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... More stand-alone instructional resource contains videos and links to websites where students can further practice graphing. Technical Requirements: To view this stand-alone instruction resource using PowerPoint: 1. Open "DJohnson StAIR" folder 2. Select the PowerPoint Slide Show "DJohnson_StAIR_Project_Graphing" 3. NOTE: There are two video clips that you will need to download within the "DJohnson StAIR" folder: "slope" and "slope intercept form." These two files do not play within the instructional resource but could be downloaded for viewing during the StAIR. Lindsay Sanders (Teacher (K-12)) This resource is jam-packed with all the information that students needs to know about slope-intercept form. The instructional design of this StAIR provides learning in various forms such as examples, videos, tutorials, animations and sound, practice problems, and applets. It was easy to navigate and the author gave clear instructions on what to click, where it would take you, and what it would show you. The design and images were also very appealing, especially to the audience that this was created for. Because graphing in slope-intercept form is a large concept, the only thing I could think you might want to consider is breaking this resource into separate resources in case students get overwhelmed with the amount of slides and content or even assign students to view only a portion of the resource. However, having it all together would be a great review resource for students before being assessed on the concept. Great job!! I love it! Technical Remarks: I couldn't get some of your videos to work. Time spent reviewing site: 30 minutes Used in course 2 years ago Kevin Karkkainen (Teacher (K-12)) What a fantastic resource. I wish I had something like this when I was learning slope-intercept. This .pps was put together very well. The information was great and the question portion seemed like a great assessment of what students should have learned. You did a nice job of breaking up the information into managable parts. This isn't always an easy concept to grasp, but I think students will benefit from using this resource. Technical Remarks: I didn't see any technical problems with this STAIR. Everything looked and functioned great. Time spent reviewing site: 15 minutes 2 years ago Leslie Sniegowski (Teacher (K-12)) This is a great resource to show students how to recognize slope-intercept form and how to make graphs from slope-intercept form. I know from experience how much students struggle to understand how to grasp slope-intercept form, but this would be a great resource to allow students extra remediation. The resource allows students to learn the material first, then provides hints and tricks to remember the slopes or the formula, and lastly allows students time to practice their skills. I really liked the video links, especially the football one, that helps students understand the vertical intercept. Students are more likely to connect to ideas that they have a personal connection to and many middle/high school students connect with sports. This is a great connection that will help students understand how to determine the vertical intercept. Great use of sound effects and animations - the practice part is crucial for students to understand math and this resource does a great job of allow time for structured practice. Technical Remarks: This is a Powerpoint Show for 97-2003 versions of Microsoft Powerpoint. If you are running Microsoft Office 2007, you will need to select "view slideshow" from the Slideshow Toolbar at the top taskbar in order to view the slideshow. The show will not begin automatically in Powerpoint 2007.
Assists teachers in understanding and interpreting the properties of numbers and provides a background to the numerous proofs... see more Assists teachers in understanding and interpreting the properties of numbers and provides a background to the numerous proofs and solutions to various mathematical equations. Material is crucial for the teaching of secondary school mathamatics.Compulsory Readings for Mathematics II: Number Theory (PDF)This archive is designed as a resource for enriching your courses with mathematical Fun Facts! It is designed to pique the... see more This archive is designed as a resource for enriching your courses with mathematical Fun Facts! It is designed to pique the interest of students in different areas of mathematics. The fun facts were originally conceived as five minute warm ups at the beginning of lectures so that non mathematics majors would not think math was just calculus. Presentation suggestions are also given.
(calc.info)Algebra 12 Algebra ********** This section covers the Calc features that help you work with algebraic formulas. First, the general sub-formula selection mechanism is described; this works in conjunction with any Calc commands. Then, commands for specific algebraic operations are described. Finally, the flexible "rewrite rule" mechanism is discussed. The algebraic commands use the `a' key prefix; selection commands use the `j' (for "just a letter that wasn't used for anything else") prefix. Note:Editing Stack Entries, to see how to manipulate formulas using regular Emacs editing commands. When doing algebraic work, you may find several of the Calculator's modes to be helpful, including algebraic-simplification mode (`m A') or no-simplification mode (`m O'), algebraic-entry mode (`m a'), fraction mode (`m f'), and symbolic mode (`m s'). Note:Mode Settings, for discussions of these modes. You may also wish to select "big" display mode (`d B'). Note:Normal Language Modes.
Linear Algebra : A Geometric standard computational aspects of linear algebra and interesting applications Linear Algebra: A Geometric Approach , Second Edition, is a text that not only presents the standard computational aspects of linear algebra and interesting applications, it guides students to think about mathematical concepts and write rigorous mathematical arguments. This thought-provoking introduction to the subject and its myriad applications is interesting to the science or engineering student but will also help the math... MOREematics student make the transition to more abstract advanced courses. The second edition has been updated with additional examples and exercises and has been streamlined for easier teaching and studying. Presenting the standard computational aspects of linear algebra and interesting applications, this text helps students to think about mathematical concepts and write rigorous mathematical arguments. The second edition has been updated with additional examples and streamlined for easier teaching and studying.
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Developmental Mathematics: Basic Mathematics and Algebra 9780321599209 ISBN: 0321599209 Edition: 2 Publisher: Addison Wesley Summary: Lial, Margaret L. is the author of Developmental Mathematics: Basic Mathematics and Algebra, published under ISBN 9780321599209 and 0321599209. One hundred sixty five Developmental Mathematics: Basic Mathematics and Algebra textbooks are available for sale on ValoreBooks.com, thirty three used from the cheapest price of $56.30, or buy new starting at $211.84.[ [morethe primary subject of this book is math. Its basic math, such as addition, subtraction, multiplication and division but not only that. It contains many more mathematical equations that are useful and good to go over and study. It was effective in my math class I was taking because it helped me not only review what I already knew but also to go over fractions which I really do not like.
Where Can I Buy It? Product Details Take the quick path to math success and build algebra skills! Product Information Quickstudy Algebra 2 provides a solid educational foundation that will raise grades and test scores and improve math skills in the classroom and beyond. Using step-by-step animations real-time quizzes and a fun 3-D interface Quickstudy Algebra 2 gives students the tools they need to master key algebra concepts. Take the stress out of high school math. The curriculum-based lessons are designed by educators to help students understand and practice critical thinking and problem-solving skills in an engaging interactive learning environment.
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Differentiation Teacher Resources Find Differentiation educational ideas and activities Title Resource Type Views Grade Rating In this calculus worksheet, students solve problems using differentiation and the chain rules. They take the derivatives of equations using specific equations. There are 21 problems with an answer key. Students read an article on how calculus is used in the real world. In this calculus lesson plan, students draw a correlation between the Battle of Trafalgar and calculus. The purpose of this article is the show everyday uses for calculus in the real world. In this implicit differentiation worksheet, students compute the determinant of the Jacobian matrix and solve equations by implicit differentiation. This two-page worksheet contains definitions, examples, and explanations. It contains approximately eight multi-step problems. In this Calculus worksheet, students are provided with practice problems for their exam. Topics covered include derivatives, area bounded by a curve, local maximum, instantaneous rate of change, and the volume of a solid of revolution. The four page document contains seventeen multiple choice questions. Answers are not included. In this Calculus learning exercise, students are provided with questions that are reflective of the content of their exam. Topics covered include derivatives, volume of a solid of rotation, local maximum and minimum, and integration. The one page learning exercise contains seventeen multiple choice questions. Answers are not provided. In this trigonometry worksheet, students differentiate the different trigonometric identities. They derive the sine, cosine, tangent and inverses of these trig identities. There are 18 questions with an answer key. Twelfth graders investigate the capabilities of the TI-89. In this calculus lesson, 12th graders explore the parametric equation for a circle, for arc length of curves, and for trajectories. Students investigate the symbolic and graphical representation of vectors. Students use polar functions of investigate the area bounded by a curve. Students investigate a 3D graphing applicationSal shows the complex solution to a challenging derivative problem about �normalines�. This is probably beyond the scope of most first year calculus students but might be an interesting problem to show how complex these problems can get. Most of the thorny computations shown utilize techniques learned in algebra, but the notation used and the multifaceted parts of the problem make it quite involved. More complex examples of derivatives are explored in this video. Sal works through examples of finding the derivative that requires using a combination of the product, quotient, and chain rules with trigonometric functions, ln x, and exDirections are written to solve a related rate problem step by step. There are five example problems to practice solving for related rates. Use of the Chain Rule and/or implicit differentiation is one of the key steps to solving these word problems. In this optimization worksheet, learners solve 20 short answer word problems. Students read, sketch, define variables, write equations, differentiate their equations, and find the maximum or minimum of each word problem. In this capacitance worksheet, students solve 19 problems about capacitance, voltage, electric charge and Ohm's Law. They use calculus to solve some of the problems and they are given equations used to solve different capacitance problems.
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Find a Wonder Lake AlgebraAlgebra 2 is a continuation of algebra 1. In algebra 2 students are introduced to polynomials. The rules for basic arithmetic operations on polynomials (addition, subtraction, multiplication, division and exponentiation) are examined. ...My demeanor is geared toward the comfort and success of the student. The student has to accept me as the director of their learning for the time we have together, and we will have success in our endeavors in gaining knowledge. I wish you all success in your efforts in learning and in finding an...
A mathematical model is a description of a system using mathematical language. Mathematical models are used not only in the natural sciences and engineering disciplines but they are also used in biology, economics and sociology. Here is a general guideline for how to build a mathematical model. Gather the following information: what you already know; sources of relevant data; your assumptions; what you'd like to predict with the model; ways of verifying that the model will be built correctly; and ways to validate the model. Simply, read the problem many times, classify knowns and unknowns and find out what is actually asked in problem. 2 Make a strategy. After classifying the data, make the strategy how to solve the problem or how to make model. Sketch simple diagrams that outline the elements in the model and how they are connected to each other. As for any complex task, diagram helps. 3 Conduct a thorough literature review. There is no need to re-invent the wheel if somebody else has developed a model that may suit your purposes already. However, you need to fully understand all the assumptions and the applicability of a model before using it. 4 Learn Data Handling.It is important to know what is missing information in the problem. So think carefully about how you are going to handle missing data. If possible, quantify the uncertainties associated with the data. Sometimes, we overlook the missing information,so gain read problem several times and carefully. 5 Begin with a simple model. Make possibilities of different applicable models and then choose the best and simple.According to Occam's Razor principle, among models with similar predictive power, the simplest one is the most desirable. 6 Identify the parameters of the equations and develop a plan how to estimate the parameters from the data. This could be done simply by fitting the equations to the data. 7 Validate your model against a data set that you have not used to build the model. 8 Constantly test your model and update your equations based on new data and information
MATHEMATICS Group, order of a group, finite and infinite groups, sub-groups, Right and Left Cosets of sub-group, Lagrange's theorem and its decuctions order of an element index of a sub-group in group. Normal Sub-group and quotient groups. Homomophisms, Isomorphisms, and. Unit - 2. Automorphisms; Kernal of a homomorphism. Fundamental theorem of homomorphism Cyclic group. Permutation group- Cycle and transposition even and old permutation. 1. Number Systems : The real field to be developed by ordered set approach. Equivalence of this approach and Dedikind's approach. Extended real number system. The complex number system Euclidean spaces. 2. Basic Topology : Finite, countable and uncountable sets Metric spaces, Neighbour hoods in metric spaces Limit points of a set, Open, closed bounded, Compact, connected and convex sub-sets of metric spaces. 3. Sequences and Series : Convergent Sequences, Sub-sequences Cauchy Sequences, upper and lower limits Special Sequences and Series Series of non-nagative terms The number Root and ratio tests. 4. Power Series with real (Complex) terms interval (circle) of convergence and radius of a power series Summation by parts absolute convergence. Addition and multiplication of series Rearrangements. 5. Limits and continuity : Limits and continuity for functions from a metric space into another metricspace continuity of a composite function, structureal properties of continuous function from a metric space into Rk. continuity and compactness. Continuity and connectedness Discontinuities Monotonity function. infinite limits and limits at infinity. Differentiation : Derivatives of a real function continuity and differentiability structural properties of the class of differentiable function, Mean value theorems. Continuity of derivatives L'Hospital's Rules Derivatives of higher order Taylor's theorems Differentiation of vector values function on (a,b). The course is roughly covered chapters 1,2,3,4,5 of the book entitled "Principles of Mathematical Analysis" by walter Rudin McGraw Hill (International student Edition) 3rd Edition. Unit - 2. Atoms of a Boolean Algebra : A (x) (the set of all the atoms of a Boolean algebra less than or equal to x) and its properties Isomorphism of a finite Boolean algebra and (P(S),C). Order of a finite Boolean algebra as 2". Boolean function / expressions. Minterms, Maxterms, representation of a Boolean expression as a sum of products canonical form and as product of sum canonocal form Karnaugh map. Minimization of a Boolean expression by Cube array method and by Karnaugh method. Unit - 1. Metric Spaces : Definition of a metric space and example, continuous function open and closed spheres and their properties, neighbourhood of a point and its properties open sets and its properties limit of a sequence, definition of closed sets and its properties. Unit - 3. Topological Space : (Cont.) Hausdorff space, definition of closure interior boundary of a set and their properties functions continuity and Homeorplisms, subspace topology and product topology Unit - 4. Connectedness :. Definitions of connected and disconected spaces connectedness on the real line and applications of connectedness, components and local connectedness Locally - connected at a point.
Mathematical Dictionary for School 9780521556576 ISBN: 0521556570 Publisher: Cambridge University Press Summary: Bolt, Brian is the author of Mathematical Dictionary for School, published under ISBN 9780521556576 and 0521556570. Ninety one Mathematical Dictionary for School textbooks are available for sale on ValoreBooks.com, fifteen used from the cheapest price of $0.01, or buy new starting at $9 [more160 pages. Softcover. Brand new book. MATHEMATICS. Contains definitions and examples of the mathematical words likely to be ncountered by students aged 11 to 16. Over 500 mat [more] 160 pages. Softcover. Brand new book. MATHEMATICS. Contains definitions and examples of the mathematical words likely to be ncountered by students aged 11 to 16. Over 500 mathematical words are defined, and there are plenty of examples and illustations to help with the concepts. (Key Words: Reference Books, Mathematics, Dictionaries, Brian Bolt, David Hobbs, Standard Deviation).[
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The discovery of algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpensive computers, has sparked a minor revolution in the study and practice of algebraic geometry. This book illustrates the uses of algebraic geometry, highlighting some of the applications of Grobner bases and resultants. more... Derived from the content of the respected McGraw-Hill Dictionary of Scientific and Technical Terms Sixth Edition, each title provides thousands of definitions of words and phrases encountered in a specific discipline. All include:. * Pronunciation guide for every term. * Acronyms, cross-references, and abbreviations. * Appendices with conversion tables;... more... The basics of the theory of elliptic curves should be known to everybody, be he (or she) a mathematician or a computer scientist. Especially everybody concerned with cryptography should know the elements of this theory. The purpose of the present textbook is to give an elementary introduction to elliptic curves. Since this branch of number theory is... more... The volume consists of invited refereed research papers. The contributions cover a wide spectrum in algebraic geometry, from motives theory to numerical algebraic geometry and are mainly focused on higher dimensional varieties and Minimal Model Program and surfaces of general type. A part of the articles grew out a Conference in memory of Paolo Francia... more... This two-volume book collects the lectures given during the three months cycle of lectures held in Northern Italy between May and July of 2001 to commemorate Professor Bernard Dwork (1923 - 1998). It presents a wide-ranging overview of some of the most active areas of contemporary research in arithmetic algebraic geometry, with special emphasis on... more... Present an overview of developments in Complex Geometry. This book covers topics that range from curve and surface theory through special varieties in higher dimensions, moduli theory, Kahler geometry, and group actions to Hodge theory and characteristic p-geometry. more... Algebraic Geometry provides an impressive theory targeting the understanding of geometric objects defined algebraically. Geometric Modeling uses every day, in order to solve practical and difficult problems, digital shapes based on algebraic models. This book is a collection of articles bridging these two areas. more... This is the first comprehensive basic monograph on mixed Hodge structures. Starting with a summary of classic Hodge theory from a modern vantage point the book goes on to explain Deligne's mixed Hodge theory. Here proofs are given using cubical schemes rather than simplicial schemes. Next come Hain's and Morgan's results on mixed Hodge... more... The two fields of Geometric Modeling and Algebraic Geometry, though closely related, are traditionally represented by two almost disjoint scientific communities. Both fields deal with objects defined by algebraic equations, but the objects are studied in different ways. This contributed book presents, in 12 chapters written by leading experts, recent... more...
Upper School Supply List There are no specific supply lists for the Upper School. Feel free to purchase typical supplies such as notebook paper, pens, pencils, highlighters, notebooks, binders, index cards, etc. Graphic calculators are required for Algebra I, Algebra II, Statistics, Pre-Calculus and Calculus students. The TI-83 or TI-84 should be purchased for use. Note: the TI-89 and TI-92 are prohibited through Pre-Calculus. If there are additional specific items that will need to be purchased, the teacher will let you know during the first week of school.
Intermediate Algebra With Early Functions and Graphing 9780321064592 0321064593 Summary: The Lial/Hornsby developmental mathematics paperback series has helped thousands of students succeed in math. In keeping with its proven track record, this revision includes a sharp new design, many new exercises and applications, and several new features to enhance student learning. Among the features added or revised include a new Study Skills Workbook, a Diagnostic Pretest, Chapter Openers, Test Your Word Power, F...ocus on Real-Data Applications, and increased use of the authors' six-step problem solving process. Lial, Margaret L. is the author of Intermediate Algebra With Early Functions and Graphing, published 2001 under ISBN 9780321064592 and 0321064593. Thirty two Intermediate Algebra With Early Functions and Graphing textbooks are available for sale on ValoreBooks.com, thirty used from the cheapest price of $0.75, or buy new starting at $24.97Midland, VAShipping:Standard, ExpeditedComments:NEW. In the original shrink wrapping. Book and MYMathLab unopened. NO remainder markings. A brand... [more]NEW. In the original shrink wrapping. Book and MYMathLab unopened. NO remainder markings. A brand new book perfect inside and out
Math for Standards 2011-12 The idea behind this blog is to allow students the chance to talk about math. Students do not often get this chance, and by talking about the different concepts, the students arrive at a better understanding. This leads them to be more involved in math. Unit 4 Preview Inductive Reasoning and Patterns- Inductive Reasoning is reasoning that solves proportions. Exp. 1. 90% of humans are right-handed. Patterns- Something that happens over again in the same exact order. Functions- One value that solves an example for the function. Linear Equations- An expression that has an equal sign. Slope- A line that shows its steepness. Direct Variation- When x increases, y increases. Systems of Linear Equations- An expression that has an equal sign. Growth formula and Interest- Used to see how much a population is growing. Inequality relations- It shows if something is greater than, less than, or equal too. Linear Inequalities and their graphs- its basically like an equation that you solve for x. Then you graph all the possible solutions to the inequality on the graph. Inverse Variation- When x increases, y decreases. Polynomial Operations- terms linked together through addition or subtraction. Quadratic Functions- f(x)=ax squared+bx+c.
in a classroom setting rather than in the Math Lab. Only open to those needing 4 or 5 credits of Arithmetic Review. Credits in this course do not apply toward graduation requirements. Explores sets; solving equations and inequalities; factoring; fractional, and rational expressions; graphing; and word problems. Credits in this course do not apply toward graduation requirements. (Offered only in the Math Lab.) Explores systems of equations; quadratic equations and inequalities; exponential functions; and logarithms. (Offered only in the Math Lab.) Credits in this course do not apply toward graduation requirements. Prerequisite: Intermediate Algebra or its equivalent and passing score on Mathematics Proficiency Exam. Explores algebraic, circular and trigonometric equations and identities; and inequalities. Credit cannot be received for this course if MAT 1112 or MAT 1114 has been taken. Prerequisite: Intermediate Algebra or its equivalent and passing score on Mathematics Proficiency Exam. Explores inequalities and algebraic functions: linear, quadratic, polynomial and rational. This is a portion of MAT 1110; credit cannot be received for taking both courses. (Offered only in the Math Lab.) Studies the development of circular and trigonometric functions; right-triangle applications; trigonometric equations; and identities. This is a portion of MAT 1110; credit cannot be received for taking both courses. (Offered only in the Math Lab.)35, nor can credit be received if 1234 or its equivalent has been taken. Prerequisite: Passing score on Mathematics Proficiency Exam and [MAT 1110 or (MAT 1112 and 1114)] or its equivalent as determined by the Calculus Placement Test. First course in calculus, emphasizing limits and derivatives of functions of one variable. Sequence begins both Autumn and Winter Quarters. Extra fee. Prerequisite: Intermediate Algebra or its equivalent and passing score on Mathematics Proficiency exam. Explores topics that illustrate how mathematical methods and models permeate our economic, political, and personal lives. By investigation of diverse applications, a variety of problem-solving techniques will be introduced, including using the computer as a tool. Prerequisite: Passing score on Mathematics Proficiency Exam or completion of Arithmetic Review. The first in a three-course sequence, this course is a study of numerical reasoning with emphasis on depth of understanding, problem solving strategies, and appropriate use of calculators and computer software. Investigations of mathematical topics include numeration systems, numerical properties and operations, concepts in number theory, and associated history of mathematics. Standards-based content preparation for teaching K-8 mathematics. Prerequisite: MAT 2530 completed with a grade of C- or better. Includes topics from probability, geometry, and measurement, and relates topics to the elementary school mathematics curriculum. Available for general education credit only to students in elementary education. Prerequisite: MAT 1560. The second in a three-course sequence, this course is a study of statistical and algebraic reasoning with emphasis on depth of understanding and appropriate use of calculators and computer software. Investigations of mathematical topics include statistics, probability, variables and their uses, proportional reasoning, linear and non-linear functions, inverse functions, proof appropriate for K-8 teachers, and associated history of mathematics. Standards-based content preparation for teaching K-8 mathematics. Prerequisite: MAT 2720 or 3749 (or MAT 3562 with permission of instructor). May be taken concurrently with instructor approval. Studies topics of classical number theory including divisibility, primes and congruences. Offered alternate years. Prerequisite: MAT 2561. The third in a three-course sequence, this course is a study of geometric reasoning with emphasis on depth of understanding and appropriate use of calculators and computer software. Investigations of mathematical topics include two- and three-dimensional geometry, measurement, proof appropriate for K-8 teachers, and associated history of mathematics. Standards-based content preparation for teaching K-8 mathematics. Prerequisite: MAT 1236 and MAT 2720 or permission of instructor. Uses the axiomatic method to prove basic results from set theory and real analysis. Topics include functions, set cardinality, the real number system, and the topology of the real line. Prerequisites: [MAT 1228, 2228, and 2375] or [MAT 2401, 3237 and 3360], and facility with mathematically oriented software. Focuses on construction and analysis of mathematical models for problems in the real world. The problems will be chosen from a variety of fields, including the biological and social sciences. Extra fee
Pre-Algebra: Order of Operations Find study help on order of operations for pre-algebra. Use the links below to select the specific area of order of operations you're looking for help with. Each guide comes complete with an explanation, example problems, and practice problems with solutions to help you learn order of operations for pre-algebra.
