then divide the total distance traveled by the circumference of the wheel to find the number of rotations it makes. Next, they must find the distance the outer wheel travels. Since the wheels are apart, the outer wheel follows a curve with radius greater than the curve the inner wheel follows, so the distance it travels is a quarter of the circumference of a circle with a radius. Then, dividing that distance by the circumference of the wheel (already found) gives the number of rotations the outer wheel makes. Finally, they must subtract to find how many more rotations the outer wheel makes than the inner.
Defining Trigonometric Functions
The Sine, Cosine, and Tangent Functions
Another way to explain the domain and range of the first three trigonometric functions is as follows: The trigonometric functions take angles as their input, and their output consists of particular ratios of side lengths.
The mnemonic SOH CAH TOA (Sin: Opposite/Hypotenuse; Cosine: Adjacent/Hypotenuse; Tangent: Opposite/Adjacent—pronounced roughly "soak a toe-a") may help students remember the ratios. Another mnemonic is "SCoTt, Oscar Has A Heap Of Apples"—that is, for Sin, Cos, and Tan respectively, the ratios are , and .
It may be worth stressing that , and are abbreviations for types of functions, and do not indicate that anything is being multiplied.
Secant, Cosecant, and Cotangent Functions
The fact that the secant, cosecant, and cotangent are reciprocals of the cosine, sine, and tangent functions respectively will be made explicit in a later section of the text, but it may be useful to point it out now, as this may make it easier for students to remember those ratios.
Trigonometric Functions of Angles in Standard Position
In example 4, you may need to clarify that although the two legs of the triangle in the diagram are labeled and , the coordinate we are working with is actually , and so when finding the values of the trig functions, we must plug in as the length of that leg. (This is where trig functions of angles of rotation start to differ from trig functions of angles in right triangles.)
Points to Consider
The Pythagorean Theorem is useful in trigonometry in at least two ways: it helps us find the third side of a right triangle when we need to, and it helps establish some important trigonometric identities. However, the latter won't be covered for a couple more lessons, so you may or may not want to even mention it at this point.
Values of trig functions can be negative when we are dealing with angles of rotation instead of angles in right triangles, because we define the functions in a slightly different way to allow us to describe many more cases. Angles in right triangles must be less than , and when we work out the trig functions for those angles, we always get positive numbers because the triangles' side lengths are always positive. But when we define the trig functions by reference to and coordinates and the unit circle, we now have a way of finding their values for angles greater than and it turns out that some of those values are negative, because the and coordinates we use to find them are sometimes negative. Similarly, trig values can be undefined when we try to find them for quadrantal angles, because some of the coordinates of those angles equal zero.
(All of this will be covered in more detail in the next lesson.)
The unit circle is useful because it gives us an easy way to calculate the trig functions for any given angle; then, because of similar triangles, we know that those values will be the same when we see that same angle in any triangle, even if the hypotenuse of the triangle is not . For example, the unit circle tells us that the cosine of is about , so whenever we see a right triangle with a angle in it, we know (because the triangles are similar) that the ratio of the adjacent leg to the hypotenuse will always be , without having to measure the sides.
Trigonometric Functions of Any Angle
Reference Angles and Angles in the Unit Circle
After example 1, you may need to show more explicitly how we know the ordered pair for 150° based on the ordered pair for . Remind students that a angle is the reflection across the axis of a angle (refer to the earlier diagram), and remind them (and demonstrate visually) that when we reflect a point across the axis, its coordinate stays the same and its coordinate changes sign.
Example 2 provides another opportunity to make this clear. Each angle that has as its reference angle is simply the angle we get if we reflect a angle across the axis (putting it in the fourth quadrant), the axis (putting it in the second quadrant), or both (putting it in the third quadrant). If we reflect it across the axis, its coordinate stays the same and its coordinate changes sign; if we reflect it across the axis, its coordinate stays the same and its coordinate changes sign; and if we do both, both coordinates change sign. So we can easily find the coordinates for any angle once we know its reference angle and which quadrant it is in.
Trigonometric Function Values in Tables
When you arrive at the table of trig function values, you may want to encourage students to compare the values of the trig functions for pairs of supplementary angles (like and , or and ). The table makes it clear that cosines of supplementary angles are equal, and sines and tangents of supplementary angles are opposites. Thinking in terms of reference angles will make it clearer why this happens: an angle between and has a reference angle that is equal to its supplement, so the values of the trig functions for that angle are closely related to the values for its supplementary angle.
Because of this fact, there is another way to find the answer to example 6a; challenge students to figure out what it is. (Hint: what is the reference angle of ?)
You may also want to encourage students to compare the sine and cosine values for pairs of complementary angles, like and ; the table shows that the sine of an angle is equal to the cosine of its complement. This fact will be useful later, and the reason for it will be clearer when we study the unit circle in more detail.
Points to Consider
Here's one way to explain the difference between the measure of an angle and its reference angle: when you start at the positive axis and rotate counterclockwise to get to the terminal side of the angle, the distance you've traveled is the angle measure. When you start at the terminal side of the angle and travel by the quickest route to the closest portion of the axis, the distance you've traveled is the reference angle. (Demonstrate this visually with at least one angle that is not in the first quadrant. For example, with a angle, you can show that is the clockwise distance from the positive axis, but is the shortest distance to the closest part of the axis.)
An angle is the same as its reference angle only when it is between and .
The simplest way to answer question #2 is by considering how we find values of trig functions on the unit circle. The values of sine and cosine there are simply equal to the coordinate and coordinate, respectively, of the ordered pair that defines the angle, so the angles that have the same (or opposite) sine (or cosine) value will simply be the ones with the same (or opposite) coordinate (or coordinate).
Review Questions
The function in problem 12 is fairly complex (although it can be simplified) and it shouldn't be immediately obvious what the graph will look like. Students should be able to simplify the expression under the square root sign based on their conjecture from the previous problem; after that, the best they can do is figure out what the function's values will be for a few key angles (, and so on), plot the points, and sketch a graph based on those points, and then graph the function on a calculator to compare it with their sketch.
Relating Trigonometric Functions
Reciprocal Identities
After explaining that we obtain the reciprocal of a fraction by flipping the fraction, you might need to clarify how to obtain the reciprocal of something that is not a fraction. For example, the reciprocal of is , and that's because is equivalent to the fraction , which we can flip to find the reciprocal. Similarly, a trig value like cos is equivalent to , so if is the reciprocal of , that means it is equivalent to .
The identity may not be immediately obvious; it hasn't previously been explicitly mentioned, although students were encouraged to discover it for themselves in Review Question 11 of the previous lesson. If you wish, you can demonstrate how to derive it from the definitions of sine and cosine and the Pythagorean Theorem: In right triangle ABC where c is the hypotenuse, by definition and ; therefore . Then if , multiplying through by yields , which we know is true because it is simply the Pythagorean Theorem.
Domain, Range, and Signs of Functions
It's much easier to remember which trig functions are positive and negative in which quadrants if we simply note that in the first quadrant they are all positive; in the second quadrant only sin and its reciprocal, csc, are positive; in the third quadrant only tan and its reciprocal are positive; and in the fourth quadrant only cos and its reciprocal are positive. This can be summarized by the mnemonic "All Students Take Calculus": All positive, Sin positive, Tan positive, Cos positive.
(The second-best way to figure out which functions are positive where is to think about which functions depend on the coordinate, which ones depend on the coordinate, and which ones depend on both, and then figure out which coordinates are negative depending on which quadrant we are considering. For example, in the third quadrant, where both coordinates are negative, sin and cos will be negative (and therefore so will sec and csc), but tan (and therefore cot also) will be positive because is positive when both x and y are negative. But this method takes longer, and is more prone to error, than simply using the mnemonic above.)
Points to Consider
It can often be easier to tell if an equation is not an identity: simply plug in a couple of values for the variables in the equation and see if the equation holds true. If it doesn't, the equation is not an identity; if it does, the equation might or might not be.
Similarly, you can verify the domain and range of a function by plugging in numbers that are inside or outside the domain or range and seeing what happens. If a number is in the domain of the function, it should yield a sensible result when you substitute it for ; if it's not in the domain, it should not yield any real-number result. If a number is in the range of the function, you should be able to get it as a result when you plug in some value of ; if it's not in the range, you shouldn't be able to for any value of .
Applications of Right Triangle Trigonometry
Solving Right Triangles
If you are going through example 2 as a class, you may want to have students stop and think about how they might solve the triangle before walking them through the solution presented in the text. First, they should assess how much information they already have available—in this case, one side and two angles. (They may only notice the one angle measure that is written out in numerals—remind them that they also know the measure of the right angle.) Then they should think about what strategies they know for finding the other sides and angles (Pythagorean theorem, trig ratios), and which numbers they would need to plug in for each of those strategies. Finally, considering what numbers they actually have available to plug in should give them some idea of which strategies they could effectively use.
To answer the question posed in the solution: Using the tangent to find the third side is better than using the sine because using the tangent allows us to plug in the side we were given at the beginning, whose length we know precisely, rather than the side we just found, whose length we only know approximately. It's always best to base our calculations on the most precise information we have available, so that rounding errors don't accumulate.
Angles of Elevation and Depression
Clinometers are tools for measuring angles of elevation and depression; theodolites can measure horizontal angles as well. More information about both of these can be found on the Internet or in an encyclopedia.
For extra precision when measuring angles of elevation and depression, you should of course subtract several inches from your total height to estimate the distance from your eyes to the ground.
Other Applications of Right Triangles
An explanation of how we know the information given in example 7: We know the distance between the moon and the earth based on calculations that will be explained later in the book. We know the angle between the moon and the sun at a given time because we can measure it directly from our vantage point on the earth. And finally, we know that the moon makes a right angle with the earth and sun at the first quarter (when the moon is halfway full) because exactly half of the portion of the moon that we can see is lit up by the sun, meaning that the sun must be shining exactly "sideways" on the moon.
Points to Consider
In addition to the situations described in this lesson, we also might use right triangles to determine the shortest distance between two points on a grid (like a grid of city blocks), or to determine how long a ladder we need to reach a certain height on a building.
Any right triangle can be solved if we have enough information; at minimum, we need to know the length of at least two sides, or one side and one angle besides the right angle.
Trigonometry can solve problems at any scale because the trig ratios are the same for any size triangle as long as the angles are the same. |
Welcome to The Pre-lab Quiz Preparation Page
This page is an index file of interactive quizzes which should help you prepare for part of the lab quiz which occurs during the start of your lab period. Note, the actual quiz covers theoretical concepts, mathematical skills and procedural material relating to the laboratory you are about to perform. The objective is to be sure you come to lab prepared. The quizzes on this site will cover the mathematical competencies associated with the theoretical concepts behind the experiment.
You must allow pop-up windows if you wish to see the hints. They are safe for your computer
Note: The printer friendly version is more concise, opens in a new window, is easier to print and is more ecologically sound. Please Do NOT print the interactive version. Thank you.
If you have any questions or comments please feel free to contact your instructor or Dr. Belford
rebelford@ualr.edu. |
Quick Overview
MATHEMATICS AND PHYSICS FOR PROGRAMMERS provides a simple but thorough grounding in the math and physics topics programmers require to write algorithms and programs.
Description
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Sooner or later, all game programmers run into coding issues that require an understanding of mathematics or physics concepts such as collision detection, 3D vectors, transformations, game theory, or basic calculus. Unfortunately, most programmers frequently have a limited understanding of these essential mathematics and physics concepts.
