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Perform basic calculations involving the above mentioned notions, both in concrete cases and in more general and abstract cases.
Describe the main ideas in proofs involving the notions above, like for instance the impossibility of trisecting the angle and doubling the cube.
Contact Information
[email protected]
Course offered (semester)
Spring
Language of Instruction
English
Aim and Content
The course covers basic theory of groups and permutations, normal subgroups, group homeomorphisms and factor groups, group actions and Sylow Theory. In addition, the course includes the basic theory of rings and fields, polynomial rings, ideals and factor rings. Studies also include field extensions, finite fields and unique factorisation domains. In the latter, the focus is on groups of utomorphisms of fields, including the Galois theory necessary to show the insolvability of the general quintic by radicals. |
American Journal of Computational Mathematics is a journal dedicated to providing a platform for publication of articles about mathematical research in areas of science where computing plays a central and essential role emphasizing algorithms, numerical methods, and symbolic methods. AJCM covers the following topics: |
mathematic... mathematical statistics and to information theory. The effective construction of probability spaces receives particular attention. Author Alfred Rényi—former Director of the Mathematical Institute of the Hungarian Academy of Sciences and an expert in the fields of probability theory, mathematical statistics, and number theory—considered effective construction of probability spaces particularly important to applying methods and results of probability theory to other branches of mathematics. Professor Rényi discusses basic theorems of probability theory in terms specific to the theorem in question, rather than in the most general form. His rigorous treatment also covers the mathematical notions of experiments and independence, the laws of chance for independent random variables, and the effects of dependence. Two brief appendixes offer helpful background in measure theory and functional analysis.
Bonus Editorial Feature:
Alfred Renyi (1921–1970) was one of the giants of twentieth-century mathematics who, during his relatively short life, made major contributions to combinatorics, graph theory, number theory, and other fields.
Reviewing Probability Theory and Foundations of Probability simultaneously for the Bulletin of the American Mathematical Society in 1973, Alberto R. Galmarino wrote: "Both books complement each other well and have, as said before, little overlap. They represent nearly opposite approaches to the question of how the theory should be presented to beginners. Rényi excels in both approaches. Probability Theory is an imposing textbook. Foundations is a masterpiece." In the Author's Own Words: "If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy."
"Can the difficulty of an exam be measured by how many bits of information a student would need to pass it? This may not be so absurd in the encyclopedic subjects but in mathematics it doesn't make any sense since things follow from each other and, in principle, whoever knows the bases knows everything. All of the results of a mathematical theorem are in the axioms of mathematics in embryonic form, aren't they?" — Alfred Rényi |
MTH 5020
Basics
Office Hours
MW: 10am-11am
TH: 2pm-3pm
or by appointment
Prerequisites:
Successful completion of MTH 1610 or successful completion of the MTH 1610 Place-Out Test administered by the Department of Mathematical and Computer Sciences, or successful completion of a course accepted for transfer as MTH 1610 by the Department of Mathematical and Computer Sciences or the College.
Requirements:
Pens preferred; graph paper, and a scientific calculator; that is, a calculator that can handle numbers in scientific notation and has [yx], [π], and [!] keys. (Cell-phone calculators, generally, are not scientific.) CELL PHONES ARE TO BE SHUT OFF AT THE BEGINNING OF CLASS (unless a prior arrangement with me has been made).
Course Overview:
This graduate course is designed to deepen and extend prospective teachers' understanding of the concepts underlying the school mathematics curriculum in grades PK-5. Teachers working in the diverse contexts of school mathematics classrooms must possess not only sound understanding of mathematical ideas, but of the processes by which this understanding develops and in which this understanding is applied. Therefore, how one does mathematics in this class is as important as the mathematical ideas themselves.
In this course, students will:
Pose and solve problems, individually, and in groups, in class and outside of class;
Describe and analyze their work and the work of others, including the mathematical thinking of children as seen in written and video cases drawn from elementary classrooms, both orally and in writing;
Use a variety of tools, including manipulative models and technology, to solve problems;
Demonstrate working knowledge of the big mathematical ideas of the course.
Examine records of elementary classroom practice – videos and samples of children's written work – to analyze children's understanding of the mathematical ideas listed in above.
Classroom Environment:
It is absolutely critical that we create a productive classroom environment that is friendly, non-judgmental, gentle and relaxed so that all class members will feel sufficiently safe to offer suggestions even when they are not absolutely sure that they are correct. So, take care with each other's feelings. Give each other permission to be unsure, and encouragement to take chances and make guesses. That's how we will all learn best. And besides, it is more fun that way.
We will be doing mathematics "one problem at a time." A "problem" is a mathematical situation for which you know no solution. An "exercise" is an opportunity to practice a known procedure. We will be exploring a lot of problems, and in the process will learn many useful strategies for solving them. The goal is to understand and explain why things are true, often in several different ways. After each class, your task is to review your notes, make sense of as much as you can and mark the parts about which you are still confused. Then ask about them with your groupmates or me. In this class, everything can make sense! ! This course does not follow a textbook, so I suggest that you keep a loose-leaf notebook that contains an accurate record of all in and out of class activities. You will refer to it frequently as your prepare your assignments and use it for the in-class exams. They are open-book!
The Mathematical "Big Ideas" of This Course:
Mathematical problem-solving, reasoning, and communication;
Proportional Reasoning;
Patterns and their identification, representation, analysis, generalization, and use;
Descriptive Statistics;
Probability;
Mathematical Disposition (This is, participating in the individual, small-group, and whole-class activities and discussions that constitute the daily work of the course; offering mathematical ideas for discussion and analysis by others, both orally and in writing; demonstrating intellectual commitment to learning and teaching mathematics.
As part of the learning process in our classroom, everyone is expected to observe the professional skills you make use of every day in your workplace. The classroom environment is one where a feeling of safety and security is necessary. Being considerate of others, their opinions and points of view is essential and expected. An atmosphere of equality,
respect and consideration are all considered part of professionalism. Behaviors that would indicate you are acting in a professional manner would include (and are not limited to):
relevant and appropriate participation in class discussions;
avoiding the use of iPods, computers, cell phones and text messaging;
preparation for class through reading all assigned material and handing assignments in on time;
use of active listening skills (even if you disagree with someone's point of view);
attentiveness when someone else is speaking and
an attitude that reflects openness and receptivity to learning and the learning process.
Part of your responsibilities as members of this classroom community includes recognizing the importance and responsibility you hold in facilitating the learning of your fellow classmates.
Attendance:
Successful completion of this course does not depend only on scores on assessments. It depends, in large part, on having participated in the set of class activities that comprise the course. Therefore, prompt attendance is required. I do understand that there might be times when you must miss class. If you must miss all or part of a class, use the office hours, phone number or e-mail address provided on page 1 to discuss the reasons with me beforehand. Whenever you miss class, you must do a 2 - 3 page "make-up" of the material that was missed. This involves writing your own set of notes about what happened that day and the results that were found in class. (This way, your personal set of class notes will be complete for use on the exams.) The "make-up" must be completed within a couple weeks of the absence. More than three absences will lower your grade by one letter, unless special arrangements are made with the instructor.
(Regular tardiness will be interpreted as a lack of intellectual commitment to the course, and will prevent a student from earning an "A.")
Assessment and Grading: Assessment in any mathematics class is the process of gathering and reporting evidence of students' developing mathematical proficiency. In this class a database of evidence, collected from a variety of sources and built throughout the semester, will be summarized as a letter grade, as described next.
1. What are the characteristics of a student who will earn a grade of "B" or better in this class?
Such a student will have, by the end of the course, provided consistent evidence of having reached an appropriate level of mathematical proficiency. Mathematical proficiency is defined as:
Conceptual understanding of the big ideas that underlie the school mathematics curriculum, and fluency with the procedures, skills and tools used to do mathematics.
The strategic competence needed to tackle novel mathematical problems, including the problems of understanding the mathematical thinking of children, and the adaptive reasoning needed to explain and justify one's own methods and solutions, and the methods and solutions offered by others;
A productive disposition toward doing and learning mathematics. A prospective teacher has a productive disposition if she views mathematics as a sensible and meaningful discipline, and if she sees herself as capable of making sense of her own mathematical ideas and those offered by children, through persistent and diligent effort.
2. How does an "A" student differ from a "B" student?
An "A" student will have distinguished herself by:
Providing convincing evidence of a level of mathematical proficiency that goes well beyond the standard set for the course;
Participating consistently in the individual, small-group, and whole-class activities and discussions that constitute the daily work of the course;
Regularly offering mathematical ideas for discussion and analysis by others, both orally and in writing;
Demonstrating, through attendance, promptness, and attitude, the intellectual commitment to learning at the heart of outstanding teaching.
3. What are the characteristics of a "C" student?
Such a student will have, by the end of the course, provided some evidence of mathematical proficiency, but not at the consistent level required to earn a grade of "B" or better. She might fall short of that standard, and earn the minimum passing grade for the course, if she:
Demonstrates proficiency in some but not all of the sections of the course;
Participates, but only intermittently, in class activities and discussions;
Demonstrates, through poor attendance, excessive tardiness, missing or late written work, or poor attitude, a lack of intellectual commitment to learning and, by extension, to teaching.
4. Why no "D" grades?
This course is required for prospective teachers, and a licensure recommendation is based on, among other things, grades of "C" or better in all required courses. A student who does not earn a grade of "C" or better will have to repeat the course, so a grade of "D" would be meaningless. A student who does not demonstrate the minimum characteristics of a "C" student, as described above, will receive a grade of "F."
5. How can a student in this class provide evidence of mathematical proficiency and commitment to teaching?
The instructor will give students opportunities throughout the semester to demonstrate mathematical proficiency, by assigning mathematical tasks to be completed in writing. The students' written work will be assessed using the attached scoring guides. These mathematical tasks will be of five types:
Embedded tasks: instructional tasks for which the student composes an individual, written response in class.
A Midterm and Comprehensive Final comprised of tasks similar to the embedded tasks described above.
Homework:
Homework will be assigned when appropriate. Sometimes, homework will be graded for completion, other times it will be graded more rigorously.
Reading Responses: Students will be assigned weekly readings that will usually be about 15-20 pages. Students will be asked to respond to the readings in writing either on-line through "Just In Time Teaching" or through a written assignment.
The instructor will also gather, in a systematic if not exhaustive way, evidence of mathematical proficiency from students' daily work in class. Therefore, participation in class discussions is a good way to meet or exceed the requirements of the course.
Grading Criteria for MTH 2620
Here is how the final course grade will be calculated. Performance on the AMTs and the Final Exam are weighted very heavily. If your actual assessments don't fit into the attached rubric then the instructor will make a judgment call.
AMT "M" or "IP" grade
An AMT will be given a grade of M when all problems meet expectations. AMTs that do not meet this standard will be given a grade of IP. Students are expected to revise and resubmit their work until they get a grade of M for each of their AMTs. Revisions will be considered late if they are turned in more than a week after they are returned. Late papers, including late revisions, will cause the numeric grade for the assignment to be lowered.