CSU Early Assessment of Readiness for College Mathematics -- Standards Assessed from the Blueprint for the California Standards Test of Algebra II Standard Description of Standard AII.1.0 Students solve equations and inequalities involving absolute value. AII.2.0 Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices. AII.3.0 Students are adept at operations on polynomials, including long division. AII.4.0 Students factor polynomials representing the the difference of squares, perfect square trinomials, and the sum and difference of two cubes. AII.5.0 Students demonstrate knowledge of how real and complex numbers are related both arithmetically and graphically. In particular, they can plot complex numbers as points in the plane. AII.6.0 Students add, subtract, multiply, and divide complex numbers. AII.7.0 Students add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial and polynomial denominators and simplify complicated rational expressions, including those with negative exponents in the denominator AII.8.0 Students solve and graph quadratic equations by factaoring, completing the square, or using the quadratic formula. Students apply these techniques in solving word problems. They also solve quadratic equations in the complex number system. AII.9.0 Students demonstrate and explain the effect that changing a coefficient has on the graph of quadratic functions; that is, students can determine how the graph of a parabola changes as a, b, and c vary in the equation y = a(x-b)2 + c AII.10.0 Students graph quadratic functions and determine the maxima, minima, and zeros of the function. AII.12.0 Students know the laws of fractional exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay. Students demonstrate and explain how the geometry of the graph of a conic section (e.g., asymptotes, foci, eccentricity) depends on the coefficients of the quadratic equation representing it. AII.17.0 Give a quadratic equation of the form ax2 + by2 + cx + dy + e = 0, students can use the method for completing the square to put the equation into standard form and can recognize whether the graph of the equation is a circle, an ellipse, a parabold, or a hyperbola. Students can then graph the equation. AII.18.0 Students use fundamental counting principles to compute combinations and permutations. AII.20.0 Students know the binomial theoreum and use it to expand binomial expressions that are raised to positive integer powers. AII.22.0 Students find the general term and the sums of arithmetic series and of both finite and infinite geometric series. AII.24.0 Students solve problems involving functional concepts, such as composition, defining the inverse function and performing arithmetic operations on functions. AII.25.0 Students use properties from number systems to justify steps in combining and simplifying functions.
Short description This book teaches the mechanics and methodology of long division, a procedure for dividing numbers without the need for an electronic calculator. Starting with basic concepts, the book explains the procedure step by step, discussing divisor, dividend, and quotient. Each chapter presents more information, gradually building an intuitive comprehension of long division. Chock full of examples and easily navigable problems with complete solutions, the student has ample opportunity to hone an understanding of long division.
Thinking Mathematically highly anticipated first edition achieves the difficult balance between coverage and motivation while helping students develop strong problem-solving skills. Blitzer's examples, problems and applications foster both an appreciation and understanding of mathematics encouraging students to take the math a step further into their everyday lives. Blitzer's use of current data and examples drawn from real life are used to develop key mathematical concepts, as well as reduce math anxiety in students.
A survey of mathematical topics will include technical problem solving, set theory, logic, number theory, application of functions, modular arithmetic, graph theory, the mathematics of finance, and the application of statistical methods to process and quality control. Thus, a primary objective of the course is an emphasis on decision making when addressing technical issues that is based on skills and knowledge acquired in this and related courses. The course is also suitable for those students that require additional skills development before enrolling in precalculus or other mathematics courses required in their field of study. Gordon Rule applies.
More About This Textbook Overview Calculus teachers recognize Calculus as the leading resource among the "reform" projects that employ the rule of four and streamline the curriculum in order to deepen conceptual understanding. The Sixth Edition uses all strands of the 'Rule of Four' - graphical, numeric, symbolic/algebraic, and verbal/applied presentations - to make concepts easier to understand. The book focuses on exploring fundamental ideas rather than comprehensive coverage of multiple similar cases that are not fundamentally unique. Editorial Reviews Booknews Calculus can be taught as nothing but rules and procedures--losing sight of both the mathematics and its inherent practical value. In 1989, the Calculus Consortium based at Harvard was formed to create a completely new calculus curriculum. A part of their endeavor is this textbook, which presents a radically different approach to the teaching and learning of the subject. The two guiding principles: 1) every topic should be presented geometrically, numerically, and algebraically; and 2) formal definitions and procedures evolve from the investigation of practical problems (the way of Archimedes 18, 2002 College book This book is used to teach Calculus at its very core and not simply mere basics. It offers questions which should be given thought to, and which are challenging in some aspects. This is very important as many degree programs like engineering where there is a need of a very strong base of maths. 1 out of 1 people found this review helpful. Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged. Anonymous Posted November 19, 2001 Horrible!! This book is horrible!! Very confusing and vague. For a first time calculus student, one would find this text to be very difficult to study from. I do not recommend this book to anyone interested in studying calculus. Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged. Anonymous Posted February 7, 2001 The WORST Focused on theory rather than the math involved in doing the problems. Impossible to self learn with this book. The examples did not help at all with the problems. Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged. Anonymous Posted December 26, 2000 DON'T BUY IT! This textbook is very vague and not clear on the explanation of concepts. The preface says that the authors wished to create a book where students could not derive the answers to exercises from looking at worked out examples. Well golly how convenient. It seems to me it's just another lame brained excuse to hand out a worthless book. My advice don't waste your money purchasing this book. Instead go to a used bookstore and buy another calculus book. Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged. Anonymous Posted January 2, 2000 Terrible Terrible Book!! Worst math book I have ever encountered...As a non-traditional student going back to school to retrain due to defense cut-backs, I have to say I have never had such a confusing text book before. I am lucky I have had calculus before and this is a refresher course for me. I am a math/science major and will never recommend this book to anyone...try instead Caluculus 9th edition by Thomas Finney...that is a great book to remove the mystery of calculus. Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged.
Hi, my high school classes have just started and I am stunned at the amount of 8th grade algebra order of operations worksheets homework we get. My basics are still not clear and a big assignment is due within few days. I am really worried and can't think of anything. Can someone guide me? Well of course there is. If you are determined about learning 8th grade algebra order of operations worksheets, then Algebrator can be of great help to you. It is made in such a manner that almost anyone can use it. You don't need to be a computer professional in order to use the program. Some professors really don't know how to discuss that well. Luckily, there are softwares like Algebrator that makes a great substitute teacher for algebra subjects. It might even be better than a real teacher because it's more accurate and quicker! Algebrator is the program that I have used through several algebra classes - Algebra 1, College Algebra and Pre Algebra. It is a truly a great piece of math software. I remember of going through difficulties with scientific notation, scientific notation and least common measure. I would simply type in a problem from the workbook, click on Solve – and step by step solution to my math homework. I highly recommend the program.
Linear Algebra Ar Vasishtha Jn Sharma 1 Summary of linear algebra and its applications in physics. Linear algebra in physics 1 1 Summary of linear algebra and its applications in physics There are basically two approaches to linear algebra: the pedestrian ap Most students learn the techniques of linear algebra fairly readily. (Lay, 2006) or Poole (2006), encourage this by linking the embodied and symbolic. of solution in linear algebra, Proceedings of Fifth Southern Hemisphere Conference on Text: Linear Algebra with Applications, Otto Bretscher, Fourth Edition We will cover a range of topics including finding solutions of systems of linear equations, matrices, vector Students electing to take exams off campus must arrange to reduced to the solution of basic Linear Algebra problems, for solving systems of the architecture for matrices of large sizes is limited by the number of pin-out count of Monte Carlo methods for the iteration of linear operators. J. Math. Phys , Encribd is NOT affiliated with the author of any documents mentioned in this site. All sponsored products, company names, brand names, trademarks and logos found on this document are the property of its respective owners.
Numbers and Functions In this new edition of Numbers and Functions, the reader is invited to tackle each of the key concepts of mathematical analysis in turn, progressing from experience through a structured sequence of several hundred problems to concepts, definitions and proofs of classical real analysis. The perfect accompaniment to any torts casebook, The Forms and Functions of Tort Law covers all the major cases and issues in the standard torts course, sharing Professor Abraham's scholarly insights ... Information on bioactive ether lipids and their involvement in neurological disorders is currently scattered throughout the literature. This book provides readers with a comprehensive description of ... "White Clover is a species of clover native to Europe, North Africa and West Asia. It has been widely introduced elsewhere in the world as a pasture crop. It grows in turfgrass, crops and landscapes. ... This book eases students into the rigors of university mathematics. The emphasis is on understanding and constructing proofs and writing clear mathematics. The author achieves this by exploring set ...
teaching volume provides extremely readable coverage of the principles of finite mathematics and their applications in business, social science, and the life sciences. Topics are presented in a straight-forward, interesting manner (with topics from elementary mathematics reviewed as the need for them arises), and an abundance of worked examples with computational details, practice problems, exercises, chapter self-assessment tests, and reviews of fundamental concepts allow readers to work through the material confidently at their own pace. Contains many examples similar to those found on CPA, GMAT, and GRE Economics exams. Features optional, explicitly detailed use of graphing calculators, electronic spreadsheets, and mathematical software, wherever relevant. Linear Equations and Straight Lines. Matrices. Linear Programming, A Geometric Approach. The Simplex Method. Sets and Counting. Probability. Probability and Statistics. Markov Processes. The Theory of Games. The Mathematics of Finance. Difference Equations and Mathematical Models. Logic. Graphs. For anyone who needs to get up to speed with the applications of mathematics in business, social sciences, or life sciences.
"This is a Khan Academy video, so it's fine. But it should be in Algebra 2 (Intermediate Algebra), not in Criminal Justice. This has been noted at least twice (now three times), so why is it still in Criminal Justice?"
Descriptions and Ratings (1) Date Contributor Description Rating 1 Feb 2013 MathWorks Classroom Resources Team Freshmen course taught by Rajeevan Amirtharajah at the University of California Davis. The goal of the course is to teach engineering problem solving using sustainable engineering as an example. Topics covered are 1D, 2D vectors and manipulations, mathematical and logical operations, loops, flow control, custom function, structures, object-oriented programming, string regular expression, Graphical User Interface design, and plotting. Students will also gain hands-on experience working with hardware (Developed based on Arduino UNO) to gather sunlight data. The course emphasizes topics in solar cell technology.
Product Description Written entirely in Spanish, these inventories give you a non-language-biased gauge of students' math abilities on three successive levels. The Level I inventory progresses from place value to interpreting simple graphs. The Level II inventory ranges from simple equations to probability. Level III progresses from simplifying mathematical expressions to factoring trinomials. The teacher guide includes English translations and answers for Level I, Level II, and Level III workbooks.
The Use of Calculators and Computers in Don's Books and Tapes Don refuses to let his students use a calculator to do simple arithmetic. Much of what he does involves doing the arithmetic in your head and looking for patterns. The arithmetic, algebra, and patterns of infinite series and infinite sequences, however, make this a worthwhile use of calculators and computers. Appendix 3 in Don's worksheet book describes how to write programs to do these jobs, and shows what programs are in each chapter. Below are some examples: With Don's help, a few students have written a program on a programmable calculator to change a fraction to its bimal. (Ch. 2) A student will iterate, by hand, a function like 5 + x/2, starting with say 1. This gives an infinite sequence, which on a calculator shows that it gets to 10. Then using Mathematica, the student can take the sequence to 100 decimal places, with 150 iterations and see that it still doesn't get to 10. (Ch. 8) Most students are asked to solve quadratic equations first by guessing and eventually finding the secrets of the sum and product of the roots. Then when they work on the quadratic equation x^2 - x - 1 = 0 by trying numbers with pencil and paper and then a calculator. They get sequences of numbers too big and too small, leading to a 5 decimal approximation of the Golden Mean. Then they can use Derive to find a quick solution and see the exact (although irrational) answer, as well as see approximations with as many places as they like. These are two of about ten ways Don gets kids to solve quadratic equations. (Ch.8) Students, after doing it with a diagram on graph paper and finding patterns, will write a program on a calculator or computer to get the sum of the infinite series 2/5 + (2/5)^2 + ...(Ch.1) A 7th-grader while trying things on a calculator, took repeated square roots of a number. He found that no matter what number he started with he would always get to 1. (Ch.10) While Ian was playing with powers of powers on his calculator during Physics class, he came across a function which goes to e as x goes to infinity. (Ch.11) Don wrote a program on a programmable calculator that finds the area under a curve by plotting points under the curve, counting these points, then finding the ratio of the number plotted to the number filling a 1x1 square. (Ch.13) Don helped Khaki use Derive to plot a graph, then zoom in on a point until the curve looks like a straight line. She found the slope of this line. Keeping track of this slope for a few points, she figured out a rule to find the slope at a given x-coordinate, arriving at the derivative! (Ch.14)
Differential Equations. This best-selling text by these well-known authors blends the traditional algebra problem solving skills with the conceptual development and geometric visualization of a modern differential equations course that is essential to science and engineering students. It reflects the new qualitative approach that is altering the learning of elementary differential equations, including the wide availability of scientific computing environments like Maple, Mathematica, and MATLAB. Its focus balances th... MOREe traditional manual methods with the new computer-based methods that illuminate qualitative phenomena and make accessible a wider range of more realistic applications. Seldom-used topics have been trimmed and new topics added: it starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout the text. This practical book reflects the new technological emphasis that permeates differential equations, including the wide availability of scientific computing environments likeMaple, Mathematica, and MATLAB; it does not concentrate on traditional manual methods but rather on new computer-based methods that lead to a wider range of more realistic applications. The book starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout the book. For mathematicians and those in the field of computer science.
A Teacher's Guide to Using the Common Core State Standards With Mathematically Gifted and Advanced Learners provides teachers and administrators with practical examples of ways to build a comprehensive, coherent, and continuous set of learning experiences for gifted and advanced students. It describes informal, traditional, off-level, and 21st century... more... This book provides fundamental knowledge in the fields of attosecond science and free electron lasers, based on the insight that the further development of both disciplines can greatly benefit from mutual exposure and interaction between the two communities. With respect to the interaction of high intensity lasers with matter, it covers ultrafast... more... It describes each strategy and clarifies its advantages and drawbacks. Also included is a large sample of classroom-tested examples along with sample student responses. These examples can be used "as is" - or you can customize them for your own class. This book will help prepare your students for standardized tests that include items requiring evidence... more... This practical and easy-to-understand learning tutorial is one big exciting exercise for students and engineers that are always short on their schedules and want to regain some lost time with the help of Simulink.This book is aimed at students and engineers who need a quick start with Simulink. Though it's not required in order to understand how Simulink... more... Topics in Matroid Theory provides a brief introduction to matroid theory with an emphasis on algorithmic consequences. Matroid theory is at the heart of combinatorial optimization and has attracted various pioneers such as Edmonds, Tutte, Cunningham and Lawler among others. Matroid theory encompasses matrices, graphs and other combinatorial entities
CompactCalc features include the following: * You can build linear, polynomial and nonlinear equation set. You are not limited by the size or the complexity of your mathematical expressions. * Scientific calculations and unlimited expression length. * Parenthesis compatible and unlimited nesting for expression. * Accurate result display - features up to 24 digits after the decimal point for scientific calculations. * Calculation range (1.79E-308, 2.22E308). * Comprehensive documentation. * CompactCalc has almost hundred of physical and mathematical constants built in, which can be easily accessed and used in calculations. No longer do you have to search the physic textbook for that common physical constant data. * Possibility to enter mathematical formulas as with a keyboard as with calculator-buttons. * The interface is straightforward and very easy to navigate through. Graph 4.4(2012-06-17) update This program is for drawing graphs of mathematical functions in a coordinate system. Graphs may be added with different color and line styles. The program supports standard, parameter and polar functions. It is possible to evaluate a function at an e... Magic Box 1.0(2012-04-29) new Magic Box is a collection of applications. In it you will find some popular jokes and puzzles such as magic square, magic eye, latent image fading dollar and math transformation. Will the program learn the unknown number? Will the program learn the d... RekenTest 4.1(2012-04-06) update RekenTest is freeware educational software to practice arithmetic skills. It supports basic arithmetic operations like addition and subtraction, the muliplication tables and so on, as well as more advanced arithmetic operations like decimals, money p... Multipurpose Calculator - MultiplexCalc 5.4.7(2012-02-07) update MultiplexCalc is a multipurpose and comprehensive desktop calculator for Windows. It can be used as an enhanced elementary, scientific, financial or expression calculator. It embodies generic floating-point routines, hyperbolic and transcendental rou... Desktop Calculator - DesktopCalc 2.1.7(2012-02-07) update DesktopCalc is an enhanced, easy-to-use and powerful scientific calculator with an expression editor, printing operation, result history list and integrated help. Desktop calculator gives students, teachers, scientists and engineers the power to find... Regression Analysis - DataFitting 1.7.7(2012-02-07) update DataFitting is a powerful statistical analysis program that performs linear and nonlinear regression analysis (i.e. curve fitting). DataFitting determines the values of parameters for an equation, whose form you specify, that cause the equation to be... Multivariable Calculator - SimplexCalc 4.1.7(2012-02-07) update SimplexCalc is a multivariable desktop calculator for Windows. It is small and simple to use but with much power and versatility underneath. It can be used as an enhanced elementary, scientific, financial or expression calculator. In addition to arit... Mathomatic 15.7.3(2012-02-01) update Mathomatic is a portable Computer Algebra System (CAS) that can solve, simplify, and compare algebraic equations, perform simultaneous real number, imaginary number, and polynomial arithmetic, etc. It does some calculus and is very easy to learn and... SimplexNumerica 9.1.1.6(2012-01-17) update SimplexNumerica is an object-oriented numerical data analyzer, plot and presentation program. SimplexNumerica is proving to be extremely popular among scientists. Ergonomic programming using the newest Windows programming guidelines with toolbars, co...
"Here is the story of algebra." With this deceptively simple introduction, we begin our journey. Flanked by formulae, shadowed by roots and radicals, but escorted by an expert who navigates unerringly on our behalf, we are guaranteed safe passage through even the most treacherous... (learn more about this book) An undergraduate-level text which challenges the student throughout with the development of topics in linear algebra. A study guide, instrutor's edition and instructor's technology resource manuals are also available... (learn more about this book)A fun little book which contains no exercises but rather simply explains the concepts, strategies, and vocabulary of algebra. What are polynomials and why do I care? What's a quadratic equation and how do I solve it? How do you multiply polynomials? What is the slope of a line? WhatRobert Sedgewick has thoroughly rewritten and substantially expanded andupdated his popular work to provide current and comprehensive coverage ofimportant algorithms and data structures. Christopher Van Wyk and Sedgewickhave developed new C++ implementations that both express the methods in... (learn more about this book)... (learn more about this book) This book brings together - in an informal and tutorial fashion - the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields. Major concepts are illustrated with running examples, and... (learn more about this book)
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... Most math and science study guides are a reflection of the college professors who write them-dry, difficult, and pretentious. The Humongous Book of Trigonometry Problems is the exception. Author Mike Kelley has taken what appears to be a typical t more... From the pyramids and the Parthenon to the Sydney Opera House and the Bilbao Guggenheim, this book takes readers on an eye-opening tour of the mathematics behind some of the world's most spectacular buildings. Beautifully illustrated, the book explores the milestones in elementary mathematics that enliven the understanding of these buildings and combines... more... Demystified is your solution for tricky subjects like trigonometry. If you think a Cartesian coordinate is something from science fiction or a hyperbolic tangent is an extremeexaggeration, you need Trigonometry DeMYSTiFieD , Second Edition, to unravel this topic's fundamental concepts and theories at your own pace. This practical guide eases you... more...
This item is unavailable. This second edition of Maths Quest 11 Mathematical Methods CAS is a comprehensive text designed to meet the requirements of VCE Units 1 and 2 Mathematical Methods CAS course. The student textbook contains the following new features: * Areas of studies dot-points * Comprehensive step-by-step CAS calculator instructions, fully integrated into Worked Examples, for the TI-Nspire CAS calculator, Operating system 2.0. * Questions from past VCAA Examination papers * Exam tips to highlight danger areas for students * Exam-practice sections with allocated time and marks. Fully worked solutions to these sections are available to students on the eBookPLUS. * Technology-free questions * Electronic Tutorials for key Worked Examples in each chapter * Interactivities * eLessons The textbook continues to offer the following award-winning features: * Full colour with stimulating photographs and graphics * Carefully graded exercises with many skill and application problems, including multiple-choice questions * Easy to follow Worked examples in the Think-Write format * Cross references throughout exercises to relevant Worked Examples * Comprehensive chapter reviews with exam-style and past exam questions * eBookPLUS references throughout to guide students and teachers to relevant on-line material What is eBookPLUS? This title features eBookPLUS which is provided FREE with the textbook, but is also available for purchase separately. eBookPLUS is an electronic version of the textbook and a complementary set of targeted digital resources. These flexible and engaging ICT activities are available to you online at the JacarandaPLUS website (
This is the free version of "Function Plotter". Completely free and without advertisements.This app, is able to draw multiple function graphs, calculate function values and value tables. It's also possible to integrate functions numerically.The following mathematical functions are available:polynomials, rational functions, trigonometric functions, inverse trigonometric functions, hyperbolic functions, natural logarithm, exponential function and all the possible combinations
Problem Solving Through Visualization and Computation With the third edition of his popular Mathematica in Action, award-winning author Stan Wagon guides readers through the important changes that have been made to Mathematica 6.0. To utilize the more sophisticated graphics capabilities of 6.0, Wagon has significantly expanded the chapters on surfaces and the parametric plotting of surfaces. The chapter on differential equations now includes material from VisualDSolve , built into Mathematica 6.0. Like previous editions, this is not only an introduction to Mathematica 6.0, but also a tour of modern mathematics by one of the field's most gifted expositors. Wagon explores some of the most important areas of modern mathematics with new chapters on optimization, including algebraic and numerical optimization, and linear and integer programming. Connections are also made to computer science with new material on graphs and networks. Wagon is the author of nine books on mathematics, including A Course in Computational Number Theory , named one of the ten best math books of 2000 by the American Library Association. He has written extensively on the educational applications of Mathematica, inlcuding the books VisualDSolve: Visualizing Differential Equations with Mathematica, and Animating Calculus: Mathematica Notebooks for the Laboratory. From Reviews of the Second Edition: 'The bottom line is that is an outstanding book containing many examples of real uses of Mathematica for the novice, intermediate, and expert user.' —Mark McClure, Mathematica in Education and Research Journal 'In a dazzling range of examples Stan Wagon shows how such features as animation, 3-dimensional graphics and high-precision integer arithmetic can contribute to our understanding and enjoyment of mathematics.' —Richard Walker, The Mathematical Gazette Table of Contents Table of Contents Preface. A Brief Introduction. Plotting. Prime Numbers. Rolling Wheels. Surfaces. Dynamic Manipulation. The Cantor Set, Real and Complex. The Quadratic Map. The Recursive Turtle. Parametric Plotting of Surfaces. Penrose Tiles. Complex Dynamics (by Mark McClure). Solving Equations. Optimization. Differential Equations. Computational Geometry. Check Digits and the Pentagon. Coloring Planar Maps. New Directions for pi. The Banach Tarski Paradox. The Riemman Zeta Function. Miscellany
report, produced by the Royal Society, has a triple purpose: • to provide a summary of the quantitative information that is available on attainment and the workforce in respect of 5–14 science and mathematics education across the UK • to explain the factors considered to have been influential in producingPublishedProvided by the Advisory Committee on Mathematics Education (ACME), this resource was written in 2002. It includes recommendations on the steps to be taken, at that time, to raise the quality of mathematical provision in schools. Concerns regarding the poor uptake of students continuing to study mathematics at Post 16, the reduced… The Royal Society provide these resources which offer an insight into reviews, which took place in the mid 1990s and early 2000s, to investigate the teaching and learning of algebra and geometry. Both reviews took place at a time of considerable discussion over developments in mathematics, both at home and at international level. TeachingThe Researching Effective CPD in Mathematics Education (RECME) project was set up under the umbrella of the National Centre for Excellence in the Teaching of Mathematics (NCETM) in England, who provide these resources. The project's aim was to provide advice, guidance and recommendations to be used by NCETM to inform future…
WARNING: MathJax requires JavaScript to process the mathematics on this page. Please be sure that it is enabled. PREREQUISITES: LANGUAGE OF MATHEMATICS ESSENTIALS Lots of math language ideas are incorporated in my online materials, many of which are not covered in traditional math curricula. The exercises below should be quick and easy, and will give you all the 'language' ideas needed to successfully read my online materials. They are based on my short book, One Mathematical Cat, Please!; this short book was then incorporated into my online algebra I course. Be sure to click-click-click through some of the exercises in each of these sections! The sections will open in a new tab/window.