MATHEMATICS AND PHYSICS FOR PROGRAMMERS, THIRD EDITION provides a simple but thorough grounding in the mathematics and physics topics that programmers require to write algorithms and programs using a non-language-specific approach. Applications and examples from game programming are included throughout, and exercises follow each chapter for additional practice. The book's companion website provides sample code illustrating the mathematical and physics topics discussed in the book |
What's New in Maple T.A. 9.5?
Maple T.A. 9.5 is an expansion of Maple T.A. 9 that provides more information to help instructors and students get started with the system, increased support for essay questions, and more control over proctored assignments. It also includes a sneak peek at some new technology we are working on: gradeable Math Apps!
Instructor Examples
Maple T.A. 9.5 includes new and improved sample content to help instructors become familiar with Maple T.A.
A sample of every question type and subtype is provided in the newly updated demo class content.
A sample assignment shows instructors what a typical assignment looks like. They can explore this assignment from both the instructor and student viewpoints to test out different options and see what the experience will be like.
Essay Annotations
Maple T.A. 9.5 includes the ability to mark up a student's essay by adding comments at selected points in the essay.
Choose from over 40 standard comments, such as "spelling," "slang," "sentence fragment," and more.
Expand the collection by adding your own comments, and embed those comments just as easily.
Provide detailed feedback that shows the location of the problem. The student can hover over each annotation marker in the corrected essay, and the comment will appear as a popup at the place in the text where the problem occurs.
Sneak Peek: Introducing Gradeable Math Apps!
Maple T.A. 9.5 includes a special sneak peek of some exciting new technology. As part of The Möbius Project initiative from Maplesoft, we have given Maple T.A. the ability to automatically grade interactive Maple applications. With gradeable Math Apps, you can ask your students to sketch graphs, provide them with specialized calculators, ask them to manipulate parameters until they have found the desired solution, give them interactive plots to explore, and much more.
This feature is offered as a technology preview so you can start getting familiar with it and begin developing content for your students. Maplesoft offers special services and support to assist instructors in creating, testing, and deploying Math Apps. Contact Maplesoft for details.
Highlights:
Math App questions let you embed an interactive Maple application inside a Maple T.A. question. Students use the app to answer the question, and Maple T.A. grades the results.
Students can interact with the Maple application using sliders, buttons, and other interactive elements, performing computations and generating plots, just as they would within Maple.
For grading, Maple T.A. compares the state of the student's app with the conditions specified by the question author, such as the location of a slider, whether or not a check box has been selected, or the contents of a math entry field.
Like other Maple-graded questions, Math App questions can be open-ended and have infinitely many correct answers and still be graded automatically.
Math App questions can make use of algorithmic variables, so not only the question, but the embedded Math App itself are changed each time the question is used.
Grading rules can be specified inside Maple T.A., as usual, or included as part of the Maple document in the startup code, where they are hidden from the students, so you can choose the authoring approach that best suits your needs.
When the student advances to another question or leaves the assignment without grading, the state of the Math App is saved so the student can return to it later. |
,...
Show More.* Understand fractions, decimals, and percents* Unravel algebra word problems* Grasp prime numbers, factors, and multiples* Work with graphs and measures* Solve single and multiple variable equations |
IBMathematicalStudies. An InThinking workshop for teachers new to the course. ... It might be something you feel passionate about at least strongly enough to have debated on it in the past. ... Here are errors that occur frequently on exam papers. Knowing the difference between the number ...
Welcome to the start of a new school year! This year, IB Learning Partners will be studying the ... The majority of these students will expect to need a sound mathematical background as they prepare for future studies in subjects ... There are two papers at the end of the two year ...
Many students taking physics courses have not reached a point of mathematical proficiency to solve computations, ... This project has been written up in previous research papers (Source 1, 2, ... IB Math Studies ...
International Baccalaureate Program IB Coordinators. ... French, Korean Physics History Psychology Biology MathematicalStudies Mathematics Film Film Admission to the Program. The ... In addition, most IB subject exams are divided into two or three different parts or "papers ...
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... (such as written papers, presentations, ... Cultures blend and the past illuminates the present through this course that examines folk talks, ... The following content will be covered in the IBMathematicalStudies SL two-year program: Review (numbers and sets, geometry, ...
MathematicalStudies SL. Level ... Evaluation in MathematicalStudiesIB will include the required informal and formal IB assessments as well as an exclusive site ... (EA) and Internal Assessment. Within the category of EA the students will be expected to write 2 papers (Paper 1 and Paper ...
International Baccalaureate Diploma Programme (IBDP) ... conducting research and the writing of research papers so that when they eventually enter university, ... Mathematics HL or SL and MathematicalStudies (only available at SL)
MathematicalStudies. SL only. 6. The arts. Visual Arts. HL and SL ... The International Baccalaureate Organization aims to develop inquiring, ... This generic term is used to describe analytic markschemes that are prepared for specific examination papers.
The International Baccalaureate® ... emotion, language and reason) and different kinds of knowledge (scientific, artistic, mathematical and historical ... and join the Spanish educational system by virtue of the validation of studies undertaken abroad will be exempted from taking any ...
understand that the nature and diversity of sources may lead to different ways of seeing or experiencing the past. ... The IB's written papers contain a more varied type of question than A Level ... The IBMathematicalStudies SL course and exams also require confident use of advanced ...
... understanding and appreciation of various aspects of past and present cultures as expressed in literature; ... IBMathematicalStudies courses prepare students to take the International Baccalaureate MathematicalStudies exam at the Subsidiary or Higher level.
... or DPMMS (the Department of Pure Mathematics and Mathematical Statistics). Both departments are located in the Centre for Mathematical ... but who is responsible for your welfare. You will also hear from your Director of Studies (DoS), ... Pastpapers are available on the internet, ...
If you wish to apply for mathematicalstudies please search for "IBmathematical" not maths. ... 3 exam papers worth 80%. Coursework ... Gathering up facts about the past is quite easy but making sense of them is more of a challenge.
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IBMathematicalStudies Standard Level. ... Students will write several papers based on the literary works read. ... and written expression. It includes Spanish pronunciation, phonetics, the most basic grammatical concepts, present and past verb tenses, most common and basic vocabulary and ...
The International Baccalaureate Organisation ... It is the process of recording, reconstructing and interpreting the past through the investigation of a variety of evidence. ... The nature of MathematicalStudies means that less formal, ...
... and interpreting a variety of forms of past and current thought, and 3) to increase the pupil's ... Course prepares students to write research papers and/or technical reports. Researching ... IBMathematicalStudies courses prepare students to take the International Baccalaureate ...
International Baccalaureate. ... trends and developments as well as continuity and change through the study of historical events which have shaped the past and ... a hobby or interest of his or her choice or her choice using skills learned before and during the mathematicalstudies ...
International Baccalaureate. Survival Manual. Mira Loma High School. ... PastIB Paper 2 Exam Prompts can be found online or provided by your teacher in the weeks leading up to the IB English exam. ... The best part about IB Math Studies is the curving of tests! This isn't a bell curve, ...
... for learning materials, assignments, past exam papers, notice ... (e.g. teaching, accountancy, engineering and finance). It also provides experience in computing (e.g. use of mathematical and statistical software) and I.T. (e.g. word ... Its two case studies are assessed in a ...
Both the International Baccalaureate Diploma (IB) and Advanced Placement (AP) ... MathematicalStudies SL. Computer Science SL Group 6 ... powerful and weak, past, present and even into the science fiction future.
... with more than 90% of exam papers marked onscreen annually. ... A visiting speaker could include a current or past PhD student or an organisation which carries out research ... Biology (IB course companion) (Oxford University Press, 2007) ISBN 9780199151455.
... examples of pastpapers and relevant mark schemes. ... The higher course is good preparation for IBmathematicalstudies. Both higher and foundation courses are good preparation for the International Diploma. How will I be assessed?
... (with some minor changes): International Baccalaureate Organization. Diploma Programme ... Must be primarily mathematical in content and must demonstrate student's ... There are a number of different documentation styles available for use when writing research papers; ...
... the four main objectives support the IB learner profile, ... make conjectures and use mathematical reasoning when solving problems in school and in real-life situations. ... Students will explore the nature of past and present communities through mathematics, ...
... Advanced Placement and International Baccalaureate courses. The time and effort you spend in higher level courses will pay dividends when you ... Theory of Knowledge is offered as a component of the IB Diploma program. In past years, ... IB Math Studies Option. Grade 9Honors Algebra II ...
International Baccalaureate 11. Applied Sciences (Industrial Technology, Family. ... MathematicalStudies SL is a two-year course for students who possess the fundamental skills of geometry and algebra. ... Precalculus with current or past enrollment in Calculus, Talk to Instructor. Elective ...
- Courses prepare students to take the International Baccalaureate Computing Studies exam at either ... and usage, as students write essays and begin to learn the techniques of writing research papers. ... Course prepares students to take the International Baccalaureate Language A exams at ...
Visible in more ways than the rigor of the International Baccalaureate or Inglemoor's dedication to ... Students display mathematical thinking through reading ... Inglemoor students may take advanced mathematics, including Pre-IB Advanced Algebra/Trigonometry, IB Math Studies, AP Stats ...
The IB exam is broken into 3 "papers" or parts. Paper 1 is a multiple choice test which consists of ... you will have already performed the investigation. Please use the past tense throughout the paper. Not every lab report will be a ... are useful mathematical tools which are used to ...
Past exam papers and markschemes (Buy from IBO) On the IB and DP. ... International Baccalaureate Diploma Programme by Jill Rutherford IB Study Guide: ... case studies on extinct, endangered and used to be endangered, now OK species .
... Vienna Institute for International Economic Studies and Eurostat data. ... A number of analytical papers on clusters by the Lithuanian Ministry of Economy are steps in the right direction. ... Despite growing quite rapidly in the past couple of years, ...
Collected Papers on Astronomy and Mathematics. Kendriya Sanskrit Vidyapeetha, Tirupati (1989). 5. ... Jyotisha Pandits concentrated their attention more on astrology than on studies and research in mathematical astronomy. However, ...
... -AP – IB – Dual or college equivalent course ... Custody Papers (if applicable). ... Students will probe essays of the past and present to discover the best in exposition, descriptions, narration and argumentation. |
MP Basic Mathematical Skills with Geometry
"Basic Mathematical Skills with Geometry, 7/e" by Baratto/Bergman is part of the latest offerings in the successful "Streeter-Hutchison Series in ...Show synopsis"Basic Mathematical Skills with Geometry, 7/e" by Baratto/Bergman is part of the latest offerings in the successful "Streeter-Hutchison Series in Mathematics". The seventh edition continues the hallmark approach of encouraging the learning of mathematics by focusing its coverage on mastering math through practice. This worktext seeks to provide carefully detailed explanations and accessible pedagogy to introduce basic mathematical skills and put the content in context. The authors use a three-pronged approach ( Communication, Pattern Recognition, and Problem Solving) to present the material and stimulate critical thinking skills. Items such as Math Anxiety boxes, Check Yourself exercises, and Activities represent this approach and the underlying philosophy of mastering math through practice. The exercise sets have been expanded, organized, and clearly labeled. Vocational and professional-technical exercises have been added throughout. Repeated exposure to this consistent structure should help advance the student's skills in relating to mathematics. The book is designed for a one-semester basic math course and is appropriate for lecture, learning center, laboratory, or self-paced courses. It is accompanied by numerous useful supplements, including McGraw-Hill's online homework management system, MathZone.Hide synopsis
Description:Fair. Book in Acceptable condition. Will show clear signs of...Fair. Book in Acceptable condition. Will show clear signs of use, water damage and/or staining that does not affect the readability of the bookDescription:Good. MP Basic Mathematical Skills with Geometry (The Streeter...Good. MP Basic Mathematical Skills with Geometry (The Streeter |
Differential Equations / With CD-ROM - 2nd edition
Summary: The authors stress a more balanced approach, one that includes analytic, numeric, and graphical techniques. The book emphasizes modeling and qualitative theory throughout the course. It employs technology significantly and consistently, presents linear and nonlinear systems in parallel, and includes an introduction to discrete dynamical systems. This text grew out of the Boston University Differential Equations Project, funded in part by the National Science Foundati...show moreon.
