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Overview
These authors understand what it takes to be successful in mathematics, the skills that students bring to this course, and the way that technology can be used to enhance learning without sacrificing math skills. As a result, they have created a textbook with an overall learning system involving preparation, practice, and review to help students get the most out of the time they put into studying. In sum, Sullivan and Sullivan's Trigonometry: Enhanced with Graphing Utilities gives students a model for success in mathematics.
Related Subjects
Meet the Author
Mike Sullivan is a Professor of Mathematics at Chicago State University and received a Ph.D. in mathematics from Illinois Institute of Technology. Mike has taught at Chicago State for over 30 years and has authored or co-authored over fifty books. Mike has four children, all of whom are involved with mathematics or publishing: Kathleen, who teaches college mathematics; Mike III, who co-authors this series and teaches college mathematics; Dan, who is a Pearson Education sales representative; and Colleen, who teaches middle-school mathematics. When he's not writing, Mike enjoys gardening or spending time with his family, including nine grandchildren.
Mike Sullivan III is a professor of mathematics at Joliet Junior College. He holds graduate degrees from DePaul University in both mathematics and economics. Mike is an author or co-author on more than 20 books, including a statistics book and a developmental mathematics series. Mike is the father of three children and an avid golfer who tries to spend as much of his limited free time as possible on the golf course.
Introduction
As professors at both an urban public university and a community college, Michael Sullivan and Michael Sullivan III are aware of the varied needs of trigonometry students. As a teacher, and as an author of engineering calculus, finite mathematics, and business calculus texts, Michael understands what students must know if they are to be focused and successful in upper level mathematics courses. As a father of four, including the co-author, he also understands the realities of college life. His co-author and son, Michael III, belies passionately in the value of technology as a tool for learning that enhances understanding without sacrificing important skills.
Together, Michael and Michael III have taken great pains to ensure that this text contains solid, student-friendly examples and exercises, as well as a clear, seamless writing style. Please share with them your experiences teaching from this text.
The Third Edition
The Third Edition builds upon a strong foundation by integrating new features and techniques that further enhance student interest and involvement. The elements of previous editions that have proved successful remain, while many changes, some obvious, others subtle, have been made. One important benefit of authoring a successful series is the broad-based feedback upon which improvements and additions are ultimately based. Virtually every change to this edition is the result of thoughtful comments and suggestions from colleagues and students who used previous editions. We are sincerely grateful for this feedback and have tried to make changes that improve the usefulness of the text for both instructors and students.
New to theThird Edition
Preparing for This Section
Most sections now open with a referenced list (by section and page number) of key items to review in preparation for the section ahead. This provides a just-in-time review for students.
Objectives
Each section also contains a numbered list of learning objectives. As the learning objective is addressed in the text, its number will appear.
Concepts and Vocabulary
At the end of every section, there is a short list of Fill-in-the-Blank and True/False items that test concepts and vocabulary in a short answer format. Several quick-answer questions are also included.
Cumulative Reviews
At the end of Chapters 2-6, exercises are provided that require skills learned in the earlier chapters. These cumulative reviews serve to continually reinforce the important concepts of trigonometry. They also make it easier for the student to prepare for a comprehensive final examination.
Content
The formula for the area of a sector and related exercises are now part off Section 2.1 Angles and Their Measure.
The Appendix has been expanded to include more review material appropriate to trigonometry.
New Chapter Projects have been added that discuss topics of current interest.
Organization
Scatter Diagrams, formerly found in Section 1.1, has been relocated to the. Appendix as part of Section A.8. This change positions the content to, where it is being used.
Graphs of the Trigonometric Functions and Sinusoidal Graphs; Sinusoidal Curve Fitting, formerly Sections 2.6 and 2.7, now is covered in three sections, 2.6, 2.7, and 2.8. This change makes it possible to teach the sections in one period each.
The Inverse Trigonometric Functions, formerly Section 3.5, now is covered in two sections at the beginning of the chapter. This change makes it possible to teach the sections in one period each. It also places the content closer to the discussion of the trigonometric functions and their graphs.
Features in the 3rd Edition
Section OBJECTIVES appear in a numbered list to begin each section.
NOW WORK PROBLEM XX. Appears after a concept has been introduced. This directs the student to a problem in the exercises that tests the concept, insuring that the concept has been mastered before moving on. The Now Work problems are identified in the exercises using orange numbers and a pencil icon.
References to Calculus are identified by a calculus icon.
Discussion, Writing, and Research problems appear in most exercise sets, identified by an icon and red numbers. These problems provide a basis for class discussion, writing projects, and library projects.
Varied applications and real-world, sourced data are abundant in Examples and Exercises.
Concepts and Vocabulary, a short list of Fill-in-the-Blank, True/False, and open-ended questions that test concepts and vocabulary in a quick-answer format, are given at the end of every section.
An extensive Chapter Review provides a list of important formulas and key definitions and theorems. The objectives of the chapter are listed by section, with page references and review exercises that relate to the objective. The authors' suggestions for a practice test are indicated by a blue number in the review exercise set.
Chapter Projects that are relevant and current, many based on newspaper articles, appear at the end of each chapter. These can serve as the basis for collaborative learning experiences.
Cumulative Reviews appear at the end of Chapters 2-6. These problem sets serve to continually reinforce skills from earlier chapters.
Using the 3rd Edition Effectively and Efficiently with Your Syllabus.
To meet the varied needs of diverse syllabi, this book contains more content than expected in a trigonometry course. The illustration shows the dependencies of chapters on each other.
As the chart indicates, this book has been organized with flexibility of use in mind. Even within a given chapter, certain sections are optional and can be skipped without fear of future problems.
Chapter 1: Functions and Their Graphs
A quick coverage of this chapter, which is mainly review material, will enable you to get to Chapter 2 Trigonometric Functions earlier.
Appendix Review
This consists of review material, which can be used as the first part of a course in trigonometry or as a just-in-time review. Specific references to this material occur throughout the text to assist in the reviewent |
As a professor of applied math at Concordia University, I taught math for the decision sciences. Among the courses taught were subjects focused heavily on deterministic methods. So it is that Linear Algebra figured heavily in my undertakings |
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Starting at $62 second book of a three-part series, An Introduction to Algebraic, Graphical, and Numerical Problem Solving, Fourth Edition, illustrates how mathematics arises naturally from everyday situations through updated and revised real-life activities and the accompanying practice exercises. Along with the activities and the exercises within the text, MathXL®and MyMathLab®have been enhanced to create a better overall learning experience for the reader. Technology integrated throughout the text helps readers interpret real-life data algebraically, numerically, symbolically, and graphically. The active style of this book develops readers' mathematical literacy and builds a solid foundation for future study in mathematics and other disciplines.
Author Biography
The Consortium for Foundation Mathematics is a team of fourteen co-authors, primarily from the State University of New York and the City University of New York systems. Using the AMATYC Crossroads standards, the team developed an activity-based approach to mathematics in an effort to reach the large population of college students who, for whatever reason, have not yet succeeded in learning mathematics.
Table of Contents
Chapter 1. Number Sense
Cluster 1. Introduction to Problem Solving
Activity 1.1 The Bookstore
Objectives:
1. Practice communication skills.
2. Organize information.
3. Write a solution in sentences.
4. Develop problem-solving skills.
Activity 1.2 The Classroom
Objectives:
1. Organize information.
2. Develop problem-solving strategies.
• Draw a picture.
• Recognize a pattern.
• So a simpler problem.
3. Communicate problem-solving ideas.
Activity 1.3 Properties of Arithmetic
Objectives:
1. Identify and use the commutative property in calculations.
2. Use the distributive property to evaluate arithmetic expressions.
3. Use the order of operations convention to evaluate arithmetic expressions.
4. Identify and use the properties of exponents in calculations
5. Covert numbers to and from scientific notation.
6. Identify, understand, and use formulas.
7. Use the order of operations convention in formulas involving whole numbers. |
Find a HaledonPrealgebra
Discussion of the subject will start from the real number system. Addition, subtraction, multiplication and division will follow, using signed numbers including integers. Fractions, decimals, exponents, graphs,and first order variable expression/equation will be considered. |
Trigonometry With Infotrac
9780534403928
ISBN:
0534403921
Edition: 5 Pub Date: 2003 Publisher: Thomson Learning
Summary: This text provides students with a solid understanding of the definitions and principles of trigonometry and their application to problem solving. Identities are introduced early in Chapter 1. They are reviewed often and are then covered in more detail in Chapter 5. Also, exact values of the trigonometric functions are emphasized throughout the textbook. There are numerous calculator notes placed throughout the text....
McKeague, Charles P. is the author of Trigonometry With Infotrac, published 2003 under ISBN 9780534403928 and 0534403921. One hundred ninety three Trigonometry With Infotrac textbooks are available for sale on ValoreBooks.com, one hundred seventy two used from the cheapest price of $0.01, or buy new starting at $24.48.[read moresome pages bent. CD included. infotrac not included. worn |
books.google.co.uk - This volume introduces mathematicians and physicists to a crossing point of algebra, physics, differential geometry and complex analysis. The book follows the French tradition of Cartan, Chevalley and Crumeyrolle and summarizes Crumeyrolle's own work on exterior algebra and spinor structures. The depth... Algebras and Spinor Structures |
The TI-84 Plus graphing calculator offers three times the memory, more than twice the speed and a higher contrast screen than the TI-83 Plus model. It's keystroke-for-keystroke compatible, too-84 Plus graphing calculator offers three times the memory, more than twice the speed and a higher contrast screen than the TI-83 Plus model. Its keystroke-for-keystroke compatible, too. |
Algebra: Graphs & Models
The Bittinger Graphs and Models Series helps readers learn algebra by making connections between mathematical concepts and their real-world ...Show synopsisThe Bittinger Graphs and Models Series helps readers learn algebra by making connections between mathematical concepts and their real-world applications. Abundant applications, many of which use real data, offer students a context for learning the math. The authors use a variety of tools and techniques--including graphing calculators, multiple approaches to problem solving, and interactive features--to engage and motivate all types of learners.Hide synopsis
Description:Fine. Hardcover. Almost new condition. SKU: 9780321725554-2-0-3...Fine. Hardcover. Almost new condition. SKU: 97803217255541725554.
Description:New in very good dust jacket. Sewn binding. Paper over boards....New in very good dust jacket. Sewn binding. Paper over boards. 862 p. Contains: Tables, black & white, Figures. Audience: General/trade. The is the instructor's copy, annotated which is the same as student copy with all the answers plus instructor's notes. Book will be shipped same day as ordered
Description:Very good. Annotated Edition. All orders ship SAME or NEXT...Very good. ANNOTATED INSTRUCTOR'S EDITION! ! This item may not...Good. ANNOTATED INSTRUCTOR'S EDITION! ! This item may not include any CDs, Infotracs, Access cards or other supplementary material.
Description:New in new dust jacket. Audience: General/trade. Brand new...New in new dust jacket. Audience: General/trade. Brand new Instructor Edition-contains even and odd answers. Will ship to you within 24 hours of your order being placed!
Description:Very Good. 0321725557 INSTRUCTOR'S REVIEW COPY. Same as student...Very Good. 0321725557 INSTRUCTOR'S REVIEW COPY |
Book summary
The first part of a self-contained, elementary textbook, combining linear functional analysis, nonlinear functional analysis, numerical functional analysis, and their substantial applications with each other. As such, the book addresses undergraduate students and beginning graduate students of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems which relate to our real world. Applications concern ordinary and partial differential equations, the method of finite elements, integral equations, special functions, both the Schroedinger approach and the Feynman approach to quantum physics, and quantum statistics. As a prerequisite, readers should be familiar with some basic facts of calculus. The second part has been published under the title, Applied Functional Analysis: Main Principles and Their Applications. [via] |
College Algebra, 2nd Edition
The new 2nd edition of Cynthia Young's College Algebra continues to bridge the gap between in-class work and homework by helping students overcome common learning barriers and build confidence in their ability to do mathematics. The text features truly unique, strong pedagogy and is written in a clear, single voice that speaks directly to students and mirrors how instructors communicate in lectures. In this revision, Young enables students to become independent, successful learners by including hundreds of additional exercises, more opportunities to use technology, and a new themed modeling project that empowers students to apply what they have learned in the classroom to the world outside the classroom. The seamlessly integrated digital and print resources to accompany College Algebra 2e offer additional tools for both instructors and students in order to help students experience success.
Significantly Expanded Exercises: Hundreds of new exercises have been added to the second edition spanning all categories: Skills, Applications, Catch the Mistake, Conceptual, Challenge, and Technology. Several of the new applications exercises require the student to model applications.
Increased number of end of section/end of chapter exercises, including more exercises at lower difficulty level
New Modeling Your World feature: Engages students by using real world data to model mathematical applications found in everyday life.
Additional Practice Test Questions:, These questions represent all relevant topics from the chapter.
New Cumulative Test feature: Included at the end of each chapter to assess and improve students' retention of material.
Applications: The second edition includes more applications to finance, biology, and chemistry.
Clear, Concise and Inviting Writing. The author's engaging and clear presentation is presented in a layout that is designed to reduce math anxiety in students.
Skills/Concepts Objectives. Objectives are divided by skill and concept so students learn the difference between solving problems and understanding concepts.
Correct vs. Incorrect. In addition to standard examples, some problems are worked both correctly and incorrectly to highlight common errors students make. Counter examples, like these, are often an effective learning approach for many students.
Catch the Mistake. In every section, 'Catch the Mistake' exercises put the students in the role of the instructor grading homework which increases the depth of understanding and reinforces what they have learned.
Your Turn. Students are often asked to work a problem immediately following an example to reinforce and check their understanding. This helps them build confidence as they progress in the chapter. These are ideal for in-class activity and preparing the student to work homework later.
Parallel Words and Math. This text reverses the common presentation of examples by placing the explanation in words on the left and the mathematics in parallel on the right. This makes it easier for students to read through examples as the material flows more naturally and as commonly presented in lecture.
Five Different Types of Exercises. Every chapter has skill, application, catch the mistake, challenge and technology exercises. The exercises gradually increase in difficulty and vary skill and conceptual emphasis. The challenge exercises specifically focus on assessing conceptual understanding.
Prerequisite and Review Chapter 0. A review of prerequisite knowledge (intermediate algebra topics) is included in Chapter 0 indicating clearly to the students what knowledge and skills are necessary for success in the course.
Review throughout the Chapter. Throughout each chapter, prerequisite concepts, i.e., LCD, long division, are reviewed as needed.
Easy Navigation. Icons throughout the chapter make it easy to navigate through the book and supplements.
Chapter Introduction Flow Chart and Objectives. A flow chart and chapter objectives give an overview of the chapter to help students see the big picture.
Chapter Review Chart. A chapter review chart organizes the topics in an easy to use one-page layout. This feature includes key concepts and formulas, as well as indicating review exercises so that students can quickly summarize a chapter and study smarter.
Author Instructional Videos. For review at home or for a class missed, each chapter has a video that includes an introduction and review. The author works some of the examples and "Your Turn" problems from the text on the videos as well.
WileyPLUS. An online graded homework, course management and tutorial system gives students immediate feedback on their homework, saves instructors grading and course administration time, and walks students through the material step-by-step.
"It is a great book. everything is in detail. It is a book which makes students less frustrated while reading it. It does need some graphical approach on defining the value of Trigonometry functions. Authur herself has a great sence of humor and welcome input by others."- Professor Mohammad Ganjizadeh, Texarkana College
"This is a great textbook. It is very "readable", yet it maintains required mathematical rigor. The organization is very good, as well as the diversity of the practice problems." -Professor Aharon Dagan, SFCC |
Other Courses
Oxford Home Schooling Maths IGCSE Course
Oxford Home Schooling's Maths IGCSE course is designed to prepare students for the Edexcel IGCSE in Mathematics (Specification A, 4MA0) for examination in June 2014 and later years. The GCSE Maths course is also available in June 2014 and later years.
The Maths IGCSE course gently guides the student through basic mathematical skills, progressing onto more advanced material as the student's skills and abilities develop. Each lesson begins with a set of clearly stated objectives and an explanation of its place in the overall programme of study.
Effective learning is encouraged through frequent activities and self-assessment questions.
There are eleven tutor-marked assignments and a practice exam paper in the OHS course.
Home Schooling IGCSE Maths: Course Overview
We have chosen this syllabus as it is the most suited to Home Schooling.
IGCSE Mathematics provides an excellent foundation for:
Students who want to continue their studies at AS and A Level and beyond
Students who need Mathematics to complement other subjects
Students who need a final qualification in Mathematics
The OHS course enables students to:
Develop their knowledge and understanding of mathematical concepts and techniques
Acquire a foundation of mathematical skills for further study in the subject or related areas
Enjoy using and applying mathematical techniques and concepts, and become confident to use mathematics to solve problems
Appreciate the importance of mathematics in society, employment and study
How does IGCSE differ from GCSE?
The IGCSE includes some topics that are beyond the GCSE syllabus, notably sets, function notation and calculus.
Assessment
Assessment comprises two papers marked by Edexcel. Each paper is assessed by a two-hour written examination. There is no coursework.
Special Requirements
A reasonable level of proficiency in arithmetical skills is assumed. This course follows on from the Oxford Home Schooling KS3 course which is recommended for younger home learners. |
Product Description
This program is a review of Linear inequalities. That's right, not everything in this world is equal. Linear inequalities are like linear equations'except they are different and this program will tell you how and why! Topics include: Linear Inequalities Graphing Linear Inequalities Systems of Linear InequalitiesGrade Level: 8-12. 26 minutes |
Common Core Standards
Steal These Tools / Professional Development Modules / Math Shifts Module
Jump to a Section Sign up to receive updates from us. Introduction to the Math Shifts Download All Send us your feedback This module provides participants with an introduction to the key shifts required by the CCSS for Math.
Here is a suggested arrangement of the high school standards into courses, developed with funding from the Bill and Melinda Gates Foundation and the Pearson Foundation, by a group of people including Patrick Callahan and Brad Findell. I haven't looked at it closely, but it seems to be a solid effort by people familiar with the standards, so I put it up for comment and discussion. There are five files: the first four are graphic displays of the arrangement of the standards into both traditional and integrated sequences, with the standards referred to by their codes. The fifth is a description of the arrangement with the text of the standards and commentary. 9_11 Scope and Sequence_traditional1
Arranging the high school standards into courses | Tools for the Common Core Standards |
WELCOME TO THE MATHEMATICAL SCIENCES DIVISION
The Division of Mathematical Sciences offers instruction to students in mathematics, computer science and engineering. Mathematics courses include basic skills and general education, courses for future teachers, and courses for students majoring in science, technology, engineering and mathematics. The computer science program includes a variety of computer language courses and preparation for students transferring to four-year computer science programs. In engineering two courses are offered.
The division is dedicated to promoting student success at all levels. For information about the El Camino College Mathematics Placement Test, go to Math Placement Test. The Mathematics Study Center (MBA 119) provides one-to-one tutoring on a drop-in basis. Many mathematics courses provide students the opportunity to use computational and homework technology, such as graphing calculators, Mathematica, WebAssign, and MyMathLab.
Course Information:
For an overview of all mathematics course offerings at El Camino College, see the diagrams of math course sequences:
Some students may have multiple possible paths in Mathematics. For information, see below.
New Accelerated Courses:
Math 37 (Formerly50D) - Basic Accelerated Mathematics designed to prepare students for Intermediate Algebra. Math 67 (Formerly 50C) - General Education Algebra designed for students who are eligible for Elementary Algebra to prepare for Statistics and other non-STEM transfer level courses. For more details see New Accelerated Mathematics Courses or come to the Division Office.
Also, for students who are trying to complete their transfer math requirements, there are several options. Among them are Math 120 - The Nature of Mathematics, and Math 130 - College Algebra. For details see Math 120 vs. Math 130 Comparison. |
ALEX Lesson Plans
Title: Graphing at all levels: It's a beautiful thing!
Description:
ThisStandard(s): [AED] VA2 (7-12) 2: Produce works of art using a variety of techniques. 40: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.* [F-TF5] [MA2013] PRE (9-12) 1: (+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. [N-CN4] [MA2013] PRE (9-12) 15: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from second-degree equations. (Alabama)
Supply and Demand
Description:
This
Standard(s): [T1] ECN (12) 3: Analyze graphs to determine changes in supply and demand and their effect on equilibrium price and quality. Supply and Demand
Title: Investigating Pick's Theorem
Description:
In quantities; graph equations on coordinate axes with labels and scales. [A-CED2] Investigating Pick's TheoremWeb Resources
Interactives/Games
Title: Karl's Function Plotter
Description: 23T (9-12) 27
Karl's Function Plotter |
97806184701Math Excursions With Cd Plus Smarthinking
A new text for the liberal arts math course by a seasoned author team, Mathematical Excursions, is uniquely designed to help students see math at work in the contemporary world. Using the proven Aufmann Interactive Method, students learn to master problem-solving in meaningful contexts. In addition, multi-part Excursion exercises emphasize collaborative learning. The text's extensive topical coverage offers instructors flexibility in designing a course that meets their students' needs and curriculum requirements.
The Excursions activity and corresponding Excursion Exercises, denoted by an icon, conclude each section, providing opportunities for in-class cooperative work, hands-on learning, and development of critical-thinking skills. These activities are also ideal for projects or extra credit assignments. The Excursions are designed to reinforce the material that has just been covered in the section in a fun and engaging manner that will enhance a student's journey and discovery of mathematics.
The proven Aufmann Interactive Method ensures that students try concepts and manipulate real-life data as they progress through the material. Every objective contains at least one set of matched-pair examples. The method begins with a worked-out example with a solution in numerical and verbal formats to address different learning styles. The matched problem, called Check Your Progress, is left for the student to try. Each problem includes a reference to a fully worked out solution in an appendix to which the student can refer for immediate feedback, concept reinforcement, identification of problem areas, and prevention of frustration.
Each Chapter Opener begins with a short introduction to a real data application, which is then highlighted again in one Excursions activity and in the corresponding Excursion Exercises at the end of a section. This specific Excursion will be denoted by an icon. A section-by-section table of contents is accompanied by a brief summary of the topics that will be covered in the chapter.
A section called Problem-Solving Strategies in Chapter 1 introduces students to the inductive and deductive reasoning strategies they will use throughout the text.
An Instructor's Annotated Edition features icons denoting tables and art that appear in PowerPoint and Word files on the Instructor CD-ROM and web site; worked-out solutions to all Check Your Progress exercises and answers to all exercises; and a time-saving listing, Suggested Assignments.
A supportive Question/Answer feature at key points throughout the text encourages students to pause and reflect on the concept being discussed and to answer the question. The answer is located in a footnote on the same page.
Extension exercises placed near the end of each exercise set present a combination of Critical Thinking, Cooperative Learning, and Exploration exercises to provide further challenge and concept extension.
Take Note boxes in the margins alert students to a point requiring special attention or amplify a concept being developed.
Math Matters essay boxes throughout the text help motivate students by demonstrating how and why math is applicable to contemporary, real-life situations. Accompanying graphs and figures help students visually interpret the material.
Point of Interest notes provide relevant, contemporary information that helps motivate learning by giving context to concepts being presented. Historical Notes offer additional context by highlighting important mathematical developments or famous individuals who have made major advancements in their fields |
Math for Elementary Teachers 1 (MATH 218)
College: College of Arts and Sciences
Department: Mathematics
Credit Hours: 3
This course has a lecture with 3 hours.
