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El Cerrito Statistics, it is intended for math majors. I got "A" in that course. My instructor was a visiting scholar and taught more theorems than other Linear Algebra sections |
Complex Analysis through Examples and Exercises
December 30, 2013 - 01:10 — Anonymous
Author(s):
Endre Pap
Publisher:
Kluwer Academic Publishers
Year:
1999
ISBN:
0-7923-5787-6
Short description:
The book consists of eleven chapters which cover basic concepts, methods and techniques of Complex Analysis through theory and problem-solving. Emphasis is given to both examples and exercises which enlighten the theory.
MSC main category:
30 Functions of a complex variable
Review:
The book provides a brief presentation of theory of the fundamentals of complex valued functions of a complex variable, together with several worked in detail examples and exercises. Emphasis is given to the understanding of properties of complex numbers, convergence of sequences and series, general properties of complex functions, conformal mappings, computational techniques of integrals, the power series representation of analytic functions, isolated singularities, Laurent series, residues, analytic continuation and integral transforms.
The book will be particularly useful to undergraduate students and beginning graduate students of both pure and applied Mathematics departments and engineering schools. The author has succeeded to provide a large collection of examples and problems with step-by-step solutions, computations and proofs.
Overall, the book is recommended for class use, as well as a supplement of standard textbooks.
Reviewer:
Themistocles M. Rassias
Affiliation:
National Technical University of Athens
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Credit only applies in mathematics education. A historical development of mathematics from primitive origins to the Twentieth Century concentrating on numeration systems, arithmetic methods. Euclidean and non-Euclidean geometries, number theory, theory of equations, and the origins of Calculus. |
Boost your students understanding of Saxon Math with DIVE's easy-to-understand lectures! Each lesson concept in SaxonMath 7/6 covers fractions, decimals, percent conversions and unit multipliers, as well as circumference, pi, angles, graphing, and prime factors. For use with 4th Edition.
System Requirements:
Mac OS 10.3.9-10.4.x
Windows 98, 2000, ME, XP, Vista, 8
Quicktime Download Required
Average Customer Rating:
4.7
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5
(10 Reviews) 10
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5 stars
7 Saxon Math 76 4th Edition DIVE CD-Rom
Review 1 for Saxon Math 76 4th Edition DIVE CD-Rom
Overall Rating:
4out of5
The DIVE CD-ROM is helpful.
Date:September 21, 2012
Jo Rotz
Location:Longview, WA
Age:35-44
Gender:female
Quality:
4out of5
Value:
3out of5
Meets Expectations:
4out of5
The CD-ROM has been great for going over new concepts in a clear and precise way. The student can re-watch it if they don't quit understand the first time through. I have even watched it with her when she was getting into things that I don't remember how to do.
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Review 2 for Saxon Math 76 4th Edition DIVE CD-Rom
Overall Rating:
4out of5
Date:October 7, 2011
suzanna
Quality:
4out of5
Value:
4out of5
Meets Expectations:
3out of5
just a few minor gaps in what is taught on the cd versus what is covered in the "new concept" part of lesson, and I wish there was more written out for the student to copy, such as note headings, etc.
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Review 3 for Saxon Math 76 4th Edition DIVE CD-Rom
Overall Rating:
5out of5
Date:September 13, 2010
Brandy Graziosi
The DIVE cd is easy to use and really help to cover the material for those visual and audio learners. My sons grades have impoved sense we started with Saxon Math 7/6. We are already at lesson 22.
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Review 4 for Saxon Math 76 4th Edition DIVE CD-Rom
Overall Rating:
5out of5
Date:August 27, 2010
Rachel Sanchez
We have just begun to use this cd. But already i know that we made the right decision to buy this. It is very user friendly and it is like having your own teacher. Plus you can rewind anytime. We love that the teacher is christian. This is a great investment.
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Review 5 for Saxon Math 76 4th Edition DIVE CD-Rom
Overall Rating:
5out of5
Date:May 11, 2010
Shannon Heynen
I am a homeschool student who didn't enjoy math at all until my mom bought me the D.I.V.E. CD-rom for Saxon math. Before I had the CD math would take me forever and I felt like I wasn't learning anything. With the CD the teacher explains the problems clearly and if I still don't understand I can rewind and listen again. I finish my math in half the time and I feel like I am understanding.
DIVE into Math is the most wonderful addition to the Saxon Math program. We have used DIVE with Dr. David Shoreman now through to Algebra 1/2.
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Review 7 for Saxon Math 76 4th Edition DIVE CD-Rom
Overall Rating:
5out of5
Date:April 22, 2008
Ari
I like the Dive CDs with the Saxon Math because the Dive Cd is fostering a transition of independent learning in my son. Also, I like the Christian comments that remind the student to work hard and appreciate the tools that they have to use for learning...(for reason that attitude is a part of ability to learn). My son is up to lesson 26 and only on the ratios lesson did I feel the Dive explaination left something that I needed to add. I recommend the Dive Cd...it sets tone and understanding for my son to then study the book and examples before going on to do the lessons that follow.
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Review 8 for Saxon Math 76 4th Edition DIVE CD-Rom
Overall Rating:
4out of5
Date:January 24, 2008
Jacquelyn Rauch
Careful visual explanations are simply delivered in an easy to use format. The student can review easily and stop where they need for working the problems. A great addition to Saxon math and a good change for those who have been reading from the text. An occasional short story with application would further create interest and life application.
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Review 9 for Saxon Math 76 4th Edition DIVE CD-Rom
Overall Rating:
5out of5
Date:January 21, 2008
Momto6
These DIVE CDs have completely changed our kids math learning experience. They look forward to doing their math and often want that to be the 1st subject of the day. An instructor walks through every lesson with them. The system also encourages them to pause the CD after the lesson. At that time they work through practice problems and check them by listening to the next section of the CD as the instructor works through the practice problems. Great program! I can't recommend it enough!
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Review 10 for Saxon Math 76 4th Edition DIVE CD-Rom
Overall Rating:
5out of5
Date:December 19, 2007
homeschool teacher of 2
Excellent tool for teaching the Saxon math course. Very clear explanations. The subject is covered very adequately without being overly long. |
What is Mathematica?
Mathematica is the world's most powerful global computing environment. Ideal for use in engineering, mathematics, finance, physics, chemistry, biology, and a wide range of other fields, it makes possible a new level of automation in algorithmic computation, interactive manipulation, and dynamic presentation--as well as a whole new way of interacting with the world of data. Getting Mathematica... Mathematica is currently installed in the following locations:
Students' personally-owned machines: Students can access Mathematica through the UNCP VCL or via a forthcoming download link behind BraveWeb.
Are you interested in putting Mathematica elsewhere? Please let DoIT know at helpdesk@uncp.edu.
What are the best steps to start using Mathematica?
If you are brand-new to Mathematica, below are some suggestions on the best ways to get started. |
Real Analysis I
This course is designed to introduce you to the rigorous examination of the real number system and the foundations of calculus of functions of a single real variable. Analysis lies at the heart of the trinity of higher mathematics – algebra, analysis, and topology – because it is where the other two fields meet.
In calculus, you learned to find limits, and you used these limits to give a rigorous justification for ideas of rate of change and areas under curves. Many of the results that you learned or derived were intuitive – in many cases you could draw a picture of the situation and immediately "see" whether or not the result was true. This intuition, however, can sometimes be misleading.
In the first place, your ability to find limits of real-valued functions on the real line was based on certain properties of the underlying field on which undergraduate calculus is founded: the real numbers. Things may have become slightly more complicated when you began to work in other spaces. For instance, you may remember from multivariable calculus (calculus in three or more real variables) that for some functions there were points where some directional derivatives existed and others did not. In fact, there exist other more exotic spaces where other complications arise.
In the second place, the techniques that you used to find limits may have been very informal. In this course, you will learn to rigorously justify every step in the limiting process or proof. Learning to do this well in the familiar context of the real line, will prepare you for wilder, more complicated mathematical situations. After a brief review of set theory, you will dive into the analysis of sequences, upon which all analysis of Euclidean space (and any separable metric space) is based.
Welcome to MA241: Real Analysis I. General information about this course and its requirements can be found below. In many ways, this course is the true gateway into the mathematics major, requiring rigorous proofs, introducing important topological concepts, and laying the groundwork for most of the remaining courses you will take as a math major. The precise mathematical definitions introduced in this course are used by many fields at the graduate level, including Economics, Physics, and Electrical Engineering. As you progress through the material, stop to reflect on each theorem or definition. Look for its motivation behind the introduction of each new concept – remember, these definitions were written by people who wished to use them for a purpose! – and try to work through each proof. Mathematics is not a spectator sport! Taking care at this time to understand the material deeply will pay dividends throughout your study of mathematics.
Course Designer: Clare Wickman
Primary Resources: This course comprises a range of different free, online materials. However, the course makes primary use of the following:
Requirements for Completion: In order to complete this course, you will need to work through each unit and all of its assigned materials.
In order to "pass" this course, you will need to earn a 70% or higher on the final exam. Your score on the exam will be tabulated as soon as you complete it. If you do not pass the exam, you may take it again.
Time Commitment: This course should take you approximately 135 hours to complete. At the beginning of each unit, there is a detailed list of time advisories for each subunit. These estimates factor in the time required to watch each lecture, work through each reading thoughtfully, and complete each assignment. However, this is a very intense course, and it may take some learners much more time than others. Do not be discouraged if you exceed the time estimates! As long as you are gaining mastery of the material, you are completing the course successfully.
Tips/Suggestions: If a lecture stops making sense to you, pause it – this is a luxury you only have in an online course of this nature! – and return to the readings to get up-to-speed on the material. Remember to note down the time at which you paused the lecture, in case your browser times out. Additionally, be sure to attempt to prove most of the theorems and lemmas for yourself before reading the proof given in the text. Also note how carefully each assumption has been chosen. Understanding the difference between necessary and sufficient conditions is essential for good mathematics and for doing well on the Final Exam for this course.
In this unit, we will learn or be reminded of the tools of set theory, which underlie rigorous mathematical proof, before investigating the real numbers as a field. Beginning with the rational numbers, we will construct the real number system, a project which took mathematicians hundreds of years to fully justify. Along the way, we will encounter several fundamental concepts, including the well-ordering principle, the completeness axiom, and the Archimedean property.
We will see the proof of the existence of irrational numbers and learn how to use proof by induction. Finally, we will see proven a number of results about the cardinality of sets.
Instructions: Please read the indicated sections, on pages 1-6. Please note that you will be returning to this resource throughout the course, so you may prefer to save the PDF to your desktop for quick reference.
Instructions: Please watch this lecture, in which Professor Su discusses set and function/relation notation. He also discusses the historical development of the study of analysis and construct (that is, rigorously justify from first principles) the rational numbers read Section 7, "Integers and Rationals," on pages 34-36. Note: The reading for this section focuses on integers and rationals, but one cannot ponder the rational numbers without considering the existence of irrationals. Hence, in the video lectures for this section, the existence of irrationals will be proven. The readings on the irrational numbers come in subunit 1.4 after a few more concepts have been developed. This difference in ordering should not interfere with your understanding of the lectures for this section.
Instructions: Please watch both of these videos. In the first lecture, Professor Su discusses the rational numbers in further detail, defining addition and multiplication, and he will use them to introduce important concepts such as ordering. He proves the existence of irrationals, such as the square root of 2. In the second lecture, Professor Su discusses Dedekind cuts, the least upper bound property of the reals (a.k.a. the completeness property). Feel free to end the lecture at 42:00 (the discussion of Dedekind cuts).
Watching these videos and pausing to take notes should take approximately 2 hours and 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpages above.
Instructions: Please watch this video. Please note that this material covers the topics outlined in sub-subunits 1.4.1 and 1.4.2. In this lecture, Professor Su further discusses Dedekind cuts and the existence of arbitrary real powers of rationals. He goes through the least upper bound property of the reals (a.k.a. the completeness property), the greatest lower bound property, and the Archimedean Property, which he proves. He proves the density of the rationals in the real line. He also gives properties of the supremum. Mastery of these topics is essential to developing a thorough understanding of analysis work through the exercises on page 30 of this PDF. Because this resource is used by some institutions of higher learning for the purposes of assigning grades and credit for classes, complete solutions to the problems are unavailable. However, it is to your benefit to attempt the problems; your solutions should mimic the style of the proofs given in the preceding chapter.
Instructions: Please read Section 1.3, "Absolute Value," on pages 31-34. The most important fact we will encounter in this section, which we will use over and over again in this course and all those which follow, is the triangle inequality.
Instructions: Work through the exercises on page 34 lectures cover the topics outlined in sub-subunits 1.9.1 and 1.9.2 of this course. Please watch each video lecture. Only watch Lecture 8 up to the 51-minute mark.
In "Lecture 7: Countable and Uncountable Sets," Professor Su revisits functions and relations between sets and important concepts such as "one-to-one/injective," "onto/surjective," and "bijective." He defines finite, infinite, countable, and uncountable sets and power sets, and he discusses the cardinality of certain important sets. In "Lecture 8: Cantor Diagonalization and Metric Spaces," Professor Su discusses cardinality and Cantor's diagonalization argument in more detail.
Watching these videos and pausing to take notes should take approximately 2 hours and 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpages above.
Work through the problems on pages 36 and 37In this unit, we will learn about various topological notions and will be introduced to the more abstract notion of a metric space. A metric is a function which takes two points in a certain set and tells how "far apart" they are and which satisfies three special requirements. The metric can be used to define many different properties of the set to which it applies (the metric space). All of the concepts which you learned in calculus, especially limits, can be understood and extended in the context of metric spaces.
Instructions: Please watch the video from the 51-minute mark to the end. In this lecture, Professor Su defines metric spaces and gives examples. He defines open balls and gives examples of open balls in a variety of metrics.
Watching this lecture and pausing to take notes should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpages above.
Instructions: Please watch these lectures. In the first lecture, Professor Su defines limit (cluster) points and goes through many examples. He also defines interior points, open sets, closed sets, and closures. In the second lecture, Professor Su defines what it means for a sequence to converge.
Watching these lectures and pausing to take notes should take approximately 2 hours and 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpages above.
Instructions: Please watch this lecture, in which Professor Su revisits the definition of open and closed sets and some of the subtleties involved in manipulating them. He proves standard results, such as that the closure of a set is closed and that a set is closed if and only if its complement is open. He also investigates unions and intersections of open and closed sets. He defines what it means for one set to be dense in another set.
Watching this lecture and pausing to take notes should take approximately 1 hour and 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpages above.
Instructions: Click on the links above, and watch these lectures. In the first lecture, Professor Su defines compactness from the topological perspective (e.g., the way it is defined in the reading of Zakon's Section 4.7 – every open cover of the set must have a finite subcover). This is because in his course he develops this concept before discussing the convergence of sequences. He also (in essence) defines what it means for a set to be relatively open with respect to another set. He proves that compact sets are bounded in Euclidean space. In the second lecture, Professor Su proves that compact sets are closed in Euclidean space. He proves that nested closed intervals in R have nonempty intersection. He also proves that R is uncountable.
Also, note that Professor Su will touch on sequential compactness in the lecture for sub-subunit 2.3.2. In this lecture and the one that follows, he uses the open-cover definition.
Watching these lecture sand pausing to take notes should take 2 hours and 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpages above.
Instructions: Please watch this lecture, in which Professor Su proves that closed, bounded intervals on the real line are compact. He then proves the Heine-Borel Theorem (this is exercise 10 in section 4.6 of Zakon's book). He states a version of the Bolzano-Weierstrass Theorem (which will be discussed in the reading under sub-subunit 2.3.1 for this course) and the Cantor Finite Intersection Property.
Watching this lecture and pausing to take notes should take 1 hour and 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpages above.
Instructions: Please watch both lectures. Watch "Lecture 16: Subsequences, Cauchy Sequences" from the 30-minute mark to the end; watch all of "Lecture 17: Complete Spaces". In the first lecture, Professor Su defines subsequences and proves several important results about them. Note the definition of sequential compactness at time 43:50. He proves the Bolzano-Weierstrass Theorem. He defines Cauchy sequence and completeness. In the second lecture, Professor Su proves that compact metric spaces are complete. He also proves that Euclidean space is complete. He constructs the completion of a metric space. He discusses bounded sequences and monotonic sequences and proves that bounded, monotonic sequences converge. He defines limit superior and limit inferior and proves several results about them.
Watching these lectures and pausing to take notes should take approximately 1 hour and 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpages above.
Instructions: Please watch these lectures. In the first lecture, Professor Su defines series convergence using partial sums (a.k.a. the Cauchy Criterion). He validates the Comparison Test. He discusses the geometric series. In the second lecture, Professor Su discusses further tests for convergence, along with the definition of absolute convergence. He gives the ratio and root tests. He defines power series. He discusses summation by parts.
Watching these lectures and pausing to take notes should take approximately 2 hours and 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpages above.
Unit 3: Functions and Continuity
In this unit, you will explore the properties of continuous functions. You should be familiar with continuity from calculus; indeed, many of the results which are proven in this unit will be familiar, such as the intermediate value theorem or the fact that the sum of two continuous functions is continuous. However, you will now be proving these results rigorously and with more generality. You will also be learning new concepts, such as uniform continuity, and you will be improving your knowledge of what might be called "mathematical culture" through exposure to famous and much-employed examples, such as the Dirichlet function and the Cantor Ternary set. Learn these examples well; they are used in many cases as counterexamples. Be sure also to note the use of the Triangle Inequality in the proof that the uniform limit of a sequence of continuous functions is itself continuous. This is a standard and well-known technique.
Instructions: Please watch the entire video. In this lecture, Professor Su defines limits and limit points of functions. He defines continuity of a function using neighborhoods and using the sequential criterion. He states several properties of continuous functions, including the fact that the inverse image of an open set (under a continuous function) is open in which Professor Su discusses the definition of continuity at a point. He proves that the inverse image of an open set under a continuous function is open and illustrates this fact with several examples. He proves that the composition of continuous functions is continuous. Finally, he proves that the forward image of a compact set under a continuous function is compact and mentions some important corollaries for real-valued functions. This lecture will cover topics you have learned in sub-subunits 3.1.1-3.1.2.
Watching this lecture and pausing to take notes should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpages above.
Instructions: Please note that this video lecture covers the topics outlined in both sub-subunits 3.1.6 and 3.1.7 of this course. Please watch this lecture, in which Professor Su recaps some basic facts about continuous functions. He defines uniform continuity and relates it to compactness, giving a number of examples. He states and proves the Lebesgue Covering Lemma (this is Theorem 1 in Section 4.7 of Zakon's book). He proves that continuous functions map connected sets to connected sets. Finally, he proves the Intermediate Value Property which reviews material from sub-subunit 3.1.5. In this lecture, Professor Su discusses some famous (or merely standard) examples of discontinuous functions, including the Dirichlet function. He discusses right-hand and left-hand limits of functions. He also discusses monotone functions and why they can only have a finite number of discontinuities.
Watching this lecture and pausing to take notes should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpages above.
Instructions: Please watch this lecture, in which Professor Su states a few more results about compactness and constructs the Cantor ternary set. He defines perfect and connected sets. He proves that nonempty closed intervals are connected play the video from the 36-minute mark to the end. In this lecture, Professor Su discusses sequences of functions and what it means for them to converge either pointwise or uniformly. He gives several classic examples of sequences of functions which converge pointwise to zero. He proves that if a sequence of continuous functions converge uniformly, their limit is continuous.
Watching this lecture and pausing to take notes should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpages above.
Unit 4: Differentiability and Integration
In Calculus you learned the limit definition of the derivative and connected it to a picture of a sequence of secant lines converging to a tangent line. Similarly, you learned how the integral is really the limit of a series of Riemann Sums. In this unit, you will go through the derivations of those concepts in more detail and with more regard for the technicalities. You will connect the derivative and the integral to what you have learned about sequences and series, and you will learn necessary and sufficient conditions for the exchange of limits. Much of this does in fact have important implications for numerical integration and differentiation, so it is important to understand the meaning of each of the conditions in theorems such as the Weierstrass M-Test.
Instructions: Please work through problems 2-7 on page 140 video lectures address topics outlined in sub-subunits 4.1.1 and 4.1.4 of this course. Watch this lecture, in which Professor Su defines the derivative and shows how to derive some of the standard rules of differentiation. He proves the existence of continuous, nowhere-differentiable functions. He states and uses the Mean Value Theorem and the Generalized Mean Value Theorem.
Watching this video and pausing to take notes should take approximately 1 hour and 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpages above.
Instructions: Please note these videos cover the topics outlined in sub-subunits 4.2.1-4.2.3 of this course. Please watch this lecture, in which Professor Feinstein defines characteristic functions and partitions, explains the Riemann integral, and states the fundamental theorem of calculus.
Watching this lecture and pausing to take notes should take approximately 1 hour and 15 minutes the convergence or lack thereof of the derivatives of a sequence of functions. (In Lecture 14, not required by this course, he discussed the convergence of the integrals of a uniformly convergent sequence of functions.) He then introduces series of functions and proves the Weierstrass M-Test, which is the most important result in this lecture. You need not watch the section on the Weierstrass Approximation Theorem, although it is very interesting.
Watching this lecture and pausing to take notes should take approximately 1 hour power series and justifies the various convergence tests (such as the root test and the ratio test). In the second half (which is optional), he proves a result about the derivative of the pointwise limit of a sequence of differentiable functions. He later discusses term-by-term differentiation (which is really an interchange of limits).
