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Casually looking through Sternberg's book, it looks not a thing like a regular Calculus book, but very much like a regular Analysis text (Pugh's), except it contains a lot of seemingly unrelated content, too. Seems like a lot of topics in these Calculus and Analysis books overlap.So, would you say Sternberg's Advanced Calculus book= Pugh's Analysis book? There is no clear distinction between rigorous calculus vs. analysis, except that the latter is a much broader topic, encompassing not just rigorous calculus but also functional analysis, measure theory, harmonic analysis, and so forth. If we restrict our attention to books covering primarily the topics associated with classical calculus: limits, continuity, differentiation, integration, series expansions and the like, then some will have analysis in the title and others will say calculus. But this does not imply anything about the level of sophistication. Loomis and Sternberg's Advanced Calculus is at least as challenging as Pugh's Real Mathematical Analysis or Rudin's Principles of Mathematical Analysis. I personally, and rather arbitrarily, consider a book to fall in the "calculus" category if it doesn't do much if any topology. Spivak's Calculus and Apostol's Calculus are the prime examples of this.
Unit Circle Approach A proven motivator for readers of diverse mathematical backgrounds, this book explores mathematics within the context of real life using ...Show synopsisA proven motivator for readers of diverse mathematical backgrounds, this book explores mathematics within the context of real life using understandable, realistic applications consistent with the abilities of most readers. Graphing techniques are emphasized, including a thorough discussion of polynomial, rational, exponential, and logarithmic functions and conics. Chapter topics include Functions and Their Graphs; Trigonometric Functions; Analytic Trigonometry; Analytic Geometry; Exponential and Logarithmic Functions; and more. For anyone interested in trigonometry.Hide synopsis Description:Good. Looseleaf. May include moderately worn cover, writing,...Good. Looseleaf. May include moderately worn cover, writing, markings or slight discoloration. SKU: 978032171710817108
King Saud University seeks to become a leader in educational and technological innovation, scientific discovery and creativity through fostering an atmosphere of intellectual inspiration and partnership for the prosperity of society. Contribution Description This activity is designed to help students gain a qualitative intuitive understanding of Fourier Analysis. It was developed to be used in a sophomore level modern physics course, after lecture instruction on atomic models. a sophomore level modern physics course. For more details about the course, please see: It is not as inquiry based as the guidelines recommend because the course requires computer grading, so the questions are very directed. ئاست Undergraduate - Intro, Undergraduate - Advanced Type Homework Subject فیزیا, بیرکاری Answers Included نا زوان English
Algebra II: Matrices Find study help on matrices for algebra II. Use the links below to select the specific area of matrices you're looking for help with. Each guide comes complete with an explanation, example problems, and practice problems with solutions to help you learn matrices for algebra II. Study Guides Introduction to Matrices You may think you know about the matrix; however, in algebra, the matrix is not another world where you can perform magical stunts and fight bad guys. In algebra, matrices are rectangular arrays of numbers. Look at the example ...
Hands-on Start to Mathematica: Methods to Get Started (Japanese) This is part 2 of an 8-part screencast series giving an overview of the benefits of Mathematica 8 for education, with a focus on different methods for getting started with Mathematica. Includes Japanese audio. Channels: Getting Started with Mathematica Mathematica 9 adds major computational areas and introduces a new interface paradigm—further expanding Mathematica's unrivaled base of algorithmic, knowledge, and interface capabilities. Get an overview of what's new in Mathematica 9 in this video. Mathematica's Image Assistant provides immediate access to common image processing tools, making it easy to interactively process images using point-and-click—all within the notebook environment. Get an overview of how to use the Image Assistant in this video. This is part 8 of an 8-part screencast series giving an overview of the benefits of Mathematica 8 for education, with a focus on building an example presentation complete with calculations, graphics, and data. This is part 2 of an 8-part screencast series giving an overview of the benefits of Mathematica 8 for education, with a focus on different methods for getting started with Mathematica. Includes Chinese translation. This is part 2 of an 8-part screencast series giving an overview of the benefits of Mathematica 8 for education, with a focus on different methods for getting started with Mathematica. Includes Japanese audio.
Math 150 (secs. 001&002), Spring 2013 Precalculus If you're having technical problems, email support@hawkeslearning.com or call 843.571.2825. Our Hawkes CourseID is LSUSPRC. If you're away from your home computer, you can visit hawkeslearning.com/LSUSPRC to find due dates, view your up-to-date grade, etc. Various problems, solutions, hints, and other stuff will show up below, as the semester progresses. Note (so you don't freak out) that some of the items below aren't discussed in our course until later in the semester. But it is more convenient for me to leave them here, and you might enjoy having a look at some of what's coming. [Re-posted Mar 29] For understanding graphs of sine and cosine functions (Section 6-4), here is a crude online quiz that generates sinusoidal curves, for testing your ability to write an equation of such a curve. [Posted Feb 10] Here are two demos concerning factored polynomials, each made a few years ago. If they sound like I'm talking to someone else, it is because I am; they were made following class discussions. If you are nice, I'll make a new one for you. Meanwhile, they have the main ideas we discussed in class. They are nearly identical, except that I use different functions, and do a few different kinds of things. POLYDEMO1POLYDEMO2 [Posted Feb 10] Here is some practice for you regarding simplification of combinations of intervals. Please try this out. INTERVAL QUIZZES Try this online quiz, "Trig-a-gnosis", for testing your understanding of the values of sines and cosines. No scores are generated, it is just for your own use. (You should also try the following: using graph paper, draw an angle θ in standard position, terminating at the point (x, y); guess the sine and cosine of θ, just by looking; measure the values of x, y, r and θ; compute the values of sin(θ) and cos(θ) from their definitions involving x, y, r; then use a calculator to check the values of sin(θ) and cos(θ) for comparison. When your guesses start to get good, you understand what sine and cosine mean.) Here is a homemade online multiple choice quiz regarding parabolas. This is practice to help you visualize lines given their equations in vertex form. Here is a similar quiz regarding power functions. A homemade online multiple choice quiz regarding straight lines. This is practice to help you visualize lines given their equations in slope-intercept form. (You need to get straight with lines. Straight lines will be a big part of EACH exam and you should have no illusions about that.) Here are some crude, homemade "webMathematica" generated quizzes on various topics. A quiz about straight lines. (There is no such thing as too much practice with these.) The author is also the Interim Chancellor (The Boss) at LSUS. Check out this Shreveport Times piece and then look at page 268 in your text! Check the Web for College Algebra or Precalculus tutorials and quizzes if you need to. You could start at the site below, but you'll probably need to dig around awhile before finding something you like. (No heavy surfing until you've done your homework.)
Week-Long Math Courses 1 - Meaningful Algebra using Technology Visual Algebra is a free research-based software platform which supports students from the early years of algebra learning to build solid foundations for their algebraic thinking and their manipulative skills. Built using TI-Nspire, but freely accessible online as well as on handheld and computer, this is a rich and powerful learning environment that offers students scaffolded support in using a range of computer-based tools and representations. Explore the ways in which this tool can change your algebra classroom at any level - and bring along your iPad or Android tablet! 2 - History of Mathematics: Algebra, Analytic Geometry and Calculus Leader: Jeff Ibbotson, Phillips Exeter Academy, Exeter, NH We will explore the invention of complex numbers, the soap opera behind the solution to the general cubic polynomial equation, the invention of analytic geometry and early aspects of the calculus. Fermat, Descartes, Cardano, Kepler and many other famous mathematicians will "join" us for chats on their life and times. If you are teaching precalculus or calculus and want to know some of the history behind the mathematics (and see some real lesser known "nuggets" of mathematics), this course is for you! 3 - Just A Bunch of Good Geometry Labs Leader: Dan Butler, Mounds View High School, Arden Hills, MN By the time students get to precalculus, a great deal of their geometry know-how has gone the way of the slide rule. Let's bring some excitement back into geometry through great problems and great explorations, and rediscover how geometry really lies at the heart of mathematics. 4 - Just Five Good Precalculus Labs Leader: Dan Butler, Mounds View High School, Arden Hills, MN Let's spice up our precalculus curriculum with some amazing labs. We will use Excel, the Geometer's Sketchpad, Geogebra, the TI-84, hands-on materials and anything else we decide to use to explore some of the concepts of precalculus through great problems and interesting constructions. We will also take some time to discuss what needs to be in a precalculus course in light of the current state mathematics education. 5 - The High School Classroom in the 21st Century While graphing calculators are not new to mathematics education, the ability to network them makes them even more valuable. In this course, participants will work with the TI-Nspire CX calculator (on loan) and TI Navigator to examine a series of problems from algebra, geometry, advanced algebra, and trigonometry. Participants will work with Vernier probes - temperature, motion, and microphone - to collect and analyze data. The TI Navigator wirelessly networks each student's calculator to a teacher computer allowing teachers to track progress, view student work, and provide instant feedback. 6 - GeoGebra for Beginners Learn how to use GeoGebra 4.2, a free and open source dynamic mathematics software program. GeoGebra is very easy to use, with a point and click interface. You and your students can quickly create interactive applets that illustrate concepts in all of the major high school mathematics curriculum areas - geometry, algebra, and calculus. This course will be geared towards users with no prior experience with GeoGebra, but participants who would like a refresher in the basics are also welcome. You will spend most of your time in this course building applets for use with your classes. 7 - GeoGebra - How to Use it in Precalculus and Calculus This course will focus on GeoGebra 4.2 in precalculus/calculus but will quickly cover some geometric constructions early in the week. GeoGebra is a free program that can perform geometric constructions, graph functions, create sliders, find derivatives and integrals and change everything dynamically. GeoGebra 4.2 has CAS (new) and enhanced statistics. Learn how to create html files that will be available to anyone with a browser. Participants can bring a laptop or use a provided classroom computer. Most of the class time will be spent creating GeoGebra applets which will be shared with all. 8 - Greatest Hits of Higher Mathematics Leader: Diana Davis, Brown University, Providence, RI This course will explore the most fascinating parts of the undergraduate math major or math graduate school curriculum: real analysis, algebra, topology, and number theory, each for one class period. The goal of the course is to dig into interesting problems, and think deeply about the nature of shapes and numbers. Only high school mathematics is required! 9 - Math Research Leader: Diana Davis, Brown University, Providence, RI In this course, we will do math research: We will work on solving a problem that no one knows the answer to, or stated differently, on understanding a system that no one else understands yet. It will be a geometric problem about a beam of light bouncing around in various tilings of the plane (contact me for specifics). Tools we may use include pencil and paper, computer programs, and group collaboration. We will write our results into a paper. No background is necessary, except for an inquiring and analytical mind! 10 - Moving Forward with Problem-Based Learning Leader: Carmel Schettino, Deerfield Academy, Deerfield, MA This is a great course for teachers who are interested in first-time learning how to integrate problem-based learning into their curriculum. Participants will discuss pedagogy, theory and student instruction using sample PBL problems from the classroom. Teachers will simulate the student process of discussion and use of prior knowledge through geometry, algebra, and trigonometry problems. Learn how to focus your class on student ideas, discourse, and reflection through problem solving while supporting student engagement and empowerment. Come get inspired to implement PBL in your classroom! 11 - Learning Mathematics through Problem Solving - Active Involvement for All Students Traditional mathematics lessons tend to be teacher-centered and targeted towards the average student. This course will provide strategies for actively engaging students of all abilities through the use of problems that allow multiple access points. The course will also have a focus on the use of differentiated instruction. Participants will explore a selection of rich problems that can be used in conjunction with a variety of curricula. 12 - Astronomy and Precalculus - A Match Made in the Heavens Where and when do you look for the moon? Can we model the motion of that "star?" Will that asteroid hit? How was the Earth's position in space determined over 2,500 years ago? Want to go to Mars? There's prep to every trip! This class will explore these and other ideas. Why? Because they get students' attention! I've tried everything from temperature, to tides, to Ferris Wheels, and overall, the response was lackluster. Then I started using astronomical ideas and things changed. No more inputting arrays of data and forcing out context, rather, we observe and model! 13 - Physics For Mathematics Teachers Participants will gain a conceptual understanding of the physics used in the secondary-school mathematics curriculum. We'll study concepts and problem solving, without laboratories. If you had physics a long time ago and remember little to nothing or have never had a physics class, this is for you! Stress level for this class is rated as ZERO! Topics include: measurement and uncertainty, dimensional analysis, kinematics (motion) in one and two dimensions, dynamics (forces) and circular motion will be covered in depth. Work, energy, and momentum will be covered, if time permits. 14 - The Geometry of Origami Leader: Philip Mallinson, Phillips Exeter Academy, Exeter, NH This workshop is about using paper folding to illustrate mathematical ideas and using mathematical ideas to explain origami phenomena. We will explore limits, how to construct regular polygons both approximately and exactly, when paper can be folded flat and how to divide a segment into an arbitrary number of equal parts. We will see that the axioms of origami are richer than Euclid's and they will enable us to trisect angles and solve cubic equations. We will explore folding polygons into polyhedra and the inverse problem of unfolding polyhedra to polygons. 15 - Challenging the Mathematically Challenged (and others) Many of the students we teach find it difficult to grasp mathematical concepts at the level of abstraction expected. They see no relevance in what they are asked to do and are unwilling to learn mathematical processes in an isolated and unrelated context. Despite this, these students can solve problems. Participants will work with existing activities as well as create their own activities using standard software packages and Internet access. Previous participants have found it useful to work in groups and have created activities for the full range of student abilities and grade levels. 16 - Mathematical Activities that Build from Year to Year This workshop allows participants to start with a series of simple, concrete activities and use them as building blocks to extend to more sophisticated concepts as students' knowledge and skills progress from middle school to high school. The activities are great for use on the TI-84, but even better on the TI-Nspire and CAS TI-Nspire. In addition to these activities, participants will have an opportunity to use the latest Navigator software and assess its potential gains for use in the classroom. 17 - Integrating Mathematics and English! Seriously! This workshop allows participants to integrate English and mathematics in a problem solving and decision making environment by examining the English material through a mathematical lens. Despite being accessible by middle school students, the level of mathematics involved is far from trivial and includes combinatorial mathematics, exponentials, sequences, geometry and trigonometry to name just a few. Participants will be encouraged to explore these samples with a view to creating new examples for their own classroom use. 18 - Using the iPad to Enrich and Revolutionize the Teaching and Learning of Mathematics We will examine the numerous ways in which iPad applications can be used by students to deepen their understanding of mathematics; make their own discoveries; use digital content such as photos, videos, newspaper articles and e-books to explore their own mathematical questions about our world; create, share and discuss solutions to mathematics problems; and experience mathematics in a dynamic environment that fosters innovation and creativity. Participants must bring their own iPad 2 or 3. 19 - Geometry 2013 Leader: Jonathan Choate, Groton School, Groton, MA Using numerous technologies, the traditional geometry course can be greatly enriched. Participants will learn how to use two- and three-dimensional geometric construction packages, the Internet and spreadsheets to teach topics in new ways. Manipulatives, such as Jovos, and Zometools, will be used to supplement the teaching of non-traditional topics. Participants will see a variety of problems that can be used to motivate important geometric concepts, as well as a collection of elegant proofs. Using technology and physical models, all high school students can explore and understand topics covered in a calculus course without actually knowing any calculus. This focus can lead to students having a more meaningful experience in their algebra, geometry and pre-calculus courses. We will work through activities related to topics such as the fundamental notion of change, max-min problems, related rate problems, and arc length. This course will be of interest to teachers looking for activities and projects that are engaging and designed to deepen students' understanding of mathematics. 21 - Introduction to Complex Systems I Leader: Maria Hernandez, The North Carolina School of Science and Mathematics, Durham, NC In the past 20 years, the study of complex systems has revived such mathematical topics as fractals and chaos and linked these topics to various sciences. We will use matrices, trigonometry, and multiple reduction copy machines to create fractals and learn about iterating both real-valued and complex-valued functions, eventually leading to the Mandelbrot set. These fascinating topics can be used to enhance a precalculus or calculus course or can serve as a basis for a stand-alone course in complex systems along with the topics studied in Introduction to Complex Systems II. 22 - Using Mathematics To Analyze Issues of Social Justice Leader: Ken Collins, Charlotte Latin School, Charlotte, NC This course focuses on how we can integrate social, political, and economic justice issues (fair voting, prison rates, pollution, affordable housing, military recruitment patterns) into our mathematics classes. We will discuss how to explore mathematical topics from a social justice perspective while making sure that the work is mathematically rigorous. Help our students recognize the power of mathematics as an analytical tool to understand and change their world, to deepen their understanding of social and economic issues, and to develop their own power to help build a democratic society. 23 - Great Simulations for Teaching Statistical Concepts Leader: Julie Graves, North Carolina School of Science and Mathematics, Durham, NC Co-Leader: Floyd Bullard The North Carolina School of Science and Mathematics, Durham, NC The best way to teach many statistical concepts is to have students see principles in action. In this hands-on course, participants will engage in classroom simulations that explore hypothesis testing, confidence intervals, power, the t-distribution family, and other difficult topics. Most of the simulations will use manipulatives, and some the TI-84. All topics are part of the AP Statistics curriculum. 24 - Technology Labs to Enliven Statistics Leader: Kyle Barriger, Castilleja School, Palo Alto, CA All students need a fundamental statistical education. This workshop will look at five technology labs that we use with our students to teach them how to work with real data using statistical analysis software (JMP from SAS). These labs are an integral part of the data analysis unit that all students take as part of their algebra 2 course. We will also look at the structure of this data analysis unit and the data used along with the technology skills that the students are taught. 25 - A Student-centered, Problem-based Approach to Algebra I Leader: Karen Geary, Phillips Exeter Academy, Exeter, NH Participants will use the Exeter Math 1 materials to explore ways we can toss out the standard textbook, to use problem-solving and a discussion format to build content with students, rather than for them. Using accessible and contextual problems, we can empower students to discover, develop, and apply general principles and transferrable techniques. The problems will span typical algebra I topics, to including some typical and atypical "word" problems. We will also discuss the way in which various forms of technology can supplement learning in this dynamic classroom format. 26 - Teach and Apply Algebra Concepts with Full Color and High Resolution in the New TI-84 C Leader: Stuart Moskowitz, Humboldt State University, Arcata, CA The TI-83/84's have been making math meaningful for our students since 1996 because they are well made and easy to use. 2013 brings the TI-84 C with a full color and high resolution screen along with innovative new functionality. Now we can import our own photographs right into the graph screen, then use concepts from algebra to analyze our own world more easily than ever! By week's end, we all will have new ways to teach (as well as a better understanding of) the algebra we already teach. TI-84 C loaners will be available. Leader: Tom Reardon, Austintown Fitch High School and Youngstown State University, Youngstown, OH Learn to incorporate and obtain all of my favorite TI-84 activities including mathematical modeling, e-Study Cards and The Great Applied Problem, but now on the new TI-84 C color graphing calculator. Learn creative teaching ideas for SMART Boards (including Fluid Math & TI-SmartView) - use color as a powerful teaching and learning tool. Obtain hundreds of colorful classroom-ready interactive documents that can be used with the new FREE Document Player (use Nspire without owning it!) For algebra 1 through AP Calculus. Investigate some of my favorite iPad APPs for high school math. 28 - A Problem-Based Approach to Trigonometry Leader: Kevin Bartkovich, Phillips Exeter Academy, Exeter, NH This course will be taught using sequences of problems that allow students to build their understanding of many important results in trigonometry at a level appropriate for precalculus classes. Technology, especially the TI-89, will be integrated seamlessly into the course. Topics to be covered include graphs of trig functions, solving triangles, periodicity, addition of sine curves, vector components, rotation matrices, and extended problems using trig models. The dynamics of a problem-based, student-centered Harkness classroom will be modeled and discussed throughout the course. 29 - Mathematics of Sustainability Leader: Kevin Bartkovich, Phillips Exeter Academy, Exeter, NH This course covers investigations related to sustainability, societal inequities, and environmental conservation. What difference will it make in carbon emissions if MPG ratings for new cars are raised by 50%? How long will the world supply of oil last? How can we quantify income inequity? These are some of the questions we will investigate by introducing the situation and then seeing where the relevant mathematics takes us. Most of the math we will use is found at the algebra 2 level and higher. The investigations are data driven; thus, facility with spreadsheet software is a prerequisite. 30 - Exploring Functions with Mapping Diagrams Leader: Martin Flashman, Humboldt State University, Arcata, CA Mapping diagrams provide a very illuminating tool to visualize functions that complement the more commonly used graph. This course will give a thorough treatment of the use of mapping diagrams for the study of functions. The coverage will connect to the mathematics curriculum from beginning and intermediate algebra through to trigonometry and college algebra with some references to calculus. The course will provide examples that illustrate the power of mapping diagrams as well as sample problems and exercises to support teachers and students who are just starting to use mapping diagrams. In the spirit of the Common Core Standards, we will use simulations and hands-on activities to focus on: 1) inference 2) probability - conditional, binomial, geometric 3) two-way tables, tree diagrams and 4) data analysis. All applications will be applicable to algebra, geometry and precalculus. A contextual approach to mathematics will be developed. Fathom will be used for demonstrations and participants are welcome to take with them the prepared demos for use in their own classroom. 32 - Dynamic Geometry with Geogebra and Sketchpad Leader: David Bannard, Collegiate School, Richmond, VA Whether you use Geogebra (free) or the Geometer's Sketchpad, make geometry dynamic. This course will teach you how to use whichever program you prefer. The course will focus on ways to design labs and demonstrations using both programs to make your geometry class more dynamic. We will also discuss and demonstrate the Exeter Geometry course, which is free to download. This material makes effective use of coordinate geometry problems to teach geometry. 33 - The iPad as a Dynamic Math Learning and Teaching Tool Leader: Nils Ahbel, Deerfield Academy, Deerfield, MA It is now possible for your iPad to be a dynamic math writing surface that, based on your own handwriting, will create graphs and tables, simplify expressions, and solve equations. Participants will learn FluidMath.net, an easy-to-use web application that interprets your math notation handwritten with your finger or a stylus. Topics from algebra to precalculus will involve both student discovery activities and teacher demonstrations, including activities that take advantage of Fluidmath's robust computer algebra system. Participants must bring their own iPad 2 or 3 with iOS5 or later. 34 - Mathematics in the 21st Century Classroom How do we create a dynamic classroom where students are engaged and motivated to learn even if we can't change the curriculum? This course will allow you to try a variety of activities for algebra I to precalculus, using new and old technologies that foster curiosity and a love of learning. Get started on Twitter where you will develop a fantastic personal learning network and discover the source of many new ideas and activities. Learn about free on-line tools, apps and some very "old school" ideas that work for both students and teachers. Come learn, share and have fun doing math! 35 - Made Possible by Wolfram Alpha Leader: Harry O'Malley, University at Buffalo, Buffalo, NY How are paper sizes related to one another? How are colors related to each other in 3-dimensional space? How close are you to a flying commercial airliner right now? Wolfram Alpha, a high quality software tool available to anyone with a web browser, can make problems like these accessible to high school students at all levels. In this course, we will engage in the fun of solving problems like these, learn tested techniques for incorporating Wolfram Alpha into our instruction, and mine Wolfram Alpha as a class, looking for more fruits to turn into great math experiences for our students. 