Numeric Grade:
The following two components will determine a student's numeric grade for the semester.
AMTs: Each problem on the first submission will be graded using the attached rubric. The numeric score for the AMT will be the average of the scores for the first submission. Re-writes of the AMT will not affect the numeric score. The semester AMT numeric score will be the average of the individual AMT scores.
Exams: Exam problems will also be graded on the attached rubric. The exam numeric score for the semester will be the average of the scores for the individual problems. The semester exam numeric score will be the average of the two individual exam scores.
Religious Holidays:
Observance of religious holidays follows College policy, which is posted on the web at in the Academic and Campus Policies for Students section. Each student is responsible for understanding and abiding by the policy.
Americans with Disabilities AccommodationsAcademic Dishonesty:
An act of Academic Dishonesty may lead to sanctions including a reduction in grade, probation, suspension or expulsion. See the Student Handbook at in the Academic and Campus Policies for Students section. |
Demystified
Unlike most books on algebra, this guide lets readers master algebra one simple step at a time--at their own speed. "Algebra Demystified" is loaded ...Show synopsisUnlike most books on algebra, this guide lets readers master algebra one simple step at a time--at their own speed. "Algebra Demystified" is loaded with diagrams to reinforce mathematical concepts, along with exercise sets, chapter ending quizzes, and final exams to master the material Algebra Demystified
Some but not many penciled in answers, but I have an eraser(haha). The book was in tact and just what I needed to advance myself and with any textbook, to move to the next level.
Very Satisfied!! I give it a Five star rating!:) |
Students will analyze two different approaches for completing a task based on a number of constraints and will determine the optimal method. Students will apply vector addition, as well as critical thinking skills.
Students will
add, subtract, and resolve displacement using unit-vector notation; and
evaluate two approaches, apply a set of constraints and choose the best alternative to the problem. |
Subtracting Integers eBook 1.0
A short ebook explaining a simple way to subtract integers for people who have trouble subtracting integers. This uses a method based on simply changing a subtraction problem to an addition problem based on helping people with algebra.
Distribution Guide 1.0
Distribution Guide is a program allowing to build various graphs of statistical distributions. It enables you to enter the parameters of the particular distribution and display the graphs of such functions as PDF, CDF, and others. Printing support...
Ruler and Compass 1.7.2001
Ge....
InterReg 1.3
Interpolation and Regression are fundamental and important calculations in mathematics. Mr. Newton and Mr. Gauss were engaged in-depth with numerical solutions for these problems. Today, there are improved algorithms, that can solve such...
HighRoad 6.3.5
HighRoad is a software package that lets you design roads as you always have - graphically. It makes use of the proven graphical interface of modern operating systems so you can use the program immediately without learning complicated commands or...
Addition Aliens Game 1.0
A great way for kids or adults to improve their addition and subtraction skills. This math game will let you blast through the alien hordes by typing out the sum or difference between the numbers you see above the aliens as they attack. There are...
GoVenture Lemonade Stand simulation 1.0
GoVenture Lemonade Stand simulation introduces you to the experience of running your own lemonade stand business. It's a first step for children or even adults who need to start with the basics of running a business. It also offers the opportunity...
MATruss 1.5
MATruss performs static strength analysis of a structure made up by truss elements.
An easy to use preprocessor make the input of model data a fast and carefree process.
A thoroughly tested and reliable solver analyses the truss model in detail...
Fomdigests 1
Fom is an automated e-mail list for discussing Foundations Of Mathematics. It is a closed and moderated list (see Stephen G. Simpson : What is Foundations of Mathematics ? for further details).Fom is also avalaible in digest format. This means...
Karnaugh map 1.2Sagata Regression Pro 1.0
Sagata Multiple Regression software offers the power of a professional regression package with the ease and comfort of a Microsoft Excel interface.Features include:Qualitative/Categorical Factors - often inputs or factors in model fitting are... |
The following modules are designed to incorporate technology in a general studies mathematics class.
The technology that has been integrated includes various types of calculators, computers
(mainly using spreadsheets), and the Internet.
Many of the activities that are set up to be done using a calculator could also be revamped
to use a spreadsheet on a computer.
The activities are designed to help students develop skills in problem solving, improve
communication skills (both written and oral), and deepen their understanding of the mathematics
being covered. Some of the activities were chosen because they cover topics with which students
in this type of class have a problem. The activities can be revised to meet the needs of each instructor
and his or her particular class. |
High School Curriculum: Mathematics
Mathematics
Aims and philosophy
The ultimate aim of the Mathematics Department is to maximize the mathematical potential
of each student, regardless of ability. The department strives to make teaching
informative, interesting and inspiring. Specifically, we aim to strengthen and develop
mathematical knowledge and skills, develop the ability to think logically, help
to understand the relevance and application of mathematics in a real-world context,
and help appreciate the power and beauty of mathematics. Equally important is to
enable the acquisition of a suitable foundation in the subject in order to facilitate
further study in mathematics or related subjects.
Curriculum by year-group
Grades 7 – 9:
In grade 7, basic skills are reviewed and consolidated, and students are thereby
encouraged to develop their understanding of the principles involved and their appreciation
of patterns and relationships in mathematics. During grade 8 and into grade 9, students
are set into ability groups. Familiar topics are explored more deeply and new concepts
are introduced. Emphasis is placed on developing a feel for 'number' and interpreting
the reasonableness of results obtained in calculations. At all times, ways of applying
mathematics to everyday situations are investigated, as well as the role of mathematics
in the world in general. As grade 9 progresses, more abstract areas are explored
more fully, especially Algebra.
At the conclusion of these three years, students will hopefully have built a strong
foundation in the major areas of Arithmetic, Algebra, Geometry, Statistics and Probability.
Grades 10 and 11: Edexcel IGCSE Mathematics (4400)
All EIS-J students follow the Edexcel IGCSE syllabus which is offered at both Higher
and Foundation levels. The ability range is wide, and following the same setting
principle as in grades 8 and 9, students are set into four Higher groups and two
Foundation groups in each grade. It is expected that the most able students, especially
those in the two top groups, will be able to achieve excellent or very good grades,
and they consistently meet these expectations. Proportionally very few Higher students
attain less than a 'C' grade (grading is A* to D), and this grade is also attainable
by some Foundation students (grading for this level is C to G).
IGCSE Mathematics can be broadly divided into four main distinct, but at times inter-related,
areas of study: Number, Algebra, Shape and Space, and Data Handling. The aims and
objectives for each level are similar, although the Higher level syllabus is technically
more demanding, especially in the use of Algebra as a tool in solving a wide variety
of problems. In both courses, the skills of interpreting the question and making
the correct decision about which method of solution is applicable, receive particular
attention. There is no coursework component on this course and it is fully expected
that students make appropriate use of a scientific calculator throughout.
Grades 12 and 13: IBDP Mathematics Higher Level, Mathematics Standard
Level, or Mathematical Studies Standard Level
These grades follow the IB diploma programme in Mathematics which includes study
at one of three levels: Mathematics Higher Level, Mathematics Standard Level, or
Mathematical Studies Standard Level. The three levels accommodate different levels
of ability, previous exam success and importantly, whether mathematics will play
a significant role, or not, in any future higher education course undertaken by
a student.
The Mathematics Higher Level course is very demanding and suitable only for the
very best students of this subject. It facilitates entry into courses with a high
mathematical content. To add to the depth of study at this level, the group of core
topics studied is supplemented by an option topic selected from a list of four advanced
and interesting areas of work.
Students on the Mathematics Standard Level course are mathematically competent,
previously demonstrating good skills and achieving good results. They study the
same core topics as on the Higher Level course but not to the same depth. On both
of these courses students must submit a portfolio for internal assessment, consisting
of two pieces of work representing two different types of task.
The Mathematical Studies Standard Level course offers a less demanding study of
the subject and is suitable for students who have previously struggled with mathematics
and/or for those whose may not be required to study the subject at such an intense
level. However, it is challenging in its own right, and should certainly not be
considered as an easy option. It includes useful practical applications, and students
must submit a project for internal assessment. |
Monday, September 28, 2009
September 28, 2009
1st Hour Algebra I/II: Today the students were given back their Chapter 1 Tests. They were allowed to make corrections to their Test, as they did not show mastery of these skills. We will continue to work on the rules of exponents and the F.O.I.L. method and take a re-test on this chapter on Thursday.
3rd Hour Algebra II: Today the students worked on the ISAT Review for the Daily Routine. We then took notes and discussed lesson 2.5, Direct Variation. We did several examples to ensure understanding. For homework, the students should do problems 4-28, the evens, and 31-34, all, on pages 109-110.
4th Hour Algebra I: Today the students worked on the ISAT Review for the Daily Routine. We then began Chapter 2, lesson 1, Rational Numbers. We took notes and discussed the first part of this lesson that discusses the different categories of numbers and graphing those numbers on a number line. For homework, the students should do problems 18-29, on page 71.
6th Hour Algebra I: Today the students took the Chapter 1 Test. For homework, they should do problems 1-16, on page 67. |
Wiki's calculus page gives a good Earth-from-space overview, and its topic-specific pages cover a lot of the material, but there's only the vaguest of hints of the order in which things go. It's still far better than Mathworld's page, though.
Concentrate on the theory behind calculus and DO NOT skip on the proofs. Once you understand the fundamental theorem of calculus everything under it falls into place. Calculus, like many other areas of math, is a large amount of memorization, and an even larger amount of understanding what you're memorizing.
Well, I already know most basic stuff for differentiation and integration (most of calc 1). So, I'm not necessarily looking for an overview of calculus, but something that I could use to study all the stuff I don't already know. Fill in the gaps/gaping holes. The wikibooks and wikisource articles look good. I wouldn't mind delving into a bit of calc 3.
In my opinion, Calc 3 is really simple. Once you have Calc 1 and 2 down, as well as an understanding of Linear Algebra concepts, I'd say you could learn it pretty quickly, if you aren't treated as an idiot.
I've found that reading the calculus textbook I was given as part of my AP Calc class is extremely useful. More useful than the teacher. I don't do the homework, I don't listen to the lessons (You probably shouldn't follow my example, but...), but when it comes for test time, I have pretty much perfect accuracy. It's pretty intuitive, once you understand what you're doing.
A conceptual understanding could definitely come that quickly, but I think you would have a hard time solving any real problems. Plus, once you get up to stuff like calculus of variations you won't have a solid foundation of understanding.
I recommend Mathematical Methods in the Physical Sciences by Mary L Boas as the most practical math textbook I've read. (get it cheap used~$20)
A conceptual understanding could definitely come that quickly, but I think you would have a hard time solving any real problems. Plus, once you get up to stuff like calculus of variations you won't have a solid foundation of understanding.