The first in a two course sequence designed to develop pre-service elementary teachers' conceptual understanding of mathematics. Topics include problem solving, set theory, number theory, rational and real numbers, and algebraic concepts. Emphasis is placed on learning through problem solving. Open only to prospective elementary teachers. Prerequisites: MATH 115 with a grade of C- or better or placement. Typically Offered Fall, Spring. |
Discussion 1 Week 5 Math 126 Essays and Term Papers
Discussion Week 1- Television, movies, electronic games, Internet sites with video animation, and mobile phones are common media for children and adults today. Discuss how regular access to these media may affect students reading and writing skills positively or negatively." EXPLAIN: yourself, wha
Kindergarten Math
Observations
Mrs. Miller, Antelope Elementary, Kindergarten
Observed: Wednesday (9:00am-10:30am) 3/27/13
Classroom rotation- children went from one room to the next for separate subjects, also each group of kids had been evaluated and put into advanced, moderate, and standard
-------------------------------------------------
Top of Form
Week 1: Introductions/Overview: An Ethical and Legal Framework - Discussion
This week's graded topics relate to the following Terminal Course Objectives (TCOs):
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Math Review for the GMAT MBA Center
By Hubert Silly, PhD & Zeyu Lee, MBA
1
2
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Acknowledgments
Creating any test preparation book requires a team of committed and talented individuals. What makes The Math Review for the GMAT unique is that our writers are also our teachers. Not on
CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL DISTRIBUTION
Cumulative probability
Entries in this table give the area under the curve to the left of the z value. For example, for z = –.85, the cumulative probability is .1977. z 0 .02 .0013 .0018 .0024 .0033 .0044 .0059 .0078 .0102 .0132
About the Cover
Peter Blair Henry received his first lesson in international economics at the age of eight, when his family moved from the Caribbean island of Jamaica to affluent Wilmette, Illinois. Upon arrival in the United States, he wondered why people in his new home seemed to have so much mo
Math Review
for the Quantitative Reasoning Measure of the GRE® revised General Test
Overview
This Math Review will familiarize you with the mathematical skills and concepts that are important to understand in order to solve problems and to reason quantitatively on the Quantit
Math Review
for the Quantitative Reasoning
Measure of the GRE® revised
General Test
Overview
This Math Review will familiarize you with the mathematical skills and concepts that are
important to understand in order to solve problems and to reason quantitatively on...
Week one Discussion question 1
Pretend you are a specialist in math anxiety disorder and you have a group of students who have signed up for therapy because they start a class in one week and have not taken math in 10 years! Based on your previous experience with studying mathematics, give the st
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Crawford states "The National Defense Education Act of 1958, passed in response to Sputnik, was the first effort at the national level to strengthen mathematics, scienc |
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Beginning and Intermediate Algebra - With CD - 2nd edition
Summary: A worktext format for basic college math or arithmetic courses including lecture-based, self-paced, and modular classes.
John Tobey and Jeff Slater are experienced developmental math authors and active classroom teachers. The Tobey approach focuses on building skills one at a time by breaking math down into manageable pieces. This building block organization is a practical approach to basic math skill development that makes it easier for students to underst...show moreand each topic, gaining confidence as they move through each section. Knowing students crave feedback, Tobey has enhanced the new edition with a "How am I Doing?" guide to math success. The combination of continual reinforcement of basic skill development, ongoing feedback and a fine balance of exercises makes the second edition of Tobey/Slater Beginning and Intermediate Algebra even more practical and accessible |
Master the basic concepts and methodologies of digital signal processing with this systematic introduction, without the need for an extensive mathematical background. The authors lead the reader through the fundamental mathematical principles underlying the operation of key signal processing techniques, providing simple arguments and cases rather than detailed general proofs. Coverage of practical implementation, discussion of the limitations of particular methods and plentiful MATLAB illustrations allow readers to better connect theory and practice. A focus on algorithms that are of theoretical importance or useful in real-world applications ensures that students cover material relevant to engineering practice, and equips students and practitioners alike with the basic principles necessary to apply DSP techniques to a variety of applications. Chapters include worked examples, problems and computer experiments, helping students to absorb the material they have just read. Lecture slides for all figures and solutions to the numerous problems are available to instructors. less |
Algebra II – Unit 8
Ascension Parish Comprehensive Curriculum
Assessment Documentation and Concept Correlations
Unit 8: Further Investigation of Functions
Time Frame: Regular – 4 weeks
Block – 2 weeks
Big Picture: (Taken from Unit Description and Student Understanding)
This unit ties together all the functions studied throughout the year.
This unit categorizes functions, graphs them, translates them, and models data with them.
The rules affecting change of degree, coefficient, and constants applied to all functions will be mastered.
Being able to quickly graph the basic functions and make connections between the graphical representation of a function and the
mathematical description of change will be mastered.
Easy translation among the equation of a function, its graph, its verbal representation, and its numerical representation will be mastered.
Documented GLEs
Activities
The essential GLES Date and Method of
Guiding Questions GLEs GLES
activities are denoted Bloom's Level Assessment
by an asterisk. Translate and show the 4
relationships among non-linear
Concept : *1 – Basic Graphs graphs, related tables of values, and
DOCUMENTATION
Investigating Functions and their algebraic symbolic representations
6, 8, 25, 27
68. Can students quickly Characteristics (GQ (A-1-H)
graph lines, power 68) Analyze functions based on zeros, 6
functions, radicals, Grade 9: 36; asymptotes, and local and global
*2 – Horizontal and characteristics of the function (A-
logarithmic, exponential, Grade 11/12:
Vertical Shifts of 3-H) (Analysis)
step, rational, and 4, 6, 7, 8, 16,
Abstract Functions Explain, using technology, how the 7
absolute value 19, 25, 27,
(GQ 68, 69, 70, 71, graph of a function is affected by
functions? 28)
72) change of degree, coefficient, and
69. Can students determine
constants in polynomial, rational,
the intervals on which a Grade 9: 35, radical, exponential, and
function is continuous, *3 – How 36; Grade logarithmic functions (A-3-H)
increasing, decreasing, Coefficients Change 11/12: 4, 6, 7, Categorize non-linear graphs and 8
or constant? Families of Functions 8, 16, 19, 25, their equations as quadratic, cubic,
70. Can students determine (GQ 68, 69, 70, 71, 27, 28) exponential, logarithmic, step
the domains, ranges, 72)
207
Algebra II – Unit 8 – Further Investigation of Functions
Algebra II – Unit 8
zeroes, asymptotes, and function, rational, trigonometric, or
global characteristics of *4 – How Absolute Grade 9: 35, absolute value (A-3-H) (P-5-H)
these functions? Value Changes 36; Grade Model and solve problems 10
71. Can students use Families of Functions 11/12: 4, 6, 7, involving quadratic, polynomial,
translations, reflections, (GQ 68, 69, 70, 71, 8, 16, 19, 25, exponential, logarithmic, step
function, rational, and absolute
and dilations to graph 72) 27, 28)
value equations using technology
new functions from (A-4-H) (Application)
parent functions? Grade 9: 35, Represent translations, reflections, 16
72. Can students determine *5 – Functions – 36; Grade rotations, and dilations of plane
domain and range Tying It All Together 11/12: 4, 6, 7, figures using sketches, coordinates,
changes for translated (GQ 70, 71) 16, 25, 27, vectors, and matrices (G-3-H)
and dilated abstract 28) (Application)
functions? Grade 9: 35, Correlate/match data sets or graphs 19
73. Can students graph 36; Grade and their representations and
piecewise defined 11/12: 4, 6, 7, classify them as exponential,
functions, which are *6 – More Piecewise logarithmic, or polynomial
8, 10, 16, 19,
composed of several Functions (GQ 73) functions (D-2-H)
24, 25, 27, 28,
types of functions? Interpret and explain, with the use 20
29) of technology, the regression
74. Can students identify the
coefficient and the correlation
symmetry of these coefficient for a set of data (D-2-H)
DOCUMENTATION
functions and define *7 – Symmetry of 4, 6, 7, 8, 16, (Application)
even and odd functions? Graphs (GQ 74) 25, 27, 28
75. Can students analyze a Explain the limitations of 22
set of data and match the predictions based on organized
sample sets of data (D-7-H)
data set to the best
(Comprehension)
function graph? Model a given set of real-life data 24
with a non-linear function (P-1-H)
*8 – History, Data 4, 6, 8, 10, 19, (P-5-H)
Analysis, and Future 20, 22, 24, 28, Apply the concept of a function 25
Predictions Using 29) and function notation to represent
Statistics and evaluate functions (P-1-H) (P-
5-H)
Compare and contrast the 27
properties of families of
polynomial, rational, exponential,
208
Algebra II – Unit 8 – Further Investigation of Functions
Algebra II – Unit 8
and logarithmic functions, with and
without technology (P-3-H)
(Analysis)
Represent and solve problems 28
involving the translation of
functions in the coordinate plane
(P-4-H)
Determine the family or families of 29
functions that can be used to
represent a given set of real-life
data, with and without technology
(P-5-H) (Analysis)
209
Algebra II – Unit 8 – Further Investigation of Functions
Algebra II – Unit 8
Algebra IIUnit 8Advanced Functions 210
Algebra II – Unit 8
Unit 8 Grade-Level Expectations (GLEs)
Teacher Note: The individual Algebra II GLEs are sometimes very broad, encompassing a
variety of functions. To help determine the portion of the GLE that is being addressed in each
unit and in each activity in the unit, the key words have been underlined in the GLE list, and
the number of the predominant GLE has been underlined in the activity. Some Grade 9 and
Grade 10 GLEs have been included because of the continuous need for review of these topics
while progressing in higher level mathematics.
GLE # GLE Text and Benchmarks
Algebra
4. Translate and show the relationships among non-linear graphs, related tables of
values, and algebraic symbolic representations (A-1-H)
6. Analyze functions based on zeros, asymptotes, and local and global
characteristics of the function (A-3-H)
7. Explain, using technology, how the graph of a function is affected by change of
degree, coefficient, and constants in polynomial, rational, radical, exponential,
and logarithmic functions (A-3-H)
8. Categorize non-linear graphs and their equations as quadratic, cubic,
exponential, logarithmic, step function, rational, trigonometric, or absolute
value (A-3-H) (P-5-H)
10. Model and solve problems involving quadratic, polynomial, exponential,
logarithmic, step function, rational, and absolute value equations using
technology (A-4-H)
Geometry
16. Represent translations, reflections, rotations, and dilations of plane figures using
sketches, coordinates, vectors, and matrices (G-3-H)
Data Analysis, Probability, and Discrete Math
19. Correlate/match data sets or graphs and their representations and classify them
as exponential, logarithmic, or polynomial functions (D-2-H)
20. Interpret and explain, with the use of technology, the regression coefficient and
the correlation coefficient for a set of data (D-2-H)
22. Explain the limitations of predictions based on organized sample sets of data
(D-7-H)
Patterns, Relations, and Functions
Grade 9
35. Determine if a relation is a function and use appropriate function notation(P-1-H)
36. Identify the domain and range of functions (P-1-H)
Grade 11/12
24. Model a given set of real-life data with a non-linear function (P-1-H) (P-5-H)
25. Apply the concept of a function and function notation to represent and evaluate
functions (P-1-H) (P-5-H)
27. Compare and contrast the properties of families of polynomial, rational,
exponential, and logarithmic functions, with and without technology (P-3-H)
28. Represent and solve problems involving the translation of functions in the
coordinate plane (P-4-H)
Algebra IIUnit 8Advanced Functions 211
Algebra II – Unit 8
GLE # GLE Text and Benchmarks
29. Determine the family or families of functions that can be used to represent a
given set of real-life data, with and without technology (P-5-H)
Purpose/Guiding Questions: Key Concepts and Vocabulary:
Quickly graph lines, power Basic graphs:
functions, radicals, logarithmic, Continuity
exponential, step, rational, and Increasing, decreasing, and constant
absolute value functions functions
Determine the intervals on which Even and odd functions
a function is continuous, General piecewise function
increasing, decreasing, or constant Function graph shifts/translations
Determine the domains, ranges,
zeroes, asymptotes, and global
characteristics of these functions
Use translations, reflections, and
dilations to graph new functions
from parent functions
Determine domain and range
changes for translated and dilated
abstract functions
Graph piecewise defined
functions, which are composed of
several types of functions
Identify the symmetry of these
functions and define even and odd
functions
Analyze a set of data and match
the data set to the best function
graph
Assessment Ideas:
One-Two major assessments recommendedActivity-Specific Assessments:
Activity 8: Data Research Project: Optional Rubric at end of Unit
Algebra IIUnit 8Advanced Functions 212
Algebra II – Unit 8
Resources:
Check shared folder for worksheets and assessments for this unit.
Sample Activities
Ongoing Activity: Little Black Book of Algebra II Properties
Materials List: black marble composition book, Little Black Book of Algebra II Properties
BLM
Activity:
Have students continue to add to the Little Black Books they created in previous units
which are modified forms of vocabulary cards (view literacy strategy descriptions).
When students create vocabulary cards, they see connections between words, examples
of the word, and the critical attributes associated with the word, such as a mathematical
formula or theorem. Vocabulary cards require students to pay attention to words over
time, thus improving their memory of the words. In addition, vocabulary cards can
become an easily accessible reference for students as they prepare for tests, quizzes, and
other activities with the words. These self-made reference books are modified versions of
vocabulary cards because, instead of creating cards, the students will keep the vocabulary
in black marble composition books (thus the name "Little Black Book" or LBB). Like
vocabulary cards, the LBBs emphasize the important concepts in the unit and reinforce
the definitions, formulas, graphs, real-world applications, and symbolic representations.
At the beginning of the unit, distribute copies of the Little Black Book of Algebra II
Properties BLM for Unit 7. This is a list of properties in the order in which they will be
learned in the unit. The BLM has been formatted to the size of a composition book so
students can cut the list from the BLM and paste or tape it into their composition books to
use as a table of contents.
The student's description of each property should occupy approximately one-half page in
the LBB and include all the information on the list for that property. The student may
also add examplesUnit 8Advanced Functions 213
Algebra II – Unit 8
Advanced Functions
1
7.1 Basic Graphs Graph and locate f(1): y = x, x2, x3, x , 3 x , x , , x , log x, 2x.
x
7.2 Continuity – provide an informal definition and give examples of continuous and
discontinuous functions.
7.3 Increasing, Decreasing, and Constant Functions – write definitions and draw example
graphs such as y 9 x 2 , state the intervals on which the graphs are increasing and
decreasing.
7.4 Even and Odd Functions – write definitions and give examples, illustrate properties of
symmetry, and explain how to prove that a function is even or odd (e.g., prove that
y = x4 + x2 + 2 is even and y = x3 + x is odd).
7.5 General Piecewise Function – write the definition and then graph, find the domain and
range, and solve the following example f ( x) R 1
2
Sxx if x 5
for f (4) and f (1).
T 2
if x 5
For properties 7.6 7.9 below, do the following:
Explain in words the effect on the graph.
Give an example of the graph of a given abstract function and then the
function transformed (do not use y = x as your example).
Explain in words the effect on the domain and range of a given function. Use
the domain [–2, 6] and the range [–8, 4] to find the new domain and range of
the transformed function.
7.6 Translations (x + k) and (x k), (x) + k and (x) k
7.7 Reflections (–x) and –(x)
7.8 Dilations (kx), (|k|<1 and |k|>1), k(x) (|k|<1 and |k|>1)
7.9 Reflections (|x|) and |(x)|
Activity 1: Basic Graphs and their Characteristics (GLEs: 6, 8, 25, 27)
Materials List: paper, pencil, graphing calculator, Math Log Bellringer BLM
In this activity, the students will work in groups to review the characteristics of all the basic
graphs they have studied throughout the year. They will also develop a definition for the
continuous, increasing, decreasing, and constant functions.
Math Log Bellringer:
Graph the following by hand, locate zeroes and f(1), and identify the function.
Algebra IIUnit 8Advanced Functions 214
Algebra II – Unit 8
(1) f(x) = x
(2) f(x) = x2
(3) f ( x) x
(4) f(x) = x3
(5) f(x) = |x|
(6) f(x) = 2x
1
(7) f ( x)
x
(8) f x 3 x
(9) f(x) = log x
(10) f ( x) x
Solutions:
(1) (5)
f (1) = 1, linear function, f(1) = 1,
zero (0,0) absolute value function, zero
(0, 0)
(2)
f (1) =1, quadratic function (6)
also polynomial function, f(1) = 2, exponential function
zero (0, 0) no zeroes
(3) (7)
f(1) = 1, radical function f(1) = 1, rational function
square root function, zero (0, 0) no zeroes
(4)
f(1) = 1, cubic function (8)
also polynomial function, f(1) = 1 , radical function
zero (0, 0) cube root function, zero (0, 0)
(9)
Algebra IIUnit 8Advanced Functions 215
Algebra II – Unit 8
f(1) = 0, logarithmic function,
zero (1, 0)
(10)
f(1) = 1,
greatest integer function,
zeroes: 0 < x < 1
Activity:
Overview of the Math Log Bellringers:
As in previous units, each in-class activity in Unit 7 is started with an activity called
a Math Log Bellringer that either reviews past concepts to check for understanding
(reflective thinking about what was learned in previous classes or previous courses)
or sets the stage for an upcoming concept (predictive thinking for that day's lesson).
A math log is a form of a learning log (view literacy strategy descriptions) that
students keep in order to record ideas, questions, reactions, and new understandings.
Documenting ideas in a log about content being studied forces students to "put into
words" what they know or do not know. This process offers a reflection of
understanding that can lead to further study and alternative learning paths. It
combines writing and reading with content learning. The Math Log Bellringers will
include mathematics done symbolically, graphically, and verbally.
Since Bellringers are relatively short, blackline masters have not been created for
each of them. Write them on the board before students enter class, paste them into an
enlarged Word® document or PowerPoint® slide, and project using a TV or digital
projector, or print and display using a document or overhead projector. A sample
enlarged Math Log Bellringer Word® document has been included in the blackline
masters. This sample is the Math Log Bellringer for this activity.
Have the students write the Math Log Bellringers in their notebooks, preceding the
upcoming lesson during beginningofclass record keeping, and then circulate to
give individual attention to students who are weak in that area.
Function Calisthenics: Use the Bellringer to review the ten basic parent graphs. Then
have the students stand up, call out a parent function, and ask them to form the shape of
the graph with their arms.
Increasing/decreasing/constant functions:
o Ask students to come up with a definition of continuity. (An informal definition of
continuity is sufficient for Algebra II.)
o Then have them develop definitions for increasing, decreasing, and constant
functions.
o Have students look at the abstract graph to the right
and determine if it is continuous and the intervals
in which it is increasing and decreasing. (Stress the
concept that when intervals are asked for, students
should always give intervals of the independent
Algebra IIUnit 8Advanced Functions 216
Algebra II – Unit 8
variable, x in this case, and the intervals should always be open intervals.)
Solution: Increasing , 1 0,
Decreasing (–1, 0)
o Have each student graph any kind of graph he/she desires on the graphing calculator
and write down the interval on which the graph is increasing and decreasing. Have
students trade calculators with a neighbor and answer the same question for the
neighbor's graph, then compare answers
Flash that Function: Divide students into groups of four and give each student ten blank
5 X 7" cards to create vocabulary cards (view literacy strategy descriptions). When
students create vocabulary cards, they see connections between words, examples of the
word, and the critical attributes associated with the word such as a mathematical formula
or theorem. Have them choose assignments – Grapher, Symbol Maker, Data Driver, and
Verbalizer. Have each member of the group create flash cards of the ten basic graphs in
the Bellringer activity, but the front of each will be different based on his/her
assignment. (They can use their Little Black Books to review the information.) The front
of Grapher's card will have a graph of the function. The front of the Symbol Maker's
card will have the symbolic equation of the function. The front of the Data Driver's card
will have a table of data that models the function. The front of the Verbalizer's card will
have a verbal description of the function. The back of the card will have all of the
following information: graph, function, the category of parent functions, family, table of
data, domain, range, asymptotes, intercepts, zeroes, end-behavior, and increasing or
decreasing. Once all the cards are complete, have students practice flashing the cards in
the group asking questions about the function, then set up a competition between groups.
Activity 2: Horizontal and Vertical Shifts of Abstract Functions (GLEs: Grade 9: 36;
Grade 11/12: 4, 6, 7, 8, 16, 19, 25, 27, 28)
Materials List: paper, pencil, graphing calculator, Translations BLM
In this activity, the students will review horizontal and vertical translations, apply them to
abstract functions, and determine the effects on the domain and range.
Math Log Bellringer:
Graph the following without a calculator: Discuss how the shifts in #25 change the
domain, range, and vertex of the parent function.
(1) f(x) = x2
(2) f(x) = x2 + 4
(3) f(x) = x2 – 5
(4) f(x) = (x + 4)2
(5) f(x) = (x – 5)2
Algebra IIUnit 8Advanced Functions 217
Algebra II – Unit 8
Solutions:
(1)
(2)
changes the range,
vertex moves up
(3)
changes the range,
vertex moves down
(4)
no change in domain and range,
vertex moves left
(5)
no change in domain or range,
vertex moves right
Activity:
Have the students check the Bellringer graphs with their calculators and use the
Bellringer to ascertain how much they remember about translations.
Vertical Shifts: f x k
o Have the students refer to Bellringer problems 1 through 3 to develop the rule that
f(x) + k shifts the functions up and f(x) – k shifts the functions down.
o Determine if this shift affects the domain or range. (Solution: range)
o For practice, have students graph the following:
(1) f(x) = x3
(2) f(x) = x3 + 4
(3) f(x) = x3 – 6
Algebra IIUnit 8 Advanced Functions 218
Algebra II – Unit 8
Solutions:
(1) (2) (3)
Horizontal Shifts: f x k
o Have the students refer to Bellringer problems 1, 4, and 5 to develop the rule that +k
inside the parentheses shifts the function left and – k shifts the function right,
stressing that it is the opposite of what seems logical when shown in the parentheses.
o Determine if this shift affects the domain or range. (Solution: domain)
o For practice, have students graph the following:
(1) f(x) = x3
(2) f(x) = (x + 4)3
(3) f(x) = (x – 6)3
Solutions:
(1) (2) (3)
Abstract Translations
Divide students into groups of two or three and distribute the Translations BLM.
Have students work the first section shifting an abstract graph vertically and
horizontally. Stop after this section to check their answers.
Have students complete the Translations BLM graphing by hand, applying the shifts
to known parent functions. After they have finished, they should check their answers
with a graphing calculator.
Check for understanding by having students individually graph the following:
(1) f(x) = 4x
(2) g(x) = 4x 2
(3) h(x) = 4x 2
Solutions:
(1) (2) (3)
Finish the class with Function Calisthenics again, but this time call out the basic
functions with vertical and horizontal shifts.
(e.g. x2, x2 + 2, x3, x3 – 4, x , x 4 , x 5 )
Algebra IIUnit 8 Advanced Functions 219
Algebra II – Unit 8
Activity 3: How Coefficients Change Families of Functions (GLEs: Grade 9: 35, 36;
Grade 11/12: 4, 6, 7, 8, 16, 19, 25, 27, 28)
Materials List: paper, pencil, graphing calculator, Reflections Discovery Worksheet BLM,
Dilations Discovery Worksheet BLM, Abstract Reflections & Dilations BLM
In this activity, the students will determine the effects of a negative coefficient, coefficients
with different magnitudes on the graphs, and the domains and ranges of functions.
Math Log Bellringer:
Graph the following on your calculator. Discuss what effect the negative sign has.
(1) f x x
(2) f x x
(3) f x x
Solutions:
(1)
(2) reflects graph across the xaxis, affects range
(3) reflects graph across the yaxis, affects domain
Activity:
Discovering Reflections:
Distribute the Reflections Discovery Worksheet BLM. This BLM is designed to be
teacherguided discovery with the individual students working small sections of the
worksheet at a time, stopping after each section to discuss the concept.
Negating the function: –f(x).
o Have the students sketch their Bellringer problems on the Reflections & Dilations
Discovery Worksheet BLM and refer to Bellringer problems #1 and #2 to develop
the rule, "that a negative sign in front of the function reflects the graph across the
x-axis" (i.e., all positive y-values become negative and all negative y-values
become positive). Have students write the rule in their notebooks.
o Determine if this affects the domain or range. (Solution: range)
o Allow students time to complete the practice on problems #1 6. Check their
answers.
Negating the x within the function: f(–x)
Algebra IIUnit 8 Advanced Functions 220
Algebra II – Unit 8
o Have the student refer to Bellringer problems #1 and #3 to develop the rule, "that
the negative sign in front of the x reflects the graph across the y-axis" (i.e., all
positive x-values become negative and all negative x-values become positive).
Have students write the rule in their notebooks.
o Determine if this affects the domain or range. (Solution: domain)
o Allow students time to complete the practice on problems #713. Check their
answers.