36 - Hands-On Calculus Leader: Maria Hernandez, The North Carolina School of Science and Mathematics, Durham, NC Participants will explore hands-on calculus problems and ways to incorporate modeling into the calculus curriculum for AP courses. We'll explore some problems that lend themselves to building physical models and others that include applications involving pollution in The Great Lakes, peak oil production and the effectiveness of blubber as an insulator for seals. These activities will give you a way to actively engage your students as they strive to build a deeper understanding of the calculus topics. Work will be done using a computer and either the TI-83/84 or TI-89. 37 - Geogebra in Calculus and Algebra Leader: David Bannard, Collegiate School, Richmond, VA Geogebra is a free, powerful, and easy-to-use program that can greatly enhance your classes. Learning to effectively use the program is easy for both teachers and students. The focus of this class is for participants to learn how to make effective demonstrations in 5 to 15 minutes that dynamically illustrate concepts, as well as create labs that enhance students' understanding. I have found that I now use Geogebra almost daily in class and students use it at home to better understand the mathematics they are studying. Leader: Tom Reardon, Austintown Fitch High School and Youngstown State University, Youngstown, OH Investigate some of my favorite iPad APPs for teaching and for presentations. Learn to use TI-Nspire CX (color) on a handheld, on desktop, and with the new FREE Document Player (use Nspire without owning it!) Obtain hundreds of colorful classroom-ready interactive documents and learn to create your own. Learn creative teaching ideas utilizing CAS (Computer Algebra Systems). We will look at how to use FluidMath on SMART Boards. See the power of TI-Nspire Navigator, a student response system and classroom management solution. For algebra 1 through AP Calculus. 39 - Winplot from Algebra I to Calculus Leader: Floyd Bullard, The North Carolina School of Science and Mathematics, Durham, NC Co-Leader: Julie Graves North Carolina School of Science and Mathematics, Durham, NC Winplot, a free, downloadable program created by Rick Parris at Phillips Exeter Academy, is a graphing tool that is as powerful as it is easy to use. In this course we'll do ten different "labs" covering problems both abstract and applied, from algebra I to calculus. In these labs students learn how a flashlight beam is focused, how credit cards work, and more. Some time will also be dedicated to showing how you can create new animated problems out of old, static ones. 40 - The Rubik's Cube - Theory and Practice Leader: Ian Winokur, Greenfield Community College, Greenfield, MA In this course you will learn how to solve the Rubik's Cube, and much more! You will develop an understanding of the theory, mechanics and history of the cube. You will calculate the number of distinct scrambles by using some beautiful combinatorics and group theory. We will use the cube to discuss factorials, inverses, modular arithmetic and commutators. No experience necessary but experienced cubers will be given tips on how to solve more fluidly and efficiently. Sign up for this course and learn how to restore your cube to a state of chromatic bliss! 41 - Introduction to Sensible Calculus - A Thematic Approach Leader: Martin Flashman, Humboldt State University, Arcata, CA Using the outlines presented in most calculus texts to make sense of the material presented in a calculus course can be a challenge. This course will provide participants with three themes for organizing calculus that connect all the major concepts, skills, and applications of calculus: modeling, approximations, and differential equations. Examples and exercises will allow participants to see how these themes connect all important topics covered in a one year course in calculus: differentiation, integration, infinite series, and applications. 42 - The Beginner's Guide to Flipping a Classroom Leader: Darren Ripley, The Davidson Academy of Nevada, Reno, NV Instructors will be be given specific skills to learn how to use what is fast becoming the wave of the future for education, flipping the classroom. By the end of the course instructors will have installed and be proficient with Camtasia screen capture software, used a Bamboo Tablet and Logitech microphone to create a lesson done completely on their computers, and uploaded the finished, edited version onto a YouTube account which they have created. The course will emphasize trouble-shooting the many problems that sometimes make classroom flipping daunting and impractical. 43 - Scaffolding and Developing a PBL course Leader: Carmel Schettino, Deerfield Academy, Deerfield, MA This course is for teachers who have an already established PBL curriculum (such as CMP, IMP or PEA materials) who want to do more with the problems and learn to adjust their pedagogy, techniques or add in more scaffolding tools. Teachers will look at how a problem can be broken down into layers and connections to prior knowledge in order to serve their particular audience. Other PBL tools like classroom discourse, metacognitive writing and student listening will be discussed. Experienced PBL teachers should bring a laptop and a part of their curriculum they would like to develop. 44 - Introduction to Complex Systems II Leader: Dan Teague, NC School of Science and Mathematics, Durham, NC The fractal and chaotic processes we found so exciting in 80's have grown up into the modern subject of complex systems. Using techniques of complex systems, calculus students can model biological, physical, economic, and social processes in ways that were unimaginable even 20 years ago. This workshop will focus on agent-based models and cellular automata, using Netlogo to develop new approaches to understanding such varied topics as the spread of infectious diseases in a network, how TI gained control of the educational calculator market, and the process of social segregation. We already solve puzzles for fun; now let's solve puzzles as a way to get kids (and teachers) to learn & love math! From Tangrams, Pentominoes, and disappearing rabbits, to trick locks, and magically appearing money, mechanical puzzles have been around for 1000s of years. We'll use slope, Fibonacci and Heron's Formula to explain how bunnies and money can appear and disappear. We'll use (and build) mechanical puzzles to study concepts in geometry, topology, and graph theory. By week's end, participants all will be puzzle collectors! A continuation of Puzzles 101, but 101's not a prerequisite. Instead of mechanical puzzles, we'll explore Monty Hall and Traveling Salesman problems, look for squares in squares, solve Kakuro, and just play with numbers (wouldn't you love students to want to play with numbers just for fun?!) We'll study number theory, logic, graph theory, probability and more. But puzzles aren't just for fun; Richard Restak writes in The Playful Brain that they stimulate brain growth, with specific puzzles targeting specific parts of the brain. Start now: What's the smallest natural number with all 6 vowels? Using the TI-84, CBR and spreadsheets, we will explore problems that can be solved with precalculus and algebra. The math includes exponential functions, trig, recursion, parametric equations, and linear and non-linear curve fitting. We will use math to explore the path of a playground swing, population of cane toads in Australia (favorite problem of summer 2012 class), predator-prey scenarios, CO2 in the atmosphere, satiation rates of mantids, and free throw percentages. Most problems lend themselves to multiple solution paths, thus allowing students to experience authentic problem solving. With all of the options, what technology works best and how do you use these tools most effectively? Through a series of problems, activities, and applications, participants will explore options like Smartnotebook, iPad apps, e-books, Geogebra, Smartview, Wolfram demonstrations, videos, and other website apps to see what you might use in your classroom. A day each will be spent using animations, simulations, and visualizations. Strategies, methods, and techniques will be discussed. No prior experience is expected, just a willingness to try new things. 49 - Creating Powerful Learning Tools with TI-Nspire Having trouble finding technology-rich support for your students? There is so much out there, and yet how often do you find something that is just right for your class? In the end, you are the best person to provide learning materials for your students! In this course, using the new TI-Nspire Lua scripting language, you will learn how easily you can create interactive learning documents. Even if you are a beginner with programming or TI-Nspire, this course will provide you with the skills and resources to develop great activities, for anything from prealgebra through geometry to calculus. 50 - Searching for Harmony and other Perfect Problems What constitutes a "perfect problem?" For me, it is one that spans the high school years, accessible for the young and less able in a genuine way, but challenging for seniors-something for everyone! It CONNECTS the various branches of mathematics, and INTEGRATES mathematics with other disciplines. It must, of course, ENGAGE and cognitively EXTEND our students but, ideally, be relatively simple in expression. Finally, it should give opportunities for creative expression. Not surprisingly, my favorite perfect problems are best explored using good technology. Come and share some of my favorites. 51 - Mathematical Research in High School Leader: Dan Teague, NC School of Science and Mathematics, Durham, NC Thousands of students completing calculus before their senior year have the mathematical creativity and intellectual curiosity to engage in a mathematical research project. In NCSSM's research course, students work for a term on research problems modified from summer REU programs. In this workshop, participants will work in teams to investigate research problems suitable for post-calculus students. We will discuss strategies for instituting and supporting student research. The instructor will work with interested teachers throughout the year via a webpage dedicated to high school research. 52 - The Exeter Mathematics Program Leader: Jeff Ibbotson, Phillips Exeter Academy, Exeter, NH The mathematics program at Exeter is structured around problem sets of integrated materials. The materials feature problems of varying levels of difficulty and are designed to prompt students to discover and construct mathematical meaning for themselves. At the same time, there is a premium placed on seminar-style discussion as a guiding element of teaching. This course will introduce teachers to both of these by allowing them to participate as students while working through selected problems from the Math 2, Math 3, and Math 4 materials. 53 - An Alternative to Precalculus Leader: Nils Ahbel, Deerfield Academy, Deerfield, MA What do you do with students who struggle in algebra 2? This course outlines a free full-year alternative to traditional precalculus which includes linear, quadratic, exponential, log, and trig functions, but in the context of rich applications that can engage all students. Curve fitting functions to data will be emphasized. The course also includes probability and statistics with an entire chapter devoted to the normal distribution. By week's end you will be able to teach the course as is or choose parts to supplement an existing course. 54 - Calculus Modeling Problems that Make Students Think Leader: Philip Rash, North Carolina School of Science and Mathematics, Durham, NC In this course we will explore several engaging calculus-based modeling problems that students will remember for years. Unlike exercises that can be solved in only a few minutes, common to most textbooks, these problems require significantly more time and demand that students think more deeply about mathematics. The problem topics will include, among others, designing a subway, skydiving, and spread of an infectious disease. TI-83/84 calculators and computer software (MS-Excel) will be used with most problems.
This text provides a creative, inquiry-based experience with geometry that is appropriate for prospective elementary and middle school teachers. The coherent series of text activities supports each student's growth toward being a confident, independent learner empowered with the help of peers to make sense of the geometric world. This curriculum is explicitly developed to provide future elementary and middle school teachers with experience recalling and appropriately using standard geometry ideas, experience learning and making sense of new geometry, experience discussing geometry with peers, experience asking questions about geometry, experience listening and understanding as others talk about geometry, experience gaining meaning from reading geometry, experience expressing geometry ideas through writing, experience thinking about geometry, and experience doing geometry. These activities constitute an "inquiry based" curriculum. In this style of learning and teaching, whole class discussions and group work replace listening to lectures as the dominant class activity. CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book.
Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for).
Students Currently in 7 th to a continuum of appropriate coursework for identified gifted learners Both Pre AP and AP English Courses are accelerated classes that exceed State at the end of 11th and/or 12th grade earn college units. know the Pythagorean theorem and solve problems in which they compute the length of an Rewrite the scientific notation numbers below in standard decimal notation. 1. 4.385 x. Grade 7. This data represents 12 scores on a math test: Mathematical Practices (MP) Grade 7 Mathematics – Unpacking the Delaware Common Core State from State Departments of Education for Utah, Arizona, North Carolina, and Ohio to make muffins to take to a neighbor that had just moved in down the street. will form a straight line through the origin (0 books cost 0 Encribd is NOT affiliated with the author of any documents mentioned in this site. All sponsored products, company names, brand names, trademarks and logos found on this document are the property of its respective owners.
The chankya shikshan sanstha has been conducted the survey about mathematical drawbacks. And it is found that, now a days number of students as well as people who are working in private or government sectors are very poor in mathematical concepts like :- Confusion in sign given to algebraic sum. for example : i) - 5 + 15 = ii) -5 - 15 = iii) 5 - 15 = iv) 5 + 15 = Confusion in sign given in product or division of same and opposite sign number. Every person has a wish to be clear and clever in mathematics concepts. He or she wanted to become an expert in mathematics. But according to school syllabus pattern, the continuity mathematics syllabus should not be retained properly because the student in the 5th class, when he goes in the 6th std. he/she forgets the important basic concepts. And it is not better, when he/she will admit in 6th std. It will creat problems. And so, we have arranged three level exam. The student in the 8th std, if he is clever he can complete 8th std syllabus easily but he wanted to learn 9th and 10th std syllabus for such a student the exam is good. In this three level mathematic exam, the syllabus of middle school/highschool isalso included. As one will complete three level course, his basic mathematic concepts will be clear and easily he/she will become an expert in mathematics.
Advanced Engineering MathematicsThrough previous editions, Peter O'Neil has made rigorous engineering mathematics topics accessible to thousands of students by emphasizing visuals, numerous examples, and interesting mathematical models. Now, ADVANCED ENGINEERING MATHEMATICS features revised examples and problems as well as newly added content that has been fine-tuned throughout to improve the clear flow of ideas. The computer plays a more prominent role than ever in generating computer graphics used to display concepts and problem sets. In this new edition, computational assistance in the form of a self contained Maple Primer has been included to encourage students to make use of such computational tools. The content has been reorganized into six parts and covers a wide spectrum of topics including Ordinary Differential Equations, Vectors and Linear Algebra, Systems of Differential Equations and Qualitative Methods, Vector Analysis, Fourier Analysis, Orthogonal Expansions, and Wavelets, and much more.
study, the author examined the relationship of probability misconceptions to algebra, geometry, and rational number misconceptions and investigated the potential of probability instruction as an intervention to address misconceptions in all
Peer Review Ratings Overall Rating: This site is a collection of geometric derivations and demonstrations of problems from many areas of mathematics including Buffon?s needle problem, an exploration of the catenary, deriving the volume of a torus, a description of the centers of triangles, a look at the Reuleaux Triangle, and an investigation of properties of electrical force fields, to name a few. The author supports his derivations visually using carefully prepared images, Java applets and downloadable Geometer?s sketchpad (GSP) sketches. In cases where derivations are not given (for example the tangent circle applets), the applets are self-explanatory and are suitable for student exploration. Learning Goals: Presentation of the derivation of various facts from geometry, physics, calculus, and algebra. Target Student Population: Varies widely. Prerequisite Knowledge or Skills: Some topics only require elementary geometry. Others (hanging ropes) require even some differential equations to fully appreciate the derivation. Evaluation and Observation Content Quality Rating: Strengths: Explanations are very well written and are carefully presented in a friendly non-technical manner, avoiding the use of jargon and all-too-deep mathematics when more intuitive methods are available. References and historical background are provided when possible and the illustrations are very helpful. Many lessons include some questions that are excellent for students doing group exploration, while others are suitable for undergraduate research problems. If the reader has Geometer's Sketchpad the nearly 30 downloadable sketches make the site worth it by themselves. These sketches allow visitors to interactively explore some fairly complicated, but very interesting mathematics, as well as being able to see some very useful and intricate GSP constructions. Concerns: None. Potential Effectiveness as a Teaching Tool Rating: Strengths: This site is an excellent supplement for any textbook covering similar materials and many of the applets could be used for demonstration purposes during a lecture. Readers that use this site will, most likely, find themselves drawn to the other parts. The sense of enthusiasm the author conveys is most certainly contagious. Some lessons, such as the Chinese Handcuffs lesson, are simply an interesting GSP sketch or java applet together with a list of questions for further exploration. Some of these questions may be (or lead to) problems that are appropriate for undergraduate research. Other lessons such as the Tangent Circles lesson have interesting questions that many students would never think to ask, such as: -Why do some configurations have fewer solutions than others? -Why do some configurations have no solutions? With its excellent visual presentation of some very interesting and (dare we say) fun problems from several fields of mathematics, this has site uses that are too numerous to list in one review Concerns: None. Ease of Use for Both Students and Faculty Rating: Strengths: Aside from the need for GSP the pages read like a well-written text. The applets and GSP sketches were either explained well or self-explanatory. But like any textbook most students will need some guidance through most of these lessons. It seems that all of the Java applets were created using GSP and Java Sketchpad, hence there is continuity to the look and operation of each interactive component. Furthermore, using the Show All Hidden command in GSP, students and teachers alike can discover some of the surprising capabilities of GSP. Concerns: None
This textbook is the third of three volumes which provide a modern, algorithmic introduction to digital image processing, designed to be used both by learners desiring a firm foundation on which to ... This is an introductory to intermediate level text on the science of image processing, which employs the Matlab programming language to illustrate some of the elementary, key concepts in modern image ...
9780471089759 ISBN: 0471089753 Publisher: Wiley & Sons, Incorporated, John Summary: Combining standard Volumes I & II into one soft cover edition, this helpful book explains how to solve mathematical problems in a clear, step-by-step progression. It shows how to think about a problem, how to look at special cases, & how to devise an effective strategy to attack & solve the problem. Covers arithmetic, algebra, geometry, & some elementary combinatorics. Includes an updated bibliography & newly expande...d index. Pólya, George is the author of Mathematical Discovery On Understanding, Learning, and Teaching Problem Solving, published under ISBN 9780471089759 and 0471089753. Three hundred fifty Mathematical Discovery On Understanding, Learning, and Teaching Problem Solving textbooks are available for sale on ValoreBooks.com, one hundred thirteen used from the cheapest price of $19.84, or buy new starting at $113.27.[read more] Ships From:Troy, MIShipping:Standard, ExpeditedComments:NORMAL USED CONDITION! Binding and cover; showing wear but functional. May have some underlining,... [more]NORMAL USED CONDITION! Binding and cover; showing wear but functional. May have some underlining, highlighting inside but appears to be less than 30% of text. Does Not Include Access Code, CD.[
Culver City Algebra 1 builds on the topics explored in Algebra 1. These topics include: real and imaginary numbers, inequalities, exponents, polynomials, equations, graphs, linear equations, functions and more. For me, the skills gained in Algebra 2 were the very foundation of my study in Civil Engineering. ...They are confronted with new ideas often expressed in an abstract manner. These can be difficult to keep track of and to understand the differences of each and of each religion. I have helped students with this as well as making Religion a subject less intimidating to study but one that they will feel encouraged to move forward in.All that has to be done to solve a problem is as follows: write down all the formulas from the summery of each chapter on a piece of paper. Make sure you understand what all the variables and constants represent and understand the units. From then on it will just be plugging in numbers into equations.
MATH 400 Methods and Materials of Teaching Middle and Secondary School Mathematics Course info & reviews Various teaching methods, strategies and materials used in teaching middle and secondary school mathematics. National and State Standards for teaching and learning mathematics. Preparation/evaluation of tests, units, and materials of instruciton. Recent developments in mathematics curriculum and in instructional alternatives. Issues in...
For algebra-based introductory physics courses taken primarily by pre-med, agricultural, technology, and architectural students.This best-selling algebra-based physics text is known for its elegant
Mathematics SL: Internal assessment - The International Moderators should contact the IB Assessment Centre for advice in this situation ... For example , if a candidate has submitted two type I tasks, moderators should ... Math IB Internal Assessment Topic? - Yahoo! AnswersI've finished IB1 (year 11) and I need to prepare a Math Internal Assessment on any topic. Our teacher has given us some examples (past ... 7 ~ 14.140.95.113 Examples of explorations - Mathematics SL and HL teacher support IB logo. Assessed student work Mathematics SL and HL teacher support material ... and others involved in the development of the new internal assessment . 8 ~ mathstudiesathighlandsecondary.blogspot.com IB - More examples of internal assessment projects - math studies at ib mathematics As a Maths tutor provider in Delhi we are able to visit you in the comfort of your own home,. You or your child can receive ... Math Studies IA Guide.pdf - Amundsen High Schoolappropriate, and, if notified, the IBO will be pleased to rectify any errors or ... General regulations and procedures relating to internal assessment have not been reproduced here ... Also included are examples of projects that. Mathematics / IB Math Studies - San Diego City SchoolsWELCOME MATH IB STUDIES STUDENTS!! Instructor: ... The following problem sets mimic the sample tests we took/are taking/are about to take. You are to ... SL: Internal Assessment Practice on InvestigationThis document contains new tasks for the portfolio in mathematics SL. 34 ~ mathstudies-inthinking.co.uk IA - Math Studies - IB Maths Studies - HidePage under Math Studies Maths Studies is an InThinking website. ... A good project for Internal Assessment can be the backbone of a good grade and good ... process efficient, like the awesome, 'google forms' for questionnaires for example . HL Math - Internal Assessment Info - Diamond Bar High SchoolDon't wait until the last minute to work on the Internal Assessment item ... in the upper right-hand corner, you should have your name, your IB number and the ... IB myths answered here - Stephen Perse Sixth FormUniversities completely understand, accept and welcome the IB . ... It is completely wrong – for example , in a subject such as geography you might need around 76% for a Level 7, in maths may be around 83% and .... Between 20% and 25% of all IB subjects are made up with internal assessment so you have this completed. International Baccalaureate Program - Internal AssessmentInternal Assessment ... well as an IB grade for this work. IB grades and requested student work samples are submitted to IB examiners. This is done to ... Math (1) ...
More About This Textbook Overview Elementary Algebra, 8/e by Baratto/Bergman is part of the latest offerings in the successful Streeter-Hutchison Series in Mathematics. The fourth edition continues the hallmark approach of encouraging the learning of mathematics by focusing its coverage on mastering math through practice. This worktext seeks to provide carefully detailed explanations and accessible pedagogy to introduce beginning and intermediate algebra concepts and put the content in context. The authors use a three-pronged approach (I. Communication, II. Pattern Recognition, and III. Problem Solving) to present the material and stimulate critical thinking skills. Items such as Math Anxiety boxes, Check Yourself exercises, and Activities represent this approach and the underlying philosophy of mastering math through practice. The exercise sets have been expanded, organized, and clearly labeled. Vocational and professional-technical exercises have been added throughout. Repeated exposure to this consistent structure should help advance the student's skills in relating to mathematics. The book is designed for a combined beginning and intermediate algebra course, or it can be used across two courses, and is appropriate for lecture, learning center, laboratory, or self-paced courses. It is accompanied by numerous useful supplements, including McGraw-Hill's online homework management system, MathZone
Mathematical Ideas Expanded clar... MOREified Collaborative Investigation: Investigating an Interesting Property of Number Squares Chapter 5 Test The Real Numbers and Their Representations Real Numbers, Order, and Absolute Value Operations, Properties, and Applications of Real Numbers Rational Numbers and Decimal Representation Irrational Numbers and Decimal Representation Applications of Decimals and Percents Extension: Complex Numbers Collaborative Investigation: Budgeting to Buy a Car Table of Contents provided by Publisher. All Rights Reserved. Vern Heeren received his bachelor's degree from Occidental College and his master's degree from the University of California, Davis, both in mathematics. He is a retired professor of mathematics from American River College where he was active in all aspects of mathematics education and curriculum development for thirty-eight years. Teaming with Charles D. Miller in 1969 to write Mathematical Ideas, the pair later collaborated on Mathematics: An Everyday Experience; John Hornsby joined as co-author of Mathematical Ideas on the later six editions. Vern enjoys the support of his wife, three sons, three daughters in-law, and eight grandchildren. John Hornsby When a young John Hornsby enrolled in Lousiana State University, he was uncertain whether he wanted to study mathematics education or journalism. Ultimately, he decided to become a teacher. After twenty five years in high school and university classrooms, each of his goals has been realized. His passion for teaching and mathematics manifests itself in his dedicated work with students and teachers, while his penchant for writing has, for twenty five years, been exercised in the writing of mathematics textbooks. Devotion to his family (wife Gwen and sons Chris, Jack, and Josh), numismatics (the study of coins) and record collecting keep him busy when he is not involved in teaching or writing. He is also an avid fan of baseball and music of the 1960's. Instructors, students, and the 'general public' are raving about his recent Math Goes to Hollywood presentations across the country.
