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course provides Mechanical Engineering students with an awareness of various responses exhibited by solid engineering... see more This these properties characterize material response; quantitative skills to deal with materials-limiting problems in engineering design; and a basis for materials selection in mechanical design. This is a free online course offered by the Saylor Foundation.'The courses included in this program are designed for the high... see more This is a free online course offered by the Saylor Foundation.'The courses included in this program are designed for the high school student preparing for college or the adult learner who needs a refresher course or two in mathematics.Each of the courses in this series includes instructional videos and practice problems from Khan Academy™ (Khan Academy™ is a library of over 3,000 videos covering a range of topics, including math and physics) that will help you master the foundational knowledge necessary for success in College Algebra (MA001: Beginning Algebra) and beyond.These courses focus on the ways in which math relates to common "real world" situations, transactions, and phenomena, such as personal finance, business, and the sciences. This "real world" focus will help you grasp the importance of the mathematical concepts you encounter in these courses and understand why you need quantitative and algebraic skills in order to be successful both in college and in your day-to-day-life.' lab series designed to familiarize students with using computer models to answer biochemical questions. ... see more Undergraduate lab series designed to familiarize students with using computer models to answer biochemical questions. Ideally, this lab would be taught as a supplement to a concurrent lecture course. Students are assumed to have completed one year of undergraduate calculus.Topics include acid-base chemistry, Gibbs free energy, Michaelis-Menten kinetics, enzyme inhibition, hemoglobin, and the Bohr effect. Math skills used include graphing (2-D and 3-D), algebra, logarithms, and numerical solutions to systems of equations
Plomplex is a complex function plotter using domain coloring. You can compose a function with a complex variable z, and generate a domain coloring plot of it. You can choose the plot range as well as ... More: lessons, discussions, ratings, reviews,... What's the reliability of cancer tests, diabetes tests, and pregnancy tests? This brief discussion shows some functions to be used on your graphing calculator to visualize a graph of the accuracy of a... More: lessons, discussions, ratings, reviews,... This physics-exploration applet allows the user to experiment with different roller coaster track designs, then test. Friction and mass are modeled. Includes hot links to explanations of various phys... More: lessons, discussions, ratings, reviews,... Windows software which allows the display of 2D and 3D diagrams both on one, and on different screens. Display 2D diagrams in the Cartesian and polar systems of coordinates. Display 3D diagrams in t... More: lessons, discussions, ratings, reviews,... Commercial site with one free access a day. Students use mapping diagram to create a relation, then they can check if it is a function from the mapping diagram, ordered pairs and graph. After studen
02620150 for Economics This text offers a comprehensive presentation of the mathematics required to tackle problems in economic analyses. To give a better understanding of the mathematical concepts, the text follows the logic of the development of mathematics rather than that of an economics course. The only prerequisite is high school algebra, but the book goes on to cover all the mathematics needed for undergraduate economics. It is also a useful reference for graduate students. After a review of the fundamentals of sets, numbers, and functions, the book covers limits and continuity, the calculus of functions of one variable, linear algebra, multivariate calculus, and dynamics. To develop the student's problem-solving skills, the book works through a large number of examples and economic applications. This streamlined third edition offers an array of new and updated examples. Additionally, lengthier proofs and examples are provided on the book's website. The book and the Web material are cross-referenced in the text. A student solutions manual is available, and instructors can access online instructor's material that includes solutions and PowerPoint slides. Visit for complete
Cal general review covers equations, functions, and graphs; limits, derivatives; integrals and antiderivatives; word problems; applications of integrals to geometry; and much more. Additional features make this volume especially helpful to students working on their own. They include worked-out examples, a summary of the main points of each chapter, exercises, and where needed, background material on algebra, geometry, and reading comprehension.
An Interactive Notebook gives students a place to: ... Your student is keeping an Interactive Notebook in Mathematics. ..... Algebra 1 is a required yearlong course for advanced middle school students. implemented field journals as an interactive experience with visual arts and academics: - Journal .... 7th grade science students refer to their field journals to create painted panels for installation in their ...
Elementary Number Number Theory, Seventh Edition, is written for the one-semester undergraduate number theory course taken by math majors, secondary education majors, and computer science students. This contemporary text provides a simple account of classical number theory, set against a historical background that shows the subject's evolution from antiquity to recent research. Written in David Burton's engaging style, Elementary Number Theory reveals the attraction that has drawn leading mathematicians and amateurs alike to number theory over the cou... MORErse of history.
Heya peeps! Is anyone here know about middle school math with pizzazz! book c,sixth grade,by creative publications? I have this set of problems regarding it that I just can't figure it out. We were tasked to answer it and know how we came up with the answer. Our Math teacher will select random students to answer it as well as show solutions to class so I require detailed explanation regarding middle school math with pizzazz! book c,sixth grade,by creative publications. I tried answering some of the questions but I think I got it completely wrong. Please help me because it's urgent and the deadline is quite near already and I haven't yet figured out how to solve this. Haha! absences are quite troublesome especially when you missed an important topic like middle school math with pizzazz! book c,sixth grade,by creative publications that is really quite complex. Have you tried using Algebrator before? As of now, this is what I can suggest you to do: try that program and you'll have no problem understanding middle school math with pizzazz! book c,sixth grade,by creative publications. It's very useful to use because it does not only solve math problems but it does explains by giving a detailed solution. Believe it or not, it made my test grades improve significantly because of this software. I just want to share this because I'm thrilled with the software's brilliance. I didn't use that Algebrator program yet but I heard from my classmates that it really does help in answering algebra problems. Since then, I noticed that my friends don't really have troubles solving some of the problems in class. It might really have been effective in improving their solving skills in math. I am eager to use it someday because I think it can be very effective and help me have a good mark in algebra. Algebrator is the program that I have used through several algebra classes - Algebra 1, College Algebra and Remedial Algebra. It is a really a great piece of math software. I remember of going through problems with conversion of units, scientific notation and parallel lines. I would simply type in a problem homework, click on Solve – and step by step solution to my algebra homework. I highly recommend the program.
including precalculus
General Relativity: An Introduction for Physicists provides a clear mathematical introduction to Einstein's theory of general relativity. It presents a wide range of applications of the theory, concentrating on its physical consequences. After reviewing the basic concepts, the authors present a clear and intuitive discussion of the mathematical background, including the necessary tools of tensor calculus and differential geometry. These tools are then used to develop the topic of special relativity and to discuss electromagnetism in Minkowski spacetime. Gravitation as spacetime curvature is then introduced and the field equations of general relativity derived. After applying the theory to a wide range of physical situations, the book concludes with a brief discussion of classical field theory and the derivation of general relativity from a variational principle. Written for advanced undergraduate and graduate students, this approachable textbook contains over 300 exercises to illuminate and extend the discussion in the text. less
books.google.com - This book contains computer-ready algorithms for many standard methods of numerical mathematics, describes the principles of the various methods, and offers support in choosing the appropriate method for a given task. Topics given special emphasis include: converging methods for solving nonlinear equations,... Algorithms With C
Maths Literacy QUESTIONS AND ANSWERS WHAT IS MATHS LITERACY? Mathematical Literacy provides learners with an awareness and understanding of the role that mathematics has in the modern world. Mathematical Literacy is a subject driven by life-related applications of mathematics. It enables learners to develop the ability and confidence to think numerically and spatially in order to interpret and critically analyse everyday situations and solve problems. WHAT IS THE PURPOSE OF MATHS LITERACY? The inclusion of Mathematical Literacy as a fundamental subject in the F.E.T. curriculum will ensure that our citizens of the future are highly numerate consumers of mathematics. In the teaching and learning of Mathematical Literacy learners will be provided with opportunities to engage with real life problems in different contexts (i.e. real life situations) and so consolidate and extend basic mathematical skills. Mathematical literacy will thus result in the ability to understand mathematical terminology and make sense of numerical and spatial information communicated in tables, graphs, diagrams and texts. Mathematical Literacy will develop the use of basic mathematical skills in critically analysing situations and creatively solving everyday problems. Mathematical Literacy will equip a learner with the skills to e.g.: budget, repay and understand loans, master interest and related concepts and manage money. The learners will be provided with real life problems in different contexts and so consolidate and extend basic mathematical skills. The learning outcomes of Mathematical Literacy are designed to enable learners to handle, with confidence, the mathematics that affects their lives and so be appropriately educated for the modern world. Students proceeding to Higher Education institutions will have acquired a mathematical literacy that will enable them to deal effectively with mathematical requirements in disciplines such as the social and life sciences. Mathematical Literacy should not be taken by those learners who intend to study disciplines which are mathematically based such as the natural sciences or engineering. The F.E.T. subject, Mathematical Literacy, should enable the learner to become a self-managing person, a contributing worker and a participating citizen in a developing democracy. Mathematical Literacy will ensure a broadening of the educations of a learner that is suited to the modern world, by ensuring that learners are able to become: A self-managing person In everyday life a person is continually faced with mathematical demands, which the adolescent and adult should be in a position to handle with confidence. These demands frequently relate to financial issues such as hire purchase, mortgage bond and investments. There are however others, such as the ability to read a map, follow timetables, estimate and calculate areas and volumes, understand house plans and sewing patterns. Activities such as cooking and the use of medicine require efficient use of ratio and proportion and are encountered on a daily basis. A contributing worker The workplace requires the use of fundamental numerical and spatial skills with understanding. This often means that a flexible understanding of mathematical principles is necessary. This literacy must enable the person to, for example, deal with work-related formulas, read statistical charts, deal with schedules and understand instructions involving numerical components. A participating citizen In order to be a participating citizen in a developing democracy it is essential that the adolescent and adult have acquired a critical stance to mathematical arguments presented in the media and other platforms. The concerned citizen needs to be aware that statistics can often be used to support opposing arguments, say for and against the use of an ecologically sensitive stretch of land for mining purposes. In the information age the power of numbers and mathematical ways of thinking often shape policy. Unless the citizen appreciates this, the citizen will not be in a position to vote appropriately. The citizen must be able to engage responsibly in quantitative arguments relating to local, national and global issues. Across the world there is evidence that the mathematics learnt at school is not transferred to other contexts. The pervasive presence of handheld calculators and computers makes it critical that people understand how to interpret the results of calculations and that they are able to decide logically what mathematics to use. Mathematical Literacy provides the context, the opportunities to analyse problems and devises ways to solve them. WHAT WILL MATHS LITERACY LEARNERS LEARN? Learners of Mathematical Literacy will learn how to: Use a basic calculator. Perform basic arithmetical operations. Work with relationships between arithmetical operations. Work with simple formulae, including formulae for perimeter, area and volume; and speed and time. Estimate and check estimates against the situation. Work with and apply the concepts of ratio/proportion, percentage and rate. Determine input and output values for formulae (solve equations). Determine and plot the points for different graphs. Interpret information and trends communicated through graphs. Measure lengths, distances, volumes and mass (weight). Convert between units of measurement. Draw and interpret scale drawings. Use grids, scales and maps. Collect information to answer questions. Organise data using tallies and tables. Summarise data using the measures of mean, median and mode. Represent data using various data graphs, including pie charts, histograms and bar graphs. Anticipate which seats in the stadium will give the best view of the game. Predict all the possible outcomes of a sports tournament and anticipate the most likely winner. Understand that games of chance have no patterns. Develop arguments based on facts and the interpretations of facts. Use resources in economical and responsible ways. WHAT IS THE DIFFERENCE BETWEEN MATHS AND MATHS LITERACY? Maths Literacy focuses on the role of mathematics in the real world, whereas Mathematics focuses on the discipline of mathematics. With maths literacy, relevant current contexts are used, whereas with maths, applications are important, but do not have to be only real life contexts. With Maths Literacy only basic mathematics is needed and a few new concepts are introduced in Grades 10 and 11. In Maths, content is expanded on as the learners progress from one year to another. In Maths Literacy the contexts become more complex from year to year whereas in Maths both the content and contexts become more complex and advanced each year. CRITERIA AT FATIMA The C.T.A. gives one a good idea about how the learner will cope with Maths Literacy, while their mark in the final grade 9 Maths exam gives a good idea of how they will cope with Maths. We use the following in the Maths exam as a guideline: Less than 50%: Definitely Maths Literacy. Greater than 75%: Definitely Maths. Between 50% and 60%: Maths Literacy is strongly advised if you have worked hard to get this mark. If you are lazy or had a bad exam in the teacher's opinion, let the teacher suggest which you do. Between 60% and 75%: You should manage with Maths, but will probably not manage the optional parts and by the time you go to matric, you must be prepared to spend a lot of extra time on your Maths.
Lecture 41: Functions Part 2 Embed Lecture Details : More examples of solving function problems 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.
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Mathematical analysis This is a module framework. It can be viewed online or downloaded as a zip file. It is as taught in the assocDesign of Dredging Equipment Dredging equipment, mechanical dredgers, hydraulic dredgers, boundary conditions, design criteria, instrumentation and automation. Study Goals: The goal of the lecture is to get insight in the procedure for designing dredging equipment based on the knowledge of the dredging processes. Special aspects during design and use of dredging equipment. Author(s): Creator not set License information Related content by-nc-sa CSET Science Subtest II: Molecular Biology and Biochemistry
Reviews Description: Core-Plus Mathematics, is a standards-based, four-year integrated series covering the same mathematics concepts students learn in the Algebra 1-Geometry-Algebra 2-Precalculus sequence. Concepts from algebra, geometry, probability, and statistics are integrated, and the mathematics is developed using context-centered investigations. Developed by the CORE-Plus Math Project at Western Michigan University with funding from the National Science Foundation (NSF), Core-Plus Mathematics is written for all students to be successful in mathematics. Core-Plus Mathematics is the number one high school NSF/reform program and it is published by Glencoe/McGraw-Hill, the nationís number one secondary mathematics company.
Maths - Multi-Dimensional Algebra So far we have been looking at equations containing real numbers, in this section we will be looking at algebras where each element is a compound type made up of multiple quantities. In geometric terms each of these real quantities represents a dimension. Most of these algebras are 'vector spaces over a field' this means that these algebras have at least two operations, addition and scalar multiplication defined as follows: operation notation explanation addition V(a+b) = V(a) + V(b) the addition of two of these compound quantities is done by adding the corresponding elements of the two quantities. scalar multiplication V(sa) = s V(a) a scalar product of a compound quantity is done by multiplying the scalar product with each of its terms individually. These operations interact according to the distributivity property: s(b+c)=sb+sc This is what gives such algebras the linear property (see Euclidean space box on right) There is also a more general family of algebras (less constrains) than 'vector spaces over a field' these are 'modules over a ring'. In addition to the 'scalar' multiplication the families of algebras we are discussing will also have additional structure defined in terms of other multiplications which will give the individual algebras their flavor, for instance: Do dimensions square to positive or negative values (real or imaginary dimensions)? Multi-Dimensional Algebra Sometimes it makes sense to combine together a set of real numbers to form a single, indivisible entity, we can then use this entity in equations in the same way that we have used real number up to now. When we do this we need to be sure that we know the rules for working with these entities, the rules may possibly be different than when we are working with real numbers. Each algebra will also have its own rules for addition and/or multiplication and each will have its own notation. For more information see this page. For such a precise subject the terminology in mathematics is difficult to tie down. It seems that when mathematitions extend the subject they tend to reinterpret what went before and we end up with overlapping terminology. I am trying to keep the terminology, on this site, consistent at much as I can: definitions on this page. Vector Spaces Vector spaces have at least one dimension that behaves like real algebra, known as a 'scalar' and it has simple rules for addition and scalar multiplication: (v1,w1) + (v2,w2) = (v1+v2 ,w1+w2) α(v,w) = (αv,αw) That is: the rule for addition is that we add corresponding terms, for scalar multiplication: to multiplying the whole term by a scalar is equivalent to multiplying each element by the scalar. In classical vector algebra the scalar is a separate quantity from the vector quantity and there are 3 types of multiplication defined: K-Algebra This is a vector space where there is a multiplication which can be applied to any terms and will always give a valid result (multiplication is closed). This result is determined by multiplying the basis elements. Matrices Matrices can represent any linear relationship. There is an isomorphism between certain matrices (orthogonal) and some hypercomplex algebras. Hypercomplex Algebras This is where the terminology is most vague 'Hypercomplex numbers' tends to be used for various generalisations of complex numbers. Here we will use 'hypercomplex' to represent algebras determine the product of two terms by: (a ei)(b ej) = abSij*(eiej) where: a, b = the scalar values. Sij = represents the sign, it is a step function which is -1 or +1 depending on i and j. eiej = represents the type given by the Kronecker product. eiej will always be the same for an algebra of a given dimension and can easily be calculated, provided the elements are represented in bit order, by taking the bitwise exclusive or of the two operands. So the nature of the entire algebra can be represented by Sijthe sign value of the product. For an 'n' dimensional algebra this can be shown by an n×n array of binary values. For a fuller explanation of this see this page. The two most important examples of hypercomplex algebras are Clifford and Cayley-Dickson Algebras (which overlap to some extent) although there may be other hypercomplex algebras? Clifford Algebras In Clifford algebras the product of two different vector basis ei^ej cannot be simplified further and is left as it is as a bivector basis. In further multiplications we bay go on to generate trivector basis and so on. Cayley-Dickson Algebras In Cayley-Dickson algebras the product of two different vector basis ei^ej is represented as a new vector basis ek and in any further iterations is treated as just another vector basis. Converting bivectors to vectors at each stage explains why the algebraic properties of these algebras degrade every time we double up the dimension. Cayley Table The Cayley Table is a good way to completely specify the multiplication rules of a multi-dimensional algebra. This allows us to easily lookup the result of multiplying any two elements of a given algebra. the result is made up of 3 parts: The scalar 'analogue' value of the result. Type of the result. Sign change of the result. This assumes that the product of any two elements will be a single type which is the case for the simpler algebras that we are concerned with. There are an infinite number of scalar values so we can't make a table from that but the type and sign can be combined into a table. Generating Geometric Algebras Vector multiplication (cross and dot product) can be very useful in physics but it also has its limitations and Geometric Algebra defines a new, more general, type of multiplication. This new type of multiplication generates new 'dimensions' so Geometric Algebra takes a vector algebra of dimension 'n' and generates an algebra of dimension n². What are the properties of these new dimensions? How much freedom do we have, in in choosing the basis vectors for example, to modify these properties?Coordinate Independent Equations In physics we have equations like T= r × F which apply independently of the origin and direction of the coordinate system that we are using. Different types of algebras like Clifford algebras and Tensor algebra give us alternative ways to bridge between the high level (coordinate free) and the coordinate specific layers: Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them. Clifford Algebras and Spinors (London Mathematical Society Lecture Note S.) Pertti Lounesto. This is very complex subject matter, however there is a lot of explanations and it is not all proofs like some mathematical textbooks. The book has a lot of information about the relationship between Clifford Algebras and Hypercomplex AlgebrasDark Basic Professional Edition - It is better to get this professional edition This is a version of basic designed for building games, for example to rotate a cube you might do the following: make object cube 1,100 for x=1 to 360 rotate object 1,x,x,0 next x
What consistent features, friendly writing style, clear examples, and exercise sets for which this text is known. edition features the exact same content as the traditional text in a convenient, three-hole- punched, loose-leaf version. Books a la Carte also offer a great value—this format costs significantly less than a new textbook. What package consists of the textbook plus an access kit for MyMathLab/MyStatL ab. Mathematical Ideas captures the interest of non-majors who take the Liberal Arts Math course by showing how mathematics plays an important role in scenes from popular movies and television. By incorporating John Hornsby's "Math Goes to Hollywood" approach into chapter openers, margin notes, examples, exercises, and resources, this text makes it easy to weave this engaging theme into your course. The Twelfth Edition continues to deliver the superlative writing style, carefully developed examples, and extensive exercise sets that instructors have come to expect. MyMathLab continues to evolve with each new edition, offering expanded online exercise sets, improved instructor resources, and new descriptions of the margin notes have been freshened, and Chapter 14: Personal Financial Management has been updated to meet the needs of today's students. With great care and effort, Vern Heeren and John Hornsby have craftedBuy 50 Mathematical Ideas You Really Need to Know by Tony Crilly and Read this Book on Kobo's Free Apps. Discover Kobo's Vast Collection of Ebooks Today - Over 3 Million Titles, Including 2 Million Free Ones! This survey of both discrete and continuous mathematics focuses on the logical thinking skills necessary to understand and communicate fundamental ideas and proofs in mathematics, rather than on rote symbolic manipulation. Coverage begins with the fundamentals of mathematical language and proof techniques (such as induction); then applies them to easily- understood questions in elementary number theory and counting; then develops additional techniques of proofs via fundamental topics in discrete and continuous mathematics. Topics are addressed in the context of familiar objects; easily- understood, engaging examples; and over 700 stimulating exercises and problems, ranging from simple applications to subtle problems requiring ingenuity. ELEMENTARY CONCEPTS. Numbers, Sets and