Some changes do not seem to make a difference. Have the students examine the
following situations and answer the questions in their notebooks:
(1) Draw the graphs of f(x) = –x2 and h(x) = (–x)2.
(2) Discuss the difference in the graphs. Explain what effect the
parentheses have.
(3) Draw the graphs of f(x) = –x3 and h(x) = (–x)3. Find f(2) and h(2).
(4) Discuss order of operations. Discuss the difference in the graphs.
Explain what effect the parentheses have.
(5) Why do the parentheses affect one set of graphs and not the other?
Discovering Dilations Discovery Worksheet BLM:
Distribute the Dilations Discovery Worksheet BLM. This BLM is designed to be
teacher-guided discovery with the individual students working small sections of the
worksheet at a time, stopping after each section to discuss the concept.
Continue the guided discovery using the problems on the Dilations Discovery
Worksheet BLM, problems #1418.
Coefficients in front of the function: k f(x) (k > 0)
o Have the students refer to problems #14, 15, and 16 to develop the rule for the
graph of k f(x): If k > 1, the graph is stretched vertically compared to the graph of
f(x); and if 0 < k < 1, the graph is compressed vertically compared to the graph of
f(x). Write the rule in #19.
o Ask students to determine if this affects the domain or range. (Solution: range)
Coefficients in front of the x: f(kx) (k > 0)
o Have the students refer to problems #14, 17, and 18 to develop the rule for the
graph of f(kx): If k > 1, the graph is compressed horizontally compared to the
graph of f(x); and if 0 < k < 1, the graph is stretched horizontally compared to the
graph of f(x). (When the change is inside the parentheses, the graph does the
opposite of what seems logical.) Write the rule in #20.
o Determine if this change affects the domain or range. (Solution: domain) Write
the rule in #21.
o Allow students to complete the practice on this section in problems #2228.
Abstract Reflections and Dilations:
Distribute the Abstract Reflections & Dilations BLM. Divide students into groups of
two or three to complete this BLM, problems #2934.
When the students have completed this BLM, have them swap papers with another
group. If they do not agree, have them justify their transformations.
Algebra IIUnit 8 Advanced Functions 221
Algebra II – Unit 8
More Function Calisthenics: Have the students stand up, call out a function, and have
them show the shape of the graph with their arms. This time have one row make the
parent graph and the other rows make graphs with positive and negative coefficients
(i.e., x2, –x2, 2x2, x3, –x3, x , – x , x ).
Activity 4: How Absolute Value Changes Families of Functions (GLEs: Grade 9: 35,
36; Grade 11/12: 4, 6, 7, 8, 16, 19, 25, 27, 28)
Materials List: paper, pencil, graphing calculator, Abstract Reflections and Dilations BLM in
Activity 3
In this activity, students will discover how a graph changes when an absolute value sign is
placed around the entire function or placed just around the variable.
Math Log Bellringer:
(1) Graph f(x) = x2 – 4 by hand and locate the zeroes.
(2) Use the graph to solve x2 – 4 > 0.
(3) Use the graph to solve x2 – 4 < 0.
(4) Discuss how the graph can help you solve #2 and #3.
Solutions:
(1) zeroes: {2, 2}
(2) x < –2 or x > 2,
(3) –2 < x < 2
(4) Since y = f(x) = x2 4, the xvalues that make the yvalues positive solve
#2. The xvalues that make the yvalues negative solve #3. Use the
zeroes as the endpoints of the intervals.
Activity:
x if x 0
Review the definition of absolute value: x and review the rules for
x if x 0
writing an absolute value as a piecewise function: What is inside the absolute value is
both positive and negative. What is inside the absolute value affects the domain.
Absolute Value of a Function: |f(x)|
o Have students use the definition of absolute value to write |f(x)| as a piecewise
f ( x ) if f ( x ) 0
function f ( x)
f ( x ) if f ( x ) 0
o Have the students write |x2 – 4| as a piecewise function and use the Bellringer to
simplify the domains.
x2 4
if x 2 4 0 x 2 4
if x 2 or x 2
Solution: x 4
2
= )
x 4 if x 4 0 x 4 if 2 x 2
2 2 2
Algebra IIUnit 8 Advanced Functions 222
Algebra II – Unit 8
o Have the students graph the piecewise function by hand reviewing what –f(x) does to
a graph and find the domain and range.
Solution: D: all reals, R: y > 0
o Have the students check the graph f(x) = |x2 – 4| on the graphing
calculator.
o Have students develop the rule for graphing the absolute value of
a function: Make all y-values positive. More specifically, keep the portions of the
graphs in Quadrants I and II and reflect the graphs in Quadrant III and IV into
Quadrants I and II.
o Ask students to determine if this affects the domain or range. (Solution: range)
o Have students practice on the following graphing by hand first, then checking on the
calculator:
(1) Graph g(x) = |x3| and find the domain and range.
(2) Graph f(x) = |log x| and find the domain and range.
(3) If the function h(x) has a domain [–4, 6] and range [–3, 10], find the domain and
range of |h(x)|.
(4) If the function j(x) has a domain [–4, 6] and range [–13, 10], find the domain and
range of |j(x)|.
Solutions:
(1) D: all reals, R: y >0
(2) D: x > 0, R: y > 0
(3) D: same, R: [0, 10]
(4) D: same, R: [0, 13]
Absolute Value only on the x: f(|x|)
o Have the students write g(x) = (|x| – 4)2 – 9 as a piecewise function.
x 4 2 9 if x 0
Solution: g(x) = x 4 9
2
x 4 9 if x 0
2
o Have the students graph the piecewise function for g(x) by hand reviewing what
the negative only on the x does to a graph.
Solution:
o Have students find the domain and range of g(x). Discuss the fact that negative
xvalues are allowed and negative y-values may result. The range is determined
by the lowest y-value in Quadrant I and IV, in this case the vertex.
Algebra IIUnit 8 Advanced Functions 223
Algebra II – Unit 8
Solution: D: all reals, R: y > 9
o Have the students graph y1 = (x – 4)2 – 9 and y2 = (|x| –4)2 – 9 on the graphing
calculator. Turn off y1 and discuss what part of the graph disappeared and why.
o Have students develop the rule for graphing a function with only the x in the
absolute value. Graph the function without the absolute value first. Keep the
portions of the graph in Quadrants I and IV, discard the portion of the graph in
Quadrants II and III, and reflect Quadrants I and IV into II and III. Basically, the
y-output of a positive x-input is the same y-output of a negative x-input.
o Have students practice on the following:
(1) Graph y = (|x| + 2)2 and find the domain and range.
(2) Graph y = (|x| – 1)(|x| 5)(|x| – 3) and find the domain and range.
(3) Graph y x 3 and find the domain and range.
(4) If the function h(x) has a domain [–4, 6] and range [–3, 10], find the domain and
range of h(|x|).
(5) If the function j(x) has a domain [–8, 6] and range [–3, 10], find the domain and
range of j(|x|).
Solutions:
(1) D: (∞, ∞), R: y > 4
(2) D: (∞, ∞), R: y > 15, this value cannot be
determined without a calculator until Calculus
because another minimum value may be lower than
the y-intercept
(3) D: x < –3 or x > 3, R: y > 0
(4) D: [–6, 6], R: cannot be determined
(5) D: [–10, 10], R: cannot be determined
o Use the practice problems above to determine if f(|x|) affects the domain or range.
Solution: f(|x|) affects both the domain and possibly the range. To find the new
domain, keep the domain for positive x-values and change the signs to include
the reflected negative x-values. The range cannot be determined unless the
maximum and minimum values of y in Quadrants I and IV can be determined.
Abstract Absolute Value Reflections: Have students draw in their notebook the same
abstract graph from the Abstract Reflections & Dilations BLM from Activity 3, then
sketch |g(x)| and g(|x|) putting solutions on the board.
Solutions:
(4, 8) (4, 8) (4, 8) (4, 8)
4 (–5, 3) 4 4
(1, 2) (1, 2) (1, 2) (1, 2)
(–5, –3) g(x) |g(x)| g(|x|)
Algebra IIUnit 8 Advanced Functions 224
Algebra II – Unit 8
Activity 5: Functions - Tying It All Together (GLEs: Grade 9: 35, 36; Grade 11/12: 4,
6, 7, 16, 25, 27, 28)
Materials List: paper, pencil, graphing calculators, Tying It All Together BLM, ½ sheet
poster paper for each group, index cards with one parent graph equation on each card
In this activity, students pull together all the rules of translations, shifts, and dilations.
Math Log Bellringer:
Graph the following by hand labeling h(1). Discuss the change in the graph and
whether the domain or range is affected.
(1) h(x) = 3x (4) h(x) = 3x + 1 (7) h(x) = 3|x|
(2) h(x) = 3x (5) h(x) = 3x + 1 (8) h(x) = 32x
x
(3) h(x) = (3x) (6) h(x) = |3 | (9) h(x) = 2(3x)
Solutions:
(1) (2) reflect across y-axis (3) reflects across x-axis
no change in D or R range changes
(4) shift left 1 (5) shifts up 1, (6) no change in graph,
no change D or R range changes no change in D or R
(7) discard graph in Q II & III (8) horizontal compression, (9) vertical stretch,
and reflect Q I into Q II, yintercept stayed the same, yintercept changed,
no change in D or R. no change in D or R no change in D or R
Tying It All Together:
Divide students into groups of two or three and distribute the Tying It All Together
BLM.
Have students complete I. GRAPHING and review answers.
Have students complete II. DOMAINS AND RANGES and review answers.
Algebra IIUnit 8 Advanced Functions 225
Algebra II – Unit 8
When students have completed the worksheet, enact the professor knowitall
strategy (view literacy strategy descriptions). Explain that each group will draw one
graph and the other groups will come to the front of the class to be a team of Math
Wizards (or any other appropriate name). This team is to come up with the equation
of the graphs.
Distribute ½ sheet of poster paper to each group. Pass out an index card with one
parent graph equation: f(x) = x, f(x) = x2, f ( x ) x , f(x) = x3, f(x) = |x|, f ( x ) 1 ,
x
f(x) = 2 , f x x , f(x) = log x, f ( x) x , to secretly assign each group a
x 3
parent graph. Tell them to draw an x and yaxis and their parent graphs with two
(or three if it is an advanced class) dilations, translations or reflections on one side
of the poster, and write the equation of the graph on the back. They should draw
very accurately and label the x and yintercepts and three other ordered pairs,
and then they should use their graphing calculators to make sure the equation
matches the graph. Circulate to make sure graphs and equations are accurate.
Tape all the posters to the board and give the groups several minutes to confer and
to decide which poster matches which parent graph. Students should not use their
graphing calculators at this time.
Call one group to the front and give it an index card to assign a parent graph. The
group should first model the parent graph using "Function Calisthenics", then find
the poster with that graph, explain why it chose that graph, and discuss what
translations, dilations or reflections have been applied. The group should write the
equation under the graph. Do not evaluate the correctness of the equation until all
groups are finished. Three other groups are allowed to ask the Math Wizards
leading questions about the choice of equations, such as, "Why did you use a
negative? Why do you think your graph belongs to that parent graph?"
When all groups are finished, ask if there are any changes the groups want to
make in their equations after hearing the other discussions. Calculators should not
be used to check. Turn over the graphs to verify correctness.
Students and the teacher should hold the Math Wizards accountable for their
answers to the questions by assigning points.
Activity 6: More Piecewise Functions (GLEs: Grade 9: 35, 36; Grade 11/12: 4, 6, 7, 8,
10, 16, 19, 24, 25, 27, 28, 29)
Materials List: paper, pencil, Picture the Pieces BLM
In this activity, the students will use piecewise functions to review the translations of all
basic functions.
Math Log Bellringer:
2 x 5 if x 0
(1) Graph f x without a calculator
x if x 0
(2) Find f(3) and f(4)
Algebra IIUnit 8 Advanced Functions 226
Algebra II – Unit 8
(3) Find the domain and range
Solutions:
(1)
(2) f(3) = 1, f(4) = 4
(3) D: all reals, R: y < 5
Activity:
Use the bellringer to review the definition of a piecewise function begun in Unit 1 a
g ( x) if x Domain 1
function made of two or more functions and written as f ( x)
h( x) if x Domain 2
where Domain 1 Domain 2 .
Picture the Pieces:
o Divide students into groups of two or three and distribute the Picture the Pieces BLM.
o Have the students work the section Graphing Piecewise Functions and circulate to
check for accuracy.
o Have the students work the section Analyzing Graphs of Piecewise Functions, then
have one student write the equation of g(x) on the board and the other students
analyze it for accuracy.
o Discuss the application problem as a group, discussing what the students should look
for when trying to graph: how many functions are involved, what types of functions
are involved, what translations are involved, and what are the restricted domains for
each piece of the function?
o When students have finished, assign the application problem in the ActivitySpecific
Assessments to be completed individually.
Activity 7: Symmetry of Graphs (GLEs: 4, 6, 7, 8, 16, 25, 27, 28)
Materials List: paper, pencil, graphing calculator, Even & Odd Functions Discovery
Worksheet BLM
In this activity, students will discover how to determine if a function is symmetric to the
y-axis, the origin, or other axes of symmetry.
Math Log Bellringer:
Graph without a calculator.
(1) f(x): y = (x)2 , f(–x): y = (–x)2 f(x): y = –x2
(2) f(x): y = log x, f(–x): y = log (–x) –f(x): y = –log x
(3) Discuss the translations made by f(x) and f(x).
Solutions:
Algebra IIUnit 8 Advanced Functions 227
Algebra II – Unit 8
(1) , ,
(2) , ,
(3) f(x) reflects the parent graph across the y-axis and f(x) reflects the
parent graph across the x-axis
Activity:
Use the Bellringer to review the reflections f(–x) and –f(x) covered in Activity 3.
Even and Odd Functions:
o Distribute the Even & Odd Functions Discovery Worksheet BLM.
o This is a guided discovery worksheet. Give the students an opportunity to graph in
their notebooks the functions in the Reflections Revisited section. Circulate to make
sure they have mastered the concept.
o Even & Odd Functions Graphically: Ask the students which of the parent functions in
the Bellringer and the worksheet have the property that the graphs of f(–x) and f(x)
match. (Solutions: f(x) = x2 and f(x) = |x|.) Define these as even functions and note
that this does not necessarily mean that every variable has an even power. Ask what
kind of symmetry they have in common. (Solution: symmetric to the y-axis)
o Ask the students which of the parent functions in the Bellringer and the worksheet
have the property that the graphs of f(–x) and –f(x) match. (Solutions: f(x) = x3,
1
f x 3 x , f x , f(x) = x). Define these as odd functions. Ask what kind of
x
symmetry they have in common. (Solution: symmetric to the origin) Discuss what
symmetry to the origin means (i.e. same distance along a line through the origin.)
o Have students graph y = x3 + 1 and note that just because it has an odd power does not
mean it is an odd function. Ask the students which of the parent functions do not have
any symmetry and are said to be neither even nor odd.
Solution: f(x) = log x, f(x) = 2x, f x x
o Even & Odd Functions Numerically: Have students work this section and ask for
answers and justifications. Discuss whether the seven sets of ordered pairs are
enough to prove that a function is even or odd. For example in h(x), h(–3) = h(3), but
the rest of the sets do not follow this concept.
o Even & Odd Functions Analytically: In order to prove whether a function is even or
odd, the student must substitute (–x) for every x and determine if f(–x) = f(x), if
f(–x) = –f(x), or if neither substitution works. Demonstrate the process on the first
problem and allow students to complete the worksheet circulating to make sure the
students are simplifying correctly after substituting x.
Algebra IIUnit 8 Advanced Functions 228
Algebra II – Unit 8
Activity 8: History, Data Analysis, and Future Predictions Using Statistics (GLEs: 4, 6,
8, 10, 19, 20, 22, 24, 28, 29)
Materials List: paper, pencil, graphing calculator, Modeling to Predict the Future BLM,
Modeling to Predict the Future Rubric BLM
This activity culminates the study of the ten families of functions. Students will collect
current real world data and decide which function best matches the data, then use that model
to extrapolate to predict the future.
Math Log Bellringer:
Enter the following data into your calculator. Enter 98 for 1998 and 100 for 2000,
etc., making year the independent variable and # of stock in millions, (i.e., use 4.551
million for 4,550,678), the dependent variable. Sketch a scatter plot and find the
linear regression and correlation coefficient. Discuss whether a linear model is good
for this data. Use the model to find the number of stocks that will be traded in 2012.
(i.e., Find f (112).)
year 1998 1999 2000 2001 2002 2003
# of GoMath 4, 550,678 4, 619,700 4,805,230 5, 250, 100 5,923,010 7, 000, 300
stocks traded
Solution:
The linear model does not follow the data very well and the correlation coefficient is
only 0.932. It should be closer to 1. In 2012, 10,812,124 stocks will be traded.
Activity:
Use the Bellringer to review the processes of entering data, plotting the data, turning on
Diagnostics to see the correlation coefficient, and finding a regression equation. Review
the meaning of the correlation coefficient.
Discuss why use 98 instead of 1998 and 4.551 instead of 4, 550,678 the calculator will
round off, too, using large numbers. Students could also use 8 for 1998 and 10 for 2000.
Have each row of students find a different regression equation to determine which one
best models the data, graph it with ZOOM , Zoom Stat and on a domain of 80 to 120 (i.e.
1980 2020), and use their models to predict how many GoMath stocks will be traded in
2012.
Algebra IIUnit 8 Advanced Functions 229
Algebra II – Unit 8
Solutions:
In 2012, 26,960,314 stocks will be traded.
In 2012, 45,164,048 stocks will be traded.
R2 = .99987079. In 2012, 56,229,191 stocks will be traded.
In 2012, 10,513,331 stocks will be traded.
In 2012, 14,122,248 stocks will be traded.
In 2012, 13,387,785 stocks will be traded.
Discuss which model is the best, based on the correlation coefficient. (Solution: quartic)
Discuss real-world consequences and what model would be the best based on end
behavior. Discuss extrapolation and its reasonableness.
Have students add the following scenario to their data: In 1997, only 1 million shares of
stock were traded the first year they went public.
(1) Have students find quartic regression and the number of stocks traded in 2012 and
discuss the correlation.
Algebra IIUnit 8 Advanced Functions 230
Algebra II – Unit 8
Solution:
R2 = .9918924557.. The correlation
coefficient is good, but the leading coefficient
is negative indicating that end-behavior is
down and hopefully the stock will not go
down in the future. In 2012, 597,220,566 stocks will be traded
(2) Have students find the cubic regression and the number of stocks traded in 2012 and
discuss the correlation.
Solution:
The R2 is not as good but the trend seems to
match better because of the endbehavior. In
2012, 181,754,238 stocks will be traded.
(3) Discuss how outliers may throw off a model and should possibly be deleted to get a
more realistic trend.
Modeling to Predict the Future Data Analysis Project:
This is an outofclass endofunit activity. The students may work alone or in
pairs. They will collect data for the past twenty years concerning statistics for their
city, parish, state, or US, trace the history of the statistics discussing reasons for
outliers, evaluate the economic impact, and find a regression equation that best
models the data. They should use either the regression equation on the calculator or
the trendline on an Excel® spreadsheet. They will create a PowerPoint® presentation
of the data including pictures, history, economic impact, spreadsheet or the calculator
graph of regression line and equation, and future predictions.
Distribute the Modeling to Predict the Future BLM with the directions for the data
analysis project and the Modeling to Predict the Future Rubric BLM. Then discuss
the objectives of the project and the list of possible data topics.
Timeline:
1. Have students bring data to class along with a problem statement (why they are
examining this data) three days after assigned, so it can be approved and they can
begin working on it under teacher direction.
2. The students will utilize one to two weeks of individual time in research and
project compilation, and two to three days of class time for analysis and computer
use if necessary.
Discuss each of the headings on the blackline master:
1. Research: Ask each group to choose a different topic concerning statistical data
for their city, parish, state, or for the US. List the topics on the board and have
each group select one. The independent variable should be years, and there must
be at least twenty years of data with the youngest data no more than five years
ago. The groups should collect the data, analyze the data, research the history of
the data, and take relevant pictures with a digital camera.
2. Calculator/Computer Data Analysis: Students should enter the data into their
graphing calculators, link their graphing calculators to the computer, and
download the data into a spreadsheet, or they should enter their data directly into
the spreadsheet. They should create a scatterplot and regression equation or
trendline of the data points using the correlation coefficient (called Rsquared
Algebra IIUnit 8 Advanced Functions 231
Algebra II – Unit 8
value in a spreadsheet) to determine if the function they chose is reliable. They
should be able to explain why they chose this function, based on the correlation
coefficient as well as function characteristics. (e.g., end-behavior, increasing
decreasing, zeroes).
3. Extrapolation: Using critical thinking skills concerning the facts, have the
students make predictions for the next five years and explain the limitations of the
predictions.
4. Presentation: Have students create a PowerPoint® presentation including the
graph, digital pictures, economic analysis, historical synopsis, and future
predictions.
5. Project Analysis: Ask each student to type a journal entry indicating what he/she
learned mathematically, historically, and technologically, and express his/her
opinion of how to improve the project. If students are working in pairs, each
student in the pair must have his/her own journal.
Final Product: Each group must submit:
1. A disk containing the PowerPoint® presentation with the slides listed in BLM.
2. A print out of the slides in the presentation.
3. Release forms signed by all people in the photographs.
4. Project Analysis
5. Rubric
Have students present the information to the class. Either require the students to also
present in another one of their classes or award bonus points for presenting in another
class. As the students present, use the opportunity to review all the characteristics of
the functions studied during the year.
Algebra IIUnit 8 Advanced Functions 232
Algebra II – Unit 8
Sample Assessments
General Assessments
Use Math Log Bellringers as ongoing informal assessments.
Collect the Little Black Books of Algebra II Properties and grade for completeness at the
end of the unit.
Monitor student progress using small quizzes to check for understanding during the unit
on such topics as the following:
(1) speed graphing basic graphs
(2) vertical and horizontal shifts
(3) coefficient changes to graphs
(4) absolute value changes to graphs
(5) even and odd functions
Administer one comprehensive assessment about translations, reflections, shifts of
functions, and graphing piecewise functions.
Activity-Specific Assessments
Teacher Note: Critical Thinking Writings are used as activity-specific assessments in many of the
activities in every unit. Post the following grading rubric on the wall for students to refer to
throughout the year. Activity 1:
Evaluate the Flash That Function flash cards for accuracy and completeness.
Activity 2: Critical Thinking Writing
Graph the following and discuss the parent function and whether there is a horizontal shift
or vertical shift.
(1) k(x) = x + 5
(2) g x x 2
(3) h x x 2
Solutions:
Algebra II-Unit 8-Further Investigation of Functions 232
Algebra II – Unit 8
(1) The parent function is the line f(x) = x, and the graph of k(x)
is the same whether you shifted it vertically up 5 or
horizontally to the left 5.
(2) and (3)The parent function is greatest integer
f x x , and both graphs are the same even though g(x)
is shifted up 2 and h(x) is shifted to the right 2.
Activity 6: Critical Thinking Writing
Mary is diabetic and takes long-acting insulin shots. Her blood sugar level starts at 100
units at 6:00 a.m. She takes her insulin shot, and the blood sugar increase is modeled by
the exponential function f(t) = Io(1.5t) where Io is the initial amount in the blood stream
and rises for two hours. The insulin reaches its peak effect on the blood sugar level and
remains constant for five hours. Then it begins to decline for five hours at a constant rate
and remains at Io until the next injection the next morning. Let the function i(t) represent
the blood sugar level at time t measured in hours from the time of injection. Write a
piecewise function to represent Mary's blood sugar level. Graph i(t) and find the blood
sugar level at (a) 7:00 a.m. (b) 10:00 a.m. (c) 5:00 p.m. (d) midnight. (e) Discuss the times
in which the function is increasing, decreasing and constant.