Introduction to Algebra - 2nd edition ISBN13:978-0198527930 ISBN10: 0198527934 This edition has also been released as: ISBN13: 978-0198569138 ISBN10: 0198569130 Summary: Developed to meet the needs of modern students, this Second Edition of the classic algebra text by Peter Cameron covers all the abstract algebra an undergraduate student is likely to need. Starting with an introductory overview of numbers, sets and functions, matrices, polynomials, and modular arithmetic, the text then introduces the most important algebraic structures: groups, rings and fields, and their properties. This is followed by coverage of vector spaces and ...show moremodules with applications to abelian groups and canonical forms before returning to the construction of the number systems, including the existence of transcendental numbers. The final chapters take the reader further into the theory of groups, rings and fields, coding theory, and Galois theory. With over 300 exercises, and web-based solutions, this is an ideal introductory text for Year 1 and 2 undergraduate students in mathematics56.37 +$3.99 s/h LikeNew PsychoBabel Books Abingdon, Oxford 2008 paperback Second Edition As New Used Paperback, as-new, minor shelfwear only. Contents clean, sound, bright. TPW
Rent Textbook Buy New Textbook Used Textbook We're Sorry Sold Out eTextbook We're Sorry Not Available More New and Used from Private Sellers Starting at $161 package contains the Access Kit for the Trigsted/Bodden/Gallaher MyMathLab eCourse plus the Guided Notebook. Developmental Mathematics by Trigsted, Bodden, and Gallaher is the first online, completely "clickable" combined Prealgebra, Beginning Algebra, and Intermediate Algebra text to take full advantage of MyMathLab's features and benefits. Kirk Trigsted saw marked improvements in student learning when he started teaching with MyMathLab, but he noticed that most students started their assignments by going directly to the MyMathLab homework exercises without consulting their textbook. This inspired Kirk to write a true eText, built within MyMathLab, to create a dynamic, seamless learning experience that would better meet the needs and expectations of his students. Completely clickable and fully integrated—the Trigsted eText is designed for today's learners. Developmental Mathematics is also available to be packaged with two printed resources to provide additional support for you: The eText Reference is a spiral-bound, printed version of the eText that provides a place for you to do practice work and summarize key concepts from the online videos and animations. In addition to the benefits it provides you, the eText Reference is also a nice resource for those instructors that prefer a printed text for class preparation. The Guided Notebook is an interactive workbook that guides you through the course by asking you to write down key definitions and work through important examples for each section of the eText. This resource is available in a three-hole-punched, unbound format to provide the foundation for a personalized course notebook. You can integrate your class notes and homework notes within the appropriate section of the Guided Notebook. Instructors can customize the Guided Notebook files found within MyMathLab. Table of Contents Module 1. Whole Numbers 1.1 Study Tips for This Course 1.2 Introduction to Whole Numbers 1.3 Adding and Subtracting Whole Numbers; Perimeter 1.4 Multiplying Whole Numbers; Area 1.5 Dividing Whole Numbers 1.6 Exponents and Order of Operations 1.7 Introduction to Variables, Algebraic Expressions, and Equations Module 2. Integers and Introduction to Solving Equations 2.1 Introduction to Integers 2.2 Adding Integers 2.3 Subtracting Integers 2.4 Multiplying and Dividing Integers 2.5 Order of Operations 2.6 Solving Equations: The Addition and Multiplication Properties Module 3. Solving Equations and Problem Solving 3.1 Simplifying Algebraic Expressions 3.2 Revisiting the Properties of Equality 3.3 Solving Linear Equations in One Variable 3.4 Using Linear Equations to Solve Problems Module 4. Fractions and Mixed Numbers 4.1 Introduction to Fractions and Mixed Numbers 4.2 Factors and Simplest Form 4.3 Multiplying and Dividing Fractions 4.4 Adding and Subtracting Fractions 4.5 Complex Fractions and Review of Order of Operations 4.6 Operations on Mixed Numbers 4.7 Solving Equations Containing Fractions Module 5. Decimals 5.1 Introduction to Decimals 5.2 Adding and Subtracting Decimals 5.3 Multiplying Decimals; Circumference 5.4 Dividing Decimals 5.5 Fractions, Decimals and Order of Operations 5.6 Solving Equations Containing Decimals Module 6. Ratios and Proportions 6.1 Ratios, Rates, and Unit Prices 6.2 Proportions 6.3 Proportions and Problem Solving 6.4 Congruent and Similar Triangles 6.5 Square Roots and the Pythagorean Theorem Module 7. Percent 7.1 Percents, Decimals, and Fractions 7.2 Solving Percent Problems with Equations 7.3 Solving Percent Problems with Proportions 7.4 Applications of Percent 7.5 Percent and Problem Solving: Sales Tax, Commission, and Discount 7.6 Percent and Problem Solving: Interest Module 8. Geometry and Measurement 8.1 Lines and Angles 8.2 Perimeter, Circumference, and Area 8.3 Volume and Surface Area 8.4 Linear Measurement 8.5 Weight and Mass 8.6 Capacity 8.7 Time and Temperature Module 9. Statistics 9.1 Mean, Median, and Mode 9.2 Histograms 9.3 Counting 9.4 Probability Module 10. Real Numbers and Algebraic Expressions 10.1 The Real Number System 10.2 Adding and Subtracting Real Numbers 10.3 Multiplying and Dividing Real Numbers 10.4 Exponents and Order of Operations 10.5 Variables and Properties of Real Numbers 10.6 Simplifying Algebraic Expressions Module 11. Linear Equations and Inequalities in One Variable 11.1 The Addition and Multiplication Properties of Equality 11.2 Solving Linear Equations in One Variable 11.3 Introduction to Problem Solving 11.4 Formulas 11.5 Geometry and Uniform Motion Problem Solving 11.6 Percent and Mixture Problem Solving 11.7 Linear Inequalities in One Variable 11.8 Compound Inequalities; Absolute Value Equations and Inequalities Module 12. Graphs of Linear Equations and Inequalities in Two Variables 12.1 The Rectangular Coordinate System 12.2 Graphing Linear Equations in Two Variables 12.3 Slope 12.4 Equations of Lines 12.5 Linear Inequalities in Two Variables Module 13. Systems of Linear Equations and Inequalities 13.1 Solving Systems of Linear Equations by Graphing 13.2 Solving Systems of Linear Equations by Substitution 13.3 Solving Systems of Linear Equations by Elimination 13.4 Applications of Linear Systems 13.5 Systems of Linear Inequalities 13.6 Systems of Linear Equations in Three Variables Module 14. Exponents and Polynomials 14.1 Exponents 14.2 Introduction to Polynomials 14.3 Adding and Subtracting Polynomials 14.4 Multiplying Polynomials 14.5 Special Products 14.6 Negative Exponents and Scientific Notation 14.7 Dividing Polynomials 14.8 Polynomials in Several Variables Module 15. Factoring Polynomials 15.1 Greatest Common Factor and Factoring by Grouping 15.2 Factoring Trinomials of the Form x2 + bx + c 15.3 Factoring Trinomials of the Form ax2 + bx + c Using Trial and Error 15.4 Factoring Trinomials of the Form ax2 + bx + c Using the ac Method
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In this course students do extensive problem-solving in groups, studying problems from a variety of areas, develop their skills at writing about mathematical ideas and problems and concepts, and research the lives and contributions of famous mathematicians. This is all done in a "user-friendly" environment which emphasizes the development of individual strengths and skills and reduces math anxiety. Topics include: the uses and limitations of inductive and deductive reasoning; different types of number sequences and their uses; the basic concepts of functions and graphing and the use of the TI-83 graphing calculator; and types of symmetry, culminating in a study of mathematical mosaics and regular and semi-regular polyhedra. For students with a documented learning disability in mathematics, MAT-1070 may count as one of the two courses in mathematics required under the Fundamental Skills component of the GECC. (Offered as circumstances warrant.)
,... read more Customers who bought this book also bought: Our Editors also recommend: Introductory Complex Analysis by Richard A. Silverman Shorter version of Markushevich's Theory of Functions of a Complex Variable, appropriate for advanced undergraduate and graduate courses in complex analysis. More than 300 problems, some with hints and answers. 1967 edition. Complex Analysis with Applications by Richard A. Silverman The basics of what every scientist and engineer should know, from complex numbers, limits in the complex plane, and complex functions to Cauchy's theory, power series, and applications of residues. 1974 edition. A Collection of Problems on Complex Analysis by L. I. Volkovyskii, G. L. Lunts, I. G. Aramanovich Over 1500 problems on theory of functions of the complex variable; coverage of nearly every branch of classical function theory. Answers and solutions. Introduction to Real Analysis by Michael J. Schramm This text forms a bridge between courses in calculus and real analysis. Suitable for advanced undergraduates and graduate students, it focuses on the construction of mathematical proofs. 1996 edition. Foundations of Analysis: Second Edition by David F Belding, Kevin J Mitchell Unified and highly readable, this introductory approach develops the real number system and the theory of calculus, extending its discussion of the theory to real and complex planes. 1991 edition. An Introduction to the Theory of Linear Spaces by Georgi E. Shilov, Richard A. Silverman Introductory treatment offers a clear exposition of algebra, geometry, and analysis as parts of an integrated whole rather than separate subjects. Numerous examples illustrate many different fields, and problems include hints or answers. 1961 edition. Nonstandard Analysis by Alain M. Robert This introduction to nonstandard analysis is based on the axiomatic internal set theory approach. A clear exposition of theory is followed by applications. Includes exercises, hints, and solutions. 1988An Introduction to Orthogonal Polynomials by Theodore S Chihara Concise introduction covers general elementary theory, including the representation theorem and distribution functions, continued fractions and chain sequences, the recurrence formula, special functions, and some specific systems. 1978 edition. Foundations of Modern Analysis by Avner Friedman Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Detailed analyses. Problems. Bibliography. Index. Complex Analysis in Banach Spaces by Jorge Mujica The development of complex analysis is based on issues related to holomorphic continuation and holomorphic approximation. This volume presents a unified view of these topics in finite and infinite dimensions. 1986 edition. Real Variables with Basic Metric Space Topology by Robert B. Ash Designed for a first course in real variables, this text encourages intuitive thinking and features detailed solutions to problems. Topics include complex variables, measure theory, differential equations, functional analysis, probability. 1993 edition. Real Analysis by Gabriel Klambauer Concise in treatment and comprehensive in scope, this text for graduate students introduces contemporary real analysis with a particular emphasis on integration theory. Includes exercises. 1973 edition. Product Description: , science and engineering. A high level of mathematical sophistication is not required. The book begins with a systematic study of real numbers, understood to be a set of objects satisfying certain definite axioms. The concepts of a mathematical structure and an isomorphism are introduced in Chapter 2, after a brief digression on set theory, and a proof of the uniqueness of the structure of real numbers is given as an illustration. Two other structures are then introduced, namely n-dimensional space and the field of complex numbers. After a detailed treatment of metric spaces in Chapter 3, a general theory of limits is developed in Chapter 4. Chapter 5 treats some theorems on continuous numerical functions on the real line, and then considers the use of functional equations to introduce the logarithm and the trigonometric functions. Chapter 6 is on infinite series, dealing not only with numerical series but also with series whose terms are vectors and functions (including power series). Chapters 7 and 8 treat differential calculus proper, with Taylor's series leading to a natural extension of real analysis into the complex domain. Chapter 9 presents the general theory of Riemann integration, together with a number of its applications. Analytic functions are covered in Chapter 10, while Chapter 11 is devoted to improper integrals, and makes full use of the technique of analytic functions. Each chapter includes a set of problems, with selected hints and answers at the end of the book. A wealth of examples and applications can be found throughout the text. Over 340 theorems are fully proved
Buy Used Textbook eTextbook 180 day subscription $93.59 New Textbook We're Sorry Sold Out More New and Used from Private Sellers Starting at $21.37MathXL Tutorials on CD for College Algebra with Modeling and Visualization and Essentials of College Algebra with Modeling and Visualization Mymathlab Mystatlab Student Access Card Mymathlab Spine Sticker Student Solutions Manual for College Algebra with Modeling and Visualization and Essentials of College Algebra with Modeling and Visualization Videos on DVD with Optional Subtitles for College Algebra with Modeling and Visualization Customer Reviews Excellent!June 24, 2011 by Karen Rockswold's focus on conceptual understanding helps students make connections between the concepts and as a result, students see the bigger picture of math and are prepared for future courses. Highly recommended for all readers interested in college algebra and trigonometry! I received the textbook way before the estimated arrival time and it was exactly in the condition it was advertised as. Thank you. College Algebra with Modeling and Visualization: 4 out of 5 stars based on 1 user reviews. Summary Gary Rockswold teaches algebra in context, answering the question, "Why am I learning this?" By experiencing math through applications, students see how it fits into their lives, and they become motivated to succeed. Rockswold's focus on conceptual understanding helps students make connections between the concepts and as a result, students see the bigger picture of math and are prepared for future courses. Introduction to Functions and Graphs; Linear Functions and Equations; Quadratic Functions and Equations; More Nonlinear Functions and Equations; Exponential and Logarithmic Functions; Trigonometric Functions; Trigonometric Identities and Equations; Further Topics in Trigonometry; Systems of Equations and Inequalities; Conic Sections; Further Topics in Algebra Features: -Applications are woven throughout to introduce mathematics topics and content. These contemporary examples draw from a wide variety of real data and enable students to see the relevance of math and become more effective problem solvers. -Making Connections features show how concepts throughout the course are interrelated by pointing out connections between previously learned material and new material. -Checking Basic Concepts exercises appear after every other section and can be used for individual or group review. These exercises require 10–20 minutes to complete and are also appropriate for in-class work. -Extensive exercise sets give students abundant opportunity for practice and review. Every exercise set has been revised to ensure that there are sufficient types of exercises for each mathematical concept and that there is a pairing of odd and even numbered exercises. -Comprehensive end-of-chapter material serves as an excellent resource for extra practice and test preparation. Each chapter concludes with a summary of key concepts, review exercises, and extended and discovery exercises. -A Graphing Calculator Appendix provides tips, techniques, and keystrokes for the popular TI-83, TI-83 Plus, and TI-84 Plus graphing calculators, allowing students to easily work on their own. This material is referenced by Calculator Help notes in the margins of the text. -"Now Try" exercise suggestions follow every example, allowing students to immediately reinforce the concepts as they are reading. -Cumulative Reviews, which appear every few chapters, require students to understand and use multiple skills from different chapters. This is an excellent test of comprehension of key concepts in the course. For all readers interested in college algebra and trigonometry. Author Biography Dr. Gary Rockswold has been teaching mathematics for 25 years at all levels from seventh grade to graduate school, including junior high and high school students, talented youth, vocational, undergraduate and graduate students, and adult education classes. He is currently employed at Minnesota State University, Mankato, where he is a full professor of mathematics and the chair of the mathematics department. He graduated with majors in mathematics and physics from St. Olaf College mathematics, he enjoys spending time with his wife and two children.
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From Kant to Hilbert Volume 1 A Source Book in the Foundations of Mathematics William Bragg Ewald This two-volume work provides an overview of this important era of mathematical research through a carefully chosen selection of articles. They provide an insight into the foundations of each of the main branches of mathematics - algebra, geometry, number theory, analysis, logic, and set theory - with narratives to show how they are linked.
You are here Modern Algebra: An Introduction Edition: 5 Publisher: John Wiley Number of Pages: 354 Price: 105.95 ISBN: 0-471-43335-7 The release of this fifth edition of Durbin's Modern Algebra has given me an opportunity to peruse a classic modern algebra book which I never had an opportunity to use in class. A colleague of mine, who has been at this longer than I have, said he has not found an undergraduate algebra text better than this one. Looking through the book, it is easy to see why he has such a high opinion. There is a very nice introduction, which tries to show students the general nature of the book's main ideas, and how they developed over time. I particularly liked the section on the three classic (impossible) straightedge and compass constructions. The author uses a picture and an equation to make the constructions concrete to the reader. For example, the squaring the circle construction is represented by pictures of a circle of radius r and a square of side s, with the equation πr2 = s2 below. As an undergraduate I always found these constructions confusing, but the explanations given by Durbin are crystal clear. There are also several appendices, on sets, proofs, induction, and linear algebra, which are well done. The book contains chapters on the standard topics one has come to expect in a modern algebra textbook. But none of these chapters are overwhelming, each averaging around twenty pages. The book does not try to give exhaustive coverage; in fact, one of its greatest strengths is its brevity. Durbin's approach is to be as clear and concise as possible, while rigorously developing the subject. He gives just what is needed to understand the topic, build on the previous chapters, and develop the theory. The proofs are also very clear, written in such a way as to be accessible to an undergraduate student. There are also chapters on a few less standard subjects, including symmetry, cryptography and algebraic coding, and lattices and Boolean algebras. An instructor lacking the time to cover these topics could easily assign some sort of project based on these chapters. The presentation is clear enough that a student could learn the material mostly independently. The changes from the past edition aren't too extensive, consisting mainly of an expanded chapter on field and Galois theory, a new chapter on cryptography, and some additional problems. My one complaint is that the exercises could be a bit more challenging. Although this is one of the changes addressed in this new edition, the exercises still consist mostly of verifying or constructing fairly straightforward examples. For undergraduates first learning the subject, certainly some routine exercises are needed. But it seems to me the book could benefit from a few challenge problems in each problem section. This is a minor point, however, in a book with very strong exposition that would make an outstanding text for an undergraduate abstract algebra course. Frederick M. Butler is Assistant Professor of Mathematics at the Institute for Mathematics Learning of West Virginia University.
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Learn Multimedia Algebra in Win95 08/01/96 Algebra in Simplest Terms is a 24-lesson CD-ROM series that reviews fundamental and teaches advanced algebra concepts, using an electronic textbook format. Based on the successful PBS College Algebra series produced by COMAP's Sol Garfunkel, Ph.D., the course combines professionally produced video and text narration with an online dictionary and graphing calculator, management system, placement tests and more. More than 2,000 instructional screens as well as 2,200 tests and exercise questions are integrated. The program starts with a lesson on the Language of Algebra and concludes with a Probabilities lesson. It also provides feedback for questions and exercises, reinforcing key concepts. Liafail, Inc., Minneapolis, MN, (612) 925-3727.W
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More About This Book Overview Special focus: Math English vocabularly, presented specifically with ESL learners in mind. This invaluable review and preparatory book is designed to help high school- and college-level non-native speakers of English prepare for standardized mathematics tests. ESL (English as a Second Language) Mathematics for Standardized Testing provides students with a comprehensive math review using simple explanations, skill-building exercises, detailed answer keys, and test-taking techniques. It's a perfect book for classroom use or self-guided math studies! Related Subjects Meet the Author Catherine Price (Ph.D., Purdue University) began her academic career at the University of Oklahoma and the University of Wisconsin, Madison. She later moved to Palo Alto College in San Antonio, Texas and became interested in English as a second language. She returned to school to pursue a master's in ESL at the University of Texas at San Antonio. Dr. Price is currently an adjunct tutor of ESL at Bridgend College, South Wales, United Kingdom. Read an Excerpt Your ESL Math Toolbox REA's ESL Mathematics for Standardized Tests answers one of the central questions in ESL education today: How can a student master the special vocabulary and syntax of an academic subject like math while learning the English language itself? The answer is an approach, used by this book and in classrooms across America, called content-based instruction. This approach allows for the integration of academic content and language learning in a way that recognizes the varied linguistic and ethnic backgrounds of diverse student populations. REA's ESL Mathematics for Standardized Tests presents English language learners with a clear path to learning math with these features: This book can be used both by secondary students and by adult ESL students enrolled in one of the large number of adult ESL programs offered by U.S. community colleges. In the end, mastering the material in this book will also help you get into the college of your choice. After all, the point of this integrated approach to learning is to aim higher. Whether for employment, citizenship, high school equivalency, or further education—or for life itself—this book serves first as a handy study aid and then as a reliable reference. Think of this book as a toolbox. Just as a screwdriver is good for some jobs and a hammer is good for others, we give you what you need, when you need it. And we clearly mark off the steps for you to follow to reach your goal of becoming better at math and more fluent in English. Along the way, you will build your comfort with, and confidence in, the subject matter. At the same time, you will refine the language skills that will allow you to express yourself clearly in your schoolwork and also as you go about daily living. Not only will you do better on the all-important standardized tests—which can greatly affect your chances for success for a long time to come—but you will also find that a simple trip to the supermarket will become more pleasant! If you're an English language learner, this book will put you in command of essential math skills. Where you take it from there is up to
Product Description Introduction to abstract algebra presents abstract algebra as the main tool underlying discrete mathematics and digital world. It helps readers fully understand groups, rings, semigroups, and monoids by rigorously building concepts from first principles.
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Summary This chapter demonstrated how you can use many of the built-in math functions and operators in conjunction with the advantages of a loosely typed language such as PHP to calculate simple but advanced computations. We first covered the basic data types and how PHP handles them when assigning and calculating values. Then we discussed the conversion of integers between different base values. Next, we talked about random numbers and how to build functions to generate random values of floating-point or string data types. The next two topics were logarithmic and trigonometric functions. These functions have a wide range of usages, but this chapter concentrated on how you can use them to generate charts and calculate the distance between two points on the earth.