ALEX Lesson Plans Title: Bloodstain Pattern Doesn't Lie...... Description: StudentsStandard(s): [S1] FOR (9-12) 9: Use laws of physics to explain forensic evidence. [S1] PHS (9-12) 12: Identify metric units for mass, distance, time, temperature, velocity, acceleration, density, force, energy, and power. [TC2] (6-8) 5: Use basic features of word processing, spreadsheets, databases, and presentation softwareS1] (8) 1: Identify steps within the scientific process Science (8 - 12), or Technology Education (6 - 8) Title: Bloodstain Pattern Doesn't Lie...... Description: Students Title: Real-World Linear Programming Description: TheStandard(s): [TC2] (0-2) 9: Identify digital tools used for problem solving. [TC2] (0-2) 7: Use digital tools to access and retrieve information. [MA2010] ALT Technology Education (K - 2) Title: Real-World Linear Programming Description: The Title: Math is Functional Description: This and discovery about slope and y-intercept will help students conceptualize material normally presented in Algebra I textbooks ALC (9-12) 12: Create a model of a set of data by estimating the equation of a curve of best fit from tables of values or scatter plots. (Alabama) AL1 (9-12) 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [F-LE1 AL1 (9-12) 13: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [A-CED2] Subject: Mathematics (9 - 12), or Technology Education (9 - 12) Title: Math is Functional Description: This and discovery about slope and y-intercept will help students conceptualize material normally presented in Algebra I textbooks. Title: You Mean ANYTHING To The Zero Power Is One? Description: This lesson is a technology-based project to reinforce concepts related to the Exponential Function. It can be used in conjunction with any textbook practice set. Construction of computer models of several Exponential Functions will promote meaningful learning rather than memorization ALC (9-12) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay 2: Rewrite expressions involving radicals and rational exponents using the properties of exponents. [N-RN2] [MA2010] AL1 (9-12) 13 1: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. [N-RN1] [MA2010] AL1 (9-12) 9: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* [A-SSE3] Subject: Mathematics (9 - 12), or Technology Education (9 - 12) Title: You Mean ANYTHING To The Zero Power Is One? Description: This lesson is a technology-based project to reinforce concepts related to the Exponential Function. It can be used in conjunction with any textbook practice set. Construction of computer models of several Exponential Functions will promote meaningful learning rather than memorization. Thinkfinity Lesson Plans Title: Counting Embedded Figures Description: In this Illuminations lesson, students look for patterns in an embedded-square problem. After looking at the patterns, students form generalizations for the pattern. This activity sharpens students algebraic thinking and visualization skills 34: Write a function that describes a relationship between two quantities.* [F-BFT (9-12) 21: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [A-CED2 Mathematics Title: Counting Embedded Figures Description: In this Illuminations lesson, students look for patterns in an embedded-square problem. After looking at the patterns, students form generalizations for the pattern. This activity sharpens students algebraic thinking and visualization skills. Thinkfinity Partner: Illuminations Grade Span: 6,7,8 Title: Gallery Walk Description: In Gallery Walk Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Title: Conduct an Experiment PRE [MA2010] AM1 (9-12) 12: Calculate the limit of a sequence, of a function, and of an infinite series. (Alabama) Subject: Mathematics,Science Title: Conduct an Experiment Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Title: The Centroid and the Regression Line Standard(s): 44: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. [S-ID Subject: Mathematics Title: The Centroid and the Regression Line Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Title: Graphing What Description: This reproducible activity sheet, from an Illuminations lesson, is used by students to record independent and dependent variables as well as the function and symbolic function rule for a set of graphs function Graphing What Description: This reproducible activity sheet, from an Illuminations lesson, is used by students to record independent and dependent variables as well as the function and symbolic function rule for a set of graphs. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Title: Least Squares Regression Description: In Standard(s): models Least Squares Regression Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Title: Graph Chart Description: This reproducible transparency, from an Illuminations lesson, contains the answers to the similarly named student activity in which students identify the independent and dependent variables, the function, symbolic function rule and rationale for a set of graphs. Standard(s): 2: Recognize and represent proportional relationships between quantities. [7-RP2 1: Create algebraic models for application-based problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. (Alabama) [MA2010] AL2 (9-12) 12: Interpret expressions that represent a quantity in terms of its context.* [A-SSE 12: Interpret expressions that represent a quantity in terms of its context.* [A-SSE1 Graph Chart Description: This reproducible transparency, from an Illuminations lesson, contains the answers to the similarly named student activity in which students identify the independent and dependent variables, the function, symbolic function rule and rationale for a set of graphs. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Title: Bathtub Water Levels Description: In Bathtub Water Levels Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Title: Northwestern Crows between Subject: Mathematics,Science Title: Northwestern Crows Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Title: The Effects of Outliers effect of outliers on a regression line and easily see their significance 43: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [S-ID3 Subject: Mathematics Title: The Effects of Outliers effect of outliers on a regression line and easily see their significance Traveling Distances Description: In Traveling Distances Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Title: Automobile Mileage: Comparing and Contrasting Description: In that describes a relationship between two quantities.* [F-BF Automobile Mileage: Comparing and Contrasting Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Thinkfinity Learning Activities Tube Viewer Simulation Description: This student interactive, from Illuminations, simulates the effect of viewing an image through a tube. As students move the location of the person or change the length of the tube, the image and measurements also change. Standard(s): Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [F-IF5 Tube Viewer Simulation Description: This student interactive, from Illuminations, simulates the effect of viewing an image through a tube. As students move the location of the person or change the length of the tube, the image and measurements also change. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Integration Two RISP activities designed for students to explore or consolidate ideas about integration. Introducing e requires students to use a graphing package to explore a variety of functions of the form y equals x to the power of n and attempt to find the value for k for which the area under the graph between 0 and k is exactly one. Students are then asked to explore different properties of this family of functions leading to a definition of the exponential function. The answer's 1: what's the question? gives students a number of graphs containing shaded areas enclosed by two functions. Given that the enclosed area has a value of one, students are asked to find the equations of the functions
The text provides an introduction to the variational methods used to formulate and solve mathematical and physical problems and gives the reader an insight into the systematic use of elementary (partial) convexity of differentiable functions in Euclidian space. By helping students directly characterize then the solutions for many minimization problems, the text serves as a prelude to the field theory for sufficiency. It lays the groundwork for further explorations in mathematics, physics, mechanical and electrical engineering, and computer science #6 English Pronunciation in Use Elementary CD-ROM#7 Reading Time 3 [Only Audio] Reading Time is a three-level reading series designed for young, beginner EFL students. Throughout the series, students will expand their basic reading ability, acquire useful and relevant vocabulary, and develop their writing skills... #8 Elementary Topology 3-08-2010, 04:58 Elementary Topology 2007 \| 400 pages \| ISBN:0821845063 \| PDF \| 8 Mb The reader who has mastered the core material acquires a strong background in elementary topology and will feel at home in the environment of abstract mathematics. With almost no prerequisites (except real numbers), the book can serve as a text for a course on general and beginning algebraic topology. #10 Elementary Concepts of Topology Concise work presents topological concepts in clear, elementary fashion without sacrificing their profundity or exactness. Author proceeds from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. #13 New Headway Video DVD 2in1 (Elementary & Pre-Intermediate) This video course can be used as a supplement to any textbook, general English language courses for high school students. Headway Videos are divided into classes, a lexico-grammatical material which promotes the development of sociolinguistic competence of students. Subjects movies different (Home Movie, Do It Yourself, Surprise, Surprise!, A New Neighbour, An Old Friend, Dinner for Two, Change of a Dress, A Perfect Day, etc.), documentary scenes alternate with productions. #14 Basic Topology 3-08-2010, 04:54 Basic Topology 2007 \| 452 pages \| ISBN:0387908390 \| PDF \| 8 Mb In this broad introduction to topology, the author searches for topological invariants of spaces, together with techniques for calculating them. Students with knowledge of real analysis, elementary group theory, and linear algebra will quickly become familiar with a wide variety of techniques and applications involving point-set, geometric, and algebraic topology. Over 139 illustrations and more than 350 problems of various difficulties will help students gain a rounded understanding of the subject
for Dummies The mere thought of having to take a required calculus course is enough to make legions of students break out in a cold sweat. Others who have no ...Show synopsis Well, the good news is that you "can" "Calculus For Dummies" is intended for three groups of readers: Students taking their first calculus course - If you're enrolled in a calculus course and you find your textbook less than crystal clear, this is the book for you. It covers the most important topics in the first year of calculus: differentiation, integration, and infinite series.Students who need to brush up on their calculus to prepare for other studies - If you've had elementary calculus, but it's been a couple of years and you want to review the concepts to prepare for, say, some graduate program, "Calculus For Dummies" will give you a thorough, no-nonsense refresher course.Adults of all ages who'd like a good introduction to the subject - Non-student readers will find the book's exposition clear and accessible. "Calculus For Dummies" takes calculus out of the ivory tower and brings it down to earth. This is a user-friendly math book. Whenever possible, the author explains the calculus concepts by showing you connections between the calculus ideas and easier ideas from algebra and geometry. Then, you'll see how the calculus concepts work in concrete examples. All explanations are in plain English, not math-speak. "Calculus For Dummies" covers the following topics and more: Real-world examples of calculusThe two big ideas of calculus: differentiation and integrationWhy calculus worksPre-algebra and algebra reviewCommon functions and their graphsLimits and continuityIntegration and approximating areaSequences and series Don't buy the misconception. Sure calculus is difficult - but it's manageable, doable. You made it through algebra, geometry, and trigonometry. Well, calculus just picks up where they leave off - it's simply the next step in a logical progression.Hide synopsis Trade paperback (US). Glued binding. 364 p. Contains:...Very good. Trade paperback (US). Glued binding. 364 p. Contains: Illustrations. For Dummies (Lifestyles Paperback).New, Publisher overstock, may have small remainder mark....New, Publisher overstock, may have small remainder mark. Excellent condition, never read, purchased from publisher as excess inventory. Reviews of Calculus for Dummies This difficult to understand branch of math was first introduced to me in a two year college as a REVIEW. Needless to say, I didn't get very far. Neither did the rest of the class except ONE (brilliant) student. This text is excellent in its presentation, both in text and graphics. I wish this had ... More I was in a jugle, a deep, dark, frightening jungle. The jungle of CALCULUS. Suddenly a light came in front. A subtle, fagile one but growing even larger and larger as I slowly crawled towards the middle of this book. Now I walk more confident, steping firmly with a backbone for dummies:-)
Synopses & Reviews Publisher Comments: This text offers a comprehensive review of all basic mathematics concepts and prepares students for further coursework. The arithmetic is presented with an emphasis on problem-solving, skills, concepts, and applications based on "real world" data, with some introductory algebra integrated throughout. About the Author High School Mathematics Instructor - 6 years, Hillsboro Union High School. Community College Mathematics Instructor - 10 years, Portland Community College. Community College Administrator - 19 years, Portland Community College. Retired as Vice President of Educational Services at Portland Community College. Co-author - 8 mathematics texts.High School Mathematics Instructor - 12 years. Portland Public Schools. Community College Mathematics Instructor- 30 years, Portland Community College. Currently retired and teaching part-time at Portland Community College. Co-author - 9 mathematics texts.Community college Mathematics Instructor - 18 years, Portland Community College. Co-author - 2 mathematics texts
Mathematical Modeling Offering a solid introduction to the entire modeling process, A FIRST COURSE IN MATHEMATICAL MODELING, 5th Edition delivers an excellent balance of ...Show synopsisOffering a solid introduction to the entire modeling process, A FIRST COURSE IN MATHEMATICAL MODELING, 5th Edition delivers an excellent balance of theory and practice, and gives you relevant, hands-on experience developing and sharpening your modeling skills. Throughout, the book emphasizes key facets of modeling, including creative and empirical model construction, model analysis, and model research, and provides myriad opportunities for practice. The authors apply a proven six-step problem-solving process to enhance your problem-solving capabilities -- whatever your level. In addition, rather than simply emphasizing the calculation step, the authors first help you learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving you in the mathematical process as early as possible -- beginning with short projects -- this text facilitates your progressive development and confidence in mathematics and modeling
MAT 525 Algebraic Structures for Teachers This is a sample syllabus only. Ask your instructor for the official syllabus for your course. Instructor: Office: Office hours: Phone: Email: Course Description Topics related to the high school algebra curriculum from an advanced standpoint, including algorithms, polynomials, groups, rings, and fields. MAT 525 meets for three hours of lecture per week. Prerequisites MAT 543, graduate standing and one year of full time secondary teaching. Objectives To improve students' mathematical thinking by: Tackling questions and discussing them; Reflecting on this experience; Monitoring and evaluating one's own thinking; Studying the process of resolving problems Noticing connections between what is learned and one's own experience. To increase students' knowledge of the algebraic properties of the mathematical systems of groups and fields by investigating the rationals and their field extentions, the reals, and the complex numbers. Students should be able to Make and understand the connections and relationships between algebraic properties; in the curriculum. Understand the justification for many of the algebraic properties of the real numbers To increase students' knowledge about the current research in mathematical thinking and problem solving by: Reading current research articles Searching additional studies Comparing and contrasting results from different studies Expected outcomes Students should be able to demonstrate through written assignments, tests, projects, and/or oral presentations, that they have achieved the objectives of MAT 525. Method of Evaluating Outcomes Evaluations are based on homework, class participation, presentations, written assignments, projects, short tests and scheduled examinations covering students' understanding of topics covered in MAT 525. Text The text and other required or recommended materials are chosen by the instructor. Grading Policy Students' grades are based on homework, class participation, short tests, projects, presentations, and/or scheduled examinations covering students' understanding of the topics covered in MAT 525. The instructor determines the relative weights of these factors. Attendance Requirements Attendance policy is set by the instructor. Policy on Due Dates and Make-Up Work Due dates and policy regarding make-up work are set by the instructor. Schedule of Examinations The instructor sets all test dates. Academic Integrity The mathematics department does not tolerate cheating. Students who have questions or concerns about academic integrity should ask their professors or the counselors in the Student Development Office, or refer to the University Catalog for more information. (Look in the index under "academic integrity
In the recent years, Linux, a public domain, freely available Unix variant has attracted the people very much. Today's complex production environments demands superior application performance. Linux is having extraordinary advantages such as : complete source code access, availability of exceptional optimization, testing tools. This book has explored... more... While managerial economics is the application of economics in decision making, financial analysis judges financial performance of a firm. Several methods of analysis have been examined in the book, the two main tools being ratio analysis and analysis of balance sheet and profit and loss account of the firms. The book examines several steps involved... more... This book is written in a simple lucid Language along with derivation of equations and supported by numerous solved problems to help the student to understand the concepts clearly.Advances in Miniaturization of Electronic Systems by ever increasing packaging densities on Integrated Circuits has made it very essential for thorough Knowledge of the concepts,... more... The aim of this book is to present the sequential steps for developing the computer programs for the design of electrical machines, using well-established design formulae. The data of magnetic and non-magnetic materials used in latest designs by industries, is applied for optimizing the design. Salient Features: MATLAB Version of C Language is used... more... Modern power systems tend to be very Complex not only due to increasing Demand for quality power, but also on Account of extensive interconnections and increasing dependence on control for optimum utilization for existing resources. A good Knowledge of system dynamics and control is Essential for secure operation of the system. This book is intended... more... The aim of this book is to present the sequential steps for developing the Computer programs for the design of electrical machines, using well-established design formulae. The data of magnetic and non-magnetic materials used in latest designs by industries, is applied for optimizing the design. more... Remote Sensing and Geographical Information Systems (GIS) deals with mapping technology, concepts of maps and all relevant terminology which are necessary for a beginner to develop his skills in this new and upcoming technology. This book provides basic principles and techniques of remote sensing, microwave remote sensing, remote sensing platforms... more... Mathematics is the basic foundation course for all Engineering students. This edition covers the topics of numerical methods, matrices, Fourier Series and Fourier transforms along with Partial differential equations and Z-transforms. The subject matter has been presented in detailed and simple lucid way. The theory aspect is explained with illustrations... more... Since early 1970, Unix Operating System has gone through many metamorphosis. As of now many variants of Unix systems are available and some of them are commercial whereas the others are freely available. As a result, many people are becoming Unix/Linux enthusiasts especially in India. Hundreds of Books have been written in the past, which explores... more...
books.google.com - Designed for students preparing to engage in their first struggles to understand and write proofs and to read mathematics independently, this is well suited as a supplementary text in courses on introductory real analysis, advanced calculus, abstract algebra, or topology. The book teaches in detail how... Accompaniment to Higher Mathematics
This course covers a variety of mathematical methods used in the sciences, focusing particularly on the solution of ordinary and partial differential equations. In addition to calling attention to certain special equations that arise frequently in the study of waves and diffusion, we develop general techniques such as looking for series solutions and, in the case of nonlinear equations, using phase portraits and linearizing around fixed points. We study some simple numerical techniques for solving differential equations. A series of optional sessions in Mathematica will be offered for students who are not already familiar with this computational tool. Class Format: lecture, three hours per week Requirements/Evaluation: evaluation will be based on weekly problem sets and several in-class exams, all of which have a substantial quantitative component
More About This Textbook Overview This book of problems is designed to challenge students learning probability. Each chapter is divided into three parts: Problems, Hints, and Solutions. All Problems sections include expository material, making the book self-contained. Definitions and statements of important results are interlaced with relevant problems. The only prerequisite is basic algebra and calculus. Editorial Reviews From the Publisher M. Capinski and T. Zastawniak Probability Through Problems "This book of problems has been designed to accompany an undergraduate course in probability. The only prerequisite is basic algebra and calculus. Each chapter is divided into three parts: Problems, Hints, and Solutions. To make the book self-contained all problem sections include expository material. Definitions and statements of important results are interlaced with relevant problems. The problems have been selected to motivate abstract definitions by concrete examples and to lead in manageable steps towards general results, as well as to provide exercises based on the issues and techniques introduced in each chapter. The book is intended as a challenge to involve students as active participants in the course."—ZENTRALBLATT MATH
such as ordinary and partial differential equations.
Math 1,001 Algebra I Practice Problems For Dummies, with free access to online practice problems, takes you beyond the instruction and guidance offered in Algebra I For Dummies, giving you 1,001 opportunities to practice solving problems from the major topics in algebra. You start with some basic operations, move on to ... Read More Fear not, help is here. Your one-year, renewable, online subscription to 1,001 Algebra I Practice Problems For Dummies gives you 1,001 opportunities to practice solving problems that you'll encounter in your Algebra I course. You start with some basic operations, move on to algebraic properties, polynomials, and quadratic equations, and finish up with graphing. Every practice problem includes ... Read More 1001 Algebra II Practice Problems For Dummies takes you beyond the instruction and guidance offered in Algebra II For Dummies, giving you 1001 opportunities to practice solving problems from the major topics in algebra II. 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With just enough refresher explanations before each set of problems, you'll sharpen your skills and improve your performance. You'll see how to ... Read More Get the skills you need to solve problems and equations and be ready for algebra class Whether you're a student preparing to take algebra or a parent who wants to brush up on basic math, this fun, friendly guide has the tools you need to get in gear. From positive, negative, and whole numbers to fractions, decimals, and percents, you'll build necessary skills to tackle more advanced topics, such as imaginary numbers ... Read More When you have the right math teacher, learning math can be painless and even fun! Let Basic Math and Pre-Algebra Workbook For Dummies teach you how to overcome your fear of math and approach the subject correctly and directly. A lot of the topics that probably inspired fear before will seem simple when you realize that you can solve math problems, from basic addition to algebraic equations. 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Free of review and ramp-up material, Calculus Essentials For Dummies ... Read More The mere thought of having to take a required calculus course is enough to make legions of students break out in a cold sweat. Others who have no intention of ever studying the subject have this notion that calculus is impossibly difficult unless you happen to be a direct descendant of Einstein. Well, the good news is that you can master calculus. It's not nearly as tough as its mystique would lead you to think. Much of calculus is really just very ... Read MoreMany of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and ... 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Type of assessment: Exam duration: Aid: Evaluation: Qualified Prerequisites: General course objectives: To introduce several algebraic constructions (groups, rings and fields). These constructions will be applied in different areas, among others geometry and discrete mathematics. Learning objectives: A student who has met the objectives of the course will be able to: give the definition of a group apply group theory to solve counting problems describe symmetries of geometric object (eg platonic solids) give the definition of a ring explain the notion of an ideal and use this to construct quotient rings explain some applications of ringtheory in praxis. understand the construction of fields from rings (especially finite fields) describe how finite fields are used Content: To introduce several algebraic constructions (groups, rings and fields). These constructions will be applied in different areas, among others geometry and discrete mathematics. An impression is given as to how the theory is applied. This course can also be seen as a preparatory course for further courses in discrete mathematics.