Benefits:
Technology is used throughout the book as a tool for illustration, experimentation, and discovery. Using the computer as a tool, students investigate solutions graphically as well as analytically, which leads to a better understanding of the properties of solutions.
This text's emphasis on interpretation, qualitative description, projects, and written explanations also leads to improvement of conceptual understanding. The chapter on discrete dynamical systems forms a connection between the topics discussed in this text and recent research in mathematics.
NEW! This edition features improved exercise sets and several new projects, including: The Flight of a Glider, A Forced Cantilever Beam, A Simple Model of the Tacoma Narrows Bridge.
NEW! A CD-ROM is now included free with the text, to simplify using technology in the course.
0534385141 |
Mathematics
Topics in Geometry
Class Level: Junior
Credits: 3
Department: Mathematics and Computing
Term:
Description: An introduction to modern geometric concepts, including foundations of geometry and non-Euclidean geometry. Incorporates use of computer software to illustrate and explore geometric concepts. Prerequisite: MAT 142, MAT 182, and CMP 150 or consent of instr
Overheard
"
Franklin College has prepared me by teaching me how to adapt to situations quickly." |
George Mason University?s Department of Computer Science is responsible for this great elementary calculus site. Each topic presented on this site contains learning objectives, definitions, examples, diagrams, and e...
The Geometry Center at the University of Minnesota has created these learning modules, which ?emphasize geometric concepts of calculus while examining applications of mathematics to the physical and life sciences.? Eac...
Created by Anne Cavagnaro and Ida Ponder of Columbia College, this course will help students develop critical thinking skills, differentiate between scientific and pseudoscientific data, apply statistics in real world...
Created by Thomas Murphy and Kerrie Murphy of Edmonds Community College, this lesson describes the LEAF School, which combines academic instruction employing service-learning with an AmeriCorps program so that students...
This lesson was created by Tom Murphy as part of Edmonds Community College's Tribal Community Project. Designed as a half-semester course, this site describes a project in which teams of approximately four students... |
Digital Challenge is a set of interactive activities for use in teaching basic digital concepts. The activities give students immediate feedback to reinforce correct responses. All student responses are corrected and ...
... >Very easy exciting and fast to use 2. Algebra : > >Can store up to three algeriac ... add, subtract, multiply, and divide of any two algebraic equations algebraically and produce an algebraic result, it ...
... allows the application of the construction concept in Algebra, Calculus, etc. Use its full potential to create interactive and dynamic math calculations and visualizations and you will discover new ways ...
... The libraries include numerical and analytical calculations, linear algebra operations, equation solving algorithms. Many libraries are based on the JAIDA classes for data manipulation, construction of histograms and functions. jHepWork ...
With Linear Algebra, you can solve systems of linear equations using the LU factorization of the matrix of coefficients. You can also perform different operations (add, subtract, multiply), finding the ...
It is a calculator for algebra.The inputs and outputs are in algebraic format.It can do the operations of add, subtract, ... factorized. It records the history of operations on algebraic functions.You can copy one function to another which ...
... in a very short time. Included areas: Arithmetic, Algebra, Geometry, Trigonometry, Analytic Geometry and miscellaneous.Visual Mathematics, a member of the VirtualDynamics Math Virtual Lab, is an Intuitively-Easy-To-Use software.Visual Mathematics modules ...
... The libraries include numerical and analytical calculations, linear algebra operations, equation solving algorithms. Many libraries are based on the JAIDA classes for data manipulation, construction of histograms and functions. SCaVis ...
Logic Minimizer is an innovative, versatile application for simplifying Karnaugh maps and logical expressions step by step. It is geared for those involved in engineering fields, more precisely digital and formal ...
Logic Minimizer is a special application for simplifying logical expressions, namely Boolean and propositional expressions. It is geared for those involved in engineering fields, more precisely digital and formal logic scholars ...
... populations in models described in the Markovian process algebra PEPA. GPA efficiently implements these techniques and extensions allowing calculation of accumulated rewards and computation of passage time probabilities. The ... |
More About
This Textbook
Overview
Teaching Secondary Mathematics - a primary text for secondary mathematics methods students - is grounded in the NCTM standards and is informed by up-to-date research and theory in mathematics education. The book is organized into three parts: General Fundamentals a broad overview of education, curriculum, learning theory, discipline, planning, and adolescent behavior; Mathematics Education Fundamentals technology, problem solving, discovery, and proof; and Content and Strategies Algebra I, Geometry, Algebra II with Trigonometry, Pre-Calculus, and Calculus.
Editorial Reviews
Booknews
This text/CD-ROM package covers general fundamentals, mathematics education fundamentals, and content and strategies, with emphasis on technology as a teaching tool. This second edition incorporates recent research and technological advancements, and contains a new chapter on probability and statistics. The CD-ROM contains MathXpert Plus Calculus Assistant, which mathematics teachers can use with secondary students. Brumbaugh teaches college and K-12. Rock is professor of mathematics education and the coordinator of secondary education at the University of Mississippi |
Core-Plus Mathematics, is a standards-based, four-year integrated series covering the same mathematics concepts students learn in the Algebra 1-Geometry-Algebra 2-Precalculus sequence. Concepts from algebra, geometry, probability, and statistics are integrated, and the mathematics is developed using context-centered investigations. Developed by the CORE-Plus Math Project at Western Michigan University with funding from the National Science Foundation (NSF), Core-Plus Mathematics is written for all students to be successful in mathematics. Core-Plus Mathematics is the number one high school NSF/reform program and it is published by Glencoe/McGraw-Hill, the nation's number one secondary mathematics company. |
The Open Door Web Site : IB Math Studies : Probability: Probability P (A) = this is perhaps the most used formulae . P (A) This represents the
probability that event A will happen. Examples. (a), What is the probability of
getting a ...
IB Mathematical Studies Yr 1 – Unit PlansIB Mathematical Studies Yr 1 – Unit Plans. Note that the number of classes ....
Make sure to use the notation and terminology that is similar to the formula sheet .
42
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ibmathstudies.yolasite.com
IB Math Studies Topic 4: Functions Topic 4.1 Domain, Range and IB Math Studies Topic 4: Functions. Topic 4.1 Domain, Range and .... This is
given to use in the formula sheet the day of the exam. Topic 4.4 Exponential ... |
Arithmetic: An Applied Approach
9780395257913
ISBN:
0395257913
Publisher: CENGAGE Learning
Summary: Aufmann, Richard N. is the author of Arithmetic: An Applied Approach, published under ISBN 9780395257913 and 0395257913. Two Arithmetic: An Applied Approach textbooks are available for sale on ValoreBooks.com, and two used from the cheapest price of $11.65.
Trade paperback (US). Glued binding. 512 pages. contains index, pages 509-512. Audience: General/trade. a work book that takes an adult through all the basic arithmetic: whole numbers, fractions, decimals, percents; then goes into consumer math, and how to read and handle paychecks, bank accounts, interest, buying a house; and then into geometry. sample tests and answers of course.[less] |
Covers the fundamental processes in arithmetic: reading mathematical notation, translating words into symbols, and properties of the real number system. Introduction to geometry and algebra. Units do not apply toward AA/AS degree. |
...
More Player is required to view the demonstrations; there are 166 at present.
Discussion for Wolfram Demonstrations Project--Calculus
GERRI GRAY
(Student)
I learned about the Wolfram Demonstrations Project while researching for a math class midterm. I've spent hours looking through the demos, learning about math topics and becoming familiar with terminology. The material effectively presents complex concepts at a beginning level. If you download the free Mathematica Player, the models provide interactive illustrations. The site is easy to navigate and the examples are not only educational, but they are also fun to watch. It is an open source site which means that all users can contribute their own examples of innovative code. This type of collaborative environment lends itself to enhancing both teaching and learning experiences. |
Print Book
Key Features
Basic concepts of optimality conditions and numerical methods are described with simple and practical examples, making the material highly teachable and learnable
Includes applications of optimization methods for structural, mechanical, aerospace, and industrial engineering problems
Introduction to MATLAB Optimization Toolbox
Practical design examples introduce students to the use of optimization methods early in the book
New example problems throughout the text are enhanced with detailed illustrations
Optimum design with Excel Solver has been expanded into a full chapter
New chapter on several advanced optimum design topics serves the needs of instructors who teach more advanced courses
Description
Introduction to Optimum Design 3e describes an organized approach to engineering design optimization in a rigorous yet simplified manner. It illustrates various concepts and procedures with simple examples and demonstrates their applicability to engineering design problems. Formulation of a design problem as an optimization problem is emphasized and illustrated throughout the text. Excel and MATLAB® are featured as learning and teaching aids.
Jasbir Arora
Jas Jas
Affiliations and Expertise
Professor in the Department of Civil and Environmental Engineering & the Department of Mechanical Engineering, University of Iowa
Appendix A: Vector and Matrix Algebra A.1 Definition of Matrices A.2 Types of Matrices and Their Operations A.3 Solving n Linear Equations in n Unknowns A.4 Solution to m Linear Equations in n Unknowns A.5 Concepts Related to a Set of Vectors A.6 Eigenvalues and Eigenvectors A.7 Norm and Condition Number of a Matrix Exercises for Appendix A |
Abstract Mathematics
This is a book about mathematics and mathematical thinking. It is intended for the serious learner who is interested in studying some deductive ...Show synopsisThis is a book about mathematics and mathematical thinking. It is intended for the serious learner who is interested in studying some deductive strategies in the context of a variety of elementary mathematical situations. No background beyond single-variable calculus is presumed.Hide synopsis
Description:with equations. Very Good Plus. Owner's name. A near fine, tight...with equations. Very Good Plus. Owner's name. A near fine, tight, bright copy. 4 lines are underlined. The text is flawless. Green cloth with gilt lettering and decoration.
Description:Good. Introduction to Abstract Mathematics. This book is in Good...Good. Introduction to Abstract Mathematics |
Bring Basic Math to Life through Visual Learning
Adriana O'BrienThis course from the Wolfram SystemModeler Virtual Conference 2012 focuses on analyzing model equations and simulation results with Mathematica. You'll also learn about the link between Mathematica and SystemModelerWolfram SystemModeler can be used to model safety-critical systems. This Wolfram Virtual Conference Spring 2013 talk takes a closer look at an aircraft flap system, showing how component faults can be modeled and how their effects on system behavior can be simulated |
This is a comprehensive guide to woodturning which will be of value and help to both new and experienced woodturners.Hugh 0'Neill covers the tools and woods used in turning, the principles of design, the lathe, wood finishing, and the techniques of turning spindles, bowls and decorative works. The book also covers the workshop and a selection of projects...Trigonometry: A Complete Introduction is the most comprehensive yet easy-to-use introduction to Trigonometry. Written by a leading expert, this book will help you if you are studying for an important exam or essay, or if you simply want to improve your knowledge. The book covers all areas of trigonometry including the theory and equations of tangent,... more...
Calculus: A Complete Introduction is the most comprehensive yet easy-to-use introduction to using calculus. Written by a leading expert, this book will help you if you are studying for an important exam or essay, or if you simply want to improve your knowledge. The book covers all areas of calculus, including functions, gradients, rates of change,... more...