Watching this lecture and pausing to take notes should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpages above |
Find an Elwood, IL a science and liberal arts educ...
...Also learning to do proofs is another important lesson for example you see a potential relationship between two things and through induction you prove this is true in all cases instead of just being a coincidental relationship. I like to apply discrete math to real life situations to make it mor... |
Graphs: An Introductory Approach - A First Course in Discrete Mathematics
An introduction to discrete mathematics, this new text on graph theory develops a mathematical framework to interrelate and solve different problems. ...Show synopsisAn introduction to discrete mathematics, this new text on graph theory develops a mathematical framework to interrelate and solve different problems. It introduces the concepts of logic, proof and mathematical problem-solving and places an emphasis on algorithms in every chapter.Hide synopsis
Description:Fair. Book is in good to acceptable condition with minor...Fair. Book is in good to acceptable condition with minor blemishes on the cover. Pages have highlighting and minor writing |
books on numerical pde solving
Can anyone recommend any good up-to-date books or journals on numerically solving PDEs?
I've a lot of experience using finite differences for parabolic pdes, and some knowledge of finite elements, wavelets, sparse grids and hierarchical grids.
I'd like extend my knowledge on this though, keep in touch with any modern developments, and play about with applications in different areas. |
This course may be used to fulfill the mathematics component of the university core curriculum and addresses core objectives established by the Texas Higher Education Coordinating Board: communication skills, critical thinking skills, and empirical and quantitative skills.
Calculus is the theory of things that change, and so is essential for understanding a changing world. Students are expected to use calculus to compute optimal strategies in a variety of settings (Chapter 3, max/min), as well as to apply derivatives to understand changing quantities in physics, economics and biology.
Students improve their number sense through qualitative reasoning and by comparing the results of formulas to those guiding principles.
Student activities include creating logically ordered, clearly written solutions to problems, and communicating with the instructor and their peers during lecture by asking and responding to questions and discussion in lecture.
Prerequisite and degree relevance:The minimum required score on the ALEKS placement exam. Only one of the following may be counted: M403K, M408C, M408K, M408N.
Calculus is offered in two equivalent sequences: a two-semester sequence, M 408C/408D, which is recommended only for students who score at least 600 on the mathematics Level I or IC Test, and a three-semester sequence, M 408K/408L/408M.
For some degrees, the two-semester sequence M 408K/408L satisfies the calculus requirement . This sequence is also a valid prerequisite for some upper-division mathematics courses, including M325K, 427K, 340L, and 362K.
M408C and M408D (or the equivalent sequence M408K, M408L, M408M) are required for mathematics majors, and mathematics majors are required to make grades of C- or better in these courses.
Course description: M408K is one of two first-year calculus courses. It is directed at students in the natural and social sciences and at engineering students. In comparison with M408C, it covers fewer chapters of the text. However, some material is covered in greater depth, and extra time is devoted the development of skills in algebra and problem solving. This is not a course in the theory of calculus.
The syllabus for M 408K includes most of the basic topics in the theory of functions of a real variable: algebraic, trigonometric, logarithmic and exponential functions and their limits, continuity, derivatives, maxima and minima, as well as definite integrals and the Fundamental Theorem of Calculus.
Overview and Course Goals
The following pages comprise the syllabus for M 408K, and advice on teaching it. Calculus is a service course, and the material in it was chosen after interdepartmental discussions. Please do not make drastic changes (for example, skipping techniques of integration). You will do your students a disservice and leave them ill equipped for subsequent courses.
This is not a course in the theory of calculus; the majority of the proofs in the text should not be covered in class. At the other extreme, some of our brightest math majors found their first passion in calculus; one ought not to bore them. Remember that 408K/L/M is the sequence designed for students who may not have taken calculus previously. Students who have seen calculus and have done well might be better placed in the faster M 408C/408D sequence.
Resources for Students
Many students find the study skills from high school are not sufficient for UT. The Sanger Learning Center ( in Jester has a wide variety of material ( drills, video-taped lectures, computer programs, counseling, math anxiety workshops, algebra and trig review, calculus review) as well as tutoring options, all designed to help students through calculus. On request they will come to your classroom and explain their services.
You can help your students by informing them of these services.
Timing and Optional Sections
A typical fall semester has 42 hours of lecture, 42 MWF and 28 TTh days, while the spring has 45 hours, 45 MWF and 30 TTh days (here, by one hour we mean 50 minutes -- thus in both cases there are three "hours" of lecture time per week). The syllabus contains suggestions as to timing, and includes approximately 35 hours. Even after including time for exams, etc., there will be some time for the optional topics, reviews, and/or additional depth in some areas. |
This book demonstrates current trends in research on combinatorial and computational commutative algebra with a primary emphasis on topics related to monomial ideals. Providing a useful and quick introduction to areas of research spanning these fields, Monomial Ideals is split into three parts. Part I offers a quick introduction to the modern theory... more...
This work is a concise introduction to spectral theory of Hilbert space operators. Its emphasis is on recent aspects of theory and detailed proofs, with the primary goal of offering a modern introductory textbook for a first graduate course in the subject. The coverage of topics is thorough, as the book explores various delicate points and hidden features... more...
500 Ways to Achieve Your Best Grades
We want you to succeed on your college linear algebra midterm and final exams. That's why we've selected these 500 questions to help you study more effectively, use your preparation time wisely, and get your best grades. These questions and answers are similar to the ones you'll find
on a typical college... more...
Traditionally, Lie Theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrisation of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry which is very helpful in understanding its structure. Geometrisation and symmetries... more...
An advanced Practice Makes Perfect workbook for linear algebra, designed to reinforce ideas and concepts, to provide 500 exercises and answers, to offer hundreds of solved problems--making this workbook the ideal complement to class study or self-study. more... |
...Precalculus is an extension of algebra 2. It covers some of the same topics (in slightly more detail and difficulty), while also exploring many interesting new topics that will be applied in calculus. It can also include trigonometry |
Elementary Algebra
9780495105718
ISBN:
0495105716
Pub Date: 2006 Publisher: Thomson Learning
Summary: Kaufmann and Schwitters have built this text's reputation on clear and concise exposition, numerous examples, and plentiful problem sets. This traditional text consistently reinforces the following common thread: learn a skill; use the skill to help solve equations; and then apply what you have learned to solve application problems. This simple, straightforward approach has helped many students grasp and apply fundam...ental problem solving skills necessary for future mathematics courses in an easy-to-read format. The Eighth Edition of ELEMENTARY ALGEBRA includes new and updated problems, revised content based on reviewer feedback and a new function in iLrn. This enhanced iLrn homework functionality was designed specifically for Kaufmann/Schwitters' users. Textbook-specific practice problems have been added to iLrn to provide additional, algorithmically-generated practice problems, along with useful support and assistance to solve the problems for students.
Kaufmann, Jerome E. is the author of Elementary Algebra, published 2006 under ISBN 9780495105718 and 0495105716. Thirty three Elementary Algebra textbooks are available for sale on ValoreBooks.com, eleven used from the cheapest price of $4.95, or buy new starting at $67.16An unread copy that is in excellent condition! Clean crisp pages. Square binding. Minor shelf wear. No dust jacket. Includes sealed Access Code & Interactive Video CD. Get it fast! DOMESTIC & INTERNATIONAL EXPEDITED SHIPPING is available for this item.Same or next Postal business day shipping. All orders securely packaged. Domestic orders include USPS Tracking[less] |
Autograph Activities: Student Investigations for 16-19
Av C N Barton
288 sidor plus CD-ROM, 585 kr (exkl. moms och frakt)
Autograph Activities: Students Investigations for 16-19 Autograph is an excellent tool for investigation, and mathematics is at its strongest and most appealing when students can embark upon such journeys of self-discovery. The ten activities are designed to allow students to fully utilise Autograph's power to explore, investigate and ultimately understand concepts at a depth which the normal classroom setting would not allow.
Students are equipped with the tools to learn and then encouraged to set off alone on their epic quest for answers. |
First Course in Mathematical Modeling
9780495011590
ISBN:
0495011592
Edition: 4 Pub Date: 2008 Publisher: Cengage Learning
Summary: Offering a solid introduction to the entire modeling process, A FIRST COURSE IN MATHEMATICAL MODELING, 4th Edition delivers an excellent balance of theory and practice, and gives you relevant, hands-on experience developing and sharpening your modeling skills. Throughout, the book emphasizes key facets of modeling, including creative and empirical model construction, model analysis, and model research, and provides m...yriad opportunities for practice. The authors apply a proven six-step problem-solving process to enhance your problem-solving capabilities -- whatever your level. In addition, rather than simply emphasizing the calculation step, the authors first help you learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving you in the mathematical process as early as possible -- beginning with short projects -- this text facilitates your progressive development and confidence in mathematics and modeling.
Giordano is the author of First Course in Mathematical Modeling, published 2008 under ISBN 9780495011590 and 0495011592. Four hundred fourteen First Course in Mathematical Modeling textbooks are available for sale on ValoreBooks.com, one hundred fifty three used from the cheapest price of $35.85, or buy new starting at $226 within U.S. will arrive in 3-5 days. Hassle free 14 day return policy. Contact Customer Service for questions.[less] |
Brian Wynne = (awesome)^n
A calculus syllabus is a calculus syllabus is a calculus syllabus. No matter where it's taught, in the end the material is the same. Because of that, math classes tend to be defined by the professor.
Enter Brian Wynne—a young, nearly fresh-out-of-graduate-school doctor of mathematics who sports a kind of nerdy approachableness. He is the type of instructor who says things like, "The good times are rolling!" when a student shares her understanding of differential equations out loud; or: "This isn't rocket science! Well, actually, it is rocket science, but it's not that hard."
Wynne is the kind of professor who has fun teaching and talking math. And it's contagious. A group of former students, for instance, decided to pay homage to him by publishing a Facebook fan page titled "Brian Wynne=(awesome)^n." If you don't get the joke, you haven't taken a math class with him yet.
His humor and general playfulness is part fun and part strategy. Math can be heavy, which is why Wynne keeps the atmosphere light, informal--joyful, even. If the mood is strategically playful, the instruction itself is intentionally methodic.
Wynne first introduces a new idea and technique. Today, it's differential equations. "A differential equation is an equation involving the derivatives of a function. They are of great importance in the sciences, where they are used to describe how physical systems change over time," he explains. "Today we'll see how the calculus we've learned this semester can be used to analyze differential equations."
Next, he talks about real world applications. Some examples: It can be a good model for population growth, or predicting bacteria growth in a lab.
Then, he works on problems. He tries to keep the tasks manageable, even when the math sprawls in a way that can intimidate some of the most gifted math students in class. Knee deep into differentiating, Wynne stops before he tackles the second part of the equation with the class. "OK, now what you have to do here is steel yourself." A student asks what that means. "It means you need to prepare, to become strong." |
Textbooks
A survey of the use of mathematics in the modern world. Topics include: theory of elections, apportionment, and fair division; use of graphs to solve the postman problem, the traveling salesman problem, minimum cost networks problems, and scheduling problems; and introduction to statistics
Each student will need to have a calculator available for some of the material of the course.A four-function calculator with a square root (/) key will suffice.
Each student must purchase an access key to MyLab/Mastering, a course presentation system provided by Pearson Publishing Company. The key may be purchased through the campus bookstore, or directly at pearsonmylabandmastering.com. The homework assignments will be done online, although quizzes and unit tests will be done in class.
The access key provides access to an electronic version of the text. Students may wish to purchase a hard copy too.
To enroll in the on-line course use the course code tucker22384 and the zip code 76308
The course is broken up into three units, each consisting of four chapters from the text. They are:
Unit 1 Social Choice Chapters 1 through 4
Unit 2 Management Science Chapters 5 through 8
Unit 3 Statistics Chapters 14 through 17
Graded work in each unit consists of homework sets and a quiz for each chapter of the unit, followed by a unit test over the entire unit (all four chapters). Homework assignments should be completed before taking the chapter quiz. However, students may redo homework problems after taking quizzes or tests to improve homework grades. All homework assignments must be completed no later than the day of the final exam.
Grading Standards
Each unit will be weighted equally in the final grade
There are three graded components to the course:
Component Weight
Homework 10%
Quizzes 15%
Unit tests 75%
All chapter homework assignments will be used to determine the homework score, but only the highest three quizzes out of the four in each unit will be used to determine the over-all quiz score.
The following grade scale will be used to determine the final grade for the course
Percentage Grade
90 - 100% A
80 - 89% B
70 - 79% C
60 - 69% D
0 - 59% F
Final Exam
5/7/2014 10:30 am to 12:30 pm
Submission Format Policy
All homework is done on MyLab/Mastering on the web.
Quizzes will be answered on the paper provided by the instructor.
Unit tests will be multiple choice and each student must provide a long Scantron form for each test, and use a pencil to fill out the form. Any changes must be made by erasing the incorrect answer neatly and completelyStudents should finish each homework assignment by the homework due date listed on the syllabus given below.
Homework
Homework
Day
Date
Chapter
Due Date
Day
Date
Chapter
Due Date
Mon
13-Jan
1
Mon
10-Mar
7
Wed
15-Jan
1
Wed
12-Mar
8
Chapter 7
Fri
17-Jan
1
Fri
14-Mar
8
Mon
20-Jan
MLK Day No Class
Mon
24-Mar
8
Wed
22-Jan
1
Wed
26-Mar
14
Chapter 8
Fri
24-Jan
2
Chapter 1
Fri
28-Mar
Unit Test 2
Mon
27-Jan
2
Mon
31-Mar
14
Wed
29-Jan
2
Wed
2-Apr
14
Fri
31-Jan
3
Chapter 2
Fri
4-Apr
14
Mon
3-Feb
3
Mon
7-Apr
15
Chapter 14
Wed
5-Feb
3
Wed
9-Apr
15
Fri
7-Feb
4
Chapter 3
Fri
11-Apr
15
Mon
10-Feb
4
Mon
14-Apr
15
Wed
12-Feb
4
Wed
16-Apr
16
Chapter 15
Fri
14-Feb
5
Chapter 4
Fri
18-Apr
16
Mon
17-Feb
Unit 1 Test
Mon
21-Apr
16
Wed
19-Feb
5
Wed
23-Apr
16
Fri
21-Feb
5
Fri
25-Apr
17
Chapter 16
Mon
24-Feb
5
Mon
28-Apr
17
Wed
26-Feb
6
Chapter 5
Wed
30-Apr
17
Fri
28-Feb
6
Fri
2-May
17
Chapter 17
Mon
3-Mar
6
Wed
5-Mar
7
Chapter 6
Wed
7-May
Final Exam
Fri
7-Mar
7
10:30 - 12:30 Unit 3 Test2012-2014 Midwestern State University Undergraduate Catalog (page 71)
Class Attendance. "Students are expected to attend all meetings of the classes in which they are enrolled... A student with excessive absences may be dropped from the course by the instructor." (Read the intervening part in the MSU Undergraduate Catalog, Volume LXXIX, Number 1, 2012-2014).
Note: If a justifiable or authorized absence should occur, it is the responsibility of the student to make up all work missed. If a student misses a scheduled exam, he/she must be prepared to take the test immediately upon returning to class, or else no makeup will be given and the grade on the exam will be a zero. If a student knows in advance that he/she will miss an exam, every effort should be made to notify the instructor of this situation prior to the exam. An "absence" is defined as not being physically present in the classroom for the entire period. A student who comes in late or leaves early may be counted absent for the class period.
"EXCESSIVE ABSENCES" will be defined as FOUR (4) OR MORE UNJUSTIFIABLE ABSENCES.
Other Policies
Electronic Communication During Class: Students may not use cell phones, computers, ipads, tablets or other electronic devices to communicate with other individuals inside or outside of the classroom.
Any student found using any device other than a calculator during a test will be considered to be cheating, and will be subject to receiving a zero on the assignment. Cell phones are not acceptable for calculators on exams.
Students may use cell phones or cameras to copy material on the board, but electronic communication during class is not permitted.
Students may use personal computers to take notes during class, but again, communication with other people, surfing the web, playing games, or working on assignments for other classes is not permitted during this class. At the teacher's sole discretion, a device capable of electronic communication may be confiscated for the remainder of the class period.
Entering the class late or leaving the class early is a disturbance to the other students and to the teacher. Each student is expected to treat the other students and the teacher with respect. Any student who is being disruptive to the class may be asked to leave the classroom and will be counted absent for that day |
Math 101: Beginning Algebra
Applications of linear functions, quadratic functions and linear systems to problems. Emphasis on the development of models of real world applications and interpretation of their characteristics. Use of technology will be an important aspect of this course. |
Dosage calculation and basic conversion is very important for nurses to know because a serious damage or even death can occur...
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Dosage calculation and basic conversion is very important for nurses to know because a serious damage or even death can occur if a wrong dose of medication is given. This web site shows you a variety of common medication calculations, practices, and quizzes.
Mathway is a mathematics problem solving tool where students can select their math course - Basic Math, Pre-Algebra, Algebra,...
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Mathway is a mathematics problem solving tool where students can select their math course - Basic Math, Pre-Algebra, Algebra, Trigonometry, PreCalculus, Calculus or Statistics and enter a problem. The computer solves the problem and shows the steps for the solution. It also has a worksheet generator.
math911 contains step by step tutorials in Introductory Algebra, Intermediate Algebra, PreCalculus and Introductory...
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math911 contains step by step tutorials in Introductory Algebra, Intermediate Algebra, PreCalculus and Introductory Statistics. The given link is to the setup file. After setup, you should see a math911 icon on the desktop. Click on the icon to run math911. Vista, Windows 7, Windows 8 users might need to right click and in the drop down list select 'Run As Administrator.'To set up a grade report file you will be asked to enter your name, birth date (or any other date) and select a course.A grade report file will be created (FLmmdd.mdb where F=first initial, L=last initial, mmdd= month and date). Grades are saved AUTOMATICALLY to this file..Select a chapter, then a lesson and a problem will appear.For a tutorial: You can step through the solution (click See Solution, See All Steps, See Next Step, etc.)To answer: Type the answer and press ENTER Only correct answers count. Wrong answers are ignored !If your answer is incorrect: Click on See All Steps, See Next Step, etc.Use the up/down arrows to enter exponents and move between the numerator and denominator of a fraction. There are up to 8 levels for each lesson and all the types of problems for you to master AlgebraIMPORTANT. math911 is activated for Introductory Algebra. For full activation to other courses, RIGHT click on the ABOUT button and enter the code: essex.Once fully activated you can switch back and forth to the other courses.Math911 is continuously updated. For technical help please call Professor Martin Weissman 347-528-7837
'Brain Teaser measures the ability to differentiate, to analyze, to reason out, and to apply knowledge. It is one of the best...
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'Brain Teaser measures the ability to differentiate, to analyze, to reason out, and to apply knowledge. It is one of the best ways to engage yourself as well as to check your intelligence.This version fixes all the issues reported by some users for previous version. We have tested each question / answer set for accuracy.HOW TO USE THIS APP ?=====================- To start, select the number of questions you want in the current session. - All the questions are in simple language. In each case 4 answers are given, and what you have to do is simply choose the right answer. - There is only one correct answer to each question. - Answer the current question to proceed to next question.SCORING / HIGH SCORE====================- The more you answer correctly more you will gain points.- You need to score at least 50% to get a chance in the High Score charts.- Keep track of your progress or compete with your friendsBENEFITS OF BRAIN TEASER=========================- Children can take this test for preparing aptitude test.- giving your brain a good exercise while you spend time in commute or a boring lecture ;)- fun to challenge your friends to beat your high score.- NO blinking ads means you can focus on the questions better.★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★This is not just a game but a POWERFUL tool to practice, learn and develop MATHS and LOGIC skills.While anyone can attempt to play this game BUT if you are looking for a real tough set of questions which are actually asked in the Competitive examinations, then this app is a must have for you.'This app costs $0.99 |
This review is from: Basic Math and Pre-Algebra For Dummies Education Bundle (Paperback)
A pair of books which complement each other well. The chapters in each book mesh into each other well and its easy to plot a path whereby you tackle the chapter in the main book and then complete the relevant exercises in the workbook. I also found on a number of occasions that the explanation given in the workbook helped to further illustrate a point made in the main book i.e. reading an explanation of a concept for the second time in a slightly different set of words helped.
I think the approach taken is better suited for self-learning adults rather than children below 16 years.
As a bundle together this would qualify as a 5 star but for one problem which is the small print used to represent symbols such as the equals and division symbols or fractions. It is very small. My eyes are OK but I often found myself misinterpreting an equals symbol for a division symbol and vice-versa.
I did wonder if the two books could have just as easily been merged into one but at the available price its very good value.
This review is from: Basic Math and Pre-Algebra For Dummies Education Bundle (Paperback)
Just bought these two books as a combined sale. Had a quick look thru them today and they both look totally superb. And the authour has done an excellent job in making something which can seem formidable to many people be easily within their grasp. |
This package consists of the textbook plus an access kit for MyMathLab/MyStatLab.
Mathematical Ideas captures the interest of non-majors who take the Liberal Arts Math course by showing how mathematics plays an important role in scenes from popular movies and television. By incorporating John Hornsby's "Math Goes to Hollywood" approach into chapter openers, margin notes, examples, exercises, and resources, this text makes it easy to weave this engaging theme into your course.
The Twelfth Edition continues to deliver the superlative writing style, carefully developed examples, and extensive exercise sets that instructors have come to expect. MyMathLab continues to evolve with each new edition, offering expanded online exercise sets, improved instructor resources, and new section-level videos.