COURSE OBJECTIVES: Students will develop computational skills in working with linear transformations and the matrices used to represent them. However, more of the course will focus on non-computational issues such as reasoning and constructing proofs. This course is intended as a transition between the beginning calculus courses and upper level courses in mathematics. CALCULATORS: This course is not focused on numerical computation. Students may wish to use calculators or computers as a study aid, but no electronic devices of any kind will be allowed on exams. See this page for some examples that illustrate the difficulties in doing numerical calculations. A calculator can give you a completely wrong answer. Techniques from numerical linear algebra are covered in a subsequent course, MATH 434. FINAL EXAM: The final exam will be a comprehensive, departmental examination. It is scheduled as a mass exam, on Wednesday, December 11, 6-7:50PM. All sections of this course will take the same final exam at the same time. LECTURES AND EXAMS: This is the tentative schedule for lectures and exams. CAAR STATEMENT: Students who request accommodation due to a physical or learning disability must contact their instructor at the beginning of the semester. The instructor has the right to see documentation of the student's condition from the CAAR office.
Presentation Description No description available. Comments Posting comment... Premium member Presentation Transcript Slide 1: Maths is my favourite subject I love maths MATHS PROJECT Polynomials Slide 2: CONTENTS 1.INTRODUCTION 2.GEOMETRICAL MEANING OF ZEROES OF THE POLYNOMIAL 3.RELATION BETWEEN ZEROES AND COEFFICIENTS OF A POLYNOMIAL 4.DIVISION ALGORITHM FOR POLYNOMIAL 5.SUMMARY 6.QUESTIONS AND EXERCISE Slide 3: ACKNOWLEDGEMENT The national curriculum framework such that children's life at school must be linked to their life outside the school. this principle marks a de portable use from the legacy of bookish learning and thus the students have been given provisions to preface some project reports on certain subjects. I express my hearty gratitude to CBSE for providing such an interesting and board scope topic for our project. I am really thankful to our respected subject teacher Ms.Nivedita Saxena who helped us in a passive way. I would also like to thank my parents and my friends for their help, encouragement and blessings. 1234567891011121314151617181920 Slide 4: Slide 5: INTRODUCTION In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative, whole-number exponents. Polynomials appear in a wide variety of areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated problems in the sciences; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; they are used in calculus and numerical analysis to approximate other functions. Slide 8: DEGREE OF A POLYNOMIAL The exponent of the highest degree term in a polynomial is known as its degree . For example : f(x) = 3x + ½ is a polynomial in the variable x of degree 1. g(y) = 2y 2 – 3/2y + 7 is a polynomial in the variable y of degree 2. p(x) = 5x 3 – 3x 2 + x – 1/√2 is a polynomial in the variable x of degree 3. q(u) = 9u 5 – 2/3u 4 + u 2 – ½ is a polynomial in the variable u of degree 5. Slide 9: CONSTANT Polynomial A polynomial of degree zero is called a constant polynomial. LINEAR polynomial A polynomial of degree one is called a linear polynomial For example: f(x) = 7, g(x) = -3/2, h(x) = 2 are constant polynomials. The degree of constant polynomials is not defined. For example: p(x) = 4x – 3, q(x) = 3y are linear polynomials. Any linear polynomial is in the form ax + b, where a, b are real nos. and a ≠ 0. It may be a monomial or a binomial. F(x) = 2x – 3 is binomial whereas g (x) = 7x is monomial. Slide 10: A polynomial of degree two is called a quadratic polynomial. f(x) = √3x 2 – 4/3x + ½, q(w) = 2/3w 2 + 4 are quadratic polynomials with real coefficients. Any quadratic is always in the form f(x) = ax 2 + bx +c where a,b,c are real nos . and a ≠ 0. QUADRATIC POLYNOMIAL CUBIC POLYNOMIAL A polynomial of degree three is called a cubic polynomial. f(x) = 9/5x 3 – 2x 2 + 7/3x _1/5 is a cubic polynomial in variable x. Any cubic polynomial is always in the form f(x = ax3 + bx2 +cx + d where a,b,c,d are real nos. Slide 19: RELATIONSIPS ON VERYFYING THE RELATIONSHIP BETWEEN THE ZEROES AND COEFFICIENTS ON FINDING THE VALUES OF EXPRESSIONS INVOLVING ZEROES OF QUADRATIC POLYNOMIAL ON FINDING AN UNKNOWN WHEN A RELATION BETWEEEN ZEROES AND COEFFICIENTS ARE GIVEN. OF ITS A QUADRATIC POLYNOMIAL WHEN THE SUM AND PRODUCT OF ITS ZEROES ARE GIVEN. Slide 20: DIVISION ALGORITHM Slide 21: If f(x) and g(x) are any two polynomials with g(x) ≠ 0,then we can always find polynomials q(x), and r(x) such that : F(x) = q(x) g(x) + r(x), Where r(x) = 0 or degree r(x) < degree g(x) ON VERYFYING THE DIVISION ALGORITHM FOR POLYNOMIALS. ON FINDING THE QUOTIENT AND REMAINDER USING DIVISION ALGORITHM. ON CHECKING WHETHER A GIVEN POLYNOMIAL IS A FACTOR OF THE OTHER POLYNIMIAL BY APPLYING THEDIVISION ALGORITHM ON FINDING THE REMAINING ZEROES OF A POLYNOMIAL WHEN SOME OF ITS ZEROES ARE GIVEN.
Advanced Studies Algebra II Mrs. Warden Contact Info: Main Line: 986-2000 Voice Mail: 986-1499 ext. 7945 Plan: 7th Hour E-mail: Melissa.Warden@leesummit.k12.mo.us Website: *Grades are available online with Parent Connect at . Grades will be updated on a weekly basis. Supplies Needed Daily:  PENCILS!! All submitted work must be completed in pencil to receive full credit.  3-ring binder with loose leaf and graph paper OR spiral notebook, graph paper, and folder.  Scientific calculator (minimum)  Textbook: McDougal Littell Algebra 2 Textbook Website:  TI-83+/TI-84 graphing calculator is STRONGLY recommended (TI-86 is acceptable) Course Description: PREREQUISITE: Teacher approval/Strongly recommend B or higher in Geometry Advanced Studies Algebra II emphasizes facility with quadratic forms, powers, and roots, and the functions based on these concepts. Students study logarithmic, polynomial, and other special functions as tools for modeling real-world situations. In addition to the traditional advanced algebra topics, Advanced Studies Algebra II begins the study of introductory statistics and probability. Major Course Goals: The course is designed to assist the student in the following:  To develop logical reasoning skills  To learn how to read and study mathematics  To apply calculus concepts to "real-world" situations  To master skills necessary for problem solving  To work collaboratively in group situations  To use technology in discovery and problem solving Class Expectations: 1. Be respectful of yourself, as well as all others. Try your best! 2. Be prepared for class each day. (homework, notebook, textbook, pencil, calculator, etc.) 3. Be on time. The tardy card policy outlined in the school planner/handbook will be strictly enforced. 4. Keep the room clean. If you bring food/drink in, make sure you take it out or throw it away! 5. Please ask questions if you do not understand! I am available before school starting at 7:10 and after school until 3:00 for additional help. A+ tutoring can be arranged through the A+ office located in Building B. After school tutoring is also available from 2:45 p.m. – 3:45 p.m. in the Tiger Tutoring Room. 6. When class time is given to work, you are to work on Advanced Studies Algebra II. 7. Follow the rules in the school handbook. Cell phones and IPODs should not be seen in the classroom as they violate school policy. The dress code will also be enforced, so please make sure that your clothing is appropriate. Instructional Philosophy: I believe that all students can learn through meaningful mathematics while developing critical thinking and problem solving skills. Classroom instruction will take various forms: direct instruction, cooperative learning (group work), discovery learning, etc. Lecture and demonstration will be utilized to introduce new concepts while individual and team practice will ensure understanding of concepts. Appropriate use of technology will be used in addition to application of real world mathematics. In order for you to be successful, it is important that you are actively involved by taking notes, paying attention, asking and answering questions, doing homework, reading, studying, and practicing your skills. Timeline: We will study six major topics per semester. Each chapter will consist of homework, quizzes, and a chapter test. At the end of each semester there will be a comprehensive semester final exam. Supplementary topics will be included in each semester. Grades: Homework (HW): 18% Tests, Quizzes, & Projects (TQP): 72% Semester Final (FINAL): 10% Class Procedures/Major Assignments and Projects: 1. At the beginning of each day you will pick up your warm-up sheet on the front table. You will be expected to be ready to do the warm-up activity when the bell rings. Questions on homework will be answered and the homework will be graded. Sometimes we will grade in class and sometimes I will collect your work. Homework will be worth 10 points. NO LATE WORK is accepted 2. It is strongly recommended that students take notes on a daily basis. Formative assessments will also be used to help remediate learning, when necessary. There will typically be class time for students to begin their homework assignment. 3. There will be at least one project per semester. One of these projects will include a research/resource-based component. The project will show your proficiency in some of the topics we have studied. A scoring guide will be given detailing what is expected. 4. Quizzes will be worth approximately 20 points each. Typically, you will have 1 – 2 quizzes per chapter. These are included on your assignment sheets for each chapter. A test will be given at the end of each chapter and are each worth 160 points. Be prepared for parts of any exam that will NOT allow the use of a calculator. If you miss the day of a quiz or test, you will make it up the NEXT TIME YOU RETURN to class. Tests cannot be retaken; however, if your homework score is a 70% or higher at the end of the semester, your lowest test score will be dropped. 5. Students will also be given take-home tests. These will consist of actual problems from IB Exams from previous years. Point values will vary. It is important to become acquainted with IB problem types as you are preparing to take the IB exam in IB Math 2. These will be graded on the accuracy of your answers and the appropriate presentation of your solutions. Keep in mind that the IB program takes communication and process very seriously in its evaluation. Make-Up Homework Due to Absences: All assignments are listed on an assignment sheet at the beginning of each chapter. If you are absent, it is your responsibility to get the notes and make-up work when you return. Notes should be posted to my website at the end of the day, as well as any handouts. Handouts can also be found in the appropriate slot in the cabinet upon your return. As stated in the student handbook, you are allowed one day for every day you are absent to make-up work. If you miss just the day of a test, you will be expected to make it up on the day you return. You are expected to inform the instructor IN ADVANCE if you will be absent due to a school function (field-trip, athletic event, competition, etc). You will receive the assignment in advance with the expectation that it be completed upon your
Getting Started with MATLAB 7 : A Quick IntroductionMATfor Scientists and Engineers employs a casual, accessible writing styl... MOREe that shows users how to enjoy using MATLAB. RG Familiarizes users with MATLAB in just a few hours though self-guided lessons RG Discusses new features and applications in MATLAB 7 RG Covers elementary, advanced, and special functions RG Includes numerous new examples and problems RG Supplements any course that uses MATLAB RG Works as a stand-alone tutorial and reference MAT for Scientists and Engineers employs a casual, accessible writing style that shows users how to enjoy using MATLAB. MATLAB is a software package designed for high-performance numerical computation and visualization. Getting Started with MATLAB 7 is an updated introduction with tutorials appropriate to MATLAB's latest version. Preface 1. Introduction 2. Tutorial Lessons 3. Interactive Computation 4. Programming in MATLAB: Scripts and Functions 5. Applications 6. Graphics 7. Errors ® Familiarizes users with MATLAB in just a few hours though self-guided lessons ® Discusses new features and applications in MATLAB 7 ® Covers elementary, advanced, and special functions ® Includes numerous new examples and problems ® Supp
Based on a series of lectures for adult students, this lively and entertaining book proves that, far from being a dusty, dull subject, geometry is in fact full of beauty and fascination. The author's infectious enthusiasm is put to use in explaining many of the key concepts in the field, starting with the Golden Number and taking the reader on... more... Learn geometry at your own pace What are congruent circles? How do you find the hypotenuse of a triangle? What is the sum of the angles in a decagon? How can you apply geometric equations to your daily life? With the unbeatable study companion Geometry: A Self-Teaching Guide, you'll discover the answers to these questions and many more. This thorough... more... You, too, can understand geometry---- just ask Dr. Math ? ! Are,...Meyer's Geometry and Its Applications, Second Edition , combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text... more... Deformable objects are ubiquitous in the world, on various levels from micro to macro. The need to study such shapes and model their behavior arises in a wide spectrum of applications, ranging from medicine to security. This book provides an overview of the state of science in analysis and synthesis of non-rigid shapes. more... Like other areas of mathematics, geometry is a continually growing and evolving field. Computers, technology, and the sciences drive many new discoveries in mathematics. For geometry, the areas of quantum computers, computer graphics, nanotechnology, crystallography, and theoretical physics have been particularly relevant in the past few years. There... more...
Graphing Calculator ti-84? What is the difference between the ti-84 and the ti-84 plus silver edition? (See answer below) Get an answer There isn't a huge difference between the TI-84 Plus and the TI-84 Plus Silver Edition. Aside from a few minor aspects, they could even be considered the same calculator. Here are some of the ... (Continued below) Complete conversation User: Graphing Calculator ti-84? What is the difference between the ti-84 and the ti-84 plus silver edition? Weegy: There isn't a huge difference between the TI-84 Plus and the TI-84 Plus Silver Edition. Aside from a few minor aspects, they could even be considered the same calculator. Here are some of the advantages the Silver Edition has over the regular edition: - More Flash ROM (SE has 1.5 MB user accessible Flash memory while regular only has 480 KB) - Comes with more preloaded apps (though you could simply transfer them onto a regular from online) - Comes in different colors - Supports interchangeable faceplates Aside from those, the two are pretty much the same thing. Auto Answered\|Score 1 Weegy: What is the difference between a Texas Instruments a TI 84 calculator ... What is the difference between a ti-89 titanium graphing calculator and a ti-84 silver plus graphing ... Auto Answered\|Score .7617 Weegy: I have a TI-84 Plus calculator and when I try to go play the game I put on it I can't because there is a ... What is the file extension 8XU for the TI-84 plus silver edition? ... Auto Answered\|Score .6248 Weegy: What is the file extension 8XU for the TI-84 plus silver edition? ... What is the file extension 8XU for the TI-84 plus silver edition? How do I download games on a TI-84 Plus ... Auto Answered\|Score .6046
Course Number and Title Number of Credits Minimum Number of Instructional Minutes Per Semester Prerequisites Math Placement Test score of 7 or better or MATH103 (C or better) Corequisites None Other Pertinent Information A comprehensive departmental final is included in the course. Catalog Course Description This course is designed to strengthen and increase the understanding of basic algebraic concepts before a student undertakes advanced study in mathematics. Topics include algebra of the real numbers, algebraic, exponential, and logarithmic functions and their graphs, systems of equations, inequalities, and absolute value. Required Course Content and Direction Learning Goals: Course Specific: The student will be able to: develop an understanding and apply the concepts and procedures for solving equations and inequalities and for simplifying expressions. demonstrate the techniques of solving a variety of applications of equations. develop a proficiency in solving linear, quadratic, polynomial, and rational functions, and in mastering techniques for graphing these functions and describing their domain and range. develop skill in using a graphing calculator. accurately use logarithmic and exponential functions and develop the skill to graph and solve logarithmic and exponential equations. Assessment Methods for Core Learning Goals: All Core Critical Thinking and Problem Solving, College Level Mathematics or Science, and Discipline-Specific Course Objectives will be assessed as follows: The student will apply mathematical concepts and principles to identify and solve problems presented through informal assessment, such as oral communication among students and between teacher and students and, for the core, formal assessment using open-ended questions reflecting theoretical and applied situations. Reference, Resource, or Learning Materials to be used by Students: There is a departmentally selected textbook and calculator. The instructor will provide specific details for each section. See Course Format.
Subject: Mathematics (8 - 12) Title: Systems of Equations: What Method Do You Prefer? Description: The purpose of this lesson is to help students apply math concepts of solving systems of equations to real life situations. The students will use the three methods of graphing, substitution, and elimination to solve the system of equations Pick's Theorem as a System of EquationsAdd Bookmark Description: In this lesson, one of a multi-part unit from Illuminations, students gather three examples from a geoboard or other representation to generate a system of equations. The solution provides the coefficients for Pick s Theorem. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Subject: Mathematics Title: Road Trip!Add Bookmark Description: In this Illuminations lesson, students investigate the famous Traveling Salesman Problem by considering the shortest route between five northeastern cities. Three different algorithms for finding the shortest route are explored, and students are encouraged to look for others. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Subject: Mathematics,Science Title: Northwestern CrowsAdd BookmarkSubject: Mathematics,Science Title: Whelk-Come to MathematicsAdd BookmarkSubject: Mathematics Title: Isosceles Triangle Investigation Add Bookmark Description: This student interactive, from an Illuminations lesson, allows students to investigate the relationship between the area of the triangle and the length of its base. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 Subject: Mathematics Title: Least Squares RegressionAdd Bookmark
A Transition to Advancedfully addressing the frustration many students feel as they make the transition from beginning calculus to a more rigorous level of mathematics, A Transition to Advanced Mathematics provides a firm foundation in the major ideas needed for continued work in the discipline. The authors guide students to think and to express themselves mathematically--to analyze a situation, extract pertinent facts, and draw appropriate conclusions. With their proven approach, Smith, Eggen, and St. Andre introduce students to rigorous thinking about sets, r... MOREelations, functions and cardinality. The text also includes introductions to modern algebra and analysis with sufficient depth to capture some of their spirit and characteristics. Bridge
Math Workbook for the GED Adults preparing to take the GED High School Equivalency Test, and who feel the need for extra help in math, will find what they are looking for in ...Show synopsisAdults preparing to take the GED High School Equivalency Test, and who feel the need for extra help in math, will find what they are looking for in this self-teaching workbook. The text has been updated in this edition to reflect latest changes in exam format and to familiarize students with use of the Casio fx-260 calculator. The book is filled with subject reviews, exercises, and worksheets covering arithmetic, measurement, geometry, algebra, number relations, and data analysis. All questions are answered, and a full-length diagnostic test plus four practice tests will help students discover their weak areas for concentrated
Geometry for Dummies 9780470089460 ISBN: 0470089466 Edition: 2 Pub Date: 2008 Publisher: Wiley & Sons, Incorporated, John Summary: Get un-stumped in a hurry! Proofs made easierMake friends with lines and angles, theorems and postulates - and prove itThe proof is in the pudding - and the parallelogram, and sometimes the rhombus. With this friendly guide, youa?ll soon be devouring proofs with relish. Youa?ll find out how a proofa?s chain of logic works and discover some basic secrets for getting past rough spots. Before you know it, youa?ll be pro...ving triangles congruent, calculating circumference, using formulas, and serving up pi.Discover how to: Identify lines, angles, and planes Calculate the area of a triangle Figure the volume and surface area of a pyramid Bisect angles and construct perpendicular lines Work with 3D shapes Ryan, Mark is the author of Geometry for Dummies, published 2008 under ISBN 9780470089460 and 0470089466. Five hundred thirty two Geometry for Dummies textbooks are available for sale on ValoreBooks.com, one hundred thirty two used from the cheapest price of $3.90, or buy new starting at $12.94.[read moreLearning geometry doesn' t have to hurt. With a little bit of friendly guidance, it can even be fun! Geometry For Dummies, 2nd Edition, helps you make friends with line [more] Learning geometry doesn' t have to hurt. With a little bit of friendly guidance, it can even be fun! Geometry For Dummies, 2nd Edition, helps you make friends with lines, angles, theorems and postulates. It eases you int.[less]
MATLAB PROGRAMMING WITH APPLICATIONS FOR ENGINEERS seeks to simultaneously teach MATLAB as a technical programming language while introducing the student to many of the practical functions that make solving problems in MATLAB so much easier than in other languages. The book provides a complete introduction to the fundamentals of good procedural programming, developing good design habits that will serve a student well in any other language that he or she may pick up later. Programming topics and examples are used as a jumping off point for exploring the rich set of highly optimized application functions that are built directly into MATLAB. Features Teaches good programming skills and habits that transfer to any other procedural programming language. A heavy emphasis is placed on using the built-in MATLAB functions for engineering applications and solving real world type problems. ´Good Programming Practice´ features emphasize good design practices. Examples of good programming practices include the use of proper program headers and data dictionaries in all programs, good commenting, proper program structure, etc. ´Programming Pitfalls´ are also emphasized. This feature highlights the most common errors that beginners make and how to avoid them. Uses a five-step program design process employed regularly throughout the text. Includes a significant section on 3D plots with an extensive example explaining the importance and operation of the difficult meshgrid function. Students learn how to use handle graphics to create simple interactive plots and animations. Includes a chapter totally devoted to MATLAB applications commonly used by engineering students. Topics include: Polynomial multiplication and division; Solving system of simultaneous equations; The concept of an ill-conditioned system; Solving underconstrained systems of equations with pseudoinverse; Solving overconstrained systems of equations; Numerical differentiation; Numerical integration; and Solving linear and nonlinear differential equations. End-of-chapter exercises are very extensive, and the problems include examples from a wide variety of engineering disciplines. All MATLAB files and code are available for Instructor´´s and Students via the companion websites.