The fundamentals of probability are integrated into diverse math courses taught in high school and college. Now your can master introductory probability quickly and easily with Video Aided Instruction's Probability. The ultimate resource for high school students, college students, and adult learners, this set covers the standard probability topics taught in math classes and is jam-packed with practice questions and strategies for tackling even the most confusing problems. Learn the basics of counting and probability from former USA Mathematical Olympiad winner David Patrick. Topics covered in the book include permutations, combinations, Pascal's Triangle, basic combinatorial identities, expected value, fundamentals of probability, geometric probability, the Binomial Theorem, and much more. Neutrosophy is a new branch of philosophy, introduced by Dr. Florentin Smarandache in 1995, which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This is the third in a series of short books on probability theory and random processes for biomedical engineers. This book focuses on standard probability distributions commonly encountered in biomedical engineering. It has been widely recognized nowadays the importance of introducing mathematical models that take into account possible sudden changes in the dynamical behavior of a high-integrity systems or a safety-critical system. Such systems can be found in aircraft control, nuclear power stations, robotic manipulator systems, integrated communication networks and large-scale flexible structures for space stations, and are inherently vulnerable to abrupt changes in their structures caused by component or interconnection failures. Used by hundreds of thousands of students, INTRODUCTION TO PROBABILITY AND STATISTICS, Fourteenth Edition, blends proven coverage with new innovations to ensure you gain a solid understanding of statistical concepts--and see their relevance to your everyday life. The new edition retains the text's straightforward presentation and traditional outline for descriptive and inferential statistics while incorporating modern technology--including computational software and interactive visual tools--to help you master statistical reasoning and skillfully interpret statistical results.
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Includes more than 1,000 book summaries that help students understand some of the most commonly studied literary works from middle school to college level. The easy, all-in-one homework assistant that helps students excel in school. Designed to be easy to use and simple to learn, Microsoft Student with Encarta Premium 2008 makes learning fun. Whether it's a math, research, or foreign language assignment, students can find the right tools and information to get homework started quickly, get fast answers to academic questions, and complete assignments that can help earn higher grades. Find trusted content when you need it. Complete with Encarta Premium 2008, the #1 best-selling encyclopedia software brand(1), it's content you can trust. With editorially approved content, students can use Web Links to more than 25,000 Web sites, preselected by Encarta editors for relevant and age-appropriate research material(2). Through multimedia content, Encarta Premium 2008 provides engaging visual tools to help explore and discover historical events and places. It even includes Encarta Kids, a separate encyclopedia geared to young learners ages 7 to 12! Get questions answered fast. With time pressures to complete assignments, it's frustrating to get stuck without knowing where to go for answers. Whether they're stumped on a math, science, or a foreign language problem, students can quickly get the answers they need. They also get helpful ideas on how to solve problems, so the next time they're more likely to figure out the answer on their own! Includes a full suite of homework tools to help students get homework done right the first time. Encarta Premium 2008 Students can fi nd the information they're looking for-quickly and easily-with Encarta Premium 2008. With trusted content that's accurate and up-to-date, Encarta has been the #1 best-selling encyclopedia software brand for the past 8 years!(1) You'll be amazed at how much time your student will spend researching-compelled by the sights and sounds of one fascinating presentation after another. Students can easily-and quickly-access trusted information provided by world experts. And since they can automatically download updates from the Encarta Web site, they'll have up-to-date and accurate reference software when they need it.(2) Microsoft Math Microsoft Math features a large collection of tools, tutorials, and instructions designed to help students learn mathematical concepts while quickly solving math problems. In an instant, they'll see how to solve problems-step by step! Works for many grade levels-from basic math, pre-algebra, algebra (including logarithms and exponents) to trigonometry! Need advanced help? A full-featured graphing calculator that's simple to learn and use (similar to those costing more than $100!) helps visualize and solve math and science problems. Triangle Solver and Equation Library. Interact with a library of more than 100 equations and explore the relationships of triangles and their parts while viewing associated rules or graphs. Templates and Tutorials Having trouble getting started on class projects? Sometimes the hardest part about completing a project is getting started. Microsoft Student with Encarta Premium 2008 includes the latest version of Learning Essentials. Get past the blank page. Easy-to-use tools, templates, and tutorials help students get past formatting questions to the core learning in assignments. Learning Essentials includes tips and tutorials for managing projects and creating high-quality reports, presentations, science projects, and other assignments. Foreign LanguageLiterature Need to know more about that literary story? Microsoft Student with Encarta Premium 2008 includes more than 1,000 book summaries that help students understand some of the most commonly studied literary works from middle school to college level. Note: 1. The NPD Group/NPD Techworld, January 2000 to February 2007. Based on total U.S. retail sales. 2. An active Internet connection is required for Math Online Help, Update Encarta, Web Links, Weather and Radio Links and Encarta Premium Online. Update Encarta and Math Online Help are available through October 2008. Access to Encarta Online Premium requires a Microsoft .NET Passport (Windows Live ID) and an Internet connection. You must be 13 years or older to create a Windows Live ID. 3. Hotmath contains primarily US-based textbook problems. Product Description Microsoft Student with Encarta Premium 2008 Win32 English US Only DVD Mini Box. Microsoft Student has lots of useful resources that is aimed from middle school to high school. Encarta dictionary was also very helpful. I was a big fan of it. Encarta is compatible with Windows Vista. If you own Microsoft Office (preferably a newer version) it adds many many helpful features for typing essays, stories and a hundred other things. I've been using Encarta along with Britannica for years. I once believed that for overall depth of content, the higher mark would go to EB. But with regard to software ease of use and organization of material, Encarta would always get the nod. Not so anymore. This new version is a step backward compared to earlier years and seems to be plagued by its own desire to be both a great encyclopedia/dictionary and a homework aid for students. In the end, it achieves only a mediocre showing in both categories. Just as an example: the new dictionary looks better and has two new tabs for translations and verb conjugations, but performs poorly compared to the 2006 version, in my opinion. It is now almost incapable of recognizing certain word inflections as typed. As an example, take the word "intoning", a present participle of "intone". Well, if you type it in to the dictionary, it will not be recognized as a word...even though if you look up "intone", you'll find the present participle form listed there. So in order to get a match, you must type in the basic form of the word in most cases. However...some words, such as "intoxicate", have separate entries for other forms (in this case, the present participle "intoxicating"). I don't recall this idiosyncrasy in the 2006 version of Encarta dictionary. In that version, any inflection you typed in would lead you back to the basic form (e.g., present indicative) definition. This new dictionary is actually fairly annoying after a few days of working with it. It also seems that some words were completely dropped. For example, "reenact" isn't a word from Encarta's perspective. You won't find it under that listing, or the hyphenated "re-enact". But you can find it in Merriam-Webster and practically every other dictionary on the planet. It's almost like they abridged what Encarta had in earlier versions. The weird thing about it is that you can find the word "reenact" in the Thesaurus and Verb Conjugation tabs...but not in the dictionary. What's up with that? Did Microsoft lay off their software testing team? Perhaps there's some logic to it all. But in my opinion, it comes across as sloppy and not very helpful. I once used the little Encarta icon on my task bar every day. Now I'm opting for Britannica 2008's Merriam-Webster component instead. Oh well, it seems that some good things come to an end through unnecessary tinkering. 23 of 25 people found the following review helpful 2.0 out of 5 starsnot for adultsMarch 10 2008 By Michael A. Johnson - Published on Amazon.com Amazon Verified Purchase Unfortunately this is not an encyclopedia and dictionary with student aids, but student programs with the encyclopedia added on. You must wade through all kinds of homework, math, etc. programs to reach the dictionary and encyclopedia. Microsoft apparently thinks that after you leave school you can never have need of an encyclopedia or dictionary again. Also once you load it on, you cannot turn it off. It will run forever on the grounds that you might have to look up something. Once you do get in, the interface is harder to move around in than in the old 2004 edition. 26 of 30 people found the following review helpful 2.0 out of 5 starsEach recent version gets worseSept. 2 2007 By Rod Walsh - Published on Amazon.com Amazon Verified Purchase I've used Encarta for many years. However, the 2004 version was the last version worthy of carrying the Encarta name. Navigation used to be extremely simple. Now, you need a PhD to get around. The use of the "find" box in 2004 is so much more helpful than the "search" box in this 2008 version. This version crashes regularly (running Vista). By regularly, I'd say it crashes 20% of the time. On the plus side, they have all been soft landings and I can re-open without a re-boot.
Introductory Algebra for College series is to provide readers with a strong foundation in Algebra. Each book is designed to develop readers' critical thinking and problem-solving capabilities and prepare readers for subsequent Algebra courses as well as ?service? math courses. Topics are presented in an interesting and inviting format, incorporating real world sourced data and encouraging modeling and problem-solving. The Real Number System. Linear Equations and Inequalities in One Variable. Problem Solving. Linear Equations and Inequalities in Two Variables.... MORE Systems of Linear Equations and Inequalities. Exponents and Polynomials. Factoring Polynomials. Rational Expressions. Roots and Radicals. Quadratic Equations and Functions. For anyone interested in introductory and intermediate algebra and for the combined introductory and intermediate algebra. Introductory Algebra for College Students, third edition, provides comprehensive, in-depth coverage of the topics required in a one-term course in beginning or introductory algebra. the book is written for college students who have no previous experience in algebra and for those who need a review of basic algebraic concepts. The goal of the Blitzer Algebra series is to provide students with a strong foundation in Algebra. Each text is designed to develop students' critical thinking and problem-solving capabilities and prepare students for subsequent Algebra courses as well as "service" math courses. Topics are presented in an interesting and inviting format, incorporating real world sourced data and encouraging modeling and problem-solving.
Applied Mathematics for the Managerial, Life, and Social Sciences APPLIED MATHEMATICS FOR THE MANAGERIAL, LIFE, AND SOCIAL SCIENCES, Soo T. Tan provides an accessible yet accurate presentation of mathematics combined with just the right balance of applications, pedagogy, and technology to help students succeed in the course. The new Third Edition includes highly interesting current applications and exercises to help stimulate student motivation. An exciting new array of supplements provides students with extensive learning support so instructors will have more time to focus on teaching the core concepts. ... MORE1. FUNDAMENTALS OF ALGEBRA. Real Numbers. Polynomials. Factoring Polynomials. Rational Expressions. Integer Exponents. Solving Equations. Rational Exponents and Radicals. Quadratic Equations. Inequalities and Absolute Value. Chapter1 Summary and Review Exercises. 2. FUNCTIONS AND THEIR GRAPHS. The Cartesian Coordinate System and Straight Lines. Equations of Lines. Using Technology. Functions and Their Graphs. The Algebra of Functions. Linear Functions. Portfolio: Carol Busa. Using Technology. Quadratic Functions. Chapter 2 Summary and Review Exercises. 3. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. Using Technology. Logarithmic Functions. Exponential Functions as Mathematical Models. Chapter 3 Summary and Review Exercises. 4. MATHEMATICS OF FINANCE. Compound Interest. Using Technology. Annuities. Using Technology. Amortization and Sinking Funds. Portfolio: John Decker. Using Technology. Arithmetic and Geometric Progressions (Optional). Chapter 4 Summary and Review Exercises. 5. SYSTEMS OF LINEAR EQUATIONS AND MATRICES. Systems of Linear Equations Introduction. Solving Systems of Linear Equations: Unique Solutions. Using Technology. Solving Systems of Linear Equations: Undetermined and Overdetermined Systems. Using Technology. Matrices. Using Technology. Multiplication of Matrices. Using Technology. The Inverse of a Square Matrix. Using Technology. Chapter 5 Summary and Review Exercises. 6. LINEAR PROGRAMMING. Graphing Systems of Linear Inequalities in Two Variables. Linear Programming Problems. Portfolio: Leanne Jenkins. Graphical Solution of Linear Programming Problems. The Simplex Method: Standard Maximization Problems. Using Technology. Portfolio: Harley Lance Kaplan. The Simplex Method: Standard Minimization Problems. Using Technology. Chapter 6 Summary and Review Exercises. 7. SETS AND PROBABILITY. Sets and Set Operations. The Number of Elements in a Finite Set. The Multiplication Principle. Portfolio: John Higgins. Permutations and Combinations. Using Technology. Experiments, Sample Spaces, and Events. Probability. Rules of Probability. Chapter 7 Summary and Review Exercises. 8. ADDITIONAL TOPICS IN PROBABILITY. Use of Counting Techniques in Probability. Conditional Probability and Independent Events. Bayes' Theorem. Distributions of Random Variables. Using Technology. Expected Value. Portfolio: Lilli Meiselman. Variance and Standard Deviation. Using Technology. Chapter 8 Summary and Review Exercises. 9. THE DERIVATIVE. Limits. Using Technology. Portfolio: James H. Chesebro, M.D. Continuity. Using Technology. The Derivative. Using Technology. Basic Rules of Differentiation. Using Technology. The Product and Quotient Rules: Higher-Order Derivatives. Using Technology. The Chain Rule. Using Technology. Differentiation of Exponential and Logarithmic Functions. Using Technology. Marginal Functions in Economics. Chapter 9 Summary and Review Exercises. 10. APPLICATIONS OF THE DERIVATIVE. Applications of the First Derivative. Using Technology. Applications of the Second Derivative. Using Technology. Curve Sketching. Using Technology. Optimization I. Using Technology. Optimization II. Chapter 10 Summary and Review Exercises. 11. INTEGRATION. Antiderivatives and the Rules of Integration. Integration by Substitution. Area and the Definite Integral. The Fundamental Theorem of Calculus. Using Technology. Evaluating Definite Integrals. Using Technology. Area Between Two Curves. Using Technology. Applications of the Definite Integral to Business and Economics. Using Technology. Chapter 11 Summary and Review Exercises. 12. CALCULUS OF SEVERAL VARIABLES. Functions of Several Variables. Partial Derivatives. Using Technology. Maxima and Minima of Functions of Several Variables. Chapter 12 Summary and Review Exercises. Answers to Selected Exercises. Index.
Mathematics: Applied eBooks For every student who has asked their math teacher, "When will I ever use this?" applied mathematics is the answer ... as long as they choose a career that involves it. If you're looking for a mathematics eBook that can be used in real-world situations, this is the place.
You are here Calculus: Modeling and Application 2nd edition David A. Smith and Lawrence C. Moore Calculus: Modeling and Application, 2nd Edition, responds to advances in technology that permit the integration of text and student activities into a unified whole. In this approach, students can use mathematics to structure their understanding of and investigate questions in the world around them, to formulate problems and find solutions, then to communicate their results to others. Calculus: Modeling and Application covers two semesters of single-variable calculus. Its features include use of real-world contexts for motivation, guided discovery learning, hands-on activities (including built-in applets), a problem-solving orientation, encouragement of teamwork, written responses to questions, tools for self-checking of results, intelligent use of technology, and high expectations of students. It is important to note that this textbook is a website. When purchasing this textbook you will have access to two versions: Computer/CAS Version. This version requires the Firefox browser for proper display of mathematics and one of the commercial computer algebra systems (Maple, Mathematica, or Mathcad) for most of the interactivity in the text. Some activities require access to a printer. Tablet/Sage Version. This version was written for the iPad but will run on other tablets or computers in either Safari or Firefox (but not Internet Explorer or Chrome). It uses the free computer algebra system Sage to provide interactivity through remotely-processed interacts. Sage interacts require only calculator-form entry of functions and numbers. You need not have Sage installed on your machine, and no printer is required. At the end of each section there are pages labeled Exercises and Problems. The Exercise pages each have a WebWork button that links to MAA's WebWork courses page. Adopters who set up WebWork courses (at MAA or on their local servers) get access to the Calculus: Modeling and Application Library (in addition to the national library), and it has problems that are more or less like the Exercises in Calculus: Modeling and Application. Instructors can make up homework sets from both the Calculus: Modeling and Application and national libraries. The authors plan to continue to add to the Calculus: Modeling and Application collection, so it will get stronger over time. All of the Exercises are potentially machine-gradable (suitable for WebWork), whereas the Problems need human responses. Access to Calculus: Modeling and Application can be purchased at maa.pinnaclecart.com. Instructors wishing to adopt the text for their course should contact the MAA Service Center (1-800-331-1MAA) about obtaining desk access. Note to professors:Some problems do not work in both versions (due to differing technologies), so if your students are using both versions, be sure to check problem numbers in both places when making homework assignments. Note to purchasers of the text: To gain easy access to the book website in the future The page that comes up will look like a receipt page and it will have a link to the text (Access Calculus ebook). BOOKMARK this page so that in the future all you have to do is click on the bookmark, the login window will pop up, you log in, and then the page with the link pops up.
1420069551 9781420069556 Shows How to Read & Write Mathematical ProofsIdeal Foundation for More Advanced Mathematics CoursesIntroduction to Mathematical Proofs: A Transition ...See more details below Details about this item Introduction to Mathematical Proofs:Shows How to Read & Write Mathematical Proofs Ideal Foundation for More Advanced Mathematics CoursesIntroduction to Mathematical Proofs: A Transition facilitates a smooth transition from courses designed to develop computational skills and problem solving abilities to courses that emphasize theorem proving. It helps students develop the skills necessary to write clear, correct, and concise proofs.Unlike similar textbooks, this one begins with logic since it is the underlying language of mathematics and the basis of reasoned arguments. The text then discusses deductive mathematical systems and the systems of natural numbers, integers, rational numbers, and real numbers. It also covers elementary topics in set theory, explores various properties of relations and functions, and proves several theorems using induction. The final chapters introduce the concept of cardinalities of sets and the concepts and proofs of real analysis and group theory. In the appendix, the author includes some basic guidelines to follow when writing proofs.Written in a conversational style, yet maintaining the proper level of mathematical rigor, this accessible book teaches students to reason logically, read proofs critically, and write valid mathematical proofs. It will prepare them to succeed in more advanced mathematics courses, such as abstract algebra and geometry. Back to top Rent Introduction to Mathematical Proofs 1st edition today, or search our site for Charles textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Chapman and Hall/CRC.
Summary: These popular and proven workbooks help students build confidence before attempting end-of-chapter problems. They provide short problems and exercises that focus on developing a particular skill, often requiring students to draw or interpret sketches and graphs, or reason with math relationships. New to the Second Edition are exercises that provide guided practice for the textbook's Problem-Solving Strategies, focusing in particular on working symbolically.
Chapter 10: Using Factoring (Goals and Objectives of each section in the chapter) vLesson 10.1 ØFinding the prime factorization of integers. ØFinding the greatest common factor (GCF) vLesson 10.2 ØUsing the GCF and the distributive property to factor polynomials ØUsing grouping techniques to factor polynomials with four or more terms vLesson 10.3 ØFactoring quadratic trinomials vLesson 10.4 ØIdentifying and factoring binomials that are the differences of squares vLesson 10.5 ØIdentifying and factoring perfect square trinomials vLesson 10.6 ØUsing the zero product property to solve equations Standards of Learning [Chapter 10] A.11The student will add, subtract, and multiply polynomials and divide polynomials with monomial divisors, using concrete objects, pictorial representations, and algebraic manipulations. A.12The student will factor completely first- and second-degree binomials and trinomials in one or two variables.The graphing calculator will be used as both a primary tool for factoring and for confirming an algebraic factorization. A.14The student will solve quadratic equations in one variable both algebraically and graphically.Graphing calculators will be used both as a primary tool in solving problems and to verify algebraic solutions. A.16The student will, given a rule, find the values of a function for elements in its domain and locate the zeros of the function both algebraically and with a graphing calculator. The value of f(x) will be related to the ordinate on the graph. Outlook and Overview of Unit Lesson Mathematical Topics, Summary, & Objectives The main focal points of this unit in Chapter 10 will focus around the concept of factoring. Students will begin by reviewing what it means to have common factors, and more so, the greatest common factor. This will hopefully guide the student's thought process into grouping and being able to pull out common terms and factors. From there the students should be able to recognize certain characteristics in factoring such as trinomial factoring and grouping. Since the concept of factoring often stumps students due to the ability to almost "luckily" see the combination of numbers at first, I have chosen to do my unit plan on that very important skill. One of the main components to this lesson will test the student's ability to make educated guesses based on the knowledge they have from factors of various numbers and terms. As always, I would also expect my students to provide a check in terms of "FOIL" and other methods to insure success! Materials & "The Bigger Picture" The materials needed for this unit of planning should require no extra materials other than those that are (generally) readily available in any classroom. This would include the following: pencil, paper, chalk/dry-erase board, overhead projector, calculator, index cards [for card activity], and tape. Although this lesson in Chapter 10 can vary from class to class, I can see this lesson taking about 2-3 block days or 4-6 regular class periods. I have only made a lesson plan for section 10-3 because I feel it is the most important in the section. The factoring in the previous sections should be a review from Pre-Algebra; however, the factoring of trinomial equations should be brand new to the children. Since sections 10-4 through 10-6 correspond to the principles used in 10-3, I chose only to focus my notes for this unit plan on that. [Plus, that was my understanding of the assignment for the unit plan.] Supplementary Materials, Activities, & Assessments There should be no apparent need for extra materials such as transparencies or handouts. The lesson is one which notes will be taken by the student, but more importantly the students will be practicing factoring alone or in small groups. The activity, "21 Card Pick Up" is a blessing for those teachers who need a little bit of piece and quite. At least for a small amount of time! The activity can be given for practice or even as a class quiz grade if needed. I liked to use it as a more interactive way of getting students up and out of their seats doing things. The formal, written assessment is designed to test whether or not the students understand the concepts and steps in factoring as well as logical thinking. I have attempted to leave ample room for scratch work if I child desires to use it. This assessment would not be effective in a classroom where the teacher does not use a "Scissors Box" even though it's basically the same concept of guess and check. Student's Expectations Throughout the entire lesson (same as for the entire year) the students will be expected to be participating in the lessons and the instruction. I like to leave my lesson plans very vague and open in order to adjust to the flow of the class. I like to allow students the opportunity to modify my lesson if they have a better example; I feel as though this helps the learning process because it gives them a more personalized meaning. In terms of formal responses, I feel as though this lesson will have many mistakes from students, and I feel as though that is a good thing. Since students will be experimenting with the different factors of trinomials, I do not anticipate a student getting the correct answer the first time every time. I feel as though checking oneself is crucial in this entire unit (as well as for the year). An example of this would be having a student factor x2 - x - 12. Upon [most likely] finding an answer of (x-3)(x+4) to be the factors, I would then see their check by "FOILing" back to reveal that the answer they found to not be the correct solution. So I would expect the student to show the checking work and show me that their solution will not FOIL back into the original answer. Then I would like for them to show the correct solution with a FOIL check. NCTM Standards Problem Solving – By using "educated guesses" the students will be able to use problem solving skills in order to see the differences in how changing certain numbers and letters will affect the final outcome and solution. Reasoning & Proof – The students should logically be able to reason through a difficult factoring problem by applying the basic concepts they know about multiplying binomials [i.e. a negative times a negative equals a positive]. By actually multiplying the factors back out, the students will be able to actually prove they are correct. Communications – Communication becomes crucial when the students will be working in the 21 Card Pick Up activity. Since the students will not be allowed to talk at first, they must rely on effective non-verbal communication skills in order to be successful in communicating exactly what they are looking for. Connections – The students will need to be able to connect their prior knowledge of composite [having factors] and prime [no factors] numbers in order to have an easier time with the lesson. If a student knows that a certain number only has 2 factors, then that will allow them to solve the problem more quickly. Representation – The best thing about this lesson is that now students will have another way to represent longer, more drawn out polynomials with their knowledge acquired from this section. This should help the students recognize that although a problems looks long and difficult does not mean that the same problem can be written in a more, easily understood form. Standards of Learning [SOL] The exact SOL's have been listed at the very beginning of the lesson plan. Please refer to the above sections for more information and detail. §Check to examine whether students recognized the different signs made the non-variable term a negative. §Make sure students understood 2x * x = 2x2 §Go over steps with students including 2x2 + 3x – 10x – 15. Then combining like terms to get 2x2 –7x – 15. vHave a group discussion to discuss WHY the middle term is negative. Ask if a students can change anything about the original binomials in order to make the "7x" term positive. vNow take the example that the students just completed [2x2 –7x – 15] and break down the factoring process ØSteps to Success in Factoring Trinomials 1. Arrange Trinomial in ORDER from highest degree 2. Draw double curves [D.C.] under the problem. Ex. () () 3. Is the last term [NON-VARIABLE TERM] positive or negative? vIf Negative… ØPut opposite signs in the double curves. Ex. (+) (-) vIf Positive… ØLook at middle [1st DEGREE TERM] for positive or negative ØIf that's positive, then put double +'s in the D.C.'s Ex. (+) (+) ØIf that's negative, then put double –'s in the D.C.'s Ex. (-) ( -) vNow check to make sure the students understand. Allow questions and any clarification vNow we will make a "Scissors Box" ØHere's an example to start… (x2 + 8x + 15) Note: Explanation with visual is easier to understand than reading off notes. 1??= 1??= ___ +8 ØNow this of the different factors for the number 15 [1,3,5,15] 1+3 = +3 1+5= +5 +8 ØNow just follow the coefficients across while placing the variable in. (1x + 3) (1x + 5) = (x2 + 8x + 15) §Remember to FOIL back out. Also, does this fit the "Steps to Success"? ØNow here's the same example showing negatives… (x2 - 8x + 15) 1-3 = -3 1-5= -5 -8 §Thus, we have (1x – 3)(1x – 5) = (x2 - 8x + 15) ØMore examples…(x2 - 2x - 15) 1+3 = +3 1-5= -5 -2 ØMore examples…(x2 + 2x - 15) 1-3 = -3 1+5= +5 +2 §Note: For simplicity reasons the first few examples will not have coefficients in from of the second degree term at first, then slowly coefficients will be added, however, this will not affect the process of the "Scissors Box" vComments, Questions, Concerns… Factoring Trinomials Activity: "21 Card Pick Up" Objective: The goal of this SILENT activity is for students to see how different trinomials only have certain solutions for factoring. Directions: - Students will randomly draw a card from the stack of 21 cards face down - Their card will either be of a binomial form or of a trinomial form. - Using their knowledge of factoring trinomials, the students must then locate the other two members in the class that make their card fit successfully in a factorization. - The catch is 3 cards and ONLY 3 cards fit together! So (for example) only Bill's card can ONLY be factored into Steve's and Dave's card. Caroline's card times Bill's card will not equal anyone else's card but Scott's. Caroline's card times Steve's card will not yield a trinomial given the 21 card pick up! - By using their knowledge of characteristics of trinomials students with trinomial cards can soon realize if their classmates can possibly even fit their card. That is, Dave (x2 + 4x + 3) should be able to recognize that anyone with a negative sign in his or her binomial card will not help her factor in any way. - Accommodations can be made to fit the appropriate class size. Completion: - Upon finding a set of 3 cards that work together, the group must write their cards up on the board to show a "FOILed" form. - After the teacher has checked the solution for accuracy, the three members must tape their cards to their bodies and link arms together. From this point on they must remained linked together as a "Factorized Problem" would appear. - Fortunately, this group will NOW be allowed to talk in order to help other people find their solutions (of course they must remain linked, and the other students must still remain silent until their solutions have been found). - Upon completing every set of trinomials [7 total] the class will then take their seats and as a group review all of the 7 equations found while answering any questions or thoughts.