MyMathLab provides a wide range of homework, tutorial, and assessment tools that make it easy to manage your course online.
Editorial Reviews
Booknews
A textbook designed with a variety of students in mind and suited for several types of courses, including mathematics for liberal arts students, survey courses in mathematics, and mathematics for prospective and in-service elementary and middle-school teachers. Some 80% of the exercises are new to this edition, which also sports extensive use of color and changes in format to create a fresh look. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Related Subjects
Meet the Author
Charles Miller has taught at America River College for many years.
Vern Heeren received his bachelor's degree from Occidental College and his master's degree from the University of California, Davis, both in mathematics. He is a retired professor of mathematics from American River College where he was active in all aspects of mathematics education and curriculum development for thirty-eight years. Teaming with Charles D. Miller in 1969 to write Mathematical Ideas, the pair later collaborated on Mathematics: An Everyday Experience; John Hornsby joined as co-author of Mathematical Ideas on the later six editions. Vern enjoys the support of his wife, three sons, three daughters in-law, and eight grandchildren.
John Hornsby: When a young John Hornsby enrolled in Lousiana State University, he was uncertain whether he wanted to study mathematics education or journalism. Ultimately, he decided to become a teacher. After twenty five years in high school and university classrooms, each of his goals has been realized. His passion for teaching and mathematics manifests itself in his dedicated work with students and teachers, while his penchant for writing has, for twenty five years, been exercised in the writing of mathematics textbooks. Devotion to his family (wife Gwen and sons Chris, Jack, and Josh), numismatics (the study of coins) and record collecting keep him busy when he is not involved in teaching or writing. He is also an avid fan of baseball and music of the 1960's. Instructors, students, and the 'general public' are raving about his recent Math Goes to Hollywood presentationswantmyboook
Posted June 12, 2010
I wish I had my book. I am still waiting for a response, a reply a book something from someone to let me know what is going on.
ordered book May 19,order# 134009217,from frtextbooks. still have not received the book sent email on 5/28 to frtextbooks, still havent received a reply. Reported it to b&n on 3 seperate occassions and still no reply or book. Extreme unprofessional service the book is ok, looked at a classmates, too bad I cant look at the one I paid for almost a month ago. I was told the book would be considered late on June 14. Per the invoice it was shipped on May 19. Guidelines state it should be shipped within 2 business days, well we are certainly past that. I have spoken with great reps at b&n, but that does not provide me with a book. Can someone email me and let me know WHERE IS MY BOOK? My class ends on July 26, so I guess I will get it on July 27 with a fake apology/lie it was lost in the mail. I deplore unprofessional business & service and that is what I am receiving. Barnes and Nobles this seller dropped the ball and by their ratings I am the 3rd customer to experience this. Please do something about sellers that disregard customers without dignifying them with a basic response "we mailed it on_______ date"
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Anonymous
Posted June 6, 2008
A reviewer
If this book is purchased with all its accompanying material it is sure to prepare students for employment in the data analyst field.
Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged. |
MA 0060 - Basic Mathematics I
Course Description
This course is an individualized program of study which covers a review of reading, writing and rounding of whole numbers, if required, as well as whole number multiplication and division. Problem-solving is emphasized throughout, and squares, square roots, and the order of operations are introduced. |
Enter any double integral function and this widget will calculate the answer. It does just what it says on the tin. So if you have homework that you need to double check, then look no further.
The widget tool is taken from the selection of tools that appears on my live worksheet app entitled Curve Sketching Multiple Integration, that appears on my wolfram alpha developer page.
Hope it proves helpfulThis app shows a table of derivative formulae, a table of integral formulae and a list of links to online derivative and integral calculators that can be opened in your android browser or another standard browser research and education.
The Wolfram Multivariable CalculusThe Wolfram General Chemistry Course Assistant is powered by the Wolfram|Alpha computational knowledge engine and is created by Wolfram Research, makers of Mathematica—the world's leading software system for mathematical research and education.
The Wolfram General ChemistryDo you need an astronomy tool that does more than just show you pictures? Something that will actually help you with your school work? The Wolfram Astronomy Course Assistant provides a suite of useful tools for helping you in your introductory computational astronomy course. From fact checking to formulas, this app provides a convenient resource to help you complete your homework and study for tests. Answers are computed on the fly using input values you specify.
This app covers the following topics, applicable to college-level Astronomy 120 or any other introductory computational astronomy course:
- Get an overview of constellations, including the effects of proper motion - Learn the celestial reference points and their location in your sky - Explore solar system objects, properties, and dynamics - Study Moon phases, eclipses, and tides - Examine properties of over 100,000 stars, including distance, parallax, luminosity, and position on the Hertzsprung–Russell diagram - Learn about the seasons and when meteor showers occur - Access formulas such as Newton's and Kepler's laws, escape velocity, moments of inertia, angular momentum, and Einstein's famous E=mc^2 - Convert between wavelength and frequency, or find the energy of a photon - Understand the cosmological effects of universal expansion on light and the gravitational effects of black holes - Determine the probability of intelligent life on other worlds
The Wolfram Astronomy Course Assistant is powered by the Wolfram|Alpha computational knowledge engine and is created by Wolfram Research, makers of Mathematica—the world's leading software system for mathematical research and education.
The Wolfram Astronomy Course Assistant draws on the computational power of Wolfram|Alpha's supercomputers over a 2G, 3G, 4G, or Wi-Fi connection.
Having trouble memorizing trig formulas, integration, and derivatives? This is the app for you! This application is a great tool for anybody who uses calculus or is taking a calculus class as well as trigonometry class. This app gives you hundreds of formulas that can help you with your studies.A list of over a hundred integrals, all of the main trigonometry formulas and identities , and tons of derivatives. Now including hyperbolics!
Taking statistics? Then you need the Wolfram Statistics Course Assistant. This definitive app for statistics—from the world leader in math software—will help you work through your homework problems, ace your tests, and learn statistics concepts. Forget canned examples! The Wolfram Statistics Course Assistant solves your specific problems on the fly, covering descriptive statistics, distributions, and much more.
This app covers the following topics applicable to Statistics and Introduction to Statistics:
- Create a bar chart, histogram, or scatter plot of any set of data - Find the mean, median, mode, standard deviation, quartiles, and interquartile range of a dataset - Calculate normal probabilities and find information about the normal distribution - Calculate binomial probabilities and find information about the binomial distribution - Compute probabilities based on dice rolls and coin flips - Find the best-fit line of a set of data points - Select random integers or random real numbers
The Wolfram Statistics Course Assistant is powered by the Wolfram|Alpha computational knowledge engine and is created by Wolfram Research, makers of Mathematica—the world's leading software system for mathematical research and education.
The Wolfram Statistics Course Assistant draws on the computational power of Wolfram|Alpha's supercomputers over a 2G, 3G, 4G, or Wi-Fi connection from |
More About
This Textbook
Overview
A First Course in Fuzzy Logic, Third Edition continues to provide the ideal introduction to the theory and applications of fuzzy logic. This best-selling text provides a firm mathematical basis for the calculus of fuzzy concepts necessary for designing intelligent systems and a solid background for readers to pursue further studies and real-world applications.
New in the Third Edition:
A
section on type-2 fuzzy sets - a topic that has received much attention in the past few years
Additional material on copulas and t-norms
More discussions on generalized modus ponens and the compositional rule of inference
Complete revision to the chapter on possibility theory
Significant expansion of the chapter on fuzzy integrals
Many new exercises
With its comprehensive updates, this new edition presents all the background necessary for students and professionals to begin using fuzzy logic in its many-and rapidly growing- applications in computer science, mathematics, statistics, and engineering.
"...provides necessary background information & then offers exercises to deepen the readers understanding of the concepts & test their ability to make the necessary calculations."
Editorial Reviews
Booknews
Derived from a one-semester graduate-level course introducing mathematical objects that model the vagueness of our natural language when we described phenomena without sharply defined boundaries, and their application in such areas as engineering and decision making. Assumes a background in calculus, some set theory and boolean logic, and some probability and statistics. After completing the course students should be able to read the technical journals as well as more advanced and specialized books |
You are here
Physical Mathematics
Publisher:
Cambridge University Press
Number of Pages:
666
Price:
85.00
ISBN:
9781107005211
This is a comprehensive and well laid out handbook of all the mathematics that physicists need to know. Very Good Feature: all the examples are real problems from physics. They are slanted toward particle physics, but cover most of mathematical physics.
It is marketed as a text for upper-division and graduate courses, but the exercises, although well-chosen, are sparse compared to the amount of material covered. I think it would work best as a handbook or supplemental work rather than the main text.
The coverage is well-balanced. The only conspicuous flaw is that it is skimpy on partial differential equations. The book covers the most common special functions of physics, but is not comprehensive even for those. There are no proofs, although some are requested in the exercises.
A somewhat similar book, although aimed at a different audience, is Kreyszig's Advanced Engineering Mathematics. This covers a lot of the same material, but has much more extensive examples and exercises. Most of Kreyszig's exercises come from physics, but it is an older physics than in Cahill, emphasizing mechanics and waves. |
Whether discussing polynomials or giving step-by-step instruction on how to use order of operations to solve equations, Jason's clear, easy-to- follow explanations and relevant, real-world examples will have even the most math-averse student basking in an a-ha moment. |
Short version
I think mathematica is a good first programming language, and Stephen Wolfram has dropped some hints in a few places that it should get even better at being a beginner programming language soon:
It'll probably be related to my goal in the next year or two of making Mathematica definitively the world's easiest to learn language...
More ...
Mathematica is the best tutorial. It is a discovery tool - just start from something that he knows a bit already and you both take one little step at a time. Just try things.
1st Thing - Try this Link => Hands-on Start to Mathematica
I personally would recommend engaging with him in a project of making an application and submitting it to the Wolfram ...
I own a copy of Modelling Financial Derivatives with Mathematica by William Shaw. I think it was a ground-breaking book for its time. However, here are some issues you should be aware of:
It was published in 1998 and is based on Mathematica version 3. We are now at 8, anticipating 9. Much of the graphics code he uses is now obsolete (eg Graphics`Graphics).
...
The course material I used to learn Mathematica myself is directed at beginners. You should have no problem following it even if you have next to zero prior programming experience. It is a bit outdated (it was written for an old version of Mathematica), but I think that it is still a very useful learning resource today. Most importantly, it includes ...
Affirming Vitaliy's suggestions I'll say something beyond his comprehensive answer and to a certain extent more specific.
A great mathematician S.Banach used to say (maybe as a joke) that children shouldn't be taught mathematics early because that would be a too sharp tool for them. There is an obvious analogy and this is why children shoudn't be taught ...
Vitaliy's suggestion is indeed very good.
What I want to add is that the Documentation is a good place to start. Say he's interested in drawing some graphs to illustrate something, then the Guide page for Graphs is a great place to start and the reference pages have tons of examples to build from.
Once one has solved a problem or two with Mathematica ...
Update: I described an alternative approach based on built in plotting functions in this answer. That approach is not very practical here though because I need to be able to handle points at arbitrary positions while built in functions work with a rectangle-based mesh. I am still looking for improvements.
I came up with this very naive approach and ...
I'm a bit late to this party, but I can assure you that it is possible to learn Mathematica as your first and only programming language. I know because I did it. It is also most certainly possible to use Mathematica as your calculation "Swiss Army knife" if you are an economist. I know because I am an economist, too, and I have been successfully using it as ...
One unconventional but possibly very useful approach it to introduce him to Project Euler. While many of the newer questions are completely beyond me (mind you that is not saying much), many of the earlier ones are quite approachable. If your friend has the desire to learn and an interest in puzzles/challenges, this site will grow as he grows.
Most of the ...
The methods NDSolve uses are documented in detail here:
Advanced Numerical Differential Equation Solving in Mathematica
This section says that PDEs are solved using the "method of lines", and explains which kinds of problems this method can deal with. There's also a detailed example of how the method works.
The numerical method of lines is a ...
I just wrote a book on financial engineering that uses Mathematica heavily. The publisher (World Scientific) says it should be available for purchase within a week or two. I have taught risk management and asset pricing and derivatives with these materials for the past few years at NYU-Poly. The point of the book is precisely to do lots of projects, the ...
I started learning Mathematica a couple of months ago, and all these suggestions are good. I'd also say that, although it's possible to surround yourself with books and tutorials, it's even more important to have some focus or goal to give shape to your learning efforts. You can find yourself bouncing from one interesting corner to the next (particularly ...
In a comment you asked about learning algorithm development and functional programming basics. Take a look at the courses at . Wolfram offers many of them as free videos that you can watch any time.
Check out the "General Mathematica" section for some introductory courses. There is also a free Functional Programming: Quick ...
I know this is an old thread now, but this might prove useful to someone. I have been teaching Mathematica to high school students for almost a year now. I have had to make my own resources, as I couldn't find any that were fit to purpose. I am happy to share them, and here is the Dropbox link:
Mathematica Exercises
All mistakes are my own! I am also happy ...
This page could be quite interesting in your case
The animations here explain some common Mathematica functions in a quite funny way.
There's a huge list of other resources here where you could pick what you think suits you.
Where can I find examples of good Mathematica ...
Here are some links I collected in my answer to the post Where can I find examples of good Mathematica programming practice?. The first link exposes quite well the new functionalities of Mathematica in this field.
Finance (some CUDA examples also)
High-Performance Computing in ...
As far as I know there's no reference book available yet that is using the new reliability functionality in Mathematica.
Two other resources are:
Reliability calculations for complex systems, academic thesis
Reliability Mathematics, Wolfram Blog
Those two focus on RBDs, Fault trees and system structures.
I've had an interest (as one can see in my other posts) in a wide range of distributed processing and parallel computing approaches and while not seen in any of my posts machine learning approaches as well. I looked at neural networks some years ago, and while they didn't suit the problems I worked on at the time I remembered the article Duncan and Tweney ...
Mathematica's documentation is also available online in the pdf format, as a tutorial collection. The place to look for it is here. Also, some books on Mathematica are now available as kindle editions, from Amazon. Finally, for those books which have Mathematica notebook versions, you can probably make a pdf from those notebooks for a personal use, if that ...
Introduction to Probability Models by Ross gives good description of stochastic processes.
Applied Intertemporal Optimization by Walde also has easy to follow structure on stochastic models in both discrete and continuous time and it is free to download pdf.
There's a second year mathematics and a computation physics course taught by Paul Abbott at the University of Western Australia that uses Mathematica for all of the lectures, workshops and assessments.
The maths course uses a customised stylesheet and the assessment notebooks have automated FTP uploading to the assignment dropbox. However, most of the ...
Although exporting x3d format maintains the light sources and exports the mesh, it isn't perfect when used with Blender (the only 3D editor I tried). However, since it's the best solution I have, I wrote some brief instructions for that procedure. It's important to note that I used Blender version 2.60 and Mathematica 9.
Since the instructions are almost ...
The GraphUtilities documentation has a whole section that should answer your question: "Algorithms for Finding Community Structure". The reference for the algorithm it uses is: A. Clauset, "Finding Local Community Structure in Networks," Physical Review E, 72, 026132, 2005 (arXiv mirror).
The references mentioned in the other answer do not really pertain too much to the problem of minimax approximation; they are more concerned with the other functions in FunctionApproximations` that deal with numerical differential equation solving; that is, the content that was once in the old NumericalMath`packages Butcher` and OrderStar`.
Indeed, a look ...
To show that your expression is real you could use ComplexExpand. By default, ComplexExpand will expand a complex expression into its real and imaginary part under the assumption that all undefined symbols occurring in the expression are real. The only problem here is that as far as I know there is no way to provide extra assumptions to ComplexExpand, ...
Here you can find some software to convert Mathematica graphics for input into POVray (untested and rather old, though)
Edit
Maeder's book and files aren't available for online downloading (you've to purchase the book)
Edit Or perhaps you can find them at the link provided in the comments
With regards to 'Learning Finance with Mathematica', one of the best sites I've seen is
It has two focuses; real estate and the financial market. The financial market end is very instructional and contains demo mathematica code as well as free downloadable code. It focuses on a number of market concepts, namely: risk, trends, ...
Mathematica is a registered trademark of Wolfram Research, Inc. While the mark is used herein with the limited permission of Wolfram Research, Stack Exchange and this site disclaim all affiliation therewith. |
Students graph polynomials functions and analyze the end behavior. For this algebra lesson, student differentiate between the different polynomials based on the exponents. They use a TI to help with the graphing.
In this algebra functions worksheet, students review the definition of a function and the four different ways to represent a function. Students then determine if the four given examples represent functions. Students explain their answers.
Starting from a brief look at functions and the mapping of domains to ranges, Sal starts out with an intuitive sense of what a function inverse is. He then, using an example, shows how to find the inverse of a function and also shows how the graph of the function and its inverse are reflections over the y = x line. This video provides a good review of function inverses for more advanced students or a nice introduction for the beginning student.
Are odd numbers connected to odd functions and even numbers to even functions? This video tries to clarify that connection. It also talks about functions that are neither odd nor even to give a more intuitive feeling about classifying these functions.
What does it mean for two things to have a functional relationship? In this video, Sal takes the example of a table of values that map a personÕs name to their height and discusses how this is a functional relationship. He also considers how the table could be changed so that the relationship is no longer a function.
We look at a number of different examples of functions and see what their domain is. Sal writes the domain in set notion and shows how different functions can have different input values that cause the function to be undefined.
Students solve formulas by using substitution. In this algebra lesson, students utilize formulas introduced in the lesson which apply to science as well as volume and area. The lesson gives detailed instruction for solving each type of problem. Detailed answers to all practice problems are provided with step by step solutions to assist.
After defining a simple function from a word problem, this video, shows how one could find the domain and the range of that function. The goals here are to reinforce the definitions of domain and range with a concrete example.
When comparing pricing models, young mathematical consumers, create linear equations and analyzing them graphically and algebraically. They look at the meaning of slope and intercepts, as well as the intersection points of lines.
Students explore the TI-92. In this secondary mathematics instructional activity, students examine the applications and functions of the TI-92. Students investigate symbolic manipulation, 2D and 3D graphing, the interactive geometry module and the programming and text editor.
Use real world scenarios to facilitate discussion of the relationship between variables and how they are represented graphically and analytically. This can work in part as an introduction to functions, as a complete lesson, or as an extension to a unit on the library of functions.
Functions are on the move! This lesson plan provides an opportunity for learners to explore transformations of functions. The activity illustrates the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for both positive and negative values of k. Working in small groups, students complete a table of values for a parent function and an assigned transformation of that function. After sketching both graphs on the same coordinate plane, they analyze their results and write a conjecture about how the value of k affects the original function. Each group shares its findings with the class. The results of the activity are reinforced by using graphing calculators to graph the functions and comparing with the sketches done with pencil and paper. The activity concludes with learners applying what they have learned to write equations for functions when given their graphs.
High schoolers are introduced to the techniques associated with interpreting functions. The vocabulary associated with this technique is reviewed, then pupils view a PowerPoint (embedded in the plan), that shows how to interpret functions. Learners then break into four groups and complete the assignments given by the teacher. Fantastic lesson!
Students explore the concept of exponents. For this exponential functions worksheet, students complete provided worksheets that require them to graph exponential functions by hand as well using graphing calculators. |
Mathematica Cookbook helps you master the application's core principles by walking you through real-world problems. Ideal for browsing, this book includes recipes for working with numerics, data structures, algebraic equations, calculus, and statistics. You'll also venture into exotic territory with recipes for data visualization using 2D and 3D graphic tools, image processing, and music.
Although Mathematica 7 is a highly advanced computational platform, the recipes in this book make it accessible to everyone -- whether you're working on high school algebra, simple graphs, PhD-level computation, financial analysis, or advanced engineering models.
Learn how to use Mathematica at a higher level with functional programming and pattern matching
Delve into the rich library of functions for string and structured text manipulation
Learn how to apply the tools to physics and engineering problems
Draw on Mathematica's access to physics, chemistry, and biology data
Get techniques for solving equations in computational finance
Learn how to use Mathematica for sophisticated image processing
Process music and audio as musical notes, analog waveforms, or digital sound samples |
Get everything you need for a successful and pain-free year of learning math! This kit includes Saxon's 3rd Edition Algebra 2 textbook and tests/worksheets book & answer key, as well as the DIVE Algebra 2 CD-ROM. A balanced, integrated mathematics program that has proven itself a leader in the math teaching field, Algebra 2 covers geometric functions like angles, perimeters, and proportional segments; negative exponents; quadratic equations; metric conversions; logarithms; and advanced factoring.
The DIVE software teaches Saxon lesson concepts step-by-step on a digital whiteboard, each lesson averaging about 10-15 minutes in length. Because
System Requirements:
Windows & Mac 98 or higher (including Vista)
Speakers
CD-ROM Drive
This Kit Includes:
Saxon Algebra 2 Math Textbook, 558 pages, hardcover, 3rd Edition
Saxon Algebra 2 Test Book, 3rd Edition
Saxon Algebra 2 Answer Key, 3rd Edition
DIVE Algebra 2 CD-ROM, for the 3rd & 2nd Edition Saxon Algebra 2 Kit & DIVE CD-Rom, Third Edition
Review 1 for Saxon Algebra 2 Kit & DIVE CD-Rom, Third Edition
Overall Rating:
5out of5
Saxon Algebra 2 w/ DIVE CD
Date:October 30, 2010
Chea
Location:Sacramento
Quality:
5out of5
Value:
5out of5
Meets Expectations:
4out of5
I've used ALL the Saxon Math books along with the DIVE CD starting in the 78 series. I've been completely satisfied with the Saxon and DIVE lessons. After finishing the Algebra II lessons, I was surprised to discover the Saxon books did not cover ALL the Algebra concepts (85%). Luckily, with the help of the DIVE CD series for Algebra II, my son was able to complete the needed Algebra to qualify to pass his CLEP exams.