It could take you an hour to learn how to use a saw, hammer, and tape measure. But building a house could take a lifetime.
Ya calculus is pretty difficult than other topics but there are many websites available online from where you can take reference and in my opinion hard copy is the best option and for that you can refer to Dr.R.D>Sharma's latest edition. |
Mathematics for the Million: How to Master the Magic of Numbers
by Lancelot Hogben Publisher Comments
Taking only the most elementary knowledge for granted, Lancelot Hogben leads readers of this famous book through the whole course from simple arithmetic to calculus. His illuminating explanation is addressed to the person who wants to understand the... (read more)
How To Solve It 2ND Edition a New Aspect of Math
by George Polya Publisher Comments
This perennial best seller was written by an eminent mathematician, but it is a book for the general reader on how to think straight in any field. In lucid and appealing prose, it shows how the mathematical method of demonstrating a proof or finding an... (read more)
Mathematics: From the Birth of Numbers
by Jan Gullberg Publisher Comments
This extraordinary work takes the reader on a long and fascinating journey--from the dual invention of numbers and language, through the major realms of arithmetic, algebra, geometry, trigonometry, and calculus, to the final destination of differential... (read more)
Mathematics : Applications and Concepts - Course 3 (04 Edition)
by Bailey And Pelfrey / Hustchens / Day / Howard Publisher Comments
Mathematics: Applications and Concepts is a three-text Middle School series intended to bridge the gap from Elementary Mathematics to High School Mathematics. The program is designed to motivate middle school students, enable them to see the usefulness... (read more)
Old Dogs, New Math: Homework Help for Puzzled Parents
by Rob Eastaway Publisher Comments students simply memorized their times tables and... (read more)
Mathematical Analysis and Proof: Second Edition
by David S. G. Stirling Publisher Comments
This fundamental and straightforward text addresses a weakness observed among present-day students, namely a lack of familiarity with formal proof. Beginning with the idea of mathematical proof and the need for it, associated technical and logical skills... (read more)
Rapid Math Tricks & Tips: 30 Days to Number Power
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Teaching Mathematics Foundations to Middle Years
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The Stanford Mathematics Problem Book: With Hints and Solutions
by George Polya Publisher Comments
This volume features a complete set of problems, hints, and solutions based on Stanford University's well-known competitive examination in mathematics. It offers students at both high school and college levels an excellent mathematics workbook. Filled... (read more)
Math and Literature
by Marilyn Burns Publisher Comments
From Quack and Count to Harry Potter, the imaginative ideas in childrens books come to life in math lessons through this unique series. Each resource provides more than 20 classroom-tested lessons that engage children in mathematical problem solving |
With comprehensive coverage of basic skills, the Spectrum Math Series features easy-to-follow instructions that give students a clear path to success in math fundamentals. The series emphasizes skill development, computation, problem solving, and provides practice with terminology. Workbooks are available separately in Grades 5-8, or as a four-book set.
The successful series is ideal for students who need special help with the basics. Because of the nature of the content and the students for whom the series is written, readability has been carefully controlled to comply with each mathematical level.
Each 150-page workbook contains a pretest, practice pages, problem-solving pages, and Answer Key. Each book also contains a handy Scope and Sequence reference chart of all the skills covered in the Spectrum Math Series.
Developmental exercises are provided at the top of the page when new skills are introduced. These exercises involve students in learning and serve as an aid for individualized instruction or independent study.
Spectrum Math, Grade 5. Table of Contents:
Addition and Subtraction (1 digit through 6 digit)
Multiplication (2 digit by 1 digit through 4 digit by 3 digit)
Division (2-, 3-, and 4-digit dividends)
Division (4- and 5-digit dividends)
Metric Measurement
Customary Measurement
Fractions
Multiplication of Fractions
Addition of Fractions
Subtraction of Fractions
Geometry
Spectrum Math, Grade 6. Table of Contents:
Addition and Subtraction of Whole Numbers
Multiplication and Division of Whole Numbers
Multiplication of Fractions
Addition and Subtractions of Fractions
Division of Fractions
Addition and Subtraction of Decimals
Multiplication of Decimals
Division of Decimals
Metric Measurement
Customary Measurement
Percent
Geometry
Spectrum Math, Grade 7. Table of Contents:
Operations Involving Whole Numbers
Operations Involving Fractions
Operations Involving Decimals
Ratio and Proportion
Decimals, Fractions, and Percent
Percent
Interest
Metric Measurement
Geometry
Perimeter and Area
Volume
Statistics and Probability
Spectrum Math, Grade 8. Table of Contents:
Operations Involving Whole Numbers, Decimals, and Fractions
Equations
Using Equations to Solve Problems
Ratio, Proportion, and Percent
Interest
Metric Measurement
Measurement and Appreciation
Geometry
Similar Triangles and the Pythagorean Theorem
Perimeter, Area, and Volume
Graphs
Probability
Special Features: An Assignment Record Sheet is provided in each workbook for students to keep track of their assignments and scores. A Record of Test Scores is provided so students can chart their progress as they complete each chapter test. |
Saturday, March 14, 2009
I'm not planning our Algebra 1 classes this year, so I have not been producing much for it. But I did put together a scaffolded introduction to inequalities. The objectives are for students to:
Compare numbers using a number line (i.e. "<" means "to the left of")
Understand the difference between open and closed circles
Graph the solutions of a statement like "x < 3"
Understand graphically why adding/subtracting by any number or multiplying/dividing by a positive number does not change the relative position of two numbers, while multiplying/dividing by a negative number does. In other words, students should understand when and why to "flip the inequality sign" when solving inequalities.
Continuing with the lessons, we learned to factor difference of squares expressions. I used a geometric approach to help make sense out of the pattern, and it has really helped some students figure out how to more easily factor the nasty ones like 25x^2 - 16y^4. A quick sketch of the squares, labeled with their side lengths, has proven quite useful.
It's been a while since I posted. The last week of February was our Junior Trip, in which we take all of our junior class on a 4-day-long trip around California to visit various CSU campuses. It's an incredibly important part of our program, because it is the time when our juniors really start to imagine themselves as college students. The tours, the student panels, seeing the dorms and classrooms, the admissions directors, and the DCP alumni all bring things into sharper focus for the 11th graders. We moved the trip earlier this year (it used to be in April) because kids come back inspired and ready to make positive changes, and so we wanted them to have more time to improve their grades before the end of the semester. It's also a great time for students and staff to bond and get to know each other in different ways. Needless to say, a 4-day, 3-night field trip with 80 high schoolers is tiring. We're all pretty much recovered now, and it's been back to business as usual. Time to catch up on some lesson postings.
In Algebra 2, we're nearing the end of the polynomials and factoring unit. I've been focusing on basic factoring techniques (look for the GCF first, then either use trinomial factoring or difference of squares, if possible). I'm still deciding whether to throw sum/difference of cubes into the mix this time around. I decided to bring simplifying and multiplying rational expressions into this unit (instead of waiting for the rationals unit) because it seemed like a good way to have them get more practice with factoring without repeating the same exact problems again and again. Plus, these questions are prominently featured on the STAR test.
One thing that has been helping students deal with factoring out the GCF is teaching them to write the prime factorization of each term in the polynomial, every time (including a -1 factor when there is a minus sign). Though it takes longer, this is pretty much a foolproof way of factoring out the GCF - many students have a lot of difficulty with the "what's the largest expression that divides into both" method |
Unit specification
Aims
The programme unit aims to introduce the basic ideas of real analysis (continuity, differentiability and Riemann
integration) and their rigorous treatment, and then to introduce the basic elements of complex analysis, with
particular emphasis on Cauchy's Theorem and the calculus of residues.
Brief description
The first half of the course describes how the basic ideas of the calculus of real functions of a real variable
(continuity, differentiation and integration) can be made precise and how the basic properties can be developed
from the definitions. It builds on the treatment of sequences and series in MT1242. Important results are the
Mean Value Theorem, leading to the representation of some functions as power series (the Taylor series), and the
Fundamental Theorem of Calculus which establishes the relationship between differentiation and integration.
The second half of the course extends these ideas to complex functions of a complex variable. It turns out
that complex differentiability is a very strong condition and differentiable functions behave very well.
Integration is along paths in the complex plane. The central result of this spectacularly beautiful part
of mathematics is Cauchy's Theorem guaranteeing that certain integrals along closed paths are zero. This
striking result leads to useful techniques for evaluating real integrals based on the `calculus of residues'.
Intended learning outcomes
On completion of this unit successful students will be able to:
understand the concept of limit for real functions and be able to calculate limits of standard functions and construct simple proofs involving this concept;
understand the concept of continuity and be familiar with the statements and proofs of the standard results about continuous real functions;
understand the concept of the differentiability of a real valued function and be familiar with the statements and proofs of the standard results about differentiable real functions;
appreciate the definition of the Riemann integral, and be familiar with the statements and proofs of the standard results about the Riemann integral including the Fundamental Theorem of Calculus;
understand the significance of differentiability for complex functions and be familiar with the Cauchy-Riemann equations;
evaluate integrals along a path in the complex plane and understand the statement of Cauchy's Theorem and have seen an outline of the proof;
compute the Taylor and Laurent expansions of simple functions, determining the nature of the singularities and calculating residues;
use the Cauchy Residue Theorem to evaluate integrals and sum series.
Future topics requiring this course unit
Real analysis is needed in more advanced courses in analysis, functional analysis and topology and some
courses in numerical analysis.
Complex analysis is needed for advanced analysis, geometry and topology, but also has applications
in differential equations, potential theory, fluid mechanics, asymptotics and wave analysis. |
This textbook entitled Trigonometry (Notes) is a complete and detailed account of trigonometry, including numerous solved problems and formula derivations with each and every step included. Furthermore, the textbook presents the development of trigonometry in a logical manner, starting with the definitions of the six trigonometric ratios on a right-triangle, and later generalizing these definitions for the rectangular coordinate system. Finally, the six trigonometric functions are abstracted from the six trigonometric functions. The textbook is essentially divided into two parts:
Trigonometry developed from the right-triangle, and
Trigonometry derived from the rectangular coordinate system.
Trigonometry (Notes) is intended for the student who wants to learn trigonometry completely and thoroughly, with a complete understanding of the concepts and their relationships to one another.
Except for the Table of Contents, the textbook is hand-written as opposed to typed; thus the word Notes in parentheses in the title.
Originally formulated for the home-schooled student, this five hundred page text and study guide provides extremely detailed explanations in simple English with numerous example problems accompanied by narrative explanations for each topic presented. Reader friendly and logically organized, this volume serves as an all-inclusive high-school algebra text for the college bound student or as an excellent study guide to accompany any serious algebra or trigonometry course. Hundreds of practice problems complete with solutions are included in the text, covering every aspect of a high school or introductory level college algebra course. Also, it is perfect as summer reading for the student who wishes to get ahead or for adults participating in continuing education courses. |
Hello there, I'm a student in high school and I'm tormented by my assignments. One of my issues is addressing online textbook mcdougal littell; Will someone on the web help me in understanding what it's all about? I need to complete this immediately! Thanks to allfor assisting.