A first course in mathematical modeling by Frank R Giordano( Book ) 19 editions published between 1985 and 2008 in 3 languages and held by 674 libraries worldwide [This book is] a bridge between the study of mathematics and the applications of mathematics to various fields. The course affords the student an early opportunity to see how the pieces of an applied problem fit together. The student investigates meaningful and practical problems chosen from common experiences encompassing many academic disciplines, including the mathematical sciences, operations research, engineering, and the management and life sciences. This text provides an introduction to the entire modeling process. -Pref. Thomas' calculus by Ross L Finney( Book ) 9 editions published between 2000 and 2003 in English and Chinese and held by 222 libraries worldwide Calcul différentiel by George B Thomas( Book ) 2 editions published between 2001 and 2003 in French and held by 12 libraries worldwide Thomas' calculus : early transcendentals by Maurice D Weir( Book ) 3 editions published between 2006 and 2007 in English and held by 12 libraries worldwide The book's theme is that calculus is about thinking; one cannot memorize it all. The exercises develop this theme as a pivot point between the lecture in class, and the understanding that comes with applying the ideas of Calculus. -
This site provides resource materials pertaining to areas such as arithmetic, algebra, geometry, and precalculus. Topics... see more This site provides resource materials pertaining to areas such as arithmetic, algebra, geometry, and precalculus. Topics featured include sequences and series, Euclidean and non-Euclidean geometry, complex numbers, fractals, chaos, and number theory. An introduction to cartography emphasizing map projections, their properties, applications and basic mathematics. Concepts... see more An introduction to cartography emphasizing map projections, their properties, applications and basic mathematics. Concepts addressed can be presented at a basic level or expanded to explore the use of more advanced mathematics.This site offers terms and formulas in a mathematical dictionary appropriate for students taking algebra and calculus... see more This site offers terms and formulas in a mathematical dictionary appropriate for students taking algebra and calculus courses. The main page contains an A to Z clickable menu displaying all of the terms in the site's dictionary that begin with that particular letter. This site is an interactive math dictionary with enough math words, math terms, math formulas, pictures, diagrams, tables, and examples from beginning algebra to calculus.
Mathematics WITH EDUCATION This research-led degree offers you a mathematics degree combined, in the final year, with educational theory and classroom practice. This school experience gives you the background required to gain a place on a teacher training course. Throughout the degree you can have the opportunity to work closely with our Centre for Teaching Mathematics and join our outreach team inspiring younger pupils with your love and knowledge of mathematics. The first and second years of this degree are common with our other mathematics degrees. This gives graduates both the expertise required to be confident in the classroom and also flexibility in their future career choices. The first year includes some content that you might expect such as calculus, linear algebra, probability and statistics. It also contains more surprising material such as the mathematics of cryptography. Our students can also master programming skills and use professional software which also open many careers. The final year includes, as well as many options in high level mathematics, an individual educational project and a year-long school placement where you gain some teaching experience every week. Your placement can be at either secondary or primary level. This degree gives our graduates excellent career prospects both as teachers and in the many careers where high-level mathematical skills are required. The course is taught by world leading researchers and the expert staff from our Centre for Teaching Mathematics, who lead the Further Mathematics Support Programme in the South West and have experience in leading A-level examinations and the design of the A-level syllabus. Students on this degree can interact with the educational research programme of the Centre for Teaching Mathematics. We are very proud of thesupport we offer our students and we place an emphasis on developing our students' oral and written professional communications skills. The school placement will particularly strengthen communication skills and greatly enhances our students' employability. TECHNOLOGY SUPPORTED LEARNING - iPad mini As a mathematics student at Plymouth, we use technology to support your learning. Our students receive an individual Apple iPad mini. This gives you access to resources that support your modules (e.g. podcasts, online videos. eBooks and electronic copies of lecture notes), as well as enabling you to participate in interactive activities such as in-class voting and feedback, and to access various University online systems such as module sites, the electronic library, and of course email. What our students say "The course at Plymouth was superb. I was able to consolidate and extend my mathematics skills whilst at the same time gaining enough experience in schools to decide if teaching was a career I wanted to pursue. The education side of the degree involved both the practical side of teaching and the theoretical aspects of the profession. I was able to go into a school on a regular basis, observe lessons and gradually build up to leading a class. At the same time I was also looking in detail at the theory behind how teachers teach and how pupils learn, a vital aspect of teaching. For me, the Mathematics with Education degree was an excellent route into teaching, ensuring that my subject knowledge was sound and giving me a rounded view of what a career in teaching would be like. The experience I gained was invaluable during my PGCE year and the ideas and knowledge I gained during the course are used every day whilst teaching my classes." Projects Teaching Mathematics at Secondary School: A Comparative Study between France and England A Case Study: Using Tactile Resources as a Kinaesthetic Approach to Algebra at Key Stage 3 An Investigation into the Problem-Solving Strategies Adopted by Children What Engages Children in the Mathematics Classroom? How Can the Move From Primary to Secondary School be Made Easier? Leading Students to the Target Concept Through Questioning Scholarships and Awards For 2014 entry we have the following scholarships. Dean's Award for Academic Excellence: £2,000 for any applicant for this course who has made Plymouth University their first choice by Wednesday 8 May 2014 and who achieves the equivalent of ABB in three A Levels (or equivalent) and enrols here in September 2014. Students are eligible if they have at least one of the following combinations listed in the qualification/grade table as well as satisfying all our entrance criteria. Mathematics Scholarship: students who do not obtain the Dean's Award are eligible for a £500 automatic scholarship if they have a grade A* in A Level Mathematics plus £500 for an A in Further Mathematics up to a total of £1,000. To be eligible for this scholarship, students must put us as their first choice before 1st August. The scholarship is paid in term one of the first year. There are additional prizes and certificates to reward high marks in later years.
SME 3023 TRENDS AND ISSUES IN EDUCATION FOR MATHEMATICAL SCIENCES TOPIC: MATHEMATICS ANXIETY NAMA : KAMARUDDIN BIN HARIJAMAN NO MATRIK : D20081033178 SEMESTER :8 PROGRAM : SAINS MATEMATIK DENGAN PENDIDIKAN PENSYARAH : PROF. DR MARZITA BT PUTEH What is mathematics anxiety? Mathematics anxiety defined as feelings of tension and anxiety that interfere with the manipulation of numbers and the solving of mathematical problems in a wide verify of ordinary life and academic situations. Mathematics anxiety can cause one to forget and lose one's self- confidence (Tobias, 1978). People feel that they are incapable of doing activities and classes that involve mathematics. So, many of them take the major that little mathematics is required. Mathematics anxiety also is emotional rather than the intellectual problem. What does this phenomenon was happen? Mathematics anxiety does not have a single cause. From the research was conducted (Puteh. 1998), it was found the causes of mathematics anxiety such as teacher personality and their style of teaching, public examination and their effect and feel worry and difficulty of mathematics. Besides, poor instruction and poorly designed mathematics circular was argued by Lazarus (1974) contributes the mathematics anxiety. Bush (1991) commented that mathematics anxiety arises from a climate in which negative attitudes and anxiety are transmitted from adults to children. Often mathematics anxiety is the result of a student's negative or embarrassing experience with math or a math teacher in previous years. Such an experience can leave a student believing him or herself deficient in math ability. This belief can actually result in poor performance, which serves as confirming evidence to the student. This phenomenon is known as the self-fulfilling prophecy. Mathematics anxiety results in poor performance rather than the reverse. Who is involved in mathematics anxiety? This mathematics anxiety is problem to many school students, college students and also teachers. Individual that related to the mathematics anxiety is among the teacher and student. There are some perception among the teacher trainees that the phobia of mathematics. They think mathematics are numbers, symbols and calculations. Besides, mathematics have to solve problems is seen as something difficult and perceived as a burden. They express their frustrations and helplessness when there were unable to solve their problem. They believed that they are not capable of solving mathematics problems that take more than a few minutes to complete and thus they give up on any problem they cannot solve. Therefore this situations is creating mathematics anxiety. All students learn mathematics at greatly different speeds. Mathematics is a difficult subject to teach and learn. Therefore teacher must build a good perception of student to their knowledge. There are many thing that contribute mathematics anxiety among student such as experienced a variety experiences in the learning of mathematics, student also get great pressure from their parents and etc. therefore student feels stress to learn mathematics so this contribute mathematics anxiety When mathematics anxiety happen? Individual that have mathematics anxiety has negative attitude towards mathematics. Five aspect of the trainees' self-image with regard to mathematics were identified from the interviews (Puteh, 1998) such as dislike being challenged, low confidence, slow learner and low self esteem, easy giving-up and self blaming for poor mathematics performance. Mathematics anxiety also occurs when student not remembering what they learn in mathematics. This especially to student that take the examination like UPSR, PMR and SPM. Therefore, if they still fail in do a task constantly, they will tend to give up in mathematics. Student who has this mathopobhia, they will turn away from mathematics problem. It will lead them to keep away their interest to mathematics subject. Who and what created mathematics anxiety? There is a factor that caused concern of mathematics anxiety is a relationship between student and teacher. The teacher-student relationship seemed to have affected their attitudes negatively. Almost of the teacher or trainees have a problem to fear of asking for help or asking the question. This attitudes caused a large gap between teacher and student. Besides, there a several teacher very strictness and fierceness towards student. The teacher attitude to the learners affects the way the learners respond to the subject. Actually the classes is interesting and stimulating but the student feel stress and uncomfortable in class because scare to teacher. Besides, the teaching skill also affecting towards mathematics anxiety. The most prominent issue raised by the trainees was that their teacher were using an old fashioned way or traditional way of teaching (Puteh, 2002). From Kogelman and Warren (1978) commented that the neglect of the individual personality which often occurs in traditional learning situations often leads to feelings of frustrations, discouragement and general mathematics avoidance. It is hard to deny that the amount of anxiety that was created in the traditional approach adopted by the teacher of these student. How to reduce mathematics anxiety? We must admit the mathematics anxiety exists. The mathematics anxiety problem can be reduce in many way. One of the way is as teacher need more strengthen of content knowledge about mathematics and pedagogy content. In addition, teacher also need to improve teaching skills and make the teaching and learning more interesting. This can avoid student feel bored in the class while the learning process conducted. Besides, relationship between student and teacher can provided confidence to student to continue learning mathematics. This relationship causes student having fun in study mathematics and can avoid the stress during learning mathematics in the class. Another way to reduce mathematics anxiety is student think that examination is indicator to measure the performance with health competition among the peers. In this situations, parents need play an important role to build motivation to student. How to eliminate mathematics anxiety? To eliminate the mathematics anxiety directly or immediately are impossible but it can be happen. There are way to overcome mathematics anxiety like shifts the mindset of mathematics and maintain a positive attitude towards mathematics itself and our ability to do a mathematics problems. Once this mindset is in place, students can focus on the math skills with an open mind, exuding confidence, hope, and interest, which will raise academic achievement and self- confidence takes the energy off the anxiety, and turns it to the positive, which is highly motivating. Besides, parents also can help like talk about past experiences of overcoming adversity and succeeding. In doing so, a shift in attitude will occur, as the student feel more confident. In addition, parents also help their children channel these feelings onto. When we recognize the anxiety before it takes over and can transform it, they can be successful in mathematics
Mathematical Modeling: Models, Analysis and Applications 9781439854518 Buy New Textbook Not Yet Printed. Place an order and we will ship it as soon as it arrives. $872 how-to guide presents tools for mathematical modeling and analysis. It offers a wide-ranging overview of mathematical ideas and techniques that provide a number of effective approaches to problem solving. Topics covered include spatial and stochastic modeling. The text provides real-life examples of discrete and continuous mathematical modeling scenarios. MATLAB ® , Mathematica ® , and MatCont are incorporated throughout the text. The examples and exercises in each chapter can be used as problems in a project.
Overview of Curriculum Mathematics and statistics are among the great achievements of human intellect and at the same time powerful tools. As Galileo said, the book of the universe "is written in the language of mathematics." The goal of the department is to enable students to appreciate these achievements and use their power. To that end, majors and minors in the department receive a firm foundation in pure mathematics and the opportunity to apply it—to statistics, physical science, biological science, computer science, social science, operations research, education, and finance—the list grows. Students typically enter our department with strong skills, but there is always room for improvement and new knowledge. Majors and minors grow in: Through core courses, students learn fundamental concepts, results, and methods. Through elective courses, they pursue special interests. In the process, students develop a further appreciation for the scope and beauty of our discipline. Graduates of the department follow many careers paths, leading them to graduate school, in mathematics, statistics, or other fields, to professional schools, or to the workplace. Introductory Courses Most first-year students entering Swarthmore have had calculus while in high school and place out of at least one semester of Swarthmore's calculus courses, whether they continue with calculus or decide, as is often best, to try other sorts of mathematics. See the discussion of placement later. However, some entering students have not had the opportunity to take calculus or need to begin again. Therefore, Swarthmore offers a beginning calculus course (MATH 015) and several courses that do not require calculus or other sophisticated mathematics experiences. These courses are STAT 001 (Statistical Thinking, both semesters), MATH 003 (Introduction to Mathematical Thinking, spring semester), and STAT 011 (Statistical Methods, both semesters). MATH 003 is a writing course. MATH 029 (Discrete Mathematics, both semesters) also does not require any calculus but is a more sophisticated course; thus, some calculus is a useful background for it in an indirect way. Once one has had or placed out of two semesters of calculus, many other courses are available, especially in linear algebra and several-variable calculus. Placement and Credit on Entrance to Swarthmore Placement Procedure To gain entrance to mathematics or statistics courses at any time during one's Swarthmore years, students are expected to take at least one of the following exams: the Advanced Placement (AP) or International Baccalaureate (IB) exams, Swarthmore's Calculus Placement Exam, or Swarthmore's Math/Stat Readiness Exam. Students who do take AP or IB exams may be required to take the departmental exams as well, or parts thereof. In particular, students intending to take either MATH 15 or MATH 28 must take Swarthmore's Calculus Placement Exam. Versions of the Calculus Placement Exam and the Readiness Exam are sent to entering first-year students over the summer, along with detailed information about the rules for placement and credit. Advanced Placement/International Baccalaureate Credit Placement and credit mean different things. Placement allows students to skip material they have learned well already by starting at Swarthmore in more advanced courses. Credit confers placement as well but also is recorded on the student's Swarthmore transcript and counts toward the 32 credits needed for graduation. The Swarthmore Calculus Placement Exam is used for placement only, not credit. Credit is awarded on the basis of the AP and the IB exams, as follows: 1 credit (for STAT 011) for a score of 4 or 5 on the Statistics AP Test of the College Board. 1 credit (for MATH 015) for a score of 4 on the AB or BC Calculus AP Test of the College Board (or for an AB subscore of 4 on the BC Test) or for a score of 5 on the Higher Level Mathematics Test of the IB. 1.5 credits (for MATH 015 and the first half of MATH 025) for a score of 5 on the AB Calculus AP Test (or for an AB subscore of 5 on the BC Test) or a score of 6 or 7 on the higher-level IB. Students who receive this credit and want to continue calculus take MATH 026. 2 credits (for MATH 015 and 025) for a main score of 5 on the BC Calculus AP Test. Alternatively, any entering student who places out of MATH 015 or 025 may receive credit for those courses by passing the final exams in these courses with a grade of straight C or better. These exams must normally be taken during the student's first semester at Swarthmore, at the time when the final exam is given for the course. Students who wish to take these exams must arrange to do so with the departmental placement coordinator and should do so during their first semester at Swarthmore. Students who are eligible on entrance for credit for a course, but who take the course anyway, will lose the entrance credit. First-year students seeking advanced placement and/or credit for calculus taken at another college or university must normally validate their work by taking the appropriate external or Swarthmore placement examination, as described earlier. The department does not grant credit directly for college courses taken while a student is in high school. For work beyond calculus completed before entering Swarthmore, students should consult the departmental placement coordinator to determine the Swarthmore courses into which they may be placed and additional materials they may need to present for this placement. The department will not normally award credit for work above the first-year calculus level completed before entering Swarthmore. The Academic Program Major and Minor Application Process Students apply for a major in the middle of the second semester of the sophomore year. Before all the usual steps of the College's Sophomore Plan process, applicants to the Mathematics and Statistics Department should begin by completing our online Major/Minor Application Form, available at After the Sophomore Plan process is over, students may apply to add or change a major or minor at any time, but applications will normally be held until the next time that sophomore applications are considered (around March 1). Course Major Acceptance into the Major The normal preparation for a major in mathematics is to have obtained credit for, or placement out of, at least four of the following five course groups by the end of the sophomore year: Calculus I (MATH 015), Calculus II (MATH 025 or 026), Discrete Mathematics (MATH 029), Linear Algebra (MATH 027 or any flavor of 028), and Several Variable Calculus (MATH 033, 034, or 035). In any event, all majors must complete the Linear Algebra and Several Variable Calculus requirement by the end of the first semester of the junior year. To be accepted as a major or a minor, a candidate normally should have a grade point average of at least C+ in courses taken in the department to date, including courses in the fall term of the first year, for which we have shadow grades. A candidate should have at least one grade at the B level. Students should be aware that upper-level courses in mathematics are typically more demanding and more theoretical than the first- and second-year courses. This is an important factor in considering borderline cases. In some cases, applicants may be deferred pending successful work in courses to be designated by the department. Basic Requirements By graduation, a mathematics major must have at least 10 credits in mathematics and statistics courses. At least 5 of the credits counted in the 10 must be for courses numbered over 040. (Courses numbered under 10 do not count toward the major in any event.) Furthermore, every major is required to obtain credit for, or place out of, each of the following course groups: MATH 015; MATH 025, or 026; MATH 027, 028, or 028S; MATH 033, 034, or 035; MATH 063; and MATH 067. The two upper-level core courses, MATH 063 (Introduction to Real Analysis) and MATH 067 (Introduction to Modern Algebra), will be offered at least every fall semester. At least one of these two should be taken no later than the fall semester of the junior year. Majors are expected to complete both MATH 063 and 067 before the spring semester of the senior year; permission to delay taking either course until the senior spring must be requested in writing as early as possible but in any event no later than the beginning of the fall semester of the senior year. Finally, course majors must satisfy the departmental comprehensive requirement by passing MATH 097, Senior Conference. Normally, at least 3 of the 5 credits for courses numbered over 040 must be taken at Swarthmore, including MATH 097 and at least one of the core courses MATH 063 and 067. Note that MATH 097 is given in the fall only. Note that placement counts for satisfying the requirements but not for the 10-credit rule. Those students who are placed out of courses without credit must take other courses to obtain 10 credits. If you believe you are eligible for credit for courses taken before Swarthmore (because of AP or IB scores) but these credits are not showing on your transcript, please see the registrar. The two required core courses, Introduction to Real Analysis (MATH 063) and Introduction to Modern Algebra (MATH 067), are offered every fall semester, and we try to create enough sections to keep them relatively small and seminar-like. We hope, but cannot promise, to offer one or the other of 063 and 067 each spring as well. Mathematics majors are encouraged to study in some depth an additional discipline that makes use of mathematics. We also recommend that they acquire some facility with computers. Students bound for graduate work should obtain a reading knowledge of French, German, or Russian. Special Emphases The preceding requirements allow room to choose an optional special emphasis within the mathematics major. For instance: A student may major in mathematics with an emphasis on statistics by taking the following courses at the advanced level: (1) the core analysis course (MATH 063); (2) Mathematical Statistics I (STAT 061); (3) Probability (MATH 105) or Mathematical Statistics II (STAT 111); (4) Data Analysis and Visualization (STAT 031); (5) the Senior Conference (MATH 097); and (6) another mathematics course numbered over 040. Students are encouraged but not required to select the core algebra course (MATH 067) if they choose this emphasis. When a student does an emphasis in statistics, STAT 031 counts as if it were numbered over 040. Students interested in mathematics and computer science should consider a mathematics major with a minor in computer science or an Honors Program with a mathematics major and a computer science minor. Details on these options are in the catalog under computer science. Students thinking of graduate work in social or management science, or a master's in business administration, should consider the following options. Basic courses: single-variable calculus (two semesters), one or more practical statistics courses (STAT 061 and 031), linear algebra, discrete math, several-variable calculus, and introductory computer science; advanced courses: (1) Modeling (MATH 056); (2) at least one of Probability (MATH 105), Mathematical Statistics I (STAT 061), and possibly Mathematical Statistics II (STAT 111); (3) at least one of Combinatorics (MATH 069) or Operations Research (ENGR 057); (4) the three required core courses (MATH 063, MATH 067 and MATH 097); and (5) Differential Equations (MATH 043 or 044). Because this program is heavy (one who hopes to use mathematics in another field must have a good grasp both of the relevant mathematics and of the intended applications), one of the core course requirements may be waived with permission of the department. Students thinking of graduate work in operations research should consider the following options. Basic courses: same as previous paragraph. Advanced courses: (1) the three required core courses (MATH 063, MATH 067 and MATH 097); (2) Combinatorics (MATH 069) and Topics in Discrete Mathematics (MATH 059 or 079); (3) Mathematical Statistics (STAT 061); and (4) at least one of Number Theory (MATH 058), Modeling (MATH 056), or Probability (MATH 105). Students interested in quantitative economics, mathematical finance, or similar fields should consider a double major in mathematics and economics, or a major in mathematics with a minor in economics. Students thinking of graduate work in quantitative economics or mathematical finance should consider a math major with a program including at least MATH 43, MATH 54, MATH 63 and STAT 61 together with appropriate additional coursework to round out a mathematics major or a mathematics major with emphasis in statistics. Course Minor Acceptance into the minors The requirements for acceptance into either course minor, such as prerequisite courses and grade average, are the same