Algebra: A Complete Introduction is the most comprehensive yet easy-to-use introduction to using Algebra. Written by a leading expert, this book will help you if you are studying for an important exam or essay, or if you simply want to improve your knowledge. The book covers all the key areas of algebra including elementary operations, linear equations,... more... |
The Mathematics Subject Classification (MSC) is used to categorize items covered by the two reviewing databases, Mathematical Reviews (MR) and Zentralblatt MATH (Zbl). The MSC is broken down into over 5,000 two-, three-, and five-digit classfications, each corresponding to a discipline of mathematics (e.g., 11 = Number theory; 11B = Sequences and sets; 11B05 = Density, gaps, topology). The current classification system, 2000 Mathematics Subject Classification (MSC2000), is a revision of the 1991 Mathematics Subject Classification, which is the classification that has been used by MR and Zbl since the beginning of 1991. MSC2000 is the result of a collaborative effort by the editors of MR and Zbl to update the classification. The editors acknowledge the many helpful suggestions from the mathematical community during the revision process.
A public voice of mathematics education supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development and research.
PhDs.org was originally created with the help of a number of students while the author was an assistant professor in the Math Department at Dartmouth College. The site was made possible by the generous support of the Alfred P. Sloan Foundation and a Burke Research Initiation Award from Dartmouth College. The author has continued to run the site on his own since moving to Microsoft Research and subsequently to a consulting career in San Francisco. |
3. Algebra Starter Lessons, Effective
The algebraic way of writing and reasoning with letters and further
symbols is a great mystery and great source of discomfort for many
students and teachers. The mystery invites rote learning and
computational approach to secondary mathematics. Many students do not end
their studies of mathematics follows from immersion. The textbooks of my
youth employed the algebra was of writing and reasoning but did not
introduce it. Mastery was left to chance. As a student, I was left to
provide my own rationalization for the shorthand role of letters and
symbols. With it I was able follow the logic in mathematics and science
texts, the mastery made the latter possible, but I lacked the verbal
ability to discuss and share my rationalization with others.
Tackling the algebra problem in secondary mathematics and calculus has
been a long-term aim. Success can be reported in the form of methods,
online here this, for introducing the algebra shorthand way of writing
and reasoning using words and gemometry. To learn how, explore the
following carefully:
Skip those on 1
Working With Sets. The presentation as is is best left to the
last years of secondary school or the first year of college.
Correct, but needs to be made more accessible.
The section 2 Formula Forward Use - Evaluation is also valuable for
the evaluation of arithmetic expressions. The section gives
instruction and multiple examples of how evaluate formulas and
arithmetic expressions, so that each step of the calculation can be
seen and checked as done or later. In evaluation and in the written
work needed for solving equations, using them forward and backward,
the aim is to show students how present their work for the efficient
confirmation or correction of skill mastery. The latter has to be
seen to believed.
The section 3 Solving Linear Equations begins with a three column
stick diagram method for solving linear equations ax+b = cx+d, a
method intended to reinforce fraction skills while leading students
from an easy manipulative approach with sticks, that is line
segments, to the standard solutions of the latter equations, one that
involves no sticks. After that this section introduces systems of
equations in essentially one-unknown and trianglar system of
equations to introduce students to the solution of systems. Most word
problems in earlier secondary school are best formulated as systems
in essentially one unknown, systems that are easily solved by
transformation into one equation in one unknown. In the early
secondary school treatment of word problems, students have to pass
through mental gymastics to arrive one equation in one unknown.
Formulating the word problem as system in essentially one unknown by
passes the mental gymnastics - provides a mechnanical alternative,
one in which algebraic skills are directly developed. Including
systems easy to solve early secondary school aims to provide skill
and confidence. In all, examples here show how to write and check
solutions so that skill can be seen or corrected as needed. The
example are accompanied by message: when a check fails, the mistake
or mistakes will be found between the start of the solution and the
end of a check. Not all checks are fault-free. Chapter 15 on Solving
Linear Equation in site volume contains more examples. The latter
include a neat example of the algebraic or literal solution of
equations ax + b = c, all to illustrate and introducte the algebraic
way of writing and reasoning.
The subsequence dicussion of equilavent computation rules sets the
stage for the explanation of axioms or rules for algebra as
statements that two computation rules with different forms may give
the same result. The latter in turn sets the stage for applying
axioms or rules of algebra to changing the form of arithmetic and
algebraic expressions in ways that leaves their values unchanged.
Jump to lesson 7 below and return to the next two lessons as needed.
The subsection 5.
Real Numbers lesson span the properties of real numbers and
their employment as coordinates along a line and in the plane. The
lesson on multiplication of real numbers echoes earlier lessons on
sign numbers. In practice, computations with real numbers are
approximately. The use of calculators allows computations to be done
to 3+ decimals, the more the better, for the sake of accuracy.
Calculators should be used to show students the decimal approximation
of the PI - the ratio of circle perimeter to its diameter, to 5+
decimal places. To many students in primary school do not learn that
PI is 3.14 approximately, to 2 decimal places - they and some of
their teacher may think the approximation is exact. The use of
calculators to display approximations to PI to 4 and more decimal
places may correct that mistaken belief. The value of PI can be
physically approximated by measuring the perimeter of a circle with a
given diameter, and then calculating the ratio. At this level, the
latter can be taken as its definition - an ideal for empirical but
not mathematical verification - oops! The mathematical fact that PI
has an infinite, non-repeating decimal expansion has to be given. At
this level, the proof of the latter is not for all. The proof is
reserved for undergraduate or graduate students in advanced
mathematics courses.
The axioms for Real Numbers etc lesson describes the arithmetic
properties of addition and multiplication only. Subtraction and
Division are not mentioned. However, subtraction of number can be
recast as adding the negative or additive inverse of the number,
while division by a number can recast as multiplying by it
multiplicative inverse or reciprocal. Once the recasting is done in
an arithmetic expression or computation rule, here an algebraic
expression, the algebraically described computation properties in the
axioms and earlier oral rules for adding and multiplying multiple
addends and terms can be applied to the recast form of the expression
or computation rule.
Chapter 18 in the site Volume 2, Three Skills for Algebra, tries
to describes and illustrate the underlying concepts. The chapter was
written in 1995-6 when I was struggling with how to make algebra
skills and concepts clearer through the use of words and numerical
examples.
Chapter 18 in the site Volume 2, Three Skills for Algebra, also
describes and illustrate the properties of real numbers given here in
a step by step, complementary manner. Two views are better than one,
we hope.
The section 6. More, Less and Greater Than Inequalities - Comparison
includes several lessons on comparing real numbers not by their
lengths or magnitudes, but essentially by their position when used as
1D coordinates along a "real number" line. Here I try to bend
previous treatments by introducing the notion of 10 be more than -5
by 15, or -1 be less than 6 by 7. I would keep the name of the less
than sign as is, but in the context of Real Numbers [as coordinates
along a line] rename the greater than sign and call it the more than
sign in order to step away from the comparison of size, magnitude or
length implicit in the comparison of unsigned numbers. This section
may be covered ligthly to introduce the less than and more than signs
in the context of signed numbers, that is Real Numbers.
1 Equivalent Computation Rules: This first amd key lesson
views the distributive law a(b+c) = ab+ac as the equivalence of
two different computation rules, one provided by h(a,b,c) =
a(b+c) and the other by h(a,b,c) = ab+ac. In the context of area
computations, the equivalence of computation rules h and g is
implied by the presume equality of two different ways of
computing the area of a rectangle with sides of length a and b+c.
The notion that h and g denote two different forms of the same
function can be discussed later. The geometric context allows the
letters a, b and c to denote the length of line segments. The
equivalence can also be verified by hand-computation, by
calculator-computation and by writing short computer programs to
evaluate each side. A counting context is also offered. Examples
of other computation rules are included in the lesson.
2 Addition and Multiplication Axioms: The second lesson casts
Addition and Multiplication Axioms for Real Numbers etc in terms
of equivalent computation rules. The distributive law again
appears here.
3 Product Axioms - Two Forms: The third lesson present two
forms of the product rule. First, we observe from the
consideration of decimals that the product of two non-zero
numbers or lengths is nonzero. The word lengths here is used to
indicate a possible extension or variant of this consideration:
The area of a rectangle with two nonzero sides, the lengths, is
"clearly" non-zero. The contrapositive form of this product rule,
it can be written as an implication rule IF A THEN B, is the
statement or axiom that if a product of two real numbers is zero
than at least one of the factors must be zero.
4 Subtraction and Division Axioms: The fourth lesson - more a
lesson idea than a lesson, adds subtraction and division axioms.
The aim here is to imply how the addition and multiplication
axioms may be applied by converting subtraction and division
operations into addition and multiplication operations through
the use of additive inverses - the negative of a number, and
through the multiplicative inverses - the reciprocal of number,
respectively.
5 Equality in Algebra: The fifth lessons discusses equality
axioms or practices. The same number may have several different
representations. Substitution Practice: All can be used
interchangeable in computations. Indeed, one representation may be
replaced by a more convenient one for the sake of aiding a
computation, while results remain repeatable and reproducible.
Equality axioms and practices show how one equation may imply
another, and vice-versa. That leads to the concept of equivalent
equations or equivalent systems of equations.
8. Unifying Theme For Algebra: In primary and secondary
level mathematics, and calculus too, many tables, rules, patterns and
formulas may be employed not only directly - in the forward manner,
but also indirectly in a backward manner. Addition and times tables
may be used backwards to answer subtraction and division questions,
some - not all. In logic, the contrapositive of an implication rule
represents an indirect or backward use or formulation. In calculus,
differentiation rules will be reversed to provide
anti-differentiation or integration methods. In secondary algebra,
the study of formulas entails not only their forward or direct use,
but also their indirect or backward use. In the UK, a quantity given
by a formula is termed the subject of the formula. The formula itself
may involve one or several other quantities or variables. Using the
formula for the original quantity to find an algebraic expression for
one of the other quantities is termed changing the subject. It
entails mastery of the algebraic or literal [with letters] way of
writing and reasoning. The aim of section lessons is gradually and
systematically develope this algebraic way of writing and reasoning.
The lessons here are unique. They endeavour to fill a gap I have seen
in the development of algebra since my own school days in the 1960s
and 1970s where I saw or sensed the algebraic ways of writing and
reasoning was required but not systematically introduced. Here is a
remedy. It may be easier and simpler than you expect. Good luck.
Some lessons duplicate material from site Volume 2, Three Skills for
Algebra. Upper level secondary mathematics and science is based on
the backward use of formulas. Talking about the latter recognizes and
vocalizes a commonality and so gives a unifying theme for the
learning and teaching of algebra.
The section 9. Proportionality Backwards and Forwards This section
includes the following webpages. Some represent lessons. Other
represent lesson ideas that tutors or instructors will have to expand
and clarify for learners. The coverage is rather rich. It may be
spread over mid- and upper secondary school level instruction in
mathematics and science.
Proportionality
Concepts and Practices- Three plus Kinds of Proportionality
Relations, Forwards and Backwards: The lesson says what is
(defines) Direct, Joint, Inverse Proportionality and describes
how to shift or generate proportionality relations from each
others. In a proportionality relation (or equations),
algebraically interchanging the dependent quantity with an
independent one via a backward use of the relation leads to
further proportionality relations of the same or different type.
The use of proportionality relations begins with the backward use
problem of finding the value of a proportionality constant. Once
its value is known, the proportionality relation can use in the
forward direction to find values of the dependent variable, or in
the backward direction to find values of a so called independent
variable.