Solution:
100 1.5t if 0 t 2
225 if 2 t 7
i (t )
25(t 7) 225 if 7 t 12
100
if 12 t 24
(a) 150 units, (b) 225 units, (c) 125 units, (d) 100 units,
(e) The function is increasing from6:00 a.m. to 8:00 a.m., constant from 8:00 a.m.
to 1:00 p.m., decreasing from 1:00 p.m. to 6:00 p.m. and constant from 6:00
p.m. to 6:00 a.m.
Activity 7: Critical Thinking Writing
Discuss other symmetry you have learned in previous units, such as the axis of symmetry
in a parabola or an absolute value function and the symmetry of inverse functions. Give
some example equations and graphs and find the lines of symmetry.
Activity 8: Modeling to Predict the Future Data Research Project
Use the Modeling to Predict the Future Rubric BLM to evaluate the research project
discussed in Activity 8.
Algebra II-Unit 8-Further Investigation of Functions 233
Algebra II – Unit 8
Grading Rubric for Critical Thinking Writing Activities:-world problem using interpolation and extrapolation,
with correct answer
10 pts. - PowerPoint® presentation - neatness, completeness, readability,
release forms (if applicable)
10 pts. - journal
Algebra II-Unit 8-Further Investigation of Functions 234
Algebra II – Unit 8
Name/School_________________________________ Unit No.:______________
Grade ________________________________ Unit Name:________________
Feedback Form
This form should be filled out as the unit is being taught and turned in to your teacher coach upon
completion 8-Further Investigation of Functions 235 |
This course will focus on using the computer to create and manipulate digitally generated waveforms. Students will learn how to use the "C" programming languageSecondEach student will begin working where their current skill level is. Appropriate skill levels for the course include algebra, calculus, and any in between. We will directly confront the fears and phobias that many of us feel and help to move beyond those fears. All students will support each other and also receive tutoring help from other students in the class. Because different texts will be used for different students, please contact the instructor before purchasing a text.This course will count towards requirements for becoming elementary, middle, or high school teachers. Students registering for 4 credits will attend only Wednesday through Friday.
This program is built around intensive study of several fundamental areas of pure mathematics. Covered topics are likely to include abstract algebra, real analysis, set theory, combinatorics and probability.The work in this advanced-level mathematics program is quite likely to differ from students' previous work in mathematics, including calculus, in a number of ways. We will emphasize the careful understanding of the definitions of mathematical terms and the statements and proofs of the theorems that capture the main conceptual landmarks in the areas we study. Hence, the largest portion of our work will involve the reading and writing of rigorous proofs in axiomatic systems. These skills are valuable not only for continued study of mathematics but also in many areas of thought in which arguments are set forth according to strict criteria for logical deduction. Students will gain experience in articulating their evidence for claims and in expressing their ideas with precise and transparent reasoning.In addition to work in core areas of advanced mathematics, we will devote seminar time to looking at our studies in a broader historical, philosophical, and cultural context, working toward answers to critical questions such as: Are mathematical systems discovered or created? Do mathematical objects actually exist? How did the current mode of mathematical thinking come to be developed? What is current mathematical practice? What are the connections between mathematics and culture? What are the connections between mathematics and art? What are the connections between mathematics and literature?This program is designed for students who intend to pursue graduate studies or teach in mathematics and the sciences, as well as for those who want to know more about mathematical thinking.
This class focuses on the mathematical content knowledge teachers and parents need in order to teach elementary and middle school mathematics. Students will develop their content knowledge in number theory (base-ten and place value, whole number operations, fractions, fraction operations, factors and multiples, proportional reasoning) and Algebra (algebra as generalized arithmetic, algebraic manipulation, linear and non-linear functions). Through this mathematical content and an examination of the Common Core State Standards, students will develop their own mathematical thinking, reasoning, and justification skills. This program is appropriate for students who intend to enroll in The Evergreen State College Master in Teaching Program or other teacher education programs and current teachers and parents who wish to further develop their understanding of mathematics.
Modern science has been remarkably successful in providing understanding of how natural systems behave. Such disparate phenomena as the workings of cell-phones, the ways in which we detect supermassive black holes in the galactic core, the use of magnetic resonance imaging in the diagnosis of disease, the effects of global carbon dioxide levels on shellfish growth, and the design of batteries for electric cars are all linked at a deeply fundamental level. This program will introduce you to the theory and practice of the science behind these and other phenomena, while providing the solid academic background in mathematics, chemistry, and physics necessary for advanced study in those fields as well as for engineering, medicine, and biology.We will integrate material from first-year university physics, chemistry, and calculus with relevant areas of history and scientific literature. The program will have a strong laboratory focus using computer-based experimental control and analysis to explore the nature of chemical and physical systems; this work will take place in a highly collaborative environment. Seminars will provide the opportunity to explore the connections between theory and practice and will provide opportunities to enhance technical writing and communication skills. The program is intended for students with solid high-school level backgrounds in science and mathematics, but the key to succeeding will be a commitment to work, learn, and collaboratePhysics is concerned with the basic principles of the universe. It is the foundation on which engineering, technology, and other sciences are based. The science of physics has developed out of the efforts of men and women to explain our physical environment. These efforts have been so successful that the laws of physics now encompass a remarkable variety of phenomena. One of the exciting features of physics is its capacity for predicting how nature will behave in one situation on the basis of experimental data obtained in another situation. In this program we will begin the process of understanding the underlying order of the physical world by modeling physical systems using both the analytical tools of calculus and the numerical tools provided by digital computers. We will also have significant laboratory experience to make predictions and explore some of these models. In this thematically-integrated program, students will cover calculus and algebra-based physics through small-group discussions, interactive lectures, and laboratory investigations. In physics, we will learn about motion, energy, models, and the process for constructing them. Through our study of calculus, we will learn how to analyze these models mathematically. We will study some of Galileo's significant contributions to classical mechanics, Kepler's astronomical observations, Newton's work on calculus and laws of motion, Euler's applications of calculus to the study of real-life problems in physics (magnetism, optics and acoustics), Maxwell's development of the unified theory of magnetism, Einstein's relativity, and many others. This program will cover many of the traditional topics of both first-quarter calculus and first-quarter physics. Covering these topics together allows for the many connections between them to be reinforced while helping make clear the value of each.
Fires and floods in Colorado, Australia, and worldwide ... Hurricanes and typhoons moving further north and getting stronger ... Mega-tornados, with extended tornado seasons and ranges ... What about tsunamis, earthquakes, and solar magnetic storms? What is extreme weather? What causes it? Is it really getting worse? Is extreme weather related to global warming?
We will learn algebra-based thermodynamics, mechanics, and Earth science to address questions such as these. We will seminar on recent writings. Students will contribute case studies from news and science articles, and will actively engage in a writing community with peers. Much of the program will be online, and we will meet for lectures and workshops. This course provides entrance requirements for degree programs such as MIT.
Prerequisites: mastery of high school algebra, good reading and writing skills, willingness to work in teams, ability to use computers and Internet for independent work online. No physics prerequisite.
The class will begin with an intense review of precalculus material most relevant to calculus. Students are expected to have had some experience with graphs and functions and trigonometry. Calculus topics will include limits, continuity, the limit definition of the derivative, differentiation rules, maxima and minima, optimization problems, Mean Value Theorem, Newton's method, and anti-differentiation. Emphasis throughout will be on modeling problems in the physical world. Students will work homework online, write exams, work in teams, and give verbal presentations of their results to the class.
This two-quarter sequence of courses will prepare students for calculus and more advanced mathematics. It is a good course for students who have recently had a college-level math class or at least three years of high school math. Students should enter the class with a good knowledge of supporting algebra. Winter quarter will include an in-depth study of linear, quadratic, exponential, and logarithmic functions. Spring will include an in-depth study of trigonometric and rational functions in addition to parametric equations, polar coordinates, and operations on functions. Collaborative learning, data analysis and approaching problems from multiple perspectives (algebraically, numerically, graphically, and verbally) will be emphasized.
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This course will focus on research design issues related to the social sciences including types of studies, sampling, data collection techniques, research ethics, and report writing. Additionally, the course will cover data analysis and presentation strategies including measures of central tendency and parametric testing (e.g., t-test, ANOVA, Pearson Correlation).
This course is intended to complement the weekend program
, but it can be taken as a stand-alone courseHow strange is the weather this year, anyway? Can we explain the broad die-off of conifers across the Rocky Mountains? How about spending tax-payers' money to provide a hot breakfast to school kids in the morning? Is it "worth it"? The answers to these questions lie in our ability to understand data. Statistics is the tool we use to understand that data. The goal of this class will be to involve the student in exploring how Statistics is used to explain natural phenomena, promote public policy, and tell us things about the world that we can never know without it.
This class covers key statistical concepts at the conceptual and computational level with an emphasis on how statistics is used in research in natural and social sciences. Important elements of research design are covered in the class. Descriptive and inferential statistical tests are covered including scales of data, measures of central tendency, normal distributions, probability, chi square, correlation and linear regression, tests of hypothesis, and Type I and Type II errors. Students will develop a clear understanding of introductory statistics and the ability to correctly interpret findings in journals, newspapers, and books. The class meets the statistics prerequisite for MES and MPA programs at Evergreen and most other graduate schools with a statistics prerequisite.
This course provides a concentrated overview of the statistics and research methodology required for the GRE and prerequisites for graduate schools in psychology, education, and other social sciences.
We emphasize hands-on, intuitive knowledge and approach statistics as a language rather than as math alone; thus this course is gentle on "math phobics." No computer skills are required. You will become an informed and savvy consumer of information, from the classroom to the workplace. We will cover descriptive and inferential statistics, research methodology and ethics.
Hardly a day goes by without dealing with some types of numbers. How do you make sense of those numbers? How can you tell which is right and which is wrong? How can we use statistical tools to inform, to explore and to empower? What are the larger frameworks behind those numbers? How do we use the theory to direct our quantitive reasoning and how do we use quantitative tools to enhance our understanding of the society? This class will put statistics into context. We will cover basic sociological concepts and theories and introduce students to basic statistics. Focus will be placed on real life scenarios and sense-making practices. Besides workshops and lectures, we will conduct social experiments and field work to get our feet wet in social scientific research experienceThe successful completion of large software systems requires strong technical skills, good design and competent management. Unfortunately, unlike hardware, software systems have proven to be notoriously difficult to build on-time, in-budget, and reliable, despite the best efforts of many very smart people over the last 50 years. This is an upper-division program intended to help students gain the technical knowledge required to understand, analyze, modify and build complex software systems.We will concentrate on learning the organization and complexity of large software systems that we do understand, and gaining practical experience in order to achieve a deeper understanding of the art, science, collaboration and multi-disciplinary skills required to develop computing solutions in real-world application domains. The technical topics will be selected from data structures, algorithm analysis, operating systems, networks, information security, object oriented design and analysis, verification techniques, scientific visualization and modeling. The program seminar will focus on various technical topics in the software industry. Students will have an opportunity to engage in a substantial computing project through all the development phases of proposal, requirements, specification, design and implementation.This program is for advanced computer science students who satisfy the prerequisites. We also expect students to have the discipline, intellectual maturity and self motivation to identify their project topics, organize project teams and resources and complete advanced work independently.
Tutoring Math and Science For Social Justice will include an examination of some of the current research on the teaching and learning of math and science in higher education and will focus this knowledge on its implications for and applications to diverse groups of learners and social justice. Students will experience and evaluate a variety of tutoring strategies as a student and as a facilitator. This class is strongly suggested for students who are planning on teaching math and/or science or who would like to tutor in Evergreen's Quantitative and Symbolic Reasoning CenterFaculty offering undergraduate research opportunities are listed below. Contact them directly if you are interested.
(chemistry) works with biophysical applications of spectroscopy to study physiological processes at the organ level, with direct applications to health problems. Students with backgrounds in biology, chemistry, physics, mathematics or computer science can obtain practical experience in applying their backgrounds to biomedical research problems in an interdisciplinary laboratory environment..
(geology, earth science) studies(biotechnology) studies the physiology and biochemistry of prokaryotes of industrial and agricultural importance. Students who commit at least a full year to a research project, enrolling for 4 to 16 credits each quarter, will learn a broad range of microbiology (both aerobic and anaerobic techniques), molecular (DNA analysis and cloning), and biochemical techniques (chemical and pathway analysis, protein isolation). Students will also have opportunities for internships at the USDA and elsewhere, and to present data at national and international conferences.
(chemistry) would like to engage students in two projects. (1) Quantitative determination of metals in the stalactites formed in aging concrete using ICP-MS. Students who are interested in learning about the ICP-MS technique and using it for quantitative analysis will find this project interesting. (2) Science and education. We will work with local teachers to develop lab activities that enhance the science curriculum in local schools. Students who have an interest in teaching science and who have completed general chemistry with laboratory would be ideal for this project.
(computer science, ecology informatics) studies how scientists might better use information technology and visualization in their research, particularly in ecology and environmental studies. She would like to work with students who have a background in computer science or one of the sciences (e.g., ecology, biology, chemistry or physics), and who are motivated to explore how new computing paradigms can be harnessed to improve the individual and collaborative work of scientists. Such technologies include visualizations, plugins, object-oriented systems, new database technologies and "newer" languages that scientists themselves use such as python or R.
(biology) aims to better understand the evolutionary principles that underlie the emergence, spread and containment of infectious disease by studying the coevolution of retroviruses and their primate hosts. Studying how host characteristics and ecological changes influence virus transmission in lemurs will enable us to address the complex spatial and temporal factors that impact emerging diseases. Students with a background in biology and chemistry will gain experience in molecular biology techniques, including tissue culture and the use of viral vectors.
(organic chemistry) is interested in organic synthesis research, including asymmetric synthesis methodology, chemical reaction dynamics and small molecule synthesis. One specific study involves the design and synthesis of enzyme inhibitor molecules to be used as effective laboratory tools with which to study the mechanistic steps of programmed cell death (e.g., in cancer cells). Students with a background in organic chemistry and biology will gain experience with the laboratory techniques of organic synthesis as well as the techniques of spectroscopy.
(biology) is interested in the developmental biology of the
embryo, a model system for analyzing how patterning occurs. Maternally encoded signaling pathways establish the anterior-posterior and dorsal-ventral axes. Individual student projects will use a combination of genetic, molecular biological and biochemical approaches to investigate the spatial regulation of this complex process.
(biochemistry) uses methods from organic and analytical chemistry to study biologically interesting molecules. A major focus of his current work is on fatty acids; in particular, finding spectroscopic and chromatographic methods to identify fatty acids in complex mixtures and to detect changes that occur in fats during processing or storage. This has relevance both for foods and in biodiesel production. The other major area of interest is in plant natural products, such as salicylates. Work is in process screening local plants for the presence of these molecules, which are important plant defense signals. Work is also supported in determining the nutritional value of indigenous plants. Students with a background and interest in organic, analytical or biochemistry could contribute to this work.
(computer science) and
(computer science) are interested in working with advanced computer topics and current problems in the application of computing to the sciences. Their areas of interest include simulations of advanced architectures for distributed computing, advanced programming languages and compilers, programming languages for concurrent and parallel computing and hardware modeling languages.
(biology, veterinary medicine) is interested in animal health and diseases that affect the animal agriculture industry. Currently funded research includes the development of bacteriophage therapy for dairy cattle uterine infections, calf salmonellosis and mastitis. A number of hands-on laboratory projects are available to students interested in pursuing careers in science.
(organic, polymer, materials chemistry) is interested in the interdisciplinary fields of biodegradable plastics and biomedical polymers. Research in the field of biodegradable plastics is becoming increasingly important to replace current petroleum-derived materials and to reduce the environmental impact of plastic wastes. Modification of starch through copolymerization and use of bacterial polyesters show promise in this endeavor. Specific projects within biomedical polymers involve the synthesis of poly (lactic acid) copolymers that have potential for use in tissue engineering. Students with a background in chemistry and biology will gain experience in the synthesis and characterization of these novel polymer materials. Students will present their work at American Chemical Society (ACS) conferences.
(computer science) is interested in working with advanced computer topics and current problems in the application of computing to the sciences. Her areas of interest include simulations of advanced architectures for distributed computing, advanced programming languages and compilers, programming languages for concurrent and parallel computing, and hardware modeling languages.
(inorganic/materials chemistry, physical chemistry) is interested in the synthesis and property characterization of new bismuth-containing materials. These compounds have been characterized as electronic conductors, attractive activators for luminescent materials, second harmonic generators and oxidation catalysts for several organic compounds. Traditional solid-state synthesis methods will be utilized to prepare new complex bismuth oxides. Once synthesized, powder x-ray diffraction patterns will be obtained and material properties such as conductivity, melting point, biocidal tendency, coherent light production and magnetic behavior will be examined when appropriate(computer science, mathematics) has several ongoing projects in computer vision, robotics and security. There are some opportunities for students to develop cybersecurity games for teaching
(physics) studies the Sun and the Earth. What are the mechanisms of global warming? What can we expect in the future? What can we do about it right now? How do solar changes affect Earth over decades (e.g., Solar Max) to millennia? Why does the Sun shine a bit more brightly when it is more magnetically active, even though sunspots are dark? Why does the Sun's magnetic field flip every 11 years? Why is the temperature of the Sun's outer atmosphere millions of degrees higher than that of its surface? Students can do research related to global warming in Zita's academic programs and in contracts, and have investigated the Sun by analyzing data from solar observatories and using theory and computer modeling. Serious students are encouraged to form research contracts and may thereafter be invited to join our research team.
Please go to the
catalog view for specific information about each option
Rigorous quantitative and qualitative research is an important component of academic learning in Scientific Inquiry. This independent learning opportunity allows advanced students to delve into real-world research with faculty who are currently engaged in specific projects. Students typically begin by working in apprenticeship with faculty or laboratory staff and gradually take on more independent projects within the context of the specific research program as they gain experience. Students can develop vital skills in research design, data acquisition and interpretation, written and oral communication, collaboration, and critical thinking that are valuable for students pursuing a graduate degree or entering the job market.
(mathematics) is interested in problems in mathematical biology associated with population and evolutionary dynamics. Students working with him will help create computer simulations using agent-based modeling and cellular automata and analyzing non-linear models for the evolution of cooperative behavior in strategic multiplayer evolutionary games. Students should have a strong mathematics or computer science backgroundcomputer science, mathematics) has several ongoing projects in computer vision, robotics and security. There are some opportunities for students to develop cybersecurity games for teaching |
Algebra and Trigonometry : Graphs and Models -Text Only - 4th edition
Summary: The authors help students "see the math" through their focus on functions; visual emphasis; side-by-side algebraic and graphical solutions; real-data applications; and examples and exercises. By remaining focused on today's students and their needs, the authors lead students to mathematical understanding and, ultimately, success in class |
Precalculus, Fifth Edition, by Lial, Hornsby, Schneider, and Daniels, engages and supports students in the learning process by developing both the conceptual understanding and the analytical skills necessary for success in mathematics. With the Fifth Edition, the authors adapt to the new ways in which students are learning, as well as the ever-changing classroom environment.
Engineers looking for an accessible approach to calculus will appreciate Young-s introduction. The book offers a clear writing style that helps reduce any math anxiety they may have while developing their problem-solving skills. It incorporates Parallel Words and Math boxes that provide detailed annotations which follow a multi-modal approach. Your Turn exercises reinforce concepts by allowing them to see the connection between the exercises and examples. A five-step problem solving method is also used to help engineers gain a stronger understanding of word problems.
As part of the market-leading Graphing Approach series by Larson, Hostetler, and Edwards, Precalculus Functions and Graphs students succeed in mathematics. This edition, intended for precalculus courses that require the use of a graphing calculator, includes a moderate review of algebra to help students entering the course with weak algebra skills.
This text, which grew out of a NSF grant, takes a fresh approach with a focus on the underlying concepts of precalculus, rather than sheer algebraic manipulation. It effectively prepares students for a new generation of calculus courses and allows instructors to become actively involved in the teaching process. The authors make extensive use of real world applications, showing students how mathematics relates to their field of study, as well as including a thorough integration of technology. Additionally, the authors have incorporated a number of learning features designed to ready students for a more positive calculus experience. |
Preparing for the Placement Exams
Math Exam
Workshops
These workshops provide an opportunity to review pre-college mathematics that you may have forgotten since you last took a math course. Plan to attend a workshop in advance of taking or retaking the math placement exam. You will need time to practice the skills you have reviewed in the workshop in order to be better prepared to take the placement exam. The time spent reviewing and studying now will help ensure you start college math at the appropriate level, and with your math skills refreshed and ready for new challenges.
The topics reviewed in each workshop are included below. Students are free to attend either workshop or a combination of the two.
Reservations are required and can be made by contacting Kyle Schwieterman, ACE/Math Lecturer, at kschwiet@iusb.edu or by calling (574) 520-4665. Kyle can answer any questions you have about the workshops.
Workshop Schedule - Spring 2014
Day
Date
Time
Topics
Location
Facilitator
Monday
May 5
5:00p - 7:00p
Part A
Northside 376
Kyle Schwieterman
Wednesday
May 7
5:00p - 7:00p
Part B
Northside 376
Kyle Schwieterman
There is no cost to attend a workshop,
* List of topics covered in the math workshops
Part A: Advanced Arithmetic
Meaning of fractions and decimals
Operations on fractions and decimal numbers
Meaning and use of percents and proportions
Operations and signed numbers
Square roots and cube roots
The Pythagorean theorem
Area and perimeter of rectangles and triangles
Part B: Beginning Algebra
Evaluation of expressions and equations
Solution of linear equations
Meaning of integer exponents
Application of rules of integer exponents
Operations on polynomials
Factoring quadratic polynomials |
: Form and Function
Form is related to function. An airplane wing has the form it does because of its lifting function. The pillars of the Parthenon and the girders of a ...Show synopsisForm is related to function. An airplane wing has the form it does because of its lifting function. The pillars of the Parthenon and the girders of a skyscraper are shaped to the purpose of supporting their massive structures. Similarly, the form of an algebraic expression or equation reflects its function. Algebra: Form and Function Preliminary Edition introduces each function--linear, power, quadratic, exponential, polynomial--and presents a study of the basic form of expressions for that function. Readers are encouraged to examine the basic forms, see how they are constructed, and consider the role of each component. Throughout the text, there are Tools sections placed at the ends of chapters to help readers acquire the skills they need to perform basic algebraic manipulations470521434-5-0-3 Orders ship the same or next business day. Expedited shipping within U.S. will arrive in 3-5 days. Hassle free 14 day return policy. Contact Customer Service for questions. ISBN: 9780470521434.
Description:Fine. Hardcover. Almost new condition. SKU: 9780471707080-2-0-3...Fine. Hardcover. Almost new condition. SKU: 97804717070801707080.
Description:Fair. 085 Item is intact, but may show shelf wear. Pages may...Fair. 085 ***ACCEPTABLE***Contains heavy Highlights, Water damages,...Fair. ***ACCEPTABLE***Contains heavy Highlights, Water damages, Markings throughout the book but legible. Heavy wears on |
AP Calculus
Ap Calculus is an advanced math class designed for students seeking to further their knowledge in mathematics. The course spans over three terms and covers Calculus I and parts of calculus II.
AP Calculus Syllabus
The AP Calculus AB course is designed to provide students with an AP experience equivalent to that of a college course in single variable calculus. This course will develop a students understanding of the concepts of calculus and provide experience with its methods and applications. The course includes limits, differentiation and integration with problem solving and applications. Problems will be expressed graphically, numerically, analytically, and verbally. This three term course is intended for students who have a thorough knowledge of college preparatory mathematics including algebra, geometry, and pre-calculus.
Instructional Procedures & Support
Students are expected to bring all supplies to class every day including the textbook, a notebook, pencil and graphing calculator. Written assignments will be given daily and should be completed before the next class period. Homework will be checked for completeness at the start of each day. Late work will not be accepted unless it is due to an excused absence. Quizzes will be given daily following a short discussion of the previous day's assignment. Tests will be given approximately once per week. Students will be allowed to retake one test per term with the condition that all assignments leading up to that test have been completed. Test retakes must be completed before or after school prior to the next test (approximately one week). |
Physics is naturally expressed in mathematical language. Students new to the subject must simultaneously learn an idiomatic mathematical language and the content that is expressed in that language. It is as if they were asked to read Les Misérables while struggling with French grammar. This book offers an innovative way to learn the differential geometry needed as a foundation for a deep understanding of general relativity or quantum field theory as taught at the college level.The approach taken by the authors (and used in their classes at MIT for many years) differs from the conventional one in several ways, including an emphasis on the development of the covariant derivative and an avoidance of the use of traditional index notation for tensors in favor of a semantically richer language of vector fields and differential forms. But the biggest single difference is the authors' integration of computer programming into their explanations. By programming a computer to interpret a formula, the student soon learns whether or not a formula is correct. Students are led to improve their program, and as a result improve their understanding. |
This
course begins with a brief introduction to
writing programs in a higher level language, such as Mathematica.