as for acceptance into the major. Students may not minor in both mathematics and statistics. By graduation, a mathematics course minor must have 6 credits in mathematics or statistics, at least 3 of which must be for courses numbered 045 or higher. Also, at least 1 of these 3 credits must be for MATH 063 or 067. Also, at least 2 of these 3 credits must be taken at Swarthmore. Basic requirements of the statistics course minor By graduation, a statistics course minor must have 6 credits in mathematics or statistics. Every statistics course minor must obtain credit for, or place out of, CPSC 21, STAT 031, and STAT 061. At least one of STAT 031 and STAT 061 must be taken at Swarthmore. Students are advised to take CPSC 21 as early as possible, as it can be difficult to add the course in junior and senior years. Honors Major All current sophomores who wish to apply for Honors should indicate this in their Sophomore Plan, should work out a tentative Honors Program with their departmental adviser, and should submit the College's Honors Program Application along with their Sophomore Plan. (All Sophomore Plan forms and Honors forms are available from the registrar or the registrar's website.) Honors applications are also accepted at the end of the sophomore year or during the junior year. Students, in consultation with their advisers, often change their Honors Programs anyway as time goes on. Basic requirements To be accepted as an Honors major in mathematics, a student should have a grade point average in mathematics and statistics courses to date of at least B+. An Honors math major program consists of three preparations of two credits each, for a total of six distinct credits. One preparation must be in algebra and one in analysis (real or complex). The student must also satisfy all requirements of the mathematics major with the exception of the comprehensive requirement (MATH 097, Senior Conference). Preparations The department offers preparations in the fields listed below. Each preparation is subject to External Examination, including a 3-hour written examination and a 45-minute oral examination. Each preparation consists of a specified pair of credits. The specified credits are listed after each field. Algebra (067 and 102) Real Analysis (063 and 101) Complex Analysis (063 and 103) Discrete Mathematics (069 and either 059 or 079) Geometry (either 055 or 075, and 106) Probability (061 and 105) Statistics (061 and 111) Topology (104, a 2-credit seminar) Since no course is allowed to count in two honors preparations, it is not possible for a student to offer both Real Analysis and Complex Analysis as fields. Similarly, one may take only one of Probability and Statistics as fields. The external examination component of the program is meant to prompt students to learn their core subjects really well and to show the examiners that they have done so—that is, show that they deserve Honors. However, no three fields cover everything a strong student would ideally learn as an undergraduate. Honors majors should consider including in their studies a number of advanced courses and seminars beyond what they present for Honors. Senior Honors Study/Portfolio None is required or offered. Honors Minor For the honors portion of their program, minors must complete one preparation chosen from those in the previous section. Transfer Credit Courses taken elsewhere may count for the major. However, the number of upper-level transfer credits for the major is limited. Normally, at least 3 of the 5 upper-level courses used to fulfill the major must be taken at Swarthmore, including at least one of the core courses MATH 063 and MATH 067. Exceptions should be proposed and approved during the Sophomore Plan process, not after the fact. Also, the usual College rules for transfer credit apply: students must see the professor in charge of transfer twice: in advance to obtain authorization, and afterwards to get final approval and a determination of credit. In particular, for MATH 063 and 067, students are responsible for the syllabus we use. If a course taken elsewhere turns out not to cover it all, the student will not get full credit (even though the transfer course was authorized beforehand) and the student will not complete the major until he or she has demonstrated knowledge of the missing topics. Similarly, for honors preparations students are responsible for the syllabi we use; we will not offer special honors exams based on work done at other institutions. Off-Campus Study Students planning to study abroad should obtain information well in advance about the courses available at the institution they plan to attend and check with the department about selecting appropriate courses. It may be difficult to find courses abroad equivalent to our core upper-level courses, or to our honors preparations, since curricula in other countries are often organized differently. Teacher Certification Swarthmore offers teacher certification in mathematics through a program approved by the state of Pennsylvania and administered by the College's Educational Studies Department. For further information about the relevant set of requirements, please refer to the Educational Studies section of the Bulletin. One can obtain certification either through a mathematics major or through a Special Major in Mathematics and Education, in either case if taken with appropriate electives. Courses Note 1: For courses numbered under 100, the ones digit indicates the subject matter, and the other digit indicates the level. In most cases, a ones digit of 1 or 2 means statistics, 3 to 6 means continuous mathematics, and 7 to 9 means noncontinuous mathematics (algebra, number theory, and discrete math). Courses below 10 do not count for the major, from 10 to 39 are first- and second-year courses, from 40 to 59 are intermediate, in the 60s are core upper-level courses; from 70 to 89 are courses that have one or more core courses as prerequisites, and in the 90s are independent reading courses. Note 2: There are several sets of courses below where a student may not take more than one of them for credit. For instance, see the descriptions of MATH 033, 034 and 035. In such cases, if a student does take more than one of them, each group is treated for the purpose of college regulations as if they have the same course number. See the Repeated Course Rule in section 8.2.4. STAT 001. Statistical Thinking Statistics provides methods for collecting and analyzing data and generalizing from their results. Statistics is used in a wide variety of fields, and this course provides an understanding of the role of statistics in these fields and in everyday life. It is intended for students who want an appreciation of statistics, including the ability to interpret and evaluate statistical claims critically but who do not imagine they will ever need to carry out statistical analyses themselves. (Those who may need to carry out statistical analyses should take STAT 011.) This course cannot be counted toward a major in mathematics, is not a prerequisite for any other course, and cannot be taken for credit after or simultaneously with any other statistics course, including AP Statistics and ECON 031. Prerequisite: Four years of traditional high school mathematics (precalculus). 1 credit. Each semester. Fall 2013. Schofield. Spring 2014. Schofield. MATH 003. Introduction to Mathematical Thinking Students will explore the world of mathematical ideas by sampling logic, number theory, geometry, infinity, topology, probability, and fractals, while we emphasize the thinking and problem-solving skills these ideas stimulate. Class meetings will involve presentation of new material; group work on problems and puzzles; and lively, maybe even passionate discussions about mathematics. This course is intended for students with little background in mathematics or those who may have struggled with math in the past. It is not open to students who already have received credit on their Swarthmore transcripts for mathematics, Advanced Placement credit included, or who concurrently are taking another mathematics course, or who have placed out of any Swarthmore mathematics course. (See "Placement Procedure" earlier.) Students planning to go on to calculus should consult with the instructor. This course does not count toward a major in mathematics. Writing course. 1 credit. Spring 2014. Gomez. MATH 007. Elementary Topics in Mathematics in Applied Contexts This course is offered occasionally and is interdisciplinary in nature. It provides an introduction to some area of mathematics in the context of its use in another discipline. In fall 2010 this was a course in biomathematics. 1 credit. Not offered 2013–2014. STAT 011. Statistical Methods STAT 011 prepares students to carry out basic statistical analyses with the aid of computer software. Topics include basic summary statistics and graphics, design of surveys and experiments, one and two-sample t-tests and tests of proportions, chi-square tests, and an introduction to linear regression and analysis of variance. The course is intended for students who want a practical introduction to statistical methods and who intend to do, or think they may eventually do, statistical analysis, especially in the biological and social sciences. Students who receive credit on entrance for the Statistics AP Exam should not take this course; they have placed out of it and will lose their AP credit if they take it. Note that STAT 011 overlaps considerably with ECON 031; both courses cover similar topics, although ECON 031 focuses more on economic applications while STAT 011 draws examples from a variety of disciplines. Eligible for Cognitive Science credit. Prerequisite: Four years of traditional high school mathematics (precalculus). 1 credit. Each semester. Fall 2013. Sedlock. Spring 2014. Cook, Everson. MATH 015. Elementary Single-Variable Calculus A first-semester calculus course with emphasis on an intuitive understanding of the concepts, methods, and applications. Graphical and symbolic methods will be used. The course will mostly cover differential calculus, with an introduction to integral calculus at the end. Prerequisite: Four years of traditional high school mathematics (precalculus) and placement into this course through Swarthmore's Math/Stat Readiness Examination. Students with prior calculus experience must also take Swarthmore's Calculus Placement Examination (see "Placement Procedure" section earlier). 1 credit. Fall 2013. Mavinga, Shimamoto. MATH 015HA. Calculus Workshop An honors-level workshop designed to support MATH 015 students who plan to take at least four other STEM courses during their time at Swarthmore. During class, students work in small groups on challenging problems designed to promote deep understanding and mastery of the material. Prerequisite: Students must apply for admission to this attachment. Admission will be determined by a commitment to both hard work and excellence, rather than by high school GPA, math SAT scores, or past performance in math classes. 0.5 credit. Graded credit/no credit. Not offered 2013–2014. STAT 021. Elementary Topics in Statistics: Quantitative Paleontology This course will explore current areas of research in paleobiology and macroevolution. For instance, does evolutionary change generally occur gradually or in short bursts? How reliably does the fossil record preserve information about ecosystems? What factors make species more likely to go extinct? To answer these and other questions, paleobiologists use a range of statistical and mathematical techniques. We will emphasize conceptual understanding and applications of such quantitative methods, rather than their underlying theory or proofs. Class meetings will include a combination of lectures, discussion of journal articles, and conversations with leading paleontologists via Skype. Prerequisite: BIOL 002, or STAT 011 or equivalent. 1 credit. Not offered 2013–2014. MATH 026. Advanced Topics in Single-Variable Calculus For students who place out of the first half of MATH 025. This course goes into more depth on sequences, series, and differential equations than does MATH 025 and includes power series and convergence tests. This course, or MATH 025, is required of all students majoring in mathematics, physics, chemistry, or engineering. Students may not take MATH 026 for credit after MATH 025 without special permission. Prerequisite: Placement by examination (see "Advanced Placement and Credit Policy" section). 1 credit. Fall 2013. Grinstead. MATH 027. Linear Algebra This course covers systems of linear equations, matrices, vector spaces, linear transformations, determinants, and eigenvalues. Applications to other disciplines are presented. This course is a step up from calculus: It includes more abstract reasoning and structures. Formal proofs are discussed in class and are part of the homework. Students may take only one of MATH 027, MATH 028, and MATH 028S for credit. Prerequisite: A grade of C or better in some math course numbered 025 or higher or placement by examination (see "Advanced Placement and Credit Policy" section). 1 credit. Each semester. Fall 2013. Campbell, Cook. Spring 2014. Campbell, Cook. MATH 028. Linear Algebra Honors Course More theoretical, abstract, and rigorous than MATH 027. The subject matter will be equally as valuable in applied situations, but applications will be emphasized less. MATH 028 is intended for students with exceptionally strong mathematical skills, especially if they are thinking of a mathematics major. Students may take only one of MATH 027, MATH 028, and MATH 028S for credit. Prerequisite: A grade of B or better in some math course numbered 025 or higher, or placement by examination, including both placement out of calculus and placement into this course via Part IV of Swarthmore's Calculus Placement Exam (see "Placement Procedure" section). 1 credit. Fall 2013. Bergstrand. Spring 2014. Johnson. MATH 028S. First-Year Seminar: Linear Algebra Honors Seminar MATH 028S covers the same material as the lecture-based MATH 028 but uses a seminar format (maximum 12 students) with additional meetings. Hands-on student participation takes the place of most lectures. Students may take only one of MATH 027, MATH 028, and MATH 028S for credit. Prerequisite: Placement by examination, including both placement out of calculus and placement into this course via Part IV of Swarthmore's Calculus Placement Exam (see "Placement Procedure" section). 1 credit. Fall 2013. Maurer. MATH 029. Discrete Mathematics An introduction to noncontinuous mathematics. The key theme is how induction, iteration, and recursion can help one discover, compute, and prove solutions to various problems—often problems of interest in computer science, social science, or management. Topics will include mathematical induction and other methods of proof, recurrence relations, counting, and graph theory. Additional topics may include algorithms, and probability. There is a strong emphasis on good mathematical writing, especially proofs. While it does not use any calculus, MATH 029 is a more sophisticated course than MATH 15 or MATH 25; thus success in a calculus course demonstrates the mathematical maturity needed for MATH 29. Prerequisite: Strong knowledge of at least precalculus, as evidenced by taking another mathematics course numbered 15 or above, or through our placement examinations (see "Placement Procedure" section). Familiarity with some computer language is helpful but not necessary. Eligible for Cognitive Science credit. Writing course. 1 credit. Fall 2013. Maurer. Spring 2014. Bergstrand. STAT 031. Data Analysis and Visualization This course will study methods for exploring and modeling relationships in data. We introduce modern techniques for visualizing trends and formulating hypotheses. We will also discuss methods for modeling structure and patterns in data, particularly using multiple regression and related methods. The format of the course emphasizes writing assignments and interactive problem solving using real datasets. Statistics Prerequisites: Credit for AP Statistics, STAT 011, STAT 061, or ECON 031; or STAT 001 and permission of the instructor. Eligible for Cognitive Science credit. Writing course. 1 credit. Fall 2013. Schofield. Spring 2014. Sedlock. MATH 033. Basic Several-Variable Calculus This course considers differentiation and integration of functions of several variables with special emphasis on two and three dimensions. Topics include partial differentiation, extreme value problems, Lagrange multipliers, multiple integrals, line and surface integrals, Green's, Stokes', and Gauss' theorems. The department strongly recommends that students take MATH 034 instead, which is offered every semester and provides a richer understanding of this material by requiring linear algebra (MATH 027 or 028) as a prerequisite. Students may take only one of MATH 033, MATH 034, and MATH 035 for credit. Prerequisite: MATH 025, or 026 or placement by examination (see "Advanced Placement and Credit Policy" section). Students who have taken linear algebra at Swarthmore or elsewhere may not take MATH 033 without the instructor's permission. 1 credit. Fall 2013. Mavinga. MATH 034. Several-Variable Calculus Same topics as MATH 033 except in more depth using the concepts of linear algebra. The department strongly recommends that students take linear algebra first so that they are eligible for this course. Students may take only one of MATH 033, MATH 034, and MATH 035 for credit. Eligible for Cognitive Science credit. Prerequisite: MATH 025, or 026; and MATH 027, 028, or 028S. 1 credit. Each semester. Fall 2013. Epstein. Spring 2014. Epstein. MATH 035. Several-Variable Calculus Honors Course This version of MATH 034 will be more theoretical, abstract, and rigorous than its standard counterpart. The subject matter will be equally as valuable in applied situations, but applications will be emphasized less. It is intended for students with exceptionally strong mathematical skills and primarily for those who have completed MATH 028 or 028S successfully. Students may take only one of MATH 033, MATH 034, and MATH 035 for credit. Prerequisite: A grade of C or better in MATH 028 or 028S, or permission of the instructor, or in the fall for entering students who have placed out of linear algebra, permission of the departmental placement coordinator. 1 credit. Fall 2013. Gomez. Spring 2014. Grinstead. STAT 032. Topics in Statistics: Data Analysis Projects in Public and Social Policy This course is offered occasionally, when it was last offered in spring 2011 it was a Community-Based Learning project course in data analysis. Students worked in teams on a semester-long data analysis problem. Projects were drawn from data from local organizations in order to attempt to answer questions of direct importance to them. A key objective of the course is to expose students to the variety of challenges faced by the data analyst. Topics may include multiple regression, analysis of variance, analysis of covariance, and other related methods. Students research the scientific background of their problem and consult with the local organizations from which their data came. Prerequisite: STAT 011, or permission of the instructor. 1 credit. Not offered 2013–2014. MATH 043. Basic Differential Equations This course emphasizes the standard techniques used to solve differential equations. It will cover the basic theory of the field with an eye toward practical applications. Standard topics include first-order equations, linear differential equations, series solutions, first-order systems of equations, Laplace transforms, approximation methods, and some partial differential equations. Compare with MATH 044. Students may not take both MATH 043 and 044 for credit. The department prefers majors to take MATH 044. Prerequisites: Several-variable calculus or permission of the instructor. 1 credit. Spring 2014. Johnson. MATH 044. Differential Equations An introduction to differential equations that has a more theoretical flavor than MATH 043 and is intended for students who enjoy delving into the mathematics behind the techniques. Problems are considered from analytical, qualitative, and numerical viewpoints, with an emphasis on the formulation of differential equations and the interpretations of their solutions. This course does not place as strong an emphasis on solution techniques as MATH 043 and thus may not be as useful to the more applied student. Students may not take both MATH 043 and 044 for credit. The department prefers majors to take MATH 044. Eligible for Cognitive Science credit. Prerequisites: Linear algebra and several-variable calculus or permission of the instructor. 1 credit. Spring 2014. Mavinga. MATH 046. Theory of Computation MATH 053. Topics in Analysis Course content varies from year to year depending on student and faculty interest. Recent topics have included financial mathematics, dynamical systems, and Fourier analysis. Prerequisites: Linear algebra and several-variable calculus. 1 credit. Alternate years. Not offered 2013–2014. MATH 054. Partial Differential Equations The first part of the course consists of an introduction to linear partial differential equations of elliptic, parabolic, and hyperbolic type via the Laplace equation, the heat equation, and the wave equation. The second part of the course is an introduction to the calculus of variations. Additional topics depend on the interests of the students and instructor. Prerequisites: Linear algebra, several-variable calculus, and either MATH 043, MATH 044, PHYS 050, or permission of the instructor. 1 credit. Alternate years. Spring 2014. Mavinga. MATH 055. Topics in Geometry Course content varies from year to year. In recent years, the emphasis has been on introductory differential geometry. See also MATH 075. Prerequisites: Linear algebra and several-variable calculus or permission of the instructor. 1 credit. Alternate years. Not offered 2013–2014. MATH 056. Modeling An introduction to the methods and attitudes of mathematical modeling. Course content varies from year to year depending on student and faculty interest. Because modeling in physical science and engineering is already taught in courses in those disciplines, applications in this course will be primarily to social and biological sciences. Various standard methods used in modeling will be introduced. These may include differential equations, Markov chains, game theory, graph theory, and computer simulation. The course will balance theory with how to apply these subjects to specific modeling problems coming from a variety of disciplines. The format of the course will include projects as well as lectures and problem sets with the hope that those enrolling will have the opportunity to apply what they have learned to appropriate problems within their own area of interest. Prerequisites: Linear algebra and several-variable calculus or permission of the instructor. 1 credit. Alternate years. Fall 2013. Campbell. MATH 058. Number Theory The theory of primes, divisibility concepts, and multiplicative number theory will be developed. Prerequisites: Linear algebra and several-variable calculus or permission of the instructor. 1 credit. Alternate years. Not offered 2013–2014. STAT 061. Probability and Mathematical Statistics I This course introduces the mathematical theory of probability, including density functions and distribution functions, joint and marginal distributions, conditional probability, and expected value and variance. It then develops the theory of statistics, including parameter estimation and hypothesis testing. The emphasis is on proving results in mathematical statistics rather than on applying statistical methods. Students needing to learn applied statistics and data analysis should consider STAT 011 or 031 in addition to or instead of this course. Prerequisites: MATH 033 or 034 or permission of the instructor. STAT 011 or the equivalent is strongly recommended. 1 credit. Fall 2013. Everson. MATH 067. Introduction to Modern Algebra This course is an introduction to abstract algebra and will survey basic algebraic systems—groups, rings, and fields. Although these concepts will be illustrated by concrete examples, the emphasis will be on abstract theorems, proofs, and rigorous mathematical reasoning. Required additional meetings. Prerequisite: Linear algebra or permission of the instructor. Writing course. 1 credit. Fall 2013. Johnson. MATH 069. Combinatorics This course continues the study of material begun in MATH 029. The primary topics are enumeration and graph theory. The first area includes, among other things, a study of generating functions and Polya counting. The second area is concerned with relations between certain graphical invariants. Additional topics may include one or more of the following topics: design theory, extremal graph theory, Ramsey theory, matroids, matchings, codes, and Latin squares. Prerequisites: Grades of C or better in MATH 029 and at least one other course in mathematics numbered 27 or higher, or permission of the instructor. 1 credit. Alternate years. Not offered 2013–2014. MATH 073. Advanced Topics in Analysis MATH 075. Advanced Topics in Geometry An advanced version of MATH 055, sometimes given instead, and typically requiring MATH 063, 067, or both. The topic for 2013–2014 is computational geometry and topology. This version of the course may not be used as part of the Honors preparation in Geometry. Prerequisites: At least one of MATH 055, MATH 063, MATH 067, or MATH 069. MATH 063 recommended especially. 1 credit. Fall 2013. Shimamoto. MATH 077. Advanced Topics in Algebra An advanced version of MATH 057, sometimes given instead, and requiring the core course in algebra. (In 2013–2014 MATH 057 will be offered instead.) Prerequisites: Linear algebra and MATH 067. 1 credit. Not offered 2013–2014. MATH 079. Advanced Topics in Discrete Mathematics MATH 093/STAT 093. Directed Reading MATH 096/STAT 096. Thesis MATH 097. Senior Conference This course is required of all senior mathematics majors in the Course Program and must be taken at Swarthmore. It provides an opportunity to delve more deeply into a particular topic agreed on by the student and the instructor. This focus is accomplished through a written paper and either an oral presentation or participation in a poster session. 0.5 credit. Fall 2013. Talvacchia. MATH 102. Modern Algebra II This seminar is a continuation of Introduction to Modern Algebra (MATH 067). Topics covered usually include field theory, Galois theory (including the insolvability of the quintic), the structure theorem for modules over principal ideal domains, and a theoretical development of linear algebra. Other topics may be studied depending on the interests of students and instructor. Eligible for Cognitive Science credit. Prerequisite: MATH 067. 1 credit. Fall 2013. Bergstrand. Spring 2014. Staff. MATH 103. Complex Analysis A brief study of the geometry of complex numbers is followed by a detailed treatment of the Cauchy theory of analytic functions of a complex variable: integration and Cauchy's theorem, power series, residue calculus, conformal mapping, and harmonic functions. Various applications are given, and other topics—such as elliptic functions, analytic continuation, and the theory of Weierstrass—may be discussed. Prerequisite: MATH 063. 1 credit. Alternate years. Fall 2013. Grinstead. MATH 106. Advanced Topics in Geometry The course content varies from year to year among differential geometry, differential topology, and algebraic geometry. In 2013, the topic is expected to be advanced differential geometry. Prerequisites: MATH 055 and 063 or permission of the instructor. 1 credit. Alternate years. Not offered 2013–2014. STAT 111. Mathematical Statistics II This seminar is a continuation of STAT 061. It deals mainly with statistical models for the relationships between variables. The general linear model, which includes regression, variance, and covariance analysis, is examined in detail. Topics may also include nonparametric statistics, sampling theory, and Bayesian statistical inference. Eligible for Cognitive Science credit. Prerequisites: Linear algebra and a grade of C+ or better in STAT 061; CPSC 021. 1 credit. Spring 2014. Sedlock.