Two and
Multiple-Term Ratios, a proportionality constant viewpoint.
Fraction and ratios are overlapping concept and have overlapping
roles in arithmetic, but they are not identical even though
fractions a/b where a and b are whole numbers may be called
ratios. In mathematics ordered pairs of whole numbers a and b may
appear in coordinate form (a,b) or [a,b]; in ratio form a:b and
in fraction form a/b.
Column Multiplication Methods for Arithmetic and Algebra
Duplicate Material, and Deliberately So
Column multiplication methods appear in primary school with decimals and
take advantage of place value. The appear in middle to senior secondary
school in the multiplication of polynomials. Such methods can be
introduced geometrically. See
Column Multiplication Methods in General. The latter ideas using
letters to denote lengths, subsegments, along the side of a rectangle.
The letters limited to two per side could also represents the integral
and fractional part of a mixed number. The result is a column
multiplication methods for the product of sums, one justified geometrical
in the case of positive or unsigned numbers. But operationally the method
works in general - we assume that in place of proving for the sake of
accessiblity. The multiplication method provides a simple, mechanical
replacement for the FOIL method taught in algebra. For polynomials, see
Column Multiplication Method.
Remark:Mastery and sanction of column multiplication methods
extends the distributive law given in algebra. The recommendation here
for the sake of an operational command of mathematics is to give the
methods and the law, and allow studies in pure mathematics if taken, to
explain the redundancy, or how the law implies the methods. The practical
aim of secondary mathematics here is not to give a lean axiomatic base
for mathematics, but an operational command based on consistent rules and
practices, axioms included. Lean may follow later in specialized courses
taken by students mastering the more theorectical aspects of university
mathematics, engineering or science. Lean too early is a burden.
Learn More - Readings for Now or Later
Volume
3 Why Slopes and More Mathematics. The algebra shorthand way of
writing and reasoning is employed at full-strength in calculus.
Chapters 2 to 7 of this work provide an algebraic light calculus
preview, one that stems from the observation that the middle part of a
calculus course is algebraically less challenging that the leading
parts. This preview may be employed at start of a first course in
calculus. It may also be used in secondary mathematics before calculus
to a context for the study of slopes and polynomial factorization, all
in a way that should advances algebra skills angles |
Beginning Algebra - 9th edition
Summary: The Lial series has helped thousands of students succeed in developmental mathematics through its friendly writing style, numerous realistic examples, extensive problem sets, and complete supplements package. In keeping with its proven track record, this revision includes a new open design, more exercises and applications, and additional features to help both students and instructors succeed.
Learning Objectives Each section opens with an application and clearly stated, numbered, learning objectives. These learning objectives are reinforced throughout the section by re-listing the objective where appropriate so that students always know exactly what is being covered.
Classroom Examples and Teaching Tips The Annotated Instructor's Edition provides answers to all text exercises and Group Activities in color in the margin or next to the corresponding exercises. In addition, Classroom Examples and Teaching Tips are also included to assist instructors in coming up with examples to use in class that are different from what students have in their textbooks, and offering guidance on presenting the material at hand.
Notes Important ideas are emphasized in Notes boxes that appear throughout the text. Calling them out stresses their importance to students.
Connections Connections boxes provide connections to the real world or to other mathematical concepts, historical background, and thought-provoking questions for writing or class discussion.
Problem Solving The Lial six-step problem-solving method is clearly explained in Chapter 2 and is then continually reinforced in examples and exercises throughout the text to aid students in solving application problems.
Cautions Students are warned of common errors through the use of Cautions that are found throughout the text where appropriate.
Technology Insights Exercises Technology Insights Exercises are found in selected exercise sets throughout the text. These exercises illustrate the power of graphing calculators and provide an opportunity for students to interpret typical results seen on graphing calculator screens (graphing calculator NOT required to complete these exercises).
Ample and Varied Exercise Sets Algebra students require a large number and variety of practice exercises to master the material they have just learned. This text contains over 7700 exercises, including over 2100 review exercises, plus numerous conceptual and writing exercises, journal exercises, and challenging exercises that go beyond the examples. Multiple-choice, matching, true/false, and completion exercises help to provide variety. Exercises suitable for calculator use are marked with a calculator icon.
Writing Exercises Writing exercises abound in the Lial series through the Connections boxes and also in the exercise sets. Some writing exercises require only short written answers, and others require lengthier journal type exercises that ask students to fully explain terminology, procedures, and methods, document their understanding using examples, or make connections between topics.
Relating Concepts Found at the end of selected exercise sets, these exercises tie together topics and highlight the relationships among various concepts and skills. For example, they may show how algebra and geometry are related, or how a graph of a linear equation in two variables is related to the solution of the corresponding linear equation in one variable. These sets of exercises make great collaborative activities for small groups of students.
Group Activities Appearing at the end of each chapter, these activities allow students to work collaboratively to solve a problem related to the chapter material.
Ample Opportunity for Review One of the most admired features of Lial textbooks is the extensive and well-thought-out end-of-chapter material. At the end of each chapter, students will find Key Terms and Symbols that are keyed back to the appropriate section for easy reference and study, and Test Your Word Power to help students understand and master mathematical vocabulary. Key terms from the chapter are presented with four possible definitions in multiple-choice format, Quick Review sections to give students not only the main concepts from the chapter (referenced back to the appropriate section), but also an adjacent example of each concept, Review Exercises keyed to the appropriate sections so that students can refer to examples of that type of problems if they need help, Mixed Review Exercises that require students to solve problems without the help of section references, Chapter Test to help students practice for the real thing, and Cumulative Review Exercises that gather various types of exercises from preceding chapters to help students remember and retain what they are learning throughout the course.
New To This Edition :
Former Section 2.1 on the Addition and Multiplication Properties of Equality has been split into two sections to allow each property to be treated individually before combining their use in Section 2.3.
All topics on graphing linear equations and inequalities in two variables are now treated in Chapter 3.
Systems of linear equations and inequalities, presented earlier than in the previous edition, are covered in Chapter 4.
Chapter 5 on exponents and polynomials has been reorganized so that the sections on exponents are covered early in the chapter.
Variation is covered in a new Section 7.8.
Three new appendixes have been included. Appendix A provides an introduction to calculators, Appendix D includes all new material on mean, median, and mode, and Appendix E covers quadratic inequalities, formerly included in the chapter on factoring.
Adjunct Support Center The Adjunct Support Center offers consultation on suggested syllabi, helpful tips on using the textbook support package, assistance with textbook content, and advice on classroom strategies from qualified mathematics instructors with over 50 years combined experience.
Now Try It Exercises To actively engage students in the learning process, each example now concludes with a reference to one or more parallel exercises from the corresponding exercise set so that students are able to immediately apply and reinforce the concepts and skills presented in the examples.
Summary Exercises Based on user feedback, we have more than doubled the number of in-chapter summary exercises. These special exercise sets provide students with the all-important mixed review problems they need to master topics. Summaries of solution methods or additional examples are often included. Topics that appear in these Summary Exercises include Solving Linear Equations, Rules for Exponents, and Factoring.
Glossary By popular demand, a comprehensive glossary of key terms from throughout the text is included at the back of the book.
New Real-Life Applications Many new or updated examples and exercises can be found throughout the text that focus on real-life applications of mathematics. These applied problems provide a modern flavor that will appeal to and motivate students.
New Figures and Photos Today's students are more visually oriented than ever. Thus, the authors have made a concerted effort to add mathematical figures, diagrams, tables, and graphs whenever possible. Many of the graphs use a style similar to that seen by students in today's print and electronic media. Photos have been incorporated to enhance applications in examples and exercises.
(Note: Each chapter ends with a Group Activity, Summary, Review Exercises, a Chapter Test and, with the exception of Ch. 1, a Cumulative Review). List of Applications. Preface. Feature Walkthrough. 1. The Real Number System.
Fractions. Exponents, Order of Operations, and Inequality. Variables, Expressions, and Equations. Real Numbers and the Number Line. Adding and Subtracting Real Numbers. Multiplying and Dividing Real Numbers. Summary Exercises on Operations with Real Numbers. Properties of Real Numbers. Simplifying Expressions.
2. Linear Equations and Inequalities in One Variable.
The Addition Property of Equality. The Multiplication Property of Equality. More on Solving Linear Equations. Summary Exercises on Solving Linear Equations . An Introduction to Applications of Linear Equations. Formulas and Applications from Geometry. Ratios and Proportions. More About Problem Solving. Solving Linear Inequalities.
3. Linear Equations and Inequalities in Two Variables; Functions.
Reading Graphs; Linear Equations in Two Variables. Graphing Linear Equations in Two Variables. The Slope of a Line. Equations of a Line. Graphing Linear Inequalities in Two Variables. Introduction to Functions.
The Product Rule and Power Rules for Exponents. Integer Exponents and the Quotient Rule. Summary Exercises on the Rules for Exponents. An Application of Exponents: Scientific Notation. Adding and Subtracting Polynomials; Graphing Simple Polynomials. Multiplying Polynomials. Special Products. Dividing Polynomials.
6. Factoring and Applications.
The Greatest Common Factor; Factoring by Grouping. Factoring Trinomials. More on Factoring Trinomials. Special Factoring Rules. Summary Exercises on Factoring. Solving Quadratic Equations by Factoring. Applications of Quadratic Equations.
9 |
"Your best class mate"
Math Helper is a comprehensive higher mathematics calculator
Actually, Math Helper is a mix of textbook and complex calculator. This means that besides calculation features, there's the theory and the calculation procedure of each math category that you can find on this app. Thus, you can look up any doubt in the theory, refresh how to calculate it and then fill up the parameters and let the app solve it.
There are four categories: Linear Algebra (including matrices and systems of linear equations, Vector Algebra (vectors and figures), The mathematical analysis (Derivatives), and Other (including probability theory and number & sequences).
We're used to review all kind of calculators. However, Math Helper goes a step further with higher mathematics, including operations like "calculate determinant of a matrix", "finding the number of permutations", "arithmetic and geometric progressions". The added-value feature of this app is precisely that it allows users to perform lots of complex calculations from a single mobile app while helping them remember main rules and theories.
Only one catch: interface should be enhanced. Anyway, recommended app |
75raise for the First Edition
"Stahl offers the solvability of equations from the historical point of view...one of the best books available to support a one-semester introduction to abstract algebra." —CHOICE
Introductory Modern Algebra: A Historical Approach, Second Edition presents the evolution of algebra and provides readers with the opportunity to view modern algebra as a consistent movement from concrete problems to abstract principles. With a few pertinent excerpts from the writings of some of the greatest mathematicians, the Second Edition uniquely facilitates the understanding of pivotal algebraic ideas.
The author provides a clear, precise, and accessible introduction to modern algebra and also helps to develop a more immediate and well-grounded understanding of how equations lead to permutation groups and what those groups can inform us about such diverse items as multivariate functions and the 15-puzzle. Featuring new sections on topics such as group homomorphisms, the RSA algorithm, complex conjugation, the factorization of real polynomials, and the fundamental theorem of algebra, the Second Edition also includes:
An in-depth explanation of the principles and practices of modern algebra in terms of the historical development from the Renaissance solution of the cubic equation to Dedekind's ideals
Historical discussions integrated with the development of modern and abstract algebra in addition to many new explicit statements of theorems, definitions, and terminology
A new appendix on logic and proofs, sets, functions, and equivalence relations
Over 1,000 new examples and multi-level exercises at the end of each section and chapter as well as updated chapter summaries
Introductory Modern Algebra: A Historical Approach, Second Edition is an excellent textbook for upper-undergraduate courses in modern and abstract algebra.