Algebraic Representation of Vectors In order to do more complex calculations with vectors, we need to understand their algebraic representation. While the geometric representation of vectors makes it easier for us to understand them, the algebraic representation makes it easier for us to perform simple calculations quickly such as addition and scalar multiplication. The algebraic representation uses the numerical components of the vector.
Math Advantage 2004 MATH ADVANTAGE 2004 for MAC brings the best presentation and tools for middle school aged children to use in order to comprehend and learn math in a fun and interactive environment. Children in grades six through twelve can use this learning system to grasp basic concepts and progress to explore more complicated concepts. From Pre-Algebra to Business Math, all the basic skills and more are covered in order to equip each player with the tools they need to succeed. Pre-Algebra is the starting level and provides the player with basic abilities they will need in Algebra from fractions to real numbers. Algebra I introduces the player to more complex math formulas and applications while developing problem-solving skills. Algebra II moves on to present the player with advanced Algebra concepts like Linear Algebra and Logarithmic Functions. Geometry develops a solid foundation is the rules of Geometry and covers a variety of topics including Pyramids and Parallel Lines. Trigonometry is an introduction to the principles of Trig and goes over 24 topics like angles and coordinates. Pre-calculus is presented through illustrated lessons and goes over topics like Continuity and Derivatives. Calculus has the player begin with basic concepts and progress onto more complex topics from differentials to integrals. Statistics are presented in a way intended to simplify a sometimes-complicated topic that can include descriptive statistics and hypothesis testing. Real World Math is an excellent introduction to explain the need for all of the preceding math lessons with maintaining budgets and making financial decisions. Business Math builds on the Real World Math by adding additional mathematical requirements for business responsibilities. MATH ADVANTAGE 2004 is an excellent way for children to play their way through learning. Students who are not fond of math, are struggling with math or even love math will want to take advantage of the original and fun presentation in this game. If this is your first time to the site, let us welcome you to what we hope will become your new daily source of Math Advantage Math Advantage 2004 reviews, previews, and news from around the net.
books.google.com - The... standard mathematical tables and formulae CRC standard mathematical tables and formulae, Volume 30 The handbook for modern mathematics, filled with tables, formulae, equations, and descriptions. From inside the book Review: CRC Standard Mathematical Tables and Formulae User Review - Amarqu Review: CRC Standard Mathematical Tables and Formulae User Review - Adam Marqu
Power Function Teacher Resources Find Power Function educational ideas and activities Title Resource Type Views Grade Rating This activity consists of three exercises in which learners sketch the graphs of various power functions on the same axes. They use their sketches to make comparisons and observations which lead to generalizations about the graphs of power functions. To aid them in their exploration, students compute specified function values at key points and find points of intersection of the graphs. The graphs can be sketched by hand or with the use of a graphing calculator. Students compare and contrast exponential and power functions. In this precalculus lesson, students identify the value of x, using the graph as a visual. They compare functions with base of greater than one, to base of less than one. In this power functions worksheet, students read about determining the brightness of stars using a magnitude scale. Students solve 4 problems including finding the magnitude differences of stars and determining equivalent magnitudes. Young scholars identify the different properties of exponential functions. In this algebra instructional activity, students graph and analyze exponential functions as it relates to growth and decay. They apply the laws of exponents to add, subtract, multiply and divide exponential functions. Students differentiate between exponential and power functions. In this algebra lesson, students identify the base, exponent and properties of exponential functions. They graph the functions using the TiCalculator. Texas Instruments has composed yet another lesson to get your class using the TI-Inspire calculator to solve power and root functions. They find similarities and differences in the graphs of even and odd power and root functions then group them as families of functions. They then examine the inverse relationship among these functions. Students explore a variety of ways of solving quadratic equations. Students choose from graphing, factoring, finding square roots, completing the square and using the Quadratic formula. They ponder in the end on polynomial equations. Students define rational functions and solve to find the long run behavior. In this algebra lesson, students identify functions by the given formula, from a graph or from a horizontal asymptote describing the long run behavior of a rational function. Students graph polynomial functions and analyze the graphs. In this algebra lesson plan, students identify the inverse of the functions and find the domain and range. They label the functions as one to one and use the horizontal and vertical line test to verify functions. Students describe the end behavior of polynomials functions. In this algebra lesson, students relate the behavior of the graph to the exponent of the graph. They differentiate graphs with odd-exponent and graphs with even exponents. Young scholars add subtract and multiply rational functions. In this algebra lesson, students identify the domain and range of each function. They predict the end behavior of the graph based on the power of the polynomial. What's my function? Your class will work in pairs to determine which type of function is described in 14 different scenarios. Linear, quadratic, exponential and power functions are represented in a variety of ways: numerically, graphically, verbally, and analytically. Included are complete lesson plans, an activity sheet with answers, and a quick assessment to use at the end of the lessonHigh schoolers manipulate an online tool to define the relationship between a data set of points and a curve used to fit the data. They study the relationships between variables using linear, exponential, power, logarithmic and other functions for curve fitting. This lesson is all about polynomial functions, graphs, and parabolas! It even comes with quite a few follow along worksheets. Get your class graphing polynomial functions with a degree higher than two, identifying the function represented by a graph, and finding the zeros and intercepts. A very thorough lesson.
This is a free, online textbook that is a wikibook. "This book will help you learn how to do mathematics using Algebra. It... see more This is a free, online textbook that is a wikibook. "This book will help you learn how to do mathematics using Algebra. It has chapters (parts of the book) with lessons (parts of the chapter about one idea). A lesson has five parts: 1.Vocabulary - gives special words you need for the lesson. 2.Lesson - gives a new idea and how to use this idea. 3.Example Problems - gives the steps to do problems using the new idea. 4.Practice Games - gives places for amusement where you do problems. 5.Practice Problems - You do problems.״ ״In this text, we present various mathematical models of games and study the phenomena that arise. In some cases, we will be... see more ״In this text, we present various mathematical models of games and study the phenomena that arise. In some cases, we will be able to suggest what courses of action should be taken by the players. In others, we hope simply to be able to understand what is happening in order to make better predictions about the future.״ ״This fascinating look at combinatorial games, that is, games not involving chance or hidden information, offers updates on... see more ״This fascinating look at combinatorial games, that is, games not involving chance or hidden information, offers updates on standard games such as Go and Hex, on impartial games such as Chomp and Wythoff's Nim, and on aspects of games with infinitesimal values, plus analyzes of the complexity of some games and puzzles and surveys on algorithmic game theory, on playing to lose, and on coping with cycles.״ ״Games of Strategy: Theory and Applications, originally published by Prentice Hall in 1961, was written by Melvin Dresher, a... see more ״Games of Strategy: Theory and Applications, originally published by Prentice Hall in 1961, was written by Melvin Dresher, a RAND research mathematician, during the heyday of Game Theory at RAND. This book introduced readers to the basic concepts of game theory and its applications for military, economic, and political problems, as well as its usefulness in decisionmaking in business, operations research, and behavioral science. More than forty years after its first publication as a RAND research study, and to celebrate RAND's 60th Anniversary, RAND is proud to bring this classic work back into print in paperback and digital formats.״ ״These are lecture notes for a course in game theory which the author taught at the University of Kaiserslautern. Game Theory... see more ״These are lecture notes for a course in game theory which the author taught at the University of Kaiserslautern. Game Theory is a formal approach to study games: conflicts where some number of players take part and each one tries to maximize his utility in taking part in the conflict. This text covers general concepts of two person games, Brouwer's fixed point theorem and Nash's equilibrium theorem, more general equilibrium theorems, cooperative games and differential games.״ ״This book is a state-of-the-art look at combinatorial games, that is, games not involving chance or hidden information. It... see more ״This book is a state-of-the-art look at combinatorial games, that is, games not involving chance or hidden information. It contains articles by some of the foremost researchers and pioneers of combinatorial game theory. The articles run the gamut from new theoretical approaches to the very latest in some of the hottest games.״ ״When The Compleat Strategyst was originally published in 1954, game theory was an esoteric and mysterious subject, familiar... see more ״When The Compleat Strategyst was originally published in 1954, game theory was an esoteric and mysterious subject, familiar only to specialized researchers, particularly in the military. Its popularity today can be traced at least in part to this book, which popularized the subject for amateurs, professionals, and students throughout the world.״
Stewart, the author of the best-selling calculus texts, along with two of his former Ph.D. students, Lothar Redlin and Saleem Watson, collaborated in writing this book to address a problem they frequently saw in their calculus courses. Many students were not prepared to "think mathematically" but attempted to memorize facts and mimic examples. This trigonometry text has been designed specifically to help students learn to think mathematically and to develop true problem-solving skills. Patient, clear, and accurate, this text consistently illustrates how useful and applicable trigonometry is to real life.
The Everything Guide to Algebra A step-by-step guide to the basics of algebra--in plain English! By Christopher Monahan, Former President Association Format: Paperback SKU# Z7917 Details Whether you need help solving equations or determining the slope of a line, this guide gives you the tools you need to find your answers! Beginning with the basics, you will learn and practice all the skills needed to enhance your algebra expertise. This comprehensive guide covers all the key concepts, including: Variables and expressions Linear equations and inequalities Monomials and polynomials Exponents Rational expressions The Pythagorean theorem Area and perimeter Graphs and charts Inside you'll find hundreds of examples to illustrate the basics and plenty of exercises to ensure mastery of these fundamentals. No matter if you're a student looking for a companion to your textbook, or a curious learner who's been away from the classroom too long, this will be your indispensable algebra primer. Christopher Monahan teaches high school mathematics in New York State and is a national instructor with Texas Instruments' Teaching Teachers with Technology program. Chris was President of the Association of Mathematics Teachers of New York State during the 2009–2010 school year, working with the state education department to assess the proposed national Common Core Standards. Additional Information SKU Z7917 Author/Speaker/Editor Christopher Monahan, Former President Association File/Trim Size 8 x 9-1/4 Format Paperback ISBN 13 9781440504587 Number Of Pages 304
Statistics, Correlation and Regression in Mathematics Statistics, Correlation and Regression in Mathematics This free online course is the first of our Upper-Secondary Mathematics suite of courses. It covers mathematical analysis, including univariate statistics and data, bivariate statistics, correlation, regression, residual analysis, non-linear data, and seasonal movements. This course is suitable for students of maths, especially those preparing for examinations. It is also suitable for those looking to refresh their knowledge of Mathematics. Understand univariate and bivariate data to display different types of data Learning Outcome On completing of this course you will have a good understanding of univariate data, the types of univariate data and displaying this type of data. You will know bivariate data such as dependent, independent variables, parallel boxplots, stemplots, graphical display and much more. You will know how to calculate the mean, median and mode when analysing statistics. You will be able to identify and calculate the interquartile range, standard deviation and boxplots using your calculator. You will know symmetry, calculating a seasonal index, coefficient, regression line, trends and much more. This course will teach you effective exam techniques and tips to help you prepare successfully for your exam.
More About This Textbook Overview Intermediate Algebra is an excellent presentation of the fundamentals of intermediate algebra. This text provides a solid mathematical foundation for students who will apply these principles in a variety of disciplines as well as those who will continue in college Algebra. Accompanied by a Student Solutions Manual that allows students to, Chris Vancil's book is the perfect addition to any college Algebra course. Related Subjects Meet the Author Geoffrey Akst and Sadie Bragg have worked together for many years as professors of mathematics at Borough of Manhattan Community College/City University of New York. They met as graduate students at Teachers College, Columbia University, where they were both working on degrees in the teaching of college mathematics. The emphasis on applications in their texts reflects a concern they share for helping students understand why the topics to be studied are useful. Dr. Akst for years has begun his classes with the payoff question:¿ Why is this material worth learning? A native New Yorker, he enjoys surfing the Web, listening to good music, and traveling to exciting places. Dr. Bragg, who began her career in math education as a high school geometry teacher, credits her teachers with inspiring her love for mathematics and an appreciation of its utility. A transplanted Virginian, she spends her time with her family and her beautiful
Written to complement the explanations provided in Understanding Mathematics: From Counting to Calculus, the books may be used as a supplement or independent core curriculum. This textbook provides problem sets that are aligned with the sections explained in Understanding Mathematics: From Counting to Calculus. 305 pages, softcover.
This book provides an introduction to the relatively new discipline of arithmetic dynamics. Whereas classical discrete dynamics is the study of iteration of self-maps of the complex plane or real line, arithmetic dynamics is the study of the number-theoretic properties of rational and algebraic points under repeated application of a polynomial or rational... more... Building on previous texts in the Modular Mathematics series, in particular 'Vectors in Two or Three Dimensions' and 'Calculus and ODEs', this book introduces the student to the concept of vector calculus. It provides an overview of some of the key techniques as well as examining functions of more than one variable, including partial differentiation... more... Building on the basic concepts through a careful discussion of covalence, (while adhering resolutely to sequences where possible), the main part of the book concerns the central topics of continuity, differentiation and integration of real functions. Throughout, the historical context in which the subject was developed is highlighted and particular... more... The theory of distributions has numerous applications and is extensively used in mathematics, physics and engineering. There is however relatively little elementary expository literature on distribution theory. This book is intended as an introduction. Starting with the elementary theory of distributions, it proceeds to convolution products of distributions,... more... The book is devoted to the mathematical theory of soliton phenomena on the plane. The inverse spectral transform method which is a main tool for the study of the (2+1)-dimensional soliton equation is reviewed. The ?-problem and the Riemann-Hilbert problem method are discussed. Several basic examples of soliton equations are considered in detail. This... more... A bestselling introductory course, this book covers all areas of calculus, including functions, gradients, rates of change, differentiation, exponential and logarithmic functions and intgration. more... A bestselling introductory course, this book covers all areas of calculus, including functions, gradients, rates of change, differentiation, exponential and logarithmic functions and intgration. more...
Grissom High School Math Team - Hosts annual math tournament with several categories including pre-algebra, algebra, geometry, algebra II. and comprehensive. Rocket City Math League - Based in Huntsville, Alabama. Website contains registration information and sample tests. The University of Alabama High School Math Tournament - Math Tournament hosted by the University of Alabama Mathematics Department each fall for excellent high school students from all over Alabama and throughout the southeast. The tournament consists of a written exam and a ciphering competition. Bay Area Math Circle - Features The Bay Area Mathematical Olympiad (BAMO) and weekly program for San Francisco Bay Area high and middle school students. High School Math Contest - Contains contest information and archives of past problems. Competition hosted by the Indiana University Purdue University Indianapolis (IUPUI) Department of Mathematical Sciences. Indiana State Mathematics Contest - Annual contest sponsored by the Indiana Council of Teachers of Mathematics. Five testing categories include Pre-Algebra, Algebra, Geometry, Algebra II, and Comprehensive. Some Canadian Mathematical Competitions Canadian Mathematics Competition - Organization that sponsors the Canadian Open Mathematics Challenge, the Euclid Contest, the Gauss Contest, with online workshop, problem archives, and other resources for students. The Indian MO-Cell - The headquarters of all Math olympiad related activity in India. Located at the Department of Mathematics of the Indian Institute of Science, Bangalore. Provides information on the Indian National Maths Olympiad and past contest problems. South African Mathematics Olympiad - The official national mathematics competition of the country. It is a three round competition with interesting questions and prizes. Site contains background, contest information, past problems, and publications.