Students are
taught fundamental principles regarding machine representation of
numbers,
types of computational errors, and propagation of errors. The numerical
methods
include finding zeros of functions, solving systems of linear
equations,
interpolation and approximation of functions, numerical integration and
differentiation, and solving initial value problems of ordinary
differential
equations. |
Algebra One on OneAlgebra One on One is a new educational game for those wanting a fun way to learn and practice algebra. This program covers 21 functions, including maximums, minimums, absolute values, averages, squares, and cubes. It has both a practice area and a game area. The Practice menu lets you practice each function individually. The Game menu lets you choose up to 21 functions. You can choose from Calculate Value, Choose Formula, or Figure Formula and Calculate. You can even compete against another player. It has a great help system that makes it simple for the beginner to understand algebra. It also has an ""Einstein"" level that even algebra experts will find fun and challenging.
Version 4.0 features improved graphics, better help, easier registration, and a registration bonus of eight other programs. This version is a 30-day trial. The registration price is $14.99.
This is a great little programme. When I needed to brush up on my skills a few years ago I tried this and loved it. Now that I'm in school again I was glad I tracked it down. High graphics would just slow it down. I think this was designed by math teachers. I like it anyway. Try it.
Rudimentary graphics aside (the hand cursor seems backward), the interface is rough. Find a designer to help you make it look prettier.
Then work on the functionality. Once I figured out what I was being asked to do, I managed to answer all the questions correctly. But I'm trying to teach someone the importance of SHOWING YOUR WORK! This program shows how the answer was reached AFTER it's been reached. Need to somehow give the user a workspace to actually work through the equation - not just in their head or, heaven forbid, with pencil and paper! ;-)
Good luck! I'll be checking back to see how it comes along in version 5.
Not the best interface, so it may take a few minutes to understand. Suprisingly, this doesn't take away from its effectiveness. The layout actually begins to make some sense as you begin using the software. The method of teaching however is excellent: Do and see the results, over and over and over. This program not only teaches you by making you do the work repetitiously, it STRENGTHENS your understanding through repetition until the subject matter sinks in, becoming second nature. By the way, you control how many times you want to continue solving practice problems. Another attractive feature is that the questions (or expressions) aren't canned. The expressions that you solve (you'll be given the answer if you can't solve it after a few tries), are created on the fly. This reduces the chance of you memorizing the answers to the expressions, and gives the software a fresh feel every time you start solving problems (unlike a book, once you solve a book's problems you can't continue to practice on new problems without buying a different book).
This program doesn't teach you anything, if they were giving it away for free, I wouldn't keep it. The graphics are terrible, no examples and logic behind the program. I put this program in the worthless category |
Precalculus, Fifth Edition, by Lial, Hornsby, Schneider, and Daniels, engages and supports students in the learning process by developing both the ...Show synopsisPrecalculus, Fifth Edition, by Lial, Hornsby, Schneider, and Daniels, engages and supports students in the learning process by developing both the conceptual understanding and the analytical skills necessary for success in mathematics. With the Fifth Edition, the authors recognize that students are learning in new ways, and that the classroom is evolving. The Lial team is now offering a new suite of resources to support today's instructors and students. New co-author Callie Daniels has experience in all classroom types including traditional, hybrid and online courses, which has driven the new MyMathLab features. For example, MyNotes provide structure for student note-taking, and Interactive Chapter Summaries allow students to quiz themselves in interactive examples on key vocabulary, symbols and concepts. Daniels' experience, coupled with the long-time successful approach of the Lial series, has helped to more tightly integrate the text with online learning than ever before.Hide synopsis
Description:Fine. Hardcover. Almost new condition. SKU: 9780321783806-2-0-3...Fine. Hardcover. Almost new condition. SKU: 978032178380683806 ***NOTICE! ! ! This book is a Brand New Annotated...New. ***NOTICE! ! ! This book is a Brand New Annotated Instructor Edition (same textbook content as the student edition, may have extra answers or notes).
Description:New. Please read description before purchase>> annotated...New. Please read description before purchase>> annotated teacher edition with publisher notation "review copy.." on cover New text no writing or marks includes all Students content and all answers. text only no access code or other supplements. ship immediately-Expedited shipping available.
Description:Very Good. 0321783808 Book is in great shape. No highlighting...Very Good. 0321783808 Book is in great shape. No highlighting or writing. May not contain CDs or access codes. Awesome customer service! We ship to APO/FPO. We ship every |
Welcome
to Project WELCOME site...
Launched in May, 2000, with the support of an NSF grant, Project WELCOME
is a new part of the MAA SUMMA Program. WELCOME brings together elements
of three MAA program themes: academic technology, professional development,
and promoting involvement of historically under-represented groups.
This
project is funded to create a library collection of "interactive
mathematical explorations" (this web site) to support a suite of
undergraduate courses in mathematics. Each exploration consists of organized
sequences of simulations, "quantitative/qualitative laboratory"
experiments, lessons, and/or open-endedexercises
tied to the conceptual themes of the targeted course.
These
explorations are created in MathwrightWeb Author
and read either online within the browser (applet mode) using Mathwrightweb
Activex Control or offline using Mathwright32
Player. However,
in
order to view the interactive explorations, you must be running
Microsoft Windows 95/98/2000/ME/XP and using Microsoft Internet
Explorer 5.0 or later.
Get
started by setting up your personal computer to play the interactive
explorations. The details are under the menu item "Start Here"
on the left.
The
Mathwright Library hosts a collection of interactive, electronic
mathematics and science "WorkBooks." These WorkBooks
have been developed by College and Secondary School mathematics
and science teachers (and sometimes by their students) since
1991. Initially funded by the National Science Foundation
and supported by the IBM Corporation, it has been in place
on the web since 1995.
This Library is an experiment in computer-based pedagogy.
Its aim is to invite students to come into the world of mathematics
and science through structured microworlds ( WorkBooks) that
will allow them to ask their own questions, to read at their
own pace, and to experiment and play withthose
topics that interest them. Library WorkBooks are hypertext
documents. They vary in size from
1 page to 40 pages. Most of them look and feel like web pages,
and that fact leverages the experience that students already
have with the web. But in the WorkBooks, students will be
able to do very interesting and exciting things.
Visit the Mathwright
Library and Cafe and explore the large collection of Mathwright
workbooks covering topics ranging across the undergraduate mathematics
curriculum ...
There
are four active teams for the academic year 2000-2001. Each team
consists of a novice developer and a mentor (experienced developer).
Mike
Pepe(right)
mentor
Seattle Central C. C.
Ravinder Kumar
developer
Alcorn University
Margie
Hale(left)
mentor
Stetson University
K.P. Satagopan
developer
Shaw University
Kyle
Siegrist
(left)
mentor
Univ. of AL, Huntsville
Mafori Moore
developer
GA Perimeter College
Jim
Miller
(left)
mentor
West VA University
Sam Masih
developer
Albany State University
Objectives:Involve
students and their teachers in computer activities for interactive exploration
of mathematical ideas; create on-line resource for students and teachers
everywhere. Funding:$300,000 NSF grant to the Mathematical Association of
America (MAA). Term:Academic years 2000-2001 and 2001-2002. Principal
Investigator (PI):James E. White. Co-PI's:Bill Hawkins, Dan Kalman, and Samad Mortabit
(1) Download and setup the appropriate player (or both). (2)Some
of the workbooks (interactive explorations) make use of Microsoft
Access databases. You DO NOT have to have Microsoft Access on your
personal computer, but you do have to configure your "data source
(ODBC)" to enable buit-in MS Access tools. To do so, go to the
configuration page. |
revision app teaches you everything you need to know for GCSE Maths. It combines the separate apps for Number, Algebra, Geometry, Measures, Statistics and Probability produced by Haslam and Hall Publishing, a leading educational publisher in the UK.
Features: * Includes Foundation and Higher levels. * Revise the key facts for GCSE Maths. * Take Quick Quizzes and try to beat your saved best score. * OVER 1000 MULTIPLE CHOICE QUESTIONS with full worked solutions. * No internet connection needed once installed. * Suitable for all exam boards (AQA, Edexcel, OCR).Take a breath and make your GCSE preparation a fun activity with our collection of GCSE apps. Here comes the most comprehensive Algebra 730 questions across 73 subtopics. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
• HIGHEST QUALITY and QUANTITY 730 questions and 73 revision notes in all just for Algebra3D coordinates Parallel and perpendicular lines Gradient-Intercept method Drawing a line with a given gradient Finding the equation of a line from its graph Uses of graphs- finding formulae or rules Significant points of a quadratic graph Cubic graphs Exponential graphs Reciprocal graphs Graphs of loci and trig functions Solving equations by the method of intersection Sine and cosine graphs Transformations of the graph y = f(x) will work on all devices, to its full capability. If you experience an error please contact us directly or via the in-app report an error function.
This GCSE revision app allows you to test yourself with over 1500 multiple choice revision questions on key topics, each with their own detailed explanatory note. You can also review past GCSE History papers from Edexcel, AQA and OCR.
Monitor your progress and share your results on Facebook and Twitter. This GCSE revison app is designed to ensure that you have a full understanding of all the facts you need in order to excel in your GCSE History exams.
Content is designed to cover the majority of exam boards – covers the full syllabus of the Edexcel syllabus, the majority of the AQA syllabus, and is looking to contain the full spread of OCR soon. Watch this space!
We have also included the relevant past papers from all three exam boards to make this the most complete revision app for GCSE Modern History.
Full details of each section can be found at
1 Britain WW1: Before, During and After 2 Britain WW2: Before, During and After 3 Germany: 1918-1939: The Rise of Hitler 4 Germany: the Weimar Republic 5 The USSR and Stalin 6 Russia: The Fall of the Tsarist Regime, the road to Communism and the development of the USSR 7 The USA: Racism and intolerance, civil rights and a changing society 8 The USA: Economic boom and the Roaring 20s 9 The USA: The Great Depression and the New Deal 10 Causes of WW1 11 The Peace Treaties and how Europe was affected 12 The road to WW2 13 Cold War Crises: Berlin, Cuba, Czechoslovakia 14 The development of the Super Powers and the Cold War 15 The end of the Cold War
Developed by Loughborough University, the mathscard GCSE app contains hundreds of examples of maths formulae, graphs and diagrams. The GCSE app is based on the hugely successful Loughborough A-level app and is designed to help students with their exam revision when at home or on the move. Number and Arithmetic, Algebra, Graphs, Statistics and Probability, Geometry and Measurement and much more are all covered in this handy resource.
Looking for success in PE? Learn, revise and prepare for PE exams with ease and confidence.
Packed with over 500 examples, explanations and definitions this app comes with exam style questions and answers along with tips on effective revision and exam technique, making the GCSE PE app perfect for learning and revision!
Who is this app for?
Anyone studying or teaching PE! This app is mainly for Year 10 and Year 11 students studying GCSE PE in the UK and worldwide. It is suitable for all exam boards. Students studying BTEC sport courses will also find this app very useful.
Who else would benefit from using this app?
The app is also really useful for AS and A2 PE students, PE teachers, instructors, lecturers and university students following PE or sport related degrees. It serves as a reference to refresh and develop knowledge and understanding of the many topics involved in studying Physical Education.
Contents
Over 500 explanations, examples and definitions appear under the following topics:
The app is designed to help you learn and revise in a convenient and easy way wherever you are. The best way to do this is to ask yourself what you already know about a piece of knowledge before you navigate to it. Test yourself to see how much you know. You can then easily navigate between terms and descriptions to check your knowledge and understanding.
We hope you enjoy learning and revising with our PE app. If you do, please tell your friends and teachers about it so that they can benefit too.
LearnersCloud revision videos for GCSE Maths make it easy to learn, revise and test yourself on the go.
Each tutor-led video has been specially developed by a fully qualified GCSE Maths teacher to take you through the key topics and techniques, step by step.
Start today and achieve the results you deserve.
Covers all UK leading exam board specifications.
Please note. *These videos are streamed on-demand for immediate viewing and require an internet connection. We recommend using a WI-FI connection to avoid charges incurred as a result of exceeding your data allowance.
GCSE English Language 2011 is an app that contains exam strategies and techniques designed to increase your grade by up to 25%. Designed and written by specialists in the field, GCSE English Language 2011 app delivers the advice needed to increase your grade to an A. Our apps are designed for use up to one hour before the exam. You don't have to learn anything new, you can simply read our app and your grade will improve! It sounds fantastic and it is! Proven techniques boost your grade by enabling you to deploy your knowledge and techniques just where they are needed. Feel free to visit our main website where you can find more help with your EnglishMore from developer
With over 800 unique multiple-choice test questions, Biology Examstutor is an essential A Level Biology exam revision app. Instant feedback for each question helps you identifying the correct response to questions you answer incorrectly. Reinforcing your understanding of key topics you may be examined on at A Level.
** This version of the app is intended for use by subscribers to examstutor.com, and is initially set to demonstration mode, and can be fully unlocked by entering your examstutor login details.
**★ This version of the app is intended for use by subscribers to examstutor.com, and is initially set to demonstration mode, it can be fully unlocked by entering your examstutor login details, giving access to further Driving Test support through examstutor.com including a fully illustrated Audio Podcast of the complete Highway Code.
★ A paid version of this app is available separately in the Android Market · it can then |
This third edition of the perennial bestseller defines the recent changes in how the discipline is taught and introduces a new perspective on the discipline. New material in this third edition includes: A modernized section on trigonometry An introduction to mathematical modeling Instruction in use of the graphing calculator 2,000 solved...Tough Test Questions? Missed Lectures? Not Enough Time?
Fortunately, there's Schaum's. This all-in-one-package includes more than 650 fully solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 25 detailed videos featuring Math instructors who explain how to solve the most commonly... more... |
both theoretical knowledge and computational experience through the coverage of the mathematical underpinnings of scientific computing methods and their algorithmic aspects. The text meets the guidelines outlined by the actuarial society. Students are encouraged to use a calculator to complete the initial steps of an algorithm in order to have a firm understanding of it before writing a computer program. Separate computer exercises require students to write computer programs. Algorithms are presented in pseudocodes adaptable to any standard computer language. Flexible organization of the text presents important concepts in early chapters, making Chapters 1-8 suitable for a one-semester course, while Chapters 9-15 provide the more advanced material covered in a two-semester course. |
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Show More highlights key information on setting up problems, understanding parts of equations, moving decimal points, and more.Spiral bound format with plenty of white space allows you to use the text as a workbook in which you can write your answers and work out problems. Consistent chapter formats make it easy to retain information and identify important content. Chapter objectives emphasize what you should learn from each chapter and how your knowledge applies to patient care. Key terms defined at the beginning of each chapter help you understand new vocabulary in the text. Chapter overviews introduce you to the topics discussed in the chapter. Example problems demonstrate and label each step to getting a solution and show you how to solve similar problems. Practice the Skill problems incorporated within the chapter for in-class discussion allow you to practice what you've learned before receiving homework assignments. Math in the Real World boxes include word problems that apply your knowledge to everyday life as well as common healthcare situations. Strategy boxes demonstrate the steps to solving topic problems and provide a helpful example for solving more problems. Human Error boxes include hints on common errors and show you how to double-check your answers. Math Etiquette boxes help you solve problems by presenting proper math rules. Chapter quizzes allow you to assess your learning and identify areas for further study |
S.O.S. Mathematics This site is a free resource for math review material from algebra to differential equations. It provides more than 2,500 pages of short and easy-to-understand explanations for subjects including algebra, trigonometry, calculus, differential equations, complex variables, matrix algebra, and various mathematical tables. The materials on this site are designed for high school students, college students, and adult learners. Links to recommended books and other math education websites are also provLinear Algebra When I started teaching this subject I found three kinds of texts. There were applications books that avoid proofs and cover the linear algebra only as needed for their applications. There were advanced books that assume that students can understand their elegant proofs and know how to answer the homework questions having seen only one or two examples. And, there were books that spend a good part of the semester multiplying matrices and computing determinants and then suddenly change level to wo Author(s): No creator set
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Applied Probability Focuses on modeling, quantification, and analysis of uncertainty by teaching random variables, simple random processes and their probability distributions, Markov processes, limit theorems, elements of statistical inference, and decision making under uncertainty. This course extends the discrete probability learned in the discrete math class. It focuses on actual applications, and places little emphasis on proofs. A problem set based on identifying tumors using MRI (Magnetic Resonance Imaging) i Author(s): No creator set
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Private Universe Project in Mathematics: Workshop 3. Inventing Notations We learn how to foster and appreciate students' notations for their richness and creativity. We also look at some of the possibilities that early work in creating notation systems might open up for students as they move on toward algebra.,15 min. Pizzas in the Classroom In Englewood, New Jersey, Blanche Young, who attended the summer workshop, tries out one of the problems with her fourth-grade students. Later, she meets with Arthur Powell to discuss the lesson. 5 min. New Brunswick, New Jersey Author(s): Harvard-Smithsonian Center for Astrophysics
Private Universe Project in Mathematics: Workshop 1. Following Children's Ideas in Mathematics An unprecedented long-term study conducted by researchers at Rutgers University followed the development of mathematical thinking in a randomly selected group of students for 12 years—from first grade through high school—with surprising results. In an overview of the study, we look at some of the conditions that made the students' math achievement possible.,10 min Building Towers Five-High The Kenilworth students in the fourth grade are seen working on the Towers problem ("How many different Author(s): Harvard-Smithsonian Center for Astrophysics
Introduction to Economic Analysis This book presents standard intermediate microeconomics material and some material that, in the authors' view, ought to be standard but is not. Introductory economics material is integrated. Standard mathematical tools, including calculus, are used throughout. The book easily serves as an intermediate microeconomics text, and can be used for a relatively sophisticated undergraduate who has not taken a basic university course in economics.
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Basic Analysis: Introduction to Real Analysis This free online textbook is a one semester course in basic analysis. These were my lecture notes for teaching Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in fall 2009. The course is a first course in mathematical analysis aimed at students who do not necessarily wish to continue a graduate study in mathematics. A Sample Darboux sums prerequisite for the course is a basic proof course. The course does not cover topics such as metric spaces, which a more advanced course woul Author(s): No creator set
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Impact of Computer Aided Learning on Children with Specific Learning Disabilities The Technology Initiatives Division of Azim Premji Foundation has launched programmes for use of computers in rural schooling. One such programme is Computer Aided Leaning (CAL) that envisages deployment of computers as a media to impact learning competencies and to create an attractive environment in the schools. The state government provides the computers in schools and the Foundation has developed required software content designed to aid classroom learning process in specific areas such as m Author(s): The Spastic Society of Karnataka Bangalore
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Algebra InterMath is a professional development effort designed to support teachers in becoming better mathematics educators. It focuses on building teachers' mathematical content knowledge through mathematical investigations that are supported by technology. InterMath includes a workshop component and materials to support instructors. For each of the following problems, consider how you would pose the same problem to your students. Would the wording need to change? Would you need to include more pictur Author(s): No creator set
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Fourier: Making Waves Learn how to make waves of all different shapes by adding up sines or cosines. Make waves in space and time and measure their wavelengths and periods. See how changing the amplitudes of different harmonics changes the waves. Compare different mathematical expressions for your waves. Author(s): No creator set
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AcknowledgementsQuantum field theory This is a module framework. It can be viewed online or downloaded as a zip file.
Last taught in Spring Semester 2006
A compilation of fourteen lectures in PDF format on the subject of quantum field theory. This module is suitable for 3rd or 4th year undergraduate and postgraduate level learners.
Suitable for year 3/4 undergraduate and postgraduate study.
Dr Kirill Krasnov, School of Mathematical Sciences
Dr Kirill Krasnov is a Lecturer at the University of Nottingham. After studying physic Author(s): Krasnov K. Dr
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How and why we do mathematical proofs This is a module framework. It can be viewed online or downloaded as a zip file.
As taught in Autumn Semester 2009/10
The aim of this short unit is to motivate students to understand why we might want to do proofs (why proofs are important and how they can help us) and to help students with some of the relatively routine aspects of doing proofs.
In particular, the student will learn the following:
* proofs can help you to really see why a result is true;
* problems that are easy to state Author(s): Feinstein Joel FSymmetry We all encounter symmetry in our everyday lives, in both natural and man-made structures. The mathematical concepts surrounding symmetry can be a bit more difficult to grasp. This unit explains such concepts as direct and indirect symmetries, Cayley tables and groups through exercises, audio and videoaths everywhereelling pollution in the Great Lakes: a review This is the fifth and final unit in the MSXR209 series on mathematical modelling. In this unit we revisit the model developed in the first unit of this series on pollution in the Great Lakes of North America. Here we evaluate and revise the original model by comparing its predictions against data from the lakes before finally reflecting on the techniques used. This unit assumes you have studied Modelling pollution in the Great Lakes (MSXR209_1), Analysing skid marks (MSXR209_2), Developing modelPricesStarting with maths: Patterns and formulas Patterns occur everywhere in art, nature, science and especially mathematics. Being able to recognise, describe and use these patterns is an important skill that helps you to tackle a wide variety of different problems. This unit explores some of these patterns ranging from ancient number patterns to the latest mathematical researchalysing skid marks This unit is the second in the MSXR209 series of five units on mathematical modelling. In this unit you are asked to relate the stages of the mathematical modelling process to a previously formulated mathematical model. This example, that of skid mark produced by vehicle tyres, is typical of accounts of modelling that you may see in books, or produced in the workplace. The aim of this unit is to help you to draw out and to clarify mathematical modelling ideas by considering the example. It assum Author(s): The Open University
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Product Description Sink or Float: Thought Problems in Math and Physics is a collection of problems drawn from mathematics and the real world. Its multiple-choice format forces the reader to become actively involved in deciding upon the answer. The book s aim is to show just how much can be learned by using everyday common sense. The problems are all concrete and understandable by nearly anyone, meaning that not only will students become caught up in some of the questions, but professional mathematicians, too, will easily get hooked. The more than 250 questions cover a wide swath of classical math and physics. Each problem s solution, with explanation, appears in the answer section at the end of the book. A notable feature is the generous sprinkling of boxes appearing throughout the text. These contain historical asides or little-known facts. The problems themselves can easily turn into serious debate-starters, and the book will find a natural home in the classroom. Book Description Over 250 problems drawn from mathematics and the real world revealing just how much can be learned by using everyday common sense. The author's easily understandable style will engage school students as well as professional mathematicians. Covers a wide range of classical maths and physics, with solutions and explanations provided. See all Editorial Reviews Product Details * Hardcover: 392 pages * Publisher: Mathematical Association of America (July 8, 2008) * Language: English * ISBN-10: 0883853396 * ISBN-13: 978-0883853399
Product Description: Game Development with C# and JavaScript Build fully functional, professional 3D games with realistic environments, sound, dynamic effects, and more! * Kick start your game development, and build ready-to-play 3D games with ease. * Understand key concepts in game design including scripting, physics, instantiation, particle effects, and more. * Test & optimize your game to perfection with essential tips-and-tricks. * Written in clear, plain English, this book takes you from a simple prototype through to a complete 3D game with concepts you'll reuse throughout your new career as a game developer. * Learn game development in Unity version 3 and above, and learn scripting in either C# or JavaScript In Detail Game Engines such as Unity are the power-tools behind the games we know and love. Unity is one of the most widely-used and best loved packages for game development and is used by everyone, from hobbyists to large studios, to create games and interactive experiences for the web, desktop, mobile, and console. With Unity's intuitive, easy to learn toolset and this book – it's never been easier to become a game developer. Taking a practical approach, this book will introduce you to the concepts of developing 3D games, before getting to grips with development in Unity itself – prototyping a simple scenario, and then creating a larger game. From creating 3D worlds to scripting and creating game mechanics you will learn everything you'll need to get started with game development. This book is designed to cover a set of easy-to-follow examples, which culminate in the production of a First Person 3D game, complete with an interactive island environment. All of the concepts taught in this book are applicable to other types of game, however, by introducing common concepts of game and 3D production, you'll explore Unity to make a character interact with the game world, and build puzzles for the player to solve, in order to complete the game. At the end of the book, you will have a fully working 3D game and all the skills required to extend the game further, giving your end-user, the player, the best experience possible. Soon you will be creating your own 3D games with ease! What you will learn from this book * An understanding of the Unity 3D Engine and game development * Write code for game development in either C# or JavaScript * Build a 3D island and set of mini-games for your players * Incorporate terrains and externally produced 3D models to get your game environment up and running * Create player character interactions * Combine scripting and animation to transform your static objects into dynamic interactive game elements * Add realistic effects to your games by using particle systems * Create a stylish and efficient menu, and animate other interface elements * Use Lightmapping to make your game environments look more professional * Deploy your game to the web and desktop and share it with the wider world for testing and feedback. Approach This book follows an informal, demystifying approach to the world of game development with the Unity game engine. With no prior knowledge of game development or 3D required, you will learn from scratch, taking each concept at a time working up to a full 3D mini-game. You'll learn scripting with C# or JavaScript and master the Unity development environment with easy-to-follow stepwise tasks. Who this book is written for If you're a designer or animator who wishes to take their first steps into game development or prototyping, or if you've simply spent many hours sitting in front of video games, with ideas bubbling away in the back of your mind, Unity and this book should be your starting point. No prior knowledge of game production is required, inviting you to simply bring with you a passion for making great games.