I think I understand what you are searching) for. Try out Algebra Buster. This is a wonderful tool that helps you get your assignments completed quicker as well as correct. It can help out with courses in online textbook mcdougal littell, inequalities plus more.
Registered: 24.10.2003
From: Where the trout streams flow and the air is nice
Posted: Sunday 21st of Nov 18:29
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Mathematical Methods of Physics/Matrices
We have already, in the previous chapter, introduced the concept of matrices as representations for linear transformations. Here, we will deal with them more thoroughly.
Definition
Let be a field and let ,. An n×m matrix is a function .
We denote . Thus, the matrix can be written as the array of numbers
Consider the set of all n×m matrices defined on a field . Let us define scalar product to be the matrix whose elements are given by . Also let addition of two matrices be the matrix whose elements are given by
With these definitions, we can see that the set of all n×m matrices on form a vector space over |
Trade in Children's Understanding of Mathematics: 11-16 for an Amazon.co.uk gift card of up to £4.501905200021","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":22.39,"ASIN":"0415266416","isPreorder":0}],"shippingId":"1905200021::CjWnnMmORDwqVscdNpGktw573TaijnjjA2QMompyX1r21lIJv9FT2xoYnqz7ZUnLaR7ByS9mc%2BPpyEDsWZd9mD3T6ay4%2Fn7V,0415266416::e98pxYZyGLAeQ8kluo6EqdOgX9iHZJqj40mFH8bAsJWcpd5WDEoDehvNRZ%2FRb1J5bFccOCGdg9SQg6lkVUXMKTa54UQ%2FQt which does what the title says. It explains some of the reasons why so many secondary pupild fail maths. It is not that they can't carry out the mathematical priocedure (although many can't) but that they don't know which procedure to apply to even simple problems.
This book is worthwhile for any one who is teaching pupils mathematics at a secondary school level with insightful looks at why pupils struggle with several key areas of the curriculum. A quick flick through this book prior to teaching one of the topics allows you too feel more prepared for the difficulties pupils may face and to forward plan how you will help them overcome these difficulties.
I would also recommend this book to parents whose children struggle with mathematics at secondary school as the insights are just as useful for how you can help them out at home. |
Algebra 2
Algebra 2 consists of many topics which are especially included for students who are weak in maths as they are quiet easy. The topics under Algebra 2 are:
1. Equations and inequalities which consist of many principles like:
Adding principle which says that if a = b, then a + c = b + c for any number c.
Multiplication principle says that if a = b, then a * c = b * c for any number c.
Here, we also deal with Fractions, decimals and if you are unaware with the term inequalities, then the problems containing <, >, <=, >= are called inequalities.
2. Graphs and Functions which includes,
finding slopes of lines, how to graph a Point and lines, functions which are Relations (usually equations) in which no two ordered pairs can have the same x-coordinate when they are graphed, parallel lines are the non-vertical lines having same slopes but different y-intercept and Perpendicular Lines are the non-vertical lines whose Slope product is -1.
3. Polynomials and Factorization which includes Combination of like terms, i.e. terms having same exponents or powers and |
Item Name: Algebra 1 Student Text Item #: 235846 Product Brand: BJU Grade 9 Recommended Grade: Grade 9 Price/ea: $37.00 The Algebra I Student Text includes scriptural principles woven throughout but also an "Algebra and Scripture" spread in each chapter. Concepts are presented with examples and explanations. Other features include "Algebra Around Us" and sections on "Probability and Statistics." Homework sections are on three levels. Cumulative Review questions are located at the end of every section. Procedures and definitions are color-coded for reference.
Quantity:
Read about how we came to homeschool our children on our About Us page. |
Introduction
This unit covers advanced integration techniques, methods for calculating the length of a curved line or the area of a curved surface, and "polar coordinates" which are an alternative to the Cartesian coordinates most often used to describe positions in the plane |
Applied Math Courseware - Metals/Welding
Description
This program provides career-based math activities related to occupational training in Metals & Welding. In addition to helping students improve their basic math skills, they will learn how these skills are used in the workplace. This multimedia presentation is packed with colorful graphics, stimulating background music, helpful math aids, and numerous skill-building activities. Over 100 reproducible activities are included in the comprehensive User's Guide. Students are first assessed using a job specific diagnostic test. The assessment is followed with a math review. There is a unit of job-related word problems. You can view and print activities. You can also view, edit, and print the student's work, as well as add you own math problems to the program. Each student works at his own speed at the computer. |
Algebra
Student success in algebra starts here. Equations, formulas, and graphs take on new meaning in a curriculum that transcends traditional methods of algebra instruction. Algebra is an innovative solution that builds upon the proven success of Modules, our industry-leading curriculum for the middle level, and teaches students abstract algebraic concepts through real-world learning experiences, differentiated instruction, and hands-on activities. It is curriculum designed to ensure student success by providing connections to the world in which they live. Like all of our Modules, Algebra places a heavy emphasis on hands-on instruction in order to engage students and provide relevant, real-world applications of algebraic concepts. |
This course begins with a brief introduction to writing programs in a higher level language, such as Matlab. Students are taught fundamental principles regarding machine representation of numbers, types of computational errors, and propagation of errors. The numerical methods include finding zeros of functions, solving systems of linear equations, interpolation and approximation of functions, numerical integration and differentiation, and solving initial value problems of ordinary differential equations.
This course introduces basic methods, algorithms and programming techniques to solve mathematical problems. The course is designed for students to learn how to develop numerical methods and estimate numerical errors using basic calculus concepts and results, as well as writing programs to implement the numerical methods with a software package, such as Matlab.
Bisection Method: use the bisection method to solve the equation f(x)=0 and estimate the number of iterations in the algorithm to achieve desired accuracy with the given tolerance;
One-Point Iteration: use the iterative method to find the fixed point of the function f(x), and analyze the error of the algorithm after n steps;
Higher-order Rootfinding Methods: use Newton's method, Newton-Raphson's method, or the secant method to solve the equation f(x)=0 within the given tolerance;
Aitken Extrapolation: understand the order of a convergent sequence and use Aitken's method to accelerate the convergence of the sequence, as well as determining the order of convergence using the iterative method combined with the Taylor formula;
Roots of Polynomials: combine Horner's method with Muller's method to compute roots of a polynomial and analyze whether a numerical root is truly a complex root, or if its imaginary part results from numerical errors.
Newton Divided Differences: derive difference formulas to approximate derivatives of functions and use the Lagrange polynomial to estimate the errors of the approximations;
Newton-Cotes Integration Methods: use the closed Newton-Cotes formula, including the Trapezoidal rule and Simpson's rule, to approximate definite integrals; use the Lagrange polynomial to estimate the degree of accuracy; derive the composite numerical integration using the closed Newton-Cotes formula;
Richardson Extrapolation: use Richardson's extrapolation to derive higher order approximation formulas for numerical differentiation and integration; |
rogram. It was and is an extremely valuable educational tool for me. We will, I am told, be using a different program next year (Algebra II), I think I will miss this one!
Reviewed by Joi Cardinal, (northern California)
I've never done well at math in high school or college, but now that I'm re-entering college in my 40s, I really have to learn it in order to succeed in biology and chemistry courses. Thank heavens my local community college has adopted K
Essentials of Technical Mathematics (3rd Edition)
Editorial review
An applications-oriented approach -- designed especially to meet the math needs of those in the various engineering technologies who have limited mathematical backgrounds.
COLLEGE ALGEBRA TRIGONOMETRY W/APPLICATN
Editorial review
Provides a step-by-step approach to algebra and trigonometry, yet introduces many topics early so that a spiraling development of these topics is possible in later chapters. Geometry is integrated throughout the text. And, chapters can be
Helping Your Child With Math
Editorial review
Designed to help children avoid "mathophobia," this book contains practical advice for parents. Brief, cursory, introductory chapters, often with too little explanation, treat motivation, instructional aids, math drills, problem solving,
A series of flash-card activities (bi-lingual in english/spanish)taching math in many areas. Topics are : Advancements in Industry , The Asts, Agriculture, The Environment, & Health, exercise & Fitness (EX...Making money in music...activi
Introductory Algebra
Editorial review
The second volume of a three-book series, Introductory Algebra, Second Edition offers students a text that is easy to read and understand. The explanations are carefully written in language that is familiar to the general student populati
Algebra of Programming, The
Editorial review
Linear Algebra for Mathematics, Science, and Engineering
Editorial review
Presenting the fundamentals of linear algebra, this book progresses from matrix theory to the abstract notions of linear space, and covers eigenvalues and eigenvectors. Applications are shown in each chapter, along with problems and exerc
Linear Algebra (2nd Edition)
Editorial review
This introduction to linear algebra features intuitive introductions and examples to motivate important ideas and to illustrate the use of results of theorems.
Reviewed by J. M. Morrison, (Chapel Hill, NC)
d suggest the reader get an exposure to matrices and related ideas from something a little more concrete.
Reviewed by trailermac "trailermac", (Houston)
Section 2.6 is a good read. One sees that Linear systems really are useful in Arbitrary (finite dim.) vector spaces.
Reviewed by Jeremy, (Tasmania Australia)
erytime this book is opened, regardless of page number I happen to flick to.
Reviewed by Francisco, (New York, NY)
I got this book for my Linear Algebra class about four years ago. This is a great book if you are getting a degree in mathematics. It won't help if you are just trying to get by the class and don't like math. It is not very practical but
Mastering Real Estate Math in One Day
Editorial review
Martha didn't want a pair of huge argyle socks for her birthday and she definitely didn't want to wear the baggy things all the way across town to thank her aunt for them.
Mathematical foundations in engineering and science: Algebra and analysis |
Welcome back to Broad Run!We are eager to begin helping you to be successful in your math class.Your success depends on your effort, your attendance, and your positive attitude.
Your effort will be shown in the notebook that you will be required to keep.In it you will write daily notes and do your assignments.You will also be REQUIRED TO DO YOUR ASSIGNMENTS AND TO TAKE YOUR QUIZZES AND TESTS IN PENCIL.Be sure to correct your errors on your assignments, quizzes, and tests – LEARN FROM YOUR MISTAKES.Always ASK questions on anything you do not understand.
It is most important that you be present and on time each day.If you have to miss class, it is YOUR responsibility to get the notes and the assignment, make arrangements to take any quiz or test that you miss, and follow school policy for assignment due dates as outlined in the Broad Run Agenda.You have one week to make up quizzes and tests.BE SURE TO REVIEW THE BROAD RUN ATTENDANCE POLICY.