Author Biography
SAUL STAHL, PhD, is Professor in the Department of Mathematics at the University of Kansas. In addition to authoring six previous books and more than thirty papers in the field of geometry, Dr. Stahl has twice been the recipient of the Carl B. Allendoerfer Award from the Mathematical Association of America. |
Introduction to Graph and Hypergraph Theory
This book is for math and computer science majors, for students and representatives of many other disciplines (like bioinformatics, for example) taking courses in graph theory, discrete mathematics, data structures, algorithms. It is also for anyone who wants to understand the basics of graph theory, or just is curious. No previous knowledge in graph theory or any other significant mathematics is required. The very basic facts from set theory, proof techniques and algorithms are sufficient to understand it; but even those are explained in the text. Structurally, the text is divided into two parts where Part II is the generalization of Part I.The first part discusses the key concepts of graph theory with emphasis on trees, bipartite graphs, cycles, chordal graphs, planar graphs and graph coloring. The second part considers generalizations of Part I and discusses hypertrees, bipartite hyper graphs, hyper cycles, chordal hyper graphs, planar hyper graphs and hyper graph coloring. There is an interaction between the parts and within the parts to show how ideas of generalizations work. The main point is to exhibit the ways of generalizations and interactions of mathematical concepts from the very simple to the most advanced. One of the features of this text is the duality of hyper graphs.This fundamental concept is missing in graph theory (and in its introductory teaching) because dual graphs are not properly graphs, they are hyper graphs. However, as Part II shows, the duality is a very powerful tool in understanding, simplifying and unifying many combinatorial relations; it is basically a look at the same structure from the opposite (vertices versus edges) point of view. |
Precalculus with Modeling and Visualization
9780321279071
0321279077
Summary: Gary Rockswold focuses on teaching algebra in context, answering the question, "Why am I learning this?" and ultimately motivating the students to succeed in this class. In addition, the author's understanding of what instructors need from a text (great 'real' examples and lots of exercises) makes this book fun and easy to teach from. Integrating this textbook into your course will be a worthwhile endeavor.
...Rockswold, Gary K. is the author of Precalculus with Modeling and Visualization, published 2005 under ISBN 9780321279071 and 0321279077. Twenty five Precalculus with Modeling and Visualization textbooks are available for sale on ValoreBooks.com, twenty three used from the cheapest price of $0.78, or buy new starting at $35.48 |
Quantitative Literacy
Drake students will learn to reason with the symbols and components of mathematical languages as well as effectively use the principles that underlie these operations. Courses that satisfy this requirement will have mathematical reasoning as their principal focus. They may also address questions that engage learners with the world around them and help them to analyze quantitative claims that arise from the study of civic, political, scientific, or social issues. Quantitative literacy courses may be focused on the mathematical needs of a specific discipline or on a specific interdisciplinary issue or problem. these courses will engage students to achieve these student learning outcomes. Students will be able to:
Analyze and present solutions to problems using symbols and components from mathematical languages and their underlying principles.
Identify and execute appropriate mathematical operations for a given question |
Academics
Infinite sequences and series, Taylor approximations, polar coordinates and complex numbers. The significance of these topics in mathematics and their applications in the natural sciences are discussed. This is a quarter-long course; it is offered in the second half of the fall and spring semesters as a follow-up to MATH 114, and in the first half of the fall semester, followed by MATH 116. |
Mathematics
"Today's world is more mathematical than yesterday's, and tomorrow's world will be more mathematical than today's. As computers increase in power, some parts of mathematics become less important while other parts become more important. While arithmetic proficiency may have been 'good enough' for many in the middle of the century, anyone whose mathematical skills are limited to computation has little to offer today's society that is not done better by an expensive machine."
- Everybody Counts
The world is shaped by math from basic addition at the checkout counter to advanced equations in engineering plans. And the future is bright for those who wish to gain a degree in Mathematics at Clarion University.
Mathematics Placement
Incoming freshmen at Clarion Campus are placed into their first college mathematics course based on the high school mathematics courses and grades in addition to the SAT and ACT mathematics score. This placement is determined during the Orientation process.
Incoming freshman at Venango College are given a mathematics placement exam to determine the appropriate mathematics course. |
Essentials of Trigonometry - With CD - 4th edition
Summary: Intended for the freshman market, this book is known for its student-friendly approach. It starts with the right angle definition, and applications involving the solution of right triangles, to help students investigate and understand the trigonometric functions, their graphs, their relationships to one another, and ways in which they can be used in a variety of real-world applications. The book is not dependent upon a graphing calculator.
0534494234 Indust. of San Diego San DIego, CA
2005 Hardcover Good
$2.00 +$3.99 s/h
Acceptable
Campus_Bookstore Fayetteville, AR
Used - Acceptable Hardcover. textbook only 4th Edition Not perfect, but still usable for class. Ships same or next day. Expedited shipping takes 2-3 business days; standard shipping takes 4-14 busines...show mores days64 wear. Text may contain some writing/highlightings but nothing majo...show morer |
Developed by Barbara Kaskosz of the University of Rhode Island and Doug Ensley of Shippensburg University, this resource from The Mathematical Association of America's Digital Classroom Resources collection will prove...
This handy program will solve any function equation entered into its screen, and provide tips for solving a similar problem on paper. After providing the answer, the program then provides further information on the key...
This website applies virtual reality to calculus in order to illustrate mathematical concepts more clearly to students. While many courses utilize computers via computer algebra systems and graphing tools to...
This website, from the University of Illinois, contains information about black holes. A brief history of black holes, a description of how black holes are formed, and the anatomy of a black hole are presented. ...
This site offers free technology, math, science, and language arts resources for K-12 educators with a special emphasis on project-based collaborative student-centered learning. Intel's 21st century teaching and... |
aurie Boswell book reviews
Algebra 1: Concepts and Skills
Algebra 1 for 8th Grade Students
This book is used at my son's school. We cannot check a book out so I ordered it online. The book has excellent examples, quizzes, tests and practice problems to keep my son getting an "A" :) |
Many schools now require
calculators. This site is not the place for a discussion of the problems
(financial and otherwise) that this can cause, or of the "philosophy"
on which these policies are often based. If you are interested in the
politically-incorrect side of this issue, visit Mathematically
Correct.
(And for an interesting discussion of the value of a broken calculator,
try here.)
But if you are wondering
which calculator to buy, the following is my advice.
Scientific, business,
etc, calculators
If you are looking for
a "scientific" or "business" or "statistics"
calculator, then there are many affordable options available to you. You
can find cheap calculators at office-supply stores, discount department
stores, and electronics stores, among other places. I have only one specific
recommendation: make sure that the calculator has a fraction key; it usually
looks something like this:
This is a very
helpful key, and will speed up fraction addition, simplification, and
conversion.
Graphing calculators:
Texas Instruments
If you are supposed to
get a "Texas Instruments graphing utility", then you would probably
want one of the calculators from their line of TI-84 models. The TI-84
is an update of their TI-83 which incorporates additional capabilities
(increased memory, computer connectivity, default apps, etc) but which
is backwards compatible with the TI-83. That is to say, the TI-84 will
allow you to do more, while still remaining largely keystroke compatible
with the TI-83 that your teacher is using.If you are supposed to get a
TI-83, you might want to look at spending a little more to get the TI-84.
ADVERTISEMENT
(Note: There are some slight
differences in the models. For information, try here.)
However, the TI-84 seems
to assume that you have reliable access to a newer computer. Much of the
manual is accessible only through the CD that comes with the calculator,
calculator-to-computer connectivity relies on USB ports, and you may need
to download and install at 23-meg Micro$oft program (.NET Framework) to
get the computer side of the calculator to work. You may also need to
upgrade your browser, since the TI-84 appears to require Internet Explorer
6 or newer. So I would recommend the TI-84 (over the TI-83) for the updated
capabilities, but only if you have ready access to an updated computer
and a good Internet connection. (Note: I have heard, from experienced
users, that installation and use is not always problematic. The above
warnings reflect my personal experience. As they say, "your mileage
may vary.")
Do NOT get a TI-92, nor
its update, the Voyage 200, unless you have verified that your school
allows them; many schools are banning them. For some reason, though the
TI-89 has many of the same capabilities that are getting the TI-92 / Voyage
200 banned, the TI-89 is generally allowed. However, it would still be
a good idea to check first. Note that many (most?) instructors, especially
at the high-school level, don't know how to use the TI-86, -89, or -92,
or the Voyage 200, so you'll be on your own when it comes to learning
how to use them. And their owners manuals tend to be the size of small
textbooks.
If the only specification
is that you are to get "a graphing utility", then the choice
is up to you. Many companies produce perfectly nice calculators, but textbooks
and teachers usually push the Texas Instruments TI-83 or -84. If you're
willing and able to read the manual for yourself, then get whatever calculator
you like. Otherwise, stick with Texas Instruments.
If you do get a TI-8X calculator,
learn where the "convert to fraction" menu item is (this varies
from model to model; check your manual). The command looks like this:
This command will convert
the last value to its fractional form, if possible. It's a very handy
command. If you have the "Custom" menu option, you might want
to install the "convert to fraction" command on your custom
menu, for convenience sake.
(By the way, if you already
have a TI-85, and would like to have the "TABLE" feature that
the TI-82, TI-83, and TI-86 have, use my "Table"
program. The page in the preceding link contains the program as a text
file; you'll have to type the program into your calculator yourself.)
Graphing calculators:
Final thoughts....
If you are thinking of
getting a Hewlett-Packard (HP) calculator (graphing or otherwise), see
if you can find a friend or a fellow student who will let you borrow one.
In my experience, people either love HPs or they really, really,hate them, and it would
be a shame to spend a couple hundred dollars just to learn that you're
one of the folks who hates 'em. They slice, they dice, they whistle "Dixie",
but they might not be your cup of tea. Take a good look first.
In "real life",
any of the scientific (or business or statistical, etc) calculators will
serve most needs. Unless you're going into courses where graphing calculators
are expected, a cheap calculator that has trigonometric keys (the "sin",
"cos", and "tan" keys) should have just about anything
you'll need. But graphing calculators can be nice, even in "real
life", for much the same reason that some of us old-timers liked
adding machines with a printout: the screen on a graphing calculator can
display more information and, in particular, can make it easier to find
one's mistakes. So, for instance, I tend to use a graphing calculator
to balance my checkbook.
There is one other consideration:
If there is no specification regarding which calculator you should get
(or if you are given a list of models from which to choose), and you are
planning on entering a scientific field of study at your college or university
(math, engineering, or physics, for instance, as opposed to Poly-Sci or
French Lit), then you might want to contact the appropriate departments
to see if those departments have their own preferences. Be forewarned:
It is entirely possible that you will be required to buy multiple calculators:
one for the math department, another for the physics department, and yet-another
for the engineering department. Calculators are very trendy, but the trend-oids
don't often think about the real-world implications of their policies.
There; now ya know: I'm
politically incorrect.
If you have lost the manual
to your Texas Instruments graphing calculator, look into downloading a
new copy from
the Texas Instruments' site.