I'm not familiar with the Saxon CD series, but we did review a sample Saxon CD and my son found he liked the DIVE better, which I enjoyed because it's cheaper then the Saxon, plus my son seemed to relate better DIVE.
I gave a four star rating for "Meets Expectation" due to the number of errors and typo's I found in this book. But luckily you can find them on the Saxon Home page. I just didn't like having to track them down. I have enough to do as a home-school mom. But I love Saxon Math and will never sell or give away my library of them. They can always be used for future grandkids too. |
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Starting at $20Math Study Skills Workbook
Math Study Skills Workbook, 4th Edition
Summary
This workbook helps learners identify their strengths, weaknesses, and personal learning styles--and then presents an easy-to-follow system to increase their success in mathematics. With helpful study tips and test-taking strategies, this workbook can help reduce "math anxiety" and help readers become more effective at studying and learning mathematics. |
0792350790
9780792350798
A Mathematical Theory of Design:This book is extremely important to the field because itpresents a unified framework for theory and practice, which is proventheoretically and by many cases from various engineering fields.Specifically, there are four major aspects that make the book unique:1) The book develops a formal systems approach to design (includingtheorems, analysis of principles of design and information theory). 2)Methods for efficient design are rigorously derived from the theory, based on AI and optimization. 3) The scope of the book covers manyengineering disciplines under a unified framework, includingmechanical, electrical, civil, industrial, manufacturing systems, andapparel industry. Thus, it applies to readers from variousdisciplines, theoreticians and practitioners. DFM and DFA are alsocovered. 4) The book provides the methodology for developing the nextgeneration computer software for advanced intelligent CAD (ComputerAided Design)."Audience: " The book is especially appropriate for courses inengineering (mechanical, industrial, electrical, and civil). It isalso a useful reference for practicing engineers interested in designand optimization, and for applied mathematicians and computer softwaredevelopers engaged in smart CAD applications.
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Rent A Mathematical Theory of Design 1st edition today, or search our site for Dan textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Springer. |
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...Research in discrete mathematics increased in the latter half of the twentieth century partly due to the development of digital computers which operate in discrete steps and store data in discrete bits. Concepts and notations from discrete mathematics are useful |
What knowledge of mathematics do secondary school math teachers need to facilitate understanding, competency, and interest in mathematics for all of their students? This unique text and resource bridges the gap between the mathematics learned in college and the mathematics taught in secondary schools |
Mathematics Modules
Mathematics module courses are for students needing to improve their skills for college-level
work. These courses are available at the Learning Commons in Glen Ellyn.
Individualized, Appointment-Based Courses
Mathematics module courses are offered in an individualized appointment-based format
through the Learning Commons in Glen Ellyn. Students meet with an instructor once
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presentations. Please call (630) 942-2131 for more |
The book consists of seven chapters written by three eminent mathematicians in the subject of Euclidean Geometry. It is especially useful for students and teachers who are preparing for National and International Mathematical Olympiads.
This book is a leisure reading of different aspects of urban life which are modeled mathematically. It tries to make accessible to an average reader a collection of arguments for analysing daily questions with elementary mathematical tools.
The book may be recommended to undergraduate students who are yet to be convinced that mathematics appear in more places than a non-math inclined person may expect.
URL for publisher, author, or book:
MSC main category:
00 General
MSC category:
00A08
Other MSC categories:
00A09
Review:
This book is a leisure reading of different aspects of urban life which can be modeled mathematically. It tries to make accessible to an average reader a collection of arguments for analysing daily questions with elementary mathematical tools.
Examples of questions appearing on the book are: how many restaurants are in a city of a given size? should we walk or run under the rain? how much a car in a dense traffic slows down the other cars? how fast cities grow depending on the available resources? how many people have ever lived in London through time? among many others.
It is very interesting how the author makes inferences without statistical real data, just gessing. And the good thing is that at least the order of magnitude of the results obtained are very likely to be correct. These mathematical problems are solved with elementary computations, accessible to undergraduate students, and even many of them to high school mathematics. The book focuses in estimations, rounding off numbers very often. This point of view is very interesting for a young reader, and it is the main
strength of the book. In general terms, the problems analysed by the book are treated in a shallow way, with very simple answers,
and not entering into very sophisticated mathematical models. Some of the later chapters (e.g. those on analysis of traffic
flows) are of higher mathematical level and require some basic knowledge of differential equations.
The book may be recommended to undergraduate students who are yet to be convinced that mathematics appear in more places than a non-math inclined person may expect. However, anyone acquainted with higher mathematical background may find it a bit boring.
This book is an exposition of geometries associated with Möbius transformations of the plane, based on properties of the group $SL_2({\mathbb R})$. The presentation is self-contained, starting from elementary facts in group theory, and unveiling surprising new results about the geometry of circles, parabolas and hyperbolas. The treatment of elliptic, parabolic and hyperbolic Möbius transformations is provided in a uniform way. This is possible due to an appropriate usage of complex, dual and double numbers, which represent all non-isomorphic commutative associative two-dimensional algebras over the real numbers.
MSC main category:
51 Geometry
Review:
This book is a deep analysis of Möbius transformations from an unusual point of view. The approach is based on the Erlangen programme of Felix Klein, who defined geometry as a study of invariants under a transitive group action. The book focuses on the group $SL_2({\mathbb R})$ and its action by Möbius transformations: $x \mapsto \frac{ax+b}{cx+d}$. This acts on the complex plane, but it also acts on the plane of dual numbers and on the plane of double numbers. Actually, these are the three possible non-isomorphic commutative associative two-dimensional algebras over the real numbers, which are ${\mathbb R}[\sigma]$, with $\sigma^2=-1,0,+1$. The corresponding actions are called elliptic, parabolic and hyperbolic Möbius transformations. The three geometries correspond to the homogeneous spaces with group $SL_2({\mathbb R})$ for the three possible one-dimensional subgroups.
The book studies in depth the geometry associated to the "cycles" in these spaces (circles in the first case, parabolas with horizontal directrix in the second, and equilateral hyperbolas in the third). There is a three dimensional real projective space parametrising such cycles, and a corresponding action of $SL_2({\mathbb R})$ on it. Moreover, there is a naturally defined (indefinite) quadratic form on the space of cycles which serves to recover the initial geometric space, and the usual geometric transformations on it. Then the books moves on to analyse many geometric properties of cycles. This is completed with several aside considerations: the relationship with the physics of Minkowski and Galilean space-time, the more classical point of view of (semi)riemannian geometry, questions on conformal geometry, and more far away subjects like optics or tropical algebra.
The book is accompanied by a DVD with a program which runs under linux (also freely available in internet) which serves the reader to perform computations that appear along the book. This is used often in the book to complete some proofs, which are done by brute force calculation. However, the use of the program requires some knowledge of programming, as the interface is not very user-friendly. This is useful to the reader to complete the arguments and get convinced that the results are true. However, I would have preferred at some points to read a concise and theoretic proof, much more appealing than checking a calculation.
The book is addressed to undergraduate and graduate students in the areas of geometry and algebra. The presentation is basically self-contained. There are many exercises scattered along the book for the interested reader. On the one hand, the point of view is not classical, so a student trying to learn basic properties of Möbius transformations and the relation with complex/Kähler geometry may not get totally satisfied. On the other hand, I think that the author has been successful in transmitting the idea (as he confess in the epilogue that this was his intention) that the three geometries: elliptic, parabolic and hyperbolic deserve to be treated on an equal footing, and that all of them are very rich.
The mathematics of the classical tower of Hanoi puzzle with 3 pegs and n disks is by now well known and optimal solutions have been described in the form of algorithms that need a minimal number of moves. Besides some historical notes and an introduction to the Chinese ring puzzle, also called Baguenaudier puzzle, the graphs, the number sequences, and in general, the mathematics and algorithms are explained for the tower of Hanoi puzzle. As far as they are currently known, also the methods for its possible generalizations and variants are given. The latter leaves many challenging open problems. Exercises are provide after each chapter.
URL for publisher, author, or book:
MSC main category:
05 Combinatorics
MSC category:
05C90
Other MSC categories:
00A08, 11B37, 20B25, 68T20
Review:
The Tower of Hanoi (TH) is a classic puzzle that was invented by Éduard Lucas (1842-1891) using the alias N. Claus (de Siam), an anagram of Lucas d'Amiens. Given three pegs, two of them empty, and a pile of disks of decreasing size is stacked on the third one. The problem is to move the stack to another peg, moving one disk at a time from one peg to another, but never putting a larger disk on top of a smaller one (the divine rule). The Chinese ring puzzle (CR) and the topologically equivalent Cardano rings are related. In the latter two the problem is to get all the rings off the upper bar or to remove the string from the linked pillar structure. (See image attached.) These puzzles are older and CR, which Lucas called Baguenaudier puzzle, has probably inspired him to formulate the TH puzzle.
So this is a book about recreational mathematics, but do not be mistaken, the origin of the questions may be recreational, the problems discussed are undeniable mathematics. There is a lot of graph theory, automata, group actions, complexity analysis and algorithmic aspects around with definitions, theorems and proofs.
Chapter 0 gives an introduction to the problem and the history of the TH puzzle and other related puzzles, but it also introduces definitions and properties of graphs that are used in solving these problems.
Then chapter 1 discusses the CR puzzle as a prototype to set up a model for approaching this kind of problems. The classical TH problem is then much more thoroughly discussed in chapter 2. Algorithms and proofs are given for optimal (w.r.t. the number of steps) solutions. The simplest problem is to move a perfect pile from one peg to another one following the divine rule. All possible intermediate states are called regular. It is more difficult to transform an arbitrary regular state into another one. To solve this, a good understanding and analysis of the associated graph becomes more important.
Lucas considered also another problem where the disks are placed randomly on the three pegs, and the goal is still to transform this irregular state to a perfect or regular state still following the divine rule. That's a short chapter 3.
The next chapter introduces another type of graphs to analyse the TH problem. They are called Sierpinski graphs because of their relation with the Sierpinski triangle.
Generalizing TH from 3 pegs to 4 or more pegs, still looking for an optimal solution (known as Reve's problem), goes way beyond a trivial step. So there is much intuition, conjectures and open problems to be found in chapter 5.
Some further variations are briefly discussed in the next 3 chapters. like more towers (of different color) and more pegs, and/or relaxing the rules of the game (chapter 6) or Towers of London: colored balls on a number of pegs to be brought form one state to another in a minimum number of steps (chapter 7) or with oriented disk moves (chapter 8).
Chapter 9 is just a list of open problems that were encountered in the previous chapters.
Chapters 0-8 are followed by a list of exercises (hints and solutions are provided in an appendix). In principle the mathematics needed are all introduced in the text, but the introduction to the necessary concepts is kept to a minimum and some basis is tacitly assumed known. For example, the notion of group is used without much ado. Hence a certain mathematical background and some familiarity with graphs is advisable and even required if you want to solve the exercises. Besides the usual subject and name indexes, the glossary of terms with one-liner definitions is quite useful to recall a concept of a previous chapter if you are not so familiar with graphs.
The authors use a very pleasant and amusing style, but they keep the discussion to the point, and leave much more to be explored using many pointers to the extensive reference list. The many illustrations make the technicalities more easy to digest.
Thus if you love puzzles, and more in particular the mathematics behind it, this is a book for you. That holds for mathematicians but for computer scientists as well. Also if you are looking for a lifelasting occupation, then you may find here a list of open problems that will keep you busy for a while. course attracks graduate students in Business-Banking,computer sciences, engineering, eonomics, physics, finance, and mathematics and others related disciplines, and may be recommended to undergraduate students who are yet convinced that the mathematics appear in more places or in differents fields of knowledge, and also suitable for individual study. The style and coverage is directed toward the theory of stochastic processes and its applications. In many instances, the gist of the problems is introduced in every-day language and then all written in a precise matematical form.
The first four chapters are in probability theory: measure and integration, probability theory, convergence and conditioning. There follows chapters on martingales and stochastics, Poisson random measures, Brownian motion and Markov Processes.
The book is full of insights and observations that only a lifetime researcher in Probability and Stochastic Processes can have.
URL for publisher, author, or book:
MSC main category:
60 Probability theory and stochastic processes
MSC category:
60-01;60A10;60B10;60C05;60F05;60G05;60J05;60H05
Other MSC categories:
60J65;60G45;60G46;60G48;60G51;60J75;60.60
Review: first four chapters are in probability theory: measure and integration, probability theory, convergence and conditioning.
The first chapter is a review of measure and integration in the context of the modern literatura on probability and stochastic processes. The second introduces probability spaces as espeila measure spaces.The chapter three is on convergence, routinely classical, and the chapter four in on conditional expectations included Radon-Nikodyn derivatives.
There follows chapters on martingales and stochastics, Poisson random measures, Brownian motion and Markov Processes.
Martingales are introduced in chapter V, the treatment of continuous martingales contain an improvement, achieved through the introductiion of a Doob martingale, a stopped martingale that is uniformly integrable. Two great theorems are considered:martingale characterization of Brownian motion due to Lévy and the characterization of Poisson process due to Watanabe.
Poisson random measures are in Chapter VI, the treatment is from the point of vue of their uses,specially,of Lévy processes. This chapter pays some attention to processes with jumps. The chapter VIII on Brownian motion is mostly on the standard material. Finally, the Chapter IX, on Markov processes, Itô diffusions and jump-diffusions are introduced via stochastic integral equations, as an integral path in a field of Lévy Proceses.
In short, the book is higher recommended. It provides new simple proofs of important results on Probability Theory and Stochastics Processes. In my opinion, it is a stimulating textbook will be for the teaching and research of the materia. A well written text with excellent tools for many instances, in every day language, and then all written precise in mathematical form. |
G22.2112-001
Scientific Computing
Aaditya Rangan
Graduate Division
Computer Science
This course is the same as the course
G63.2043.001 SCIENTIFIC COMPUTING
The course description below is copied from the math department
webpage:
This course is intended to provide a practical introduction to
computational problem solving.
The order in which the subject material will be covered will
approximate the following outline:
- The notion of well conditioned and poorly conditioned problems, with
examples drawn from linear algebra
- The concepts of forward and backward stability of an algorithm, with
examples drawn from floating point arithmetic and linear-algebra
- Basic techniques for the numerical solution of linear and nonlinear
equations, and for numerical optimization, with examples taken from
linear algebra and linear programming
- Principles of numerical interpolation, differentiation and
integration, with examples such as splines and quadrature schemes
- An introduction to numerical methods for solving ordinary
differential equations, with examples such as multistep, Runge Kutta
and collocation methods, along with a basic introduction of concepts
such as convergence and linear stability
- An introduction to basic matrix factorizations, such as the SVD,
along with basic techniques for computing matrix factorizations, with
examples such as
the QR method for finding eigenvectors
- Basic principles of the discrete/fast Fourier transform, with
applications to signal processing, data compression and the solution of
differential equations.
This is not a programming course but programming in homework projects
with Matlab/Octave and/or C is an important part of the course work.
As many of the class handouts are in the form of Matlab/Octave scripts,
students are strongly encouraged to obtain access to and familiarize
themselves with these programming environments.
No single textbook is required for this class, but there are several
optional texts which are recommended:
Numerical Linear Algebra, David Bau III & Lloyd N. Trefethen, SIAM,
2000;
Scientific Computing with MATLAB and Octave, Alfio M. Quarteroni &
Fausto Saleri, Springer, 2006 (available electronically through the
library);
An Introduction to Programming and Numerical Methods in MATLAB, Stephen
R. Otto & James P. Denier, Springer, 2005 (available electronically
through the library) |
Most Mathematics courses have prerequisites that are listed as part of the course description in the Schedule of Classes. Before registering for a Mathematics course, be sure you have completed the stated prerequisite.
Note to all Algebra students:
The Math Department uses a single textbook for the Elementary and Intermediate Algebra sequence. This allows students to complete the Algebra sequence in three different ways: a four semester sequence of MATH 111, 112, 122, and 123 each covering one fourth of the book; a two semester sequence of MATH 110 and MATH 120 each covering half of the book; or a combination of the above. Please see your counselor to be sure you take the correct course.
Description: Self-paced, individualized instruction is provided in selected areas to be arranged with an instructor and student and approved by the dean. Varying modes of instruction can be used -- lecture, laboratory, research, skill development, etc. May be repeated for credit up to 6 units. Transfer: CSU. |
Introduction to Ordinary Differential Equations
9780486659428
ISBN:
0486659429
Pub Date: 1989 Publisher: Dover Pubns
Summary: A thorough, systematic 1st course in elementary differential equations for undergraduates in mathematics and science, requiring only basic calculus for a background, and including many exercises designed to develop students' technique in solving equations. With problems and answers. Index.
Landin, Joseph is the author of Introduction to Ordinary Differential Equations, published 1989 under ISBN 9780486659428... and 0486659429. Five hundred twenty one Introduction to Ordinary Differential Equations textbooks are available for sale on ValoreBooks.com, one hundred twenty one used from the cheapest price of $5.24, or buy new starting at $2 |
Modelling With Force and Motion The School Mathematics Project
9780521408912
ISBN:
0521408911
Pub Date: 1993 Publisher: Cambridge University Press
Summary: The aim of 16-19 Mathematics has been to produce a course which, while chaallenging, is accessible and enjoyable to all students. The course develops ability and confidence in mathematics and its applications, together with an appreciation of how mathematical ideas help in the understanding of the world and society in which we live. The unit: · helps develop an ability to use the concepts introduced in Newton's laws ...of motion to study projectiles, forces, circular motion at constant speed, and statics of rigid bodies; · provides insight into the potential of mathematics for modelling physical phenomena; · helps foster an appreciation of the links between mathematics and the real world; · develops a basis for further study in engineering and science; · fosters an ability to model both in familiar and unfamiliar contexts within the field of mechanics.
School Mathematics Project Staff is the author of Modelling With Force and Motion The School Mathematics Project, published 1993 under ISBN 9780521408912 and 0521408911. Two Modelling With Force and Motion The School Mathematics Project textbooks are available for sale on ValoreBooks.com, one used from the cheapest price of $2.49, or buy new starting at $16.44.[read more |
Course Description: An in-depth study of algebraic equations and inequalities. Comprehension of the underlying algebraic structure will be stressed as well as appropriate algebraic skills. The study will include polynomials, rational, exponential, and logarithmic equations as well as systems of equations/inequalities. |
Students define the product rule and use it to solve problems. In this calculus lesson, students review rules they learned and memorize the new rules as it relates to derivatives. They solve problems through differentiation by proving the product ruleTwelfth graders explore the concept of limits. In this calculus lesson, 12th graders investigate the limit rules for both finite and infinite limits through the use of the TI-89 calculator. The worksheet includes examples for each rule and a section for students to try other examples.
Students investigate derivatives using the product rule. In this derivatives using the product rule lesson, students use the Ti-89 to find the derivatives of functions such as x^2 and sin(x) using the product rule. Students visualize the process of finding the derivatives using the product rule on the Ti-89.
In this calculus worksheet, students solve 10 different problems that include determining the first derivative in each. First, they apply properties of logarithmic functions to expand the right side of each equation. Then, students differentiate both sides with respect to x,using the chain rule on the left side and the product rule on the right. In addition, they multiply both sides by y and substitute.
Pupils solve problems using integration by parts in this calculus instructional activity. Learners apply the product rule and integration by parts. They graph the equation and use the TI to observe the integration process.
This lesson plan provides an introduction to integration by parts. It helps learners first recognize derivatives produced by the product rule and then continues with step-by-step instructions on computing these integrals. It also shows integrating special forms with e and trigonometric functions. This resource includes handouts and a practice worksheet.
In this calculus learning exercise, students perform integration by parts. They solve differential equations as they use integration by part to solve unlike terms. There are 23 problems with an answer key.
Sal starts with an example of finding dy/dx of y = x2 and builds to showing the solution to the more complicated implicit differentiation problem of finding the derivative of y in terms of x of y = x ^ x ^ x .In this calculus activity, students use integration to solve word problems they differentiate between integration and anti derivatives, and between definite and indefinite integrals. There are 3 questions with an answer key.
Twelfth graders assess their knowledge of trig functions and their properties. For this calculus lesson, 12th graders take a test on derivatives, trig functions, and the quotient rule. There are 2 different versions of the same test available.
Students review integrals and how they apply to solving equations. In this calculus lesson plan, students assess their knowledge of derivatives, rate of change, and lines tangent to a curve. This assignment contains two version of the same test concept.
Students review derivatives and equations for their test. For this calculus lesson, students review average rate, parametric equations, tangent line to a curve and value of a derivative to prepare and show mastery on a chapter test. They show proficiency on rig derivatives and differential equations. |
This is a sample syllabus only. Ask your instructor for the
official syllabus for your course.
Instructor:
Office:
Office hours:
Phone:
Email:
Revised Course Description
This course is designed for prospective elementary school
teachers. Topics include elementary geometry from an intuitive
standpoint, constructions, symmetry, translations, rotations,
patterns, measurement and computation of length, area, volume,
and angles, units and the metric system, creating and
interpreting charts and graphs, and some introductory topics of
probability and statistics.