Mathematics for Year 5 (second edition) presents a comprehensive and rigorous course in mathematics at Year 5 level. The book provides students with the structure and content to work efficiently at their own rate,with the help of worked examples, exercises, activities and answers. The topics do not have to be addressed in the same order as they are listed. However, Numeracy chapters should be covered before Fractions andDecimals. Fractions, Decimals and Money should be addressed in that order. Measurement is reliant on the Decimals chapter.
Part of the ongoing Psychological Disorders series, this book will be most helpful when read with a counselor or as a prompt to group discussion. The authors are professionals in the field, and they write with authority about the many kinds of anxiety disorders including panic attacks, obsessive-compulsive behavior, phobias, post-traumatic stress, and separation anxiety. For each disorder, they discuss statistics, causes, diagnoses, long-term risks, intervention, and more. Their heavy jargon ("somatic management skills training," "problem-focused coping," etc.) will be too much for many YAs, and the extensive notes and references cite mostly professional journals. However, the page design is attractive, and the accessible personal accounts from young patients will encourage readers to find out more and seek help for themselves or someone they know.
This book is characterized by its problem-solving approach with extensive reference charts and tables. First published in 1962, this was the first book on the identification of organic compounds using spectroscopy. Now considered a classic, it can be found on the shelf of every Organic Chemist. The key strength of this text is the extensive set of real-data problems in Chapters 8 and 9. Even professional chemists use these spectra as reference data.
Applied Principles of Horticultural Science is that critical thing for all students of horticulture – a book that teaches the theory of horticultural science through the practice of horticulture itelf. The book is divided into three sections – Plant science, Soil science, Pest and disease. Each section contains a number of chapters relating to a major principle of applied horticulture. Each chapter starts with a key point summary and introduces the underpinning knowledge which is then reinforced by exercises. The book contains over 70 practical exercises, presented in a way that makes students think for themselves. Answers to the exercises are given at the end of chapters. Clear step-by-step instructions make practical work accessible to students of all abilities. This new third edition provides an even wider sweep of case studies to make this book an essential practical workbook for horticulture students and gardners alike. Updated material fits with the latest RHS, City and Guilds and Edexcel syllabus. It is particularly suitable for the RHS Certificate, Advanced Certificate and Edexcel Diplomas as well as for those undertaking NPTC National, Advanced National courses and Horticulture NVQs at levels 2 and 3, together with the new Diploma in Environmental and Land-based studies. Laurie Brown is a horticultural scientist and educator. He is Director of Academex, a consultancy company aspiring to excellence in teaching and learning. Laurie previously worked with the Standards Unit on the design of exemplary teaching resources in the land-based sector. |
Summary
Maple is a powerful software tool for mathematical computations and visualization. The goal of this manual is to introduce Maple to students who are taking first year calculus. As such, Maple is a tool to solve problems that are too difficult to solve by hand. In addition, students will improve their understanding of the concepts of calculus. The order of the material is organized by computational topic and should be suitable for most texts on Single Variable calculus. |
I am a high school student and would like to pursue a career in mathematics and I am hoping to find a serious explanatory book on math (geometry, algebra, calculus, functions and trigonometry) for further advanced studies in math. Does anyone know any very good textbooks that will truly make me a better mathematician?
I have removed the "logic" tag; the question is not really about mathematical logic. (Proof techniques like the ones in "How to prove it" are not mathematical logic in any genuine sense, they are just a part of basic mathematics).
–
Carl MummertOct 6 '13 at 20:03
4 Answers
There is a fantastic book, which you may have seen already - *What is Mathematics" by Courant and Robbins, see The point is, before you will become a "better mathematician", you should become a mathematician at all. The book shows what this means, and what are the possibilities.
I would recommend learning number theory, in particular reading "An Introduction to the Theory of Numbers" by Hardy and Wright. Number theory has the advantage of requiring no prerequisite knowledge (other than of elementary arithmetic) and leads naturally into the study of (abstract) algebra, which has tremendous applications to later topics like geometry, topology, etc.
The suggestion to work through Spivak's Calculus is good: rigorous analysis was one of the first subjects that really opened up mathematics to me and showed me how beautiful it can be (That said, there are lots of people who can't stand $\varepsilon$s and $\delta$s). Spivak's book is quite big and long though: for an introduction to Analysis, I prefer R. P. Burn's Numbers and Functions (CUP), which is shorter and leads you through the subject in a sequence of well chosen questions. |
This course focuses on mathematics as the science of identifying, understanding and describing patterns. Patterns that occur in nature and empirical studies can be identified and modeled using fundamental ideas such as functions (mathematical rules), probability (long term behavior), exploratory data analysis (statistics) and geometry. Through a series of guided investigations students will master the reasoning used to identify the patterns, the mathematical model used to describe the pattern and the computational techniques necessary to further explore and apply the pattern in new situations. This course is designed specifically for students intending to become elementary or middle school teachers. However, the course is open to anyone and has no pre-requisites. It does not fulfill the GEP Mathematics requirement; it does fulfill a GER Mathematics requirement. |
Arguably the reason why high school students commit suicide, and the most difficult concept of Algebra 2. A complete waste of time, as there are various other methods of solving matrices that don't involve half-hour long porcesses that are very liable to error. |
Modify Your Results
This is the book that high school calculus teachers have been wanting for a long time. Totally revised from its first edition, this book completely reflects the content, goals, and philosophy of the new advanced placement course description. In both the ordering of topics and the rich applications of calculus to real-world situations, this text can be used without supplementation to totally prepare students for the advanced placement exam.
The esteemed author team is back with a fourth edition of Calculus: Graphing, Numerical, Algebraic written specifically for high school students and aligned to the guidelines of the AP Calculus exam. The new edition focuses on providing enhanced student and teacher support; for students, the authors added guidance on the appropriate use of graphing calculators and updated exercises to reflect current data. For teachers, the authors provide lesson plans, pacing guides, and point-of-need answers throughout the Teachers Edition and teaching resources. Learn more.
The topics described in the Standards for Mathematical Content will vary from year to year. However, the way in which you learn, study, and think about mathematics will not. The Standards for Mathematical Practice describe skills that you will use in all of your math courses. These pages show some features of your book that will help you gain these skills and use them to master this year's topics.
In order to be a good problem solver, you need to use a good problem-solving plan. The plane used in this book is detailed below. If you have another plant that you like to use, you can use it as well.
In this Seventh Edition of Precalculus, a book that is designed for instructors and written for students, the authors encourage graphical, numerical, and algebraic modeling of functions as well as a focus on problem solving, conceptual understanding, and facility with technology.
In this new edition of Precalculus,Seventh Edition, the authors encourage graphical, numerical, and algebraic modeling of functions as well as a focus on problem solving, conceptual understanding, and facility with technology. They responded to many helpful suggestions provided by students and teachers in order to create a book that is designed for instructors and written for students. As a result, we believe that the changes made in this edition make this the most effective precalculus text available today.
This textbook helps students truly understand the fundamental concepts of algebra, trigonometry, and analytic geometry, foreshadows important ideas of calculus, and shows how algebra and trigonometry can be used to model real-life problems.
This seventh edition of Precalculus, designed for instructors and written for students, encourages graphical, numerical, and algebraic modeling of functions as well as problem solving, conceptual understanding, and facility with |
Algebra 1 also includes some statistics and probability and a small amount of geometry. Here are the modules for which you may need my support:
-Expressions
-Positive and Negative Numbers
-Solving equations
-Solving inequalities
-Relations and functions
-Linear equations
-Polynomials
-Factoring... |
Larson's TRIGONOMETRY is known for delivering sound, consistently structured explanations and exercises of mathematical concepts. With the ninth edition, the author continues to revolutionize the way students learn material by incorporating more real-world applications, ongoing review, and innovative technology. How Do You See It? exercises give students practice applying the concepts, and new Summarize features, Checkpoint problems, and a Companion Website reinforce understanding of the skill sets to help students better prepare for tests.
Trigonometry: Search Results
Book Description:2014. Hardcover. Book Condition: New. 5th or later Edition. (5c) PLEASE READ BEFORE ORDERING: This book is an ANNOTATED INSTRUCTOR'S EDITION. New and unused 9th edition which ships lightning quick (your order ships within 24-hours on any given business day). Choose EXPEDITED shipping (USPS Priority Mail), as delivery takes a mere 2-5 business days. Media Mail can take up to 10 business days. This book's paging is the same as the student edition. May contain black tape on front, back and spine of book; may contain some or all answers within the body, front and back pages of the text; may contain annotations within page margins; may not contain Infotrac, MyMathLab, Connect and/or other online accessed codes; may not include other study or lab manuals required by your instructor as course materials. Please do not order this Annotated Instructor's Edition if you're having any doubts about this item. A return and refund is a time and cost consuming option for us all. If you have any questions PLEASE inquire before ordering. Bookseller Inventory # ABE-12646780307
Book Description:Cengage Learning. Hardcover. Book Condition: New. 1133954332 US Hardback copy. Identical to student edition except has publisher markings on cover and answers to the problems. Great opportunity to save on this book. WE SHIP DAILY!!!. Bookseller Inventory # SKU20225981133954330
Book Description:Cengage Learning. Book Condition: New 001474
Book Description:Cengage Learning. Book Condition: New. 1133954332 Bookseller Inventory # Z1133954332ZN
Book Description:Brooks/Cole, Cengage Learning, 2014. Hardcover. Book Condition: New. Ninth Edition. New ANNOTAED INSTRUCTOR EDITION, content same as the student Edition with All Answers Added in back of the book. Bookseller Inventory # 003540
Book Description:Cengage Learning. Book Condition: New. 1133954332 Bookseller Inventory # Z1133954332 |
Algebra Activities are designed to teach students algebraic concepts by having them seek out patterns, understand subtle differences in notation, and find similarities between algebraic structures in different topic areas. Many of the activities are really more like puzzles, and all of them are designed to make classroom use easy for math instructors.
Algebra Activities Student Workbooks contain all the activities and assessments for the chapters that correlate with your textbook. These workbooks are available with the all Cengage Learning Algebra texts:
Sometimes it is difficult to know what concepts a class is going to struggle with until you're actually in the classroom. Using student workbooks allows your teaching to be flexible. When you discover that students need more time engaging with a particular topic, you will be able to find just the right activity without pre-planning the copies.
Although instructors who have adopted the texts have permission to make classroom copies from the IRB activities and assessments, it might put a strain on your department's copying budget, and your time, to make so many copies for each class. Consider that at this moment, there are over 450 pages of activities and assessments written for this book. If you copied half the activities and assessments for a class of 30 students, then each class section would cost your department $270 for copying (assuming 4 cents a page). |
Students
preparing to take an introductory course in physics in college may want to review some, or
all, of the math topics listed below. The student with a good high school background in
math should be familiar with most of these topics.
Students planning on
enrolling in the College Physics sequence [111 & 112] should review the topics
highlighted in red. College Physics is the non-calculus based introductory sequence.
Potential General Physics [125 & 126] students may wish to review all topics. These
are calculus based introductory courses.
[Note: These materials were
created in Microsoft WORD and are saved in this form. Ifyour
computer's word processor will not reproduce these, copies are obtainable from your
instructor] |
Mathematical Formulas for Industrial and Mechanical Engineering
Description
Mathematical Formulas For Industrial and Mechanical Engineering serves the needs of students and teachers as well as professional workers in engineering who use mathematics. The contents and size make it especially convenient and portable. The widespread availability and low price of scientific calculators have greatly reduced the need for many numerical tables that make most handbooks bulky. However, most calculators do not give integrals, derivatives, series and other mathematical formulas and figures that are often needed. Accordingly, this book contains that information in an easy way to access in addition to illustrative examples that make formulas clearer. Students and professionals alike will find this book a valuable supplement to standard textbooks, a source for review, and a handy reference for many years |
Why do I need to study algebra? When am I ever going to have to use algebra in the real world?
Many people, not just algebra students, wonder why mathematics is important. Algebra 1 is designed to answer those questions through integration, applications, and connections.
Did you know that algebra and geometry are closely related? Topics from all branches of mathematics, like geometry and statistics, are integrated throughout the text.
How to develop a management team plan to outline the key executives and decision makers in the business. The management team plan describes the responsibilities, skills, and experience of the partners, key employees, advisors, and service providers. The management team's experience and qualifications should convince potential investors that the business has a management team with the experience and skills necessary for success.A media approach that builds art appreciation Exploring Art gives students insights into the ways artists are inspired, and the reasons they choose particular media to realize their artistic visions. From drawing and painting to architecture, graphic design, and photography, the chapters interweave compelling lessons on elements and principles of art, art history, and criticism with opportunities for studio production.
The book explores each of the 16 career cluster options and workplace reality for middle school students. This text prepares students for the rapidly changing opportunities in the work world. As they explore each of the 16 U.S. Department of Education career clusters, they'll build foundation skills and workplace competencies and learn how each new skill can help them build successful careers.
Exploring Theatre focuses on the development of the total student, which includes developing personal resources, self-confidence, the ability to work well with others, and a life-long appreciation of theater; learning to bolster self-concepts, build an ensemble, observe people and places more closely, move expressively, and become more aware of the senses; learning basic acting skills such as improvisation, characterization, role preparation, and stage movement; exploring a range of career or avocational opportunities in theater and theater education; understanding the various aspects of the production process; and studying special topics such as storytelling, clowning, oral interpretation, readers theater, and puppetry. This text is an ideal introductory theater text for both middle and high school.
Comprehensive grammar and composition handbooks for every grade level! Glencoe's Grammar and Composition Handbook provides full coverage of the writing process with practice exercises for grammar, usage, and mechanics |
Pre-Algebra students are introduced to linear relationships by plotting points that satisfy the equation on a coordinate grid and seeing how the points can be connected to form a
line. Concepts of slope, equation of the line, and intersections of two lines (solving simultaneous equations) are covered at an introductory level. |
Functions 1.00
Easy to use, intuitive program to visualize and study functions of one variable to find roots, maxima and minima, integral, derivatives, graph. Results, including the graph, can be saved or printed. You can also copy the graph to the clipboard,... View More
FindGraph FindGraph is a graphing, curve-fitting, and digitizing tool for engineers, scientists and business. Discover the model that best describes your data. Download Now!
School Calendar School Calendar will help you with assignment organization, project due dates, and scheduling. It can even remind you when your scheduled event is about to happen. Included are two viewing modes, search, auto-backup, iCalendar data exchange. Download Now!
Prime Number Spiral The Prime Number Spiral (a.k.a. the Ulam Spiral) is formed by marking the prime numbers in a spiral arrangement of the natural numbers. This is software is for exploring the Prime Number Spiral. Download Now!
Breaktru Fractions n Decimals Download Now!
Archim Archim is a program for drawing the graphs of all kinds of functions. You can define a graph explicitly and parametrically, in polar and spherical coordinates, on a plane and in space (surface). Archim will be useful for teachers and students. Download Now!
Inverse Matrices The program provides detailed, step-by-step solution in a tutorial-like format to the following problem: Given a 2x2 matrix, or a 3x3 matrix, or a 4x4 matrix, or a 5x5 matrix. Find its inverse matrix by using the Gauss-Jordan elimination method. The... Download Now!
3DMath Explorer is a computer program that pilots 2D and 3D graphs of mathematical functions and curves in unlimited graphing space. It has many useful feature screen est.
Approximates tabulated functions in 1 to 4 independent variables by finite power and/or trigonometric series. Approximates tabulated functions in 1 to 4 independent variables by finite power and/or trigonometric series. The program fits the function exactly at the grid points.
Visualize and analyze math functions with this tool. Visualize and analyze math functions with this tool. Function Plotter help you visualize most mathematical functions by specifying the function equation and its parameters. The user may experiment with up to four parameters, A...D, which are...
Free math / graphing program - type and graph an equation! Free math / graphing program - type and graph an equation!
AnalyticMath is a FREE, cross-platform math / graphing program with a powerful editor and integrated 'auto-calc' features that will help you develop and visually analyse mathematical... |
Questions About This Book?
The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any CDs, lab manuals, study guides, etc.
Summary
John Squires and Karen Wyrick have used their successes in the classroom and the lab to design the MyMathLab for Developmental MathematicseCourse. This new MyMathLab eCourse offers students a guided learning path through content that has been organized into smaller, more manageable portions. This course structure includes pre-made tutorials and assessments for every topic in the course, giving instructors an eCourse that can be easily set up and customized for a variety of learning environments.
Author Biography
John Squires has been teaching math for over 20 years. He was the architect of the nationally acclaimed "Do the Math" program at Cleveland State Community College and is now head of the math department at Chattanooga State Community College, where he is implementing course redesign throughout the department. John is the 2010 Cross Scholar for the League for Innovation and the author of the 13th Cross Paper which focuses on course redesign. As a redesign scholar for The National Center for Academic Transformation (NCAT), John speaks frequently on course redesign and has worked with both colleges and high schools on using technology to improve student learning.
Karen Wyrick is the current chair of the math department at Cleveland State Community College and has been teaching math there for over 18 years. She is an outstanding instructor, as students have selected her as the college's best instructor more than once! Karen played an integral role in Cleveland State's Bellwether Award-winning "Do the Math" redesign project, and she speaks frequently on course redesign at colleges throughout the nation and also serves as a redesign scholar for The National Center for Academic Transformation (NCAT).
Mini-Mod 18 Slope and the Equation of a Line Topic 18.1 The Slope of a Line Topic 18.2 Slope-Intercept Form Topic 18.3 Graphing Lines Using the Slope and y-Intercept Topic 18.4 Writing Equations of Lines Using a Point and Slope Topic 18.5 Writing Equations of Lines Using Two Points |
Algebra adds value to mathematical biology education
Jul 30, 2009
As mathematics continues to become an increasingly important component in undergraduate biology programs, a more comprehensive understanding of the use of algebraic models is needed by the next generation of biologists to facilitate new advances in the life sciences, according to researchers at Sweet Briar College and the Virginia Bioinformatics Institute (VBI) at Virginia Tech.
In the paper, "Mathematical Biology Education: Beyond Calculus," which is featured in the July 31, 2009 issue of Science, VBI Professor Reinhard Laubenbacher and Sweet Briar College Mathematical Sciences Professor Raina Robeva highlight algebraic models as one of the diverse mathematical tools needed in the professional development of up-and-coming life scientists. Despite this critical need, the authors explain, algebraic models have played a less substantial role in undergraduate curricula than other methods.
Future generations of biologists will routinely use mathematical and computational approaches to develop and frame hypotheses, design experiments, and analyze results. Sound mathematical models are essential for this purpose and are currently used in the field of systems biology to understand complex biological networks. Two types of mathematical models, in particular, have been successfully used in biology to reproduce network structure and dynamics: Continuous-time models derived from differential equations (DE models) focus on the kinetics of biochemical reactions, while discrete-time algebraic models built from functions of finite-state variables focus on the logic of the connections of network variables. According to Laubenbacher and Robeva, while DE models have been included more often in undergraduate curricula integrating mathematics and biology, algebraic models should also be viewed as an important training component for students at all education levels.
"Discrete-time algebraic models created from finite-state variables, such as Boolean networks, are increasingly being used to model a variety of biochemical networks, including metabolic, gene regulatory, and signal transduction networks," says Laubenbacher. "Often, researchers do not have enough of the information required to build detailed quantitative models. Algebraic models need less information about the system to be modeled, making them useful for instances where quantitative information may be missing. All the work that goes into building them can then be used to construct detailed kinetic models, when additional information becomes available. In addition, algebraic models are much more intuitive than differential equations models, which makes them more easily accessible to life scientists."
Using algebraic models is a relatively quick, easy and reliable way for students to integrate mathematical modeling into their life sciences coursework. Creating algebraic models of biochemical networks requires only a modest mathematical background, which is usually provided in a college algebra course. Without the complexities involved in teaching students how to construct more complicated models, algebraic models make the introduction of mathematical modeling into life sciences courses more accessible for faculty members as well.
According to Robeva, "The exciting thing about algebraic models from an educational perspective is that they highlight aspects of modern-day biology and can easily fit in both the biology and mathematics curricula. At the introductory level, they provide a quick path for introducing biology students to constructing and using mathematical models in the context of contemporary problems such as gene regulation. At the more advanced level, the general study and analysis of such models often require sophisticated mathematical theories. This makes them perfect for inclusion into mathematics courses, where the biology can provide a meaningful framework for many of the abstract structures. As educators, we should actively be looking for the best ways to seize this opportunity for advancing mathematical biology."
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Nevada State Standards for Mathematics: Grade 9
Currently Perma-Bound only has suggested titles for grades K-8
in the Science and Social Studies areas. We are working on expanding
this.
NV.A.
Problem Solving: Students will develop their ability to solve problems by engaging in developmentally appropriate opportunities where there is a need to use various approaches to investigate and understand mathematical concepts in order to: formulate their own problems; find solutions to problems from everyday situations; develop and apply strategies to solve a variety of problems; and integrate mathematical reasoning, communication and connections.
NV.B.
Mathematical Communication: Students will develop their ability to communicate mathematically by solving problems where there is a need to obtain information from the real world through reading, listening, and observing in order to: translate information into mathematical language and symbols; process information mathematically; present results in written, oral, and visual formats; discuss and exchange ideas about mathematics as a part of learning; read a variety of fiction and nonfiction texts to learn about mathematics; and use mathematical notation to communicate and explain problems.
B.4.
Communicate and evaluate mathematical thinking based on the use of definitions, properties, rules, and symbols in problem solving.
B.5.
Use everyday language, both orally and in writing, communicate strategies and solutions to problems using appropriate mathematical language.
NV.C.
Mathematical Reasoning: Students will develop their ability to reason mathematically by solving problems where there is a need to investigate mathematical ideas and construct their own learning in all content areas in order to: reinforce and extend their logical reasoning abilities; reflect on, clarify, and justify their thinking; ask questions to extend their thinking; use patterns and relationships to analyze mathematical situations; and determine relevant, irrelevant, and/or sufficient information to solve mathematical problems.
C.1.
Recognize and apply deductive and inductive reasoning.
C.2.
Review and refine the assumptions and steps used to derive conclusions in mathematical arguments.
C.3.
Make and test conjectures about algebraic and geometric properties based on mathematical principles.
C.4.
Justify the validity of an argument.
C.5.
Construct a valid argument.
NV.D.