The guidebooks are Adobe Acrobat documents, and fairly large ones at that,
so you might want to download the manual one chapter at a time if you
have a slow or twitchy connection. |
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Functions and Graphs - 96 edition
Summary: This volume presents students with problems and exercises designed to illuminate the properties of functions and graphs. The 1st part of the book employs simple functions to analyze the fundamental methods of constructing graphs. The 2nd half deals with more complicated and refined questions concerning linear functions, quadratic trinomials, linear fractional functions, power functions, and rational functions.1969 edition.12.20 +$3.99 s/h
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Today's Developmental Math students enter college needing more than just the math, and this has directly impacted the instructor's role in the classroom. Instructors have to teach to different learning styles, within multiple teaching environments, and to a student population that is mostly unfamiliar with how to be a successful college student. Authors Andrea Hendricks and Pauline Chow have noticed this growing trend in their combined 30+ years of teaching at their respective community colleges, both in their face-to-face and online courses. As a result, they set out to create course materials that help today's students not only learn the mathematical concepts but also build life skills for future success. Understanding the time constraints for instructors, these authors have worked to integrate success strategies into both the print and digital materials, so that there is no sacrifice of time spent on the math. Furthermore, Andrea and Pauline have taken the time to write purposeful examples and exercises that are student-centered, relevant to today's students, and guide students to practice critical thinking skills. Intermediate Algebraand its supplemental materials, coupled with ALEKS or Connect Math Hosted by ALEKS, allow for both full-time and part-time instructors to teach more than just the math in any teaching environment without an overwhelming amount of preparation time or even classroom time.
Table of Contents
Chapter S: Success Strategies
S.1: Time Management and Goal Setting
S.2: Learning Styles
S.3: Study Skills
S.4: Test Taking
S.5: Blended and Online Classes
Chapter 1: Real Numbers and Algebraic Expressions
1.1: Sets and the Real Numbers
1.2: Operations with Real Numbers and Algebraic Expressions
1.3: Properties of Real Numbers and Simplifying Algebraic Expressions
Chapter 2: Linear Equations and Inequalities in One Variable
2.1: Solving Linear Equations
2.2: Introduction to Applications
2.3: Formulas and Applications
2.4: Linear Inequalities and Applications
2.5: Compound Inequalities
2.6: Absolute Value Equations
2.7: Absolute Value Inequalities
Chapter 3: Graphs, Relations, and Functions
3.1: The Coordinate System, Graphing Equations, and the Midpoint Formula
3.2: Relations
3.3: Functions
3.4: The Domain and Range of Functions
Chapter 4: Linear Functions and Linear Inequalities in Two Variables
4.1: Linear Functions and Equations in Two Variables
4.2: Graphing Linear Equations and Linear Functions
4.3: The Slope of a Line
4.4: Writing Equations of Lines
4.5: Linear Inequalities in Two Variables
Chapter 5: Systems of Linear Equations and Inequalities
5.1: Solving Systems of Linear Equations in Two Variables Graphically
5.2: Solving Systems of Linear Equations in Two Variables Algebraically |
The
Interactive Mathematics Program (IMP) is a growing collaboration
of mathematicians, teacher-educators, and teachers who have been
working together since 1989 on both curriculum development and professional
development for teachers.
With the support of the National Science Foundation, IMP has created
a four-year program of problem-based mathematics that replaces the
traditional Algebra I, Geometry, Algebra II/Trigonometry, Precalculus
sequence and that is designed to exemplify the curriculum reform
called for in the Curriculum and Evaluation Standards of the National
Council of Teachers of Mathematics (NCTM).
The IMP curriculum integrates traditional material with additional
topics recommended by the NCTM Standards, such as statistics, probability,
curve fitting, and matrix algebra.
IMP units are generally structured around a complex central problem.
Although each unit has a specific mathematical focus, other topics
are brought in as needed to solve the central problem, rather than
narrowly restricting the mathematical content. Ideas that are developed
in one unit are usually revisited and deepened in one or more later
units.
The IMP curriculum has been thoroughly field-tested and enthusiastically
received by hundreds of classroom teachers around the country. Their
enthusiasm is based on the success they have seen in their own classrooms
with their own students.
These informal observations are backed by more formal evaluations.
Dr. Norman Webb, of the Wisconsin Center for Education Research,
has done several studies comparing the performance of students using
the IMP curriculum with the performance of students in traditional
programs. |
Tagged Questions
I want some recomendation on which software I should install on my computer, an open source program for general abstract mathematical purposes (as opposed to applied mathematics).
I would likely use ...
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Students calculate area under a curve using Riemann Sums. In this calculus lesson, students investigate the integral through estimation and calculation. They compare their approximate answer to their true answer.
In this circuits learning exercise, students answer 25 questions about passive integrator circuits and passive differentiator circuits given schematics showing voltage. Students use calculus to solve the problems.
In this capacitance learning exercise, students solve 19 problems about capacitance, voltage, electric charge and Ohm's Law. They use calculus to solve some of the problems and they are given equations used to solve different capacitance problems.
Students calculate the maxima and minima of quadratic equations. In this calculus lesson, students apply the derivatives by finding the maxima and minima using real life application. They solve optimization using the derivative.
Students define the different methods used for optimizing a particular element of a problem. In this optimization problem lesson, students optimize appropriate details of a problem using data collection, algebra, technology, and/or calculus. Students also complete the inquiry-based worksheets included with the lesson.
Young scholars derive functions given a limit. In this calculus lesson, student define the derivative of f at x=a, knowing the derivative is a point or just a number. This assignment requires students to work independently as much as possible.
Students discuss the following topics of Calculus: The Tangent Line Problem, The Area Problem, and Exercises. They find limits graphically and numerically. Students write a mathematical autobiography, they write their earliest memories of mathematics or numbers.
In this solar flare reconstruction worksheet, students read about the 'saturation' point of satellite detectors when solar flares are at their most intense phase of brightness. Students are given x-ray flare data and they re-plot the data to estimate the peak of intensity. They create 2 exponential functions to fit the data and estimate the peak intensity and time. Students use calculus to integrate one of the functions and calculate the total energy radiated by the flare.
Students use the derivative and integral to solve problems involving areas. For this calculus lesson, students calculate the area under a curve as they follow a robot off road making different curves along the drive. They use Riemann Sums and Trapezoidal rules to solve the problem.
Students read about AP calculus online. In this calculus lesson, students learn real life usage for calculus. They read about instructors and their experience teaching and incorporating calculus into the real world.
Young scholars review and analyze topics needed to be successful in calculus. In this precalculus lesson plan, students review the unit circle and its properties. The trigonometric ratios and its identities.
Young scholars calculate the volume of solids. In this calculus instructional activity, students apply the Disk and Washer Method to solve for the volume of three dimensional objects. They calculate the volume caused by rotation that create sections that are perpendicular to the axis of rotation.
Students use the Fundamental Theorem of Calculus to solve problems. In this calculus activity, students use the TI to solve the graphing porting of the problem. They practice graphing functions and discuss their place in the real world.
Students calculate the area under a curve. In this calculus lesson plan, students use Riemann sums to find and approximate the area under a curve. They use the derivative and differential equations to solve.
Students investigate an article on local linearity. In this calculus lesson, students read about the application of math in the real world. They gain insight from the teachers view of how to teach and relate the topic to the real world. |
Construct tables of values to understand constant percent growth rate in an exponential function. This lesson contains a handout to different problems that help provide insight into exponential functions.
High schoolers graph exponential equations and solve application problems using exponential functions. They re-enact a story about a peasant worker whose payment for services is rice grains doubled on a checker board. They place M & Ms on a checkerboard and mark the number on a graph. They double the number for each space on the board and create a graph of the data.
Money, money, money. A complete instructional activity that makes use of different representations of simple and compound interest, including written scenarios, tables, graphs, and equations to highlight similarities and differences between linear and exponential functions.
Introduce the concept of exponential functions with an activity that extends the definition of exponents to include rational values. Start with a doubling function at integer values of time, then expand table to include frational time units. Lesson includes a detailed commentary on how to work each problem.
Ninth graders investigate the functional relationship of different environmental phenomena. In this math lesson, 9th graders create models of various natural disasters. They use logarithmic and exponential functions to interpret population growth.
Students explore the calculator function of the TI-Nspire. In this secondary mathematics lesson, students investigate many of the features of the calculator function of the TI-Nspire. Students review basic computation, square roots, absolute values, exponential functions, logarithmic functions, trigonometric functions, summations and matrices as they explore the TI-Npsire.
Students take derivatives of exponential functions. In this taking derivatives of exponential functions instructional activity, students prove the derivative of an exponential function is the exponential function. Students find derivatives where the base is a constant and the exponent is a variableStudents study exponential decay and its application to radiocarbon dating. In this exponential decay lesson, students use candy to model the time it takes for something to decay. Students also graph the data they collect and describe using an algebraic formula that gives the age of an object as a function.
Ninth graders investigate exponential regression. In this Algebra I lesson plan, 9th graders explore the rebound heights of a racquetball bouncing and develop an exponential data model. The lesson plan is intended to be an introduction to exponential regression explore the concept of piecewise functions. In this piecewise functions lesson, students discuss how to make a piecewise function continuous and differentiable. Students use their Ti-89 to find the limit of the function as it approaches a given x value. Students find the derivative of piecewise functions.
Twelfth graders assess their knowledge of logarithmic and exponential functions. In this calculus lesson, 12th graders demonstrate their knowledge of all concepts of logarithmic and exponential functions. Students apply the derivatives of the logs and exponential functions.
In this complex exponential worksheet, students identify an entire function and explore how to show a function is analytic. This two-page worksheet contains four problems, as well as explanations and examples.
In this function worksheet, students use various methods to solve functions. They explore the logarithm function, the derivative of an exponential function, and compose a function with a linear equation. This four-page worksheet contains explanations, examples, and four problems.
Sal continues his discussion of decay by showing students the math involved in determining how much a substance is left after one half-life, two half-lives, and even three half-lives have gone by. He sets up a general function of time that can be used to determine the remaining amount of a substance after 10 minutes, or three billion years have elapsed! |
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Algebraic thinking is an important strand of both the NCTM and the Common Core Math Standards. Yet, for many students, the abstract nature of algebra poses a formidable emotional and conceptual challenge. By providing students with Dr. Borenson's unique visual and kinesthetic approach, they actually understand the concepts and experience success, thereby enhancing their interest in mathematics. In this workshop you will see how Hands-On Equations demystifies the learning of algebra and thereby provides students with a solid foundation for algebraic thinking and for a traditional Algebra 1 |
Students explore a linear, a parabolic, and a log function. In this Algebra II/Pre-calculus instructional activity students investigate the graph a line, a parabola, and a log function. Students examine the three graphs as they compare and contrast the three in a problem solving context.
Students solve problems using implicit differentiation. In this calculus lesson, students take the derivative to calculate the rate of change. They observe two robots and draw conclusion from the data collected on the two robots.
Sal explores more complex limit problems including showing how to take the limit of an expression with a square root by using the conjugate and how to simplify trigonometric functions that are part of limit problems. Note: A mistake is made on the last step of first problem where multiplication should have been used instead of addition, resulting in the correct answer of 3/16.
In this math worksheet, students complete a series of mathematical investigations to determine readiness for the course of study they are enrolled in. This worksheet is problem set four in a set of worksheets for calculus.
Students discuss the importance of fundamental theorems in math. In this calculus lesson plan, students define the fundamental theorem of calculus and discuss why it is so important they understand it. They work problems to model how this theorem works.
Twelfth graders discuss attitude necessary to be successful in calculus. In this calculus lesson plan, 12th graders review famous quotes about success to help them get motivated to learn and be successful in the classroom. This assignment contains interactive links.
Students explore the concept of minimization. In this minimization worksheet, students determine the least expensive box given specific requirements. Students solve a question from the AP Calculus exam in 1982; the same question from the movie Stand and Deliver.
Twelfth graders review the fundamental theorem of calculus and solve for the area under the curve. In this calculus lesson, 12th graders differentiate between the area under the curve and the definite integral as it related to the fundamental theorem of calculus. They work lots of examples with the instructor before being on their own.