Mathematics: Calculus eBooks Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. A course in calculus is a gateway to more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has widespread applications in science, economics, and engineering and can solve many problems for which algebra alone is insufficient. eBookMall offers eBooks in calculus, pre calculus, and study guides covering calculus topics.
Function Notation Teacher Resources Find Function Notation educational ideas and activities Title Resource Type Views Grade RatingUsing a TI-Nspire calculator, learners will work to better understand function notation and input/output functions. They write equations with a function symbols, identify what makes an equation a function, and graph lines in order to classify them as functions or not. Students solve quadratic equations using graphing. For this algebra lesson, students apply the correct form of functions notations. They solve parabolas by graphing and by algebraic expressions and equations. Learners apply the concept of functions to the real world. In this algebra lesson, students define inverse function and practice using the correct function notations. They graph and define functions as relations. Young scholars differentiate between function and relation by analyzing graphs and data to determine if the pair of coordinates are a function or not. They rewrite functions using the correct notations. This lesson is broken down into timed segments which makes for easy planning. Students investigate reflections and symmetry about a line. In this algebra instructional activity, students apply function notations correctly to solve problems. They differentiate between even and odd function and discuss the reason for their names. Students, after completing a warm up exercise on one proportion word problem, distinguish between functions and non-functions. They identify domain and range on a function as well as recognize and implement function notation. They solve problems on the board in groups. The purpose of this exercise is to give practice in reading information about a function from its graph. Learners are given graphs of two functions on the same axes. The task is to locate and label various key points on the graph that are identified using function notation. The activity is appropriate for instruction to help facilitate understanding of functions or as an assessment item. The longer you wait to try the new pizza place, the more it's going to cost you! This real-world problem about how the cost of pizza varies with respect to time is a good example of how piecewise functions are used to describe relationships between quantities in everyday life. Learners use the given function to answer questions about the price of a pizza in six different scenarios. The exercise is suitable for either instruction or assessment. Graph piecewise functions as your learners work to identify the different values that will make a piecewise function a true statement. They identify function notations and graph basic polynomial functions. This lesson includes a series of critical thinking questions and vocabulary. Explore the concept of transforming polynomial functions! In this transforming polynomial functions lesson, students enter a polynomial into their calculator. They shift the graph vertically and horizontally using the function menu, then examine how certain changes to the parent graph shift the function using tables and the graph of the function. Students differentiate polynomial graphs based on their vertical and horizontal shifts. In this algebra lesson plan, students explain what happens during a vertical and horizontal shift. They examine their equation written in vertex form to help them decipher the shift of their graph. Students rewrite word problems using algebraic symbols. In this algebra lesson, students explore piecewise functions through graphing and identifying the reasons for open and closed dots or solid and dotted lines. They derive the formula given the graph of a piecewise.
Intermediate Algebra 9780495108405 ISBN: 0495108405 Edition: 8 Pub Date: 2007 Publisher: Thomson Learning Summary: Algebra is accessible and engaging with this popular text from Charles "Pat" McKeague! INTERMEDIATE ALGEBRA is infused with McKeague's passion for teaching mathematics. With years of classroom experience, he knows how to write in a way that you will understand and appreciate. McKeague's attention to detail and exceptionally clear writing style help you to move through each new concept with ease. Real-world applicatio...ns in every chapter of this user-friendly book highlight the relevance of what you are learning. And studying is easier than ever with the book's multimedia learning resources, including ThomsonNOW for INTERMEDIATE ALGEBRA, a personalized online learning companion. McKeague, Charles P. is the author of Intermediate Algebra, published 2007 under ISBN 9780495108405 and 0495108405. Five hundred thirty two Intermediate Algebra textbooks are available for sale on ValoreBooks.com, two hundred ninety three used from the cheapest price of $0.22, or buy new starting at $61Ogden, UTShipping:Standard, ExpeditedComments:ALTERNATE EDITION: This is an instructors or review edition. Binding is tight. Book is in good used shape with signs... [more]ALTERNATE EDITION: This is an instructors or review edition. Binding is tight. Book is in good used shape with signs of normal wear. May contain some highlighting. This book needs to be rebound
This course will benefit current college students preparing them for higher math course (at Trine University MA 103, MA153 or MA173) or adults who have been out of school for a while and want to refresh their math skills and be able to perform basic Algebra operations. Topics include arithmetic review (adding, subtracting, multiplying and dividing real numbers), working with fractions, computation with integers and rational numbers using correct order of operations, ratio and proportions. The student also learns percent concepts and solving equations involving percentages. Other covered topics are exponents, simple roots, simplifying and solving equations and inequalities with one variable, analyzing and displaying data. Problem solving is integrated throughout and appropriate use of calculators is expected.
GAP: - Groups, Algorithms, Programming - a system for computational discrete algebra, with particular emphasis on Computational Group Theory. GAP provides a programming language, a library of thousands of functions implementing algebraic algorithms written in the GAP language as well as large data libraries of algebraic objects. See also the overview and the description of the mathematical capabilities. GAP is used in research and teaching for studying groups and their representations, rings, vector spaces, algebras, combinatorial structures, and more. The system, including source, is distributed freely. Coordinated by CIRCA at St. Andrews, UK. MACSYMA At Scientek Inc. --- This venerable computer algebra system, in an obvious sense probably the first commercial such, went out of business: but it's back at version 2.4 in Korea! [See also further information MATLAB: The MathWorks produces software for technical computing and Model-Based Design for engineers, scientists, mathematicians, and researchers. Our two core products are MATLAB®, used for performing mathematical calculations, analyzing and visualizing data, and writing new software programs; and Simulink®, used for modeling and simulating complex dynamic systems, such as a vehicle's automatic transmission system. We also produce more than 90 additional tools for specialized tasks such as processing images and signals and analyzing financial data. Since its founding in 1984, The MathWorks has become the leading global provider of software for technical computing and Model-Based Design. Headquartered in Natick, Massachusetts, The MathWorks currently employs more than 2,000 people worldwide. MAXIMA: a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, and sets, lists, vectors, matrices, and tensors. Maxima yields high precision numeric results by using exact fractions, arbitrary precision integers, and variable precision floating point numbers. Maxima can plot functions and data in two and three dimensions. [a descendant of Macsyma, the legendary computer algebra system developed in the late 1960s at the Massachusetts Institute of Technology.] PARI-GP Number Theory and Algebra program: a widely used computer algebra system designed for fast computations in number theory (factorizations, algebraic number theory, elliptic curves...), but also contains a large number of other useful functions to compute with mathematical entities such as matrices, polynomials, power series, algebraic numbers etc., and a lot of transcendental functions. PARI is also available as a C library to allow for faster computation. REDUCE: a system for doing scalar, vector and matrix algebra by computer, which also supports arbitrary precision numerical approximation and interfaces to gnuplot to provide graphics. It can be used interactively for simple calculations but also provides a full programming language, with a syntax similar to other modern programming languages. implemented in Standard Lisp expressed in an intuitive imperative-style notation called RLISP. The latter is used as a basis for REDUCE's user-level language. SAGE: free open-source mathematics software system licensed under the GPL. It combines the power of many existing open-source packages into a common Python-based interface, which grew out of its early version as Software for Algebra and Geometry Experimentation. [an interactive 3D viewing program for Unix;written at the Geometry Center at the University of Minnesota between 1992 and 1996 used by thousands of people around the world. Through the volunteer work of the original authors and other volunteers, Geomview continues to evolve. Runs on most Unix platforms, including GNU/Linux] "Magma is a large, well-supported software package designed to solve computationally hard problems in algebra, number theory, geometry and combinatorics. It provides a mathematically rigorous environment for computing with algebraic, number-theoretic, combinatoric and geometric objects."
Publisher Comments: Whether you're looking for an in-depth treatment of the entire subject matter or occasional reinforcement of key algebra concepts, this is the place to find it.. CliffsQuickReview Algebra II is a comprehensive study guide to the many topics of a second course in algebra, including information on linear equations, complex numbers, and conic sections. In no time, you'll be ready to tackle other concepts in this book such as Linear equations in one, two, and three variables Factoring polynomials Relations and functions Quadratic systems Exponential and logarithmic functions CliffsQuickReview Algebra IISynopsis: About the Author Ed Kohn is an outstanding educator and author, with over 33 years' experience teaching mathematics. Currently, he is the testing coordinator and math department chairman at the Sherman Oaks Center for Enriched Studies. Formerly an instructor at Fairleigh Dickinson University, David Alan Herzog is the author of over 100 audio visual tides and computer programs and has written and edited several books in mathematics and science. "Synopsis" by Ingram, Wiley, Libri,
Rather than being taught as a separate unit, problem solving will be integrated throughout the course. Problems relevant to each particular strand will be covered in each unit. Students will develop skills in selecting and using an appropriate problem solving strategy. Appropriate technologies including computers and graphic calculators will be used throughout the course to further students' understanding and problem solving skills. UNIT #1 -Systems of Equations solving systems in two variables by graphing and by algebraic techniques (substitution & elimination) solving systems in three variables algebraically and by using technology [enrichment: by matrices] Due to the heavy emphasis in Math 12 on these topics, I will introduce a probability unit at this time and cover some of the foundational skills: basic probability, counting theorems, permutations, combinations to aid students in mastering the component in Math 12 that covers 25% of their course. AssessmentGrading will be done in three terms and not cumulatively: Please view the following link for Mr. Harwood's assessment guiding principles: AssessmentNotes Homework is a key component of a work habits assessment. Homework is essential for developing a complete understanding of the mathematical concepts. Therefore, late homework will also be assessed. Unit Tests and Assignments will determine a report card grade. [Most tests will have a rewrite available if the student studies to learn from their mistakes. At the completion of a rewrite, students must indicate to me which test they want to stand before I mark a rewrite. This demonstrates their confidence and understanding of how well they are doing. The last exam marked stands for that unit.] Grades reported on each report card will represent this particular terms grade and a fresh start will be offered students at the start of each term.. The three terms will be averaged to give a class mark entering the final exam and used to determine the final grade. 0. Problem Solving: It is expected that students will use a variety of methods to solve all forms of problems (real-life, practical, technical, theoretical). It is expected that students will: solve problems that involve one and more than one content area solve problems that involve mathematics within other disciplines analyse a problem and identify the significant elements develop specific skills in selecting and using an appropriate problem-solving strategy or combination of strategies chosen from, but not restricted to, the following: guess and check / look for a pattern / make a systematic list / eliminate possibilities / work backward / analyse key words / make and use a drawing or model / simplify the original problem / develop alternative original approaches demonstrate the ability to work individually & co-operatively to solve problems determine that their solutions are correct and reasonable, and clearly communicate the process used to solve the problem use appropriate technology to assist in problem solving I. Patterns and Relations (Relations and Functions I): It is expected that students will demonstrate an understanding of relation & function terminology and notation as part of using algebraic and graphical models to generalize patterns, make predictions, and solve problems. It is expected that students will: express a relation between 2 quantities in table, graph, or equation form solve systems of linear equations by each of the following methods: graphing / substitution / addition and multiplication / using appropriate technology determine if a linear system has no, one, or infinite solutions solve applied problems using systems of linear equations II. Patterns and Relations (Relations and Functions III): It is expected that students will apply knowledge of relations and functions as part of using algebraic and graphical models to generalize patterns, make predictions, and solve problems. It is expected that students will: express variations in the form of equations (direct, interval, joint, combined) transform equation of a parabola from general to standard form, & vice versa analyse the equation of a parabola to determine the domain, range, intercepts, vertex , axis of symmetry , & max or min values solve problems involving maximum or minimum values III. Patterns and Relations (Relations and Functions II): It is expected that students will demonstrate an understanding of graphing techniques as part of using algebraic and graphical models to generalize patterns, make predictions, and solve problems. It is expected that students will: distinguish between functions and non-functions use and interpret function notation identify an appropriate graph for a given relation graph relations or functions of the following types and analyse them to determine domain, range, symmetries, vertices, asymptotes, intercepts, and maximum or minimum values: V. Patterns and Relations (Variables and Equations II): It is expected that students will simplify and manipulate numeric and algebraic radical expressions as part of representing them in multiple ways. rationalize the numerator or denominator of expressions containing radicals (including the use of conjugates) extend their knowledge of exponent laws to include rational exponents and their radical equivalents VI. Patterns and Relations (Variables and Equations III): It is expected that students will perform algebraic calculations and apply them to solve problems, using appropriate technology, as part of representing algebraic expressions in multiple ways. determine if solutions are reasonable within the context of the problem VII. Shape and Space (3-D Objects & 2-D Shapes): It is expected that students will demonstrate an understanding of circle properties and their applications in solving applied & theoretical problems, as part of describing the characteristics of 3-D objects and 2-D shapes, and analysing the relationships among them. It is expected that students will: recall the properties of parallel lines, similar and congruent figures, polygons, angle relationships, angle measurement, and basic compass and straightedge construction demonstrate an understanding of the following properties of a circle: perpendicular bisector of chord passes through the centre of the circle the line joining midpoint of a chord to the centre is perpendicular to the chord the line through the centre, perpendicular to a chord, bisects the chord central angles containing equal chords or arcs are equal (the converse is also true) inscribed angles containing the same or equal chords (on same side of chord) or arcs are equal an inscribed angle equals half the central angle containing the same or equal chords (on same side of chord) or arcsare equal an inscribed angle in a semi-circle measures 90° opposite angles of a cyclic (inscribed) quadrilateral are supplementary a tangent is perpendicular to the radius at the point of contact (converse true also) tangents from an external point are equal the angle between a chord & tangent equals the inscribed angle on the opposite side of the chord (the converse is also true) demonstrate and clearly communicate deductive reasoning in the solution of applied problems VIII. Shape and Space (Measurement I): It is expected that students will demonstrate an understanding of primary trigonometric functions as part of describing and comparing real-world phenomena using measurement. It is expected that students will: recall basic primary trigonometric ratios determine the quadrant for +ve and -ve angles in standard position identify coterminal angles determine primary trig function values for angles in standard position identify reference angles evaluate primary trig functions for any angle given a variety of conditions IX. Shape and Space (Measurement II): It is expected that students will solve trigonometric equations as part of describing and comparing real-world phenomena using measurement. use the trigonometric definitions to deduce unknown trigonometric values from given values X. Shape and Space (Measurement III): It is expected that students will use trigonometry to solve applied and theoretical problems, as part of describing and comparing real-world phenomena using measurement. It is expected that students will: use right triangle trigonometry to solve problems use the formula: Area = 1/2 bc sin A to find the area of a triangle solve triangles with the sine law & the cosine law solve applied problems using trigonometric ratios, sine and cosine laws, and area formulae XI. Statistics & Probability (Data Analysis) as time allows: New Discoveries Interested in what McRoberts students have been discovering lately? Check out the link bleow. The newest ones are at the bottom.
MATH 3312: Numerical Analysis(Fall 2012) Teaching Assistant:Li Wenbin (lwb@ust.hk) (Office hours to be arranged by the TA) Course Description This course presents numerical methods for solving mathematical problems. It deals with the theory and application of numerical approximation techniques as well as their computer implementation. It covers computer arithmetic, solution of nonlinear equations, interpolation and approximation, numerical integration and differentiation, solution of differential equations, and matrix computation. 4.Use 5-(significant) digit rounding arithmetic (see the exact definition in the textbook) in major steps of calculations. Marks: 100 Topics to be tested: All materials taught in the whole semester will be tested, although including those already tested in the midterm test, however with focus on those not tested in the midterm test. Intended learning outcomes: Upon the end of the course, students should be able to: 1. Develop an understanding of the core ideas and concepts of Numerical Methods. 2. Be able to recognize the power of abstraction and generalization, and to carry out investigative mathematical work with independent judgment. 3. Be able to apply rigorous, analytic, highly numerate approach to analyze and solve problems using Numerical Methods. 4. Be able to communicate problem solutions using correct mathematical terminology and good English.
Essentials Learning a new skill, especially a computer program in this case, can be overwhelming. However, if we build on what we already know, the process can be handled rather effectively. In the preceding chapter we learned about MATLAB Graphical User Interface (GUI) and how to get help. Knowing the GUI, we will use basic math skills in MATLAB to solve linear equations and find roots of polynomials in this chapter. Basic Computation Mathematical Operators The evaluation of expressions is accomplished with arithmetic operators as we use them in scientific calculators. Note the addtional operators shown in the table below: Table 1: Operators Operator Name Description + Plus Addition - Minus Subtraction * Asterisk Multiplication / Forward Slash Division \ Back Slash Left Matrix Division ^ Caret Power .* Dot Asterisk Array multiplication (element-wise) ./ Dot Slash Right array divide (element-wise) .\ Dot Back Slash Left array divide (element-wise) .^ Dot Caret Array power (element-wise) Note: The backslash operator is used to solve linear systems of equations, see Section 12. Important: Matrix is a rectangular array of numbers and formed by rows and columns. For example A=(12345678910111213141516)A12345678910111213141516. In this example A consists of 4 rows and 4 columns and therefore is a 4x4 matrix. (see Wikipedia). Important: Row vector is a special matrix that contains only one row. In other words, a row vector is a 1xn matrix where n is the number of elements in the row vector. B=(12345)B12345 Important: Column vector is also a special matrix. As the term implies, it contains only one column. A column vector is an nx1 matrix where n is the number of elements in the column vector. C=(12345)C12345 Note: Array operations refer to element-wise calculations on the arrays, for example if x is an a by b matrix and y is a c by d matrix then x.y can be performed only if a=c and b=d. Consider the following example, x consists of 2 rows and 3 columns and therefore it is a 2x3 matrix. Likewise, y has 2 rows and 3 columns and an array operation is possible. x=(123456)x123456 and y=(102030405060)y102030405060 then x.y=(104090160250360)x.y104090160250360 Example 1 The following figure illustrates a typical calculation in the Command Window. Figure 1: Basic arithmetic in the command window. Operator Precedence MATLAB allows us to build mathematical expressions with any combination of arithmetic operators. The order of operations are set by precedence levels in which MATLAB evaluates an expression from left to right. The precedence rules for MATLAB operators are shown in the list below from the highest precedence level to the lowest. Parentheses () Power (^) Multiplication (), right division (/), left division (\) Addition (+), subtraction (-) Mathematical Functions MATLAB has all of the usual mathematical functions found on a scientific calculator including square root, logarithm, and sine. Important: Typing pi returns the number 3.1416. To find the sine of pi, type in sin(pi) and press enter. Important: The arguments in trigonometric functions are in radians. Multiply degrees by pi/180 to get radians. For example, to calculate sin(90), type in sin(90pi/180). Warning: In MATLAB log returns the natural logarithm of the value. To find the ln of 10, type in log(10) and press enter, (ans = 2.3026). Warning: MATLAB accepts log10 for common (base 10) logarithm. To find the log of 10, type in log10(10) and press enter, (ans = 1). Practice the following examples to familiarize yourself with the common mathematical functions. Be sure to read the relevant help and doc pages for functions that are not self explanatory. Example 2 Calculate the following quantities: 2332−123321, 50.5−150.51 π4⁢d24d2 for d=2 MATLAB inputs and outputs are as follows: 2332−123321 is entered by typing 2^3/(3^2-1) (ans = 1) 50.5−150.51 is entered by typing sqrt(5)-1 (ans = 1.2361) π4⁢d24d2 for d=2 is entered by typing pi/42^2 (ans = 3.1416) Example 3 Calculate the following exponential and logarithmic quantities: e22 ln510510 log105105 MATLAB inputs and outputs are as follows: exp(2) (ans = 7.3891) log((5^10)) (ans = 16.0944) log10(10^5) (ans = 5) Example 4 Calculate the following trigonometric quantities: cosπ66 tan4545 sinπ+cos4545 MATLAB inputs and outputs are as follows: cos(pi/6) (ans = 0.8660) tan(45pi/180) (ans = 1.0000) sin(pi)+cos(45pi/180) (ans = 0.7071) The format Function The format function is used to control how the numeric values are displayed in the Command Window. The short format is set by default and the numerical results are displayed with 4 digits after the decimal point (see the examples above). The long format produces 15 digits after the decimal point. Variables In MATLAB, a named value is called a variable. MATLAB comes with several predefined variables. For example, the name pi refers to the mathematical quantity π, which is approximately pi ans = 3.1416 Warning: MATLAB is case-sensitive, which means it distinguishes between upper- and lowercase letters (e.g. data, DATA and DaTa are three different variables). Command and function names are also case-sensitive. Please note that when you use the command-line help, function names are given in upper-case letters (e.g., CLEAR) only to emphasize them. Do not use upper-case letters when running functions and commands. Declaring Variables Variables in MATLAB are generally represented as matrix quantities. Scalars and vectors are special cases of matrices having size 1x1 (scalar), 1xn (row vector) or nx1 (column vector). Declaration of a Scalar The term scalar as used in linear algebra refers to a real number. Assignment of scalars in MATLAB is easy, type in the variable name followed by = symbol and a number: Example 6 a = 1 Figure 2: Assignment of a scalar quantity. Declaration of a Row Vector Elements of a row vector are separated with blanks or commas. Example 7 Let's type the following at the command prompt: b = [1 2 3 4 5] Figure 3: Assignment of a row vector quantity. We can also use the Variable Editor to assign a row vector. In the menu bar, select File > New > Variable. This action will create a variable called unnamed which is displayed in the workspace. By clicking on the title unnamed, we can rename it to something more descriptive. By double-clicking on the variable, we can open the Variable Editor and type in the values into spreadsheet looking table. Figure 4: Assignment of a row vector by using the Variable Editor. Declaration of a Column Vector Elements of a column vector is ended by a semicolon: Example 8 c = [1;2;3;4;5;] Figure 5: Assignment of a column vector quantity. Or by transposing a row vector with the ' operator: c = [1 2 3 4 5]' Figure 6: Assignment of a column vector quantity by transposing a row vector with the ' operator. Or by using the Variable Editor: Figure 7: Assignment of a column vector quantity by using the Variable Editor. Declaration of a Matrix Matrices are typed in rows first and separated by semicolons to create columns. Consider the examples below: Example 9 Let us type in a 2x5 matrix: d = [2 4 6 8 10; 1 3 5 7 9] Figure 8: Assignment of a 2x5 matrix. Figure 9: Assignment of a matrix by using the Variable Editor. Example 10 This example is a 5x2 matrix: Figure 10: Assignment of a 5x2 matrix. Linear Equations Systems of linear equations are very important in engineering studies. In the course of solving a problem, we often reduce the problem to simultaneous equations from which the results are obtained. As you learned earlier, MATLAB stands for Matrix Laboratory and has features to handle matrices. Using the coefficients of simultaneous linear equations, a matrix can be formed to solve a set of simultaneous equations. Example 11 Let's solve the following simultaneous equations: x+y=1xy1 (1) 2⁢x−5⁢y=92x5y9 (2) First, we will create a matrix for the left-hand side of the equation using the coefficients, namely 1 and 1 for the first and 2 and -5 for the second. The matrix looks like this: (112−5)1125 (3) The above matrix can be entered in the command window by typing A=[1 1; 2 -5]. Second, we create a column vector to represent the right-hand side of the equation as follows: (19)19 (4) The above column vector can be entered in the command window by typing B= [1;9]. To solve the simultaneous equation, we will use left division operator and issue the following command: C=A\B. These three steps are illustrated below: The result C indicating 2 and 1 are the values for x and y, respectively. Polynomials In the preceding section, we briefly learned about how to use MATLAB to solve linear equations. Equally important in engineering problem solving is the application of polynomials. Polynomials are functions that are built by simply adding together (or subtracting) some power functions. (see Wikipedia). a⁢x2+b⁢x+c=0ax2bxc0 (5) f(x)=a⁢x2+b⁢x+cf(x)ax2bxc (6) The coeffcients of a polynominal are entered as a row vector beginning with the highest power and including the ones that are equal to 0. Example 12 Create a row vector for the following function: y=2⁢x4+3⁢x3+5⁢x2+x+10y2x43x35x2x10 Notice that in this example we have 5 terms in the function and therefore the row vector will contain 5 elements. p=[2 3 5 1 10] Example 13 Create a row vector for the following function: y=3⁢x4+4⁢x2−5y3x44x25 In this example, coefficients for the terms involving power of 3 and 1 are 0. The row vector still contains 5 elements as in the previous example but this time we will enter two zeros for the coefficients with power of 3 and 1: p=[3 0 4 0 -5]. The polyval Function We can evaluate a polynomial p for a given value of x using the syntax polyval(p,x) where p contains the coefficients of polynomial and x is the given number. Example 14 Evaluate f(x) at 5. f(x)=3⁢x2+2⁢x+1f(x)3x22x1 (7) The row vector representing f(x) above is p=[3 2 1]. To evaluate f(x) at 5, we type in: polyval(p,5). The following shows the Command Window output: >> p=[3 2 1] p = 3 2 1 >> polyval(p,5) ans = 86 >> The roots Function Consider the following equation: a⁢x2+b⁢x+c=0ax2bxc0 (8) Probably you have solved this type of equations numerous times. In MATLAB, we can use the roots function to find the roots very easily. Example 15 Find the roots for the following: 0.6⁢x2+0.3⁢x−0.9=00.6x20.3x0.90 (9) To find the roots, first we enter the coefficients of polynomial in to a row vector p with p=[0.6 0.3 -0.9] and issue the r=roots(p) command. The following shows the command window output: Splitting a Statement You will soon find out that typing long statements in the Command Window or in the the Text Editor makes it very hard to read and maintain your code. To split a long statement over multiple lines simply enter three periods "..." at the end of the line and carry on with your statement on the next line. Example 16 The following command window output illustrates the use of three periods: Comments Comments are used to make scripts more "readable". The percent symbol % separates the comments from the code. Examine the following examples: Example 17 The long statements are split to make it easier to read. However, despite the use of descriptive variable names, it is hard to understand what this script does, see the following Command Window output
Infinite Series and Infinite Sequences.- Operations with Power Series.- Linear Transformations of Series. A Theorem of Cesàro.- The Structure of Real Sequences and Series.- Miscellaneous Problems.- Integration.- The Integral as the Limit of a Sum of Rectangles.- Inequalities.- Some Properties of Real Functions.- Various Types of Equidistribution.- Functions of Large Numbers.- Functions of One Complex Variable. General Part.- Complex Numbers and Number Sequences.- Mappings and Vector Fields.- Some Geometrical Aspects of Complex Variables.- Cauchy's Theorem. The Argument Principle.- Sequences of Analytic Functions.- The Maximum Principle.