MAT 207 meets for four hours of lecture per week.
Prerequisites
Students must have satisfied the ELM requirement before
enrolling in MAT 207.
understand the concept of measurement units in both the
standard and metric systems, be able to convert measurements
within systems (e.g. yards to inches) and from one system to
another (e.g. miles to kilometers)
Expected outcomes
Students should be able to demonstrate through written
assignments, tests, and/or oral presentations, that they
have achieved the objectives of MAT 207.
Method of Evaluating Outcomes
Depending on the instructor, grading may be based on
homework, class participation, short tests, scheduled
examinations, journals, and portfolios covering students'
understanding of problem-solving; geometry, probability, and
statistics and other topics that are covered in MAT 207.
Text
Mathematics for Elementary Teachers: A Contemporary
Approach (8th edition), by Gary Musser and William
Burger
Table of contents
Chapter 1-Introduction to Problem-Solving
Preview and review
Chapter 10-Statistics
Gathering, analyzing, and displaying data
Measures of Central Tendency and Dispersions
Graphs and their interpretations
Chapter 11-Probability
Simple, Complex, and Conditional Probabilities
Experimental and Theoretical Probability
Odds, Expected Value, and Simulation
Chapter 12-Geometric Shapes
Recognizing Geometric Shapes and Describing their
Characteristics
Two-Dimensional and Three-Dimensional Shapes
Chapter 13-Measurements
Nonstandard and Standard Units
Units of Length Weight and Capacity in the Standard
and Metric Systems
Perimeter, Area, and Volume in the Standard and
Metric Systems
Chapter 14-Geometry Using Triangle Congruence and
Similarity
Congruence and Similarity of Triangles
Euclidean Constructions
Grading Policy
Students' grades may be based on homework, class
participation, short tests, journals, portfolios, and scheduled
examinations covering students' understanding of the topics
covered in MAT 207. The instructor will determine the relative
weights |
Find a Winthrop Harbor Algebra 1The objective of prealgebra is to prepare the student for the study of algebra. Prealgebra includes several broad subjects:
•Review of natural number arithmetic
•New types of numbers such as integers, fractions, decimals and negative numbers
•Factorization of natural numbers
•Properties of oper |
Friendly Introduction to Number Theory, A courses in Elementary Number Theory for non-math majors, for mathematics education students, and for Computer Science students. This is an introductory undergraduate text designed to entice non-math majors into learning some mathematics, while teaching them to think mathematically at the same time. Starting with nothing more than basic high school algebra, the reader is gradually led from basic algebra to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing style is informal and includes many numerical examples, which are analyzed for patterns and used to make conjectures. The emphasis is on the methods used for proving theorems rather than on specific results. |
to Mathematics: v. 2
Countdown to Mathematics has been written to help self-study students to revise and practise basic skills in arithmetic, algebra, geometry, graphs ...Show synopsisCountdown to Mathematics has been written to help self-study students to revise and practise basic skills in arithmetic, algebra, geometry, graphs and trigonometry. The nine teaching modules in Countdown to Mathematics have been split into two separate books. Volume 1 consists of Modules 1-4 and concentrates on basic mathematical skills. It deals with arithmetic, simple algebra, how to plot and read graphs, and the representation of data. Where possible, the techniques are illustrated with real-world applications. Volume 2 consists of Modules 5-9 and covers geometry, graphs, trigonometry and algebra.. The emphasis here is on the manipulative skills which are necessary for most mathematical courses beyond GCSE standardPrentice Hall,
1981
Description:This is an ex-library book and may have the usual library/used...This is an ex-library book and may have the usual library/used-book markings inside. This book has soft covers. Ex-library, With usual stamps and markings, Discoloured with age. Signs of wear to cover **SHIPPED...Good. Discoloured with age. Signs of wear to cover |
California's mathematics academic content standards establish what every student in California can and needs to learn in mathematics. The standards focus on essential content for all students and prepare students for the study of advanced mathematics. These standards emphasize computational and procedural skills, conceptual understanding, and problem solving. These three components of mathematics instruction and learning are not separate from each other; instead, they are intertwined and mutually reinforcing. |
Summary: Demonstrates how some of the fundamental ideas of algebra can be introduced, developed, and extended. Focuses on repeating and growing patterns, introducing the concepts of variable and equality, and examining relations and functions. Features activities with questions that stimulate students to think more deeply about the mathematical ideas. Discusses expectations for students' accomplishment and provides helpful margin notes and blackline masters.
Edition/Copyright: 01 Cover: Paperback Publisher: National Council of Teachers of Mathematics Published: 01/28/2001 International: No
2001 Paperback 2001. A good used copy with clean pages, usual school markings and moderate cover wear. Book only-does not include additional resources. Booksavers receives donated books and recycles...show more them in a variety of ways. Proceeds benefit the work of Mennonite Central Committee (MCC) in the U.S. and around the world. ...show less
$21.57 +$3.99 s/h
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Ships same day or next business day! UPS(AK/HI Priority Mail)/ NEW book |
Beginning and Intermediate Algebra: An Integrated Approach
9780495831433
ISBN:
0495831433
Edition: 6 Pub Date: 2010 Publisher: Brooks Cole
Summary: Brooks Cole published this text book in 2010, and here you have a chance to buy or rent your own copy of this 6th edition version. Buy Beginning and Intermediate Algebra: An Integrated Approach online from us today for an affordable price. Cheap Beginning and Intermediate Algebra: An Integrated Approach couldn't be easier to get. The book is written by David R Gustafson, Rosemary Karr and Marilyn Massey, and you can ...find out everything there is to know about learning algebra at this level. Sell back to us as well if you already own a copy, because our buyback system makes it easy to do so.
Gustafson, R. David is the author of Beginning and Intermediate Algebra: An Integrated Approach, published 2010 under ISBN 9780495831433 and 0495831433. Four hundred seventy five Beginning and Intermediate Algebra: An Integrated Approach textbooks are available for sale on ValoreBooks.com, two hundred fifty four used from the cheapest price of $49.04, or buy new starting at $245.71 TEXTBOOK ONLY - Annotated Instructor Copy 6th Edition May contain highlighting/underlining/notes/etc. May have used stickers on cover. Ships same or nex [more]
ALTERNATE EDITION: Used - Good Hardcover. TEXTBOOK ONLY - Annotated Instructor Copy most useful thing about this book was the breakdown of examples in each lesson. It really helped me figure out each problem. I also liked that it provided the answers in the back of the book for the odd problems. I liked that each lesson gave plenty of examples for different problems making it easier to follow and go look back if needed. I loved that the book provided definitions for terms even if they were terms I should already know, it was good to have them there just in case. The book also provided a formula key where needed that really helped! I would definatly recommend this book to beginner math students. The way this book is set up and the way it walks you through everything so smoothly makes this the perfect math book to begin the college experience with. It's not overwhelming with math jargon that will confuse you.
I needed this book from math 98 and math 100. My teacher wasn't dry good so I was glad I had this book because I was able to go back in the book and figure out what she wasn't teaching me right. My class was a basic math and algebra course. |
Resena: Here is a comprehensive introduction to yoga geared to men of all ages and backgrounds-whether they're athletic or sedentary, young or old, or devotees of yoga who seek new information to enha...
Resena: In Qigong for Health and Vitality, Michael Tse, a Qigong (pronounced chee-gong) master trained by some of China's finest Qigong practitioners, explains the philosophy and practice of Qigong, ...
Resena: Take on these fiendish puzzles devilishly created to either make or break your IQ. They're the toughest examples of the most popular logic puzzle types: Find the Missing Figure, Guess the Pict...
Resena: Mathematics for Electrical Engineering and Computing embraces many applications of modern mathematics, such as Boolean Algebra and Sets and Functions, and also teaches both discrete and conti... |
Step-By-Step Math Review helps relieve math anxiety for University of Phoenix students
Have you ever studied rigorously for a math exam, only to go totally blank once the test begins? Does the very notion of taking a math class or even picking up a math textbook fill you with dread? If so, then you understand math anxiety firsthand.
"Math anxiety is very real," says Clifton Luke, PhD, a former math instructor and the vice president of learning products for University of Phoenix. "Many of our students haven't had a math class in decades, and that can compound math anxiety."
In Fall 2011, the University launched the Step-By-Step Math Review, an online pre-algebra skills refresher to prepare students for required math courses.
"The United States currently has an overall math education deficit, and it affects students at all levels and across all institutions," says Luke. "So, we wanted to develop a program that helps all of our students brush up on their pre-algebra math skills, and addresses areas where they might need some extra help."
The more confident you are in your math skills, the better you are at math.
Accordingly, all University of Phoenix students in undergraduate degree programs must pass MTH 208 and MTH 209, so developing the necessary math skills to succeed in these courses is essential.
"We want all of our students to master the math material and skills required to pass these courses," says Luke.
The Step-By-Step Math Review covers 14 key pre-algebra concepts, which are prerequisite skills for required University math courses. It includes interactive modules that automatically adapt the content and problems to the skill level of the individual student, providing very specific feedback and hints to students as they're working through each problem. |
...
More About
This Book
inequalities, relations and functions, graphing linear equations and inequalities, pairs of linear equations and inequalities, polynomials, algebraic fractions, algebraic proportions, and quadratic, cubic, and radical equations. Students will also find a helpful glossary of math terms.
Related Subjects
Meet the Author
Donna Osborn has taught math for 34 years. She has won the Presidential Award for Excellence in the Teaching of Mathematics for Indiana, the Albert Einstein Distinguished Educator Fellowship, the Purdue University Distinguished Alumna Award, and the Christa McAuliffe Award for |
SaxonMathCourse2 Solution Manual pdf - SAXON PUBLISHERS. The lesson plans telling you will have been using a full home. We hear from a time to, ... I am extremely important book to buy books answer which includes answers and literature extensions.
Where can I find the answer key to a 7th grade Saxonmathbook? SaxonMathCourse 1 (9781591417835) :: Homework Help and ... Oct 19, 2011 · what is the answer to saxonmath lesson 29 ChaCha Answer: SaxonMath offers a variety of books. ...
SaxonMath 54 (2nd Edition) Tex T: SaxonMath 54 (2nd Edition) In T roduc TI on ... Read the Preface in the Saxon textbook. The course is designed for the student tp pace himself, ... the student through each lesson in the Saxonbook; the CD has audio and video.
... (or "cook book approach") in that they are basically "how to" books; i.e., here is the technique you use to find the answer to this type of math problem. Saxon saw a dilemma (failing test scores) and, ... exams and the course).
... no part of this book may be reproduced in any form, electronic or mechanical, including photocopy, ... Find each answer. a. ( 6.1)( 3.2)(10) b. 1 1 2 3 8 Solution a. ... The test scores for the math exam were as follows: 75, 87, ...
(No student workbooks for Math K.) Meeting Book - Use for the daily opening ... each course. Each kit includes a textbok, an answer ... 3rd Edition, 120 Lessons. Algebra 1, like all SaxonMath courses, includes five instructional components; introduction of the new incre-ment; examples with ...
recommended for each course. This includes a series of Teaching Tips, ... A preliminary sample is presented here for one of these courses. ALGEBRA 1 (3RD EDITION) The Saxonmath program has two important aspects. It uses incremental ... that 2math periods per day be scheduled, one in the ...
to the Saxonmath program. ... Math 65, Math 76, Math 87, and Algebra 1/2. Please note that this placement test is not infallible. It is simply one indicator that teachers may use to place new students. ... For each correct answer, place a check mark in the corresponding box. For each
Math Algebra 1 Saxon Algebra 1, ... geometry and constructions are reserved for the final chapters of the book. 2 In each lesson, a new concept is presented, ... Saxon Algebra 2, 4th edition This course is a college preparatory course that enables students to tackle even more
New Literacy, etc. A fascinating book that documents the horrible consequences of the "New Education" is entitled All Must ... Saxonmath students can apply math in new ... also understands science, the primary course where mathematics is applied. Bottom line: if you want "A ... |
A no-nonsense, practical guide to help you improve your algebra skills with solid instruction and plenty of practice, practice, practice
Practice Makes Perfect: Algebra presents thorough coverage of skills, such as handling decimals and fractions, functions, and linear and quadratic equations. Inside you will find the help you need for... more...
Practice Makes Perfect has established itself as a reliable practical workbook series in the language-learning category. Now, with Practice Makes Perfect: Geometry, students will enjoy the same clear, concise approach and extensive exercises to key fields they've come to expect from the series--but now within mathematics. Practice Makes Perfect:... more...
Sales Handle A no-nonsense practical guide to trigonometry, providing concise summaries, clear model examples, and plenty of practice, making this workbook the ideal complement to class study or self-study, preparation for exams or a brush-up on rusty skills. About the Book Established as a successful practical workbook series with over 30... more...
Take it step-by-step for pre-calculus success!
The quickest route to learning a subject is through a solid grounding in the basics. So what you won?t find in Easy Pre-calculus Step-by-Step is a lot of endless drills. Instead, you get a clear explanation that breaks down complex concepts into easy-to-understand steps, followed by highly focused—without ever breaking a sweat! First, you'll determine exactly how much time you GRE General Test—without ever breaking a sweat! First, you'll determine exactly how much... more...
The easy way to prepare for officer candidate tests Want to ace the AFOQT, ASVAB or ASTB? Help is here! Officer Candidate Tests For Dummies gives you the instruction and practice you need to pass the service-specific candidate tests and further your military career as an officer in the Army, Air Force, Navy, Marine Corps, or Coast Guard. Packed... more...
Get a plan to ace the exam—and make the most of the time you have left Whether you have two months, one month, or even just a week left before the exam, you and get a trusted and achievable cram plan to ace the GMAT Reflects the latest changes that will be administered to the GMAT in June 2012 Each plan includes a diagnostic test, subject... more...
Get?without ever breaking a sweat! First, you'll determine exactly how much time you have... more... |
Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for).
Pc Calculator is a clever note and formula editor combined with an advanced and strong scientific calculator. Being an editor it is extremely user-friendly allowing all possible typing and other errors to be easily corrected and fast recalculated. |
Concepts of Modern Mathematics (Dover Books on Mathematics)
Some years ago, "new math" took the country's classrooms by storm. Based on the abstract, general style of mathematical exposition favored by research mathematicians, its goal was to teach students not just to manipulate numbers and formulas, but to grasp the underlying mathematical concepts. The result, at least at first, was a great deal of confusion among teachers, students, and parents. Since then, the negative aspects of "new math" have been eliminated and its positive elements assimilated into classroom instruction. In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts underlying "new math": groups, sets, subsets, topology, Boolean algebra, and more. According to Professor Stewart, an understanding of these concepts offers the best route to grasping the true nature of mathematics, in particular the power, beauty, and utility of pure mathematics. No advanced mathematical background is needed (a smattering of algebra, geometry, and trigonometry is helpful) to follow the author's lucid and thought-provoking discussions of such topics as functions, symmetry, axiomatics, counting, topology, hyperspace, linear algebra, real analysis, probability, computers, applications of modern mathematics, and much more. By the time readers have finished this book, they'll have a much clearer grasp of how modern mathematicians look at figures, functions, and formulas and how a firm grasp of the ideas underlying "new math" leads toward a genuine comprehension of the nature of mathematics itself |
Algebra - 91 edition
Summary: This introduction to modern algebra emphasizes concrete mathematics and features a strong linear algebra approach. Covers exclusively topics that are of importance to the average mathematician. Focuses on the solution of interesting special cases and applications of theory.
Presents main examples before abstract definitions and covers technical points only where necessary.
Fine Pages are clean. Boards are solid, and spine is square and tight. Excellent condition inside and out. No damage to the book. All items guaranteed, and a portion of each sale supports social pro...show moregrams in Los Angeles. Ships from CA. ...show less
$96.67 +$3.99 s/h
Good
Books Revisited Chatham, NJ
Possible retired library copy, some have markings or writing.
$111 |
This learning object from Wisc-Online covers the fundamental laws of algebra. The interactive activity includes slides which cover the following topics: the commutative, associative and distributive laws as applied to...
This module focuses on hurricane history, development, and paths. The hurricane theme is embedded in computational science activities that use math and statistical analysis. Students work in small groups and as...
This interdisciplinary learning activity illustrates the differences between the amplitude and magnitude of earthquakes in a mathematical context. Students will express earthquake magnitude as a logarithmic function of...
This series of lectures, created by Gilbert Strang of the Massachusetts Institute of Technology, provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers.... |
Norwood, PA Geometry can guide, but students must do the work.Introduction to the basics of symbolic representation and manipulation of variables. Liberal use of concrete examples. May require review of arithmetic concepts, including fractions and decimals |
manual provides worked-out, step-by-step solutions to the odd-numbered problems in the text. This gives students the information as to how these ...Show synopsisThis manual provides worked-out, step-by-step solutions to the odd-numbered problems in the text. This gives students the information as to how these problems are solved Student Solutions Manual for Gustafson/Frisk's Beginning...Good. Student Solutions Manual for Gustafson/Frisk's Beginning and Intermediate Algebra: An Integrated App |
There
are a variety of geometry courses: some take an intuitive, coordinate, vector,
and/or synthetic approach; others focus on Euclidean geometry and include metric
and synthetic approaches as axiomatic systems; and still others include topics
in Euclidean and non-Euclidean geometries and provide opportunities for
comparisons and contrasts between the two.
What approaches are
best?
What are
particularly good topics with which to begin geometry courses?
What are some of the most enjoyable proofs to share
with students?
What are the best ways in which to explore polyhedra,
tessellations, symmetry groups and coordinate geometry?
How can we help students to develop the visualization
skills for two and three dimensions as well as to help them to develop the
mathematical reasoning skills that are important for
studying/exploring/applying geometry at any level?
What are the best ways in which to compare and
contrast Euclidean and non-Euclidean geometry?
How can we best convey the beauty of geometry to
students?
This
session invites presentations that address these questions as well as those
that involve geometric topics from other courses including those for
pre-service teachers. Presenters are welcome to share interesting applications,
favorite proofs, activities, demonstrations, projects, and ways in which to
guide students to explore and to learn geometry. Presentations providing
resources and suggestions for those teaching geometry courses for the first
time or for those wishing to improve/redesign their geometry courses are
encouraged.
The
spreadsheet is an excellent and engaging tool for facilitating student investigations
of a wide range of concepts from geometry. This presentation presents
illustrative examples of the analytic geometric use of Excel in algebra,
geometry, calculus, linear algebra, and other classes. We present
eye-catching animated models for the construction of pedal and inverse
curves, evolutes, and similar topics, as well as the use of geometry in the
classes listed above, and in the creation of attractive drawings for cultural
designs and alphabet books. In the process of creating these models, students
learn the underlying geometrical concepts through their implementations.
In
this presentation, I will discuss how I use the free software GeoGebra to help students understand constructive proofs
in geometry. My examples will include proofs in both Euclidean geometry and
hyperbolic geometry. I will also discuss ways that GeoGebra
can be used to help students form conjectures about properties of geometric
objects.
Designs
with iteratively inscribed triangles can easily be created using dynamic
software programs such as Geometer's Sketchpad. Besides their visual appeal,
these designs can be used in serious mathematical proofs that combine
elements of classical geometry with the concept of limit. We demonstrate how
to use iterated inscribed triangles to create a simple "Voila!" proof of the
Euler line property. We will also show how iterated inscribed triangles can
be used to characterize and locate any triangle's Brocard
points, and to characterize these points as points of concurrence of a
special set of logarithmic spirals. These proofs are amenable to the
discovery approach, and may be used in the classroom. All our demonstrations
utilize "Compass and Ruler", a freely-available Java applet that enables
dynamic, iterative geometrical constructions.
Researchers
in Mathematics Education often draw a distinction between a proof that
convinces and a proof that explains. In this talk we will discuss a
quintessential experience of this distinction for a result in the elementary
geometry of the circle. Dissatisfaction with a proof that convinced, but
failed to explain to the author's satisfaction, led to an exploration on
Geometer's sketchpad. This provided insight which enabled construction of a
different proof which the author believes has more explanatory power. We will
discuss the process and the proof.
We
will show student projects involving classification of quadratic and cubic
surfaces using singularities, symmetry groups, lines and curves on them as
well as other geometric invariants. The visualization of these surfaces using
modern software produce beautiful and unexpected
images that serve as a motivation for students to work on semester long
projects.
Marshall
University offers a four hour freshman honors seminar in mathematics and art,
with emphasis on geometry. The beauty and usefulness of mathematics is
enhanced by a studio component taught by an art professor. Topics covered
include perspective, symmetry, mathematical themes in art, and studio skills.
In
this talk I will describe the course I developed that teaches geometry within
an historical context. This approach has many positive features. Students
read the first book of Euclid's Elements to review some basic Euclidean
geometry. Students learn that important contributions were made by
mathematicians from various civilizations. Students discover that geometry
has developed over the years and that every development in mathematics, e.g.,
algebra, calculus, and abstract algebra, has provided new tools and raised
new questions for geometry. Students realize that geometry is much broader
than they thought and remains an area of active mathematical research and
development.
I
will describe a project that I developed for my geometry course. I
collaborated with an architecture professor to select a number of floor plans
designed by architecture students. Then I let the math students loose to
prepare a lease space analysis applying basic concepts from two and three
dimensional geometry.
What
should a geometry course for non-majors look like? In particular, what topics
will convey the beauty of geometry and, at the same time, attract students
from the humanities who only want to satisfy their general reasoning requirement?