The Big Idea The patterns found in mathematical data can be represented with expressions and equations. Algebra 1 studies the modeling of data using linear, exponential and quadratic functions. Wednesday, September 11, 2013 September 11 Wednesday Lord, make me a channel of your peace **Remind your parents to sign up for Conferences at Back to School Night tonight. I am available on Monday and Tuesday of conference week. Essential Question: How can you use the properties of arithmetic to make a problem simpler? Class Objective: Students will use the properties of arithmetic to simplify expressions and move to evaluate simple equations.
Graffito:Kimothy: Their definitely not using trig or calculus, unless they pursued careers that use those things. My brother cannot understand the different between growth at a slower rate and shrinking. This impacts his ability to understand all manner of social and economic issues. Even if you don't solve trig and calculus problems everyday, mastering those concepts allows you to better understand the world around you. TheBeastOfYuccaFlats:slayer199: AsMaybe, but everyone should be forced to take Probability and Stats in college. Kimothy:I think it's more a problem of not knowing how to teach math, or teaching it in a way that's supposed to help students pass the four or five standardized tests a year rather than really understanding mathematical concepts. Reduce the emphasis on testing and emphasize actual knowledge, application, and critical thinking and you'll see students improve. That said, I don't think I use much math beyond the stuff you learn in elementary school, except maybe some geometry now and then, and I think that's probably a pretty typical thing. Most people aren't using algebra in their everyday lives. Their definitely not using trig or calculus, unless they pursued careers that use those things. The problem is, the author's argument can be applied to lots of subjects. People don't need history everyday, either, but that doesn't mean those subjects aren't valuable. I'll bet you use algebra more than you think. Any time you see a package of 10 somethings for y dollars you might think about how each one of those things costs y/10. That's algebra, Bud. I would say that we teach advanced mathematics (beyond "counting out change") because by the time one student out of fifty decides he wants to study something actually challenging, it's too late to start teaching him real math. If everyone gets algebra crammed into their skulls in middle school, the ones who discover they need calculus and statistics in high school will be ready to take them. wingedkat: I guess, you could make it like a detective story: "A detective is investigating a robbery and the suspect was seen leaving the supermarket and throwing away the receipt, which would have his finger prints. There are 4 receipts, but they only indicate the price spent/item. The clerk doesn't remember the price of the meat, but does remember that the suspect bought 3 pounds of beef, currently $3.99. There was a 15% sale on all items in the store which ended recently. Which receipt has the suspect's fingerprints?" That's probably too long and complicated, but at least more interesting. This fits in the narrative better, and also makes detail important to the story/problem. /No more word problems with Ida and Susan building quadrilateral walls around their garden. University education, especially liberal arts education, is more important than you might think. Requiring engineering students to learn a foreign language and understand philosophy makes them better engineers because it allows them to think about things in different ways (at a potentially fundamental level), as well as just making them better people in general. Besides, engineers need to be able to write well and read well to perform research. Also, many 18 year olds don't even know what they want to do yet. Some aren't even aware that there are options out there. I know plenty of people who started out as CS majors and turned into pure math majors, or EEs or philosphy majors (and not just to get an "easy degree"). I'm lucky in that I've known what I wanted to do for as long as I can remember, but that's not true for everyone. If you only want to take classes that are relevant to your career, fine, go to ITT Tech. The problem is that you'll miss out on the whole universe of knowledge and information that would have (a) made your life richer and (b) made you a better network engineer in incalcuable (but real) ways. Lord Dimwit:In my opinion the solution is to make teaching a respectably paid vocation, such that it will attract people who could easily get work in the business sector, but might choose to become teachers if it didn't mean settling for a life of extraordinarily limited earning potential. I had a music teacher in seventh grade who decided to lecture the class on the need for attaining a well-rounded education (just to be clear, I actually agree with the sentiment). His example was that we could compute the odds of winning the pick-4 lottery by multiplying 4 x 3 x 2 x 1 = 24, so its 1 in 24. In summary: 1) He completely botched the math (the real odds are 1 in 10,000) 2) Based on this math, he came to the wrong conclusion (If the jackpot were anything over $24, and we used his math, we'd be buying as many lottery tickets as we could) At what point will brake application result in insufficient reduction of momentum to avoid collision requiring you to calculate the proper trajectory and starting velocity in which to disembark the train with statistically the least likely result being farked up beyond all recognition? slayer199:Evilumad:slumad: slLordOfThePings: Lord Dimwit: My high school honors (!) geometry teacher told me that pi is an irrational number because we can't measure it because we can't draw a perfect circle. If we could draw a perfect circle, the exact value of pi would be known. Duuuuude! Your teacher ever share the bong? And just to be clear, I mean that she thought that pi was irrational because every time we measure a circle, our measurements are slightly off. She thought there was a finite decimal expansion of pi, we just hadn't discovered it yet. "The problem with American schoolsMooseUpNorth:It should be noted that a BSc-Math degree doesn't qualify one to start an elementary certification program under typical state NCLB standards. You would need an extra year or so of general arts credits beyond your degree to qualify. Basically, you'd have to hybrid into the equivalent of a BA (Math). Math majors generally certify at middle or high school. The converse is not true. One or two math credits are sufficient for an Arts or History major. Worse, most teacher college professors appear to have been drawn from the huge pool of English/History majors. You're very lucky if you have a math or science background professor who can teach that aspect of education to the elementary school teacher candidates. The problem with the way we teach math is that it propagates itself... people who are capable of understanding it the way it is currently taught do well, learn to love it, study it in college, then go on to teach it the same way they learned it, leaving far too many of the students confused as to how it could ever be useful in their lives. I want to break the cycle, let people learned math to use it because it works teach it. I don't advocate those programs that grab random engineers, give them a month's course in "how to teach", and throw them into problem schools. Teaching is a hard skill, and requires a lot more than just knowledge of the subject matter. I just think "I Love Math" > "Math Major" > "Mathematics Education" is more often a bad idea than a good one. All_Farked_Up:Surool: "That was 30 years ago, and it's only gotten worse. What the deuce are they teaching in math that's so hard? HS level math is fairly trivial. Fark man, my second year integrals course in University - there's nooo way you could teach that in HS. I suppose they could teach matrices. OTOH they're pretty easy but very useful. I'm taking college algebra (and have a solid A going 2 days from the final) so I'm getting a kick out of these replies. Wish I'd have done it earlier in life, but I -really- hated being shown something, understanding it, and being told I needed to do it 50 more times every night. Fark that method, I like this one better...here's some problems to try, solutions are in the back so if you get stuck, you can figure out why that answer is the right one. There is a quiz at the beginning of class covering the previous day's stuff. If you didn't quite have it when you left and didn't work some problems that night, you're going to be screwed. If you did understand, and didn't have to work the problems, you'll be golden. I think that's a better model, at least for me it is. /There is, no shiat, a middle schooler in my class-had to get instructor permission because they're too young to enroll at the university for HS credit. //Yes, it's an Asian kid. slayer199:AsI use the computer for all my math and language translation needs. "As far as what he hates algebra (and still do), I would not give up teaching. Engineering is a useful statistics can be useful. However, before forcing Calculate College Faculty and students of algebra than ever in need of either a waste." rumpelstiltskin:John P. Smith III, an educational psychologist at Michigan State University who has studied math education, has found that "mathematical reasoning in workplaces differs markedly from the algorithms taught in school." No shiat. That's because you aren't supposed to learn the algorithms; you're supposed to learn how abstraction and reasoning lead to the algorithms. We don't need any more people in the workforce who are experts in applying the quadratic formula, but that simply isn't the point. Mathematical reasoning in workplaces takes the form of abstraction and identification of relationships between abstractions. These are the skills you are supposed to begin to develop in high school "algebra" and geometry. And if you can't, you should be a barrista or some kind of clerk. You have no business making decisions. Or you could be a political science professor, who's work depends heavily on numbers he doesn't understand. You could do that, too. I agree that it isn't about solving specific complex problems. There are people with a home project, like remodelling a bathroom, that can't do the simplest of mathematical reasoning. How much tile is needed? How about paint? What angle should I cut this board? I can't imagine going through life without the math skills I have. It'd be like not being able to read. ElLoco:Babwa Wawa: I went into that article thinking you could get rid of algebra if you replaced it with something more relevant like statistics. The nation would be much better off if everyone had a basic understanding of stats. That's funny... I was just having a discussion maybe 2 days ago about the reasoning behind why stats isn't a required part of a high school education. Not necessarily a whole semester of stats, but all the basics. I even discussed a single semester of algebra and stats combined. Advanced material from either one of them is all but useless to most students, but the basics learned from both carry on to a number of things in the job market that are not science related. The difficulty is that survey-level stats is about as useful as pre-calculus physics -- can may be able to memorize the formulae, but you don't have the first clue where they come from, why, or what they mean. Stats really requires and understanding of calculus, and is often even opaque with that. wingedkat:Because People in power are Stupid: wingedkat: 1. Math majors shouldn't teach math. I found some of your homework. [filehurricane.com image 494x371] hmm.... uh huh... yeah, turns out I don't see what you did there. It would make more sense if you had not made it my homework. hmm... uh huh... yeah, turns out that I don't care about who you are really care about you or want to know that you are an AP Political Science major . Christ, did a cow crap in here? Figures the article would come from a liberal arts major. Know what, take David Copperfield and shove it up your bung hole! If you can't learn a concept that is a few hundred years old, you're an idiot. Math, at its core, is about problem solving whether it is useful for you in life or not, it builds cognitive skills in looking at a problem, breaking it down and finding a solution. It trains the brain to solve problems. Painting happy trees every day will not help you tackle problems you might encounter in the workplace (though they will make your cubicle friendlier). School teaches you a bunch of mathematical operations, like adding, multiplying, integrating, etc. While useful in their own right, it leaves a bit of a gap in math-like thinking. The entire purpose of math is to make things easier, not more difficult. I think students need more examples of how math makes complex problems easier to describe, instead of solely increasing the repertoire of operations they know how to perform really care about you or want to know that you are an AP Political Science major . * Or something Here's some more [edge.ebaumsworld.com image 400x216] I find those to be creative (and accurate, in a sense) answers to math questions that might be given by liberal arts majors. I wonder if there are similar answers to English problems submitted by math majors. umad:I had to take college bound English before I went to college to major in Engineering. You can take a little bit of math, cupcake. It won't kill you. Taking statistics would be much more useful for non-STEM students throughout their lives. Pre-calc is a waste of time if you are not going to learn calculus. Taking a college bound English course before majoring in Engineering seems useful. I've met a lot of engineers who couldn't write coherent instructions and some who bragged about never reading, even in college. The point is not to avoid math, but to teach useful math skills, which means calculus for some and statistics for others. FTA: "And if there is a shortage of STEM graduates, an equally crucial issue is how many available positions there are for men and women with these skills. A January 2012 analysis from the Georgetown center found 7.5 percent unemployment for engineering graduates and 8.2 percent among computer scientists. " Let's see... bust your balls taking the hardest courses, the most units (and some of the highest debt because you don't have time to work) and still get paid like sh*t while watching your back (if you can even find a job) because your idiot potential employers would rather H1-B or outsource your ass as soon as they can... or skate though taking business courses, have a life and work on Wall Street for moar money than gawd... weiserfireman:I think that we have been trying to find "easier" ways to teach math for over 40 years Evidence is that for the most part, the easier ways are failures. The key to being good at math is the same as being good at reading. You have to do it and do it and do it and do it. In other words, those old fashioned work books that were full of excercise problems are the way to go. Teach the concept, show some sample problems, have the students do 20 problems over night. Check their work, if they don't have the idea, find common threads in the lack of understanding, assign 50 more problems designed to address the problems. Check them the next day, if they have it, go to the next concept. The other problem is that many teachers, especially at the elementary level, don't really understand math well enough to understand whether their students get it or not, much less why they don't get it. This is how I learn math down to a tee. Understand the ideas and methodology, and then practice the heck out of it until it clicks. After a little while I tend to get a a ha moment and it is easily understood from then on. Most people at college didn't want to sit down and practice. They wanted a life and chase girls. I was married, so that wasn't a problem.
College Algebra Essentials -With CD - 3rd edition Summary: Chapter P. Prerequisites: Fundamental Concepts of Algebra.P.1 Algebraic Expressions, Mathematical Models, and Real Numbers1. Evaluate algebraic expressions.2. Use mathematical models.3. Find the intersection of two sets.4. Find the union of two sets.5. Recognize subsets of the real numbers.6. Use inequality symbols.7. Evaluate absolute value.8. Use absolute value to express distance.9. Identify properties of the real numbers.10. Simplify algebraic expressions.P.2 Exponents and Scient...show moreific Notation1. Use the product rule.2. Use the quotient rule.3. Use the zero-exponent rule.4. Use the negative-exponent rule.5. Use the power rule.6. Find the power of a product.7. Find the power of a quotient.8. Simplify exponential expressions.9. Use scientific notation.P.3 Radicals and Rational Exponents1. Evaluate square roots.2. Simplify expressions of the form ?a23. Use the product rule to simplify square roots.4. Use the quotient rule to simplify square roots.5. Add and subtract square roots.6. Rationalize denominators.7. Evaluate and perform operations with higher roots.8. Understand and use rational exponents.P.4 Polynomials1. Understand the vocabulary of polynomials.2. Add and subtract polynomials.3. Multiply polynomials.4. Use FOIL in polynomial multiplication.5. Use special products in polynomial multiplication.6. Perform operations with polynomials in several variables.Mid-Chapter Check PointP.5 Factoring Polynomials1. Factor out the greatest common factor of a polynomial.2. Factor by grouping.3. Factor trinomials.4. Factor the difference of squares.5. Factor perfect square trinomials.6. Factor the sum or difference of two cubes.7. Use a general strategy for factoring polynomials.8. Factor algebraic expressions containing fractional and negative exponents.P.6 Rational Expressions1. Specify numbers that must be excluded from the domain of rational expressions.2. Simplify rational expressions.3. Multiply rational expressions.4. Divide rational expressions.5. Add and subtract ...show less and Precalculus, all published by Pearson Prentice Hall4
First Year Academics: Calculus Mathematics is the common language of science and engineering and is essential for understanding many aspects of the physical world. To provide a solid mathematical foundation, MIT has a two-subject General Institute Requirement in calculus. If you take Calculus at MIT, which version of 18.01 and 18.02 should you take? The choice of subjects will depend on your background, preparation, and interests. 18.01 Calculus I: Prerequisite: High school algebra and trigonometry. For students who have a year or less of high school calculus and no AP credit. 18.014 and 18.024 Calculus with Theory:Prerequisite: Strong interest and ability in mathematics, interest in rigorous proofs. This is intended as a two-semester sequence, but students completing 18.014 will be well-prepared for all versions of 18.02. Students choosing 18.014 should be familiar with the computational aspects of single-variable calculus, though these aspects may be reviewed during the term. If you have credit for 18.01 via AP or other exam score, ASE, or Transfer Credit, you may register for 18.02 or any of its variants. See the Math Department's Calculus page for descriptions of classes.
MATH363-12S2 (C)Semester Two 2012 Dynamical Systems Description An introduction to nonlinear systems, the use of linearisation techniques and bifurcation theory. Dynamical systems is the study of global, long-term behaviour of mathematical systems whose state evolves with time. Most of the systems studied arise from differential equations models of an applied problem from Physics, Biology, Economics, Chemistry, Engineering, etc. The aim of this course is to understand asymptotic behaviour using a combination of geometric reasoning, intelligent approximations, computer assistance and mathematical insight. This will be accomplished without grinding out the solutions of special classes of differential equations. Learning Outcomes • to develop insight into the qualitative behaviour of the solutions to differential equations; in particular, the effects of nonlinearity • to obtain a greater understanding of the use of differential equations in modelling physical systems; including the role of parameters, and the interplay between solutions to the model and experiments • to apply relevant computational and geometric techniques to analyse systems of differential equations; and to communicate the mathematical results clearly and coherently Other recommended reading: Jim Meiss Differential dynamical systems, SIAM, 2007. This is an excellent text which includes proofs of many of the important theorems; it also includes many other interesting things.
Derivative Calculator and Integral Calculator Online symbolic calculators for derivatives and integrals. Both tools are designed for intuitive user interaction. While you type in your expression, it is transformed into a graphical formula in real-time and shown to you, which helps reducing input mistakes. The calculators do not show step-by-step differentiation or integration (not intended for cheating) but work great for checking your homework, or finding the derivative or integral for some other usage. Calculus7.com Contains video animations on calculus topics that are most useful for college and high school math instructors to reinforce or clarify what is explained in the class/lecture. calculus7.com Books Calculus by Ron Larson Larson's Calculus is a basic textbook with long history on the market. It contains lots of illustrations and plenty of exercises. It has been praised by a students and professors for its effective pedagogy that addresses the needs of a broad range of teaching and learning styles and environments. Mathematical Modeling and Computational Calculus This is a DIFFERENT kind of calculus book: it doesn't go through theorems and such, but instead teaches you about mathematical modeling using differential equations that are computed with the aid of computers, without the need of any advanced mathematics. Systems studied include satellite orbits, the orbits of the earth and moon, rocket trajectories, the Apollo mission trajectory, the Juno space probe, electrical circuits, oscillators, filters, tennis serves, springs, friction, automobile suspension systems, lift and drag, and airplane dynamics. Calculus Without Tears Calculus Without Tears is a collection of worksheets (in 4 volumes) that teaches basic concepts of calculus very step-by-step, without need of much algebra. They are intended to be self-teaching workbooks that even students before high school can study. Calculus Without Tears starts with studying the simplest of motions, which is a runner running with constant speed (or sometimes standing still!). Volume 2 (Newton's Apple) concentrates on the motion of a falling apple. Volume 3 goes about finding the derivatives of polynomials, trigonometric functions, roots, exponential and logarithmic functions. See my review. Calculus Made Easy Calculus Made easy is a classic textbook, making the subject at hand still more comprehensible to readers of all levels. Martin Gardner, himself an American mathematical landmark, says, "This is the leanest and liveliest introduction to calculus ever written." The book concentrates on little bits of x, called dx, their differences and sums among all kinds of functions, their geometric meaning, and what they can do for you. Graphing Desmos A free, online graphing calculator that is incredibly easy and intuitive to use, yet very powerful. You can use parameters with sliders, define your own functions and constants, graph inequalities, derivatives, and more. You can save, email, print, and embed your graphs. WebGraphing.com An online graphing calculators for functions, equations, and inequalities with automatic analysis of graphs' properties. Automatic optimal viewing window, displays asymptotes, discontinuities, piecewise graphing, etc. Also 'guess the graph', galleries, articles on graphing concepts and tricks. Very useful for high school students and teachers. Function Flyer Creates graphs of functions but also allows the manipulation of constants and coefficients in any function so the user can explore the effects on the graph by changing those numbers. Great tool! Student would get more out of it if there was a guideline or lesson plan to follow in the explorations. Calc98 Engineering, scientific and financial freeware calculator for Windows. Functions for statistics, use of different number bases, metric units conversions and physical properties and constants. Also has financial and time functions including investment, loan and mortgage calculations, a stopwatch. Price: Free SpeQ Mathematics Small but extensive math program for calculations and graphing. Can also define variables and save your calculations. Price: Free SVGCalc An open-source scientific graphing calculator for web browsers. It can be stored on a hard drive, accessed over a local or wide area network, or made available via an internet webpage. Provides calculation and graphing tools commonly needed by high school math and science students. Price: Free svgcalc.software.informer.com MathGV Function Plotting Freeware for Windows Plot 2 dimensional, parametric, polar, and 3 dimensional functions. You can add lines, rectangles, circles, round rectangles, flood fills, and text for labels or for artistic effects. Because the plots are shown with a big screen, and are extremely easy to zoom in/out or move around, MathGV is excellent for visualizing graphs and functions in middle/high school. It does NOT have calculus or tracing tools. Price: Free Mathscribe Lite 2.5.1 Mathscribe is a simple dynamic graphing and mathematical modeling program for algebra, trigonometry and precalculus classes. The free download includes 13 ready-to-print-n-use assignments, which I consider a real benefit of this program. They cover linear equations, systems of linear equations, and quadratic equations. Also, the program comes with lots of pre-made examples of different kinds of functions for the high school algebra/pre-calculus student. You can also use Mathscribe to mathematically model scientific data, either by typing in the data from scratch, or simply pasting it from a spreadsheet or other program. Mathscribe lacks the zooming in/out and centering functions present in many plotting programs. Its strength is in the ready-made examples and lab sheets, helping the student to connect both symbolic and visual thinking through guided discovery. Price: Free InquiSoft A software that includes eight different graphing modes, including implicit mode for conic sections. Other modes support polar, parametric, and piecewise-defined functions, as well as slope fields. You can save your graphs or copy and paste them into other programs, and you can customize colors, line styles, captions, and legends. Includes over 100 built-in functions from calculus, statistics, vectors, complex numbers, and more. Price: $29 MathProf A comprehensive program, like a math professor on your desktop. Not only for algebra, but for analysis, geometry, 3D figures, stochastics, vector algebra, and linear algebra. Download is free. Price: $45. Graphmatica Very easy to use, fast, compact graphing program. Plots 2D graphs, implicitly defined functions, in polar coordinates, piecewise, parametric graphing. Finds derivative and area under curve. Use a parameter/free variable. Data plotting, curve fitting, differential equations. Recommended for middle school/high school algebra and calculus. Price: It's up to you what you pay; if you find Graphmatica easy, helpful, and convenient to use, you are asked to support the release of future versions by sending your contribution to the developer.