Mathematical Logic: A Course with Exercises Logic forms the basis of mathematics and is a fundamental part of any mathematics course. This book provides students with a clear and accessible introduction to this important subject, using the concept of model as the main focus and covering a wide area of logic. The chapters of the book cover propositional calculus, boolean algebras, predicate calculus and completelness theorems with answeres to all of the excercises and the end of the volume. This is an ideal introduction to mathematics and logic for the advanced undergraduate student.
The chapters in this volume convey insights from mathematics education research that have direct implications for anyone interested in improving t...show moreeaching and learning in undergraduate mathematics. This synthesis of research on learning and teaching mathematics provides relevant information for any mathematics department or any individual faculty member who is working to improve introductory proof courses, the longitudinal coherence of precalculus through differential equations, students' mathematical thinking and problem solving abilities, and students' understanding of fundamental ideas such as variable, and rate of change. Other chapters include information about programs that have been successful in supporting students' continued study of mathematics. The authors provide many examples and ideas to help the reader infuse the knowledge from mathematics education research into mathematics teaching practice.University mathematicians and community college faculty spend much of their time engaged in work to improve their teaching. Frequently, they are left to their own experiences and informal conversations with colleagues to develop new approaches to support student learning and their continuation in mathematics. Over the past 30 years, research in undergraduate mathematics education has produced knowledge about the development of mathematical understandings and models for supporting students' mathematical learning. Currently, very little of this knowledge is affecting teaching practice. We hope that this volume will open a meaningful dialogue between researchers and practitioners toward the goal of realizing improvements in undergraduate mathematics curriculum and instruction
Posts Tagged MATH EDUCATION Published by EducationNews.org – "The student-engagement bandwagon has gone too far." Emmanuel Schanzer majored in Computer-Science at Cornell University. With such a high-value degree, he knew he could sail into a lucrative, snazzy job. But he was keenly aware that he was a C.S. hotshot (my word) because he'd entered college with good math skills already […] PPublished by EducationNews.org – Methods are about HOW to solve problems, not solving problems themselves. Back in the 1990s, circumstances so maddened Dr. Matthias Felleisen, he felt forced to create Program by Design (PxD) to bring life back to computer science and algebra, both. Since then, thousands of students have used it to learn the elements […] Published by EducationNews.org – For far too long, project-based or "constructivist" learning has been at war with the "drill-and-kill" focus on building skills first. A balance is best. Five high-school seniors cluster behind a pillar in a lecture hall at Rhode Island College. Behind them is a movie-sized screen, and in front looms a modest but intimidating stadium […] Published by EducationNews.org– Creative approaches to algebra — like using computer science and technology — can help improve math education outcomes. Recently, in the New York Times opinion section, Professor Andrew Hacker asked, Is Algebra Necessary? Surely he knew the educated, newspaper-reading public would revile him for such heresy. He states obvious truths, however. Algebra, and […]
The focus of this website is to help in the transition from a paper oriented environment to one using OER materials with an... see more The focus of this website is to help in the transition from a paper oriented environment to one using OER materials with an emphasis in elementary and secondary school mathematics. The website's material is divided into five major topics: 1. Why OER materials? 2. The learner's environment - a world in change. 3. Mathematics past and present. 4. Exploring OER materials and 5. International mathematics education developments. An emphasis has been placed on linking to other OER materials to cover and expand on each topic. online book that contains exercises regarding current assets. There are 8 problem sets that contain... see more This is a free, online book that contains exercises regarding current assets. There are 8 problem sets that contain worksheets and solutions. One must sign up for their newsletter to download the free book. This guide introduces the student to the fundamental principles of project scheduling and control. On completion of the... see more This guide introduces the student to the fundamental principles of project scheduling and control. On completion of the session the student will be able to: •Gather information from all the relevant stakeholders and sequence project activities; •Determine the activity time durations using all relevant information available; •Calculate the project duration using established planning techniques; •Analyse the project resource schedules; •Use an appropriate medium to communicate the schedule to all project participants •Monitor the project progress, updated schedules and present the information to the client.A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically such a... see more A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically such a student will have taken calculus, but this is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form.PDF versions are available to download for printing or on-screen viewing, an online version is available, and physical copies may be purchased from the print-on-demand service at Lulu.com. GNU Free Documentation License
Apply mathematics in a variety of settings Mathematics Essential Skill Description Interpret a situation and apply workable mathematical concepts and strategies, using appropriate technologies where applicable. Produce evidence, such as graphs, data, or mathematical models, to obtain and verify a solution. Communicate and defend the verified process and solution, using pictures, symbols, models, narrative or other methods. Mathematics Essential Skill Graduation Requirement Students first enrolled in Grade 9 in the 2010-2011 school year and beyond are required to demonstrate that they are proficient in the Mathematics Essential Skill in order to graduate. Students fulfill this graduation requirement by earning at, or above, a specific score (the achievement standard) on one of the approved assessment options.
Next: Addition and Subtraction Phrases as Expressions Previous: Data Display Choices Chapter 12: Equations and Functions Chapter Outline Loading Contents Chapter Summary Image Attributions Description Presents information about equations, functions, and probability, including writing expressions and equations, solving equations using addition and subtraction, solving equations using multiplication and division, an introduction to functions and graphing functions, an introduction to probability, finding outcomes, and understanding the probability of independent events
This website is intended to provide extra learning resources in algebra for middle school and high school students. The... see more This website is intended to provide extra learning resources in algebra for middle school and high school students. The approach is to teach math concepts in basic terms using examples and diagrams, if necessary.
I have the first and third books and the first one is an introductory book but there is still an assumption that you're educated in undergraduate linear algebra and calculus. If you've never taken math at that level or are very rusty you'll have a hard time following. You have to be completely honest about how good your math skills are as most people believe they can just learn it when they need to but the truth is if you couldn't learn it while in school you probably can't learn it on your own.
What does e + π mean and how can we evaluate it? What is the difference in the meaning of the equals sign between x2 −1 = 0, x2 −1 = (x−1)(x+1), (x2 −1)/(x−1) = x+1 and √x2 = x? What does it mean for a line to be straight? Are there lines that are not straight? In Math 499 we will be addressing these questions and more! In this class we will explore the foundations of mathematics and how we acquire and process mathematical knowledge. We will revisit K-12 mathematics from the point of view of a mathematician. We will explore the roles of metaphors, models, and definitions. We will discuss the use of symbols and see that even in mathematics their meanings are often contextual. We will compare and contrast proofs and convincing arguments and think about the roles they play in developing and understanding mathematics. We will discuss the relationship between mathematics and our physical world and how we use mathematics to understand the physical world. We will consider various algorithms common in K- 12 mathematics and discuss why and how they work. We also will read and discuss the literature on how K-12 mathematics is taught and how we learn and process that knowledge. Throughout the semester, you will also the opportunity to observe and participate in classes at AUGUSTUS HAWKINS High School. This is a new school with a modern curriculum implementing an initiative called the Algebra Project. This class has no prerequisites. In particular, it is not necessary to have taken any college level math classes; you are only expected to know how to count (albeit fairly well!). However, students must be willing to engage with the material at a mathematically sophisticated level. There will be very little lecturing. There will be a lot of discussion, group work, and both oral and written presentations. This class will be valuable for math majors, anyone with an interest in teaching mathematics, and sociology and psychology majors interested in the science of learning Schlumberger is looking for individuals who seek challenges, are self motivated, and have a high energy level to apply for the Petrotechnical positions. These positions are demanding jobs involving state of the art technology to optimize solutions for Exploration and Production companies. Our petrotechnical experts – Geoscientists, Petroleum Engineers, IT Specialists, Mathematicians, & Physicists – play a vital role in our success. Info Session: Monday, October 28, 2013 Time: 6:00-8:00pm Location: SGM 101 We invite you to meet with us for an inside look to the upcoming available Petrotechnical Positions. You will have an opportunity to talk one on one with Schlumberger representatives and learn more about who we are and what we do as an Oilfield Servicing Company. Food and Beverages will be provided!Phi Sigma will be having its third meeting on March 13 AT 6pm in ZHS 360. Want to find out more about joining and what we're all about? Check out our website at This will be the last day that you will be able to join the USC chapter of Phi Sigma Biological Sciences Honor Society this semester, as this is the late date that membership applications will be due. Please be sure that your ENTIRE application is filled out, especially if you are applying for full membership. This means every blank that addresses you or needs your signature needs to be filled out. All other blanks that address e-board members or whatnot will be filled out accordingly later. Don't forget that for the full membership form, there is a front page that you need to sign as well. If you do not have this complete, you will not be able to be officially recognized as a member by the national Phi Sigma organization. We will be sending in all dues and forms to the national organization by March 15, 2013, so please be prepared with your dues and filled-out forms at the meeting. If you are interested in joining, please visit our page at for details. If you cannot make it, arrange a time with us independently to drop things off.
Algebra I Workbook For Dummies Book Description: From signed numbers to story problems — calculate equations with ease100s of problems!Hundreds of practice exercises and helpful explanationsExplanations mirror teaching methods and classroom protocolsFocused, modular content presented in step-by-step lessonsPractice on hundreds of Algebra I problemsReview key concepts and formulasGet complete answer explanations for all problems
This worksheet will allow you to visually see how slope changes using ... (more) This worksheet will allow you to visually see how slope changes using dynamic text and Sliders. By using Sliders students can see how the slope or the steepness of the line changes with respect to the values of x and y. Students will al (less) Elementary Algebra is a work text that covers the traditional topics studied ... (more) Elementary Algebra is a work text In F.LE Equal Differences over Equal Intervals 2, students prove the property in general (for equal intervals of any length). (less) In this task students observe using graphs and tables that a quantity ... (more) In this task students observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. (less) In this task students have the opportunity to construct linear and exponential ... (more) In this task students have the opportunity to construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). (less) This lesson is designed for students to gather and analyze data about ... (more) This lesson is designed for students to gather and analyze data about baseball figures. The student will use the Internet or other resources to collect statistical data on the top five home run hitters for the current season as well as their career home run totals. The students will graph the data and determine if it is linear or non-linear. (less) This task emphasizes the expectation that students know linear functions grow by ... (more) This task emphasizes the expectation that students know linear functions grow by constant differences over equal intervals and exponential functions grow by constant factors over equal intervals. (less)
Almost any workflow involves computing results, and that's what Mathematica does from building a hedge fund trading website or publishing interactive engineering textbooks to developing embedded image recognition algorithms or teaching calculus. Mathematica is renowned as the world's ultimate application for computations. But it's much more, it's the only development platform fully integrating computation into complete workflows, moving you seamlessly from initial ideas all the way to deployed individual or enterprise solutions. Over 20 Years of Experience—Millions of Users With more than 20 years of experience and millions of users from Fortune 500 companies to government departments to thousands of universities worldwide, Mathematica technology lies behind many of the world's most impressive projects, processes, and organizations—and your future innovation? What's New in Mathematica 8New workflow end points include deployment of standalone applications or interactive document Top 8 Reasons to Upgrade to Mathematica 8 1. Enter your queries in plain English using new free-form linguistic input 2. Access more than 10 trillion sets of curated, up-to-date, and ready-to-use data 3. Import all your data using a wider array of import/export formats 4. Use the broadest statistics and data visualization capabilities on the market 5. Choose from a full suite of engineering tools, such as wavelets and control systems 6. Use more powerful image processing and analysis capabilities 7. Create interactive tools for rapid exploration of your ideas 8. Develop faster and more powerful applications Mathematica Features Compute Numerics of any precision, symbolics, or visualization—Mathematica is the ultimate computational tool, with systemwide technology to ensure reliability, ease of use, and performance. Use Mathematica computation directly, as the engine in an infrastructure, or integrated into a standalone application. Develop Develop tools, applications, documents, or infrastructure components using Mathematica's seamless workflow, unique symbolic language, and advanced code editing environment, achieving fast turnaround on small projects and record times on large systems. Deploy Whether your deliverables are interactive documents, presentations, applications, or enterprise systems, Mathematica can deploy your results in a wide range of formats locally or across a network. With many ways to connect to and work with external systems, Mathematica is designed to maximize your productivity. Homepage:
You can count on a good plan A successful building or remodeling job requires not only a plan, but also the skill to interpret it and an understanding of the mathematics behind it. Whether you are a builder by trade or a do-it-yourself carpenter by choice, turn to this newly updated guide for easy explanations of the math involved and clear instructions on developing and using the necessary plans and specifications. * Explore the different types of wood products and learn what is best for your purpose * Choose appropriate building materials for weather and other natural factors * Refresh your knowledge of fractions, ratios, geometry, and measurement * Understand how to use basic surveying tools * Become familiar with the design process and recognize various styles of architecture * Learn to read architectural drawings and work with computer design less
Finite Mathematics - 7th edition ISBN13:978-0495118428 ISBN10: 0495118427 This edition has also been released as: ISBN13: 978-0495118480 ISBN10: 0495118486 Summary: Get the background you need for future courses and discover the usefulness of mathematical concepts in analyzing and solving problems with FINITE MATHEMATICS, 7th Edition. The author clearly explains concepts, and the computations demonstrate enough detail to allow you to follow-and learn-steps in the problem-solving process. Hundreds of examples, many based on real-world data, illustrate the practical applications of mathematics. The textbook also includes technology g...show moreuidelines to help you successfully use graphing calculators and Microsoft Excel to solve selected Good 0495118427 Good condition, cover has some wear, might have some writings. $2.53 +$3.99 s/h Good Jaros Elverta, CA Hardcover Good 0495118427 Good condition, cover has some wear, might have some writings. $2.597023.75 +$3.99 s/h Good CR Booksellers Punta Gorda, FL 0495118427 Used, in good condition. Book only. May have interior marginalia or previous owner's name. $29.19 9780495118428
1279115 / ISBN-13: 9780321279118 Algebra and Trigonometry: Graphs and Models The Graphs and Models series by Bittinger, Beecher, Ellenbogen, and Penna is known for helping students "see the math" through its focus on ...Show synopsisThe Graphs and Models series by Bittinger, Beecher, Ellenbogen, and Penna is known for helping students "see the math" through its focus on visualization and technology. These books continue to maintain the features that have helped students succeed for years: focus on functions, visual emphasis, side-by-side algebraic and graphical solutions, and real-data applications. This package contains: Algebra and Trigonometry: Graphs and Models, Fifth EditionHide synopsis ...Show more mastery and success in class1279115 No excessive markings and minimal...Very Good. 0321279115
books.google.com - This market leader is written as an elementary introduction to the mathematical theory of probability for readers in mathematics, engineering, and the sciences who possess the prerequisite knowledge of elementary calculus. A major thrust of the Fifth Edition has been to make the book more accessible... first course in probability A first course in probability This market leader is written as an elementary introduction to the mathematical theory of probability for readers in mathematics, engineering, and the sciences who possess the prerequisite knowledge of elementary calculus. A major thrust of the Fifth Edition has been to make the book more accessible to today's readers. The exercise sets have been revised to include more simple, "mechanical" problems and new section of Self-test Problems, with fully worked out solutions, conclude each chapter. In addition many new applications have been added to demonstrate the importance of probability in real situations. A software diskette, packaged with each copy of the book, provides an easy to use tool to derive probabilities for binomial, Poisson, and normal random variables. It also illustrates and explores the central limit theorem, works with the strong law of large numbers, and more. From inside the book User ratings 5 stars 3 4 stars 2 3 stars 0 2 stars 1 1 star 0 Review: A First Course In Probability User Review - Michael - Goodreads As the saying goes, probability is inherently challenging, not trivial like calculus. If your feelings about calculus are a bit different, you might find this book not so much a "first course" as a confusing deathmarch. This ISBN is the 2nd Edition.Read full review Review: A First Course in Probability User Review - Goodreads If you love probability.. you will love this book. Concise, detailed and loaded with examples. This is the book that your professor is really teaching you from! About the author (1984) Sheldon M. Ross is the Epstein Chair Professor at the Department of Industrial and Systems Engineering, University of Southern California. He received his Ph.D. in statistics at Stanford University in 1968 and was formerly a Professor at the University of California, Berkeley, from 1976 until 2004. He has published more than 100 articles and a variety of textbooks in the areas of statistics and applied probability, including Topics in Finite and Discrete Mathematics (2000), Introduction to Probability and Statistics for Engineers and Scientists, Fourth Edition (2009), A First Course in Probability, Eighth Edition (2009), and Introduction to Probability Models, Tenth Edition (2009), among others. Dr Ross serves as the editor for Probability in the Engineering and Informational Sciences.