Get a good grade in your precalculus course with Cohen's PRECALCULUS: A PROBLEMS-ORIENTED APPROACH and it's accompanying CD-ROM! Written in a clear, student-friendly style and providing a graphical perspective so you can develop a visual understanding of college algebra and trigonometry, this text provides you with the tools you need to be successful in this course. Preparing for exams is made easy with iLrn, an online tutorial resource, that gives you access to text-specific tutorials, step-by-step explanations, exercises, quizzes, and one-on-one online help from a tutor. Examples, exercises, applications, and real-life data found throughout the text will help you become a successful mathematics student! This Enhanced Edition includes instant access to Enhanced WebAssign®, the most widely-used and reliable homework system. Enhanced WebAssign® presents thousands of problems, links to relevant textbook sections, video examples, problem-specific tutorials, and more, that help students grasp the concepts needed to succeed in this course. As an added bonus, the Start Smart Guide has been bound into this text. This guide contains instructions to help students learn the basics of WebAssign quickly228.95 Purchase Options Instructor Assigned Hardcover $182.99 $182.99 Save $4556.99 from$56.99 Save up to $171.96! Rent thru 06/09/14 for $56.99 $56.99 Save $171.96! Rent thru 12/06/14 for $65.49 $65.49 Save $163.46! Rent thru 12/01/15 for $70.99 $70.99 Save $157.96! Rent thru 11/20/17 for $79.49 $79.49 Save $149 eBook
Elements of Advanced Mathematics - 2nd edition Summary: Clearly written and easy to understand, The Elements of AdvancedMathematics covers logic, set theory, methods of proof, and axiomatic structures, providing an excellent grounding in analytical thinking. It facilitates the transition from elementary mathematics, generally characterized by problem-solving techniques, to advanced mathematics, characterized by theory, rigor, and proofs. This text clearly identifies and explains the components and methods of advanced math...show moreematics. Each chapter contains exercises designed to assist the reader in understanding the material. ...show less 1584883030 Item in good condition. Textbooks may not include supplemental items i.e. CDs, access codes etc... All day low prices, buy from us sell to us we do it all!!06
I'm currently completing tertiary eduction in order to be accepted into a CS course at university, and I would like to know what options are available to me to improve my knowledge of programming and mathematics at home. I did not finish high-school, and have a pretty basic understanding of mathematics though I've never struggled with it. I'm not sure what level of mathematics I am at, suffice to say I would struggle with solving complex algebraic equations. I've never had any formal education in programming, but I've been doing it since I knew what it was. I'd say that I have OK practical knowledge, but next to no understanding of anything advanced. To improve my mathematics knowledge, I need a list of topics which should be covered, starting from the level of an average 16/17 year old. I'd also need to know which topics to cover before others. My first thought is to buy a highschool maths textbook to start with. I'm not sure what I should be doing to improve my programming knowledge, but I sure know that I am far, far off from answering questions such as: "Using only line drawing primives, construct a wireframe 3d car demo where the player can drive the car." (to use an example from a pretty out-there job application task). I'm not sure what I am expecting in the way of answers, perhaps just advice from people who have been in similar situations. I've got a year before I enter the CS course and I want to come in with all guns blazing. It does depend a little on which CS course you're going into and even what type of programming you want to get involved with. Strong mathematical knowledge is always a plus, but there are certain branches of mathematics that are more geared towards CS than others (graph theory, discrete to name a couple). – Martijn VerburgJan 20 '11 at 10:11 It also depends what country you are in. The difference – Loki AstariJan 20 '11 at 11:01 gnat, MichaelT, Dan Pichelman, Yannis Rizos 6 Answers You'll find people who tell you programming and mathematics go hand in hand, and others who tell you that they never use more than the simplest mathematics in their programming. I belong to the first group. Perhaps my vision won't suit you. But here it is. Computer science is about understanding the ways that data can be manipulated according to the rules of a machine, as well as orchestrating manipulations that achieve a desired result. Mathematics is about understanding the ways that statements can be manipulated according to the rules of symbol system, as well as performing such manipulations in order to obtain a desired result. There is a strong connection between the two. Getting experience in one helps you with the other, sometimes directly, sometimes more subtly. I would suggest you start with mathematical logic. Consider the statement "If A is True and B is True, then A is False." Note that A and B aren't variables; they're placeholders for statements which are either true or false. For instance "If I am a cat, and I am a dog, then I am not a cat." If you learn the techniques of mathematical logic (and convince yourself that they make sense - which isn't hard), you understand the main mechanism in mathematics. So I would suggest you start here. This kind of stuff is often taught in first year CS, sometimes as part of "Discrete Mathematics". You may find something like this book useful. After that, let your interests drive your learning. Algebra is extremely useful, but if you find it tedious then it will probably be easier if you pick it up whilst doing something else - be it geometry or number theory or financial stuff or physics simulations. I liked to explore the things I learned in maths by writing programs. More recently I learned how to analyse programs mathematically (both from a performance perspective and a correctness perspective). Check out projecteuler.net. On the programming side, know that there is no magic in any program. I learned how to program by saying "I bet I could do that myself". I started by generating prime numbers, and then it was a GIF decoder, then a chat server, then an OS kernel. (Among much else.) Doing something without being told how, without reading about it first, is a great way to improve your problem-solving and critical thinking. If you don't already know any fancy sorting algorithms, try to come up with one yourself. Could it sort a million items in reasonable time? Once you've had a few attempts, read about the topic and evaluate what you did. Or do a similar thing with compression. One last thing: I would suggest learning the Haskell language. It has strong mathematical overtones and is - I believe - challenging and rewarding. Practice a lot - see UVa Online Judge for some other interesting problems to solve Finally, after you've been programming for a while I recommend you to look at some design patterns. I could only appreciate the usefulness of some patterns after I have already written some code that could be better if I had known a pattern for solving that problem already existed. That's how it worked for me to understand what the fuzz about design patterns was without embracing them in some esoteric fashion, without understanding what they're for. The preface would be a way to see some of the style of the book if you want a peek behind the cover. The book was a textbook for an advanced Graduate course I took called, "Asymptotic Enumeration," though we did skip many chapters of the book to get to that part. There is a lot about theoretical computer sciences, but I don't really understand how can they be useful for a non-researcher. Subjects that are just mind blowing are file compression algorithm, encryption, graphes, computability (the O(n) notation), and other bits that mortal programmer will never have to code themselves. I can assure you that you are saved from those evil things. There are, other than those subjects, topics that requires mathematics, but where you need to make your own wheel. A good example is3D game programming: 3D matrix transformation, quaternions, simple algebra with powers, exponentials, parametric curves, simple solid & point mechanics, physics law for light emissions, etc. Another hard subject that you may have to deal with, is differential equations (1st and 2nd degrees). Those are the most important mathematic tool, and rightly represents that simple enough maths can be daunting enough to get along with. This might make you understand that even if you don't deal with "cool maths", when you are in computer sciences, you don't really deal with those research-abstract-impossible-to-read stuff. I disagree with your view about encryption, graphs, computability, and O(n) notation. Some programmers won't need them, but many will find them useful. Compression and encryption are best left to the experts, although any programmer who is significantly reliant on encryption must appreciate how it works, otherwise security holes result. Personally I find compression and encryption much easier and more interesting than differential equations. My main point is that everybody is different, and should let their interests guide them (without being blind to everything else). – ArteliusJan 21 '11 at 6:38
I've always wanted to excel in how babylonians solved specified system of equations, it seems like there's a lot that can be done with it that I can't do otherwise. I've browsed the internet for some good learning resources, and consulted the local library for some books, but all the data seems to be targeted at people who already understand the subject. Is there any resource that can help new students as well? Well of course there is. If you are confident about learning how babylonians solved specified system of equations, then Algebrator can be of great benefit to you. It is made in such a manner that almost anyone can use it. You don't need to be a computer expert in order to use the program. I agree, a good software can do miracles . I used a few but Algebrator is the greatest. It doesn't make a difference what class you are in, I myself used it in Intermediate algebra and Algebra 2 too, so you don't have to worry that it's not on your level. If you never had a software before I can tell you it's not hard, you don't need to know anything about the computer to use it. You just have to type in the keywords of the exercise, and then the software solves it step by step, so you get more than just the answer. A extraordinary piece of algebra software is Algebrator. Even I faced similar problems while solving angle complements, factoring and perpendicular lines. Just by typing in the problem workbookand clicking on Solve – and step by step solution to my math homework would be ready. I have used it through several algebra classes - Algebra 2, Algebra 2 and College Algebra. I highly recommend the program.
* An introduction that appeals to the reader's reason rather than to her/his ability to memorize. * A complete tool for... see more * An introduction that appeals to the reader's reason rather than to her/his ability to memorize. * A complete tool for teaching "developmental" students twice a week for 15 weeks. * A way for adults to learn some mathematics—more or less in the same spirit as mathematicians do. * A text, with a story-line, written to be read and reread. * A presentation that pays pedantic attention to the linguistic difficulties the reader is likely to have in mathematics. * A political act to "enable people to get on better terms with reason—to learn to live with the truth." [Colin McGinn] * An anti "Show a Template Example, Drill and Test" manifesto. * An open source package written in LaTeX with lots of vector graphics. * A standalone version of part of From Arithmetic to Differential Calculus. (In Preparation.) * An instance of a model-theoretic approach to mathematical exposition. * A treatment that, while not rigorous in the usual mathematical sense, sins only by venial omission. * A work by a mathematician who, almost fifty years ago, got interested in reconciling "just plain folks" with mathematics. 'From the MAA review of this book: "The discussions and explanations are succinct and to the point, in a way that pleases... see more 'From the MAA review of this book: "The discussions and explanations are succinct and to the point, in a way that pleases mathematicians who don't like calculus books to go on and on.״There are eleven chapters beginning with analytic geometry and ending with sequences and series. The book covers the standard material in a one variable calculus course for science and engineering except for numerical integration. The size of the book is such that an instructor does not have to skip sections in order to fit the material into the typical course schedule.There are sufficiently many exercises at the end of each sections, but not as many as the much bigger commercial texts. Some students and instructors may want to use something like a Schaum's outline for additional problems.' According to The Orange Grove, "In this PDF textbook from the Metropolitan Museum of Art, works in the Museum's collection... see more According to The Orange Grove, "In this PDF textbook from the Metropolitan Museum of Art, works in the Museum's collection that embody the Renaissance interest in classical learning, fame, and beautiful objects are illustrated and discussed. This resource is designed to help educators introduce the richness and diversity of Renaissance art to their students. Primary source texts explore the great cities and powerful personalities of the age. By studying gesture and narrative, students can work as Renaissance artists did when they created paintings and drawings. Learning about perspective, students explore the era's interest in science and mathematics. Through projects based on poetic forms of the time, students write about their responses to art. The activities and lesson plans are designed for a variety of classroom needs and can be adapted to a specific curriculum as well as used for independent study.״ ״This manuscripts is designed for an introductory course in the theory of interest and annuity. Each section contains the... see more ״This manuscripts is designed for an introductory course in the theory of interest and annuity. Each section contains the embedded examples with answer keys. The manuscript is suitable for a junior level course in the mathematics of finance.״ According to The Orange Grove, this is "a book introducing basic concepts from computational number theory and algebra,... see more According to The Orange Grove, this is "a book introducing basic concepts from computational number theory and algebra, including all the necessary mathematical background. The mathematical prerequisites are minimal: no particular mathematical concepts beyond what is taught in a typical undergraduate calculus sequence are assumed. The computer science prerequisites are also quite minimal: it is assumed that the reader is proficient in programming, and has had some exposure to the analysis of algorithms, essentially at the level of an undergraduate course on algorithms and data structures.״ According to OER Commons, 'These are the lecture notes of a one-semester undergraduate course which we taught at SUNY... see more According to OER Commons, 'These are the lecture notes of a one-semester undergraduate course which we taught at SUNY Binghamton. For many of our students, Complex Analysis is their first rigorous analysis (if not mathematics) class they take, and these notes reflect this very much. We tried to rely on as few concepts from real analysis as possible. In particular, series and sequences are treated "from scratch." This also has the (maybe disadvantageous) consequence that power series are introduced very late in the course.' 'This book is designed for the transition course between calculus and differential equations and the upper division... see more 'This book is designed for the transition course between calculus and differential equations and the upper division mathematics courses with an emphasis on proof and abstraction. The book has been used by the author and several other faculty at Southern Connecticut State University. There are nine chapters and more than enough material for a semester course. Student reviews are favorable.It is written in an informal, conversational style with a large number of interesting examples and exercises, so that a student learns to write proofs while working on engaging problemsA System of Logic was first published in 1843 and immediately enjoyed a wide circulation, going through numerous editions. Mill himself made substantial changes in the third edition, published in 1850, and the eighth edition, published in 1872, a year before his death. This book is Mill's most comprehensive and systematic philosophical work, elaborating his inductive method, which helped to free the empirical sciences from the rigidity of analysis by way of syllogisms. Syllogisms are arguments grounded in general principles, in which two premises are used to deduce a third premise, or conclusion. In A System of Logic, Mill breaks away from this age-old practice and instead proposes the use of a form of logic derived from the principles of the natural sciences. He uses his method to address questions of language and logic, induction, the relativity of knowledge, the structure of the scientific method, the structure of arithmetic and geometry, and the principles of the moral sciences. In effect, Mill provides a solid, scientific methodology for reasoning and for philosophy, derived from science and mathematics.The introduction discusses the role and purpose of logic in human understanding. Logic is the art and science of reasoning, a means for the pursuit of truth. However, logic is only concerned with making inferences from observed phenomena, not with intuitive truths. Logic does not produce new evidence, but it can determine whether something offered as evidence is valid. Logic judges but does not observe, invent, or discover. Logic serves a purpose in some larger project of inquiry that gives it meaning. Fundamentally, logic is a method of evaluating evidence tablets. Download the app for your device and start reading for free.'This book was converted from its physical edition to the digital format by a community of volunteers.''Hume begins by arguing for the validity of empiricism, the premise that all of our knowledge is based on our experiences, and using this method to examine several philosophical concepts. First, he demonstrates that all of our complex ideas are formed out of simpler ideas, which were themselves formed on the basis of impressions we received through our senses. Therefore, ideas are not fundamentally different from experiences. Second, Hume defines "matters of fact" as matters that must be experienced, not reasoned out or arrived at instinctually. Based on these two claims, Hume attacks metaphysical systems used to prove the existence of God, the soul, divine creation, and other such ideas. Since we have no experience of any of these things and cannot receive a direct impression of them, we have no real reason to believe that they are true.Hume systematically applies the idea that ideas and facts come from experience in order to analyze the concepts of space, time, and mathematics. If we have no experience of a concept, such as the size of the universe, that concept cannot be meaningful. Hume insists that neither our ideas nor our impressions are infinitely divisible. If we continued to try to break them down ad infinitum, we would eventually arrive at a level too small for us to perceive or grasp conceptually. Since we have no experience of infinite divisibility, the idea that things or ideas are infinitely divisible is meaningless. Mathematics, however, is a system of pure relations of ideas, and so it retains its value even though we cannot directly experience its phenomena. Many of its principles do not hold in matters of fact, but it is the only realm of knowledge in which perfect certainty is possible anyway.Hume introduces two of his three tools of philosophical inquiry, the "microscope" and the "razor." The microscope is the principle that to understand an idea we must first break it down into the various simple ideas that make it up. If any of these simple ideas is still difficult to understand, we must isolate it and reenact the impression that gave rise to it. The razor is the principle that if any term cannot be proven to arise from an idea that can be broken into simpler ideas ready for analysis, then that term has no meaning. Hume uses his razor principle to devalue abstract concepts pertaining to religion and metaphysics.'
This book presents the fundamentals of multiple regression, linear modelling, multivariate analysis, and other statistical methods for the elucidation of complicated data. The author uses the basic terms of matrix algebra to provide a clear and accessible guide for biologists, engineers, students of statistics, and others concerned with data analysis. Numerical methods for matrices are described and the book contains a set of algorithms to make such methods generally available. Introducing Matrices Determinants Inverse Matrices Linear Dependence and Rank Simultaneous Equations and Generalized Inverses Linear Spaces Quadratic Forms and Eigensystems Matrix Algorithms
Missouri Western State University Developmental Math Program (DMP) COURSE NAME: Foundations for University Mathematics COURSE OBJECTIVES: The objective of this course is to provide the student with the fundamentals of arithmetic and algebra, and the other mathematical skills necessary to succeed in College Algebra, Finite Mathematics or Contemporary Problem Solving. Assessment of a student's knowledge and skill level in the following will determine the specific topics that a student will study. Arithmetic operations and properties of real numbers. Subtract, multiply and divide algebraic expressions. Properties of exponents of algebraic expressions. Linear equations and inequalities in a single variable. Factoring algebraic expressions. Solving quadratic equations by factoring. Graphing and manipulation of linear equations and inequalities in two variables. Graph linear equations and inequalities in two variables, and graph quadratic equations.
A Fresh Start for Collegiate Mathematics: Rethinking the Courses below Calculus gordonsp@farmingdale.edu fgordon@nyit.edu College Algebra and Precalculus Each year, more than 1,000,000 students take college algebra, precalculus, and related courses. The Focus in these Courses Most college algebra courses and certainly all precalculus courses were originally intended and designed to prepare students for calculus. Most of them are still offered in that spirit. But only a small percentage of the students have any intention of going on to calculus! Enrollment Flows Based on several studies of enrollment flows into calculus: • Less than 5% of the students who start college algebra courses ever start Calculus I • Virtually none of the students who pass college algebra courses ever start Calculus III • Perhaps 30-40% of the students who pass precalculus courses ever start Calculus I • Only about 10% of students in college algebra are in majors that require calculus. Why Students Take These Courses • Required by other departments • Satisfy general education requirements • To prepare for calculus • For the love of mathematics What the Majority of Students Need • Conceptual Understanding, not rote manipulation • Realistic applications and mathematical modeling that reflect the way mathematics is used in other disciplines • Fitting functions to data • Recursion and difference equations – the mathematical language of spreadsheets The Link to Calculus Calculus and Related Enrollments In 2000, about 676,000 students took Calculus, Differential Equations, Linear Algebra, and Discrete Mathematics (This is up 6% from 1995) Over the same time period, however, calculus enrollment in college has been steady, at best. Calculus and Related Enrollments In comparison, in 2000, 171,400 students took one of the two AP Calculus exams – either AB or BC. (This is up 40% from 1995) In 2004, 225,000 students took AP Calculus exams In 2005, about 240,000 took AP Calculus exams Reportedly, about twice as many students take calculus in high school, but do not take an AP exam. Some Implications Today more students take calculus in high school than in college And, as ever more students take more mathematics, especially calculus, in high school, we should expect: • Fewer students taking these courses in college • The overall quality of the students who take these courses in college will decrease. Another Conclusion We should anticipate the day, in the not too distant future, when college calculus, like college algebra, becomes a semi-remedial course. (Several elite colleges already have stopped giving credit for Calculus I.) Who Are the Students? Based on the enrollment figures, the students who take college algebra and related courses are not going to become mathematics majors. They are not going to be majors in any of the mathematics intensive disciplines. Associates Degrees in Mathematics In 2000, • There were 564,933 associate degrees • Of these, 675 were in mathematics This is one-tenth of one percent! Bachelor's Degrees in Mathematics In 2000, • There were 457,056 bachelor's degrees • Of these, 3,412 were in mathematics This is seven-tenths of one percent! Some Conclusions Few, if any, math departments can exist based solely on offerings for math and related majors. Whether we like it or not, mathematics is a service department at almost all institutions. And college algebra and related courses exist almost exclusively to serve the needs of other disciplines. Some Conclusions If we fail to offer courses that meet the needs of the students in the other disciplines, those departments will increasingly drop the requirements for math courses. This is already starting to happen in engineering. Math departments may well end up offering little beyond developmental algebra courses that serve little purpose. Responding to the Challenges Four Special Invited Conferences • Rethinking the Preparation for Calculus, • Forum on Quantitative Literacy, • CRAFTY Curriculum Foundations Project, • Reforming College Algebra, Common Recommendations • ―College Algebra‖ courses should stress conceptual understanding, not rote manipulation. • "College Algebra‖ courses should be real-world problem based: Every topic should be introduced through a real-world problem and then the mathematics necessary to solve the problem is developed. Common Recommendations • ―College Algebra‖ courses should focus on mathematical modeling—that is, – transforming a real-world problem into mathematics using linear, exponential and power functions, systems of equations, graphing, or difference equations. – using the model to answer problems in context. – interpreting the results and changing the model if needed. Common Recommendations • "College Algebra‖ courses should emphasize communication skills: reading, writing, presenting, and listening. These skills are needed on the job and for effective citizenship as well as in academia. • "College Algebra‖ courses should make appropriate use of technology to enhance conceptual understanding, visualization, inquiry, as well as for computation. Common Recommendations • ―College Algebra‖ courses should feature student-centered rather than instructor-centered pedagogy. - They should include hands-on activities rather than be all lecture. - They should emphasize small group projects involving inquiry and inference. Important Volumes • AMATYC