My solution is "Symmetry and Shape," a 100-level course that examines
geometric concepts as it engages students with hands-on explorations and
examples from art and nature. Although I originally designed the course to
appeal to students from the arts, it has also been a popular choice for
preservice elementary teachers and majors in biology, theatre, and history.
This talk will address issues in designing the course, including topic
selection and assessment options. I'll list the major topics covered and give
examples of innovative assignments, in-class explorations, technology-based
labs, and available resources. I'll also describe assessment components,
including two portfolio projects: one focused on examples of symmetry from
students' environment, and another featuring original student art based on
concepts studied in the course (culminating in a display for the campus Arts
Week).
According
to Euclid, if two points are taken at random on the circumference of a
circle, then the straight line joining the points falls within the circle.
Starting from this example, we show how topological data analysis could
reshape the teaching of geometry. In particular, we outline a course in
elementary geometry aiming to engage students in learning via modeling.
My
geometry course is a whirlwind tour through different geometries such as
Euclidean, hyperbolic, analytic, finite, and transformational. Geometry is
offered every two years so the students enter the course with a very diverse
mathematical background. This presentation will examine a series of hands-on
activities done throughout the course including constructions, paper folding
and the creation of hyperbolic paper. We will discuss how my goals of the
activities: to develop visualization skills for all students, to motivate
proof-writing for second-year majors , and to give pre-service teachers
examples of activities they can use in their future classes were met and look
at student responses to the activities.
With
the increased emphasis on Transformational Geometry in the PreK-12
curriculum, and the continued need to study Euclidean Geometry, a rethinking
of Geometry courses for preservice teachers may be necessary. One way of
preparing future teachers, well as current teachers, is to combine Euclidean
and Transformational Geometries into a single study rather than treating each
as a separate topic. In this presentation, I will share some paper folding
and Patty Paper activities that invite preservice students to more actively
engage in the study of Geometry and also provide these students with
opportunities to explore both Transformational and Euclidean techniques for
creating proofs. In addition, some of these activities can be extended to
explore ideas in Non-Euclidean Geometries.
Geometry
students benefit from "playing" with geometrical objects. I have students use
mirrors, basketballs, approximations of hyperbolic planes, both knitted and
plastic, and other toys. These experiences help them develop valuable
geometrical intuition and make conjectures. I will discuss how I have used
hands on experiences to help students develop geometrical approaches to
proofs and understand mathematical ideas. |
8 Actions
How do you rebuild your Math skills after college? Incidentally, for me it seems getting a job at a Machine Learning company has helped the most. It's forced me to review a lot of old material, as well as take some Coursera courses to build my statistical base a bit.
How do you rebuild your Math skills after college? So I had a mix across various professors' classes. I believe the general problem solving strategies (algebraic logic, decomposition, etc) are preserved in some form or another, but more complex/specific things are not. For example, if asked, I could not perform a Laplace Transform, or even recall what it was really for. |
Workshop Precalculus provides students with a bridge to the study of calculus and helps them develop the confidence, understanding, and skills necessary for continuing their study of mathematics. Based on the premise that students learn better by doing and constructing their own knowledge, the Workshop approach involves instructors giving up some command and control of the classroom in favor of giving the students more responsibility for their own learning; this approach eliminates the distinction between classroom and laboratory work.
By systematizing and supporting a simple interactive teaching format, Workshop Precalculus helps instructors implement sound methods that alternate between three primary components: Summary Discussions, Introductory Remarks, and Collaborative Activities. While students benefit greatly from performing computations and symbolic manipulations and sketching graphs by hand, the text integrates the use of the graphing calculator so that students learn to regard technology as a valuable tool.
The Instructor Resources to accompany Workshop Precalculus help instructors create a fully investigative and collaborative learning environment for students and support a simple "interactive teaching format" which consists of: Introductory Remarks, Collaborative Activities, and Summary Discussions. With the help of the Instructor Resources, all motivated faculty members can make the transition, with minimal obstacles, from the course they've always taught to the course they've always wanted to teach. |
Street Mathematics and School Mathematics
(Paperback)
Street Mathematics and School Mathematics Book Description
People who learn to solve problems 'on the job' often have to do it differently from people who learn in theory. Practical knowledge and theoretical knowledge is different in some ways but similar in other ways - or else one would end up with wrong solutions to the problems. Mathematics is also like this. People who learn to calculate, for example, because they are involved in commerce frequently have a more practical way of doing mathematics than the way we are taught at school. This book is about the differences between what we call practical knowledge of mathematics - that is street mathematics - and mathematics learned in school, which is not learned in practice. The authors look at the differences between these two ways of solving mathematical problems and discuss their advantages and disadvantages. They also discuss ways of trying to put theory and practice together in mathematics teaching.
About the Author :
Terezinha Nunes has contributed to Street Mathematics and School Mathematics as an author.
Nunes is Lecturer in the Department of Child Development and Primary Educaton at the Institute of Education, University of London.
Analucia Dias Schliemann has contributed to Street Mathematics and School Mathematics as an author.
Schliemann is Associate Professor in the Department of Psychology, Federal University of Pernambuco, in Recife, Brazil.
David William Carraher has contributed to Street Mathematics and School Mathematics as an author.
Carraher is Associate Professor of Psychology at Federal University of Pernambuco in Recife, Brazil.
Popular Searches
The book Street Mathematics and School Mathematics by Terezinha Nunes, Analucia Dias Schliemann, David William Carraher
(author) is published or distributed by Cambridge University Press [0521388139, 9780521388139].
This particular edition was published on or around 1993-4-30 date.
Street Mathematics and School Mathematics has Paperback binding and this format has 184 number of pages of content for use.
This book by Terezinha Nunes, Analucia Dias Schliemann, David William Carraher |
For many students, calculus can be the most mystifying and frustrating course they will ever take. This study guide works as a supplement to any single-variable calculus course or textbook. It includes more than 475 examples (ranging from easy to hard) that provide step-by-step reasoning.
Covers topics such as: Pure Mathematics; Proof Mechanics; and, work and energy Statistics. This title includes key features such as: definitions of more than 600 key terms; hundreds of helpful graphs, tables, and figures; and, presentations of formulae, rules, proofs, and equations.
Offers you 3,000 solved problems covering various areas of calculus. Featuring many diagrams and illustrations, this text highlights the problem-solving skills you need to know. It helps you to shorten your study time, increase your test scores, and get your best possible final grade. |
Yes, I agree that there are many subjects where needing reference material is going to be a serious problem. I still don't believe that a lot of mathematics is in that category, though.
Much of biology, medicine, anthropology, etc. are knowledge-based sciences. Math and physics tend to be computation-based sciences. Obviously, if you don't have the basic knowledge, you can't even start the computation. However, speed of computation is very different than speed of knowledge recall. |
Algebra Explained c. 1 Order of Operations LITE
This LITE version allows you to "try before you buy" and includes 2 lessons, 2 study card stacks and 2 sets of practice problems.
Algebra Explained includes the following features: • Each lesson is an expertly produced video with clear examples that use coloring and animation to highlight key concepts • 10 thoughtfully created and sequenced practice problems per lesson • Study cards for key facts with the ability to edit, create or delete study cards • Email your study cards to yourself or a friend • Electronic scratch paper • Electronic graph paper • Calculator • Quizzes and a test • Problems & lessons that emphasize personal finance • History of practice sessions • Souvenir diploma for graduates
The FULL VERSION of Chapter 1 covers the following concepts: • Introduction to exponents • The order of operations • Review of fractions • Evaluating algebraic expressions • Euler's Number, "e"
The FULL VERSION of Chapter 1 includes connections to the following real-world topics: • Basketball • Interest • Investing • Credit cards • Heart rate • Pie... lots and lots of pie • The lottery • Present value of money |
Precalculus - 3rd edition understa...show morend the material.
Features
Functions Early and Integrated: Functions are introduced right away in Chapter 1 to get students interested in a new topic. Equations and expressions are reviewed in the second chapter showing their connection to functions. This approach engages students from the start and gives them a taste of what they will learn in this course, instead of starting out with a review of concepts learned in previous courses.
Algebraic Visual Side-by-Sides: Examples are worked out both algebraically and visually to increase student understanding of the concepts. Additionally, seeing these solutions side-by-side helps students make the connection between algebraic manipulation and the graphical interpretation.
Zeros, Solutions, and x-Intercepts Theme: This: In each chapter, optional Technology Connections guide students in the use of the graphing calculator as another way to check problems.
Review Icon: These notes reference an earlier, related section where a student can go to review a concept being used in the current section.
Study Tips: These occasional, brief reminders appear in the margin and promote effective study habits such as good note taking and exam preparation.
Connecting the Concepts: Comprehension is streamlined and retention is maximized when the student views a concept in a visual form, rather than a paragraph. Combining design and art, this feature highlights the importance of connecting concepts. Its visual aspect invites the student to stop and check that he or she has understood how the concepts within a section or several sections work together.
Visualizing the Graph: This feature asks students to match an equation with its graph. This focus on visualization and conceptual understanding appears in every chapter to help students see ''the big picture.''
Vocabulary Review: Appearing once per chapter in the Skill Maintenance portion of an exercise set, this feature checks and reviews students' understanding of the language of mathematics.
Classify the Function: With a focus on conceptual understanding, students are askedOnly lightly used. Book has minimal wear to cover and binding. A few pages may have small creases and minimal underlining. Book321460065Once Upon A Time Books AR Tontitown, AR
2007 Hardcover Our goal with every sale is customer satisfaction, so please buy with confidence. Every order is shi pped the same day or the next day. This is a used book, in good condition, that ma...show morey show some signs of use or wear. ...show less
$13.75 +$3.99 s/h
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Friends of the Phoenix Library Phoenix, AZ
2007 Hardcover Good Domestic Media Mail shipping ONLY. This is a former library copy with library stickers and stamps. 100% of this purchase will support literacy programs through a nonprofit organ...show moreization!90 Your |
practical guide to modern financial risk management for both practitioners and academics The recent financial crisis and its impact on the broader economy underscore the importance of financial risk management in today's world. At the same time, financial products and investment strategies are becoming increasingly complex. Today, it is more important than ever that risk managers possess a sound understanding of mathematics and statistics. In a concise and easy-to-read style, each chapter of this book introduces a different topic in mathematics or statistics. As different techniques are introduced, sample problems and application sections demonstrate how these techniques can be applied to actual risk management problems. Exercises at the end of each chapter and the accompanying solutions at the end of the book allow readers to practice the techniques they are learning and monitor their progress. A companion website includes interactive Excel spreadsheet examples and templates. Covers basic statistical concepts from volatility and Bayes' Law to regression analysis and hypothesis testing Introduces risk models, including Value-at-Risk, factor analysis, Monte Carlo simulations, and stress testing Explains time series analysis, including interest rate, GARCH, and jump-diffusion models Explores bond pricing, portfolio credit risk, optimal hedging, and many other financial risk topics If you're looking for a book that will help you understand the mathematics and statistics of financial risk management, look no further. |
Calculus Revisited: Single Variable Calculus
by MIT OpenCourseWare
To listen to an audio podcast, mouse over the title and click Play. Open iTunes to download and subscribe to iTunes U collections.
Description
Calculus Revisited is a series of videos and related resources that covers the materials normally found in a freshman-level introductory calculus course. The series was first released in 1970 as a way for people to review the essentials of calculus. It is equally valuable for students who are learning calculus for the first time.
About the Instructor
Herb Gross has taught math as senior lecturer at MIT and was the founding math department chair at Bunker Hill Community College. He is the developer of the Mathematics As A Second Language website, providing arithmetic and algebra materials to elementary and middle school teachers.
You can read more about Prof. Gross on his website.
Acknowledgements
Funding for this resource was provided by the Gabriella and Paul Rosenbaum Foundation.
Name
Description
Released
Price
1
VideoPreface
Calculus Revisited is a series of videos and related resources that covers the materials normally found in a freshman-level introductory calculus course.
Finding the derivative when the functional relationship is implied; application to the case of x to the n where n is a rational number; the use of implicit differentiation in the study of related rates.
Axiomatic approach to area; area approximations by upper and lower bounds; the method of exhaustion; using limits to find areas of nonrectilinear regions; piecewise continuity; trapezoidal approximations.
The concept of the natural logarithm; the notion of the rate of change being proportional to the amount opresent; the general concept of a logarithmic function; ln x in terms of differential and integral calculus...
The concept of partial fractions; finding f(x) when f'(x) is the quotient of two polynomials; some notes about identities; application of partial fractions to the case where f is of the form f(sinx, cos x).
Discussion of how infinity differs from "very large"; some sublte and not-so-subtle consequences of the difference; the case against intuition; motivating infinite series in terms of finding area as a limit.
Customer Reviews
One of the best math teachers in the world!
by
TimeRelic
This course is so well done and presented by one of the best math teachers in the world. The professor's ability to simplify and explain math terms and notations is incredible. Even though in black and white and on an old chalkboard you just find yourself learning calc every step of the way.
MIT please post more videos of Professor Herbert Gross if you have them in your archive.
Simple Explained
by
Viktor Kilgore
This podcast is an excellent source of know Calculus. The fact of it being older makes connections with modern day language fascinating.
Amazing resource!
by
dfs90aa
Kudos for this professor, great teaching style and understandable examples. |
kuta software infinite pre algebra answers
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Question:Alright, so I got my schedule, and I was asking other previous eighth graders about my math teacher and they all said he was really mean, and he always picks on people who he knows don't know the answer, so my friend told me this,
"you learn % you learn cross multiplication you learn some decimal stuff you learn probability"
Now I need you guys to write info down to help me study and get ready for his class, thank you allll soooo much:)
Best answer get ten points!
Answers:Absolute Value: The distance of a number from the origin. Absolute value is an example of a norm.
Arithmetic: Arithmetic is the branch of mathematics dealing with numerical computation. Arithmetical operations include addition, congruence calculation, division, factorization, multiplication, power computation, root extraction, and subtraction.
Arithmetic Series: A series in which the difference between any two consecutive terms is a constant.
Associative: An operation * is associative if x*(y*z) = (x*y)*z for all x, y, and z.
Base: The number of digits in a number system. The same word is used in the context of logarithms.
Cartesian Coordinates: The usual coordinate system, originally described by Descartes, in which points are specified as distances to a set of perpendicular axes. Also called rectangular coordinates.
Commutative: An operation * is commutative if x*y = y*x for all x and y.
Decimal Expansion: The usual "base 10" representation of a real number.
Distributive: Having the property, in multiplication, that x(y+z) = xy + xz.
Divisor: An integer that divides a given integer with no remainder. A synonym for factor.
Factorial: The product of the first n positive integers, denoted n!.
Fraction: A rational number expressed in the form a/b, where a is known as the numerator and b as the denominator.
Function Graph: The set of points showing the values taken by a function. This type of plot is called simply a "graph" in common parlance, but is distinct from a collection of points and lines that mathematicians refer to when they speak of a "graph."
Geometric Series: A series in which the ratio of any two consecutive terms is always the same.
Greatest Common Divisor: For two or more integers, the largest integer dividing all of them.
Integer: One of the numbers ..., -2, -1, 0, 1, 2, ....
Intersection: (1) For two sets A and B, the set of elements common to A and B. (2) For two or more geometric objects, the set of points that are common to both of them.
Interval: A connected piece of the real number line. An interval can be open or closed at either end.
Irrational Number: A number that cannot be written as a fraction. Irrational numbers have decimal expansions that neither terminate nor become periodic.
Least Common Multiple: For two or more integers, the smallest number that is a multiple of all of them.
Line: The infinite extension in both directions of a line segment, which is the path of shortest distance between two points.
Origin: The point with all-zero coordinates in Cartesian coordinates, or the central point in polar coordinates.
Polynomial: A mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.
Power: An exponent to which a given quantity is raised.
Prime Factor: A divisor that is also a prime number.
Prime Factorization: The factorization of a number into its constituent primes. Also called prime decomposition.
Prime Number: A positive integer that has exactly one positive integer divisor other than 1 (i.e., no factors other than 1 and itself). Prime numbers are often simply called primes.
Pythagorean Theorem: An equation relating the lengths of the sides of a right triangle. Given two sides, the length of the third can be determined.
Quotient: The result of dividing one number by another.
Rational Number: A real number that can be written as a quotient of two integers.
Real Line: A line with a fixed scale so that every real number corresponds to a unique point on the line.
Real Number: The set of all rational and irrational numbers.
Relatively Prime: A term describing integers that share no common positive divisors except 1.
Right Angle: An angle that measures exactly ninety degrees.
Rounding: The approximation of a number by truncating and possibly adjusting the last digit of interest based on digits appearing after it.
Sequence: A (possibly infinite) ordered list of numbers.
Series: An often infinite sum of terms specified by some rule.
Set: A finite or infinite collection of objects in which order has no significance and multiplicity is generally also ignored.
Square Number: An integer that is the square (i.e., second power) of another integer.
Square Root: A square root of x is a number r such that r*r = x.
Question:It's not a homework problem, I'm just curious as to how we know Pi is irrational. I mean, we keep calculating digits of Pi. How do we know that someday we won't find a perfect decimal that really does equal Pi?
I'm Algebra one, so I can't comprehend Calculus, which is what most people seem to use to prove Pi is irrational. An Algebraic answer would be highly appreciated. Thanks!
Answers:Great question! Unfortunately, I don't see any "easy" proofs, and I'm sure if there were one, it would be plastered all over the Internet. It's great that you're asking such questions...number theory is an undervalued part of pre-university mathematics! In high school we never proved this even once we got to calculus, and even looking at the proofs on wikipedia right now, they kind of blow my mind.
All the proofs I see for the irrationality involve some combo of:
1) Infinite sequences / limits
2) Integration (ie calculus)
3) Trigonometric functions
All of those are out of your reach at this moment probably...but don't worry! You'll get there.
I wish I could give you a more satisfactory answer. Hopefully you've encountered the proof that SQRT(2) ir irrational...it's a classic proof because it involves:
1) Proof by contradiction (a VERY important proof technique!)
2) Some basic number theory arguments involving odd and even numbers
One other fun fact: pi is even worse than merely irrational. It's transcendental! What does that mean? Well, SQRT(2) is a solution to the equation x^2 = 2. Pi will NEVER be the solution to ANY polynomial with coefficients that are integers. What's the solution to 4x^4 - 3x^3 + 2x^2 + 9x - 39 = 0? NOT PI!
So basically, the set of real numbers has both rational and irrational numbers. Within irrational numbers, there are "algebraic" well-behaved numbers like SQRT(2), and "transcendental" numbers like pi.
There's another number 'e' that's also famous for being transcendental. It's equal to about 2.71. You'll learn more about e in Algebra II (in a couple of years). There's also one other weird number that's transcendental:
0.1234567891011121314151617....
It's not a simple rational number, because it doesn't have a "repeating" pattern.
Question:couple examples and very detailed or possibly one that has helped you.thank you so much i really do appreciate it and again thank you so much!
Answers:We ordered a pre-algebra book online and if our son was having to much trouble then he would look at the book for help on a question. I'm not sure of the exact link online for the book we ordered but maybe these will help. You can also do a search like typing in free math problem answers algebra solutions and it may show how to solve certain problems. Here is one link for free help
Here is a link where you can type in a problem and it shows you how to solve some.
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Algebra & Trigonometry
Course Description
Prerequisite: MATH 102 or equivalent. Continuation of MATH 102 introduces the basics of trigonometry and reviews basic properties of the complex number system. The concept of function is applied to algebraic, rational, exponential, logarithmic and trigonometric functions. Emphasis on applications of trigonometry to right and oblique triangles and vectors. Assistance available at Center for Academic Success. A scientific calculator is required. Three class hours weekly. |
Prerequisites to follow this textbook are pre-calculus algebra and one year of calculus. The first six chapters are accessible to an average (European) high-schooler. The author says that the ultimate goal is to reach a substantial result in abstract algebra, namely, the classification of finite fields; this reviewer thinks that the crowning jewel of the book is the section on quadratic reciprocity law. The starting point is very elementary and passage to more complicated topics is fairly smooth. Every section is accompanied by a set of exercises, mostly easy, but some challenging. Motivating illustrations are often given by way of modern applications (within 50 years), notably almost all in computer domain (cryptography, etc). Alas the credit number check (Luhn's algorithm) does not seem to work on any of this reviewer's credit cards, perhaps indicating that the algorithm is no longer used for that purpose; Luhn's patent application was in 1954 granted in 1960). An attempt is made to revisit same topics from different points of view, as the new material is developed. The author rightly teaches the reader that many deep theorems that are used today, and in applications at that, go back to the old Greece. The author made a wise choice to include actual formulas for roots of polynomial equations of 3rd and 4th degrees; so was also the choice of not-so-frequent-to-be-found estimates of polynomial roots in terms of their coefficients (but see more general estimates in: [R. Dimitrić, Math. Balk., New Ser. 11, No. 3–4, 203–206 (1997; Zbl 1032.12002)].
Reviewer's remark: A spot-check revealed a few misprints. There are some problems common with (calculus) textbooks that have to cover a large stretch of the mathematical cultural territory within the short spectrum of abilities of an average (American) student. Thus the notions of range and codomain of functions are confused, as typically found in such textbooks.