rete Mathematics and Its Applications The goal of this text is a focused introduction to the primary themes in a discrete mathematics course, as introduced through extensive applications, ...Show synopsisThe goal of this text is a focused introduction to the primary themes in a discrete mathematics course, as introduced through extensive applications, expansive discussion, and detailed exercise sets. These themes include mathematical reasoning, combinatorial analysis, discrete structures, algorithmic thinking, and enhanced problem-solving skills through modeling. Its intent is to demonstrate the relevance and practicality of discrete mathematics to all students. The fifth edition includes a more thorough and linear presentation of logic, proof types and proof writing, and mathematical reasoning. This enhanced coverage will provide students with a solid understanding of the material as it relates to their immediate field of study and other relevant subjects. The inclusion of applications and examples to key topics has been significantly addressed to add clarity to every subject. True to the fourth edition, the text specific web site supplements the subject matter in meaningful ways, offering additional material for students and instructors. Discrete math is an active subject with new discoveries made every year. The continual growth and updates to the web site reflect the active nature of the topics being discussed. This text is designed for a one- or two-term introductory discrete mathematics course to be taken by students in a wide variety of majors, including computer science, mathematics, and engineering. College Algebra is the only explicit prerequisite BRAND NEW US edition / FREE UPGRADE to FedEx, UPS or...New. BRAND NEW US edition 0073383090 Brand New International Edition. Guaranteed...New. 0073383090 Brand New International Edition. Guaranteed Super Fast Delivery. Same Contents as US Editions. Cover & ISBN of the book could be different from US Edition. Description:New. 0071315012 Brand new book. International Edition. Ship...New. 0071315012Beware of international editions. The one my son received did not have the same questions in it as the american one and therefore we had to buy the american edition as his instructor required these questions be anwsered as part of his assignment
Beginning And Intermediate Algebra An Integrated Approach 9780495117933 ISBN: 0495117935 Edition: 5 Pub Date: 2007 Publisher: Thomson Learning Summary: Easy to understand, filled with relevant applications, and focused on helping students develop problem-solving skills, BEGINNING AND INTERMEDIATE ALGEBRA is unparalleled in its ability to engage students in mathematics and prepare them for higher-level courses. Gustafson and Frisk's accessible style combines with drill problems, detailed examples, and careful explanations to help students overcome any mathematics anx...iety. Their proven five-step problem-solving strategy helps break each problem down into manageable segments: analyze the problem, form an equation, solve the equation, state the conclusion, and check the result. Examples and problems use real-life data to make the text more relevant to students and to show how mathematics is used in a wide variety of vocations. Plus, the text features plentiful real-world application problems that help build the strong mathematical foundation necessary for students to feel confident in applying their newly acquired skills in further mathematics courses, at home or on the job. Gustafson, R. David is the author of Beginning And Intermediate Algebra An Integrated Approach, published 2007 under ISBN 9780495117933 and 0495117935. One hundred eighty three Beginning And Intermediate Algebra An Integrated Approach textbooks are available for sale on ValoreBooks.com, seventy five used from the cheapest price of $0.95, or buy new starting at $78495117933-4-1-3 Orders ship the same or next business day. Expedited [more] Missing components. May include moderately worn cover, writing, markings or slight discoloration. SKU:97804951179
Common Core Algebra 1/Integrated 1 Practice Test #2 PDF (Acrobat) Document File Be sure that you have an application to open this file type before downloading and/or purchasing. 1.11 MB \| 20 pages PRODUCT DESCRIPTION Because of the new common core and new tests being active this year, there are little to no resources for us teachers to use to prepare our students for their End-of-Course exams. Because of this, I created a practice test for us to use to help prepare our students for what they will encounter at the end of their Algebra 1 and Integrated 1 experiences. This is a 50 question practice EOC test for Algebra 1 and Integrated 1. All of the questions are originally written and all graphs are originally produced using the new standards and released tests as a guide. An answer key as well as a blank answer sheet for the students to fill in are both included! Please use this as you see fit for review - as a classroom tool, a homework packet, for group work, or centers! I hope that you find it useful in your endeavors to help your students be as successful as possible! A Common Core Alignment Sheet is also included to show where each question lines up with the new Common Core! Product Questions & Answers Be the first to ask Mitchell's Math Mad
Elementary Statistics - With CD (High School) - 2nd edition Summary: For algebra-based Introductory Statistics courses. Elementary Statistics teams the proven authorship and pedagogical expertise of Larson with Farber's 30 years of statistics-teaching experience. It will appeal to today's visually oriented and more technologically savvy students. Highlights Graphical Approach that incorporates the graphical display of data throughout. Flexible tec...show morehnology--Introduces each new technique with hand calculations before a worked-out Technology Example is presented. More than 1,700 exercises--Includes a wide variety in each section that moves from basic concepts and skill development to more challenging problems. Titled examples paired with unique Try It Yourself problems--Illustrates every concept in the text with step-by-step examples numbered and titled for easy reference, Immediately followed with a similar problem. "Real Statistics, Real Decisions" challenges students to make decisions about which techniques to use. Buy with Confidence. Excellent Customer Support. We ship from multiple US locations. No CD, DVD or Access Code Included. $29.99 +$3.99 s/h VeryGood ChattanoogaBookServices CHATTANOOGA, TN 2003-01-01 Hardcover 2nd Very Good DOES NOT INCLUDE CD-2ND EDITION 2003 COPYRIGHT VERY GOOD USED CONDITION-SLIGHT CLASSROOM WEAR DELIVERY CONFIRMATION ON EVERY ORDER! $40.99 +$3.99 s/h VeryGood Butlerbooks concord, NC Upper Saddle River 2003 Hard cover 2nd edition. Very good in very good dust jacket. Audience: College/higher education. $43.57 +$3.99 s/h VeryGood AlphaBookWorks Alpharetta, GA 01304888
YTH-449 - Basic Algebra (Grades 6-8) This class will focus on reviewing concepts learned during the previous school year. Topics may include: Place value and scientific notation, comparing and ordering numbers, addition, subtraction, multiplication and division of fractions, percents, geometry, and working with data (graphs).
Instructor Class Description Introduction to Elementary Functions Covers college algebra with an emphasis on polynomial, rational, logarithmic, exponential, and trigonometric functions. Prerequisite: either a minimum grade of 2.5 in B CUSP 121 or a score of 147-150 on the MPT-GSA assessment test. Offered: AWSp. Class description The purpose of this course is to expand studentsí algebra concepts and skills to the college level and to extend their knowledge of mathematics through visualization, relevant mathematical modeling with everyday life applications, critical thinking skills, and the use of appropriate technologies. Functions are the core of this course. Topics include graphs, functions, equations, inequalities and also polynomial, rational, logarithmic and exponential functions. Student learning goals Understand and interpret concepts and properties of different functions. Enhance critical and creative thinking through modeling and solving everyday life problems. General method of instruction The class will be taught with a mixture of group activities and labs, as well as interactive lectures. Recommended preparation Appropriate score on the UWB math placement test. To prepare for this class, please review your high school algebra materials. Everything we do will build on these skills. Class assignments and grading Homeworks will be completed using the Pearson (MyMathLab) online system. You will need to purchase a registration code for this. Since that registration code includes a complete electronic version of the textbook, there is no need to buy hard copy of the text unless you prefer that and do not wish to print pages from the electronic version yourself. In addition to online homeworks, in-class worksheets, quizzes, Bilin Z Stiber Date: 01/27/2012 Office of the Registrar For problems and questions about this web page contact icd@u.washington.edu, otherwise contact the instructor or department directly. Modified:November 27, 2013
Barron's E-Z Calculus (Barron's E-Z) Synopses & Reviews Publisher Comments: The author of this imaginative self-teaching book tells an entertaining story about travels in the fictional land of Carmorra. In the process he introduces a series of problems and solves them by applying principles of calculus. Readers are introduced to derivatives, natural logarithms, exponential functions, differential equations, and much more. Skill-building exercises are presented at the end of every chapter. Books in Barron's new E-Z series are enhanced and updated editions of Barron's older, highly popular Easy Way books. New cover designs reflect the brand-new interior layouts, which feature extensive two-color treatment, a fresh, modern typeface, and more graphic material than ever. Charts, graphs, diagrams, line illustrations, and where appropriate, amusing cartoons help make learning E-Z in a variety of subjects. Barron's E-Z books are self-teaching manuals focused to improve students' grades in skill levels that range between senior high school and college-101
What's new in HSC maths? Algebraic and graphical representations of functions. Quadratic polynomials, inequalities and the roots of quadratic equations. Calculus and its applications including higher derivatives, logarithmic, exponential and trigonometric functions and ratios. Applications of calculus will extend to real world problems. Probability studies involving tree diagrams. Sequence and series (arithmetic and geometric). Main content of HSC maths HSC Maths starts with a recap of basic arithmetic and algebra topics: rational numbers, quadratic surds, inequalities, linear equation, algebraic fractions, quadratic and simultaneous equations. Topics in consumer mathematics will involve the concepts of compound interest, hire purchase and replacement plans. Algebra and geometry topics will begin with simple functions and conclude with applications in calculus. Calculus and its applications are the core topics of HSC Maths curriculum. Differentiation and Integration (calculus) will be studied from first principle and through different rules before they are applied to polynomials, quadratics, geometry, trigonometry, logarithms, exponential functions, volumes, areas, velocity and acceleration. Common challenges for students in HSC Maths The biggest challenge for students in HSC maths is calculus. Not only is it an entirely new concepts, it represents a shift in mathematical thinking and its applications can be found in almost all areas of HSC maths. Difficulty in grasping calculus will significantly affect students this year. A more general but serious challenge for students is unifying their knowledge and understanding the interconnectedness of topics. In the HSC maths curriculum, topics overlap considerably and knowing how to apply concepts from one topic to solve a problem in a seemingly unrelated topic can be challenging. Main outcomes for HSC maths At the end of HSC maths, students must be able to solve all problems in basic algebra, trigonometry and geometry. This includes consumer mathematics, quadratics and polynomials, both as equations and as functions. Likewise, they must be able to differentiate and integrate simple and complex mathematical functions, use the applicable computational rules to solve calculus problems and apply everything learnt in calculus to grasp applied calculus problems. The ability to use an interdisciplinary approach to finding solutions is essential to this course. Students of HSC maths must learn to take a holistic approach to dealing with abstract and real world problems. Most important concepts to ensure your child understands in year 12 Maths Calculus is the most important concept to understand in HSC maths. Along with it, it is important to have grasped all the basics of algebra, geometry and trigonometry. New topics such as logarithmic and exponential functions are also important. However, a full grasp of the applications of calculus is the single greatest achievement your child can have in the HSC. If hiring a tutor, what study habits and content to focus on in HSC maths? Encourage a concentration in calculus from the tutor you get. You should also advise a stepwise treatment of calculus e.g. differentiating from first principle before the use of rules in calculus; calculus involving simple functions before higher derivatives and applications. Main challenges involved in tutoring a HSC maths student All the main challenges involved in tutoring a HSC maths student involve the volume of topics to be covered this year. It may look like calculus is the only uphill task for the year but it is tied to other topics and it is really a wide topic to cover. Students who have difficulty grasping an aspect may be demotivated to continue. Some good ideas on how to help your child in HSC maths There is no substitute for time and more practice this year. Afford your child those by getting a capable tutor who can dedicatedly help him/her in preparation. Only a tutor or teacher can quickly see where your child is lacking in topics from previous years. Only a tutor or teacher can prepare a quick refresher course to bring your child up to speed. Try to guide your child through the load of work needed to be covered well in time for the final exams. You should also focus on revision and exam preparation. Students often get caught up in understanding the most recent maths content at the expense of revision. Effective study habits, exam prepatation and time management are essential in senior maths. Teach your child to plan their study time, to plan what will be revised and when as they prepare for examinations. A strong sense of direction can make a world of difference. What they say about our tutoring: Thank you for the follow up. Sinan is working out fine. He has connected with Matthew well. Matthew has indicated that Sinan is explaining some of the mathematical concepts better than what his teacher is explaining, which is a good start. Hopefully this will translate into a better maths grade. I was very happy with your service and team. I was fortunate to have met two tutors and both were reliable and most importantly helpful. I came to you as I was attracted to your approach and no upfront fees or contracts....you pay for what you receive at very competitive rates. I was particularly impressed with your assessments and reports. The communication is outstanding between client and company as well as tutor and client. I would highly recommend your service. Gabie got to where she needed to and at this stage is doing very well. If she will require any further assistance you will be our first call. Many thanks for everything so far. In response to your earlier email, I am absolutely delighted with Nick. Tabi trusts that Nick can help her and is beginning to deal with the sense of panic she builds up when confronted with problems she is not sure how to solve or techniques taught in class that she did not understand. I can see Tabi beginning to feel more confident and she certainly feels supported by Nick. Just got Tahli's report. She got 55/100 last report and now 73/100 with position of 2/62 in her year. I have thanked Vashika for her work with Tahli and sorry to lose her next year but thanks to Ezy maths for giving my child confidence in maths! Darius is fantastic. He is extremely dedicated and well mannered. He often stays more than 1 hour to make sure Harry understands everything they have covered. Harry has become enthusiastic toward maths and he can already see improvements. Thank you so much for referring Darius, he has been a life saver! Harry got 83% in his yearly maths test. Last year he got 33% so Michael is doing a really good job. I would like to take this opportunity to thank you and your team for giving the guidance and support, that we were given for our son Ryan. The tutoring that was provided by Victor was of the highest standard and this showed in Rhys' end of year maths results. Ryan was absolutely thrilled with his results, what a difference a few months makes. I would like to thank Victor for all the support and that making Ryan understand how easy it is to be able to achieve good results. Victor was always very friendly and reliable this helped Ryan settle in quickly. Look forward to continuing in the new year.
Edgenuity Geometry is a two-semester, hands-on and lecture-based course featuring an introduction to geometry, including reasoning and proof and basic constructions. Triangle relationships (similarity and congruency) and... Edgenuity Algebra is a two-semester course that provides in-depth coverage of writing, solving and graphing a variety of equations and inequalities, as well as linear systems. Functions are a central theme of the course... Algebra II begins with a review of algebraic properties and equation and inequality solving. Students will study relations and functions, including linear, quadratic, and radical functions, and be able to graph these... In this course students will use their prior knowledge to learn and apply Algebra II skills. This course includes topics such as functions, radical functions, rational functions, exponential and logarithmic functions,... The goal of this course is to help students become better informed, more effective participants in the American political system. This course will help students acquire the necessary knowledge and understanding of... The Chemistry course takes students into the composition, structure, and reactions of matter. This course encourages students to ask questions about things that occur in nature and determine the underlying chemical... The purpose of this year-long Physics course is to help students to see physics as a way to understand their world. To this end, we ask them to think critically, while sharpening their observation skills, analyze and... Physics A encourages students to observe and relate physics principles to the world around them and investigate various physical phenomena related to forces, vectors, Newton's laws of motion, acceleration, velocity,... Publisher: University of Nebraska-Lincoln Independent Study High School Welcome to Physics World, an exciting theme park with rides and pavilions that guide students in their study of physics. The theme park motif provides an engaging context for students to study the concepts, theories,...
Greetings, I am a high-school student and at the end of the termI will have my exams in algebra. I was never into math, but this time I am really afraid that I will fail this course. I came across domain and range function online calculator and some other math issues that I can't understand. These topics really made me panic: difference of cubes and decimals .paying for a tutor is not an option for me, because I don't have any money. Please help me!! Algebrator is one of the most powerful resources that can offer a helping hand to a person like you. When I was a novice, I took help from Algebrator. Algebrator offers all the basics of Basic Math. Rather than utilizing the Algebrator as a step-by-step guide to solve all your math assignments, you can use it as a tutor that can offer the basics of evaluating formulas, hypotenuse-leg similarity and adding fractions. Once you get into the basics, you can go ahead and work out any tough assignments on College Algebra within minutes. Algebrator is really a good software program that helps to deal with math problems. I remember facing difficulties with side-angle-side similarity, gcf and relations. Algebrator gave step by step solution to my algebra homework problem on typing it and simply clicking on Solve. It has helped me through several math classes. I greatly recommend the program. trigonometry, interval notation and adding matrices were a nightmare for me until I found Algebrator, which is really the best algebra program that I have ever come across. I have used it through many algebra classes – Algebra 1, Pre Algebra and Intermediate algebra. Just typing in the math problem and clicking on Solve, Algebrator generates step-by-step solution to the problem, and my algebra homework would be ready. I highly recommend the program.
books.google.co.jp - The... Algebra for College Students Intermediate Algebra for College Students The and inviting format, incorporating real world sourced data and encouraging modeling and problem-solving. Algebra and Problem Solving. Functions, Linear Functions, and Inequalities. Systems of Linear Equations and Inequalities. Polynomials, Polynomial Functions, and Factoring. Rational Expressions, Functions, and Equations. Radicals, Radical Functions, and Rational Exponents. Quadratic Equations and Functions. Exponential and Logarithmic Functions. Conic Sections and Nonlinear Systems of Equations. Polynomial and Rational Functions. Sequences, Probability, and Mathematical Induction. For anyone interested in introductory and intermediate algebra and for the combined introductory and intermediate algebra. 著者について (2001) Community College for nearly 30 years. He has received numerous teaching awards, including Innovator of the Year from the League for Innovations in the Community College, and was among the first group of recipients at Miami-Dade Community College for an endowed chair based on excellence in the classroom. In addition to Intermediate Algebra for College Students, Bob has written Introductory Algebra for College Students, Introductory and Intermediate Algebra for College Students, Algebra for College Students, Thinking Mathematically, College Algebra, Algebra and Trigonometry, and Precalculus, all published by Prentice Hall.
For my technology class I was asked to complete a StaIR. This stands for Stand-Alone Instructional Resource. This is a... see more For my technology class I was asked to complete a StaIR. This stands for Stand-Alone Instructional Resource. This is a resource that a student could use to learn a topic completely independently. It teaches the topic, includes independent practice, and feedback. When asked to do this I wanted to make this for something that could be used within my classroom. I chose to complete a resource for the Pythagorean Theorem. This is a standard that is necessary for all seventh grade students. I will be able to use this to differentiate this in both my Math 7 and Pre-Algebra class Visually searchable database of algebra 1 videos. Click on a problem to see the solution worked out on YouTube. The... see more Visually searchable database of algebra 1 videos. Click on a problem to see the solution worked out on YouTube. The solutions are meant to accompany the free and open textbook Elementary Algebra that can be found on the flat world knowledge website. Visually searchable collection of algebra 2 videos. Click on a problem to see the solution worked out on YouTube. These... see more Visually searchable collection of algebra 2 videos. Click on a problem to see the solution worked out on YouTube. These videos are meant to accompany the free and open textbook Intermediate Algebra that can be found on the flat world knowledge website. This site provides links to 109 podcasts.'The Math Dude makes understanding math easier and more fun than your teachers ever... see more This site provides links to 109 podcasts.'The Math Dude makes understanding math easier and more fun than your teachers ever led you to believe was possible. Host Jason Marshall provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most mathphobic people looking forward to working out whatever math problem comes their way. If you're getting ready to take the SAT, GRE, or any of the other standardized tests; or if you're going back to school and need to brush up on the basics, the Math Dude's Quick and Dirty Tips to Make Math Easier will strengthen your fundamental skills, help you better understand the language of math, and succeed when it comes to taking a test. And if you just want to calculate the tip without using your iPhone and impress all your friends, his tips and tricks are for you too.'According to one user, 'I find this series very useful for students who need a different way to think about Math. The visual that is described and repetition of examples during the podcast are extremely helpful and go beyond memorization.'
Orlando Meetings: Presentation Summary This is the summary of a presentation given at the Joint Mathematics Meetings, January 10-13, 1996, Orlando, Florida. Patterns, Functions, and Recursion for the Middle School Teacher A "guess my rule" approach to functions dominates the elementary grades. Many functions which can be constructed with manipulatives are recursive in nature and the closed form of the function may not be easily determined. However, the recursive function expression reflects directly the representation of the concrete manipulatives. Elementary students should be exposed to recursive function expressions as well as the closed form, certainly by the middle school grades. Discrete mathematics uses recursion in its approach to functions. Spreadsheets and the graphing calculator, which build terms of the functions from an initial value and a sequencing pattern, offer effective means with which to explore functions. The opportunity to move quickly between the recursive form, seed and sequence in a table, and the graph of table values exhibit multiple representations of the function and often lead to a discovery of the closed form. A recursive approach also fosters exploration of different types of functions which otherwise would be postponed for study to a secondary mathematics class. This session will present functions for the middle school from a recursive viewpoint using manipulatives and the Tl-82 graphing calculator.
McGraw-Hill's 500 College Linear Algebra Questions to Know by Test Day (McGraw-Hill's 500 College Questions to Know by Test Day) Synopses & Reviews Publisher Comments: A wealth of problem-solving practice in the format that you want This book is the ideal way to sharpen skills and prepare for your exams Get the problem-solving practice you need with McGraw-Hill's 500 College Linear Algebra Questions to Know by Test Day. Organized for easy reference and intensive practice, the questions cover all essential college linear algebra topics and include detailed answer explanations. Inside you will find: 500 college linear algebra questions and answers organized by subject Step-by-step solutions to every problem Content that follows the current college course curriculum Synopsis: 500 Questions and answers organized by subject with detailed answers. This book follows the current college 101 course curriculum for linear algebra. This is a perfect resource for last-minute study. "Synopsis" by Ingram, 500 Questions and answers organized by subject with detailed answers. This book follows the current college 101 course curriculum for linear algebra. This is a perfect resource for last-minute
General Relativity Without Calculus" offers a compact but mathematically correct introduction to the general theory of relativity, assuming only a basic knowledge of high school mathematics and physics. Targeted at first year undergraduates (and advanced high school students) who wish to learn Einstein's theory beyond popular science accounts, it covers the basics of special relativity, Minkowski space-time, non-Euclidean geometry, Newtonian gravity, the Schwarzschild solution, black holes and cosmology. The quick-paced style is balanced by over 75 exercises (including full solutions), allowing readers to test and consolidate their understanding.
Award-winning original fiction for learners of English. At seven levels, from Starter to Advanced, this impressive selection of carefully graded readers offers exciting reading for every student's capabilities.Do you want to better understand the statistics you hear everyday - and recognise if you're being misled? Here is a straightforward introduction to the principles of this vital field of mathematics. Assuming minimal knowledge and using examples from a wide variety of everyday contexts, this book makes even complex concepts and techniques easy to grasp. NOT... more...