Introduction James Stewart's Calculus (Textbook by James Stewart) Study Guide: Homework Help Why is calculus important?Why is calculus so important? Since you listed a textbook you might be looking for a specific answer. In general, calculus has many practical applications. It is used in business in project management and finance. It is also useful in engineering and medicine. We would not have many of our innovations if it were not...
Course notes from previous instructor, Dominik Schoetzau. There are several things bundled together here. First are some notes on finite difference methods. Second is a list of some FEM reference books. Then come several chapters on the FEM, implementation and analysis.
4868 / ISBN-13: 9781576854860For new algebra students or those seeking a refresher, this book offers a series of simple 20-step lesson plans that emphasize quick learning of practical, essential skills.For new algebra students or those seeking a refresher, this book offers a series of simple 20-step lesson plans that emphasize quick learning of practical, essential skills Contains: Illustrations. Algebra Success in 20 Minutes a Day
No offence but I always put all of my effort in class, in which the teacher has noted, and I like barely do my homework. But there's going to be a website were you can make quizzes or take them and see what you need to work on and what you know. If the book has a website do some online quizes there and some lessons if you're really struggling with it. I find that there is no need to study for math but that's probably because it is my best class and I surprisingly find it fun. Also I don't see what you can study other than formulas. And I just want you to know that by the bad spelling and short explanations I can tell a thread that's yours from a mile away. Well i never study for anything and always get A's sooo im not really sure what to do. If you know how to do a certain problem that will be on a test, try to teach someone else how to do it. Thats when you know material. Repetition is extremely important to success in Math. You have to truly understand what you're doing in order to breeze by it. Don't think too much about the numbers, think more about the algorithms that are behind the problems. Anyone can deal with numbers sooner or later, it's what you do with them that matters. Maths is quite a hard topic to study. The best way to study is to understand the basics of the topic within the subject, for example, Algebra, try to understand the concept of it, then move on to difficult algebra once you understand the basics. Also repetition is quite important, you can easily breeze through questions if you just understand the concept and the method to solve it. Also equations are extremely useful. For anything, it is best if you study/practice the things you struggle on or don't know. Don't waste your time doing all the easy problems. Do the problems that are giving you trouble and don't be afraid to ask for help.
Mathematics For ElementaryMathematics for Elementary School Teachers," 3/e, offers pre-service teachers a comprehensive mathematics course designed to foster concept development through examples, investigations, and explorations. Visual icons throughout the main text allow instructors to easily connect the text to the hands-on activities in the corresponding Explorations Manual."Classroom Connections" in both the exposition and the exercises guide students to connect the mathematics being taught with effective teaching strategies. Students must analyze educational math... MOREematics research, evaluate common student errors, and see alternative solution methods, enabling them to better prepare for their future teaching careers."Investigations" encourage students to think about a topic before discussing the math or viewing examples. These can be used as classroom discussion questions, for independent reading, or as review."Multiple Strategies" presented throughout the examples and exposition of the text allow students to analyze numerous approaches to solving problems. Note: Each chapter concludes with an Investigation, Exercise, a Chapter Summary and Review Exercises
Center for Applied Probability - Georgia Tech Formed in the Spring of 1995, run by a group of faculty members in the School of Mathematics and the School of Industrial and Systems Engineering (ISyE) at Georgia Tech. Members, events, mailing list, links to other sites. ...more>> CMP Unit Organizers - Art Mabbott To introduce students to new units from the Connected Mathematics Project (CMP), Art Mabbott has developed a set of Unit Organizers. Adapting work done by B. Keith Lenz, of the University of Nebraska, Mabbott has also shared his MS Word documents with ...more>> Cool School Tools - Tim Fahlberg Shockwave whiteboard movies on algebra, geometry, probability, statistics, the mathematics of finance, and more. A whiteboard movie (WM) is a multimedia screen recording of writing on an electronic whiteboard (real or virtual) with or without voice and/or ...more>> CPO Online - Cambridge Physics Outlet A company founded by teachers and scientists that creates hands-on equipment and curriculum for teaching science, math, and technology from grades 4-12 and beyond, and provides effective professional development in science and math that is both content ...more>> CTAP Middle School Math Project - CTAP Region IV A database of online technology resources supporting California middle school math content standards for grades 6, 7, and algebra. Designed for use in classroom instruction or as homework helpers for students, the matrices resources align to state standards Bruce Wilson David Bruce Wilson researches probability, combinatorics, and theoretical computer science. Abstracts of his articles on these subjects are available on the web and may be downloaded in PostScript or .dvi formats. Software available for download includes ...more>>
utorials and Examples Introduction This module presents step-by-step instructions for creating, and then editing well-known formulas to illustrate how to use the editor. The example and what properties of the editor it illustrates are listed below. All of these assume you have a blank Math Editor open. Quadratic Equation As a simple example, we'll step through several ways of writing the well-known Quadratic Equation (with real or complex coefficients): a⁢x2+b⁢x+c=a⁢(x−−b+b2−4⁢a⁢c2⁢a)⁢(x−(−b)−b2−4⁢a⁢c2⁢a)ax2bxcaxbb24ac2axbb24ac2a Method 1: Pure Keyboard Probably the quickest way to enter math is by using the keyboard. This method requires entering a total of 3 statements and a few Tab key presses. Step 1. Start off with a blank editor. Step 2. Enter the following into the main editing area "ax^2+bx+c=a(x-(-b+root)/(2a))(x-(-b+root)/(2a)) ". See below for details . Step 3. Press the Enter key. This will cause the text to be parsed and converted into math. Most of the text in step 2 should look similar to the notation used in calculators, except for "root ". Many calculators follow different conventions for entering complicated math operations like integrals and vectors. For this version of the editor we decided to wait for feedback from users on which convention to adopt. Until one is chosen, any math element defined in the W3C MathML Specification can be entered. The toolbar also provides a way to see the available commands. Finish Entering Equation At this point the editor should have 2 remaining boxes that need to be filled out, and 2 optional ones (the degree of the root). To fill in the rest, you will need to do the following: Press Shift+Tab four times to move to the first empty block. (That is, hold down the Shift key, press the Tab key, and release the Shift key four times). Enter "b^2-4ac " into the empty block under the radical. Press the Enter key to convert the input into math. Press Shift+Left arrow key to select b2−4⁢a⁢cb24ac Press Ctrl+C to copy the selection to the clipboard. Press the Tab key twice to move to the other empty block. Press Ctrl+V to paste the selection into the current block. Now, the equation should be complete. In the previous steps we used the Tab key to navigate to empty blocks that still needed information in them, skipping over optional ones. We used Shift+ arrow keys to select math and Ctrl+C and Ctrl+V to copy and paste that math. Paste into Connexions Finally, we need to copy the math and paste it back into a module. We already used the same technique above. Right now, the cursor should be just to the right of the second b2−4⁢a⁢cb24ac . The following steps will place the newly created quadratic equation back into the Connexions module. Step 1. Press Ctrl+A to select the entire formula, or Shift+Right (or Shift+Left) until the math you want to copy is selected. Step 2. Press Ctrl+C to copy it to the clipboard. Step 3. Switch back to the window where you were editing the module. Step 4. Place the cursor at the location you want to insert the quadratic formula. Step 5. Press Ctrl+V to insert the formula. Summary In this tutorial we entered the quadratic equation entirely through the keyboard. We used the Tab and arrow keys to navigate through math content, the Return key to convert input text into math, and Ctrl+C and Ctrl+V to copy and paste both within the editor and between the editor and the main module editor. Next, we will do the same example using the mouse and toolbar. Method 2: Toolbar This method requires a bit more time because we will need to click the toolbar for every character (like "+", "*", or "/" in the previous method). Instead of doing the entire equation, this tutorial will step through creating only part of it: −b+b2−4⁢a⁢c2⁢abb24ac2a Step 1. Start off with a blank editor. Step 2. Click the "Arithmetic" category in the toolbar. Step 3. Click the "Divide" operation in the menu. Step 4. Click the top empty block (numerator). Step 5. Click the "Arithmetic" category in the toolbar and the "Plus" operation in the menu. Step 6. Click the left empty block. Step 7. Click the "Arithmetic" category and the "Negate" operation in the menu. Step 8. Enter "b" in the top-left empty block Step 9. Click the other empty block in the numerator. Step 10. Click the "Arithmetic" category and the "Root" operation in the menu. Step 11. Click the empty block under the radical. Step 12. Click the "Arithmetic" category and the "Minus" operation in the menu. Step 13. Click the left empty block. Step 14. Click the "Arithmetic" category and the "Power" operation in the menu. Step 15. Enter "b" and "2". Step 16. ... Using the toolbar is a bit more tedious, but serves as a way to find operations that can be expressed in MathML. Some operations have variations (A sum can take a variable and limits, or a variable and a condition) but see Limitations on how to enter them in. Paste into Connexions Pasting the Math back into Connexions can be done the same way as before, or can be done via the Edit menu in the browser. Again, we must select the entire equation. This can be done by highlighting the equation using the mouse, or double-clicking the division bar (since it is the outer-most operation). Once highlighted, you can Click Edit, and either Cut or Copy from the main browser menu bar. If you switch back to the Connexions module editor, you can Click Edit and then Paste again from the menu to paste the newly created math back into a module. Summary In this tutorial we entered a part of the quadratic equation using the mouse and toolbar buttons. We used the mouse to select move the cursor and select math, the toolbar to insert new operations, and the browser's Edit menu to copy and paste math between the editor and the main module editor. Next, we will discuss some more advanced math editing. Advanced Editing So far we've gone through creating math from scratch. In this section, we will look at how to insert more elaborate symbols, change how variables look (Presentation MathML), and customize some of the operations provided in the toolbar. Elaborate Symbols So far we've used simple characters available from the keyboard. The quadratic formula is frequently written with a plus-minus sign like: −b±b2−4⁢a⁢c2⁢ab±b24ac2a In order to get this, we will need a little bit of Presentation MathML. This is because plus-minus is not an operation represented in Content MathML. Step 3. Highlight everything in the numerator (it should be the entire plus operation) Step 4. Replace it with "mrow " and press the enter key Step 5. Enter "-b " and move to the next block Step 6. Enter "± " and move to the next block Step 7. Paste the part of the formula we copied earlier mrow is used to control how Math is displayed to the user. In this case we used it to insert a plus-minus symbol between −bb and b2−4⁢a⁢cb24ac . The Unicode standard defines many characters but the Unicode Mathematical Operators document may be a useful reference. Customize the Look of Variables There are many elaborate ways to customize how a variable looks. These are defined in the W3C MathML Specification . We will list off a few common ways to customize. Subscripts like xixi can be entered by typing "x_i " or using "msub " A variable with both subscripts and superscripts can be entered using "msubsup " Backets like −∞00 can be added using "mfenced " and then changing the symbol used for the open and close bracket (by editing the source). Unlike subscripts which place content above/below and to the right, "munderover " places math directly above or below. A table can be added using "mtable " Customize Toolbar Operations Many operations that operate on a range have several ways of specifying the range they work on. For example, the following are equivalent: ∑i=1ni2i1ni2∑i∈Si2S=i(i>0)∧(i≤n)iSi2Sii0in Changing the range these operations required switching to the MathML source and being familiar with the W3C MathML Specification . To change the former to the latter, we start with a clean "sum " operation. Then, to decrease the amount of hand editing, we can type "i in S " to the right of the equal sign. Then, we switch to MathML Source and replace every occurrence of "interval " with "condition " and removing the special "<block ...> " element just above the </condition>
... Show More algebraic manipulations. Students of computer science whose curriculum may not allow the study of many ancillary mathematics courses will find it particularly useful. Mathematics students seeking a first approach to courses such as graph theory, combinatorics, number theory, coding theory, combinatorial optimization, and abstract algebra will also enjoy a clear introduction to these more specialized fields. The main changes to this new edition are to present descriptions of numerous algorithms on a form close to that of a real programming language. The aim is to enable students to develop practical programs from the design of algorithms. Students of mathematics and computer science seeking an eloquent introduction to discrete mathematics will be pleased by this work
Descriptions and Ratings (1) Date Contributor Description Rating 18 Jun 2013 MathWorks Classroom Resources Team Software Carpentry helps researchers be more productive by teaching them basic computing skills. We run boot camps at dozens of sites around the world, and also provide open access material online for self-paced instruction. The benefits are more reliable results and higher productivity: a day a week is common, and a ten-fold improvement isn't rare.
Algebra has been developing through the interaction between the investigation of its own algebraic structures and its applications to different areas of Mathematics and other branches of Science. This informative research volume consists of survey and original articles by reputed algebraists which are refereed by the experts in the relevant fields. The survey articles provide an excellent overview of the various areas of research in Algebra. The original articles by reputed algebraists in Ring Theory, Module Theory, Semigroup Theory, Lattice Theory, Category Theory, Derivations, Hyper and Fuzzy Structures etc. exhibit new ideas, tools needed for the successful applications and discuss newMore... techniques and methodologies for current research in different branches of Algebra. Over 300 bibliographic references make Algebra and its Applications: Recent Developments an indispensable resource book for the beginners and advanced experts in Algebra
Course Content includes the following: • Creating a worksheet and an embedded chart • Working with formulas, functions and formatting – such as entering formulas in a worksheet Using, average, max and min functions • What-if analysis – Making decisions using the IF Function • Financial functions still use PowerPoint for presentations and still teach the uses of Microsoft Applications to others. I had an extraordinary understanding of prealgebra in 6th grade, and would often tutor my classmates to help them better understand it. In terms of teaching pre-algebra, I've taught the subject to various students in my high school who asked for assistance
Poole's innovative book prepares students to make the transition from the computational aspects of the course to the theoretical by emphasizing vectors and geometric intuition from the start. Designed for a one- or two-semester introductory course and written in simple, "mathematical English" the book presents interesting examples before abstraction. This immediately follows up theoretical discussion with further examples and a variety of applications drawn from a number of disciplines, which reinforces the practical utility of the math, and helps students from a variety of backgrounds and learning styles stay connected to the concepts they are learning. Poole's approach helps students succeed in this course by learning vectors and vector geometry first in order to visualize and understand the meaning of the calculations that they will encounter and develop mathematical maturity for thinking abstractly.
School Pre-Calculus Tutor Specifically designed to meet the needs of high school students, REA's High School Pre-Calculus Tutor presents hundreds of solved problems with step ...Show synopsisSpecifically designed to meet the needs of high school students, REA's High School Pre-Calculus Tutor presents hundreds of solved problems with step-by-step and detailed solutions. Almost any imaginable problem that might be assigned for homework or given on an exam is covered. Topics include algebraic laws and operations, coordinate system relations, linear functions, sequences, series, graphing, limits, and applications. A valuable study aid for students taking upper-level mathematics courses. Fully indexed for locating specific problems rapidly.Hide synopsis Description:New. Specifically designed to correspond to high school pre...New. Specifically designed to correspond to high school pre-calculus courses. Topics include algebraic laws and operations, coordinate system relations, linear functions, sequences, series, graphing, limits, and applications. A valuable study aid for stud
The history of computing could be told as the story of hardware and software, or the story of the Internet, or the story of ďsmartĒ hand-held devices, with subplots involving IBM, Microsoft, Apple, Facebook, and TwitterStudents will save time and master non-calculus-based probability and statistics with this powerful study guide. It simplifies difficult theories and focuses on making clear the areas students typically find hardest to understandSolving the problems in this book will help demonstrate mastery of the mathematical concepts taught in elementary school. They are represented in a visually engaging manner in order to make mathematics more fun and interesting. More emphasis is paid to problem solving abilities rather than the usual mathematics grind.
New Scientist full online access is exclusive to subscribers. Registered users are given limited access to content, find out more. To read the full article, log in or subscribe to New Scientist. Physics tool makes students miss the point Software designed to help physicists tackle complicated mathematics seems to be encouraging students to focus on the wrong aspects of scientific problems. Interested in how students use computer programs to solve problems, physicists Thomas Bing and Edward Redish of the University of Maryland, College Park, analysed videos of teams of students as they worked on their assignments. Among other tools, the students used Mathematica, a program that crunches not only numbers but also symbols, enabling it to do algebra and calculus. By solving equations that might take days to solve with a pencil and paper, Mathematica frees up researchers to explore larger questions and to explore more problems. But this comes at a cost, Bing and Redish warn. Using Mathematica for physics involves two stages: choosing a strategy for solving the problem, and then implementing that strategy by typing in a few lines of computer code. Although
App Detail » Math 42 App Description Back to school promotion — MATH 42 helps students from the 5th to 12th grade with their math homework by (1) presenting them with intelligent reccomendations, showing them how to solve a problem, by (2) giving detailed, illustrated step by step solutions, and (3) an easy, simple way of inputing your problem without the need of complicated commands. MATH 42 includes a test mode in which students can practice solving problems and record their progress. It can illustrate functions intelligently by including zeros, maximums, minimums, inflexion points and asymptotes. Problems and answers can be posted on Facebook or sent per eMail. Mathematics and expensive tutoring are the Nr. 1 problem of parents and students. MATH 42 is the answer to this problem by basically eliminating the need for an expensive tutor. It is always close at hand and accessible thanks to its offline operation. Features • Simple entry of problems including variables, parameters and numbers - as simple as a normal calculator without complicated commands. • Intelligent propositions for answers - shows you how a problem can be solved using different paths organized by methods used. • One touch suffices to get the answer step by step, like with a good math tutor, including the possibility to hide and show specific steps. • The test mode with included problems, organized by methods used and difficulty as well as an indicator of progress. Unsolved problems are calculated and explained step by step. • Detailed explanations for every step and term. • Help adapted to context. • Intelligent plotting function - Zeros, maximums, minimums, turning points, asymptotes and areas of definitions of functions are displayed. • Innovative calculator - processes variables and numbers in an expression and displays its calculations step by step in a comprehensive simple way. • Sharing function - Problems and step by step answers can be posted on Facebook or sent by eMail for a receiver to import onto his MATH 42 with just one click. • Automatically saves all problems. • MATH 42 works without templates or preformed answers. • The problem at hand is solved on-the-spot, like a real math tutor. • MATH 42 is an algebraic system that works symbolically • MATH 42 uses artificial intelligence (intelligent propositions and answers...) • MATH 42 does not require a internet connection. It operates completely offline. • The entire intelligence behind MATH 42 is included within the program. About us Many of the ideas behind MATH 42 were inspired by the chess computer Mephisto (chess computer world champion) and the patents for learning devices ( "Learning Heating", "Intelligent Switch") of Thomas Nitsche.
I am in a biological field (medicine) but I have genuine passion for mathematics. I want to learn it on my own , in my spare time. Mathematics , as I gather, is learned best when you have grasped the prerequisite concepts for the area you are currently interested in. Kindly suggest a sequence of study for the following areas ... 1) Algebra 2) Calculus 3) Discrete math 4) Geometry 5) Probability and statistics 6) Mathematics Software Packages (which one do you suggest for primarily educational, nonprofessional use) 6) Any other areas of fundamental importance that I may have missed 5 Answers I'm unclear what you mean by "Algebra"; if you mean stuff like working with polynomials, basic equations, symbolic manipulation, etc., then that goes first. If you mean "abstract algebra", then you can wait. Added. Likewise: if by "geometry" you mean classical geometry, or even projective geometry, then the following applies. Calculus, Discrete Mathematics, and Geometry, are independent enough that their order doesn't matter. Added. However, if by "geometry" you mean analytic geometry, then it should definitely precede calculus, and the same is true if it means trigonometry. I think it unlikely that you meant "differential geometry" or "algebraic geometry", but if you did those are very advanced topics that should wait until well after calculus, abstract algebra, and real/complex analysis. For introductory probability and statistics you'll find Discrete Mathematics very useful; for more advanced probability and statistics, Calculus is a must. An "introduction to proofs", which would include some set theory, some basic logic, etc., can be done at the same time as Discrete Mathematics, or immediately after. After all this, then you can hit linear algebra, abstract algebra, real or complex analysis, in pretty much any order (though complex analysis should follow real). Abstract algebra is a bit easier if you've taken linear algebra, but this is not strictly necessary. If you happen to find probability and statistics very interesting, then you should do some measure theory after the real analysis. Similar to what you wrote about "algebra", the statement "calculus, discrete mathematics, and geometry, are independent enough" really depends on what the OP meant by geometry. Classical euclidean geometry? I agree. Analytical and differential geometry? I think those are rather deeply connected with calculus. Metric geometry? That often uses quite a bit of tools from discrete mathematics. – Willie Wong♦Feb 14 '11 at 0:22 Any duplicates on a line means that you can learn them simultaneously! I would assume that you would cover some calculus rigorously in analysis and also touch upon some set theory, and of course, learn the fundamentals of "proofs." You'll find a math software package takes a while to get used to (esp if you don't have a programming background). So starting with one right away is a good idea. Octave is a free version of MATLAB. Be warned: Octave can be painful to use at times. MATLAB is the Cadillac. Also if you're doing proof-based study, you'll find a lot of calculus and algebra (at least as it appears to me at the moment) is mostly orthogonal. That is, the Fundamental Theorem of Calculus won't really help you to prove the Triangle inequality. But how to prove and your way of thinking should be exercised by proving in either topic. I think I can recommend some books on algebra, such as the book An introduction to field theory by Iain.T.Adamson or the book Galois Theory by Joseph Rotman of which I think as pretty suitable for beginners. As for further study, I am wondering if you are interested in algebraic number theory or other ones(As Gauss once said, Mathematics is the king of science and Number Theory is the queen of Mathematics). As Jurgen Neukirch said, Number theory is Geometry, you might firstly be familiar with analysis or geometry to study Numbers. Of course you might not be interested in numbers, nonetheless, if you do, get the book by Hilbert whenever you can fully understand it. As for calculus, the books by Richard Courant is absolutely good and worth studying.
What I recommend is you going to the nearest college bookstore, and looking at Schaum's Outline Series, Calculus (there are several titles, my favorite is Calculus of Scientists and Engineers). Take a look, they are excellent with solved problems, and other problems with answers given. BarnesNoble also has these in stock. Algebra 1 - Hello! :-) Can some please explain to me or provide a website that ... Math - Hello! Please help me out here. How do you find the circumference of ... English - 1. Hello. May I speak to Tom? Speaking. Who's this? Hi,Tom. This is ... social studies - I know that their are many ways to say hello in japanese, but ... Grade 12 Calculus University - Hello ^___^ Please help me! Thank you very very ... English - Hello. Will you help me with one more sentence please? Is the sentence... Calculus - what is the derivative of: y=2sinxcosx Calculus Please Help - Hello I'm reposting this question because right now it's ... Calculus 3 - Hello, Please help!! Show that the parabola y=ax^2 has its largest ... Chemistry :( - hello, i would be glad if someone answer to my question fast ...

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