To insure your success, you need to keep a positive attitude about your work, to review your work each night, and to PRACTICE, PRACTICE, PRACTICE!Pay close attention in class and ask us for help.We are happy to help you understand a concept better or to find an error for you.If you feel you need a tutor, please contact the GUIDANCE OFFICE.Also, for those of you enrolled in any SOL math class teachers are available to tutor every day during lunch in the MATH LAB.Math Lab is in room 108 on A days and room 103 on B days.
Broad Run will be continuing a 15-minute reading session during the beginning of the first Flex Period.Be sure to bring reading materials with you.Flex Period is not a study hall.Its primary purposes are for teacher-guided review and remediation.Tests and quizzes may be made up during the next available flex period.
Please cover your book and treat it with care.We encourage students to purchase a TI-84 series graphing calculator.Please do not buy a TI-89, TI-92, or any other symbolic manipulator since they are not approved for use on state SOL assessments.
Your nine weeks' grade will be the average of your quizzes, tests, a homework grade, and other graded assignments.Your homework grade is determined by your EFFORT not the number of correct answers.As far as the quizzes and tests are concerned, study hard and seek answers to your questions from us.We want you to be successful so that you can continue in other math courses with confidence and with an excellent math background! |
Seventh Grade Mathematics
Mathematics is indispensable for understanding our world. In addition to providing the tools of arithmetic, algebra, geometry and statistics, it offers a way of thinking about patterns and relationships of quantity and space and the connections among them. Mathematical reasoning allows us to devise and evaluate methods for solving problems, make and test conjectures about properties and relationships, and model the world around us. |
amental Mathematics Through Applications
Fundamental Mathematics through Applications focuses on relevant content, motivating real-world applications, examples, and exercises demonstrating ...Show synopsisFundamental Mathematics through Applications focuses on relevant content, motivating real-world applications, examples, and exercises demonstrating how integral mathematical understanding is to student mastery in other disciplines, a variety of occupations, and everyday situations. A distinctive side-by-side format pairing an example with a corresponding practice exercise encourages students to get actively involved in the mathematical content from the start. Unique Mindstretchers target different levels and types of student understanding in one comprehensive problem set per section incorporating related investigation, critical thinking, reasoning, and pattern recognition exercises along with corresponding group work and historical connections. Compelling Historical Notes give students further evidence that mathematics grew out of a universal need to find efficient solutions to everyday problems. Plenty of practice exercises provide ample opportunity for students to thoroughly master basic mathematics skills and develop confidence in their understanding.Hide synopsis
Description:New. 0321228308 Purchased as new and in great condition. We...New. 0321228308 |
Applied math means that mathematics is applied to any field of science, engineering, or even business and economics. If a mathematical topic (e.g. calculus) can be used to solve a certain real-world practical topic such as estimating the peak of growth of bacteria, i.e. using differential equation, then you have now applied mathematics. |
This course emphasizes further development of mathematical knowledge and skills to prepare students for success in their everyday lives, in the workplace, and future math courses.The course is organized by three strands related to money sense, measurement, and proportional reasoning.In all strands, the focus is on developing and consolidating key foundational mathematical concepts and skills by solving authentic, everyday problems.Students have opportunities to further develop their mathematical literacy and problem-solving and to continue developing their skills in reading, writing, and oral language through relevant and practical math activities.There is a $10.00 fee for the workbook. |
This is probably one
of the more important sections here and also one of the most over looked. Learning from your mistakes can only help
you.
Review Homework. When you get your homework back review
it looking for errors that you made.
Review Exams. Do the same thing with exams.
Understand the Error. When you find an error in your homework
or exams try to understand what the error is and just what you did
wrong. Look for something about the
error that you can remember to help you to avoid making it again.
Get Help. If you can find the error and/or don't
understand why it was an error then get help. Ask the instructor, your tutor, or a
classmate who got the problem correct.
Rushed Errors. If you find yourself continually making silly
arithmetic or notational errors then slow down when you are working the
problems. Most of these types of
errors happen because students get in a hurry and don't pay attention to
what they are doing.
Repeated Errors. If you find yourself continually making
errors on one particular type of problem then you probably don't have a
really good grasp of the concept behind that type of problem. Go back and find more examples and
really try to understand just what you are doing wrong or don't
understand.
Keep a List of Errors. Put errors that you keep making in a
"list of errors". With each error
write down the correct method/solution.
Review the list after you complete a problem and see if you've made
any of your "common" errors. |
Introduces precalculus concepts using computer and calculator-based graphing. --This text refers to an out of print or unavailable edition of this title.
Reviewed by a reader
This book should not be used in a honors-level class. But this book is good for high school students.
Intermediate Algebra: Student's Solutions Manual
Reviewed by a reader
This workbook was really helpful in learning the correct way to work algebra problems. It's money well spent!
College Algebra Graphs and Models
Editorial review
e text and have text section references to further aid students. For anyone interested in learning algebra.
Reviewed by a reader
I read this book as a refresher of the high school algebra I'd forgotten (or slept through). This book flows well from one topic to the next. Unlike my high school textbooks, this book carefully covers everything you need to know before t
Circles: Fun Ideas for Getting A-Round in Math
Editorial review
Mathematics comes alive with Circles, a comic, full-color activity book. By playing with a flying disk, a geodesic dome, psychedelic designs, and more, kids teach themselves such concepts as pi, ellipses, and parabolas. Circles reveals th
A text/CD-ROM package, consisting of 29 Maple learning modules covering the entire introductory linear algebra course as taught at most colleges and universities. The modular structure is designed to permit flexibility in teaching and le
Linear Algebra and Its Applications: Study Guide (update)
Editorial review
computer exercises are given using Maple, Mathematica, and MATLAB. Book News, Inc.®, Portland, OR --This text refers to an out of print or unavailable edition of this title.
Reviewed by Charles R. Williams, (Akron, OH United States)
I just used this book for an undergraduate LA course.Most of the book is remarkably clear and straight-forward. For example, the authors manage to avoid sigma notation entirely in the proofs. The book has a nice balance of applications, c
Intermediate Algebra : A Graphing Approach
Editorial review
Takes a graphing approach. Fully integrates graphing technology. Contents will match a standard course syllabi for intermediate algebra as it has typically been taught. DLC: Algebra.
Introduction to Linear Algebra (5th Edition)
Editorial review
is text refers to an out of print or unavailable edition of this title.
Reviewed by Robert Keller, (Nasa Ames Research Center)
This review is of the 2nd edition printed in '89. I bought this book off the shelf at SCU as a review source. The texts chosen at SCU have a tendency to lean toward the practical applications side and away from the theoretical. Johnson's
Linear Algebra and Differential Equations
Editorial review
This text aims to provide a foundation in both linear algebra and differential equations, with an emphasis on finding connections between the two subjects. It's applications are relevant to areas including engineering, business and life s
For those of us who would like to learn and master concepts of Linear Algebra and Differential Equations without too much useless theories, this book is for you. Teaches all concepts well, many examples and good explanations. Also really
Just-in-Time Algebra and Trigonometry for Students of Calculus, 2/e (2nd Edition)
Reviewed by a reader
.
Reviewed by "sdb_8", (portland, or United States)
n we find more? My school is full of passive aggressive math professors who know their stuff but cant teach.thank you for the help
Reviewed by Richard Wladkowski, (Groveland, MA United States)
this is what you'd get. This book is great. It's based on the theory that most of the problems that students have with calculus is not the calculus itself but the aspects of algebra and trig involved in performing calculus problems. One o
Scott Foresman - Addison Wesley Middle School Math, Course 1
Reviewed by Jessica, (Henderson, NV United States)
The 1998 Middle School Math book, Course 1 just tries too hard, and ends up being a big mish mash of confusion.I believe the authors tried so hard to make the math program relevant and interesting that they forgot their audience: children
Scott Foresman Addison Wesley Middle School Math: Course 2
Reviewed by a reader, (Wayland, MA United States)
My daughter used this book last year, and I spent many an evening in it with her. The book uses multiple methods to introduce each concept, but, ends up confusing rather than helping. The problems provide a good review of all the material |
This chart maps out all the courses in the discipline and shows the links between courses and the minimum requirements for them. It does not attempt to depict all possible movements from course to course.
Note: MHF4U1 - While MCV4U can be taken concurrently with MHF4U, it is strongly recommended students take MHF4U before MCV4U
MPM1D1 (Academic) Principles of Mathematics This course enables students to develop understanding of mathematical concepts related to algebra, analytic geometry, and measurement and geometry through investigation, the effective use of technology, and abstract reasoning. Students will investigate relationships, which they will then generalize as equations of lines, and will determine the connections between different representations of a relationship. They will also explore relationships that emerge from the measurement of three-dimensional objects and two-dimensional shapes. Students will reason mathematically and communicate their thinking as they solve multistep problems. Prerequisites: None Credits: 1 Note: Students considering Univerity programs, who earned mostly Level 3 and 4 in Grade 8 Math, and who are comfortable with abstract thinking in Math (e.g. Algebra), should consider this course.
MFM1P1 (Applied) Foundations of Mathematics This course enables students to develop understanding of mathematical concepts related to introductory algebra, proportional reasoning, and measurement and geometry through investigation, the effective use of technology, and hands-on activities. Students will investigate real-life examples to develop various representations of linear relationships, and will determine the connections between the representations. They will also explore certain relationships that emerge from the measurement of three-dimensional objects and two-dimensional shapes. Students will consolidate their mathematical skills as they solve problems and communicate their thinking. Prerequisites: None Credits: 1 Note: Students who learn best through a hands-on approach, and who struggled with some concepts in Grade 8 Math should consider this course which leads to College and some Univserity Level senior Courses. MAT1L1 (Locally Developed) Grade 9 Mathematics This course emphasizes further development of mathematical knowledge and skills to prepare students for success in their everyday lives, in the workplace, in the Grade 10 MAT2L1 (Locally Developed) course, and in the Mathematics Grade 11 and Grade 12 Workplace Preparation courses. The course is organized in three strands related to money sense, measurement, and proportional reasoning. In all strands, the focus is on developing and consolidating None Credits: 1 Note: Students who worked on Math expectations below Grade Level in Grade 8 should consider this class to have the opportunity to consolidate skills, and if successful could then take MFM1P1
MPM2D1 (Academic) Principles of Mathematics This course enables students to broaden their understanding of relationships and extend their problem-solving and algebraic skills through investigation, the effective use of technology, and abstract reasoning. Students will explore quadratic relationships and their applications; solve and apply linear systems; verify properties of geometric figures using analytic geometry; and investigate the trigonometry of right and acute triangles. Students will reason mathematically as they solve multistep problems and communicate their thinking. Prerequisites: MPM1D1 Credits: 1
MFM2P1 (Applied) Foundations of Mathematics This course enables students to consolidate their understanding of relationships and extend their problem-solving and algebraic skills through investigation, the effective use of technology, and hands-on activities. Students will develop and graph equations in analytic geometry; solve and apply linear systems, using real-life examples; and explore and interpret graphs of quadratic relationships. Students will investigate similar triangles, the trigonometry of right-angled triangles, and the measurement of three-dimensional objects. Students will consolidate their mathematical skills as they solve problems and communicate their thinking. Prerequisites: MPM1D1 or MFM1P1 Credits: 1 Note: Students who learn best through a hands-on approach, benefit from multiple representations or who struggled in the academic path should consider this course which leads to College and some University level senior courses.