Thank you for participating in the Mathematics & Statistics Alumni Survey. We are very interested in what you and your fellow graduates are doing. All surveys received by April 13, 2012 will be entered in the drawing for a Barnes & Noble NOOK. * First Name * Last Name * Address * City * State * Zip Code * E-mail * Graduation Year * Which of the following best describes your current educational status? A. I have obtained another degree and/or certificate since leaving Saint Mary's B. I am currently enrolled in a program leading to another degree C. I am currently enrolled in classes, but not leading to a specific degree D. None of the above If you answered A or B, please list your Degree, Subject Area and University. Current job title (and description if necessary) Do you have any former jobs that potential mathematics majors might be interested in hearing about? If so, what are they (add description if necessary)? We are exploring the idea of having current/potential math majors make connections with alums with similar occupational interests. Would you be interested in participating in this program? If yes, in what ways (if no leave blank):
Search form You are here Mathematics Union's Mathematics Department look forward to connecting with you. We have information and ideas to share. If you wonder what people do with a major in mathematics, we refer you to the following website as a starter:
Past Catalogs Reed College Catalog Mathematics The mathematics curriculum emphasizes solving problems by rigorous methods that use both calculation and structure. Starting from the first year, students discuss the subject intensely with one another outside the classroom and learn to write mathematical arguments. The major is grounded in analysis and algebra through the four years of study. A student typically will also take upper-division courses in areas such as computer science, probability and statistics, combinatorics, and the topics of the senior-level courses that change from year to year. In particular, the department offers a range of upper-division computer science offerings, while recent topics courses have covered elliptic curves, polytopes, modular forms, Lie groups, representation theory, and hyperbolic geometry. A year of physics is required for the degree. The yearlong senior thesis involves working closely with a faculty member on a topic of the student's choice. The department has a dedicated computer laboratory for majors. Mathematics majors sometimes conduct summer research projects with the faculty, attend conferences, and present papers, but it is more common to participate in a Research Experience in Mathematics (REU) program elsewhere to broaden experience. Many students from the department have enrolled in the Budapest Semester in Mathematics program to study in Hungary. Graduates from the mathematics department have completed Ph.D.programs in pure and applied mathematics, computer science and engineering, statistics and biostatistics, and related fields such as physics and economics. Graduates have also entered professional careers such as finance, law, medicine, and architecture. First-year students who plan to take a full year of mathematics can select among Calculus (Mathematics 111), Introduction to Computing (Mathematics 121), Introduction to Number Theory (Mathematics 131), Introduction to Combinatorics (Mathematics 132), or Introduction to Probability and Statistics (Mathematics 141) in the fall, and Introduction to Analysis (Mathematics 112) or Introduction to Probability and Statistics in the spring. The prerequisite for all of these courses except Analysis is three years of high school mathematics. The prerequisite for Analysis is a solid background in calculus, usually the course at Reed or a year of high school calculus with a score of 4 or 5 on the AP exam. Students who intend to go beyond the first-year classes should take Introduction to Analysis. In all cases, it is recommended to consult the academic adviser and a member of the mathematics department to help determine a program. Mathematics 111 - Calculus Full course for one semester. This includes a treatment of limits, continuity, derivatives, mean value theorem, integration—including the fundamental theorem of calculus, and definitions of the trigonometric, logarithmic, and exponential functions. Prerequisite: three years of high school mathematics. Lecture-conference. Mathematics 112 - Introduction to Analysis Full course for one semester. Field axioms, the real and complex fields, sequences and series. Complex functions, continuity and differentiation; power series and the complex exponential. Prerequisite: Mathematics 111 or equivalent. Lecture-conference. Mathematics 121 - Introduction to Computing Full course for one semester. An introduction to computer science, covering topics such as elementary data structures, algorithms, computability, floating point computations, and programming in a high-level language. Prerequisite: three years of high school mathematics. Lecture-conference and lab. Mathematics 131 - Introduction to Number Theory Full course for one semester. A rigorous introduction to the theorems of elementary number theory. Topics may include: axioms for the integers, Euclidean algorithm, Fermat's little theorem, unique factorization, primitive roots, primality testing, public-key encryption systems, Gaussian integers. Prerequisite: three years of high school mathematics or consent of instructor. Lecture-conference. Mathematics 132 - Introduction to Combinatorics Full course for one semester. Permutations and combinations, finite mathematical structures, inclusion-exclusion principle, elements of the theory of graphs, permutation groups, and the rudiments of Pólya theory will be discussed. Prerequisite: three years of high school mathematics. Lecture-conference. Not offered 2011–12. Mathematics 141 - Introduction to Probability and Statistics Full course for one semester. The basic ideas of probability including properties of expectation, the law of large numbers, and the central limit theorem are discussed. These ideas are applied to the problems of statistical inference, including estimation and hypothesis testing. The linear regression model is introduced, and the problems of statistical inference and model validation are studied in this context. A portion of the course is devoted to statistical computing and graphics. Prerequisite: three years of high school mathematics. Lecture-conference and lab. Mathematics 211 - Multivariable Calculus I Full course for one semester. A development of the basic theorems of multivariable differential calculus, optimization, and Taylor series. Inverse and implicit function theorems may be included. Prerequisite: Mathematics 112 or consent of the instructor. Lecture-conference. Mathematics 212 - Multivariable Calculus II Full course for one semester. A study of line, multiple, and surface integrals, including Green's and Stokes's theorems and linear differential equations. Differential geometry of curves and surfaces or Fourier series may be included. Prerequisite: Mathematics 112 and 211 or consent of the instructor. Lecture-conference. Mathematics 311 - Complex Analysis Mathematics 321 - Real Analysis Full course for one semester. A careful study of continuity and convergence in metric spaces. Sequences and series of functions, uniform convergence, normed linear spaces. Prerequisite: Mathematics 212. Mathematics 331 must be taken before or at the same time as this course. Lecture-conference. Mathematics 322 - Ordinary Differential Equations Full course for one semester. An introduction to the theory of ordinary differential equations. Existence and uniqueness theorems, global behavior of solutions, qualitative theory, numerical methods. Prerequisite: Mathematics 212 and 331. Lecture-conference. Offered in alternate years. Mathematics 331 - Linear Algebra Full course for one semester. A brief introduction to field structures, followed by presentation of the algebraic theory of finite dimensional vector spaces. Geometry of inner product spaces is examined in the setting of real and complex fields. Prerequisite: Mathematics 112 and 211, or consent of the instructor. Lecture-conference. Mathematics 332 - Abstract Algebra Full course for one semester. An elementary treatment of the algebraic structure of groups, rings, fields, and/or algebras. Prerequisite: Mathematics 331. Lecture-conference. Mathematics 341 - Geometry Full course for one semester. Topics in geometry selected by the instructor. Possible topics include the theory of plane ornaments, coordinatization of affine and projective planes, curves and surfaces, differential geometry, algebraic geometry, and non-Euclidean geometry. Prerequisite: Mathematics 331 or consent of the instructor. Lecture-conference. Offered in alternate years. Not offered 2011–12. Mathematics 351 - Mathematical Logic Full course for one semester. This course will be concerned with one or more of the following areas of mathematics: recursive function theory, model theory, computability theory, and general theory of formal systems. Prerequisite: two years of college mathematics. Lecture-conference. Offered in alternate years. Not offered 2011–12. Mathematics 361 - Number Theory Full course for one semester. A study of integers, including topics such as divisibility, theory of prime numbers, congruences, and solutions of equations in the integers. Prerequisite: Mathematics 331 or consent of the instructor. Mathematics 332 is recommended. Lecture-conference. Offered in alternate years. Not offered 2011–12. Mathematics 372 - Combinatorics Full course for one semester. Emphasis is on enumerative combinatorics including such topics as the principle of inclusion-exclusion, formal power series and generating functions, and permutation groups and Pólya theory. Selected other topics such as Ramsey theory, inversion formulae, the theory of graphs, and the theory of designs will be treated as time permits. Prerequisite: Mathematics 211. Lecture-conference. Offered in alternate years. Mathematics 382 - Algorithms and Data Structures Full course for one semester. An introduction to computer science covering the design and analysis of algorithms. The course will focus on various abstract data types and associated algorithms. The course will include implementation of some of these ideas on a computer. Prerequisites: Mathematics 121 and 211 or consent of the instructor. Lecture-conference. Mathematics 384 - Programming Language Design and Implementation Full course for one semester. A study of the organization and structure of modern programming languages. This course will survey key programming language paradigms, including functional, object-oriented, and logic- and constraint-based languages. A formal approach will be taken to understanding the fundamental concepts underlying these paradigms, including their syntax, semantics, and type systems. The course will cover selected topics in the implementation of language systems such as parsers, interpreters, and compilers, and of run-time support for high-level languages. Prerequisite: Mathematics 121. Lecture-conference. Mathematics 391 - Probability Full course for one semester. A development of probability theory in terms of random variables defined on discrete sample spaces. Special topics may include Markov chains, Stochastic processes, and measure-theoretic development of probability theory. Prerequisite: Mathematics 212. Lecture-conference. Mathematics 392 - Mathematical Statistics Full course for one semester. Theories of statistical inference, including maximum likelihood estimation and Bayesian inference. Topics may be drawn from the following: large sample properties of estimates, linear models, multivariate analysis, empirical Bayes estimation, and statistical computing. Prerequisite: Mathematics 391 or consent of the instructor. Lecture-conference. Offered in alternate years. Mathematics 411 - Topics in Advanced Analysis Full course for one semester. Topics selected by the instructor. Prerequisite: Mathematics 321 or consent of the instructor. Lecture-conference. Mathematics 412 - Topics in Algebra Full course for one semester. Topics selected by the instructor, for example, commutative algebra, Galois theory, algebraic geometry, and group representation theory. Prerequisite: Mathematics 332 or consent of the instructor. Lecture-conference. Mathematics 441 - Topics in Computer Science Theory Full course for one semester. Exploration of topics from advanced algorithm design and theoretical computer science including complexity theory, cryptography, computational geometry, and randomized algorithms, as selected by the instructor. Prerequisite: Mathematics 382 or consent of the instructor. Lecture-conference. Offered in alternate years. Not offered 2011–12. Mathematics 442 - Topics in Computer Science Systems Full course for one semester. A study of the design and implementation techniques used in a particular area of computer science as selected by the instructor. Students will implement a working system in that area. Recent offerings have covered distributed and networked systems, compilers, and computer game design. Prerequisite: Mathematics 382 or consent of the instructor. Lecture-conference. Offered in alternate years. Mathematics 470 - Thesis Full course for one year. Mathematics 481 - Independent Study One-half course for one semester. Independent reading primarily for juniors and seniors. Prerequisite: approval of the instructor and the division.
This book is a self-contained treatment of all the mathematics needed by undergraduate and masters-level students of economics. Building up gently from a very low level, the authors provide a clear, systematic coverage of calculus and matrix algebra. The second half of the book gives a thorough account of optimisation and dynamics in discrete and continuous time. The final two chapters are an introduction to the rigorous mathematical analysis used in graduate-level economics. The emphasis throughout is on intuitive argument and problem-solving. All methods are illustrated by well-chosen examples and exercises selected from central areas of modern economic analysis. The book's careful arrangement in short chapters enables it to be used in a variety of course formats for students with and without prior knowledge of calculus, as well as for reference and self-study. New features of the third edition include: > sections on double integration and dynamic programming; > substantial rewriting and expansion of early chapters, making the book highly accessible for the complete beginner. > answers to all exercises and full solutions to all problems are available free online at < Malcolm Pemberton is Senior Lecturer in Economics at University College London This is a great text to learn from – the authors do an excellent job providing intuitive explanations, making connections between results and illustrating the use of mathematics in solving economics problems, and there is a host of solved exercises which perform two roles: providing essential practice material and introducing further applications in economics. Andrew Chesher, Director of The Centre for Microdata Methods and Practice, IFS and UCL 'In spite of the wide scope of this textbook, its presentation is clear and crisp. read more
Mathematics for College Physics - 04 edition Summary: A supplementary text for introductory courses in Algebra-Based Physics. Designed for concurrent self-study or remedial math work for students in introductory courses, this text is ideal for students who find themselves unable to keep pace because of a lack of familiarity with necessary mathematical tools. It not only shows them clearly how mathematics is directly applied to physics, but discusses math anxiety in general and how to overcome it. Instead of a ...show morerigorous development of the concepts of mathematics (as is found in a typical math book), the text describes the various mathematical concepts and tools (including algebra, trigonometry, geometry, vector, and statistics) and their direct use in solving physics problems. Almost all sections end with worked-out examples and exercises directly from introductory physics. Features : Ideal for students with weak mathematics backgrounds. Helps students improve their math skills generally and develop competence and confidence in using math in a physics course. A discussion on math anxiety. Helps students understand the basis of their anxiety and offers suggests on how to deal with it. Shows common math mistakes. Points out traps and pitfalls that students often encounter. Worked-out examples and problems from physics--In almost all sections. Shows students how the concept of mathematics is directly applied to physics. An abundance of tables and figures--Many (e.g., the units of base and derived quantities) highlighted in boxes. Offers support for visual learners and provides convenient study and review tools. Appendices. Provides students with a convenient source of important physical constants, useful data, and conversion factors. 1. Fun with Physics and Mathematics. 2. Algebra: Dealing with Numbers and Equations in Physics. 3. Trigonometry: A Powerful Tool to Solve-Real-World Problems. 4. Geometry: Dealing with Shapes and Plots. 5. Vectors: Tracking the Direction of a Change. 6. Probability and Statistics: Analysis of Data and Predicting Future from the Present. Former Library book. Shows some signs of wear, and may have some markings on the inside. 100% Money Back Guarantee. Shipped to over one million happy customers. Your purchase benefits world literacy! $3.89 +$3.99 s/h Acceptable GICW Books Hillsboro, OR Reading copy. May have notes, underlining or highlighting. Dust jacket may be missing. $3.89 +$3.99 s/h Good GICW Books Hillsboro, OR Textbook may contain underlining, highlighting or writing. Infotrac or untested CD may not be included. $4.45 +$3.99 s/h Acceptable Silver Arch Books St Louis, MO Selection as wide as the Mississippi. $4.48779 +$3.99 s/h Good Big Planet Books Burbank, CA 2003-08-29 Paperback Good Expedited shipping is available for this item! $23.79 +$3.99 s/h Good Big Planet Books Burbank, CA 2003-08-29 Paperback Good Expedited shipping is available for this item!
Lecture 15: Taking percentages Embed Lecture Details : Taking a percentage of a number. Course Description : This is the original Algebra course on the Khan Academy and is where Sal continues to add videos that are not done for some other organization. It starts from very basic algebra and works its way through algebra II.
Browse Reference Articles General Circulation Models (GCMs) are a class of computer-driven models for weather forecasting, understanding climate and projecting climate change, where they are commonly called Global Climate ... > more Bioinformatics and computational biology involve the use of techniques including applied mathematics, informatics, statistics, computer science, artificial intelligence, chemistry and biochemistry to ... > more In probability theory and statistics, correlation, also called correlation coefficient, indicates the strength and direction of a linear relationship between two random variables. In general ... > more Euclidean geometry is a mathematical well-known system attributed to the Greek mathematician Euclid of Alexandria. Euclid's text Elements was the first systematic discussion of geometry. It has been ... > more A parallelogram is a four-sided plane figure that has two sets of opposite parallel sides. Every parallelogram is a polygon, and more specifically a quadrilateral. Special cases of a parallelogram ... > more Calculus is a central branch of mathematics. Calculus is built on two major complementary ideas, both of which rely critically on the concept of limits. The first is differential calculus, which is ... > more Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It is applicable to a wide variety of academic disciplines, from ... > more Algebraic geometry is a branch of mathematics which, combines abstract algebra, especially commutative algebra, with geometry. It can be seen as the study of solution sets of systems of polynomials.
This book is a wonderful resource for teachers of Mathematics. It is an easily read and absorbing overview of the history of mathematics with suggestions for its use in the classroom. The history of each major branch of mathematics (Number, Computation, Algebra, Geometry, Trigonometry and Calculus) is individually summarized and followed by brief essays on specific topics of significance within each branch. This organization makes it easy to find and quickly read the informative articles on any chosen topic. The writing style and reading levels of most articles also make them available to high school students. The last two chapters of the book present an overview of the development of modern mathematics originating in the nineteenth century and a perspective on contemporary mathematics as a science of patterns. These chapters give a brief, integrated view of the direction of mathematics development over the last century. Again, the treatment is very easy to read and very informative for teachers and more advanced students. Finally an Appendix that discusses other resources and two bibliographies (original and updated) aid the teacher to include historical topics in teaching mathematics While originally published in 1969, and updated in 1989, this most recent printing continues to offer high school and university teachers an excellent tool for the classroom and their own development. Hopefully, a new edition will soon be published with updates to the chapters on modern mathematics and the Appendix and Bibliographies to include some of the excellent work published over the last fifteen years. Tim Keenan,Mathematics Teacher,Osbourn Park High School,Prince William County, Virginia
You are here Course Communities So far, we have identified resources for one-variable calculus, multivariable calculus, a first course in ordinary differential equations, and a probability course, as well as for a pseudocourse containing resources for developmental mathematics. Check out and rate the resources, make comments, start discussions, and recommend additional resources. Dummy View - NOT TO BE DELETED Featured Items This is an interactive graphical representation of the universe of probability distributions. Users can search, explore, discover or investigate the intrinsic properties of different probability distributions and inter-distribution relations. In addition, users may utilize many of the web-based probability calculators, simulators and virtual experiments. This resource is an article in Mathematics Magazine (2009); it also appears in Classroom Capsules and Notes. "The author proposes two extensions of the Monte Hall problem, with solutions involving the numbers $\pi$ and $e$, respectively." The lesson begins with an application problem to motivate the necessity and use of a logarithm. The formal definition linking logs and exponents is then introduced. Exercises in writing exponential equations as logarithms follows before a calculator based method for approximating logarithmic values is discussed. The common log, i.e. logs of base $10$, is introduced and a procedure for solving common log equations with a calculator is presented, along with various caveats about proper syntax for the calculator. This applet allows one to change the frequency of two waves between 5 and 20 Hz with a slider scale as well as classify the waves as in or out of phase. You obtain the wave motion over time. The differential equation is not shown.
including algebra 1, algebra 2 andincluding algebra 1, algebra 2 and geometry
Discusses calculating with natural numbers, the first extension of the notion of number, special properties of integers, and complex numbers; algebra-related subjects such as real equations with real unknowns and equations in the field of complex quantities. Also explores elements of analysis, with discussions of logarithmic and exponential functions, the goniometric functions, and infinitesimal calculus. 1932 edition. 125 figures. Widely regarded as a classic of modern mathematics, this expanded version of Felix Klein's celebrated 1894 lectures uses contemporary techniques to examine three famous problems of antiquity: doubling the volume of a cube, trisecting an angle, and squaring a circle. Today's students will find this volume of particular interest in its answers to such questions as: Under what circumstances is a geometric construction possible? By what means can a geometric construction be effected? What are transcendental numbers, and how can you prove that e and pi are transcendental? The straightforward treatment requires no higher knowledge of mathematics. Unabridged reprint of the classic 1930 second edition. This collection of essays by a distinguished mathematician and teacher examines important issues of dynamics from the viewpoint of the theory of functions of the complex variable. Based on a series of lectures delivered by Felix Klein in conjunction with Princeton Universitys 150th anniversary, these presentations center on the problem inherent in the motion of a topthat is, a rigid body rotating about an axiswhen a single point in this axis other than the center of gravity is fixed in position. The contents of this volume render discussions of dynamics-related issues simpler, more attractive, and relevant not only to mathematicians but also to engineers, physicists, and astronomers. Unabridged republication of the classic 1897 edition. The two volumes collected here represent what were to be the first two parts of Klein's plan to write a complete history of the mathematics of the 19th Century. This remarkable book was written by Klein during the last years of his life, a time coinciding with exciting mathematical activity and also the first World War. It is his personal view of the significant developments in mathematics in the 1800s (and early 1900s), especially those connected with the German school. This period includes the time of Klein's greatest activity and influence as a mathematician. The selection of topics reflects Klein's own interests in mathematics. The topics in the first volume include: Gauss's work in pure and applied mathematics; mathematics in France during the early decades of the 19th Century; the contributions of Mobius, Plucker and Steiner to the development of algebraic geometry; mechanics and mathematical physics in England and Germany up to the 1880s; complex analysis according to Riemann and according to Weierstrass; automorphic functions and the interplay between group theory and function theory. The second volume focuses on invariants and their applications in mathematical physics, with particular emphasis on special relativity. Both volumes were published after Klein's death. The final draft for the first volume was prepared by Courant and Neugebauer. The second volume was prepared by Courant and Cohn-Vossen. [via]
Also not I am not trying to insult you, but the fact that someone has to start at intermediate algebra at the college level shows how pathetic our educational system is.....3rd world countries have a standard of making high school graduates learn calculus.....and our standard is to make sure they can divide and multiply.... no calculators is a dumb rule....they are needed and become as important as a pen and paper....students should be taught how to properly use them from day 1..... I agree the common math is complicated but for more advanced math you need to be able to break things down a certain way...once again I am not sure if that is what they are trying to do, but there is not reason to dismiss it without further studies or explanation.... I do agree with you...after taking calc 3 and moving some of the higher maths, I did find that I would depend on my calculator for everything, even the simplest of arithmetic.........its probably not good, but some advanced math does require you use a calculator..... I am just saying that maybe its used to prep kids to do the higher level math....there is a certain level of critical thinking needed to understand calculus.... I wouldn't mind seeing a few studies to see how this effects critical thinking in children...
0195385861Differential Equations with Linear Algebra explores the interplay between linear algebra and differential equations by examining fundamental problems in elementary differential equations. With a systems-first approach, the text is accessible to students who have completed multivariable calculus and is appropriate for courses in mathematics, science, and engineering that study systems of differential equations. Because of its emphasis on linearity, the text opens with an introduction to essential ideas in linear algebra. Motivated by future problems in systems of differential equations, the material on linear algebra introduces such key ideas as systems of algebraic equations, linear combinations, the eigenvalue problem, and bases and dimension of vector spaces. These key concepts maintain a consistent presence throughout the text and provide students with a basic knowledge of linear algebra for use in the study of differential equations. This text offers an example-driven approach, beginning each chapter with one or two motivating problems that are applied in nature. The authors then develop the mathematics necessary to solve these problems and explore related topics further. Even in more theoretical developments, an example-first style is used to build intuition and understanding before stating or providing general results. Each chapter closes with several substantial projects for further study, many of which are based in applications. Extensive use of figures provides visual demonstration of key ideas while the use of the computer algebra system Maple and Microsoft Excel are presented in detail throughout to provide further perspective and enhance students' use of technology in solving problems. Support for the use of other computer algebra systems is available online. Related Subjects Meet the Author Matt Boelkins is Associate Professor of Mathematics at Grand Valley State University. Merle C. Potter is Professor Emeritus of Engineering at Michigan State University and was the first recipient of the Teacher-Scholar award. He has authored or coauthored twenty-four textbooks and exam review books. Jack Goldberg is Professor Emeritus of Mathematics at the University of Michigan. He has published several textbooks and numerous research papers
Modern Algebra An Introduction 9780471433354 ISBN: 0471433357 Edition: 5 Pub Date: 2004 Publisher: John Wiley & Sons Inc Summary: The author has written this book with two main goals in mind: to introduce the most important kinds of algebraic structures, and to help students improve their ability to understand and work with abstract ideas. Durbin, John R. is the author of Modern Algebra An Introduction, published 2004 under ISBN 9780471433354 and 0471433357. Three hundred thirty three Modern Algebra An Introduction textbooks are availa...ble for sale on ValoreBooks.com, twenty five used from the cheapest price of $4.01, or buy new starting at $33
There's something about a language of symbols and equations that most people find intimidating. Mathematician Colin Pask gently introduces you to the main ideas of mathematics and painlessly demonstrates how they are expressed in terms of symbols, and not only teaches the reader why symbols are used, and how and whyIn its largest aspect, the calculus functions as a celestial measuring tape, able to order the infinite expanse of the universe. Time and space are given names, points, and limits; seemingly intractable problems of motion, growth, and form are reduced to answerable questions. Calculus was humanity's first attempt to represent the... Read more >
You are here Basic Algebra Publisher: Birkhäuser Number of Pages: 717 Price: 69.95 ISBN: 0817632484 Anthony W. Knapp's Basic Algebra aims to teach the student algebra in a somewhat different way than is the norm. Together with its sequel, Advanced Algebra, the book proposes to take an aspiring mathematician from his first exposure to algebra proper, right after calculus, through his graduate training in algebra — and a bit further, to "what [every] young mathematician needs to know" (p. xiii). Knapp says that the litmus test for topics included is whether a plenary lecturer at a mathematics meeting would presuppose the according knowledge on the part of his audience. Therefore, Basic Algebra is something like an algebra vade mecum as well as a text for a more holistic approach to undergraduate algebra. Actually Basic Algebra does a good deal of graduate level algebra, too, at least as far as what one would need for a typical PhD qualifying examination, so Knapp's vision certainly extends beyond the first four years of university education in mathematics. (Advanced Algebra addresses more esoteric or eclectic material, starting, as it does, with "Transition to Modern Number Theory," and ending with "Methods of Algebraic Geometry." See p. x of Basic Algebra.) To use Basic Algebra in a standard undergraduate curriculum would entail spreading the material over several semesters, since the book can be used for linear algebra, group theory (Chapter IV is a gem!), rings and fields, Galois theory, a second course in group theory, and even a course on modules. Presumably a more holistic pedagogical approach, in line with what Knapp seems to have in mind, would engender the "simple" manouevre of defining an autonomous two-year course titled "Algebra," and going through the book in linear order. Of course, in the surreal world of the contemporary academy anything this simple is far too suspect to the martinets in charge to have a reasonable chance of succeeding, but hope springs eternal. Some remarks about Knapp's exercises are in order. In a word, they are superb. The problems to Chapter VII, "Advanced Group Theory," for example, feature involving one of Burnside's theorems to show that the smallest non-abelian simple group has order 60 (it is A5, of course), an n-handle-body, the Baer product, Fourier analysis (including Poisson), FFT's, and even some representation theory. Such wonderful depth and variety is typical of all the exercise sections, and there are over ninety pages of hints toward the problems' solution at the end of the book. À propos, the exercises on p. 298 ff. present a good, if succinct, treatment of some Lie theory, underscoring Knapp's generalist pedagogical objectives as delineated above. The book also has a very evocative cover, containing the diagram (cf. p. 500) attending Gauss' construction of the regular 17-gon. Basic Algebra is a very interesting and well-written book, and is indeed well suited for the approach to algebra the author intends, and, for that matter, usable for commonplace approaches as well. Michael Berg is Professor of Mathematics at Loyola Marymount University in California. Contents.- Preface.- Guide for the Reader.- Preliminaries about the Integers, Polynomials, and Matrices.- Vector Spaces over Q, R, and C.- Inner-Product Spaces.- Groups and Group Actions.- Theory of a Single Linear Transformation.- Multilinear Algebra.- Advanced Group Theory.- Commutative Rings and Their Modules.- Fields and Galois Theory.- Modules over Noncommutative Rings.- Appendix.- Index.