In this A.P. Calculus worksheet, students complete a sixteen question test covering trigonometric integration, area under a curve, differential equations, and slope fields. Some of the problems are multiple choice, while others are free-response.
Looking for an interractive presentation for your high schoolers dealing with calculus? Then this PowerPoint is for you! Problems that cover area, volume, and other calculus-related topics are presented. Students are led through the steps necessary to solve the problems, and are given instant feedback. |
CHANGES INMATHEMATICS AND INMATHEMATICSEDUCATION
The mathematics taught in school must change in support of the way mathematics is used in our society.
Since 1900, the growth of the mathematical sciences—in scope and in application—has been explosive.5 The last 40 years have been especially productive, as advances in high-speed computing have opened up new lines of research and new ways mathematics can be applied. Problems in economics, social science, and life science, as well as large-scale problems in natural science and engineering, used to be unapproachable through mathematics. Suddenly, with the aid of computers and the new tools provided by research, many of these problems have become accessible to mathematical analysis. Applications derived from data analysis and statistics, combinatorics and discrete mathematics, and information theory and computing have greatly extended the definition and reach of the mathematical sciences.
An explosion in the way mathematics is used in society mirrors the explosion in mathematics itself. Today we encounter uses of mathematics in every corner of our lives. Graphs, charts, and statistical data appear on television and in newspapers. The results of opinion polls are reported along with their margins of error. Lending institutions advertise variously computed interest rates for loans. We listen to music composed and performed with the aid of computers, and we watch the fantastically detailed pictures of imaginary worlds that computers draw. Computers also do a host of ordinary tasks. They scan bar codes on purchases, keep track of inventories, make travel reservations, and fill out income tax forms. The citizen's need to perform simple calculations may have decreased, but there has been a dramatic increase in the need to interpret, evaluate, and understand quantitative information presented in a variety of contexts.
Although some people do not need or use highly technical mathematics in their daily jobs, many others do. The complexity of daily life requires that we all be able to reason with numbers. Any car or home buyer ought to understand how interest rates work even though a computer may be doing the calculation. Anyone building a house or redecorating a room should be able to make and read a scale drawing. Newspaper readers and television viewers |
Business Math Problems?
Answer
Business Math is used by businesses to record and manage their business transactions. Typical Business Math problems include loans, interest rates, insurance, credit, taxes, and payroll to name a few. In order to take Business Math a person should have a basic understanding of fractions, percents and decimals, whole number, basic algebra, understand mean, median and mode and read charts and graphs. |
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This market-leading text continues to provide students and instructors with sound ipad for dummies free download, consistently structured explanations of the mathematical concepts ipad for dummies free download. Designed for a two-term course ipad for dummies free download, the new Eighth Edition retains the features that have made Algebra and Trigonometry a complete solution for both students and instructors: interesting applications, cutting-edge design, and innovative technology combined with an abundance of carefully written exercises ipad for dummies free download. |
Math Center FAQs & Resources
FAQs
What services does the Math Center provide?
The Math Center offers one-on-one and group instruction by peer tutors. We assist students with the development of the mathematical understanding necessary to succeed in their undergraduate courses.
Who are the tutors that work in the Math Center?
All Math Center tutors are Fisher undergraduate students, most of whom are math majors. The staff also includes MSTI, Science, Business, and English majors.
Can all the tutors assist me?
Yes and no. Tutor expertise varies, so you should determine which tutors are designated for your course (see the Tutor Specialties page) and note their availability on the Tutor Schedule page. You can also find this information on the bulletin board in the Math Center.
What is the procedure for using the Math Center services?
We are a drop-in facility. This means that we do not schedule appointments. If you would like assistance, just stop by the Math Center and ask for a tutor who specializes in your course. If one is not available, we will help you find a time when you can receive the assistance you need.
Do you have to be taking a math class to come to the math center?
No. Tutors can assist you with math skills and concepts that are related to non-math courses such as CHEM101 or ECON221. You can also come to the Math Center to work on the basic computational and algebraic skills that are necessary to succeed in your present or future courses. In addition, we help students prepare for math entrance and certification exams.
How do I prepare for a math tutoring session?
Prior to coming to the Math Center, students should review relevant course material such as the class notes, textbook, and syllabus. Make an attempt to complete any assignments or practice exercises beforehand. Tutors will not do your work for you, but they will answer your questions and help you work through problems.
What resources are available in the Math Center?
In the Math Center you will find textbooks for all math courses, tutorial handbooks for many areas of mathematics, basic skills practice books and flashcards, and handouts on math study skills. Computers and printers are also available for student use day, evening, or weekends.
How do I become a tutor in the Math Center?
If you enjoy helping others and have a love and aptitude for mathematics then you are a great candidate. Please see the Math Center Director for more details.
Where can I get more information about the Math Center?
You can find us on the upper level of the Golisano Gateway, email us at mathcenter@sjfc.edu, or call 385-8407. You can reach Rebecca Tiffin, Math Center Director, at 385-7395. |
NCTM – NavigationSeries G5 Geometric patterns The student uses a variety of representations to describe geometric relationships and solve problems. G5B The student is expected to use numeric and geometric patterns
NCTMNavigationSeries Navigating Through Geometry Grades 3-5 Zome Geometry Book, Key Curriculum Press Equity Provide ample time for students during the exploration/discovery phase. Be sure all groups get to share their ideas.
NCTMNavigationSeries: Xxx - xxxx Not sure how to apply the properties in an everyday situation for my students? Would like some additional resources and sample lessons for this standard.
NCTMNavigationSeries Navigating Through Geometry Grades 3-5; 6-8; and 9-12 Wysiwyg://4/ Equity Provide ample time for students during the exploration/discovery phase. Be sure all
sources including the NCTMNavigationSeries. Topics will include discrete and continuous probability models, data analysis, and statistical inference. Graphing calculators and computers will be used as tools in the study of data.
• Reviewer for the NCTMNavigationSeries for The Oregon Mathematics Teacher (TOMT), 2004-2007 • MAA Liaison to the Mathematics Department at Western Oregon University Institutional Service • Mathematics Department Co-chair with Dr. Hamid Behmard, 2006-present
on seven text series at both elementary and secondary levels as well as eight books for the NCTMNavigationSeries, Making Math Meaningful to Canadian Students: K-8, Big Ideas from Dr. Small: Grades 4-8, Grades K- 3, and Grades 9 - 12 published by Nelson
NavigationSeries The Navigations Series may be purchased through NCTM ( These books include detailed tasks for all grade levels and content strands, and a CD with blackline masters and additional readings.
• Explored the NCTMNavigationseries. • Developed Powerpoint presentations in collaboration with Dr. Hargrove • Became familiar with the new North Carolina Standard Course of Study that will begin to be used in 2004-2005 school year.
NavigationSeries The Navigations Series may be purchased through NCTM ( These books include detailed tasks for all grade levels and content strands, and a CD with blackline masters and additional readings.
NCTMNavigation project, a series of 35 books which was developed for math classroom teachers and students, and in 2005 received the Lifetime Achievement Award from NCTM. Peggy was recognized by Zonta for her effectiveness as a female role
curricula, some textbooks, and a number of websites (e.g., NCTMNavigationSeries, NCTM Illuminations website at Math Forum at
School Mathematics (E-Standards) includes tools to enhance navigation of the document, as well as a more extensive set of electronic examples (e- ... A series of in-stitutes, organized by NCTM's new Academy for Professional Develop-ment, ...Navigationseries, NCTM Daily Data Organize, represent, and interpret data with up to three categories, discuss how many more and how many less, use >, <, and = Number Talks Strategies for combining numbers - counting on,the Navigationseries of the NCTM. Her main interests are mathematics education and interactions between affect and cognition during mathematical problem solving. Susan K. Eddins, NBCT, MA, (Mathematics, University of Illinois, Urbana/Champaign) ...
textbook series (for grades 9-12) dedicate several units to DM topics such as ... permutations; Hart, DeBellis, Kenney and Rosenstein have a forthcoming NCTM book titled Navigation through Discrete Mathematics in Pre-Kindergarten to Grade 12. There are also many websites available that ...
To help teachers visualize the standards in their classrooms, NCTM sponsored the Navigationseries, a set of documents framing the standards in each of the content areas and grade levels described in the Standards, ...
Part of the series Math in a Cultural Context: ... Star Navigation: Explorations into Angles and Measurement (Grade 6, ... (NCTM) for school mathematics as described in Principles and Standards for School Mathematics (c.f., Adams
Williams,and The National Council of Teachers of Mathematics (NCTM). ™ 2002-2003 NASA CONNECT™ Series Data Analysis and Measurement:Dancing in the Night Sky ... radio navigation, some defense-related radar systems, ...
Full-Color Testing Materials—Stanford 10 is the only achievement test series to provide full-color ... Clear Navigation—The student-friendly test pages have been carefully designed to emphasize ... (NCTM) Principles and Standards for School Mathematics.
DVD series during early release times (6-7 for 2008-9, and 7-8 during 2009-10) Summer 2008 2008-2009 2008-2010 ... NCTMNavigation Through Measurement activities K-5 at the following costs: K-2 (82 page books@ $27.00 per teacher
NCTM Principles and Standards - Algebra - Geometry - Measurement ... This problem is part of a series of problems that apply Math and ... Shuttle Guidance, Navigation, and Control - AP Calculus Keywords: |
Learn about linear graphs and vectors simply by just a swipe. Select graphs or vectors on intro page.
Find the relationship between lines, gradients, vectors and equations by drawing a graph with your finger while this app does the rest.
No input of values is necessary. This is an automatic graph app.
Math Graph app – you draw graph, it works out the equation for you.
Trace the graph with your finger. When done, sit back and study your graph.
The app will draw the line and calculate gradient.
It will also write down the graph equation at bottom left of screen.
On vectors screen, you draw vectors with your finger, and this app analyzes them for you. It is an easy way to learn about simple vectors including addition of vectors.
This native math app is meant for beginners in graphical methods, the first 2 years of learning graphs.
If you have studied complex graphical methods but would still like to remind yourself about the basics, this app will do just that.
You can work with the equations produced at your leisure, re-arranging them to discover more about graphical maths60 total
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A Google UserA Google UserUser reviews
A Google User A Google User August 30, 2012SimilarGraph 89 - Emulator for the TI-89 graphing calculator. The ROM image is not included. You need to extract this from you own calculator. Make sure you have the ROM ready before downloading this emulator.
The program allows draw functions graphs in specified area. The area is defined by the X min, X max, Y min, Y max values and division values for X and for Y. Functions are defined by the expression string and color. You should click on function string in the table to edit it. Only "x" symbol should be used as a varible. After area and functions data input click "Redraw" button to draw it. On phones graph is drawn on a full screen. Via the menu You can maximize graph on the full screen, get help about functions, about program, save the graph as a picture or sent e-mail with it (with help of mail client app,such as gmail). The advertisement will be shown after the 5 redraws, and may be closed via the menu (or shown). And please, sometimes click advertisement - it may help for developer))). button |
MULTIPLY your chances of understanding DISCRETE MATHEMATICS If you're interested in learning the fundamentals of discrete mathematics but can't seem to get your brain to function, then here's your solution. Add this easy-to-follow guide to the equation and calculate how quickly you learn the essential concepts. Written by award-winning math professor... more...
Here's the perfect self-teaching guide to help anyone master differential equations--a common stumbling block for students looking to progress to advanced topics in both science and math. Covers First Order Equations, Second Order Equations and Higher, Properties, Solutions, Series Solutions, Fourier Series and Orthogonal Systems, Partial Differential... more... |
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