Mathematical Connections: Students will develop the ability to make mathematical connections by solving problems where there is a need to view mathematics as an integrated whole in order to: link new concepts to prior knowledge; identify relationships between content strands; integrate mathematics with other disciplines; and allow the flexibility to approach problems in a variety of ways within and beyond the field of mathematics.
D.1.
Use mathematical ideas from one area of mathematics to explain an idea from another area of mathematics.
D.2.
Explain the relationship between concepts and procedures.
D.3.
Use the connections among mathematical topics to develop multiple approaches to problems.
D.4.
Apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as rhythm in music and motion in science.
D.5.
Identify, explain, and apply mathematics in everyday life.
NV.1.0.
Numbers, Number Sense, and Computation: Students will accurately calculate and use estimation techniques, number relationships, operation rules, and algorithms; they will determine the reasonableness of answers and the accuracy of solutions to solve problems, communicate, reason, and make connections within and beyond the field of mathematics.
1.12.6
Estimating and Estimation Strategies
1.12.6.a.
Determine an approximate value of radical and exponential expressions using a variety of methods.
1.12.8.a.
Identify and apply real number properties to solve problems.
NV.2.0.
Patterns, Functions, and Algebra: Students will use various algebraic methods to analyze, illustrate, extend, and create numerous representations (words, numbers, tables, and graphs) of patterns, functions, and algebraic relations as modeled in practical situations to solve problems, communicate, reason, and make connections within and beyond the field of mathematics.
2.12.1
Patterns
2.12.1.a.
Use algebraic expressions to identify and describe the nth term of a sequence.
2.12.2
Variables and Unknowns
2.12.2.a.
Isolate any variable in given equations, inequalities, proportions, and formulas to use in mathematical and practical situations.
2.12.5.a.
Solve systems of two linear equations algebraically and graphically and verify solutions (with and without technology).
2.12.6
Algebraic Representations and Applications
2.12.6.a.
Solve mathematical and practical problems involving linear and quadratic equations with a variety of methods, including discrete methods (with and without technology).
NV.3.0.
Measurement: Students will use appropriate tools and techniques of measurement to determine, estimate, record, and verify direct and indirect measurements to solve problems, communicate, reason, and make connections within and beyond the field of mathematics.
3.12.1
Comparison, Estimation, and Conversion
3.12.1.a.
Estimate and convert between customary and metric systems.
3.12.2
Precision in Measurements
3.12.2.a.
Justify, communicate, and differentiate between precision, error, and tolerance in practical problems.
3.12.3
Formulas
3.12.3.a.
Select and use appropriate measurement tools, techniques, and formulas to solve problems in mathematical and practical situations.
3.12.5.a.
Determine the measure of unknown dimensions, angles, areas, and volumes using relationships and formulas to solve problems.
NV.4.0.
Spatial Relationships, Geometry, and Logic: Students will identify, represent, verify, and apply spatial relationships and geometric properties to solve problems, communicate, and make connections within and beyond the field of mathematics.
4.12.1
Two-Dimensional Shapes
4.12.1.a.
Identify and use the parts of a circle to solve mathematical and practical problems.
4.12.1.b.
Identify and apply properties of interior and exterior angles of polygons to solve mathematical and practical problems.
4.12.2
Congruence, Similarity, and Transformations
4.12.2.a.
Apply properties of similarity through right triangle trigonometry to find missing angles and sides.
4.12.5
Algebraic Connections
4.12.5.a.
Determine the slope of lines using coordinate geometry and algebraic techniques.
4.12.9.a.
Formulate, evaluate, and justify arguments using inductive and deductive reasoning in mathematical and practical situations.
NV.5.0.
Data Analysis: Students will collect, organize, display, interpret, and analyze data to determine statistical relationships and probability projections to solve problems, communicate, reason, and make connections within and beyond the field of mathematics.
5.12.1
Data Collection and Organization
5.12.1.a.
Organize statistical data through the use of tables, graphs, and matrices (with and without technology). |
Offers a flexible organization, enabling instructors to adapt the book to their particular courses. This book gives emphasis on algorithms and applications. Including exercises, it features numerous computer science applications.
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Features
Statistics Today problems open every chapter. These real-life problems, accompanied by a photo or graphic and sometimes a news item, show students the relevance of the chapter's topic. The answer is provided at chapter end.
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Allan G. Bluman is Professor of Mathematics at Community College of Allegheny County, near Pittsburgh. For the McKeesport and New Kensington Campuses of Pennsylvania State University, he has taught teacher-certification and graduate education statistics courses. Prior to his college teaching, he taught mathematics at a junior high school.
Professor Bluman received his B.S. from California State College in California, Penn.; his M.Ed. from the University of Pittsburgh; and, in 1971, his Ed.D., also from the University of Pittsburgh. His major field of study was mathematics education.
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The first book of theMathematics in Actionseries,Prealgebra Problem Solving,Fourth Editionillustrates how mathematics arises naturally from everyday situations through updated and revised real-life activities and accompa...show morenying practice exercises.
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FYI, there is a book called Perspective Made Easy with illustrated masters
that can be reproduced found in the Sax VAR catalog. It includes lessons,
drawings and assignments. Maybe this is what would help you. Product #572
929J $17.95 Judy Nagel BTW we also carry the eyewitness on Perspective
book and the Masters of Illusion video if you're interested.
Check the eyewitness series on Perspective. It's useful enough to buy for
the classroom library. There are mathmatical layouts I believe and lots of
diagrams that could be photographed in slide form for a lecture accompanying
your class.
I am developing a lesson on linear perspective (one point) for an 8th grade
math class which I will be team teaching with the math teacher. He is not
an artist and I am no mathematician. Does anyone know of math formulas that
I can apply to the lesson, preferably dealing with the calculation of
distances between objects (or transversals on a 1 point persp. grid) as they
recede into the distance. I have found many books which talk about the
ideas of Alberti, Leonardo, and Brunelleschi, but none that show their
calculations.
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Advanced Modern Algebra - 02 edition
Algebra is used by virtually all mathematicians, be they analysts, combinatorists, computer scientists, geometers, logicians, number theorists, or topologists. Nowadays, everyone agrees that some knowledge of linear algebra, groups, and commutative rings is necessary, and these topics are introduced in undergraduate courses. We continue their study.
This book can be used as a text for the first year of graduate algebra, but it is much more than that. It can also serve more advanced graduate students wishing to learn topics on their own; while not reaching the frontiers, the book does provide a sense of the successes and methods arising in an area. Finally, this is a reference containing many of the standard theorems and definitions that users of algebra need to know. Thus, the book is not only an appetizer, but a hearty meal as well.
Let me now address readers and instructors who use the book as a text for a beginning graduate course. If I could assume that everyone had already read my book, A First Course in Abstract Algebra, then the prerequisites for this book would be plain. But this is not a realistic assumption; different undergraduate courses introducing abstract algebra abound, as do texts for these courses. For many, linear algebra concentrates on matrices and vector spaces over the real numbers, with an emphasis on computing solutions of linear systems of equations; other courses may treat vector spaces over arbitrary fields, as well as Jordan and rational canonical forms. Some courses discuss the Sylow theorems; some do not; some courses classify finite fields; some do not.
To accommodate readers having different backgrounds, the first three chapters contain many familiar results, with many proofs merely sketched. The first chapter contains the fundamental theorem of arithmetic, congruences, De Moivre's theorem, roots of unity, cyclotomic polynomials, and some standard notions of set theory, such as equivalence relations and verification of the group axioms for symmetric groups. The next two chapters contain both familiar and unfamiliar material. "New" results, that is, results rarely taught in a first course, have complete proofs, while proofs of "old" results are usually sketched. In more detail, Chapter 2 is an introduction to group theory, reviewing permutations, Lagrange's theorem, quotient groups, the isomorphism theorems, and groups acting on sets. Chapter 3 is an introduction to commutative rings, reviewing domains, fraction fields, polynomial rings in one variable, quotient rings, isomorphism theorems, irreducible polynomials, finite fields, and some linear algebra over arbitrary fields. Readers may use "older" portions of these chapters to refresh their memory of this material (and also to see my notational choices); on the other hand, these chapters can also serve as a guide for learning what may have been omitted from an earlier course (complete proofs can be found in A First Course in Abstract Algebra). This format gives more freedom to an instructor, for there is a variety of choices for the starting point of a course of lectures, depending on what best fits the backgrounds of the students in a class. I expect that most instructors would begin a course somewhere in the middle of Chapter 2 and, afterwards, would continue from some point in the middle of Chapter 3. Finally, this format is convenient for the author, because it allows me to refer back to these earlier results in the midst of a discussion or a proof. Proofs in subsequent chapters are complete and are not sketched.
I have tried to write clear and complete proofs, omitting only those parts that are truly routine; thus, it is not necessary for an instructor to expound every detail in lectures, for students should be able to read the text.
When I was a student, Birkhoff and Mac Lane's A Survey of Modern Algebra was the text for my first algebra course, and van der Waerden's Modern Algebra was the text for my second course. Both are excellent books (I have called this book Advanced Modern Algebra in homage to them), but times have changed since their first appearance: Birkhoff and Mac Lane's book first appeared in 1941, and van der Waerden's book first appeared in 1930. There are today major directions that either did not exist over 60 years ago, or that were not then recognized to be so important. These new directions involve algebraic geometry, computers; homology, and representations (A Survey of Modern Algebra has been rewritten as Mac Lane-Birkhoff, Algebra, Macmillan, New York, 1967, and this version introduces categorical methods; category theory emerged from algebraic topology, but was then used by Grothendieck to revolutionize algebraic geometry).
Here is a more detailed account of the later chapters of this book.
Chapter 4 discusses fields, beginning with an introduction to Galois theory, the interrelationship between rings and groups. We prove the insolvability of the general polynomial of degree 5, the fundamental theorem of Galois theory, and applications, such as a proof of the fundamental theorem of algebra, and Galois's theorem that a polynomial over a field of characteristic 0 is solvable by radicals if and only if its Galois group is a solvable group.
Chapter 6 introduces prime and maximal ideals in commutative rings; Gauss's theorem that R x is a UFD when R is a UFD; Hilbert's basis theorem, applications of Zorn's lemma to commutative algebra (a proof of the equivalence of Zorn's lemma and the axiom of choice is in the appendix), inseparability, transcendence bases, Lüroth's theorem, affine varieties, including a proof of the Nullstellensatz for uncountable algebraically closed fields (the full Nullstellensatz, for varieties over arbitrary algebraically closed fields, is proved in Chapter 11); primary decomposition; Gröbner bases. Chapters 5 and 6 overlap two chapters of A First Course in Abstract Algebra, but these chapters are not covered in most undergraduate courses.
Chapter 8 introduces noncommutative rings, proving Wedderburn's theorem that finite division rings are commutative, as well as the Wedderburn-Artin theorem classifying semisimple rings. Modules over noncommutative rings are discussed, along with tensor products, flat modules, and bilinear forms. We also introduce character theory, using it to prove Burnside's theorem that finite groups of order pmqn are solvable. We then introduce multiply transitive groups and Frobenius groups, and we prove that Frobenius kernels are normal subgroups of Frobenius groups.
Chapter 9 considers finitely generated modules over PIDs (generalizing earlier theorems about finite abelian groups), and then goes on to apply these results to rational, Jordan, and Smith canonical forms for matrices over a field (the Smith normal form enables one to compute elementary divisors of a matrix). We also classify projective, injective, and flat modules over PIDs. A discussion of graded k-algebras, for k a commutative ring, leads to tensor algebras, central simple algebras and the Brauer group, exterior algebra (including Grassman algebras and the binomial theorem), determinants, differential forms, and an introduction to Lie algebra.
Chapter 10 introduces homological methods,beginning with semidirect products and the extension problem for groups. We then present Schreier's solution of the extension problem using factor sets, culminating in the Schur-Zassenhaus lemma. This is followed by axioms characterizing Tor and Ext (existence of these functors is proved with derived functors), some cohomology of groups, a bit of crossed product algebras, and an introduction to spectral sequences.
Chapter 11 returns to commutative rings, discussing localization, integral extensions, the general Nullstellensatz (using Jacobson rings), Dedekind rings, homological dimensions, the theorem of Serre characterizing regular local rings as those noetherian local rings of finite global dimension, the theorem of Auslander and Buchsbaum that regular local rings are UFDs.
Each generation should survey algebra to make it serve the present time |
Students solve differential equations. In this differential equations lesson, students use their TI-89 calculator to explore slope fields and find solutions to a differential equation. They graph their solutionsStudents use their TI-89 calculator to compute derivatives and anti-derivatives. In this differential equation lesson, students follow detailed directions to complete one table of derivative/anti-derivative values. They compute the anti-derivative of one equation and find the derivative of one equations.
Twelfth graders solve problems using differential equations. In this Calculus lesson plan, 12th graders analyze data regarding the spread of a flu virus. Students use the symbolic capacity of the TI-89 to develop a model and analyze the spread of the disease.
Students explore how to graph differential equations using a TI calculator. In this math instructional activity, students solve systems of equations using the calculator. Students explore graphing and use it to interpret experimental data.
For this differential equations worksheet, students solve systems of simultaneous differential equations using linear algebra. This six-page worksheet contains approximately six problems, with explanations and examples.
Twelfth graders investigate differential equations. In this calculus lesson, 12th graders are presented with a step-by-step illustrated review of the process used in solving differential equations and an application problem. Students solve differential equations and application of differential equations.
Students identify and familiarize themself with the features and capabilities of the TI-92 Plus calculator. They also find symbolic solutions of differential
equations and general solutions or to find particular solutions of initial-value and boundary-value problems. Finally, students use TRACE to find numerical values for this phase-plane graph differential equations and slope fields. In this differential equations and slope fields lesson, students determine how much time can pass before a cup of coffee is safe to drink. Students use a differential equation to solve the problem algebraically. Students create a slope field to represent the time at which it is safe to drink the coffee.
Twelfth graders investigate exponential decay. In this Calculus lesson, 12th graders explore Newton's Law of cooling which can be modeled by a differential equation. Students use the model to solve a murder as they examine the temperature of a body to determine time of death.
Students follow detailed instructions for using their TI-86 graphing calculator to find solutions to differential equations. In this lesson plan, students learn to use their graphing calculator to solve 12 differential equations.
In this methods of applied mathematics worksheet, students solve 5 various types of problems that relate to variational calculus equations. First, they determine a second order differential equation for the geodesic. Then, students write down Euler Lagrange equations for 2 dependent variables, and then determine a system of first order differential equations describing motion of an object.
In this calculus learning exercise, students integrate various functions, find the sum of a series, and solve differential equations. There are 16 questions including multiple choice and free response.
Investigate differential equations with your class. They use the TI-89 to explore differential equations analytically, graphically, and numerically as the examine the relationships between each of the three approaches.
Differential Equations |
GraphSight Junior Desciption:
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GraphSight is a feature-rich comprehensive 2D math graphing utility with easy navigation, perfectly suited for use by high-school an college math students. The program is capable of plotting Cartesian, polar, table defined, as well as specialty...
JFDraw is a pure Java based graphics application and library package. JFDraw used a little features of Java2D, and expanded a lot of graph routines for more complex vector graph processing. You can run JFDraw under any operating systems that suport...
3DMath Explorer is a computer program that pilots 2D and 3D graphs of mathematical functions and curves in unlimited graphing space. It has many useful feature such as 3D curve ploting in real time, perspective drawing, graph scaling (zooming), active...
Plotting functions (usual and parametric) with more possibilities.Differentiation of any order (with simplification). Construction of tangents to the graph. The simple and clear interface with the detailed documentation and examples of work. The...
It can compute and plot a very high amount of functions, including many probability functions and is fairly good configurable.
A maximum number of three graphs can be displayed in one image.
Installation
Upload the files to the webserver and point...
This software utility can plot regular or parametric functions, in Cartesian or polar coordinate systems, and is capable to evaluate the roots, minimum and maximum points as well as the first derivative and the integral value of regular functions. Easy...
Visual Fractal is an interesting grapher to create a graph of fractal. With this tool, you can use Newton's method to solve a complex equation and show the fractal graph in the plot area. Mandelbrot set and Julia set can also be plotted. Graphs created...
Graph is the program for those people who draw different graphs of mathematical functions. It can be very useful for students, and maybe for adults either. It calculates the given expression and then draws its graph. This new version is more stable,... |
Grasping Graphing Anne Patterson Active involvement and infusion of mathematics into familiar, everyday experience are essential elements in challenging students to engage in true thinking. The concept of graphing is a natural vehicle for achieving this objective.
Making the Black Box Transparent Lawrence Lesser Focusing on a common example in technology-rich mathematics curricula, namely, the line of best fit, followed by a discussion of two additional examples—interpolating polynomials and complete graphs. In each case, connections between theory and technology do not appear to be as widely known and used as they could be.
Astronomical Math Robert Ryden The NCTM's Standards stress the importance of connections among various branches of mathematics and between mathematics and other disciplines; the astronomy problems that follow combine algebra, geometry, trigonometry, data analysis, and a bit of physics. My geometry and algebra students have seen most of these problems and could understand them. They have also been able to experience making distance measurements themselves by using the method of parallax, which is explained in this article.
Geometry's Giant Leap Alan Brown A major goal of the project was for the students to use this new technology in studying geometry. Each student group compiled its project report on a computer word processor with appropriate visual examples from the calculator.
Triangular Numbers in Problem Solving Walter Szetela A surprising number of mathematics problems have solutions that involve triangular numbers. This article gives some of these problems, as well as many of their interesting extensions. It also suggests other extensions for further investigation.
______ and the Volume of a Cone Cedric Greive The first part of this article derives the volume of a right circular cone, and the second part describes a teaching approach that can make this exercise a valuable problem-solving activity for upper secondary students.
The National Council of Teachers of Mathematics is the 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. |
Authors Wayne Winston and Munirpallam Venkataramanan emphasize model-formulation and model-building skills as well as interpretation of computer software output. Focusing on deterministic models, this book is designed for the first half of an operations research sequence. A subset of Winston's best-selling OPERATIONS RESEARCH, INTRODUCTION TO MATHEMATICAL PROGRAMMING offers self-contained chapters that make it flexible enough for one- or two-semester courses ranging from advanced beginning to intermediate in level. The book has a strong computer orientation and emphasizes model-formulation and model-building skills. Every topic includes a corresponding computer-based modeling and solution method and every chapter presents the software tools needed to solve realistic problems. LINDO, LINGO, and Premium Solver for Education software packages are available with |
Find a Novato CalculusMany of the concepts in it apply to real life and are more intuitive than a lot of students believe. That |
Pupils, with the assistance of their TI-84 Plus / TI-83 Plus calculators, distinguish meanings from right, left and symmetric difference quotients that include rate of change and graphical interpretations. They utilize symmetric difference quotients to approximate instantaneous rate of changes.
Students explore the local linearity of several functions at different points. They investigate the local linearity given a function and a point and then connect that notion with the function's differentiability at that point.
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.
Here is one lesson on interpreting algebraic expressions. Pupils evaluate expressions given an input, play a game in cooperative groups, match algebraic expressions to their quantity in context, and participate in a group discussion. The plan concretely connects the abstract expressions of Algebra to real-life situations. Your class will be hooked with the mention of chocolateMathematicians use a symmetric secant line to prove the derivative at a point. In this trigonometry lesson, students create secant lines on the navigator to analyze the derivative. They move the lines around and make observations.
Students explore the concept of related rates. In this related rates lesson, students collect data about the position of a ball as it is dropped and the shadow of the ball. Students calculate the rates of the ball position v. time and shadow v. time. Students use proportions and derivatives in determining the related rates between position, time, and the shadow of the dropped ball.
Students develop strategies for solving problem situations. In this "actions" for problem situations lesson, students examine each operation (addition, subtraction, multiplication, and division) for further understanding. Then by using act it out, mental images, making models, and drawing pictures to represent "actions" in problem situations, students determine the operation needed for solution.
Learners calculate the velocity of object as they land or take off. In this calculus lesson, students are taught how to find the velocity based on the derivative. They graph a picture the represent the scenario and solve for the velocity.
High schoolers investigate logistic models by making a scatter plot of internet phone users over 5 years. They find a logistic model that fits their data and then discuss what the instantaneous rate of change means in the context of the problem. Very relevant and applicable!
In this partial derivatives worksheet, students complete one word problem by finding the (x,y) coordinates of a point when it moves parallel to one axis. When given a function, they find six partial derivatives. Students solve four multivariable derivatives. They prove that partial differentiation can be easier than ordinary differentiationLearners explore the concept of derivatives. For this derivatives lesson, students find the derivatives of the cosine function on the Ti-Nspire. Learners use the definition of derivative to find the derivative of the cosine function as h approaches zero. Students compare their answer with the derivative through differentiation.
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 name and sketch numerical expressions. In this order of operation lesson, students add, subtract, multiply and divide using the correct order of operation. They perform four specific calculations for their motivation lesson.
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.
Virtual math manipulatives are tools designed to help pupils understand mathematical concepts. Sixth graders will use a manipulative called Laser Beams to practice estimating to find sums, differences, quotients, and products. This is fine as a way to practice a skill, but it is inadequate as a mode of teaching.
Students explore the slope of a line. In this Pre-Algebra/Algebra I activity, students investigate the coordinates of points that are horizontal or vertical and the slope of the line going through those points. Students also explore positive and negative slopes. Ti-nspire handheld required. |
Algebra I Training [Mega] (Leído 48 veces)
Algebra I is one of the most critical courses that students take in high school. Not only does it introduce them to a powerful reasoning tool with applications in many different careers, but algebra is the gateway to higher education. Students who do well in algebra are better prepared for college entrance exams and for college in general, since algebra teaches them how to solve problems and think abstractly-skills that pay off no matter what major they pursue.
For other news, visit my profile every day! To Unzip the files use 7zip or WinRar. I recommend to download as fast as you can or you will lose file you need ( Links dead because of Copyright Infringement ) |
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Overview
Designed for a one-semester beginning or introductory algebra course, this successful worktext is appropriate for lecture, learning center, laboratory, or self-paced courses.Maintaining its hallmark features of carefully detailed explanations and accessible pedagogy, this edition of Beginning Algebra also addresses the AMATYC and NCTM Standards. In addition to the changes incorporated into the text, a new integrated video series and multimedia tutorial program are also available |
Q&A: What other math courses should I take before Calculus?
What other math courses should I take before Calculus? Calculus I is a required course for the major I want in college; aerospace engineering. I am planning to take other math courses online at BYU if it would be best to. But I just need to know what other math classes are recommended to better understand Calculus I?
Suggestion by Lewis G you've taken pretty much everthing. i'd say pre-calculus or trigonmetry if they offer it at your school, but even know i'd say you're prepared for calculus. honestly its not that hard though so don't stress about it.
Suggestion by lovinit usually, before taking calculus, your pre-req is usually college algebra. you've taken all the developmental courses leading up to college algebra, but have not taken it yet, and you may have to in order to get in to calculus. check your college's aerospace engineering degree requirements- it usually spells everything out for you. good luck!
Know better? Leave your own answer in the comments!
Is finite math hard for someone who only knows algebra? I have to take developmental courses in basic math & pre algebra. Then my choices for credit are Finite math or pre calculus algebra. Now, when I transfer to the 4 year college (Im at a cc right now) Pre calculus algebra wont transfer. Only finite math will. So will Finite math be hard for me if I never took calculus? I dont want to take the pre calculus class if it wont transfer.
Suggestion by MsMath You do not need calculus to take finite math.
Some topics in finite math are algebra, matrices, probability, and linear programming.
Give your answer to this question below!