MAT2L1 (Locally Developed) Grade 10 Mathematics This course emphasizes the extension of mathematical knowledge and skills to prepare students for success in their everyday lives, in the workplace, and in the Mathematics Grade 11 and Grade 12 Workplace Preparation courses. The course is organized in three strands related to money sense, measurement, and proportional reasoning. In all strands, the focus is on strengthening and extending MAT1L1, MFM1P1 or MPM1D1 Credits: 1 Note: This course is appropriate for students who need to consolidate skills after completing MAT1L1; students who achieve considerable success in MAT1L1 could consider MEL3E1. MCR3U1 (University) Functions This course introduces the mathematical concept of the function by extending students'ominal and rational expressions. Students will reason mathematically and communicate their thinking as they solve multi-step problems. Prerequisites: MPM2D1 Credits: 1 Note: Students who earn Level 3 or 4 with good Learning Skills in MPM2D1 are prepared for this course; students who earn Level 1 or 2 in MPM2D1 should consider the MCF3M1. MCF3M1 (University/College) Functions and Applications This course introduces basic features of the function by extending students' experiences with quadratic relations. It focuses on quadratic, trigonometric, and exponential functions and their use in modelling Prerequisites: MPM2D1 or MFM2P1 Credits: 1 Note: MCF3M1 is a prerequisite for MCT4C1 and MDM4U1 courses; students who do very well in MFM2P1 (strong Level 3 and Level 4) or who need consolidation after MPM2D1 (earned Level 1 or Level 2) should consider this course.
MBF3C1 (College) Foundations for College Mathematics This analysing, and evaluating data involving one and two variables. Students will consolidate their mathematical skills as they solve problems and communicate their thinking. Prerequisites: MFM2P1 Credits: 1 Note: MBF3C1 is the prerequisite for MAP4C1, but MCF3M1 is required for MCT4C1 - study the flowchart at the beginning of this section to ensure you are choosing the right course for your post-secondary plans.
MEL3E1 (Workplace) Mathematics for Work and Everyday Life This Prerequisites: MPM1D1, MFM1P1, MAT2L1 or MFM2P1 Credits: 1 Note: MEL3E1 is appropriate for students who are planning to enter the work force or going on to College preparation programs after graduating. MCV4U1 (University) Calculus and Vectors This course builds on students previous experience with functions and their developing understanding of rates of change. Students will solve problems involving geometric and algebraic representations of vectors, and representations of lines and planes in three-dimensional space; broaden their understanding of rates of change to include the derivatives of polynomial, rational, exponential, and sinusoidal functions; and apply these concepts and skills to the modelling of real-world relationships. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended for students who plan to study mathematics in university and who may choose to pursue careers in fields such as physics, engineering and science. Prerequisites: MHF4U1 Credits: 1 Note: While MCV4U1 can be taken concurrently with MHF4U1, it is strongly recommended that students take MHF4U1 before MCV4U1.
MHF4U1 (University) Advanced Functions
This course extends students experience with functions. Students will investigate the properties of polynomial, rational, logarithmic, and trigonometric functions; broaden their understanding of rates of change; and develop facility in applying these concepts and skills. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended both for students who plan to study mathematics in university and for those wishing to consolidate their understanding of mathematics before proceeding to any one of a variety of university programs.
Prerequisites: MCR3U1 or MCT4C1 Credits: 1 Note: MHF4U1 is appropriate for students who showed considerable proficiency in MCR3U1 and who have good learning skills.
MDM4U1 (University) Mathematics of Data Management This course broadens students understanding of mathematics as it relates to managing data. Students will apply methods for organizing large amounts of information; solve problems involving probability and statistics; and carry out a culminating project that integrates statistical concepts and skills. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. Students planning to enter university programs in business, the social sciences, and the humanities will find this course of particular interest. Prerequisites: MCF3M1 or MCR3U1 Credits: 1
MCT4C1 (College)Offered 2014 - 2015 Mathematics for College Technology This course enables students to extend their knowledge of functions. Students will investigate and apply properties of polynomial, exponential, and trigonometric functions; continue to represent functions numerically, graphically, and algebraically; develop facility in simplifying expressions and solving equations; and solve problems that address applications of algebra, trigonometry, vectors, and geometry. Students will reason mathematically and communicate their thinking as they solve multi-step problems. This course prepares students for a variety of college technology programs. Prerequisites: MCF3M1 or MCR3U1 Credits: 1 Note: MCT4C1 is appropriate for students who showed considerable proficiency in MCF3M1 and is recommended by a variety of College Technology programs; though not required, students who take MCT4C1 are more successful in College Technology programs. MAP4C1 (College) Foundations for College Mathematics This course enables students to broaden their understanding of real-world applications of mathematics. Students will analyse data using statistical methods; solve problems involving applications of geometry and trigonometry; simplify expressions; and solve equations. Students will reason mathematically and communicate their thinking as they solve multi-step problems. This course prepares students for college programs in areas such as business, health sciences, and human services, and for certain skilled trades. Prerequisites: MBF3C1 Credits: 1
MEL4E1 (Workplace) Mathematics for Work and Everyday Life This course enables students to broaden their understanding of mathematics as it is applied in the workplace and daily life. Students will investigate questions involving the use of statistics; apply the concept of probability to solve problems involving familiar situations; investigate accommodation costs and create household budgets; use proportional reasoning; estimate and measure; and apply geometric concepts to create designs. Students will consolidate their mathematical skills as they solve problems and communicate their thinking. Prerequisites: MEL3E1 Credits: 1 Note: MEL4E1 is appropriate for students who are planning to enter the work force or going on to College preparation programs after graduating. back to top |
Industry Applications of Maple 17
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Description
This webinar offers a quick and easy way to learn some of the fundamental concepts for using Maple. Learn the basic steps on how to compose, plot and solve various types of mathematical problems. This webinar will also demonstrate how to create professional looking documents using Maple, as well as the basic steps for using Maple packages.
During the session we'll explore some of the new tools and resources available in Maple 17. Maple 17 contains new features that support all aspects of your work, including a new advanced code editor; embedded video functionality; a new Signal Processing and Group Theory package, as well as improvements to existing packages; and more! |
The competition is kindly supported by the Maths, Stats and
Operational Research Network, a Subject Centre of the Higher
Education Academy, and the London Mathematical Society .
"It was people telling the big mathematical stories that made me realise at
school that there was much
more to maths than simple long division," says Marcus du Sautoy, author of the
best-selling book The
music of the primes and one of the judges of last year's Plus new writers award.
"Reading these stories
inspired me to want to make my own mathematical breakthroughs. The future of
mathematics depends
on capturing the imaginations of those who will become the next generation of
mathematicians." The
competition will be judged by three prominent mathematicians and science
writers.
There are three categories: secondary school and sixth form students, university
students (both undergraduate and postgraduate ) and the general public.
• University students and the general public are invited to write a 1500 word
piece on any
mathematical subject of their choice. Helpful hints are given in the guidelines
for universities and
the general public entrants.
If you think you can share your passion for maths with the general public,
download your entry pack
today and get writing!!
• Competition prizes
• Guidelines for school entrants
•Guidelines for university student and general public entrants
• Rules of the competition
• Download competition poster
•Download entry pack (PDF or Word) (includes guidelines, rules, entry form and
copyright form)
•Subscribe to the Plus fortnightly newsletter for competition updates
NOTE: As you begin this course you must be able to ADD,
SUBTRACT, MULTIPLY, and DIVIDE WITHOUT THE USE OF A CALCULATOR and be
knowledgeable of basic mathematics skills including whole numbers, fractions,
mixed numbers, decimal notation, percent, and ratio & proportion. If you lack
these skills consider enrolling in Math 20, Basic Math Review .
CALCULATOR: A
scientific calculator is required and useful in this course. However, we
encourage you to do most of your numeric work in this course by hand (to
reinforce basic skills) THEN use a calculator to check your work . You are to
provide your own calculator. Some exams do not allow use of calculators with the
intention of helping you to maintain computational skills.
HINTS FOR SUCCESS and HOW TO DO YOUR HOMEWORK:
1. Establish a regular daily schedule for doing your math homework and stick
with it.
2. Try to do your work in the Math Resource Center where tutor help is available
when you need it.
3. Try to stay on schedule to meet your suggested
4. Use the tutors and video tapes. "On Schedule" test dates.
5. Follow the Lesson/ Homework Assignment guide on the following pages.
6. Before starting on the assigned homework study the text discussion & examples
and work "check point" problems for practice.
7. Then, neatly work homework problems on your own paper. Try to do them without
looking at examples or a solutions manual. You must show each step of your
solution. Then grade yourself . Try to fix your mistakes and then get tutor help
or refer to the Student Solutions Manual
8. Finally, take your completed homework assignment and Study Guide to a tutor
to verify completion and receive their stamp of approval.
HOW TO BE PREPARED & TAKE EXAMS IN THIS COURSE:
1. Complete your homework and check it as described above in "Hints for
Success."
2. After all the assigned work has been checked by a tutor, we suggest you try
to work the Chapter Test in the text without looking at any solved problems .
Grade it and get help if needed. Now you are almost ready to take the graded
test .
3. With your tutor stamped Study Guide go to the Reception Counter and ask for a
Practice Module Test. Since the only difference between practice and graded
tests is that your score on the practice test will not count, taking a practice
test gives you a realistic, objective check of your skill level without
affecting your grade for the course. Work each question on the test like you did
in your homework, showing each step. You are allowed to take more than one
practice test, if you so choose. When your practice test score is above 80%, you
should be ready to take the graded exam.
4. Once you have completed Steps 1, 2, and 3 you are ready to take the Graded
Module Test. Go to the Reception Counter, show your Study Guide, and check in to
take the test for a grade. Relax, take your time, show your work, and
demonstrate what you have learned. We want you to earn a score of 80% or better
before you test on material from the next set of homework assignments.
NOTE:
Homework will receive a date stamp from a tutor only if it is done neatly
with step-by-step solutions shown .
All graphing should be done using graph
paper.
A PAGE OF ANSWERS WITHOUT WORK SHOWN WILL NOT BE ACCEPTED.
BEST WISHES &
GOOD LUCK !!
You must show step-by-step solutions (not just a list of
answers) to receive credit for your work. Odd = 1,3,5,7,9,etc.; Eoo = every
other odd: 1,5,9,13,17,21, etc.