"Determinants" go only to size 3 by 3. A pedagogical assumption is made throughout the book that more special is clearer, than more general. On p.172 a nonsensical claim is made that order of an element in a finite cyclic group and least common multiple of two numbers are "similar" notions... |
NCTM - Principles and Standards 2000
Standards for grades 9-12
Standard 1: Number and Operation
Mathematics instructional programs should foster the development of
number and operation sense so that all students-
A. Understand numbers, ways of representing numbers,
relationships among numbers, and number systems
1. increase their understanding of systems for representing
numbers and quantities, including matrix representations for
arrays of quantities;
2. compare and contrast properties of numbers and number
systems;
3. begin to understand complex numbers as a superset of the real
numbers and as a system containing solutions for equations
that are not solvable over the real numbers;
4. become familiar with finite sequences and series, including
arithmetic and geometric examples, and develop an informal
understanding of some infinite sequences and series,
especially geometric series.
B. Understand the meaning of operations and how they
relate to each other
1. develop an understanding of the meaning of and
representations for operations on vectors and matrices and,
with appropriate technology, be able to use these operations to
solve systems of linear equations;
2. develop fluency operating on real and complex numbers,
vectors, and matrices, using by-hand operations for simple
cases and using technology for more complex cases;
3. continue to develop an understanding of permutations and
combinations as counting techniques in increasingly complex
situations.
C. Use computational tools and strategies fluently and
estimate appropriately
1. analyze algorithms for operations with numbers, recognize
some of the roles and limitations of particular algorithms, and
be able to verify the viability of selected algorithms;
2. develop an understanding of the effects of measurement error
on computed values;
3. develop the ability to distinguish between estimation and
approximation and use each appropriately in technological and
non-technological settings.
Page 1 of 9
NCTM - Principles and Standards 2000
Standards for grades 9-12
Standard 2: Patterns, Functions, and Algebra
Mathematics instructional programs should include attention to
patterns, functions, symbols, and models so that all students-
A. Understand various types of patterns and functional
relationships
1. be familiar with classes of functions, including linear,
quadratic, power, polynomial, rational, absolute value,
exponential, logarithmic, trigonometric, and step functions;
understand piecewise-defined functions and their properties;
analyze the effects of parameter changes; and describe local
and global behavior;
2. select appropriate representations (numerical, graphical,
verbal, and symbolic) for the functions and relations
embedded in quantitative situations, convert flexibly among
representations, interpret representations, and use them to
interpret the situations represented;
3. use a variety of symbolic representations, including recursive
definitions and parametric equations, to explore the behavior
of functions and relations;
4. reason (from graphs, tables, and formulas) about functions
derived from other functions via transformation (e.g., g(x) = 3
f(x - 2) + 5), inversion, composition, and arithmetic
combination.
B. Use symbolic forms to represent and analyze
mathematical situations and structures
1. represent situations that involve variable quantities with
expressions, equations, inequalities, and systems of equations
using a variety of equivalent forms;
2. develop fluency operating on polynomials, vectors, and
matrices using by-hand operations for the simple cases and
using technology for more complex cases;
3. understand symbolic algebra as abstracted arithmetic;
4. be able to explain, compare, and contrast the major properties
of the objects and operations defined within and across
systems (e.g., rational numbers, polynomials, matrices, and
functions) as they follow certain rules or laws of structure;
5. develop strategies for deciding whether symbolic results
generated with technological tools are reasonable, and
interpret such results in meaningful ways.
C. Use mathematical models and analyze change in both
real and abstract contexts
1. model a wide range of phenomena with a variety of functions
including linear, quadratic, exponential, rational,
trigonometric, and recursively defined functions and recognize
that a particular type of function can model many different
situations;
2. approximate and interpret accumulation and rates of change,
both graphically and numerically, for functions representing a
variety of situations;
Page 2 of 9
NCTM - Principles and Standards 2000
Standards for grades 9-12
3. approximate and find intercepts, local extreme values, and
asymptotic behavior of functions, and interpret such results in
given contexts.
Page 3 of 9
NCTM - Principles and Standards 2000
Standards for grades 9-12
Standard 3: Geometry & Spatial Sense
Mathematics instructional programs should include attention to
geometry and spatial sense so that all students-
A. Analyze characteristics and properties of two- and
three-dimensional geometric objects
1. explore relationships among, make and test conjectures about,
and solve problems involving classes of two- and three-
dimensional geometric objects;
2. connect geometry to other strands of mathematics (e.g.,
measurement, algebra, trigonometry), relate it to other areas of
interest (e.g., art, architecture), and use it to solve problems;
3. recognize geometry as an example of a deductive system, built
from undefined terms, axioms, definitions, and theorems; and
use deduction to establish the validity of geometric conjectures
and to prove theorems.
B. Select and use different representational systems,
including coordinate geometry and graph theory
1. investigate and verify conjectures and solve problems
involving two- and three-dimensional figures, represented with
rectangular coordinates;
2. explore other coordinate systems (e.g., navigational, polar,
spherical) and their uses;
3. explore discrete/finite geometry systems (networks) and their
characteristics and applications;
4. use trigonometric relationships to solve problems.
C. Recognize the usefulness of transformations and
symmetry in analyzing mathematical situations
1. represent translations, reflections, rotations, and
dilations/contractions of objects in the plane using sketches,
coordinates, vectors, or matrices and use these
2. representations to gain information about the transformation;
3. extend transformations to three-dimensions, to include
reflectional and rotational symmetry of solids;
4. understand transformations (under the operation of
composition) as an algebraic system of functions.
D. Use visualization and spatial reasoning to solve
problems both within and outside of mathematics
1. draw and interpret two- and three-dimensional objects
including those involving overlapping figures/objects and
those requiring auxiliary lines;
2. analyze cross-sections, truncations, and
compositions/decompositions of three-dimensional objects;
3. visualize three-dimensional objects and spaces from different
perspectives.
Page 4 of 9
NCTM - Principles and Standards 2000
Standards for grades 9-12
Standard 4: Measurement
Mathematics instructional programs should include attention to
measurement so that all students-
E. Understand attributes, units, and systems of
measurement
1. select an appropriate unit of measurement or scale and
understand the effects of the choices that are made;
2. analyze how changes in the measurement of one attribute of an
object relate to others, such as how the change in the radius or
height of a cylinder affects the surface area or volume of the
cylinder;
3. understand rate of change as a quotient of two different
measures;
4. use successive approximations to find areas and instantaneous
rates of change.
F. Apply a variety of techniques, tools, and formulas for
determining measurements
1. apply scaling techniques to view a problem from different
perspectives, such as window changes in the graphs of
functions;
2. use radian and degree measures;
3. understand and apply the concepts of variance and standard
deviation as measures of spread in a distribution;
4. use dimensional analysis for unit conversion and to verify that
expressions and equations make sense;
5. determine precision, accuracy, and measurement errors;
identify sources (measurement or round-off errors) and
magnitudes of possible errors in a measurement setting;
understand how errors propagate within computations; and
determine how much imprecision is reasonable for various
measurements;
6. use successive approximations to illustrate and use the
formulas for the volume of a sphere, a general cylinder, and a
cone;
7. informally apply limit concepts to further develop the concepts
of area and instantaneous rate of change;
8. combine measurements (e.g. length, time, mass, area, volume)
using ratios to produce measures such as acceleration,
velocity, pressure, and density as well as dimensionless
measures such as trigonometric ratios;
9. combine measurements (e.g. mass, acceleration, distance)
using multiplication to produce measures such as force, work,
and person-hours.
Page 5 of 9
NCTM - Principles and Standards 2000
Standards for grades 9-12
Standard 5: Data Analysis, Statistics, and Probability
Mathematics instructional programs should include attention to data
analysis, statistics, and probability so that all students-
G. Pose questions and collect, organize, and represent data
to answer those questions
1. design and carry out appropriate methods for
gatheringunivariate data, both to study the distribution of a
variable in one population and to compare the distributions of
the same variable in two different populations;
2. design appropriate methods for collecting, recording, and
organizing data to obtain bivariate data in order to study the
association between two variables;
3. select appropriate graphical representations and numerical
summaries of data;
4. understand how a change in a representation (e.g., scales on a
scatterplot, categories in a two-way table, and bin size of a
histogram) affects the information it conveys;
5. use calculators and computer applications (e.g., spreadsheets,
simulation software, and statistical software) appropriately to
assist in data collection, organization, and representation.
H. Interpret data using methods of exploratory data
analysis
1. compute, identify and interpret measures of center and spread
(e.g., range, variance and standard deviation, and interquartile
range);
2. describe shapes of one- and two-dimensional data sets;
3. look for symmetry and skewness, clusters and gaps, and
possible outliers in data and consider their effects on the
interpretation of the data;
4. recognize how sample size or transformations of data affect
shape, center, and spread;
5. use a variety of representations of data, including scatterplots,
frequency distributions, and two-way tables;
6. be able to recognize trends in bivariate data, visually and
numerically, and use technology to determine how well
different models (e.g., linear, exponential, and quadratic) fit
data, while understanding that a perfect fit is unlikely for
empirical data.
I. Develop and evaluate inferences, predictions, and
arguments that are based on data
1. understand the elements involved in finding good models for
phenomena;
2. apply well-fitting models to predict unobserved outcomes;
3. evaluate conclusions based on data;
4. use data from samples to estimate population statistics;
5. use and interpret the normal and binomial distributions
Page 6 of 9
NCTM - Principles and Standards 2000
Standards for grades 9-12
appropriately.
J. Understand and apply basic notions of chance and
probability
1. understand that some phenomena are random and apply the
law of large numbers to predict long term behavior;
2. use probability distributions to compute probabilities of
events.
Page 7 of 9
NCTM - Principles and Standards 2000
Standards for grades 9-12
Standard 6: Problem Solving
Mathematics instructional programs should foster the development of
number and operation sense so that all students-
K. build new mathematical knowledge through their work
with problems;
L. develop a disposition to formulate, represent, abstract, and
generalize in situations within and outside mathematics;
M. apply a wide variety of strategies to solve problems and
adapt the strategies to new situations;
N. monitor and reflect on their mathematical thinking in
solving problems.
Standard 7: Reasoning and Proof
Mathematics instructional programs should focus on learning to reason
and construct proofs as part of understanding mathematics so that all
students-
O. recognize reasoning and proof as essential and powerful
parts of mathematics;
P. make and investigate mathematical conjectures;
Q. develop and evaluate mathematical arguments and proofs;
R. select and use various types of reasoning and methods of
proof as appropriate
Standard 8: Communication
Mathematics instructional programs should use communication to
foster understanding of mathematics so that all students-
S. organize and consolidate their mathematical thinking to
communicate with others;
T. express mathematical ideas coherently and clearly to peers,
teachers, and others;
U. extend their mathematical knowledge by considering the
thinking and strategies of others;
V. use the language of mathematics as a precise means of
mathematical expression.
Page 8 of 9
NCTM - Principles and Standards 2000
Standards for grades 9-12
Standard 9: Connections
Mathematics instructional programs should emphasize connections to
foster understanding of mathematics so that all students-
W. recognize and use connections among different
mathematical ideas;
X. understand how mathematical ideas build on one another to
produce a coherent whole;
Y. recognize, use, and learn about mathematics in contexts
outside of mathematics.
Standard 10: Representation
Mathematics instructional programs should emphasize mathematical
representations to foster understanding of mathematics so that all
students-
Z. create and use representations to organize, record, and
communicate mathematical ideas;
AA. develop a repertoire of mathematical representations that
can be used purposefully, flexibly, and appropriately;
BB. use representations to model and interpret physical, social,
and mathematical phenomena |
Combinatorics and Reasoning Representing, Justifying and Building Isomorphisms
Description: Combinatorics and Reasoning: Representing, Justifying and Building Isomorphisms is based on the accomplishments of a cohort group of learners from first grade through high school and beyond, concentrating on their work on a set of combinatoricsMore...
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Combinatorics and Reasoning: Representing, Justifying and Building Isomorphisms is based on the accomplishments of a cohort group of learners from first grade through high school and beyond, concentrating on their work on a set of combinatorics tasks. By studying these students, the editors gain insight into the foundations of proof building, the tools and environments necessary to make connections, activities to extend and generalize combinatoric learning, and even explore implications of this learning on the undergraduate level.This volume underscores the power of attending to basic ideas in building arguments; it shows the importance of providing opportunities for the co-construction of knowledge by groups of learners; and it demonstrates the value of careful construction of appropriate tasks. Moreover, it documents how reasoning that takes the form of proof evolves with young children and discusses the conditions for supporting student reasoning |
Graphing Calculator Tutorial for Statistics:Organized by topic, this tutorial will guide students through the keystrokes needed to most efficiently use their graphing calculator. Although based on the TI-84 Plus Silver Edition, operating system 2.30, the keystrokes for this calculator are identical to those on the TI-84 Plus, and very similar to the TI-83 and TI-83 Plus. This tutorial should be helpful to students using any of these calculators, though there may be differences in some lessons.
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Rent Graphing Calculator Tutorial for Statistics 10th edition today, or search our site for textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Pearson. |
Assist students to easily transition from arithmetic to algebra! Teachers can use the Helping Students Understand series as a full unit of study or as a supplement to their curriculum while parents can use this series to help their struggling students grasp algebraic concepts. This book includes step-by-step instructions with examples, practice problems using the concepts, real-life applications, a list of symbols and terms, tips, answer keys, reference, and NCTM Standards and Expectations for 2004. 128 pages Helping Students Understand Algebra online from Wayfair, we make it as easy as possible for
you to find out when your product will be delivered.
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available to help. Whether you just want to buy a <strong>Carson Dellosa Publications</strong> Helping Students Understand Algebra or shop for your entire home, Wayfair has a zillion things home. |
This text, which grew out of a NSF grant, takes a fresh approach with a focus on the underlying concepts of precalculus, rather than sheer algebraic manipulation. It effectively prepares students for a new generation of calculus courses and allows instructors to become actively involved in the teaching process. The authors make extensive use of real world applications, showing students how mathematics relates to their field of study, as well as including a thorough integration of technology. Additionally, the authors have incorporated a number of learning features designed to ready students for a more positive calculus experience.
Whether making a presentation or dealing one on one, interacting at a meeting or just answering questions, do others listen when you talk? This book explains how to communicate successfully so people listen, understand, and are persuaded. It is a comprehensive guide to every aspect of communicating in the workplace and beyondReal World Windows 8 Development is a developer's handbook - an essential guide to building complete, end-user ready Windows 8 applications on the XAML and C# programming stack from start to finish. Starting with Windows 8 basics and walking through practical aspects of building your Windows 8 application, you'll find step-by-step instructions and practical advice that will leave you with a modern, elegant app written to the highest of standards. |
How to Solve It: A New Aspect of Mathematical Method
(Paperback)
How to Solve It: A New Aspect of Mathematical Method Book Description
George Polya was a Hungarian mathematician. He wrote this, perhaps the most famous book of mathematics ever written, second only to Euclid's "Elements." "Solving problems," wrote Polya, "is a practical art, like swimming, or skiing, or playing the piano: You can learn it only by imitation and practice. This book cannot offer you a magic key that opens all the doors and solves all the problems, but it offers you good examples for imitation and many opportunities for practice: If you wish to learn swimming you have to go into the water and if you wish to become a problem solver you have to solve problems." The method of solving problems he provides and explains in his books was developed as a way to teach mathematics to students.
About the Author :
George Polya has contributed to How to Solve It: A New Aspect of Mathematical Method as an author.
Biography of George Polya Born in Budapest, December 13, 1887, George Polya initially studied law, then languages and literature in Budapest. He came to mathematics in order to understand philosophy, but the subject of his doctorate in 1912 was in probability theory and he promptly abandoned philosophy. After a year in Gottingen and a short stay in Paris, he received an appointment at the ETH in Zurich. His research was multi-faceted, ranging from series, probability, number theory and combinatorics to astronomy and voting systems. Some of his deepest work was on entire functions. He al
Popular Searches
The book How to Solve It: A New Aspect of Mathematical Method by George Polya, Sam Sloan
(author) is published or distributed by Ishi Press [4871878309, 9784871878302].
This particular edition was published on or around 2009-6-1 date.
How to Solve It: A New Aspect of Mathematical Method has Paperback binding and this format has 280 number of pages of content for use.
This book by George Polya, Sam Sloan |
Shorewood Chemistry completed the class discrete mathematics for computer science while in college. The topics covered were logic, proofs, mathematical induction, sets, relations, graph theory etc. I apply this knowledge almost daily when I program in excel. |
hands to explore and build proficiency and eventually to replicate... I've previously taken regular calculus classes with engineers and won... This is not the same at all. We were solving real problems every day...Students work through problems using an online interactive textbook D...When teams become stuck on a problem Chiel or a teaching assistant m...
hands, to explore and build proficiency, and, eventually, to replicate and build on recent math models used in the biological sciences. The course is cross-listed as both a biology and biomedical engineering class.
"I've previously taken regular calculus classes with engineers and wondered what would the classes ever be useful for," said Kate Coyle, a biology major who completed the Dynamics class and graduated this semester. "Labs I've had in biology and physics show you the protocol and the expected result.
"This is not the same, at all. We were solving real problems every day."
Students work through problems using an online interactive textbook, Dynamics of Biological Systems: A Modeling Manual Chiel wrote and the computer programming language Mathematica, which scientists worldwide rely on to build mathematical models of complex systems. Chiel's book is available free to students as well as teachers who may want to use it as is or as a model for their own classes.
When teams become stuck on a problem, ,Chiel or a teaching assistant makes suggestions, gives clues and tries to coax out the answer. After success, teachers quiz individuals about how they found the solution and what they'd learned.
The class of 30 is spread out among hexagonal tables. Teams power up their laptops and go to work. Each day the teachers rotate to a different group of students, and after each class they compare notes on who has mastered the skills and who needs extra help, Gill said.
When the second half of the semester begins, teams choose a mathematical model that was recently published in a scientific journal, begin reconstructing and analyzing it and then writing in detail what they learn. The students then extend the model to answer new questions that they ask themselves, and write up results as if they were writing for a scientific journal.
Coyle and her teammates Valencia Williams and Joshua DeRivera focused on a pa |
Maths
In essence Mathematics is fundamental, engaging and opens doors in Business, Science, Technology and beyond. Our desire at St Andrew's is to develop numerical fluency, effective problem-solving skills and a pursuit of understanding in all our students. There is inherent beauty in the discovery and appreciation of mathematical theorems and appreciating this elegance is a goal the department share; fundamentally, it is also the range of applications and versatility of the subject that makes it invaluable to the student and the prospective employer.
At St Andrew's, we follow the Edexcel IGCSE course, with all students sitting the Higher tier papers at the end of Year 11. A calculator may be used in both papers, and there is no coursework. From early in Year 9, students are set according to their abilities and speed of learning, with the top set steadily and deliberately stretched beyond the syllabus in order to provide further challenge and to deepen their understanding. With hugely experienced staff in the department, each student has a teacher who is an expert in their profession as evidenced by the consistently impressive grades at IGCSE.
Students progressing to A level Mathematics normally have an A or A* grade at IGCSE and require an enjoyment of the subject and a relish for the algebraic aspects in particular. We continue to follow the Edexcel syllabus, sitting the Core Mathematics 1 and 2 and Statistics 1 modules in the Lower Sixth, and Core Mathematics 3 and 4 and Mechanics in the Upper Sixth. Further Mathematics is also available for the strongest mathematicians, and involves taking the whole A level in the first year, and then a further six modules in the final year.
A good result in A level Mathematics is essential for most university courses in Mathematics, Science and Engineering, as well as Economics and Business related courses. |
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. Three hundred thirty eight Mathematical Dictionary for School textbooks are available for sale on ValoreBooks.com, one hundred eighteen used from the cheapest price of $0.01, or buy new starting at $6.38 [more which may show some signs of use or wear. [less]
A Mathematical Dictionary for Schools contains contains over 500 definitions of technical terms found within GCSE syllabuses. Key words and phrases are explained in clear, si [more]
A Mathematical Dictionary for Schools contains contains over 500 definitions of technical terms found within GCSE syllabuses. Key words and phrases are explained in clear, simple language with illustrations to aid understanding of more difficult terms |
Product Description
Instead of memorizing formulas and equations, Videotext Algebra helps students to understand math through mastery learning, encouraging them to solidify each concept before moving on the next. A copy of the print materials needed for this module is included.
Solving Relations (Given Slope & intercept, Given Slope & One Solution, Given two solutions, special cases, Principle of Zero Products, Common Factor, Difference of Squares, Perfect Square Trinomial, General Trinomial, Four or More Terms, Sum or Difference of Cubes, General Strategy, Synthetic Division, Literal Equations)
Product Reviews
VideoText Interactive Algebra Module D DVD
5
5
1
1
This product is amazing.
This is such an impressive lesson plan. Especially, if your child struggles with Algebra/Geometry. It doesn't come any clearer or easier. It's a little expensive, but you will not be disappointed.
January 4, 2011 |
Summary
Key Message: Lialrs"sDevelopmental Mathematicsgives readers effective design with many exercises and applications to enhance comprehension of basic mathematics and algebra. Key Topics: Whole Numbers, Multiplying and Dividing Fractions, Adding and Subtracting Fractions, Decimals, Ratio and Proportion, Percent, Geometry, Statistics, The Real Number System, Equations, Inequalities, and Applications, Graphs of Linear Equations and Inequalities in Two Variables, Exponents and Polynomials, Factoring and Applications, Rational Expressions and Applications, Systems of Linear Equations and Inequalities, Roots and Radicals, Quadratic Equations Market: For all readers interested in mathematics.