Fourier Analysis James S. Walker Table of Contents PART I: Introduction to Fourier Series PART II: Convergence of Fourier Series PART III: Applications of Fourier Series PART IV: Some Harmonic Function Theory PART V: Multiple Fourier Series PART VI: Basic Theory of the Fourier Transform PART VII: Applications of Fourier Transforms 1. Partial Differential Equations 2. Fourier Optics PART VIII: Legendre Polynomials and Spherical Harmonics PART IX: Some Other Transforms 1. The Laplace Transform 2. The Radon Transform PART X: A Brief Introduction to Bessel Functions A. Divergence of Fourier Series B. Brief Tables of Fourier Series and Integrals
This page is updated frequently. Hit "reload" to make sure you are viewing the most recent version and not an old cache. Remember: Learning mathematics is like constructing a building; it first requires a strong foundation. We believe that completing all of the problems listed below provides a foundation for understanding the material in that section. Only the problems in bold red should be turned in. We strongly suggest working other problems in each section to reinforce these foundations and prepare you for upcoming material.
COT 2104 MATHEMATICS FOR COMPUTING Course info & reviews THIS COURSE BUILDS BASIC MATHEMATICAL LOGIC SKILLS AND FOUNDATIONS OF COMPUTING. STUDENTS WILL KNOW AND UNDERSTAND THE BASIC CONCEPTS OF MATHEMATICS AS THEY APPLY TO COMPUTING AND HAVE DEVELOPED AN APPRECIATION OF THE WAY THAT DISCRETE MATHEMATICS CAN ASSIST THEIR OWN PROBLEM SOLVING AND IMPLEMENTATION OF SOLUTIONS
THE USE OF CAS IN SCHOOL MATHEMATICS: POSSIBILITIES AND LIMITATIONS Gunnar Gjone University of Oslo, Oslo, Norway; gunnar.gjone@ils.uio.no By using examples from upper secondary mathematics given for the Casio ClassPad tool, this presentation deals with determining equivalence of algebraic expressions, relating different representations, and making Computer Algebra Systems (CAS) techniques transparent and congruent with their paper-and-pencil versions. For each of these three topics, the presentation underlines its importance for CAS-based research, shows what best can be achieved with this tool at present, and summarizes limitations that should be addressed in a future version of the tool. In order to do mathematics with CAS in a better way, both CAS features and their use need to be improved. INTRODUCTION The use of CAS has been an important issue in secondary school mathematics for more than ten years (see From the beginning of using such tools in the 1980s, there has been a development in improving their possibilities. By applying the perspective of working mathematically, this paper presents examples of possibilities and limitations of Casio ClassPad ( These examples are given for three topics that are particularly relevant to CAS- based school mathematics. These topics are determining equivalence of algebraic expressions, relating different representations, and making CAS techniques transparent and congruent with their paper-and-pencil versions. Screenshot 1 DETERMINING EQUIVALENCE OF ALGEBRAIC EXPRESSIONS Topic importance A large part of doing mathematics deals with transforming expressions to fit imposed requirements. Considering equivalent expressions is hence an important topic in mathematics teaching. Reasoning about equivalent algebraic expressions is an important research area not only in traditional mathematics education, but also in CAS-based mathematics education [1], where due to CAS limitations, students should skillfully use various CAS commands (e.g. the equality test and solve) to find out whether two expressions are equivalent. Tool affordances There is a ClassPad command named judge that is able to provide the answer to the question of equivalence in most cases. But, as shown on Screenshot 1, despite 1 a restriction of domain (with "\|"command), the use of judge may be of little value with special subtle cases. The strength of command judge may be improved as presented on Screenshot 2. We find here that the user, perhaps believing f(x) and g(x) are not equivalent, applies function test_le (defined by him/her or other user) and gets message "ERROR: Non-Real in Calc". Issues to improve According to [2], equivalence of expressions is not a decidable problem. In other words, due to theoretical reasons, equivalence of expressions cannot be Screenshot 2 verified in all cases even by ideal CAS. Because of that, subtle user-defined functions (created by teacher or able students) need to be used. This approach is not well supported by ClassPad at present as, for example, functions cannot be defined in several lines, or by using several commands in a line separated by ":". Also, there may be problems when using if-then-else statement implemented as piecewise function (see the appendix). RELATING DIFFERENT REPRESENTATIONS Topic importance Using different representations of the same mathematical entity is one of the most important aspects of doing mathematics. A flexible dealing with different representations is usually seen as a step towards understanding of mathematical entities. As CAS are essentially representa- tion tools, the question of creating, using and relating different representations is highly relevant to CAS-based mathematics education [3]. Tool affordances Screenshot 3 present a ClassPad feature, Geometry Link, that links an algebraic representation Screenshot 3 2 of a function with its graphical representation in such a way that any change in one representation is reflected in the other. This feature is particularly useful in examining graphs of elementary functions under certain transformations (e.g. y=x2 vs. y=(x−1)2−5). Screenshot 4 presents how two geometry links can be used in solving systems of equations, where solutions (2, 1) and (1, 2) can be recognized as the points of intersection of the two graphs. Issues to improve The Geometry Link feature is limited, however. Indeed, if we change the values of parameters p and q (Screenshot 4), the solutions of a new system will be found, but the two graphs will not change. Also, a geometry link with a function on a restricted domain (e.g. y=x2 \| x > 0) will wrongly result in the graph of that function on its full domain. Screenshot 4 These two examples evidence that ClassPad applications (e.g. e-Activity and Geometry) need to be better linked in a future version of the tool. MAKING CAS TECHNIQUES TRANSPARENT AND CONGRUENT WITH THEIR PAPER-AND-PENCIL VERSIONS Topic importance Paper-and-pencil techniques may not be reflected in their CAS versions (e.g. factorization of x9 – 1). Also, CAS technique (i.e. the way in which CAS solves a class of problems) is not open to its user (hence the requirement: turn a back box of CAS technique into a white box or a grey one. (Term technique is used in the sense of the French school [4].). The success in doing mathematics with CAS is thus considerably constrained by the transparency of CAS technique as well as the congruence of that technique with its paper-and-pencil version [5]. Without reducing these constraints, CAS cannot be used in a functional, strategic and pedagogical way as properly required by [6]. Screenshot 5 (provided by Dj. Kadijevich) Tool affordances In order to have equation and inequality solving with CAS that is transparent and mirrors the usual paper-and-pencil work, several functions can be defined (by 3 teacher or able students), explained to students, and used by students to help them be more aware of the solving processes. An example is given in Screenshot 5 (we divided both sides of the initial equation by x and then by x−1 and obtained proper answers). Like the Casio FX2.0 CAS calculator, ClassPad also sometimes accepts syntax where parentheses are left un-closed (e.g. solve(x3−1=0 returns {x=1}). Some students like to use this time-saving, but counter-mathematical, feature. Issues to improve In order to improve shortcomings concerning issues of transparency and congruence, better CAS commands and appropriate user-defined functions are needed. These functions can be defined with ClassPad in a limited way as described in the end of the section on expressions equivalence. Also, some useful functions known to ClassPad (e.g. element({1, 2, 3}, 2) and completeSqr(x2−4x)) cannot be found in the ClassPad manuals. Finally, some functions may still work in a strange way (e.g. mode({a, b, a}) is a, mode({true}) is TRUE, whereas mode({true, false, true}) is {TRUE, FALSE, TRUE}). All these make the work with user-defined functions a hard and somewhat frustrating job. CLOSING REMARKS Good user-defined functions are crucial to improving CAS. This requires CAS manufacturers to provide better conditions for the development of user-defined functions, taking into account critical issues given in this paper. Contrary to paper-and-pencil mathematics, "defining a function is required before an expression such as f(x) or f(2) can be used." [4, p. 68]. Further CAS- based research may focus on the work with user-defined functions. ACKNOWLEDGEMENT The preparation of this paper and its presentation is supported by CASIO Europe. REFERENCES [1] Kieran, C., & Saldanha, L. (2005). Computer algebra systems (CAS) as a tool for coaxing the emergence of reasoning about equivalence of algebraic expressions. In H. L. Chick & J. L. Vincent (Eds.). Proceedings of the 29 th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 193-200). Melbourne: PME. [2] Richardson, D. (1968). Some undecidable problems involving elementary functions of a real variable. The Journal of Symbolic Logic, 33(4), 514-520. [3] Heid, K. M. (2002). How theories about the learning and knowing of mathematics can inform the use of CAS in school mathematics: One perspective. The International Journal of Computer Algebra in Mathematics Education, 8(2), 95-112. [4] Artigue, M. (2002). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematical Learning, 7, 245-274. [5] Drijvers, P. (2004). Learning algebra in a computer algebra environment. The International Journal of Computer Algebra in Mathematics Education, 11(3), 77-89. 4 [6] Pierce, R., & Stacey, K. (2004) A framework for monitoring progress and planning teaching towards the effective use of computer algebra systems. International Journal of Computers for Mathematical Learning, 9, 59-93. APPENDIX − USING PIECEWISE FUNCTION Piecewise(0, 1, 2, 3) returns "2", piecewise(2, 1, 2, 3) returns "1", whereas piecewise(x, 1, 2, 3) return "3" although "3" should be returned in each of these three cases as the first argument of this if-then-else-error function is not a relation. By exploiting this behavior in a constructive way, define the following function: define eq_div(eq,a)=piecewise(a, getLeft(eq)/a=getRight(eq)/a, "Division by 0!", piecewise(judge(getLeft(eq)=getRight(eq) \| solve(a)), {getLeft(eq)/a=getRight(eq)/a, "Solution set reduced for:", solve(a)}, getLeft(eq)/a=getRight(eq)/a)) Screenshot 6 evidences that this function cannot be executed directly because Casio ClassPad returns piecewise(x−3, … ), which is executed by using system variable ans containing this intermediate answer. Screenshot 6
Lessons Include: Ratios, Unit Rates, Proportions, Solving Proportions, Fractions and Percents, Decimals and Percents, Find the Percent, Percent of a Number (Finding the Part) Finding a Number When the Percent is Known, Discount, Markup, Percent of Increase, Percent of Decrease Lessons Include: Area of a Triangle, Area of a Parallelogram, Area of Similar Figures, Area of a Trapezoid, Area of a Rhombus or Kite, Area of a Circle, Area of a Sector of a Circle, Area of Regular Polygons, Area of an Irregular Shape, Comparing Area and Perimeters, Using Trigonometry to Find the Area of a Triangle, Geometric Probability Lessons Include: What is a Polynomial? Adding Polynomials, Subtracting Polynomials, Multiplying a Polynomial, Multiplying Binomials, Squaring a Binomial, The Difference of Two Squares, Finding the Greatest Common Factor for Variable Terms, Factoring a Binomial, Factoring a Polynomial, Factoring Trinomials in the Form x² + bx + c. Factoring Trinomials in the Form ax² + bx + c Lessons Include: Graphing Quadratic Functions, Properties of a Graph of a Quadratic Function, Writing a Quadratic Function from its Graph, Quadratic Function in Intercept Form, Solving Quadratic Equations Using Square Roots, Solving a Quadratic Equation by Completing the Square, Quadratic Formula, Solving a Quadratic Equation by Factoring, Using the Discriminant, Methods for Solving Quadratic Equations, Writing an Equation of an Ellipse, Foci of an Ellipse Lessons Include: Raising a Power to a Power, Raising a Product to a Power, Raising a Quotient to a Power, Dividing Powers with the Same base, Simplifying Rational Expressions, Multiplying Rational Expressions, Dividing Rational Expressions, Finding the ICD of a Rational Expression, Adding Rational Expressions, Subtracting Rational Expressions Lessons Include: Relations and Functions, Types of Functions, Direct Variation, Inverse Variation, Slope-Intercept Form, Point-Slope Form I, Point-Slope Form II, Linear Parametric Equations, Writing a System of Equations as a Matrix, Using Matrices to Solve a System of Two Equations, Cramer's Rule Help students succeed in class & on tests with these fun, whiteboard-ready daily exercises that provide essential practice in proofreading for spelling, punctuation, capitalization, grammar, and more. Perfect for starting the day or reviewing skills, these motivating, interactive activities will get even your most reluctant learner to participate. Includes a CD of ready-to-go Notebook files to use with your SMART Board! puzzle activities
Find a Inverness, IL Algebra 2Subject Content Outcomes: 1) Use the terms, definitions, and notation of Basic Algebra 2) Identify and make use of real number properties and evaluate real number expressions 3) Sketch the Graph of a Linear Function and Identify the Slope and Intercepts 4) Perform operations with Polynomials 5) ...
and Technics / Science / Mathematics / Calculus2013-12-22T04:56:57ZPre-Calculus Know-It-All Gibilisco looking to ramp up your skills. Provi...608 pages11.2 MB18.29Practice Makes Perfect Calculus William Clark McCune Makes Perfect has established itself as a reliable practical workbook series in the language-learning category. Now, with Practice Makes Perfect: Calculus, students will enjoy the same clear, concise approach and extensive exercises to ke...208 pages13 MB9.49Business Calculus Demystified Huettenmueller Professional2005-12-12Take the FEAR OUT of Business CalculusBusiness Calculus Demystified clarifies the concepts and processes of calculus and demonstrates their applications to the workplace. Best-selling math author Rhonda Huettenmueller uses the same combination of...384 pages20.5 MB15.99A Tour of the Calculus Berlinski its largest aspect, the calculus functions as a celestial measuring tape, able to order the infinite expanse of the universe. Time and space are given names, points, and limits; seemingly intractable problems of motion, growth, and form are red...352 pages4.1 MB13.99Calculus Made Easy P. Thompson Press2008-05-17Many of the earliest books, particularly those dating back to the 1900s and before, are now extremely scarce and increasingly expensive. We are republishing these classic works in affordable, high quality, modern editions, using the original text ...316 pages13.3 MB10.79Schaum's 3,000 Solved Problems in Calculus Mendelson Tough Test Questions? Missed Lectures? Not Enough Time?Fortunately for you, there's Schaum's.More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and ...480 pages58.5 MB21.29Calculus - A Complete Introduction: Teach Yourself Neill Yourself2013-05-30Calculus: A Complete Introduction is the most comprehensive yet easy-to-use introduction to using calculus. Written by a leading expert, this book will help you if you are studying for an important exam or essay, or if you simply want to improve y...20.9 MB8Projects for Calculus the Language of Change: Calculus: The Language of Change D. Stroyan Press1998-11-02Projects for Calculus is designed to add depth and meaning to any calculus course. The fifty-two projects presented in this text offer the opportunity to expand the use and understanding of mathematics. The wide range of topics will appeal to both...326 pages5.2 MB35.79501 Calculus Questions Learning Express Express, LLC2013-05-19This comprehensive study guide walks you step-by-step though 501 calculus questions-helping you sharpen your skills, prepare for academic exams, and build math problem-solving techniques.384 pages4.5 MB7.49Pre-Calculus Workbook For Dummies Kuang Rose Gilman Dummies2011-03-15Get the confidence and math skills you need to get started with calculusAre you preparing for calculus? This hands-on workbook helps you master basic pre-calculus concepts and practice the types of problems you'll encounter in the course. You'll g...360 pages16.2 MB11.99Calculus Demystified 2/E G. Krantz Professional2010-11-22Calculate this: learning CALCULUS just got a whole lot easier!Stumped trying to understand calculus? Calculus Demystified, Second Edition, will help you master this essential mathematical subject.Written in a step-by-step format, this practical gu...416 pages14.6 MB14.79Schaum's Outline of Calculus, 6th Edition Ayres Mendelson hig...552 pages48.7 MB14.79Schaum's Outline of Calculus, 5ed : Schaum's Outline of Calc, 5ed Ayres Mendelson pages34.2 MB14.79Schaum's Outline of Mathematica, 2ed Don Test Questions a...384 pages16.6 MB15.79Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering H. H. Strogatz Press2008-08-03"This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples and geome"352 pages19.7 MB28.99Advanced Calculus Demystified Bachman Professional2007-06-05Your INTEGRAL tool for mastering ADVANCED CALCULUS Interested in going further in calculus but don't where to begin? No problem! With Advanced Calculus Demystified, there's no limit to how much you will learn. Beginning with an overview of...274 pages5.5 MB15.99Frechet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179) Lindenstrauss Preiss Ti?er University Press2012-02-20This book makes a significant inroad into the unexpectedly difficult question of existence of Fréchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. Because the question turns out to be closely related to porous set...424 pages23.9 MB76.79
Advancing Math Education with Wolfram Technologies Wolfram technologies, including Mathematica and Wolfram\|Alpha, are broadening your math education pipeline—from interactive courseware authoring to cutting-edge research collaboration. Learn more in this video. Wolfram technologies, including Mathematica and Wolfram\|Alpha, are broadening your math education pipeline—from interactive courseware authoring to cutting-edge research collaboration. Learn more in this video. Wolfram technologies offer the world's largest integrated web of mathematical capabilities and algorithms. See the ultimate mathematical computational tools, including Mathematica and Wolfram\|Alpha, in action in this video. In this Wolfram Technology Conference presentation, Radim Kusak shares his experiences in creating the course, Introduction to Wolfram Mathematica for Teachers, for his colleagues at Charles University in Prague. See how Wolfram technologies like Mathematica and Wolfram\|Alpha enhance math education. The video features visual examples of course materials, apps, and other resources to help teachers and students cover math from algebra to calculus to statistics and beyond. Watch an introduction to the Wolfram Demonstrations Project, a free resource that uses dynamic computation to illuminate concepts in science, technology, mathematics, art, finance, and a range of other fields. This screencast from the Wolfram Mathematica Virtual Conference 2011 explores the various ways that mobile devices can tap into the power of Mathematica and Wolfram\|Alpha to enhance learning in math, science, and even music classrooms. Eric Schulz created the electronic version of Calculus: Early Transcendentals as a Computable Document Format (CDF) ebook. In this talk from the Wolfram Technology Conference 2011, he shares wisdom gained from his experience. In this video, get a quick introduction to the Wolfram Education Portal, which features teaching and learning tools created with Mathematica and Wolfram\|Alpha, including a dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. computerbasedmath.org is a project to build a new math curriculum with computer-based computation at its heart. In this talk from the Wolfram Technology Conference 2011, Conrad Wolfram discusses the concept, progress, and plans. Explore the various ways mobile devices can tap into the power of Mathematica and Wolfram\|Alpha to enhance learning in math, science, and even music classrooms in this recorded presentation from the Wolfram Technology Conference 2011. Get help and answers with precalculus, including limits, with the Wolfram Precalculus Course Assistant iPad app. This video shows you how the app's easy interface guides you through course topics and demonstrates how its calculators and solvers can help you with your homework. Learn music theory with the help of the Wolfram Music Theory Course Assistant iPad app. This video gives a quick overview of how the app guides you through learning, practicing, and understanding the fundamentals of music theory. Get answers for your pre-algebra problems with the Wolfram Pre-Algebra Course Assistant iPad app. This video gives you a quick tour of the app's easy-to-use interface as well as its calculators and solvers to help you with your homework. Get help and answers for your calculus classes with the Wolfram Calculus Course Assistant iPad app. This video gives you a quick tour of the app's intuitive interface for guiding you through course topics as well as its calculators and solvers to help you with your homework.
Chapter 3. Algebra of Matrices Introduction: Order of Matrix, Matrix and its types, Square Matrix, Diagonal elements, Identity or Unit Matrix, Properties of Addition, Properties of Scalar Multiplication, Product of matrices, Properties of Matrix Multiplication,Properties of transpose of a matrix, 17 Example with solutions (17 problems solved step by step) ` Chapter 4. Determinants Introduction, Properties of Matrices with 11 Solved Problems, Different Properties of Determinants with 16 solved problems, Properties of Determinants with 20 Solved Problems, Minors, Co-factors and its Application Chapter 7. Integrals Chapter 8. Applications of the Integral Applications of the Integrals: Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only), Area between the two above said curves (the region should be clearly identifiable) Chapter 9. Differential Equations Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables, homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type: dy / dx+ py = q, where p and q are functions of x or constant dx / dy + px = q, where p and q are functions of y or constant Chapter 10. Vectors Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Scalar (dot) product of vectors, projection of a vector on a line. Vector (cross) product of vectors. Scalar triple product of vectors. Chapter 11. 3D Geometry Direction cosines and direction ratios of a line joining two points. Cartesian and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane. Angle between (i) two lines, (ii) two planes. (iii) a line and a plane. Distance of a point from a plane. Chapter 12. Linear Programming
lessons for mastering essential culinary math skills. Culinary Math presents proven step-by-step methods for understanding foodservice mathematics and using it appropriately. Throughout, the book includes concrete examples that connect math concepts to real-world applications, as well as self-tests to help readers develop problem-solving skills. Authored by instructors at The Culinary Institute of America, this easy-to-use reference reviews basic addition, subtraction, multiplication, and division; presents the units of measure used in most professional kitchens in the United States; and offers simple methods for converting weight and volume measures. It also shows how to: Calculate yield percent Determine costs, edible portion costs, and recipe costs Find out the amount of a product needed for a particular use Carry out conversions for purchasing and food costing Understand and use kitchen ratios Convert U.S. measures to metric units and vice versa Culinary Math is an indispensable companion for students as well as for professional chefs, caterers, and others in need of a reliable training resource or handy quick reference.