Crossroads Standards. • NCTM, Principles and Standards for School Mathematics. • CUPM Curriculum Guide: Undergraduate Programs and Courses in the Mathematical Sciences, MAA Reports. • Ganter, Susan and Bill Barker, Eds., A Collective Vision: Voices of the Partner Disciplines, MAA Reports. Important Volumes • Madison, Bernie and Lynn Steen, Eds., Quantitative Literacy: Why Numeracy Matters for Schools and Colleges, National Council on Education and the Disciplines, Princeton. • Baxter Hastings, Nancy, Flo Gordon, Shelly Gordon, and Jack Narayan, Eds., A Fresh Start for Collegiate Mathematics: Rethinking the Courses below Calculus, MAA Notes. AMATYC Crossroads Standards • In general, emphasis on the meaning and use of mathematical ideas must increase, and attention to rote manipulation must decrease. • Faculty should include fewer topics but cover them in greater depth, with greater understanding, and with more flexibility. Such an approach will enable students to adapt to new situations. • Areas that should receive increased attention include the conceptual understanding of mathematical ideas. CUPM Curriculum Guide • All students, those for whom the (introductory mathematics) course is terminal and those for whom it serves as a springboard, need to learn to think effectively, quantitatively and logically. • Students must learn with understanding, focusing on relatively few concepts but treating them in depth. Treating ideas in depth includes presenting each concept from multiple points of view and in progressively more sophisticated contexts. CUPM Curriculum Guide • A study of these (disciplinary) reports and the textbooks and curricula of courses in other disciplines shows that the algorithmic skills that are the focus of computational college algebra courses are much less important than understanding the underlying concepts. • Students who are preparing to study calculus need to develop conceptual understanding as well as computational skills. Voices of the Partner Disciplines CRAFTY's Curriculum Foundations Project Curriculum Foundations Project A series of 11 workshops with leading educators from 17 quantitative disciplines to inform the mathematics community of the current mathematical needs of each discipline. The results are summarized in the MAA Reports volume: A Collective Vision: Voices from the Partner Disciplines, edited by Susan Ganter and Bill Barker. What the Physicists Said • Students need conceptual understanding first, and some comfort in using basic skills; then a deeper approach and more sophisticated skills become meaningful. Computational skill without theoretical understanding is shallow. What the Physicists Said • Students should be able to focus a situation into a problem, translate the problem into a mathematical representation, plan a solution, and then execute the plan. Finally, students should be trained to check a solution for reasonableness. What the Physicists Said • The learning of physics depends less directly than one might think on previous learning in mathematics. We just want students who can think. The ability to actively think is the most important thing students need to get from mathematics education. What Business Faculty Said • Courses should stress conceptual understanding (motivating the math with the ―why's‖ – not just the ―how's‖). • Students should be comfortable taking a problem and casting it in mathematical terms. • Courses should use industry standard technology (spreadsheets). Common Themes from All Disciplines • Strong emphasis on problem solving • Strong emphasis on mathematical modeling • Conceptual understanding is more important than skill development • Development of critical thinking and reasoning skills is essential Common Themes from All Disciplines • Use of technology, especially spreadsheets • Development of communication skills (written and oral) • Greater emphasis on probability and statistics • Greater cooperation between mathematics and the other disciplines A Fresh Start for Collegiate Mathematics: Rethinking the Courses below Calculus Nancy Baxter Hastings Florence Gordon Sheldon Gordon Jack Narayan MAA Notes, January 2006 A Fresh Start to Collegiate Math Introduction Nancy Baxter Hastings Overview of the Volume Jack Narayan & Darren Narayan The Conference: Rethinking the Preparation for Calculus Lynn Steen Twenty Questions about Precalculus Background Mercedes McGowen Who are the Students Who Take Precalculus? Steve Dunbar Enrollment Flow to and from Courses below Calculus Deborah Hughes What Have We Learned from Calculus Reform? The Road to Hallett Conceptual Understanding Calculus and Introductory College Mathematics: Current Trends and Susan Ganter Future Directions A Fresh Start to Collegiate Math New Visions for Introductory Collegiate Mathematics Shelly Gordon Preparing Students for Calculus in the Twenty-First Century Bernie Madison Preparing for Calculus and Preparing for Life Don Small College Algebra: A Course in Crisis Scott Herriott Changes in College Algebra One Approach to Quantitative Literacy: Mathematics in Public Janet Andersen Discourse The Transition from High School to College Zal Usiskin High School Overview and the Transition to College Dan Teague Precalculus Reform: A High School Perspective Eric Robinson & The Influence of Current Efforts to Improve School John Maceli Mathematics on Preparation for Calculus A Fresh Start to Collegiate Math The Needs of Other Disciplines Bill Barker and Fundamental Mathematics: Voices of the Partner Susan Ganter Disciplines Rich West Skills versus Concepts Allan Rossman Integrating Data Analysis into Precalculus Courses Student Learning and Research Assessing What Students Learn: Reform versus Florence Gordon Traditional Precalculus and Follow-up Calculus Student Voices and the Transition from Standards-Based Rebecca Walker Curriculum to College A Fresh Start to Collegiate Math Implementation Robert Megginson Some Political and Practical Issues in Implementing Reform Implementing Curricular Change in Precalculus: A Dean's Judy Ackerman Perspective Alternatives to the One-Size-Fits-All Precalculus/College Bonnie Gold Algebra Course Preparing for Calculus and Beyond: Some Curriculum Design Al Cuoco Issues Lang Moore and David Smith Changing Technology Implies Changing Pedagogy Sheldon Gordon The Need to Rethink Placement in Mathematics Influencing the Mathematics Community Launching a Precalculus Reform Movement: Influencing the Bernie Madison Mathematics Community Bonnie Saunders Mathematics Programs for the "Rest of Us" Sheldon Gordon Where Do We Go from Here: Forging a National Initiative A Fresh Start to Collegiate Math Ideas and Projects that Work , Part 1 Doris An Alternate Approach: Integrating Precalculus into Schattschneider Calculus College Algebra Reform through Interdisciplinary Bill Fox Applications Elementary Math Models: College Algebra Topics and a Dan Kalman Liberal Arts Approach Brigette Lahme, Jerry Morris and Elias Toubassi The Case for Labs in Precalculus Ideas and Projects that Work , Part 2 Gary Simundza The Fifth Rule: Experiential Mathematics Darrell Abney and James Reform Intermediate Algebra in Kentucky Community Hougland Colleges Marsha Davis Precalculus: Concepts in Context A Fresh Start to Collegiate Math Benny Evans Rethinking College Algebra Sol Garfunkel From the Bottom Up Florence Gordon & Shelly Gordon Functioning in the Real World Deborah Hughes Hallett Importance of a Story Line Functions as a Model Nancy Baxter Using a Guided-Inquiry Approach to Enhance Student Learning Hastings in Precalculus Allan Jacobs Maricopa Mathematics Linda Kime Quantitative Reasoning Developmental Algebra: The First Course for Many College Mercedes McGowan Students Allan Rossman Workshop Precalculus: Functions, Data and Models Chris Schaufele & Nancy Zumoff The Earth Math Projects Don Small Contemporary College Algebra A Fresh Start to Collegiate Math Ernie Danforth, Brian Gray, Arlene Kleinstein, Rick Patrick and Mathematics in Action: Empowering Students with Sylvia Svitak Introductory and Intermediate College Mathematics Todd Swanson Precalculus: A Study of Functions and Their Applications David Wells Lynn Tilson Successes and Failures of a Precalculus Reform Project Distribution Plan With support from the NSF, the MAA has developed a distribution plan to provide one free copy to any department that requests one. Announcements will be sent to all department chairs informing them of the details in February. Common Themes Common Themes • Conceptual Understanding is more important than rote manipulation • The Rule of Four: Graphical, Numerical, Algebraic and Verbal Representations • Realistic Applications via Math Modeling • Non-routine problems and assignments • Algebra in Context – Not Just Drill Common Themes • Families of Functions – Linear, Exponential, Power, Logarithmic, Polynomial, and Sinusoidal • The significance of the parameters in the different families of functions • Limitations of the models developed – the practical significance of the domain and range Common Themes • Data Analysis • Connections to Other Disciplines • Writing and Communication • More Active Classroom Environment – Group Work, Collaborative Learning, Exploratory Approach to Mathematics • Use of Technology in Teaching and Learning Conceptual Understanding • What does conceptual understanding mean? • How do you recognize its presence or absence? • How do you encourage its development? • How do you assess whether students have developed conceptual understanding? What Does the Slope Mean? Comparison of student response to a problem on the final exams in Traditional vs. Reform College Algebra/Trig Brookville College enrolled 2546 students in 1996 and 2702 students in 1998. Assume that enrollment follows a linear growth pattern. a. Write a linear equation giving the enrollment in terms of the year t. b. If the trend continues, what will the enrollment be in the year 2016? c. What is the slope of the line you found in part (a)? d. Explain, using an English sentence, the meaning of the slope. e. If the trend continues, when will there be 3500 students? Responses in Traditional Class 1. The meaning of the slope is the amount that is gained in years and students in a given amount of time. 2. The ratio of students to the number of years. 3. Difference of the y's over the x's. 4. Since it is positive it increases. 5. On a graph, for every point you move to the right on the x- axis. You move up 78 points on the y-axis. 6. The slope in this equation means the students enrolled in 1996. Y = MX + B . 7. The amount of students that enroll within a period of time. 8. Every year the enrollment increases by 78 students. 9. The slope here is 78 which means for each unit of time, (1 year) there are 78 more students enrolled. Responses in Traditional Class 10. No response 11. No response 12. No response 13. No response 14. The change in the x-coordinates over the change in the y- coordinates. 15. This is the rise in the number of students. 16. The slope is the average amount of years it takes to get 156 more students enrolled in the school. 17. Its how many times a year it increases. 18. The slope is the increase of students per year. Responses in Reform Class 1. This means that for every year the number of students increases by 78. 2. The slope means that for every additional year the number of students increase by 78. 3. For every year that passes, the student number enrolled increases 78 on the previous year. 4. As each year goes by, the # of enrolled students goes up by 78. 5. This means that every year the number of enrolled students goes up by 78 students. 6. The slope means that the number of students enrolled in Brookville college increases by 78. 7. Every year after 1996, 78 more students will enroll at Brookville college. 8. Number of students enrolled increases by 78 each year. Responses in Reform Class 9. This means that for every year, the amount of enrolled students increase by 78. 10. Student enrollment increases by an average of 78 per year. 11. For every year that goes by, enrollment raises by 78 students. 12. That means every year the # of students enrolled increases by 2,780 students. 13. For every year that passes there will be 78 more students enrolled at Brookville college. 14. The slope means that every year, the enrollment of students increases by 78 people. 15. Brookville college enrolled students increasing by 0.06127. 16. Every two years that passes the number of students which is increasing the enrollment into Brookville College is 156. Responses in Reform Class 17. This means that the college will enroll .0128 more students each year. 18. By every two year increase the amount of students goes up by 78 students. 19. The number of students enrolled increases by 78 every 2 years. Understanding Slope Both groups had comparable ability to calculate the slope of a line. (In both groups, several students used x/y.) It is far more important that our students understand what the slope means in context, whether that context arises in a math course, or in courses in other disciplines, or eventually on the job. Unless explicit attention is devoted to emphasizing the conceptual understanding of what the slope means, the majority of students are not able to create viable interpretations on their own. And, without that understanding, they are likely not able to apply the mathematics to realistic situations. Further Implications If students can't make their own connections with a concept as simple as slope, they won't be able to create meaningful interpretations on their own for more sophisticated concepts. For instance, • What is the significance of the base (growth or decay factor) in an exponential function? • What is the meaning of the power in a power function? • What do the parameters in a realistic sinusoidal model tell about the phenomenon being modeled? • What is the significance of the factors of a polynomial? • What is the significance of the derivative? • What is the significance of a definite integral? Further Implications If we focus only on manipulative skills without developing conceptual understanding, we produce nothing more than students who are only Imperfect Organic Clones of a TI-89 Results of the Study The study involved 10 common questions on the final exam in college algebra/trigonometry, most of which were basically computational in nature. The students in the reform sections outscored those in the traditional, algebraic-oriented, sections, on 7 of the 10 questions. Follow-Up Results in Calculus The students involved in the precalculus study were then followed in Calculus I the next term. The calculus course was a reform course with emphasis also on conceptual understanding, not just manipulation. Follow-Up Results in Calculus On every weekly quiz, on every class test, and on the final exam, the students from the reform sections of precalculus consistently scored higher than the students from the traditional sections. On an attitudinal survey, the students from the reform section had significantly better attitudes toward mathematics, its usefulness, and the importance of technology for problem solving. Follow-Up Results in Calculus 77% of the students who had been in a reform section of precalculus ended up receiving a passing grade in Calculus I. 41% of those who had been in a traditional section of precalculus received a passing grade in Calculus I. Developing Conceptual Understanding Conceptual understanding cannot be just an add-on. It must permeate every course and be a major focus of the course. Conceptual understanding must be accompanied by realistic problems in the sense of mathematical modeling. Conceptual problems must appear in all sets of examples, on all homework assignments, on all project assignments, and most importantly, on all tests. Otherwise, students will not see them as important. Conclusions We cannot simply concentrate on teaching the mathematical techniques that the students need. It is as least as important to stress conceptual understanding and the meaning of the mathematics. We can accomplish this by using a combination of realistic and conceptual examples, homework problems, and test problems that force students to think and explain, not just manipulate symbols. If we fail to do this, we are not adequately preparing our students for successive mathematics courses, for courses in other disciplines, and for using mathematics on the job and throughout their lives. Some Illustrative Examples of Problems to Develop or Test for Conceptual Understanding Identify each of the following functions (a) - (n) as linear, exponential, logarithmic, or power. In each case, explain your reasoning. (g) y = 1.05x (h) y = x1.05 (m) (n) x y x y 0 (i) y = (0.7)t (j) y = v0.7 0 3 5 1 (k) z = L(-½) (l) 3U – 5V = 14 1 5.1 7 2 2 7.2 9.8 3 3 9.3 13.7 For the polynomial shown, (a) What is the minimum degree? Give two different reasons for your answer. (b) What is the sign of the leading term? Explain. (c) What are the real roots? (d) What are the linear factors? (e) How many complex roots does the polynomial have? The following table shows world-wide wind power generating capacity, in megawatts, in various years. Year 1980 1985 1988 1990 1992 1995 1997 1999 Wind power 10 1020 1580 1930 2510 4820 7640 13840 15000 10000 5000 0 1980 1985 1990 1995 2000 (a) Which variable is the independent variable and which is the dependent variable? (b) Explain why an exponential function is the best model to use for this data. (c) Find the exponential function that models the relation- ship between power P generated by wind and the year t. (d) What are some reasonable values that you can use for the domain and range of this function? (e) What is the practical significance of the base in the exponential function you created in part (c)? (f) What is the doubling time for this exponential function? Explain what it means. (g) According to your model, what do you predict for the total wind power generating capacity in 2010? Biologists have long observed that the larger the area of a region, the more species live there. The relationship is best modeled by a power function. Puerto Rico has 40 species of amphibians and reptiles on 3459 square miles and Hispaniola (Haiti and the Dominican Republic) has 84 species on 29,418 square miles. (a) Determine a power function that relates the number of species of reptiles and amphibians on a Caribbean island to its area. (b) Use the relationship to predict the number of species of reptiles and amphibians on Cuba, which measures 44218 square miles. The accompanying table and associated scatterplot give some data on the area (in square miles) of various Caribbean islands and estimates on the number species of amphibians and reptiles living on each. Number o f Speci es Island Area N 100 Redonda 1 3 80 60 Saba 4 5 40 Montserrat 40 9 20 Puerto Rico 3459 40 0 Jamaica 4411 39 0 15000 30000 45000 Area (square miles) Hispaniola 29418 84 Cuba 44218 76 (a) Which variable is the independent variable and which is the dependent variable? (b) The overall pattern in the data suggests either a power function with a positive power p < 1 or a logarithmic function, both of which are increasing and concave down. Explain why a power function is the better model to use for this data. (c) Find the power function that models the relationship between the number of species, N, living on one of these islands and the area, A, of the island and find the correlation coefficient. (d) What are some reasonable values that you can use for the domain and range of this function? (e) The area of Barbados is 166 square miles. Estimate the number of species of amphibians and reptiles living there. Write a possible formula for each of the following trigonometric functions: The average daytime high temperature in New York as a function of the day of the year varies between 32F and 94F. Assume the coldest day occurs on the 30th day and the hottest day on the 214th. (a) Sketch the graph of the temperature as a function of time over a three year time span. (b) Write a formula for a sinusoidal function that models the temperature over the course of a year. (c) What are the domain and range for this function? (d) What are the amplitude, vertical shift, period, frequency, and phase shift of this function? (e) Predict the high temperature on March 15. (f) What are all the dates on which the high temperature is most likely 80? Some Other Issues Regarding the Need to Refocus the Courses below Calculus The Need to Rethink Placement in Mathematics Rethinking Placement Tests Four scenarios: 1. Students come from traditional curriculum into traditional curriculum. 2. Students from Standards-based curriculum into traditional curriculum. 3. Students from traditional curriculum into reform curriculum. 4. Students from Standards-based curriculum into reform curriculum. A National Placement Test 1. Square a binomial. 2. Determine a quadratic function arising from a verbal description (e.g., area of a rectangle whose sides are both linear expressions in x). 3. Simplify a rational expression. 4. Confirm solutions to a quadratic function in factored form. 5. Completely factor a polynomial. 6. Solve a literal equation for a given unknown. A National Placement Test 7. Solve a verbal problem involving percent. 8. Simplify and combine like radicals. 9. Simplify a complex fraction. 10. Confirm the solution to two simultaneous linear equations. 11. Traditional verbal problem (e.g., age problem). 12. Graphs of linear inequalities. A Modern High School Problem Given the complete 32-year set of monthly CO2 emission levels (a portion is shown below), create a mathematical model to fit the data. Year Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Avg 1968 322 323 324 325 325 325 324 322 320 320 320 322 323 1969 324 324 325 326 327 326 325 323 322 321 322 324 324 A Modern High School Problem 1. Students first do a vertical shift of about 300 ppm and then fit an exponential function to the transformed data to get: F (t )  1.656e 0.03923t  299.5 2. They then create a sinusoidal model to fit the monthly oscillatory behavior about the exponential curve   1  S  t   3.5sin  2  t     0.5   24   3. They then combine the two components to get   1  C  t   F  t   S  t   1.656e 0.03923 t  3.5sin  2  t     299   24   4. They finally give interpretations of the various parameters and what each says about the increase in concentration and use the model to predict future or past concentration levels. Placement, Revisited Picture an entering freshman who has taken high school courses with a focus on problems like the preceding one and who has developed an appreciation for the power of mathematics based on understanding the concepts and applying them to realistic situations. What happens when that student sits down to take a traditional placement test? Is it surprising that many such students end up being placed into developmental courses? What a High School Teacher Said ―If you try to teach my students with the mistaken belief that they know the mathematics I knew at their age, you will miss a great opportunity. My students know more mathematics than I did, but it is not the same mathematics; and I believe they know it differently. They have a different vision of mathematics that would be helpful in learning calculus if it were tapped.‖ Dan Teague The Need to Rethink Course Content What Can Be Removed? How many of you remember that there used to be something called the Law of Tangents? What happened to this universal law? Did triangles stop obeying it? Does anyone miss it? What Can Be Removed? • Descartes' rule of signs • The rational root theorem • Synthetic division • The Cotangent, Secant, and Cosecant were needed for computational purposes. Just learn and teach a new identity: 1  tan x  cos2 x 2 1 How Important Are Rational Functions? • In DE: To find closed-form solutions for several differential equations, (usually done with CAS today, if at all) • In Calculus II: Integration using partial fractions–often all four exhaustive (and exhausting) cases • In Calculus I: Differentiating rational functions • In Precalculus: Emphasis on the behavior of all kinds of rational functions and even partial fraction decompositions • In College Algebra: Addition, subtraction, multiplication, division and especially reduction of complex fractional expressions In each course, it is the topic that separates the ―adults‖ from the ―children‖! But, can you name any realistic applications that involve rational functions? Why do we need them in excess? Challenges to Be Faced The Challenges Ahead • Convincing the math community 1. Conducting a series of extensive tracking studies to determine how many (or how few) students who take these courses actually go on to calculus. 2. Identifying and highlighting ―best practices‖ in programs that reflect the goals of this initiative. The Challenges Ahead • Convincing college administrators to support (both academically and financially) efforts to refocus the courses below calculus. What Can Administrators Do? When the University of Michigan wanted to change to calculus reform, including going from large lectures of 800 students to small classes of 20 taught by full-time faculty, the department argued to the dean that by saving only 2% of the students who fail out because of calculus, the savings to the university would exceed the $1,000,000 annual additional instructional cost. The dean immediately said ―Go for it.‖ The Challenges Ahead Convincing academic bodies outside of mathematics to allow alternatives to traditional college algebra courses to fulfill general education requirements. An Example: Georgia The state education department in Georgia had a mandate for general education that every student must take college algebra. A group of faculty from various two and four year colleges across the state lobbied for years until they finally convinced the state authorities to allow a course in mathematical modeling at the college algebra level to serve as an alternative for satisfying the Gen Ed math requirement. The Challenges Ahead Convincing the testing industry to begin development of a new generation of placement and related tests that reflect the NCTM Standards-based curricula in the schools and the kinds of refocused courses below calculus in the colleges that we hope to being about. The Challenges Ahead Gaining the active support of representatives of a wide variety of other disciplines in the effort to refocus the courses below calculus. • CRAFTY and MAD (Math Across the Disciplines) committee have launched a second round of Curriculum Foundations workshops to address this issue. The Challenges Ahead Gaining the active support of representatives of business, industry, and government in this initiative. • Discussions are underway about revisiting some of the participants in the Forum on Quantitative Literacy. The Challenges Ahead Developing a faculty development program to assist faculty, especially part time faculty and graduate TA's, to teach the new versions of these courses. • NSF has funded a demonstration project through CRAFTY involving 11 schools. • 200 other departments wanted to be part of this project. The Challenges Ahead Influencing teacher preparation programs to rethink the courses they offer to prepare the next generation of teachers in the spirit of this initiative. The Challenges Ahead Influencing funding agencies such as the NSF to develop new programs that are specifically designed to promote both the development of new approaches to the courses below calculus and the widespread implementation of existing ―reform‖ versions of these
Mathematics: The Next Generation Subject: Overview Mathematics is important to us all. So it is important to enable young mathematicians, clear-thinking and passionate about their subject, to contribute at the highest level. Peter Cameron will talk about his experience designing and presenting a course for first-semester university students aiming to produce mathematicians.