Table of Contents
Whole Numbers
Reading and Writing Whole Numbers
Adding Whole Numbers
Subtracting Whole Numbers
Multiplying Whole Numbers
Dividing Whole Numbers
Long Division
Rounding Whole Numbers
Exponents, Roots, and Order of Operations
Reading Pictographs, Bar Graphs, and Line Graphs
Solving Application Problems
Summary
Review Exercises
Test
Multiplying and Dividing Fractions
Basics of Fractions
Mixed Numbers
Factors
Writing a Fraction in Lowest Terms
Multiplying Fractions
Applications of Multiplication
Dividing Fractions
Multiplying and Dividing Mixed Numbers
Summary
Review Exercises
Test
Adding and Subtracting Fractions
Adding and Subtracting Like Fractions
Least Common Multiples
Adding and Subtracting Unlike Fractions
Adding and Subtracting Mixed Numbers
Order Relations and the Order of Operations
Summary
Review Exercises
Test
Decimals
Reading and Writing Decimals
Rounding Decimals
Adding and Subtracting Decimals
Multiplying Decimals
Dividing Decimals
Writing Fractions as Decimals
Summary
Review Exercises
Test
Ratio and Proportion
Ratios
Rates
Proportions
Solving Proportions
Solving Application Problems with Proportions
Summary
Review Exercises
Test
Percent
Basics of Percent
Percents and Fractions
Using the Percent Proportion and Identifying the Components in a Percent Problem |
How to Teach Mathematics - 2nd edition
Summary: This expanded edition of the original bestseller, How to Teach Mathematics, offers hands-on guidance for teaching mathematics in the modern classroom setting. Twelve appendices have been added that are written by experts who have a wide range of opinions and viewpoints on the major teaching issues.
Eschewing generalities, the award-winning author and teacher, Steven Krantz, addresses issues such as preparation, presentation, discipline, and grading. ...show moreHe also emphasizes specifics--from how to deal with students who beg for extra points on an exam to mastering blackboard technique to how to use applications effectively. No other contemporary book addresses the principles of good teaching in such a comprehensive and cogent manner.
The broad appeal of this text makes it accessible to areas other than mathematics. The principles presented can apply to a variety of disciplines--from music to English to business. Lively and humorous, yet serious and sensible, this volume offers readers incisive information and practical applications5.646.0951 +$3.99 s/h
Good
Campus_Bookstore Fayetteville, AR
Used - Good TEXTBOOK ONLY! 2nd75 +$3.99 s/h
New
Dream Books Company, LLC Englewood, CO
1999 Paperback New Book may contain minor shelf wear.
$24.97 +$3.99 s/h
Good
One Stop Text Books Store Sherman Oaks, CA
1999 |
A series of online tutorial units with quizzes designed for students in the introductory college or university physics course. The page includes topics from math, physics, and biophysics. Remedial material includes...
This simulation-based laboratory activity allows the student to practice several types of graphs and explore the types of information that we can collect from graphs. Coverage include exploration of linear, non-linear...
Richard Lowry of Vassar College has created a log-linear analysis which is a version of chi-square analysis. The relevant values are calculated by way of weighted natural logarithms. This page will calculate several...
This interdisciplinary learning activity illustrates the differences between the amplitude and magnitude of earthquakes in a mathematical context. Students will express earthquake magnitude as a logarithmic function of...
This algebra lesson helps students connect how logarithms work to the real world example of financing a car. Students will use a formula to calculate the number of months it will take them to pay off a car loan based on... |
1. Introduction
Volume 3, Why Slopes and More Math.
A Calculus Preview
Slopes for the graphs of straight lines, that is, linear functions
y = mx+b are met in high school algebra or
trigonometry. Many problems involving the slopes of linear functions can
often be resolved by setting up and solving two linear equations in two
unknowns.
Slopes for the graphs of both linear and nonlinear curves y =
f(x) are met in late high school or early college calculus
courses along with rules for their calculation. In calculus, slopes are
called derivatives. Formulas for slopes are obtained or derived
from formulas for curves y = f(x).
A simple geometric interpretation of slopes follows. The graph of a
function y = f(x) gives a two-dimensional trail
through hills and valleys. A skier in crossing such two or three
dimensional hills is aware of the slope of the ground and how this slope
changes. The skier in question can tell when or where the uphill and
downhill sections are located from the slope of a ski. This represents
the first easily visualized physical or geometry interpretation of
slopes. Further examples will be given.
Rules for differentiation (slope calculation) give formulas for the
slopes of functions y = f(x). In the opposite
direction, formulas for functions y = f(x) may in
some instances be found by reversing the methods of slope calculation, a
process called anti-differentiation or integration. Finding a function
f(x) from a knowledge of its slope etc., leads to and
justifies common formulas for the perimeters, areas of regions in the
plane, the length of curves and the volumes, weights and masses of
solids.
Other Books
The following why slopes chapters complement what is usually
written in algebra and calculus texts about the calculation of slopes and
their geometrical or physical interpretation. Their aim is to explain in
a simple way why slope calculation (differentiation rules) and the
reversal of the slope calculation process (anti-differentiation rules)
are of interest. The rules for differentiation and anti-differentiation
are somewhat involved. But it is possible without them to grasp clearly
many of the ideas and motivations for slope-related computations.
Most of the material below may fit between the definition of slopes for
straight lines in a high school algebra or trig course and the
calculation of slopes for nonlinear functions in calculus courses. The
remaining material may be read in or along side a first or second course
on calculus or read before by gifted students (avid readers) still in
school.
Remark: The following texts or others will supply the missing
details.
Calculus with Analytic Geometry by D. G. Zill, PWS Publisher,
1985
Calculus of One and Several Variables, by S. L. Salas and E.
Hille (John Wiley & Sons 1971 and 1974, ISBN 0-471-00956-3).
The above books or others on calculus should be in a public
library or a school library. Just as two views are better than one, so
are two calculus books better than one. When the wording in one is
obscure or not readily understood, the slightly different description or
ordering of the same topics in the other may clarify matters. This advice
applies even to the pages of this book. A break from reading might also
have the same effect.
Remark: The formal or proper presentation of mathematics
requires no diagrams and no physical interpretation/reasoning. But
without diagrams and without geometric or physical interpretations in
examples, mathematical ideas can be without motivation. The following
pages put the motivation first angles |
ccwatcher monitors the progress of computational chemistry calculations during runtime. It has both a GUI and a "Command Line Interface" to which it parses important output and plots SCF energies. Avogadro plugin capability is planned.
Features
* Su
Microsoft Mathematics 4.0 (32- Description
Microsoft Mathematics provides a set of mathematical tools that help students get school work done quickly and easily. With Microsoft Mathematics, students can learn to solve equations step-by-step while gaining a better understanding of fundamental concepts in pre-algebra, algebra, trigonometry, physics, chemistry, and calculus. Microsoft Mathematics includes a full-featured graphing calculator that's designed to work just like a handheld calculator. Additional math tools help you evaluate triangles, convert from one system of units to another, and solve systems of equations. Features: The Step-by-Step Equation Solver Graphing calculator Formulas and Equations Library Triangle Solver Unit Conversion tool Requires: Microsoft .NET Framework 3.5 SP1. |
helpful hints and easy-to-understand examples, this book covers the type of mathematical problems that face golf course superintendents every day. How to handle budgeting estimates, apply fertilizers and pesticides accurately, the ordering of topdressing, irrigation volume and coverage, area and volume calculations, and many other parts of golf course operation require a thorough understanding of basic mathematical principles. This book has the solution you need! Example problems, and the answers, along with additional practice material is guaranteed to help you get the job done right. |
Geometry Seeing, Doing, Understanding
9780716743613
ISBN:
0716743612
Edition: 3 Pub Date: 2003 Publisher: W H Freeman & Co
Summary: Jacobs innovative discussions, anecdotes, examples, and exercises to capture and hold students' interest. Although predominantly proof-based, more discovery based and informal material has been added to the text to help develop geometric intuition.
Jacobs, Harold R. is the author of Geometry Seeing, Doing, Understanding, published 2003 under ISBN 9780716743613 and 0716743612. One hundred sixty nine Geometry ...Seeing, Doing, Understanding textbooks are available for sale on ValoreBooks.com, twenty five used from the cheapest price of $54.57, or buy new starting at $166Tempe, AZShipping:StandardComments:WE HAVE NUMEROUS COPIES -HARDCOVER, Mild shelf wear to cover, edges, and corners, a ding to the ... [more]WE HAVE NUMEROUS COPIES -HARDCOVER, Mild shelf wear to cover, edges, and corners, a ding to the top and bottom of spine, otherwise book is NEW. [less] |
Student Solutions Manual for Faires/Burden's Numerical Methods, 4th
Book Description: Contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer. |
Marketing Math Essentials provides an interactive learning experience to help marketing students understand the key concepts
behind commonly used marketing analyses. More than just an online problem set, the application presents the definitions, formulae,
and examples for most of the quantitative analyses required in the course.
Although statistical analysis and modeling in marketing research can be very sophisticated, much of the day-to-day number
crunching for managers is simple arithmetic and algebra. The calculations themselves are not difficult; the challenge
lies in knowing which analyses to employ and what to conclude from the results. Real day-to-day problems are messy. They do not
come pre-packed like a homework assignment and certainly do not have "answers in the back of the book." Marketing Math Essentials presents
problems in a "real-life" format, enabling students not only to practice the calculations, but also to
reason out which calculations are appropriate in each scenario. |
More About
This Textbook
Overview
Three-disc CD-ROM multimedia presentation of the most important principles of the algebra- and trigonometry-based physics course. Content screens provide in-depth coverage of abstract and often difficult principles, building connections between physical concepts and mathematics. The presentation contains more than 350 movies-both animated and live video-including laboratory demonstrations, "real world" examples, graphic models, and step-by-step explanations of essential mathematics. An accompanying workbook contains practical physics problems directly related to the presentation, along with worked solutions. This CD can be used with any algebra/trig based introductory physics |
ocused on helping readers understand and construct proofs – and, generally, expanding their mathematical maturity – this best-seller is an accessible introduction to discrete mathematics. Takes an algorithmic approach that emphasizes problem-solving techniques. Expands discussion on how to construct proofs and treatment of problem solving. Increases number of examples and exercises throughout |
This applet allows a person to test several numerical integration approximation methods by having the user fill out theleft...
see more
This applet allows a person to test several numerical integration approximation methods by having the user fill out theleft and right endpoint fields, type in the formula, select the method, and pressing the calculate button. For example trytyping in -1 for the left endpoint, 1 for the right endpoint, and y=x^2 for the formula then press calculate. For each method selected, the estimated integral for that method will appear in the text area at the bottom. Certainfunctions will also appear on the graph on the left. The java graph class is still experimental and does not use equalstretch principles. y = x2 from -1 to 1 will appear the same as y = x2 from -100 to 100.
A series of tutorials on basic measurement theory, including such topics as experimental errors, measurement, accuracy and...
see more
A series of tutorials on basic measurement theory, including such topics as experimental errors, measurement, accuracy and precision, exact numbers, and significant figures (digits). Applet calculators included, along with quizzes.
Examine how electrons flow within a circuit consisting of a capacitor and battery using...
see more
Examine how electrons flow within a circuit consisting of a capacitor and battery using this tutorial. Visitors can throw a virtual switch to connect the circuit and observe the battery charge the capacitor. Once the capacitor is fully charged, the switch can be reversed to discharge the capacitor.
QuickMath is an automated service for answering common math problems over the internet. ...
see more
QuickMath is an automated service for answering common math problems over the internet. Think of it as an online calculator that solves equations and does all sorts of algebra and calculus problems - instantly and automatically! When you submit a question to QuickMath, it is processed by Mathematica, the largest and most powerful computer algebra package available today. The answer is then sent back to you and displayed right there on your browser, usually within a couple of seconds. Best of all, QuickMath is 100% free! |
Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer Algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and more |
MATH10131 - Calculus and Vectors B
Requisites
Aims
The course unit aims to provide an introduction to the basic elements of calculus.
Brief Description
This lecture course introduces the basic ideas of complex numbers relating them the standard transcendental functions of calculus. The basic ideas of the differential and integral calculus are revised and developed. Vectors in two and three dimensions are introduced and this leads on to the calculus of functions of more than one variable and the beginnings of vector calculus.
Learning Outcomes
On successful completion of this module students will have acquired an active knowledge and understanding of some basic concepts and results in calculus.
More on Complex Numbers. Euler's Theorem and De Moivre's Theorem; polar form of complex numbers (polar representation of the plane); roots of unity; complex forms of sin and cos, relationship to trigonometric identities.
Functions of more than One Variable. Partial derivative, chain-rule, Taylor expansion; turning points (maxima, minima, saddle-points); grad, div and curl and some useful identities in vector calculus; integration in the plane, change of order of integration; Jacobians and change of variable; line integrals in the plane; path-dependence, path independence; Stokes' theorem and Green's theorem.
Teaching & Learning Process (Hours Allocated To)
Lectures
Tutorials/Example Classes
Practical Work/Laboratory
Private Study
Total
33
11
0
106
150
Assessment and Feedback
Assessment:
Supervision attendance and participation; Weighting within unit 10%
Coursework; One in-class test, weighting within unit 15%
Two and a half hours end of semester examination; Weighting within unit 75% |
Student Success in
Mathematics: Guiding
Principles
Teresa Thiel
Monica Brown
Shahla Peterman
Math Technology Learning Center
University of Missouri-St. Louis
The Problem
College Algebra is required for many
majors, including all the sciences
Student success (a grade of C- or better)
was low
Drop-rate was high
Students hated math and procrastinated
as long as possible
Students had to retake College Algebra
Concerns of the math faculty
High failure rate
Effect on student
retention
Sacrificing quality
for quantity
Lack of uniformity
among course
sections
Our Goals
Increase student
understanding and
success in math
Better prepare students
for success in future
courses
Provide uniformity among
all the sections of the
course
Increase student retention
Increase students'
confidence in their math
ability
Increase in Student Success
Student Success Rate in College Algebra
Post
100% Pre
90%
80%
Success Rate
70%
60%
50%
40%
30%
20%
10%
0%
01-02 02-03 03-04 04-05 05-06
Academic Year
Structure of the Redesigned
Course
One 75 minute
lecture
Two 75 minute labs
in the Math
Technology Learning
Center (MTLC)
Homework online
using software called
CourseCompass
Pre-Lecture Preparations
Weekend Prior to the
Lecture
"Task of the Week"
Worksheet
Outline of material
CourseCompass
homework – can be
done at home or in
MTLC
"Lecture"
Present overview
of new topics
Answer questions
Review for
upcoming tests
No formal lecture
Sample problems
worked for
students
Sources of Student Help
Online tutorials and
guided solutions
"Ask My Instructor" online
help
Peer tutoring
TA and faculty
Math Technology Learning Center
Complete
homework
Individual
help
Peer
tutoring
Take quizzes and exams
Assessment
Weekly online
homework
Weekly online
quizzes
Four hourly
exams
Comprehensive
final exam
What are the results?
Increased passing rate
in the course
Fewer repetitive
questions in class
Fewer student
complaints
Better prepared
students for the future
Why does it work?
Guiding Principles
Principle 1: Provide a clear structure for
the course that helps the students
through the course
Principle 2: Provide sufficient time-on-
task and enforce deadlines
Principle 3: Reward students for their
efforts
Guiding Principles
Principle 4: Provide regular assessment of
progress
Principle 5: Accommodate diverse styles
of learning
Principle 6: Stay in touch
Principle 1: Provide a clear structure for the
course that guides the students through the
course
The lecture session provides an anchor and structure for
the course that helps the students to focus on the tasks
they need to complete that week.
– Online, post lecture outlines, a worksheet, and the tasks for next
week
– Open homework for the next week
– Since many of the students have already worked on the
homework at home before they come to the lecture class they
are better prepared to ask questions
The responsibility for learning is on the shoulders of the
students.
The instructors are there to provide structure, guidance,
and to help students in their learning.
Principle 2: Provide sufficient time-on-task
and enforce deadlines
Use technology to provide sufficient information and
practice problems for students to learn at their own pace.
Not a self-paced course. Less interested and motivated
students require a high degree of structure to be
successful in courses they do not want to take.
Use a rigid schedule, use technology to open and close
student access to assignments, to quizzes and exams.
– Students must complete the assignments within a specified
window of time or the opportunity is lost.
Tutorials and problems are always available so students
who get behind can catch up, but they lose points if they
do not complete an assignment on time.
When a new instructor complains that the homework
system is not working, it is generally because homework
deadlines are not enforced.
Principle 3: Reward students for their efforts
Students can retry a homework problem multiple times,
and many will try until they get the correct answer.
The reward is a higher score if they succeed.
The homework contributes one-eighth of their final grade
and their homework score is entirely under their control.
More effort leads to a higher grade.
The weekly quizzes have the same types of problems as
the homework, so students who have practiced the
problems to increase their homework scores also score
better on the quizzes.
Students who spend the time to improve their homework
scores actually understand the concepts, know how to
work the problems, and therefore do well on the exams.
Principle 4: Provide regular assessment of
progress
Online homework and quizzes with online
grading provide students with
– immediate feedback
– the opportunity to correct their homework mistakes
– ongoing assessment of their success in the course
Students have both the responsibility for their
own learning and the means to be successful in
learning math.
Online grade book - students know their grades,
know when they need help and know where to
find it.
Principle 5: Accommodate diverse styles of
learning
Students seek and benefit from help that is available in a
variety of forms.
Some successful students work individually using the
tutorials and guided solutions that are available with the
software.
Most students benefit from the resources provided in the
MTLC where the instructor and several teaching
assistants are available for individual assistance.
The MTLC also allows students to collaborate, teaching
each other and solving problems together.
The MTLC also has an area with tables and white-
boards for small group lectures and discussions.
Especially for students who are not comfortable with the
subject, the availability of help in the MTLC is critical to
their success.
Principle 6: Stay in touch
Even with guidance, structure and help, some students
fall behind.
Many students prefer anonymity; however the online
grade book makes their progress easy to track.
A missed assignment triggers a quick message offering
help.
Intervention must begin early and must be maintained
with reluctant students. Once these students get off the
right track it can be very difficult to get them back on.
The personal attention of the instructor often provides all
the motivation a student needs to complete the
assignments.
Benefits
Uniformity in course content
Promotes active learning
Provides students with individualized assistance
Promotes student collaboration and peer
learning
Builds in ongoing assessment and prompt
feedback
Ensures sufficient time on task and monitors
student progress
Applying These Principles
across the Curriculum
Less lecture time – more time in active learning
– Smaller classes - group discussion and presentation interspersed with
short lectures
– Larger classes, personal response systems, keep students engaged
– Points for active learning experiences within a lecture setting increases
student engagement
Defined course structure with clear expectations for students
– Many students overwhelmed by the amount of work expected of them in
college courses
– The less structure, the more likely students are to procrastinate
– Homework assignments with a firm deadline can enhance student
success in many courses
Technology can increase contact with students, personalizing
interaction
– Communication by e-mail and instant messenger is not only normal for
most students, it is perceived as personal.
– Small gestures such as using a student's name in an e-mail can further
the sense of connection and motivate students who often feel invisible.
Cost issues
Negative - Course reductions for the faculty who
were developing the redesign.
Negative - $350,000 for the MTLC
Positive - increase in class size (35 to 70),
which decreased instructional costs over the
longer term. Despite increase, more individual
student attention.
Positive - cost savings from the increased
student retention and progression to graduation.
Negative ($) and positive (success) - decline in
enrollment because many students do not
retake the course.
Cost of Shattered
Dreams
• Pre-pharmacy major
• Failed College Algebra
twice
• Changed major to
Communication
• Took College Algebra in
MTLC – earned an A
• Took Calculus in MTLC-
earned an A
• Changed major back to
pre-pharmacy
Facilitating Change
Maintain flexibility, make incremental changes, remember that slow
progress is better than no progress, and keep both a sense of
perspective and a sense of humor.
Faculty resist change.
– Be respectful but insistent that technology, used appropriately, not only
enhances student learning but also frees their time to work individually
with students
Provide adequate training in the guiding principles, the techniques
for implementation of these principles, and in the technology.
Students resist change.
– They are accustomed to having a passive role in their learning and often
object when the responsibility is placed on their shoulders.
– Many of them do not want to use technology as a major tool for
learning.
– Be respectful but insistent that they learn best when they are actively
engaged in the process of learning and that help is available.
Acknowledgements
Roadmap to Redesign Program – Carol Twigg
Mark Burkholder, Dean of the College of Arts
and Sciences
Prabhakar Rao, Chair of Mathematics
Jim Tom, Associate Vice Chancellor
for Information Technology Services
Glen Cope, Provost and Vice
Chancellor for Academic Affairs
Many math faculty who
worked on the redesign |
Algebra: Form and Function
9780471707080
ISBN:
0471707082
Edition: 1 Pub Date: 2009 Publisher: Wiley
Summary: This text offers a fresh approach to algebra that focuses on teaching readers how to truly understand the principles, rather than viewing them merely as tools for other forms of mathematics. It relies on a storyline to form the backbone of the chapters and make the material more engaging.
Connally, Eric is the author of Algebra: Form and Function, published 2009 under ISBN 9780471707080 and 0471707082. Five ...hundred seventy two Algebra: Form and Function textbooks are available for sale on ValoreBooks.com, one hundred sixty five used from the cheapest price of $30.33, or buy new starting at $153 |
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