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Triangle Precalculus work the first 6 or 7 problems as quickly as possible, and bubble in your choice. Elementary math includes the 4 basic operations with whole numbers and fractions. The fraction work includes common fractions and decimal fractionsMany people find Pivot Tables a hard concept, but I have been successful in fixing that. In addition, database systems, such as SQL Server 2012, may provide data in a Pivot Table and so it is important to be able to deal with them. SQL Server DBA with 9 years experience. ...I used COBOL for many of my undergrad projects, including one of my advanced programming courses, which used COBOL. I
Introductory Technical Mathematics - 5th edition ISBN13:978-1418015435 ISBN10: 1418015431 This edition has also been released as: ISBN13: 978-1418015459 ISBN10: 1418015458 Summary: Introductory Technical Mathematics, 5th Edition provides current and practical vocational and technical math applications for today's sophisticated trade and technical work environments. Each unit delivers practical math concepts alongside step-by-step examples and problems drawn from various occupations. The plentiful examples and problem sets emphasize on-the-job applications of math. Enhancements to the fifth edition include improved algebra coverage, a new sectio...show moren on basic statistics, new material on conversions from metric to customary systems of measure, and a section that supplements the basics of working with spreadsheets for graphing. Features: a new section on basic statistics features an all-new chapter on statistics and a chapter that consolidates all the statistical graphing techniques of bar, line, and circle graphs into one location79751418015435
Part I: Recommendations for departments, programs and all courses in the mathematical sciences Part I: Recommendations for departments, programs and all courses in the mathematical sciences General Resources for the CUPM Curriculum Guide David Bressoud, chair of CUPM, has written a series of 'Launchings� describing aspects of implementation of the CUPM Curriculum Guide. Topics through August 2007 are Introduction, Who are we teaching?, Teaching Students to Think, Only Connect!, Math & Bio 2010, Computational Science in the Mathematics,On Sustaining Curricular Innovation and Renewal, Targeting the math-averse, The Challenge of College Algebra, Avoiding Dead-End Courses, How to find more majors, Teaching for Transference, Keeping the Gates Open, Preparing K-8 teachers, Transition to Proof, Statistics for the Math Major, Writing to Learn Mathematics, The Role of Technology, Geometry in the Mathematics Major, Learning to Think as a Mathematician, Expanding the Boundaries of the Mathematics Curriculum, Attracting and Retaining Majors, Preparing Secondary Teachers, Preparing Our Majors, What has happened to Modern Algebra and Real Analysis?, Return to College Algebra, The Crisis of Calculus, Holding on to the Best and Brightest, Reform Fatigue, The Dangers of Dual Enrollment, and What You Test is What They Learn. 1: Understand the student population and evaluate courses and programs Mathematical sciences departments should: Understand the strengths, weaknesses, career plans, fields of study, and aspirations of the students enrolled in their courses; Determine the extent to which the goals of courses and programs offered are aligned with the needs of students and the extent to which these goals are achieved; Continually strengthen courses and programs to better align with student needs, and assess the effectiveness of such efforts. Assessing Programs, Courses, and Blocks of Courses Supporting Assessment of Undergraduate Mathematics (SAUM) is an MAA sponsored project to support mathematics departments in strengthening their courses and programs based on assessment information. The project supports faculty members and departments across a variety of institutions in efforts to assess student learning in individual courses, coherent blocks of courses, and entire degree programs, using a range of assessment tools. (Madison, 2001) Blocks of courses targeted by the project include the major in mathematics, courses for future teachers, college placement programs, and general education courses, including those aimed at quantitative literacy. Recognizing that much mathematics is learned outside mathematics courses, this last block addresses the mathematical and quantitative literacy achieved in entire degree programs. Institutions that use assessment for program improvement, including research on learning, are of special interest to the project. A great deal of information to support assessment efforts can be found in the project's initial volume, Assessment Practices in Undergraduate Mathematics, edited by Bonnie Gold, Sandra Keith and William Marion, which is available in its entirety on the website. The volume includes a series of articles that address assessment and evaluation from many perspectives, and it contains over seventy case studies of assessment at institutions across the U.S. Since publication of this volume, the SAUM project has supported workshops to assist teams of faculty in developing and implementing assessment plans. Reports on the projects are posted on the SAUM website. One study, Undergraduate Mathematics Program Assessment ' A Case Study, fromAmericanUniversity examined the complete departmental mathematics program. Faculty found that their learning goals were difficult to assess and were not leading to informed program change. In response, they sent a team to the SAUM PREP workshop in 2003. This led to productive conversations within the department, revised learning goals that concentrated on results rather than process, and multiple means of assessment. Another study, 'Assessing Allegheny College's introductory calculus and precalculus courses � focused on a block of courses. This study assessed the effectiveness of the introductory calculus and precalculus courses using analyses of grade data, conversations with client departments, and information about such courses at similar institutions. The initial assessment led to substantial revisions in the department's course offerings. The study 'Assessing Written and Oral Communication of Senior Projects� from Saint Mary's University of Minnesota evaluated the success of a single course. Through this assessment process, the mathematics department learned that while its majors perform well in oral presentations and write well on general topics, their communication about technical aspects of mathematics could be improved. The report describes the changes made to the Senior Seminar course in response to the assessment findings, and changes that were incorporated into the mathematics major program as a whole. Faculty in the OberlinCollege mathematics department developed a set of objectives for the mathematics major that addresses both content and attitudes. To assess the success of their majors in accomplishing these objectives, and to inform the effort to improve their program, the department maintains a file of syllabi and major assignments for each course, conducts an annual survey of post-graduate Activity, collects a statistical profile of the mathematics majors in each class, and administers sequenced surveys to mathematics majors when they declare a major, when they graduate, and 5 years after graduation. For further information, contact Michael Henle. St. Olaf's mathematics department conducted a faculty retreat as part of a department self-study. To prepare for the retreat, faculty completed a questionnaire covering the department's mission, its curriculum and programs, staffing, students and assessment, faculty, communication, "fun stuff," and technology, resources, and facilities. Questions included: What should the goals of the department be in the next 5 years? How well does the mathematics curriculum serve (a) math majors; (b) students completing general education requirements; (c) students majoring in other areas? How can we best gauge how well we serve our students? What kind of support do you need to engage in your own professional activities? Are you receiving it? Which department activities do you value most? Results of the questionnaire were included with other data in a summary document used by outside reviewers and by the department in connection with its self-study. Outcomes of the self-study continue to develop, but they include new emphasis on undergraduate research and interdisciplinary collaboration. Significant structural changes to the mathematics major are also under consideration. These changes would encourage students to view mathematics, its applications, and its connections with allied areas more broadly than before. For further information, contact Paul Zorn. External Support for Assessing Undergraduate Mathematics The National Science Foundation has supported a variety of professional development opportunities that provide hands-on experience in assessment for both faculty and graduate students, including the series of workshops organized in connection with the SAUM project. Although these workshops are no longer available to new faculty, there is an online guide that can be freely used and adapted. Another NSF-funded project is investigating the long-term impact that the use of technology in introductory college mathematics courses has on students in STEM (Science, Technology, Engineering, and Mathematics) disciplines. Individuals at six institutions collect data locally while working as a team with experts who provide training and support. For more information, contact project directors Susan Ganter and Jack Bookman. As a result of a recent reorganization, the assessment of student achievement, including research on assessment and the development of assessment tools and practices, has been designated as one track of the National Science Foundation's Division of Undergraduate Education (DUE) Course, Curriculum, and Laboratory Improvement (CCLI) program. The Colorado School of Mines has produced a website, Assessment Resource Page, for departments developing their departmental assessment plans. Links are provided to departmental assessment plans that are publicly available on the worldwide web. Assessment Tools for the Classroom Part II of SAUM's publication, Assessment Practices in Undergraduate Mathematics, entitled Assessment in the Individual Classroom, provides examples of specific classroom assessment practices that can be useful in attempting to understand students' thinking and determining what they understand. As David Bressoud writes in an article in this section, 'No matter how beautifully prepared our classroom presentation may be, what the student hears is not always what we think we have said.� A widely used technique based on Angelo and Cross's Classroom Assessment Techniques (Angelo & Cross, 1993), is the One-Minute Paper, in which students are given the last few minutes of class to write the answer(s) to one or two questions, such as 'What was the most important point in the lecture?� or 'What is the slope of the graph of a function at a point?� or 'How comfortable do you feel asking questions?� or 'How clear was today's lecture for you?� Additional classroom assessment techniques are organized into the categories Testing and Grading, Classroom Assessment Techniques, Reviewing Before Examinations, What Do Students Really Understand?, Projects and Writing to Learn Mathematics, Cooperative Groups and Problem-Centered Methods, Special-Needs Students, and Assessing the Course as a Whole. The monograph Keeping Score by Ann Shannon discusses a variety of issues involved in designing assessment tasks, especially those that aim to evaluate a broad range of mathematical skills and abilities. An executive summary is available from the publisher, The National Academy Press. The article 'Mathematics performance assessment: A new game for students� by Ann Shannon and Judith S. Zawojewski (Mathematics Teacher, 88(9), 752'757) considers how to teach students to understand and benefit from new forms of assessment that may initially seem strange to them. Placement Exams Colleges and universities frequently use placement exams to gather information about entering students' mathematical abilities. Assessment Practices in Undergraduate Mathematicsedited by B. Gold et al. contains two articles on placement exams. One describes the placement procedures at St.OlafCollege, and the other describes the methods at the University of Arizona. At St.OlafCollege there are three levels of placement exam (basic, regular and advanced) to respond to the varied mathematical backgrounds of incoming students. Each exam includes subjective questions about students' mathematical motivation, background, calculator experience, and plans for college mathematics study. At the University of Arizona there are two levels of placement exam (intermediate algebra and college algebra/ trigonometry). Both schools report that a significant commitment is needed from the department and its faculty to complete the placement testing and assign students to appropriate courses. But they also report that these efforts bear dividends, as students enrolled in appropriate courses tend to be more successful. At the University of Arizona placement exam data have also been used to analyze the mathematics program, inform future decisions on course offerings, and improve testing procedures. Norma G. Rueda & Carole Sokolowski, MerrimackCollege, wrote Mathematics Placement Test: Helping Students Succeed, which describes their study comparing the performance of students who took the course recommended by their mathematics placement exam score and students who did not take the recommended course. They found that students who followed the recommendation did much better than those who took a higher-level course or did not take the placement exam. Because of the careful statistical nature of the study, its results have been useful in convincing students to follow placement exam guidelines. Assessing student background is especially important in 'open-door� institutions, where any high school graduate can be admitted. For example, the CBMS2000 survey (p. 141) found that in two-year colleges, 'diagnostic or placement testing [was] � almost universal in availability.� The Transition Mathematics Project is a collaborative project of K-12 schools, community and technical colleges and baccalaureate institutions to assist with the transition from high school to college/university mathematics in the State of Washington. Its Resource Center contains information about placement tests and placement test issues, as well as much other information. Alvin Baranchik and Barry Cherkas conducted a study of placement exams taken by more than 1000 students at an urban four-year college and published the results in 'Differential Patterns of Guessing and Omitting in Mathematics Placement Testing� (in Dubinsky et al. (Eds.), Research in Collegiate Mathematics Education, II, 1996, AMS, 177-193). They found that the tendency to guess, omit answers, or not finish the exam varied by gender, ethnicity, first language, and birthplace, in ways that could not be fully explained by prior mathematical skill. The authors concluded that scoring by number of correct answers reduces the representation in gateway courses of certain cultural and gender groups for reasons unrelated to mathematical skill. They recommend that colleges either employ 'formula scoring,� which assigns a small penalty for guessing or a small bonus for omitting questions, or that they provide the following instructions at the beginning of the test: 'Because of the way this test is scored and interpreted, to be fair to yourself you must answer all questions, even if you must guess. You will not be penalized for guessing or incorrect answers.� In January 2005 Derek Bruff, Harvard University, posted a list of resource articles about placement exams on the discussion list for the Special Interest Group of the MAA on Research in Undergraduate Mathematics Education (SIGMAA-RUME). Mathematical Autobiography A mathematical autobiography is a written assignment in which the writer relates and reflects on memories of his or her experiences with mathematics. Reading students' mathematical autobiographies can help instructors understand that their students' mathematical experiences may be very different from their own. An instructor's awareness and acknowledgment of these differences may facilitate classroom communication, especially in lower-division courses. According to M. A. Conway, the assignment is most productive when it prompts a purposeful, extended, memory-search and is rewarded (Conway, 1990). For example, it might receive a grade or extra credit or be used to replace a test score. A sample of such an assignment is from Shandy Hauk, University of NorthernColorado Advising Interacting with students through the advising process can help faculty understand students and their goals and improve the effectiveness of a department's program. The University of Southern Mississippi has developed a comprehensive advising program from providing mentors for freshmen to conducting a survey of graduating students. MountHolyokeCollege provides a webpage, Beginning the Study of Mathematics and Statistics at Mount Holyoke: A "User's Guide" to selecting a first course, to advise students who are starting their collegiate mathematics study. The page explains that most students begin with a calculus course, a quantitative reasoning or data analysis course, a seminar course, or a computer science course. The webpage then describes the options within each type of course and helps each student choose the most appropriate one for his or her mathematical background and interests. The website for the mathematics department at the University of North Texas includes links for academic advising and placement, course information, student resources, and career information. The site provides information for students on choosing their first math class, preparing for the placement exam, and fulfilling the general education requirement. It also includes course descriptions and sequencing information, tips for success with mathematics courses, information about the mathematics laboratory and tutoring help, description of math club activities, and extensive program and career information for mathematics majors, including links to outside resources. Students at KenyonCollege are offered 'Advice to New Students,� about how their choice of a first mathematics course could fit their academic plans. For example, students who want only an introduction to mathematics or a course to satisfy a distribution requirement can select from Elements of Statistics, Surprises at Infinity, Quantitative Reasoning, Pre-Calculus, Calculus A, and Introduction to Computer Science. The University of Michigan at Dearborn publishes an 'Advising Newsletter� each semester. The newsletter is sent to all declared mathematics majors and contains information on courses, careers, competitions, scholarships, and on-campus jobs for math majors. It is available through the mathematics department's link Information for Students. Redesigning Courses and Programs in Response to Information about Students High drop-out and failure rates for certain groups of minority students in calculus at the University of California at Berkeley, despite their relatively high mathematics entrance scores, prompted Uri Treisman to investigate the study habits of both successful and unsuccessful students. Based on his findings, he introduced a mathematics workshop supplement for the Berkeley calculus course, recruiting African-American and Latino students who had relatively high SAT Mathematics scores and/or intended to major in a mathematics-based field. Key elements of the workshop involved: * the commitment to help minority studentsexcelat the University rather than merely avoid failure; * collaborative learning and the use of small-group teaching methods; and * faculty sponsorship, which has nourished the program and enabled it to survive. (Treisman, 1985, pp. 30'31) The program at Berkeley 'replaces regular calculus discussion sections with workshop-style discussion sections, in which the students collaborate on non-textbook, non-routine problems.� During these work sessions (which meet for larger blocks of time than traditional classes), '[students] begin working the problems individually, then, when things get tough, in collaboration with one another. These experiences lead to a strong sense of community and the forging of lasting friendships� (Gillman, 1990, p. 8). The Berkeley program has been so successful that it has been adapted by universities and colleges throughout the country. Treisman has stressed that the program is not remedial ' and should not be ' and care is taken to prevent implementations from reverting to remedial programs. Eric Hsu's website at San FranciscoStateUniversity contains a number of resources for Treisman-style workshops, including a database of workshop problems and a handbook developed for instructors and teaching assistants in the Berkeley program. Additional information available on the Internet includes a history of the programs, summaries of evaluations (p.18), and details of one evaluation. Another detailed evaluation is in An Efficacy Study of the Calculus Workshop Model (Bonsangue, 1994). A few websites for existing Treisman-style programs are University of Wisconsin-Madison, Wayne State University, and University of Texas at Austin. At CarnegieMellonUniversity before 1995, between 7 and 10 percent of students enrolled in the computer science program were female and their dropout rate was far higher than that of men. Educational researcher Jane Margolis and computer scientist Allan Fisher redesigned the computer science program, and the percentage of women receiving degrees increased considerably. Margolis and Fisher's study of the Carnegie Mellon program and how the program was redesigned are described in Unlocking the Clubhouse: Women and Computing. Further changes are described in the webpage Women in Computer Sciences: Closing the Gender Gap in Higher Education. Although the situation at Carnegie Mellon concerned women and computer science, the book may be useful for those thinking of studying and redesigning mathematics programs.
Elementary Algebra for College Students The Angel author team meets the needs of today's learners by pairing concise explanations with the new Understanding Algebra feature and an updated approach to examples. Discussions throughout the text have been thoroughly revised for brevity and accessibility. Whenever possible, a visual example or diagram is used to explain concepts and procedures. Understanding Algebra call-outs highlight key points throughout the text, allowing readers to identify important points at a glance. The updated examples use color to highlight the variables and important notation to clearly illustrate the solution process. Customer Reviews: 8th edition of this book By The Bouncer "The Bouncer 2007" - March 17, 2011 This book is an assigned book at MCC for the 098 Math course. Likewise the Intermediate book by this same author is for their 104 Math Course. This comes as no suprise since the author was the head of the mathematics department many years ago at MCC. This review is for the Elementary Algebra book This book has too much going on it. It is very confusing. Visually its like they spent time trying to make it look good versus giving you the information you require to do math correctly. The overusage of colors throughout the book makes it very distracting to the reader. Many things are in orange, yellow and blue making it very distracting with all of the callouts it the equivalent of an obstacle course in a textbook. Many of the examples shown in the book lack critical information needed to complete all the problems at the end of the section. For instance in some of the examples they will show you how to do a certain problem, for example say x 1/2 +8x - y... read more Elementary Algebra for College Students By Sophie's Choice - February 19, 2010 This text is required for the course. It is well written and clearly explains algebra for those new to the subject and for those who are taking a refresher course. There are complete worked out solutions to test exercises which are very helpful. book By karina - March 3, 2013 it was the wrong book. i need the intermediate algebra for college students not the elementary algebra for college students but couldn't see it said elementary instead of intermediate
prominent mathematician presents the principal ideas and methods of number theory within a historical and cultural framework. Oystein Ore's fascinating, accessible treatment requires only a basic knowledge of algebra. Topics include prime numbers, the Aliquot parts, linear indeterminate problems, congruences, Euler's theorem, classical construction problems, and many other subjects. {"currencyCode":"USD","itemData":[{"priceBreaksMAP":null,"buyingPrice":12.81,"ASIN":"0486656209","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":10.4,"ASIN":"0486663485","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":10.83,"ASIN":"048646931X","isPreorder":0}],"shippingId":"0486656209::An9I4vGiRh8LvlRgeRtSvpbV%2Bsrca3FQFqOwi0N%2BIxcWJarjezcCYC8gIztqRDYSBS%2Fv2CqEbhsFL4uwsn2TXjCYD87UOzaZ%2FwkBpUwx4Ms%3D,0486663485::WAJWf6LBB7guicioE%2BpXhXjvlOO0P%2Ba1hxdh0fdRECmlXlcXLMPNE1YVv7XWfK4o5PsoIvDSJF4u4%2BzYi3RnXUU81lMs43uFdSKB7Vw%2BWWs%3D,048646931X::Pr%2BT6YEbbUNwDhIBuV2smIOQTmfatbFOjCp7a19%2FSuEQWGkhwX%2BOkNB9HahN6pw9QZeFVWYxiSQ%2Bma%2BzoGCqzgA%2FV8%2FuMKT3KXDppXwADThis book goes into detail on number theory, but it is often hard to follow with the history mingled with the theory. More advanced material is referenced without proofs. Two readers will especially like this book: those who want an introduction to number theory and those who want a good introduction to the history of number theory.A noted conjecture of the author's on the harmonic mean of the divisors is tucked unobtrusively in this pleasant reader: "Every harmonic number is even." See problem B2 in Richard K. Guy's Unsolved Problem's in Number Theory. A good book (but not a great book). Very basic. For the more advanced historical approach, Andre Weil's Number Theory: An approach through history" is to be recommended. Or even Guy's book mentioned above.
Math-o-mir This product is basically an Equation Editor. However it is not centered over one single equation but you can write your mathematical text over several pages. Inside your mathematical document, you can copy equations and expressions easily by mouse click. You can also make simple drawings or sketches. Added function plotter and symbolic calculator can assist you... Engineers can use it to make quick informal calculations; students can use it as a real-time math note-taking tool; math teachers can prepare electronic exams to be solved by their students. Is support for your OS or mail server being terminated? Then this is one Hangout you won't want to miss. Watch now as Google experts outline strategies for coping with impending product retirements. Learn more now.
And not to think for themselves. It has nothing to do with higher critical thinking skills. And provides no knowledge of the world, while preventing children from engaging in learning that essential to self-knowledge and awareness. Algebra is a form of thought/mind control that steals from the potential of the time spent in school. If we want people who can take orders and obey the rules, then Algebra is the ticket. If we want people who can make decisions on their own, and manage their lives without someone telling them what to do, then Algebra is of zero
This course develops students' number fluency and understanding of the rational number system, extending students' understanding of fractions and decimals to the introduction of rates, ratios, proportions, and percent. Students will also write, simplify, and evaluate numerical and algebraic expressions and they explore the meanings of variables and formulas. Students will generalize their understanding of inverse operations as they learn to solve one-step equations and inequalities and model real-world situations using this algebraic notation. After a targeted exploration of area and volume, measures of spread, and graphs and plots, the course concludes with an in-depth study of numbers and their opposites—represented numerically, algebraically, and graphically.
PreCalculus with Solutions 9780495018872 ISBN: 0495018872 Edition: 4 Pub Date: 2006 Publisher: Brooks/Cole Summary: Authored by Faires and DeFranza. Besides providing complete solutions to all odd-numbered exercises in the text, this guide includes additional material for students who want a more intensive review of algebra and trigonometry. The Study Guide also includes two copies of an examination - one copy to be taken at the beginning of the course to test their readiness for PreCalculus and a second copy to be used at the end... of the course so students can assess their improvement and readiness for calculus

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