9780534419417 ISBN: 0534419410 Edition: 4 Pub Date: 2006 Publisher: Thomson Learning Summary: The Fourth Edition of Yoshiwara and Yoshiwara's MODELING, FUNCTIONS, AND GRAPHS: ALGEBRA FOR COLLEGE STUDENTS includes content found in a typical algebra course, along with introductions to curve-fitting and display of data. Yoshiwara and Yoshiwara focus on three core themes throughout their textbook: Modeling, Functions, and Graphs. In their work of modeling and functions, the authors utilize the Rule of Four, which... is that all problems should be considered using algebraic, numerical, graphical, and verbal methods. The authors motivate students to acquire the skills and techniques of algebra by placing them in the context of simple applications that use real-life data. Yoshiwara, Katherine is the author of Modeling, Functions, And Graphs Algebra for College Students (With Printed Access Card Ilrn Tutorial Student), published 2006 under ISBN 9780534419417 and 0534419410. Seven hundred ninety one Modeling, Functions, And Graphs Algebra for College Students (With Printed Access Card Ilrn Tutorial Student) textbooks are available for sale on ValoreBooks.com, one hundred seventy two used from the cheapest price of $12.39, or buy new starting at $2384419417 ISBN:0534419410 Edition:4th Pub Date:2006 Publisher:Thomson Learning is the college student's top choice for cheap Modeling, Functions, And Graphs Algebra for College Students (With Printed Access Card Ilrn Tutorial Student) rentals, or used and new copies that can get to you quickly.
Why study mathematics? Many students are attracted to mathematics at school by the clear unequivocal nature of the answers to the questions. Mathematics is a discipline in which, at university level too, precise propositions can lead, through elegant arguments, to far-reaching consequences, including surprising applications. The clear-cut nature of the subject means that a higher proportion of mathematics students obtain first-class degrees than in most other subjects. Why study mathematics at Essex? Students in a big city university often feel that the staff do not know them at all. This is not the case at Essex where students and staff have regular contact with each other. The transition from school/college to university is therefore not as daunting and you will soon get to know the other people in the Department. We maintain an 'open door' policy which means that whenever you are stuck on a problem, you are likely to find a lecturer available to give help. Our Department is home to one of the area co-ordinators for the East of England Further Mathematics Support Programme, which promotes and aids the teaching of A-level Further Mathematics, meaning we are at the forefront of what is happening in schools and colleges. Flexibility to change courses We recognise that the journey from school/college to university is a trip into the unknown. This is particularly the case if you choose a joint honours course and have not studied your chosen second subject before coming to university. We allow you the flexibility to experiment with new subjects: most students can change from their initial choice of course to single-honours courses up to the start of the second year, and many can change from joint honours to single honours up to the start of the final year. Flexibility to change modules Our courses are tailored with particular outcomes in mind, so in most cases there are rather few options in the first two years of a course. However, in all courses there are options in the third year. In any term, when you have options, you are encouraged to sit in on several modules before making a final choice, and staff are happy to give advice. Departmental scholarships and bursaries Major scholarships (worth £2,000 over two years for single-honours students) are awarded to those who obtain AAA (including A in Mathematics) in three full A-levels. Minor scholarships (worth £1,000 over two years for single-honours students) are awarded to those who obtain ABB or AAC (including A in Mathematics) in three full A-levels. If you are taking a joint honours course you will also receive these scholarships, but at half the full rate. Renewal of scholarships is subject to good performance in the first-year examinations. To qualify for one of these awards you must have placed Essex as your firm UCAS choice. Additionally, a one-off payment of £250 will be awarded to you if you achieve grade A or B in A-level Further Mathematics. Single-honours students who do well in the second-year exams are awarded a final-year bursary of £500. For full details, please visit: prospective_students/undergraduates/ scholarships.aspx for full details.
Jobs Mathematics GCSE Introduction to course 1year, assessed by exams GCSE Maths is essential for entry onto many university level courses - and employers look for it, too, in most business areas. If you obtained a grade D from school, then during your time with us our friendly teachers will help you to improve your grade with this very popular resit course. Course Details We follow a modular Edexcel course and you may sit a combination of higher and foundation modules, depending on how you progress with the course. Entry Requirements This GCSE resit course is suitable for students who have previously obtained a grade D in GCSE Maths at school and wish to improve it to a grade C. Where the course lead GCSE Maths grade C is an essential requirement for nearly all university degree courses. This course is not suitable with GCSE re-sit English (you will have to sit English first and do Maths the following year). Course Assessment You will be given the opportunity to sit this exam in November or you will sit 2 modules in March and 2 modules in May. Sir George Monoux College tries to ensure the accuracy of the information contained in this web site. However, such accuracy cannot be guaranteed. The College reserves the right to make changes in regulations, the offering and structure of courses and programmes without notice.
Synopses & Reviews Publisher Comments: Helps you pinpoint where you need the most help and directs you to the corresponding sections of the book Topic Area Reviews Math basics Factoring and solving equations Function operations and transformations Polynomials Exponential and logarithmic functions Graphing Other equations Conic sections Systems of equations and inequalities Systems of linear equations with three or more variables Customized Full-Length Exam Covers all subject areas Synopsis: "Synopsis" by Ingram,
You are here Mathematical Methods in Science Publisher: Mathematical Association of America Number of Pages: 234 Price: 18.95 ISBN: 978-0-88385-626-0 This book, first published almost fifty years ago, was one product of the School Mathematics Study Group (SMSG) series on enrichment topics not incorporated into the standard high school syllabus. Pólya's message, however, is as clear and striking today as it was when first written: mathematics is about problem solving, It is my personal opinion that there is nothing of greater importance to be taught in mathematics to the high school student than the business of setting up equations… without getting to understand what a problem is about and what is relevant to it and (when appropriate) translating it from words in formulae, there is no mathematical education (p. 136). And problem solve he does. The book is organized into four content-rich chapters separated by one single-page chapter marking what Pólya terms the "tidal flow" between mathematics and physics. The chapters are long, subdivided into sections, and full of applications that follow the historical development of mathematics and physics. It is not an easy read — the reader has to do the mathematics along with Pólya — but his explanations are clear and his dry wit lightens the work along the way. Topics are arranged historically and one follows developments with a sense of a time traveler watching the concepts as they unfold. The volume will appeal to a broad audience. Certainly the original addressees, high school teachers, could benefit from the plentiful selection of applications of mathematics. Not only are examples presented but solution strategies are reinforced. Pólya repeatedly asks the questions that we ask when modeling problem solving, "What is given? What is to be found? How many equations? (p. 147)" A second audience, not mutually exclusive from the first, is secondary and tertiary instructors who are interested in the history of mathematics. He flavors each section with a sense of the time and place in which the mathematician labored. Finally, the close link between physics and mathematics makes this text a tool that can be used by teachers in either discipline. Katherine Safford-Ramus is Professor of Mathematics at Saint Peter's College, the Jesuit College of New Jersey. She has been teaching mathematics at the tertiary level for 28 years. From October 2005 to October 2006, she served as the co-director of the Adult Numeracy Initiative, a project of the United States Office of Vocational and Adult Education, a division of the Department of Education. Safford is the author of Unlatching the Gate: Helping Adult Students Learn Mathematics. Her current research continues to focus on adults learning mathematics and, in particular, professional development of teachers as adult learners.
National Curriculum: Mathematics The National Curriculum for Mathematics was introduced into England, Wales and Northern Ireland as a nationwide curriculum for primary and secondary state schools following the Education Reform Act 1988. The basis of the curriculum and its associated testing was to standardise the content taught across schools in order to raise standards of attainment in mathematics. The National Curriculum (NC) went hand-in-hand with the development of national tests (SATs) at the end of the Key Stages. The NC introduced Programmes of Study (PoS), Attainment Targets (AT) levels and Statements of Attainment (SoA). Following the Cockcroft committee recommendations (Mathematics Counts), Using and Applying Mathematics was a significant inclusion in the curriculum through ATs 1 and 9 which included using mathematics in practical tasks, in real life problems and to investigating within mathematics itself. The National Curriculum required all schools to address the issue of teaching solely for the acquisition of knowledge and skills in isolation from the application of mathematics, and to develop a teaching and learning approach in which the uses and applications of mathematics permeate and influence all work in mathematics. This was a major undertaking for schools, and perhaps the single most significant challenge for the teaching of mathematics required by the National Curriculum in its aim of raising standards for all students. The National Curriculum required students to develop a range of methods for calculating - from mental methods through to the use of electronic calculators. In order to progress through the levels, students at every stage were to be encouraged to develop their own methods for doing calculations, a feature which was developed further through the Numeracy project and the Framework for Teaching Mathematics. Although Mathematics in the National Curriculum underwent a number of revisions, the mathematical content changed very little and kept assessment as a major constituent. To enable teachers to make sense of the new curriculum, non-statutory guidance and training materials were published to go alongside training for all teachers
The Theory of Algebraic Numbers The Theory of Algebraic Numbers An excellent introduction to the basics of algebraic number theory, this concise, well-written volume examines Gaussian primes; polynomials over a field; algebraic number fields; and algebraic integers and integral bases. After establishing a firm introductory foundation, the text explores the uses of arithmetic in algebraic number fields; the fundamental theorem of ideal theory and its consequences; ideal classes and class numbers; and the Fermat conjecture. 1975 edition. References. List of Symbols. Index. Reprint of the Mathematical Association of America, second, 1975 edition.
A Brief Encounter with Vectors Spreadsheet (Excel) File Be sure that you have an application to open this file type before downloading and/or purchasing. 1.02 MB \| 19 pages PRODUCT DESCRIPTION This is a brief encounter with vectors: After the nine lessons the student should be able to translate the skills gained herein to other disciplines. Four lessons including review and quiz for both plane and space vectors with a bridge discussion (see the preview) of similarities and differences between 2 and 3 dimensions summarize the unit. A brief encounter with Vectors by Orrin White is licensed under a Creative Commons Attribution 3.0 United States License. Average Ratings Comments & Ratings Product Questions & Answers Be the first to ask Orrin White
An algebra practice program for anyone working on simplifying expressions and solving equations. Create your own sets of problems to work through in the equation editor, and have them appear on all of... More: lessons, discussions, ratings, reviews,... Use your TI-Nspire to consider this scenario and question: Sam and Teri have bank accounts. Sam always withdraws money; Teri always saves it. When will they have equal balances -- or will they ever?
Book Description: Three components contribute to a theme sustained throughout the Coburn Series: that of laying a firm foundation, building a solid framework, and providing strong connections. Not only does Coburn present a sound problem-solving process to teach students to recognize a problem, organize a procedure, and formulate a solution, the text encourages students to see beyond procedures in an effort to gain a greater understanding of the big ideas behind mathematical concepts. Written in a readable, yet mathematically mature manner appropriate for college level students, Coburn's Trigonometry uses narrative, extensive examples, and a range of exercises to connect seemingly disparate mathematical topics into a cohesive whole. Coburn's hallmark applications are born out of the author's extensive experiences in and outside the classroom, and appeal to the vast diversity of students and teaching methods in this course area. Benefiting from the feedback of hundreds of instructors and students across the country, Trigonometry, Second Edition, continues to emphasize connections in order to improve the level of student engagement in mathematics and increase their chances of success in trigonometry
Module Description The module teaches the necessary mathematical techniques required for a modern degree in Economics. It focuses entirely on economics examples so that students not only learn important mathematical skills but also learn how to apply those skills to problems of economic interest. The module starts at a basic level and so is ideal for students with a weak background in mathematics. The module, however, progresses fairly quickly so that, by the end of the year, the student has the tools to attack relatively sophisticated economics problems. Throughout the year an extra remedial class is provided to help the weakest students keep pace with the module. Successful completion of the module will provide the student with a strong grasp of fundamental mathematical concepts. Students will be able to solve elementary economics problems and so obtain a more sophisticated understanding of economic principles. The test and assignments will allow students to demonstrate their problem-solving skills to solve real economic problems. Learning & Teaching Methods Assessment Whichever is the Greater: EITHER 50 per cent Coursework Mark, 50 per cent Exam Mark OR 100 per cent Exam Mark Coursework: Two tests, one in the autumn term and one in the spring term. Exam Duration and Period 3:00 hour exam during Summer Examination period. Other information This course is designed to complement, EC114, Introduction to Quantitative Economics EC115 is compulsory for all single honours economics schemes and is strongly recommended for all students who plan to take economics courses in years 2 and 3. First year students with a background in mathematics may substitute a more advanced course for EC115 with permission from the department. (If you are interested in this option, please send an email message to ueco@essex.ac.uk.) Students at Essex only for the Autumn term only are assessed on the basis of at least two pieces of work (assignments or tests), the average of which is the final mark for the course.
From the pyramids and the Parthenon to the Sydney Opera House and the Bilbao Guggenheim, this book takes readers on an eye-opening tour of the mathematics behind some of the world's most spectacular buildings. Beautifully illustrated, the book explores the milestones in elementary mathematics that enliven the understanding of these buildings and combines... more... 500 Ways to Achieve Your Best Grades. We want you to succeed on your college algebra and trigonometry midterm and final exams. That's why we've selected these 500 questions to help you study more effectively, use your preparation time wisely, and getyour best grades. These questions and answers are similar to the ones you'll find on a typical... more... Karl Gustafson is the creater of the theory of antieigenvalue analysis. Its applications spread through fields as diverse as numerical analysis, wavelets, statistics, quantum mechanics, and finance. Antieigenvalue analysis, with its operator trigonometry, is a unifying language which enables new and deeper geometrical understanding of essentially every... more... This book covers a wide range of topics, from orthogonal polynomials to wavelets. It contains several high-quality research papers by prominent experts exploring trends in function theory, orthogonal polynomials, Fourier series, approximation theory, theory of wavelets and applications. The book provides an up-to-date presentation of several important... more... CliffsQuickReview course guides cover the essentials of your toughest classes. Get a firm grip on core concepts and key material, and test your newfound knowledge with review questions. CliffsQuickReview Trigonometry provides you with all you need to know to understand the basic concepts of trigonometry — whether you need a supplement to your... more... The learn-by-doing way to master Trigonometry Why CliffsStudySolver Guides? Go with the name you know and trust Get the information you need--fast! Written by teachers and educational specialists Get the concise review materials and practice you need to learn Trigonometry, including: Explanations of All Elements and Principles * Angles and quadrants... more... Presents the results on positive trigonometric polynomials within a unitary framework; the theoretical results obtained partly from the general theory of real polynomials, partly from self-sustained developments. This book provides information on the theory of sum-of-squares trigonometric polynomials in two parts: theory and applications. more...
Synopses & Reviews Publisher Comments: This book is intended to provide students with an efficient introduction and accessibility to ordinary and partial differential equations, linear algebra, vector analysis, Fourier analysis, and special functions and eigenfunction expansions, for their use as tools of inquiry and analysis in modeling and problem solving. It should also serve as preparation for further reading where this suits individual needs and interests. Although much of this material appears in Advanced Engineering Mathematics, 6th edition, ELEMENTS OF ADVANCED ENGINEERING MATHEMATICS has been completely rewritten to provide a natural flow of the material in this shorter format. Many types of computations, such as construction of direction fields, or the manipulation Bessel functions and Legendre polynomials in writing eigenfunction expansions, require the use of software packages. A short MAPLE primer is included as Appendix B. This is designed to enable the student to quickly master the use of MAPLE for such computations. Other software packages can also be used. About the Author Served on the faculty at the University of Minnesota, The College of William and Mary in Virginia, where he was chairman of mathematics, and the University of Alabama at Birmingham, where he was chairman of mathematics, dean of natural sciences and mathematics, and university provost. Primary research interests are in graph theory, combinatorial analysis and applications of mathematics to problems in the physical and biological sciences and engineering
Mathway is a Web calculator that not only solves math problems for you, but also shows you how it got to the answer with step-by-step directions. It's the kind of service that would have utterly ruined me in middle school if I had wanted to cruise through the stacks of homework without doing any of the actual computations. Mathway covers several types of math genres, including high school level stuff like trigonometry and calculus. It'll also take any "basic math," like what you'd do with a calculator, although it's kind of a waste since most problems only involve one line of explanation. I'm guessing most people would simply open up their computers' calculator instead. In addition to its problem solver, Mathway has a built-in graphing tool and a glossary--just in case the solver throws some terminology around that you haven't heard before. You can also embed any answer to show it off to others--although I'm betting more people are likely to use the e-mail link instead
Product Details Combinatorics: A Guided Tour by David Mazur Combinatorics is mathematics of enumeration, existence, construction, and optimization questions concerning finite sets. This text focuses on the first three types of questions and covers basic counting and existence principles, distributions, generating functions, recurrence relations, Pólya theory, combinatorial designs, error correcting codes, partially ordered sets, and selected applications to graph theory including the enumeration of trees, the chromatic polynomial, and introductory Ramsey theory. The only prerequisites are single-variable calculus and familiarity with sets and basic proof techniques. The text emphasizes the brands of thinking that are characteristic of combinatorics: bijective and combinatorial proofs, recursive analysis, and counting problem classification. It is flexible enough to be used for undergraduate courses in combinatorics, second courses in discrete mathematics, introductory graduate courses in applied mathematics programs, as well as for independent study or reading courses.
Comment: I spent about 15 minutes on this website, being quizzed/tutored. The content is useful if someone wants to brush up on... see more Comment: I spent about 15 minutes on this website, being quizzed/tutored. The content is useful if someone wants to brush up on skills, but I think it would be more helpful if you could ask it specific questions. It has the potential to help people who mabey havent taken a math class recently, or who ust want to get in some pratice. Its pretty easy to use, but mabey you can ask specific questions, and I just was unable to find that area. Author: Heather Ennis (Student) Date Added: Sep
More About the Author Alan Graham has worked in Mathematics Education at the Open University since 1977, prior to which he taught mathematics in a secondary school. He has also worked on a Schools Council Project on Statistical Education (POSE) based at Sheffield University. He has written over 20 short plays for BBC Schools Radio under the series title Calculated Tales. Over the last 10 years, his work has concentrated on two main areas, Statistics and Teaching Mathematics using ICT. He has published numerous books in these and other areas, including Teach Yourself Statistics, Teach Yourself Basic Maths and most recently, 'The Sum of You'. Alan Graham's goal has been to help make the learning of mathematics both fun and accessible to all, taking in a variety of contexts including music and art. Outside mathematics, his main interest is music and he plays the whistle and guitar in the Irish band, Betty's Kitchen. Product Description Book Description Teach Yourself Basic Mathematics will teach you all the maths you need for everyday situations. If you are terrified by maths, this is the book for you. --This text refers to an out of print or unavailable edition of this title. About the Author Alan Graham has been a Lecturer in Mathematics Education at the Open University for over 30 years and has worked widely with schools and the media. --This text refers to an out of print or unavailable edition of this title. Inside This Book(Learn More) Browse and search another edition of this book. This books comes from the "Teach Yourself" series and in my opinion this is a good recommendation in itself. As you would expect in a book on basic mathematics, it starts with the basics. So if you are just starting maths or want to refresh and update your knowledge, then this is a good starting point.The book is set out in progressive chapters. So you can focus on what you want to learn. If you have children, think of how you can help them with their homework. I find it a good way of spending some quality time together. Worth every penny. An interesting book to support this is -Success with Mathematics (Routledge Study Guides). You will find it readable and full of useful guidance. I bought this and it is full of errors. I would not trust this book at all. Only done the first 4 chapters but there were at least 7 errors in the answers section! My maths is rusty but dividing 5 cakes between 6 people does not give them 1/3 each. And 10/20 is not the same as 12/21 and 1/3 is not 900/1000. I have written to Hodder Education pointing out the errors. They have offered me another book. I think I shall decline.