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Mathletics is a remarkably entertaining book that shows readers how to use simple mathematics to analyze a range of statistical and probability-related questions in professional baseball, basketball, and football, and in sports gambling. How does professional baseball evaluate hitters? Is a singles hitter like Wade Boggs more valuable than a power hitter like David Ortiz? Should NFL teams pass or run more often on first downs? Could professional basketball have used statistics to expose the crooked referee Tim Donaghy? Does money buy performance in professional sports? In Mathletics, Wayne Winston describes the mathematical methods that top coaches and managers use to evaluate players and improve team performance, and gives math enthusiasts the practical tools they need to enhance their understanding and enjoyment of their favorite sports--and maybe even gain the outside edge to winning bets. Mathletics blends fun math problems with sports stories of actual games, teams, and players, along with personal anecdotes from Winston's work as a sports consultant. Winston uses easy-to-read tables and illustrations to illuminate the techniques and ideas he presents, and all the necessary math concepts--such as arithmetic, basic statistics and probability, and Monte Carlo simulations--are fully explained in the examples. After reading Mathletics, you will understand why baseball teams should almost never bunt, why football overtime systems are unfair, why points, rebounds, and assists aren't enough to determine who's the NBA's best player--and much, much more. In a new epilogue, Winston discusses the stats and numerical analysis behind some recent sporting events, such as how the Dallas Mavericks used analytics to become the 2011 NBA champions.
Master the business modeling and analysis techniques that help you transform data into bottom-line results. For more than a decade, Wayne Winston has been teaching corporate clients and MBA students the most effective ways to use Excel to solve business problems and make better decisions. Now this award-winning educator shares the best of his expertise in this hands-on, scenario-focused guide--fully updated for Excel 2010!
Use Excel to solve real business problems--and sharpen your edge!
Model investment risks and returns
Analyze your sales team's effectiveness
Create best, worst, and most-likely case scenarios
Compare lease vs. buy, and calculate loan terms
See how price, advertising, and seasonality affect sales
Manage inventory with precision
Quantify the value of customer loyalty
Calculate your break-even number and ROI
Maximize scheduling efficiency
Express "home-field advantage" in real numbers
Project company growth, predict election results, and more!
Plus--introduce yourself to PowerPivot for Excel
Your companion web content includes:
Downloadable eBook
Hundreds of scenario-based practice problems
All the book's sample files--plus customizable templates
Customer Service Note: We are sorry for the inconvenience, but the code for accessing the eBook version of this title was accidentally left out of the first printing. However, the code is available for buyers of the first printing by contacting O'Reilly Media, the official distributor for Microsoft Press books, at mspbooksupport@oreilly.com or 800-889-8969. All subsequent printings include the access code and instructions inside the book.
Master business modeling and analysis techniques with Microsoft Excel 2013, and transform data into bottom-line results. Written by award-winning educator Wayne Winston, this hands-on, scenario-focused guide shows you how to use the latest Excel tools to integrate data from multiple tables--and how to effectively build a relational data source inside an Excel workbook.
Solve real business problems with Excel--and sharpen your edge
Summarize data with PivotTables and Descriptive Statistics
Explore new trends in predictive and prescriptive analytics
Use Excel Trend Curves, multiple regression, and exponential smoothing
Master advanced Excel functions such as OFFSET and INDIRECT
Delve into key financial, statistical, and time functions
Make your charts more effective with the Power View tool
Tame complex optimization problems with Excel Solver
Run Monte Carlo simulations on stock prices and bidding models
Apply important modeling tools such as the Inquire add-in this award-winning educator shares the best of his classroom experience in this practical, business-focused guide. Each chapter advances your data analysis and modeling expertise using real-world examples and learn-by-doing exercises. You also get all the book's problem-and-solution files on CD--for all the practice you need to solve complex problems and work smarter with Excel.
Learn how to solve real business problems with Excel!
Create best, worst, and most-likely scenarios for sales
Calculate how long it would take to recoup a project's startup costs
Plan personal finances, such as computing loan terms or saving for retirement
Estimate a product's demand curve
Simulate stock performance over a year
Determine which product mix will yield the greatest profits
Interpret the effects of price and advertising on sales
Assign a dollar value to customer loyalty
Manage inventory and order quantities with precision
Create customer service queues with short wait times
Estimate the probabilities of equipment failure
Model business uncertainties
Get new perspectives on data with PivotTable dynamic views
Help predict quarterly revenue, outcomes of sporting events, presidential elections, and more!
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Practice files for all the book's exercises
Solutions for problem setsMaster the analysis and business modeling techniques that help you transform your data into bottom-line results. Award-winning business professor and corporate consultant Wayne Winston shares the best of his real-world experience in this practical guide--now updated for Excel 2007. Use Wayne's proven practices and hands-on exercises to help you work smarter, make better decisions, and gain the competitive edge.
Solve real-world business problems with Excel 2007!
Maximize profits--determine NPV, optimize your product mix, calculate ROI
Create best, worst, and most-likely case scenarios for sales
Analyze investment performance and help minimize risk
Track your personal finances, calculate loan terms, and plan for retirement
Use trend and seasonality to forecast revenue
Estimate a product's demand curve and manage inventory with precision Interpret the effects of price and advertising on sales
Assign a dollar value to customer loyalty
Solve work scheduling problems and shorten wait times for customer service queues
PLUS--predict outcomes of sporting events, presidential elections, and more!
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The print version of this book ships with a CD or DVD. For those customers purchasing one of the digital formats in which this book is available, we are pleased to |
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Math Placement Exam
Regardless of your major, all students are required to take a sequence of mathematics courses. As part of the orientation process, you will take a placement exam to determine what level of math courses you should enroll in.
The placement test covers a wide variety of skills from both algebra and trigonometry, including, but not limited to:
Working with numbers and expressions in the form of fractions, exponents, and logarithms
Reading graphs and tables, and plotting functions in the xy-plane
Finding compositions and inverses of functions
Solving word problems
Trigonometry
Evaluating trigonometric functions for common angles
Solving trigonometric equations
Plotting basic trigonometric functions
Working with trigonometric identities
Please note: the use of calculators and cell phones is not permitted during the diagnostic exam.
Students whose performance on this test indicates proficiency in these skills will be placed in the appropriate calculus course for the discipline in the fall. In order to prepare for this exam, we recommend that you review the topics listed above and practice doing some examples without the use of your calculator. Some useful online sites to refresh your knowledge are: |
Introduction to the theory of sets by Josef Breuer(
Book
) 3
editions published
between
1958
and
1964
in
English and German
and held by
5 WorldCat member
libraries
worldwide
Set theory permeates much of contemporary mathematical thought. This text for undergraduates offers a natural introduction, developing the subject through observations of the physical world. Its progressive development leads from finite sets to cardinal numbers, infinite cardinals, and ordinals. Exercises appear throughout the text, with answers at the end. 1958 edition |
Books on Mathematics > Algebra > Linear
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This volume presents a fairly self-contained theory of certain singular coverings of toposes, including branched coverings. This is a field that should be of interest to topologists working in knot theory, as well as also to certain categorists. An unusual feature which distinguishes this book from classical treatments of the... more |
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The 5 Elements of Effective Thinkingpresents By using the straightforward and thought-provoking techniques inThe 5 Elements of Effective Thinking, you will regularly find imaginative solutions to difficult challenges, and you will discover new ways of looking at your world and yourself--revealing previously hidden opportunities. The book offers real-life stories, explicit action items, and concrete methods that allow you to attain a deeper understanding of any issue, exploit the power of failure as a step toward success, develop a habit of creating probing questions, see the world of ideas as an ever-flowing stream of thought, and embrace the uplifting reality that we are all capable of change. No matter who you are, the practical mind-sets introduced in the book will empower you to realize any goal in a more creative, intelligent, and effective manner. Filled with engaging examples that unlock truths about thinking in every walk of life,The 5 Elements of Effective Thinkingis written for all who want to reach their fullest potential--including students, parents, teachers, businesspeople, professionals, athletes, artists, leaders, and lifelong learners. Whenever you are stuck, need a new idea, or want to learn and grow,The 5 Elements of Effective Thinkingwill inspire and guide you on your way.
Make mathematics fun and satisfying for everyone Math can be a living source of powerful ideas that transcend mathematics; a window into mind-opening philosophical concepts such as infinity, fourth dimensions, chaos, and fractals; and a practical training ground for developing skills in analysis, reasoning, and thought if you have the right approach and the right guide. The Heart of Mathematics: An Invitation to Effective Thinking, now in its third edition, transforms mathematics into an engaging, relevant experience even for the most math-phobic student. Infusing this book with humor and enthusiasm, Edward B. Burger and Michael Starbird both recipients of the Mathematical Association of America's foremost national teaching award and countless state, regional, and campus-wide teaching honors introduce students to the most important and interesting ideas in mathematics while inspiring them to actively engage in mathematical thinking. Richer and more rewarding than ever, this new edition features: An emphasis on mathematical methods of investigation Visualization techniques that make key concepts easier to understand Accessible, friendly writing style that encourages critical thinking "Life Lessons"-effective methods of thinking that students will retain and apply beyond the classroom End of section Mindscape activities for the development of application, problem-solving, and argumentation skills |
This course is primarily for liberal arts and education majors, and emphasizes mathematical systems and reasoning. Course content includes sets, symbolic logic, and elementary probability and such optional topics as basic statistics, game theory, or linear programming.
VII. Required Course Content and Direction
Learning Goals:
Course Specific
The student will be able to:
analyze, represent, and solve elementary problems in logic, set theory and probability.
recognize and apply the characteristics of a mathematical structure.
analyze and apply the concepts and principles of mathematics in varying situations.
Category III: Critical Thinking and Problem Solving: The student will be able to reason from what they know to form new knowledge, draw conclusions, solve problems, explain, decide, and/or predict (Inductive and/or Deductive Reasoning Skills).
The instructor may elect to cover logic, set theory, or probability in more depth or discuss some optional topics, such as game theory, statistics, or linear programming.
Assessment Methods for Core Learning Goals:
All Core Critical Thinking and Problem Solving, College Level Mathematics or Science, and Discipline-Specific Course Objectives will be assessed as follows:
The student will apply mathematical concepts and principles to identify and solve problems presented through informal assessment, such as oral communication among students and between teacher and students and, for the core, formal written assessment using open-ended questions reflecting theoretical and applied situations.
Reference, Resource, or Learning Materials to be used by Students:
Departmentally selected textbook. Details provided by the instructor of each course section. See Course Format.
VIII. Teaching Methods Employed
Use of lecture, recitation, problem solving, and class discussion as appropriate. |
gebra Survival Guide Workbook
Following on the success of the Algebra Survival Guide, the Algebra Survival Guide Workbook presents thousands of practice problems (and all answers) ...Show synopsisFollowing on the success of the Algebra Survival Guide, the Algebra Survival Guide Workbook presents thousands of practice problems (and all answers) to help children master algebra. The problems are keyed to the pages of the Algebra Survival Guide, so that children can find detailed instructions and then work the sets. Each problem set focuses like a laser beam on a particular algebra skill, then offers ample practice problems. Answers are conveniently displayed in the back. This book is for parents of schooled students, homeschooling parents and teachers. Parents of schooled children find that the problems give their children a leg up for mastering all skills presented in the classroom. Homeschoolers use the Workbook - in conjunction with the Guide - as a complete Algebra 1 curriculum. Teachers use the workbook's problem sets to help children sharpen specific skills - or they can use the pages as tests or quizzes on specific topics. Like the Algebra Survival Guide, the Workbook is adorned with beautiful art and sports a stylish, teen-friendly design |
MATH CLUB @ WMU
Mathematics Organizations
Mathematical Associations For Students
The diversity and vitality of the mathematical community is expressed by the wide variety
of mathematics organizations. It's never too early to get involved!
Below are a few pages aimed at the needs of students, especially undergraduates:
Founded in 1888 to further the interests of mathematical research and scholarship,
the AMS serves the national and international community through its publications,
meetings, advocacy and other programs.
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.
SIAM fosters the development of applied mathematical and computational methodologies
needed in these various application areas. Through publications, research, and community,
the mission of SIAM is to build cooperation between mathematics and the worlds of science and technology. |
Book Description: This textbook provides thorough coverage of all traditional Algebra 2 concepts and skills. At the beginning of the course, the lessons review and extend key Algebra 1 concepts and skills |
TheHandbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within thethemes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, thehandbook is enhanced by more than 150 illustrations and an extended bibliography.
A spectacle of magnificent proportions, Kon Ichikawa's Tokyo Olympiad ranks among the greatest documents of sport ever committed to film. Utilizing glorious widescreen cinematography, Ichikawa examines the beauty and rich drama on display at the 1964 Summer Games in Tokyo, creating a catalogue of extraordinary observations that range from the expansive to the intimate. The glory, despair, passion, and suffering of Olympic competition are rendered with lyricism and technical mastery, culminating in an inspiring testament to the beauty of the human body and the strength of the human spirit.
Presenting mathematical prerequisites in summary tables, this book explains fundamental techniques of mathematical modeling processes essential to the food industry. The author focuses on providing an in-depth understanding of modeling techniques, rather than the finer mathematical points.
Because of the numerous applications involved in this field, thetheory of special functions is under permanent development, especially regarding the requirements for modern computer algebra methods. TheHandbook of Special Functions provides in-depth coverage of special functions, which are used to help solve many of the most difficult problems in physics, engineering, and mathematics. The book presents new results along with well-known formulas used in many of the most important mathematical methods in order to solve a wide variety of problems. It also discusses formulas of connection and conversion for elementary and special functions, such as hypergeometric and Meijer G functions.
Image processing is fast becoming a valuable tool for analyzing multidimensional data in all areas of natural science. Since the publication of the best-selling first edition of this handbook, the field of image processing has matured in many of its aspects from ad hoc, empirical approaches to a sound science based on established mathematical and physical principles. |
All Global Mindset courses are self-paced free training courses that are divided into short lessons with slide examples to illustrate issues clearly and in real-world settings. Plenty of practice situations, drag-and-drop interactive choices, and feedback allow you to engage the concepts and remain fairly active throughout.
This free course is made possible by the support of the following free retail math training sponsors:
I learned a lot of the basics in a relevant manner. The material had examples that were easy to relate to and made working through the course very smooth. I feel prepared after completing it.
However, I found a mistake in the math in the "Maintained Markup" section. The course equation says to use (1 - %markup/100) but in the example, they use .45 as %markup instead of 45. In the course's math, that would be (1 - .45/100) or (1 - .0045) which equals .9955 but they answer they were looking for was .55.
Found the course to be very helpful. When the course tells you the correct answer to the problems, I would have preferred if they had explained how they got the answer they came to. THis would have helped me determine how to go about coming to that conclusion. |
Combinations of Operations with Fractions
Summary: This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses combinations of operations with fractions. By the end of the module students should gain a further understanding of the order of operations |
Working in tandem with the Harvard-Smithsonian Center for Astrophysics, the team of experts at the Annenberg Media Foundation has created this excellent instructional series. In this eight-part program, educators can...
Wolfram Research, the maker of the popular software Mathematica, recently added a comprehensive database of mathematical functions to its Web site. There are tens of thousands of formulas that can be browsed...
An experiment in the use of the World Wide Web as a teaching aid for a course in multivariable calculus, using Maple as a symbolic calculator. Topics include Review of Calculus 1; Vector Geometry; Geometric Algebra;...
Discussing functions can be a tricky endeavor, but having a handy interactive way to talk about functions can relieve a great deal of stress. As part of the Mathematical Sciences Digital Library, this Functions Grapher...
Zona Land, created by Ed Zobel, is a science and mathematics resource site for students and teachers. The site illustrates mathematical and physical principles by the use of Java applets and VRML simulations. The... |
West Bridgewater PhysicsIf algebra is the foundation of mathematics, then calculus is the foundation of physics, statistics, and applied mathematics. It is not an exaggeration to say that our modern world exists thanks to Liebnitz and Newton, who separately invented calculus at the same time. Despite its seminal importance in the modern world, calculus introduces only one truly new concept: the limit. |
First work through the recommended practice problems listed in the following table from the 7thedition of DiscreteMathematicsandItsApplications by K.H. Rosen. You do not need to hand these ... 1.2 Applications of Propositional Logic 1, 3, 5 ... functions and identify its domain.
First work through the recommended practice problems listed in the following table from the 7thedition of DiscreteMathematicsandItsApplications by K.H. Rosen. You do not need to hand these in. Once you have completed these, ...
Required Text: Rosen, DiscreteMathematicsanditsApplications, 7thEdition Learning Outcomes ... The student will gain an understanding of functions on discrete domains and ranges and specifically be introduced to discrete functions such as floor, ...
Materials: The textbook is DiscreteMathematicsanditsApplications (7thedition), by Kenneth H. Rosen, published by McGraw-Hill. We will be covering portions of chapters 1, 2, 4, 5, 6, and 9. Information about the course will be posted on the course page at learn.ou.edu.
Some of the exercises for this tutorial are taken from Chapter 1 of the book: Kenneth Rosen, DiscreteMathematicsanditsApplications, 7thEdition, McGraw-Hill, 2012. For the first two exercises, assume you are on an island inhabited only by knights and knaves, where |
A textbook that covers the traditional topics studied in a modern prealgebra course, as well as topics of estimation,...
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A textbook that covers the traditional topics studied in a modern prealgebra course, as well as topics of estimation, elementary analytic geometry, and introductory algebra. It is intended for students who (1) have had a previous course in prealgebra, (2) wish to meet the prerequisite of a higher level course such as elementary algebra, and (3) need to review fundamental mathematical concepts and techniques
This tutorial goes through the three different ways that we learn how to graph linear equations. This will allow student to...
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This tutorial goes through the three different ways that we learn how to graph linear equations. This will allow student to review the process for each as well as provide the student with a short quiz at the end of the tutorial
You will cover set notations, operations with fractions, real numbers and their properties, order of operations, linear...
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You will cover set notations, operations with fractions, real numbers and their properties, order of operations, linear equations, inequalities, formulas, absolute value equations and inequalities, graphs, systems of linear equations and inequalities, polynomials, exponents, radicals, factoring, rational expressions, quadratic equations, operations with functions, solving and graphing quadratic, rational, exponential, and logarithmic equations, and solving quadratic and rational inequalities andIntermediate Algebra carefully builds on the basics learned in Elementary Algebra and introduces the more advanced topics,...
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Intermediate Algebra carefully builds on the basics learned in Elementary Algebra and introduces the more advanced topics, enhancing it all with with the modern amenities that only a free online text can deliver.It is essential to lay a solid foundation in mathematics if a student is to be competitive in today's global market. The importance of algebra, in particular, cannot be overstated, as it is the basis of all mathematical modeling used in applications found in all disciplines. Traditionally, the study of algebra is separated into a two parts, Elementary and Intermediate Algebra. This textbook by John Redden, Intermediate Algebra, is the second part. Written in a clear and concise manner, it carefully builds on the basics learned in Elementary Algebra and introduces the more advanced topics required for further study in applications found in most disciplines. Used as a standalone textbook, Intermediate Algebra offers plenty of review as well as something new to engage the student in each chapter. Written as a blend of the traditional and graphical approaches to the subject, this textbook introduces functions early and stresses the geometry behind the algebra. While CAS independent, a standard scientific calculator will be required and further research using technology is encouraged. Intermediate Algebra is written from the ground up in an open and modular format, allowing the instructor to modify it and leverage their individual expertise as a means to maximize the student experience and success. A more modernized element, embedded video examples, are present, but the importance of practice with pencil and paper is consistently stressed. Therefore, this text respects the traditional approaches to algebra pedagogy while enhancing it with the technology available today. The importance of Algebra cannot be overstated; it is the basis for all mathematical modeling used in all disciplines. After completing a course sequence based on Elementary and Intermediate Algebra, students will be on firm footing for success in higher-level studies at the college level.
This site provides a brief textual overview of the field of cryptography and related issues including popular techniques,...
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This site provides a brief textual overview of the field of cryptography and related issues including popular techniques, applications and standards. It is part of a larger body of information provided by RSA Laboratories, a division of RSA Security.
From the preface: "This is a book on linear algebra and matrix theory. While it is self-contained, it will work best for...
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From the preface: "This is a book on linear algebra and matrix theory. While it is self-contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more analysis than this, however." A solutions manual to the exercises in the textbook is included. |
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This book gives a systematical presentation of stochastic approximation methods for models of American-type options with general pay-off functions for discrete time Markov price processes. It is the first volume of the comprehensive two volumes monograph. more...
This photocopy master book, which has proven extremely popular over the years, provides a range of 30+ problem solving activities using strategies such as: Developing logical thinking; Using number concepts to develop logical thinking; Logical reasoning; Developing visual imagery; and Pattern perception using number. more...
Photocopy Master book. Includes problem solving strategies such as Guess and Check, Act It Out, Make A Model, Look for a Pattern, Construct a Table and so on. These strategies are applied to a range of interesting problem situations. Children will enjoy the variety of characters that provide an amusing element to the serious business of solving mathematical... more...
Photocopy Master book. Students are required to utilise a range of problem
solving strategies in their approach to reaching solutions for these
interesting problems. Cool cartoon characters add a highly motivating element
to the process of working through the problems.
more...
New look versions of Pythagoras, Galileo and Archimedes are some of the
characters presented in cartoon form in this photocopy master book, lending a stimulating
element to problem solving. A variety of brain teasers is also included
for copying onto cards to make class sets.
more...
Sequential blackline master activities
in the area of geometry and spatial mathematics. Covers the major learning areas
such as identifying different types of angles, using a protractor to measure
angles, using known rules to calculate the size of angles and construction of
angles using either a compass or a protractor. more...
Learn how to easily do quick mental math calculations Speed Math for Kids is your guide to becoming a math genius--even if you have struggled with math in the past. Believe it or not, you have the ability to perform lightning quick calculations that will astonish your friends, family, and teachers. You'll be able to master your multiplication tables... more...
Bob Miller's fail-safe methodology helps students grasp basic math and pre-algebra All of the courses in the junior high, high school, and college mathematics curriculum require a thorough grounding in the fundamentals, principles, and techniques of basic math and pre-algebra, yet many students have difficulty grasping the necessary concepts.... more...
Everything you need to know to ace the math sections of the NEW SAT!... more... |
Non-Parametric Analyses A Step by Step Guide is the seventh and final volume from the series of Advanced Educational...
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Non-Parametric Analyses A Step by Step Guide is the seventh and finalThis is a free app
Collaborative Statistics was written by Barbara Illowsky and Susan Dean, faculty members at De Anza College in Cupertino,...
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Collaborative Statistics
This is a free online textbook offered by BookBoon.'Blast into Math! A fun and rigorous introduction to pure mathematics, is...
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This is a free online textbook offered by BookBoon.'Blast into Math! A fun and rigorous introduction to pure mathematics, is suitable for both students and a general audience interested in learning what pure mathematics is all about. Pure mathematics is presented in a friendly, accessible, and nonetheless rigorous style. Definitions, theorems, and proofs are accompanied by creative analogies and illustrations to convey the meaning and intuition behind the abstract math. The key to reading and understanding this book is doing the exercises. You don't need much background for the first few chapters, but the material builds upon itself, and if you don't do the exercises, eventually you'll have trouble understanding. The book begins by introducing fundamental concepts in logic and continues on to set theory and basic topics in number theory. The sixth chapter shows how we can change our mathematical perspective by writing numbers in bases other than the usual base 10. The last chapter introduces analysis. Readers will be both challenged and encouraged. A parallel is drawn between the process of working through the book and the process of mathematics research. If you read this book and do all the exercises, you will not only learn how to prove theorems, you'll also experience what mathematics research is like: exciting, challenging, and fun!' |
2Strong algebra skills are crucial to success in applied calculus. This text is designed to bolster these skills while students study applied calculus. As students make their way through the calculus course, this supplemental text shows them the relevant algebra topics and points out potential problem spots. the table of contents is organized so that the algebra topics are arranged in the order in which they are needed for applied calculus. |
hi, i need someone who understands any one of the topic below:
1) Introduction Real Functions and Graphs is a reminder of the principles underlying the sketching of graphs of functions and other curves.
2) Group Theory (A) Symmetry studies the symmetries of plane figures and solids, including the five 'Platonic solids', and leads to the definition of a group.
3) Linear Algebra Vectors and Conics is an introduction to vectors and to the properties of conic sections.
4) AnalysisMathematician, Statistician with interest in Arbitrage Required for project work for arbitrage network - must have experience in statistical analytics, and risk. Good hourly rates plus split of profits.
We have a large amount of items and you need be very good at understanding maths to do this
You will need to calculate costs for air shipping and container shipping, you add weight, then cubic meters and add price to what is most Monet weight or cube
Please reply and tell me how you fit this role and why you will be good at it |
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