Mathematics Courses
MAT032-H Arithmetic for College Students A 2
This course consists of instruction in basic math including
addition, subtraction, multiplication, and division of whole
numbers, fractions, and decimals. It also includes percents,
ratios, and proportion.
MAT033-H Arithmetic for College Students B 2
This course consists of instruction in measurement under both
the customary and metric systems. Topics also include signed
numbers, solving equations, real numbers, and graphing.
MAT101-A Intermediate Algebra 3
This course is applicable only to students who already have
basic knowledge of algebra. Reinforcement of topics from
Elementary Algebra stressing problem solving, drills, conclusion
obtained from graphs and other data, and a substantial
expansion of radical equations are covered . New topics are
variations, exponential functions and logarithms, and quadratic
equations. This course is counted for graduation credit
toward AAS degree but not the AA nor the AS degree. This
is also a preparatory course for college algebra .
MAT102-A Intermediate Algebra 4
This course is designed to provide you with the basic algebra
skills needed prior to the study of college algebra and trigonometry.
The emphasis is on using the concept of algebraic function
to model real-life situations. Different types of models including
linear, quadratic, and exponential models will be presented
along with the supporting algebraic skills and procedures. You
are required to have a graphing calculator for this course .
The TI-83 or TI-84 is strongly recommended. One year of
high school algebra or MAT106-E is required.
MAT104-C Applied Math Topics 3
This course is designed to give you a thorough review of the
four basic functions of addition, subtraction, multiplication, and
division of whole numbers, decimals, fractions, integers,
measurements and percents. Basic linear equations and basic
geometric figures for perimeter, area, and volume will be
covered. You are then given exercises in using these mathematical
skills in special occupational applications.
MAT106-E Elementary Algebra 3
This course provides you with basic algebra skills. It will
cover topics of linear equations and inequalities, formulas,
systems of equations, quadratic equations, and factoring.
Prerequisite: One year high school algebra or equivalent
MAT108-C Math Fundamentals 3
This course is designed to provide you with a broad overview
of mathematical concepts including operations and problem
solving with fractions, decimal numbers, percents, ratio and
proportion problems, measurement, basic statistics, and
basic geometry. Estimation and number sense are stressed
throughout the course. Calculator usage is also covered.
MAT110-A Math for Liberal Arts 3
This course is designed to introduce you to a variety of interesting
mathematics topics. Emphasis will be on problem solving
and real-life applications of these topics. This course is designed
for anyone seeking a two-year degree or any other student
who is interested in learning a variety of mathematics topics.
One year of high school algebra is recommended but not
required.
MAT111-A Math for Liberal Arts 4
A mathematics course designed for the liberal arts student.
The course covers a broad spectrum of topics designed to help
the student survey and develop skills that lead to appreciation
for the uses and values of mathematics. Topics include: Critical
thinking skills, sets, logic, numeration systems, number theory,
mathematical systems, geometry, counting methods, probability,
and statistics. Enrichment topics may include social
choice and decision making, and the mathematics of finance.
MAT121-A College Algebra 4
This course is designed to strengthen and expand the algebra
skills required for further mathematical study in trigonometry
and calculus. The emphasis is on using the concept of an
algebraic function to model real-life situations. Different
types of models including linear, polynomial, exponential,
and logarithmic models are presented along with the supporting
algebraic skills and procedures. You are required to
have a graphing calculator for this course. A TI-83 or TI-84
is strongly recommended. Two years of high school algebra
or MAT102-A are required.
MAT123-E Basic Algebra and Trigonometry 4
The mathematical subjects of this course are developed in simple stages and are applied to the solution of practical
problems. The topics of the course are a review of arithmetic,
units of measurement, basic algebra, basic geometry, right
triangle trigonometry, functions and graphs, simultaneous
linear equations, and basic solid geometry. Prerequisite:
One year high school algebra or equivalent
MAT124-E Algebra and Trigonometry 3
This course is a continuation of Basic Algebra & Trigonometry.
The topics of the course are trigonometric functions of any
angle, vectors, exponents and radicals, the j-Operator, exponential
and logarithmic functions, addition types of equations,
and systems of equations. Prerequisite: MAT123-E
MAT125-A Precalculus 3
An intensive course in college algebra and trigonometry.
Topics include functions and their graphs, exponential and
logarithmic functions, trigonometric identities and equations,
sequences and series, limits, mathematical induction, the binomial theorem , permutations and combinations, probability,
and applications. Graphing, calculator, and computer use
throughout.
MAT129-A Precalculus 5
An intensive course in college algebra and trigonometry.
Topics include functions and their graphs, exponential and
logarithmic functions, trigonometric identities and equations,
sequences and series, limits, mathematical induction, the
binomial theorem, permutations, and combinations, probability,
and applications. Graphing, calculator, and computer
use throughout.
MAT130-A Trigonometry 3
This course is designed to develop your knowledge of
trigonometry and related skills prior to the study of calculus.
The six trigonometric functions and applications of those
functions are emphasized. Other topics covered may include
graphing of the trigonometric functions, trigonometric identities
and equations, analytic geometry, and exponential and
logarithmic functions. A graphing calculator is required for
this course. Prequesities: Two years of high school algebra,
MAT102-A or MAT121-A
MAT132-E Algebra, Geometry and Trigonometry I 4
The topics of this course are developed in simple stages
and are applied to the solution of practical problems . The
topics of the course are a review of algebra, units of measurement,
basic geometry, trigonometry, functions and graphs,
systems of linear equations, quadratic equations, and vectors.
Prerequisites: High School Algebra I and II
MAT133-E Algebra, Geometry and Trigonometry II 3
This course is a continuation of Algebra, Geometry, and
Trigonometry I. The topics of the course are exponents and
radicals, complex numbers, exponential and logarithmic
functions, additional types of equations and systems of
equations, equations of higher degree, inequalities, variation,
trig identities, and plane analytic geometry. Prerequisite:
MAT132-E
MAT140-A Finite Math 3
This course is designed to provide you with skills in finite
mathematics. Topics covered will include linear equations,
matrices, linear programming, sets and counting, probability
and statistics, and finance. Other topics may be covered as
time permits. Many types of applications will be presented
throughout the course. This math course is appropriate for
any first or second year college student and is especially
useful for those students majoring in business or in the
social or biological sciences. Prerequisite: One year of high
school algebra, MAT110-A or MAT106-E
MAT150-A Discrete Math 3
This course is designed to introduce you to topics and concepts
in discrete mathematics. Discrete mathematics is that part of mathematics dealing with finite—but often large—
sets of objects. Discrete mathematics is to be contrasted with
'continuous' mathematics, for example the classical theory
of calculus. Its rise in popularity coincides with the rise of
the computer. Topics covered in this class will include logic
and methods of proof , sets, relations, functions, recursion,
induction, and counting principles.
MAT156-A Statistics 3
This course is designed to provide you with a foundation of
statistical concepts and procedures that can aid the student
as both a consumer and producer of statistical information.
The emphasis is on collecting data, descriptive statistics,
probability, binomial and normal distributions, estimating,
hypothesis testing, and regression analysis. One year of
high school algebra or MAT106-E is required.
MAT210-A Calculus I 4
This course is designed to provide you with a basic knowledge
of calculus. Topics covered include the notion of limit,
the derivative, and the integral as well as practical applications
of these concepts. Topics will be approached from numerical,
graphical, and analytical standpoints. You are required to
have a graphing calculator for this course. Prerequisite:
MAT121-A and MAT130-A or four years of advanced high school math
MAT211-A Calculus I 5
A review of analytic geometry and functions; a study of limits,
continuity, differentiation, and integration. Emphasis on theory,
applications, and computer use throughout. Prerequisite:
College Algebra or Trigonometry or appropriate CPT score
on math assessment
MAT216-A Calculus II 4
The study of calculus is expanded in this course to include more
advanced topics. Logarithmic, exponential, and trigonometric
functions will be expanded in detail. Other topics include infinite
series, analytic geometry, and polar coordinates. The emphasis
of the course will be on problem solving techniques and
theory. You are required to have a graphing calculator for this
course. Prerequisite: MAT210-A or an equivalent Calculus I
course
MAT772-C Applied Math 3
This course is designed to acquaint the student with the
mathematics necessary to function within technical careers
and to become a more aware consumer. Topics include:
review of arithmetic operations; measurement; metric system;
fundamentals of geometry; introductory statistics and
probability; graphs; and elementary algebra concepts with
emphasis on applications |
The book is directed toward students with a minimal background who want to learn class field theory for number fields. The only prerequisite for reading it is some elementary Galois theory. The first three chapters lay out the necessary background in number fields, such as the arithmetic of fields, Dedekind domains, and valuations. The next two chapters discuss class field theory for number fields. The concluding chapter serves as an illustration of the concepts introduced in previous chapters. In particular, some interesting calculations with quadratic fields show the use of the norm residue symbol.
For the second edition the author added some new material, expanded many proofs, and corrected errors found in the first edition. The main objective, however, remains the same as it was for the first edition: to give an exposition of the introductory material and the main theorems about class fields of algebraic number fields that would require as little background preparation as possible. Janusz's book can be an excellent textbook for a year-long course in algebraic number theory; the first three chapters would be suitable for a one-semester course. It is also very suitable for independent study.
Readership
Mathematics graduate students and faculty.
Reviews
"Gives a highly readable introduction into class field theory ... clearly written and may be recommended to everybody interested in the subject."
-- Zentralblatt MATH
"Provides a quick and self-contained introduction to the subject using only limited mathematical tools, hence it is accessible to a broader audience than most of the other texts on this topic." |
REA'S Problem Solvers®: The Complete Step-by-Step Solution Guides Useful, practical, and informative, these study aids are excellent review books and textbook companions, making them perfect for high school, undergraduate and graduate studies, and beyond.
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Educators consider Problem Solvers® the most effective and reliable study aids; students describe them as "fantastic"—the best review books available.
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Algebra & Trigonometry Problem SolverŪ by Jerry R. Shipman REA's Algebra and Trigonometry Problem Solver Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. Answers to all of your questions can be found in one convenient source f... read more
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Physics Problem SolverŪ by The Editors of REA, Joseph Molitoris REA's Physics Problem Solver Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. Answers to all of your questions can be found in one convenient source from one of the mo... read more |
Mathematics Faculty
What we are trying to achieve with students
We endeavour to provide all pupils with an understanding of Mathematics in an enjoyable and relevant way so as to initiate an enthusiasm and interest for the subject to enable pupils to use mathematics in real life problems.
We as a department believe that "every child has a right to understand and apply mathematics outside the classroom". We aim to:
Extend and stimulate gifted and talented pupils, encouraging them to think independently and apply Mathematics to many different situations.
Motivate pupils who simply enjoy solving mathematical problems.
Encourage and assist pupils who struggle with mathematical concepts and will need their numeracy skills in the future.