Vectors Mathcentre provide these resources which cover aspects of vectors, often used in the field of engineering. They include descriptions of the notation often used to describe vectors and how to calculate the modulus of vector given in cartesian form, as well as how to calculate scaler and vector products. Comprehensive notes, with clear descriptions, for each resource are provided, together with relevant diagrams and examples. Students wishing to review, and consolidate, their knowledge and understanding of vectors will find them useful, as each topic includes a selection of questions to be completed, for which answers are provided
Revised (07-53) DELAWARE TECHNICAL & COMMUNITY COLLEGE Campus: WILMINGTON Department: MATHEMATICS Course Number and Name: MAT 155 Mathematics of Finance Pre-requisites: MAT 015 - Elementary Algebra Course hours and Credits: 3:0:3 Course Description: A study of the mathematics of buying and selling, personal finance, depreciation, inventory control, payroll, banking, annuities, business statistics, and applied problems. Required Text: Miller/Salzman, Business Mathematics, Pearson/Addison Wesley, 2006. Method of Instruction: Classroom Lecture Required Equipment: Each student is required to have an electronic calculator capable of scientific calculations. The math department strongly recommends the TI 84 PLUS calculator. Core Course Performance Objectives: At the end of this course, the student will be able to: 1. Solve application problems involving the mathematics of buying and selling. 2. Analyze problems involving personal finance. 3. Solve application problems involving depreciation. 4. Solve application problems involving inventory control. 5. Use principle of accounting mathematics to prepare financial statements and ratio analysis. 6. Solve application problems involving annuities and sinking funds. 7. Solve application problems involving insurance and securities. 8. Draw and analyze graphs, solve problems in business statistics with applications. Measurable Performance Objectives: 1. Review the fundamentals of the Mathematics of Finance. 1.1 Perform basic operations using positive and negative rational numbers. 1.2 Solve linear equations in one variable. 1.3 Solve applications problems, including percents, using proportions. 1.4 Solve application problems, including percents, using linear equations. 2. Solve application problems involving the mathematics of buying and selling. 2.1 Compute the net price, given the list price and a single trade discount. 2.2 Compute the net price and the single discount equivalent, given the list price and a series of discounts. 2.3 Compute the cash discount and the amount due given the invoice amount, the invoice date, the payment date, and the terms of the invoice. 2.4 Compute the selling price, markup, percent of markup or cost of an item, when the markup is based on cost. 2.5 Compute the selling price, markup, or cost of an item, when the markup is based on selling price. 2.6 Compute the markdown, percent of markdown, or the sale price of an item. 2.7 Compute the turnover at cost and the turnover at selling price. 2.8 Use EXCEL to calculate amounts of discount and net prices. 3. Analyze problems involving personal finance. 3.1 Compute simple interest problems: the interest, principle, time or rate of personal loans. 3.2 Compute the exact and ordinary interest given the principle, rate and time of personal loan. 3.3 Find the exact time and the approximate time between two given calendar dates for a personal loan. 3.4 Prepare reconciliation of personal banking statements. 4. Solve application problems involving depreciation. 4.1 Compute the annual and total depreciation of an asset, using the straight line method. 4.2 Compute the annual and total depreciation of an asset, using the declining balance method. 4.3 Compute the annual and total depreciation of an asset, using the MACRS method. 5. Solve application problems involving inventory control. . 5.1 Compute the average inventory, when inventory is taken at cost. 5.2 Compute the average inventory, when inventory is taken at selling price. 6. Calculate gross and net pay for employees earning wages, salaries and commission. 6.1 Compute monthly and weekly gross earnings, given the amount of the annual salary. 6.2 Compute hourly rate given weekly, biweekly, semi-monthly or annual salary. 6.3 Compute gross earnings, given the salary, the overtime rate, and the number of hours worked. 6.4 Compute gross earnings, given the rate of commission and net sales. 6.5 Compute gross earnings, given the piecework rate and the amount of production. 6.6 Compute various types of deductions including: Federal Withholding Tax, FICA (Social Security Tax), State and/or Local Withholding Tax. 6.7 Compute net pay. 7. Solve application problems involving annuities and sinking funds. 7.1 Compute the discount and the proceeds for a non-interest bearing note. 7.2 Compute the maturity value, the discount, and the proceeds for an interest-bearing note. 7.3 Compute the amount, discount rate, or time for an interest-bearing note. 7.4 Compute the compound amount, the compound interest, and the present value, using the compound interest formula and the compound interest tables. 8. Draw and analyze graphs. 8.1 Construct a frequency distribution from a data set. 8.2 Construct a bar graph, picture graph, line graph, component part graph, histogram, and frequency polygon from a given set of data. 8.3 Construct a bar graph, picture graph, line graph, histogram, pie chart and frequency polygon from a given set of data on a computer using EXCEL. 8.4 Interpret pictorial and tabular representation of data. 9. Solve problems in business statistics with applications. 9.1 Calculate and interpret the mean, median, mode, and mid-range. 9.2 Calculate and interpret the range. Evaluation Criteria: Students will demonstrate proficiency on all Measurable Performance Objectives at least to the 75% level. The grade will be determined using the College Grading System. 92 – 100 = A 83 – 91 = B 75 - 82 = C 0 – 74 = R Students should refer to the Student Handbook for further information on Academic Standing Policy, Academic Honesty Policy, Student Rights and Responsibilities and other policies relevant to their academic
Book Description: This text provides a solid foundation in the basic logical concepts for most of the subjects encountered in university mathematics, including basic college-level algebra and analysis. The first edition has been completely rewritten and expanded in response to a decade of teaching the subjects. This text is written for the students beginning "abstract pure mathematics" at university or college level. For the student beginning to study mathematics at this level there is a distinction between what she or he has done in the past and what lies ahead. What the student needs to acquire mastery of what is virtually an entirely new language -the language of mathematics- and to adopt an entirely new way of thinking. Featured Bookstores Buyback (Sell directly to one of these merchants and get cash immediately)
College Mathematics Basic College Mathematics Basic Mathematics Basic Mathematics Basic Mathematics Basic Mathematics Basic Mathematics Basic Mathematics BASIC MATHEMATICS Basic Mathematics ( AIE ) Collaborative Learning Activities Manual Student Solutions Manual for Basic College Mathematics Video Resources on DVD with Chapter Test Prep Videos for Basic College Mathematics Worksheets for Classroom or Lab Practice for Basic College Mathematics Summary This interactive tutorial CD-ROM provides algorithmically generated practice exercises that are correlated at the objective level to the exercises in the textbook. Every practice exercise is accompanied by an example and a guided solution designed to involve students in the solution process. Selected exercises may also include a video clip to help students visualize concepts. The software provides helpful feedback for incorrect answers and can generate printed summaries of students' progress.
Elementary Linear Algebra comes to learning linear algebra, engineers trust Anton. The tenth edition presents the key concepts and topics along with engaging and contemporary applications. The chapters have been reorganized to bring up some of the more abstract topics and make the material more accessible. More theoretical exercises at all levels of difficulty are integrated throughout the pages, including true/false questions that address conceptual ideas. New marginal notes provide a fuller explanation when new methods and complex logical steps are included in... MORE proofs. Small-scale applications also show how concepts are applied to help engineers develop their mathematical reasoning.
Research Projects for Students A research project can be a very important part of an education inmathematics. Besides the greatly increased learning intensity that comes from personal involvement with a project, and the chance to show colleges or graduate schools and potential employers the student's ability to initiate and carry out a complex scientific task, it gives the student an introduction to mathematics as it is: a living and developing intellectual organism where progress is achieved by the interplay of individual creativity and collective knowledge. High school and college students often have trouble finding appropriate topics for research projects in mathematics. This page presents some suggestions of where to look. These sources do not list project topics! But they present a wealth of mathematical subjects in an accessible way. Each of these subjects will have areas that invite further investigation. The Math Forum website posts Problems of the Week in geometry, algebra, discrete math, trig & calculus. The site also links to Problems of the Week administered by others, including the challenging college-level problems of Macalester College, the interactive ESCOT Problem of the Week, and several team-based projects. This link is to a list of Research Project Ideas. This list is a copy of the list "Possible Science Fair Mathematics Projects" which was created by Afton H. Cayford, at TheUniversity of British Columbia. A little dated now, but may be useful. What's Happening in the Mathematical Sciences is a series of publications from the AMS and can be ordered from the AMS Bookstore. Each issue has 10 or more articles by a science writer, covering a new development in the mathematical sciences. Subjects treated are on the frontiers of mathematical research,but reading about them can be useful in searching for an area to explore. ABC News maintains an archive of John Allen Paulos' columns "Who's Counting". An excellent source of project ideas in probability and statistics. +plus magazineis a monthly web publication, part of the Millenium Mathematics Project sponsored by the University of Cambridge and Cambridge University Press. Every month there are 5 or 6 very accessible articles onmathematical topics (along with puzzles and news).
Changing Shapes With Matrices from Don's book of that name in English (1995), and in Japanese (2001), with Ms. Noriko Arai, here using an interactive Java applet created by Fukushima Kazuhiro at IES in Japan The form of the multiplication of matrices used here is: The reason Don uses this form is that all his young students have done some graphing, where the points are in the form (x,y). When he uses the matrix [x y] for the point (x,y) on the left, it is natural and easily understood. The multiplication is done by going across in the first matrix, and down in the second, multiplying, then adding.
Autumn 2013. The Fundamental Theorem of Calculus, area, volume, and area length calculations, properties and applications of the integra/. • interpret, describe, compare, and produce functions and their antiderivatives. • apply methods and tools learned in class to real-life situations. critical thinking communication quantitative reasoning General method of instruction Hybrid class. Almost all of the in-class time will be group work. Recommended preparation bcusp 124 with a 2.0 Alexandre Barchechat Date: 07/04/2013 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
Le Moyne College Academics \| Academic Support \| Math Anxiety. Math Anxiety WHAT IS MATH ANXIETY? "Math anxiety is a learned emotional response to one or more of the following: participating in a math class, listening to a lecture, working through problems, or discussing mathematics." Explores WHERE DOES MATH ANXIETY COME FROM? The ON COURSE NEWSLETTER publishes innovative strategies for helping students become active, responsible learners. To subscribe to this bi-weekly (monthly in the summer) e-newsletter, click hereand send the resulting e-mail. No need to type anything. Our computer will automatically add your return address to the list of subscribers. You're always in charge of your subscription, with a subscribe/unsubscribe link in every newsletter. Have a best practice to share? Click here and request our publication guidelines.
Differences between linear and exponential growth functions. A student page instructs students to locate four specified sites on the Internet. After data are collected, pattern predictions are made. Graphing the collected data is done using ClarisWorks' spreadsheet or pencil and grid paper. Student description and analysis. Aligned to the California State Standards. From the Schools of California Online Resources for Educators SCORE Mathematics Lessons.
Mathematical Software Mathematical software is often used to analyse data, do calculations or test theoretical expressions. ICT has software licenses currently for the following software. More details are available through the links attached to the software names. While a general description is given, all of te packages have more features than can be given on a single line.
book's clear, well-constructed and straightforward writing style makes it accessible to even the most apprehensive math students. The primary ...Show synopsisThis book's clear, well-constructed and straightforward writing style makes it accessible to even the most apprehensive math students. The primary focus of the pedagogy, presentation and other elements is to ease the transition into algebra; for example, emphasis is placed on basic arithmetic operations within algebraic contexts. The Second Edition includes a greater integration of NCTM and AMATYC standards, including more emphasis on visualization, problem solving and data analysis.Hide synopsis Description:Paperback. Instructor Edition: Same as student edition with...Paperback. Instructor Edition: Same as student edition with additional notes or answers. New Condition. SKU: 978032162919728862. arithme...
Indian Institute for Studies in Mathematics, or IISMA, is an organisation dedicated to improving the quality of mathematical education at all levels. IISMA was founded in October 2004 by a bunch of like-minded individuals, who firmly believed that the present education scenario does not focus strongly enough on fundamentals and their application, which tends to make mathematics feared rather than enjoyable. We have been striving to change this scenario ever since. MTSE Awards MathGym Publications Downloads Maths Talent Search Examination is a competitive math-based exam for the students of Class III, IV, V, VI, VII, VIII and IX designed to test and identify the talented young. Our aim is to not only identify but also inspire and reward the talent by awarding scholarships. Scholarships worth more than Rs. 3.5 lacs are awarded every year. Mathgym is an online service where students get unlimited practice on various topics in mathematics. Mathgym will prove useful to the students who are preparing for IISMA's MTSE exam. In order to allow students to prepare comprehensively for MTSE and give them a glimpse of what to expect, we bring out a range of publications including model papers. The Information Brochure for MTSE 2014 as well as the Registration Form for the same are available for download under the Downloads section. IISMA's journey down the years has been filled with memories and benchmarks that signify our endeavour. Our picture gallery tells this story by successfully capturing these nostalgic memories and achievements that keep inspiring us and strengthening our resolve. Click the link below to visit our picture gallery and take a trip down that memory lane.
Buy PDF Understanding the basic theories of finance is crucial to anyone planning on entering the financial arena. Financial theories are the basis for most methodologies and models, and therefore it is an important part of an investor's repertoire. Finance for Beginners teaches basic methods, tools and theories used today. The subjects range from principal and learning how to calculate interest rates, to risk factors, measures and shares. Presented in a clear and straightforward format, with illustrations and easy-to-read graphs, learning theory is made simple in this beginner's course. A concluding quiz will examine your comprehension at the end of each lesson.
UA preparatory math goes virtual Apr 26, 2011 By La Monica Everett-Haynes Is this what flashes across your mental screen when you think about math? The UA's mathematics department is piloting a new course, Math 100, which is designed to help students who struggle with university-level math. The course provides personalized instruction with a heavy emphasis on tutoring, peer support and the use of technology. The University of Arizona's math department is experimenting with a novel approach to early math instruction – one with a heavy emphasis on technology and peer-to-peer tutoring. Arguably, few other required college-level courses elicit the same frustration or the intimidation factor as mathematics. Some commonly talk about holding a hatred for math, believe they are no good at it or think up strategies to avoid it all together. But one University of Arizona team is working to unravel the enigmatic nature of math for the very students who struggle the most with it – those who do not test into college-level math. Math 100, now in the second semester of its pilot phase, has a heavy emphasis on both self-paced progress and peer-to-peer support while being offered through Elluminate, a web-conferencing system. "Students are so used to being online. We thought that if we put the course online we could interact more," said Michelle Woodward, who coordinates the pilot course being offered by the UA mathematics department. The number of section offerings will be expanded during the fall to accommodate more UA students who do not test into algebra-level mathematics. Woodward said the course is being emphasized and expanded because it is especially important for new students to grasp college math, especially algebra – a curricular core – early. Algebraic skills have long been associated with giving students the ability to think in more complex ways. A student's ability to comprehend algebra has long been upheld as an indication of college-readiness, particularly for study in science and engineering-related disciplines. "It's the foundational material they need to be prepared for college algebra," Woodward said. "My whole goal in this is to make an online environment that is as close to what students would do in person. I want the environment to be as interactive as possible," Woodward said, adding that another program, the ALEKS Learning Module, provides both structure and flexibility while also offering the course content. "I have done a lot of work with students who needed individualized plans. ALEKS does that for me," she said. "I could not do that for 300 students, it doesn't replace me – it frees me up to work with students individually, the kind of work I didn't have time to do before." Over the course of the semester, the 300 students currently enrolled in one dozen Math 100 sections meet three hours weekly, receiving self-paced instruction mediated by Elluminate. Students complete assignments, learning to master algebraic expressions and graphing techniques and, all the while, ALEKS tracks their progress. "We are able to personalize the lessons much better than we have. It's been wonderful," said Cheryl Ekstrom, a mathematics lecturer who initiated the idea to incorporate Elluminate. "You aren't stuck listening to a lecture on things you already know or breezing by things you don't understand." This is in direct contrast to more established and traditional ways of teaching math. "In a traditional class, it doesn't matter if it's hard for you," said Shailendra Simkhada, an electrical engineering senior also studying math. "Each day in a regular class, you might get a new chapter or deadline to meet but, here, they can work at their own pace," he said. "It's not that they do less work, but if you don't understand something you get more information and one-on-one help so that they stay on track," he added. If fact, students designate their goals at the start of the class, deciding what sections they want to master and what math class they hope to test into at the end of the term. Students also engage in weekly virtual classroom meetings, sharing their computer screens and conversing online with student leads and support staff – UA students who are advanced in math and receive more than 15 hours of training. Kirandeed Banga, a UA sophomore studying biology, is a member of the student lead and support staff. Each week, Banga joins the other leads and support staff members in a classroom in the Math Building where they each log online to tutor and monitor student work. "With it being completely online, it's hard to get their trust. But we try to talk to them as much as possible," said Banga who, like others on the team, also offer office hours. "And we put them into virtual groups, so they are also able to help one another," she added. "They obviously are used to the technology, so they can adapt to it." Also built into the design of the course is extensive support to the UA students facilitating the class. Ivvette Rios, a UA math and French major, observes the virtual sessions and conducts weekly meetings with all of the students offering tutoring and support. Her role is to ensure that the leads and support staff have everything they need to appropriately help the hundreds of students enrolled. Rios said the time for self-evaluation and self-reflection is critical for those involved, and helps to ensure that the structure is working well for all involved. "We are always thinking of ways we can do this better; to make it more and more like our everyday experience," Rios said. "It's work out way better than we thought it would." Leo Shmuylovich knows a lot about how tutoring can take a student from confused to confident. The Washington University graduate student has worked as a tutor for several test preparatory companies over the years, helping ... (PhysOrg.com) -- New research from the University of Notre Dame suggests that even though adults tend to think in more advanced ways than children do, those advanced ways of thinking don't always override old, incorrectConsidering how many fools can calculate, it is surprising that it should be thought either a difficult or tedious task for any other fool to learn how to master the same tricks. Some calculus-tricks are quite easy. Some are enormously difficult. The fools who write the text-books of advanced mathematics-and they are mostly clever fools-seldom take the trouble to show you how easy the calculations are. On the contrary, they seem to desire to impress you with their tremendous cleverness by going about it in the most difficult way." Calculus Made Easy, Silvanus P. Thompson, Prologue, 1910 population
Calculus : Early Transcend (Cloth) - 2nd edition ISBN13:978-1429208383 ISBN10: 1429208384 This edition has also been released as: ISBN13: 978-1429260091 ISBN10: 1429260092 Summary: What's the ideal balance? How can you make sure students get both the computational skills they need and a deep understanding of the significance of what they are learning? With your teaching-supported by Rogawski's Calculus Second Edition-the most successful new calculus text in 25 years! Widely adopted in its first edition, Rogawski's Calculus worked for instructors and students by balancing formal precision with a guiding conceptual...show more focus. Rogawski engages students while reinforcing the relevance of calculus to their lives and future studies. Precise mathematics, vivid examples, colorful graphics, intuitive explanations, and extraordinary problem sets all work together to help students grasp a deeper understanding of calculus. Now Rogawski's Calculus success continues in a meticulously updated new edition. Revised in response to user feedback and classroom experiences, the new edition provides an even smoother teaching and learning95 +$3.99 s/h VeryGood BookCellar-NH Nashua, NH 1429208384109.95 +$3.99 s/h VeryGood BookCellar-NH Nashua, NH 1429208384
Welcome to Algebra 1. This course will make math come alive with its many intriguing examples of algebra in the world around you, from baseball to theater lighting to ... Welcome to Algebra 1. This course will make math come alive with its many intriguing examples of algebra in the world around you, from baseball to theater lighting to ... 1 teacher book.html The Language of Literature, Grade 10 Kentucky Department of Education 2005 Text in blue is from the Textbook Reviewers The Language of Literature, Grade 10 McDougal ... a little place called click on the level then click on your book. after your on your book, type in the page number and click on the problem. click on ... the activation code for classzone book grade 8.html Getting Started This is my first time to ClassZone. How do I get started? Where can I find the Teacher Access Code in order to register for ClassZones teacher ... Enter the following ctivation Code: 2517245-390 and then click ... Simply go to log in, click on the lgebra 2 textbook icon, and then click on the ... Best Answer: You have to be a teacher to log in. If you are a teacher, sign up for a code, or ask one of your friendly co-workers for their code. If youu0027re a student ... Where can you find an answer key for the Mcdougal littell algebra 2 2004 edition online?
This textbook is intended for introductory statistics courses being taken by students at two– and four–year colleges who are majoring in fields other than math or engineering. The book focuses on applications of statistical knowledge rather than the theory behind it. Elementary Algebra is a work text that covers the traditional topics studied in a modern elementary algebra course. It is intended for students who (1) have no exposure to elementary algebra, (2) have previously had an unpleasant experience with elementary algebra, or (3) need to review algebraic concepts and techniques. Fundamentals of Mathematics is a work text that covers the traditional topics studied in a modern prealgebra course, as well as topics of estimation, elementary analytic geometry, and introductory algebra.

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