We believe in using ICT, encouraging mathematical discussion, and allowing pupils to experience their mathematics.
The courses we run
At KS3 the course seeks to reinforce and develop the skills learnt at KS2. Pupils work in a variety of styles which are aimed at challenging and motivating individual students and developing their thinking and problem solving skills.
At KS4 most students in Year 11 follow the OCR A modular course. This course comprises of three modules. Students sit module A and B during year 10 and Module C in year 11. Modules A and C are allowed a calculator, module B is non-calculator.
Some students will follow the OCR B Linear Higher course and some the Edexcel Linear Foundation course. This course is examined with two examinations, one calculator and one non-calculator, during Year 11.
Year 10 students will either follow the OCR B Linear Higher course or the Edexcel Linear Foundation course. This course is examined with two examinations, one calculator and one non-calculator, during Year 11.
The accelerated mathematics group sit their GCSE early and then study a FSMQ in Additional Mathematics. This course gives UCAS points and is an excellent bridge from GCSE to A level.
Sets in year 10 and 11 are streamed to allow a greater flexibility in movement to suit the individual needs of students.
At KS5 we follow the MEI (OCR) specification. Students are offered the opportunity to study either a mechanics or statistics course covering a variety of topics including projectile motion, forces, Binomial Distribution and probability. We also offer an A level in Further Mathematics which builds upon the knowledge gained at A level and allows students to explore in more depth some of the more complicated elements of Pure Mathematics.
Gifted and Talented Students
Pupils who are Subject Specialists in Maths are likely to:
Grasp new ideas quickly
Work analytically and logically
Apply their knowledge to new/unfamiliar contexts
Creatively approach problem-solving
Maintain their concentration in longer tasks and persist in seeking solutions |
Prealgebra: Operations
Introduction and Summary
Almost all of mathematics involves the use of the four basic mathematical
operations--addition, subtraction, multiplication, and division. Understanding
these basic mathematical operations is crucial to everything covered both in
Pre-Algebra and in more complicated mathematics. It is impossible to master
the complex principles of Pre-Algebra without first mastering the operations
and their properties.
You are probably used to working with the four basic operations, but there are
some things about these operations that you may not know. In particular, these
operations have certain properties that can make evaluating complex
expressions a lot easier.
The first section will explain how to correctly evaluate a
complicated expression using the Order of Operations,
which specifies the order in which to carry out operations when evaluating an
expression. The Order of Operations is important to know; if you do not follow
it correctly and instead carry out the operations in the incorrect order,
your answer will also be incorrect.
Section two will teach some properties
of addition that will make it easier to evaluate an expression without
depending on a calculator. These properties are the Commutative
Property, the Associative Property, and the
Identity Property.
The third section will teach some
properties of multiplication. Like addition, multiplication has its own
version of the Commutative Property, the Associative Property, and the Identity
Property. Multiplication has two additional properties--the Zero Product
Property and the Distributive Property.
The fourth and final section will
discuss inverse operations, which "reverse" other operations. These will
be especially useful for future algebra.
Each section will teach something about basic operations that will help you
evaluate expressions correctly and easily. These properties will also be
useful when you approach more difficult topics in pre-algebra, such as
solving an algebraic equation for a variable. |
Description Calculus 3 is considered by most to be a very difficult course to master in the realm of Calculus. This is because you will learn about many different topics, and each topic builds on the previous. If you don't understand something early on, the chances of "catching up" are drastically reduced as time goes on.
Most topics in calculus 3 are challenging because almost all of the problems are 3-dimenstional in nature. It takes time for the student to master how to visualize the problems in order to solve them. Once this is done, things are much easier. This DVD course teaches by example and you gain practice immediately with this visualization and problem solving techniques.
Our calculus video tutor lectures are based on a singular principle - and that is the fact that if a student needs help with calculus, the task of learning becomes much easier when the calculus lectures are taught by someone who understands the frustration of a new student who is just starting out with this subject.
No matter if you are in business calculus, if you are a mathematics major, if you are a high school calculus student, a homeschooled calculus student, or an engineering student, our calculus video lectures will help you learn calculus. We back up this claim with a money back guarantee!
If you need calculus help, you'll be interested to know that every single calculus video lecture features numerous solutions to calculus problems that you are likely to encounter in class. Furthermore, our lectures do not only deal with the easier calculus problems. Our calculus lectures feature calculus problems of all complexities ranging from the elementary problems all the way to the challenging problems that you will likely find on your exams.
You will also find that our calculus video lectures serve as a fantastic reference for calculus solutions as you work through homework problems. In many cases it is very helpful to see a similar problem worked out in detail as a guide to your own homework problems. When viewing a solution to a similar problem in calculus, it can in many cases help you turn the corner in discovering the solution to your homework problems.
How are the MathTutorDVD.com line of DVDs different from others? The answer is simple. Most math instruction involves a lengthy discussion of the abstract theory behind the Math before instructing the student in how to solve problems. While there are some merits to this style, in the vast majority of the cases the student quickly gets bored and frustrated by the time he or she starts to solve the problems. This DVD, in contrast, teaches all of the concepts by working fully narrated problems step-by-step, which is a much more engaging way to learn.
Exceptional value and affordability. MathTutorDVD.com believes in providing value for our customers. This is a 11 Hour DVD course. We could have easily split this content into many DVD courses costing the same price but instead chose to keep the cost down so that this content is affordable to all. The techniques of triple integration, for example, is explained by working many problems in step-by-step detail. We begin with the easier problems and work our way up to the harder problems. The |
First Course in Probability, A, CourseSmart eTextbook, 9th Edition
Description
A First Course in Probability, Ninth Edition, features clear and intuitive explanations of the mathematics of probability theory, outstanding problem sets, and a variety of diverse examples and applications. This book is ideal for an upper-level undergraduate or graduate level introduction to probability for math, science, engineering and business students. It assumes a background in elementary calculus.
Table of Contents
1. Combinatorial Analysis
2. Axioms of Probability
3. Conditional Probability and Independence
4. Random Variables
5. Continuous Random Variables
6. Jointly Distributed Random Variables
7. Properties of Expectation
8. Limit Theorems
9. Additional Topics in Probability
10. Simulation
Appendix A. Answers to Selected Problems
Appendix B. Solutions to Self-Test Problems and Exercises |
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Mathematics: Applications and Concepts is a three-course middle school series intended to bridge the gap from elementary mathematics to Algebra 1. The program is designed to motivate your students, enable them to see the usefulness of mathematics in the world around them, enhance their fluency in the language of mathematics, and prepare them for success in algebra and geometry. |
Our goal is to develop your capacity for reading, writing, and speaking mathematics.
The first two-thirds of this course concentrates on a core which investigates basic
mathematical paradigms and objects: sets, proof techniques, functions, and relations
(chapters 1--4 of our text).
We follow this with an foray into cardinality
and the topology of the reals
(chapter 5 and supplementary notes).
A rough approximation for our progress toward address these topics is shown in the
Schedule Guesstimate below.
We hope that your experience in this course will serve as a gentle initiation
into the larger mathematical community.
One technical aspect of this initiation will be an introduction to LaTeX,
a markup system for producing mathematical documents on a computer.
Other ways this will be fostered will be through outside readings and participation
in activities of the Bernard Mathematics Society, including Math Coffees.
Your involvement in some of these activities may have tangible rewards
towards your course grade, but others will be expected of you
as fledgling members of the fellowship of mathematicians.
We will have two take-home writs, one in-class review,
and a self-scheduled final examination.
Homework will be assigned regularly and collected weekly.
Auxiliary activities may include the D. H. Hill Problem Contest, Math Coffees,
the Bernard Lecture and other mathematics events on campus.
A culminating activity in the course (along with the final examination)
will be the compilation of a proof portfolio.
The portfolio will include at least a dozen examples of your proof-writing from homework,
each showing your progression from initial effort to polished revision.
Your choices for inclusion in the portfolio should
provide a broad representation of topics and proof techniques from our course.
A rough recipe for the proportions in which these events combine
to produce your evaluation is
2 parts writs,
2 parts review,
3 parts examination,
2 parts portfolio,
2 part homework and other considerations.
(An explanation of my grading system is available in a web-based
memo.)
The portfolio, writs, review and final examination are pledged events;
you are expected to be vigilant in upholding the Honor Code.
Collaboration on homework is encouraged.
However, anything you present or turn in should represent your own
understanding of the material.
If you have any questions regarding ground rules for individual events,
do not hesitate to ask for clarification. |
Algorithmic Puzzles
Interprets puzzle solutions as illustrations of general methods of algorithmic problem solving
Contains a tutorial explaining the main ideas of algorithm design and analysis for a general reader
Algorithmic puzzles are puzzles involving well-defined procedures for solving problems. This book will provide an enjoyable and accessible introduction to algorithmic puzzles that will develop the reader's algorithmic thinking.
The first part of this book is a tutorial on algorithm design strategies and analysis techniques. Algorithm design strategies — exhaustive search, backtracking, divide-and-conquer and a few others — are general approaches to designing step-by-step instructions for solving problems. Analysis techniques are methods for investigating such procedures to answer questions
about the ultimate result of the procedure or how many steps are executed before the procedure stops. The discussion is an elementary level, with puzzle examples, and requires neither programming nor mathematics beyond a secondary school level. Thus, the tutorial provides a gentle and entertaining introduction to main ideas in high-level algorithmic problem solving.
The second and main part of the book contains 150 puzzles, from centuries-old classics to newcomers often asked during job interviews at computing, engineering, and financial companies. The puzzles are divided into three groups by their difficulty levels. The first fifty puzzles in the Easier Puzzles section require only middle school mathematics. The sixty puzzle of average difficulty and forty harder
puzzles require just high school mathematics plus a few topics such as binary numbers and simple recurrences, which are reviewed in the tutorial.
All the puzzles are provided with hints, detailed solutions, and brief comments. The comments deal with the puzzle origins and design or analysis techniques used in the solution. The book should be of interest to puzzle lovers, students and teachers of algorithm courses, and persons expecting to be given puzzles during job interviews.
Readership: Students and teachers of algorithm courses, puzzle enthusiasts, and anyone wishing to learn more about how to solve puzzles and/or develop algorithmic thinking
Anany Levitin is a professor of Computing Sciences at Villanova University. He is the author of a popular textbook on design and analysis of algorithms, which has been translated into Chinese, Greek, Korean, and Russian. He has also published papers on mathematical optimization theory, software engineering, data management, algorithm design techniques, and computer science education.
Maria Levitin is an independent consultant specializing in web applications and data compression. She has previously worked for several leading software companies |
Washington, NJ PrecalculusWe study elementary set theory and use Venn diagrams. We also spend time studying combinatorics, since this is very beneficial for brain development and also because combinatorics is linked to probability theory. How do we study probability? |
Put the fun into functional skills with specially written engaging real-life situations that use mathematics. Students will become confident in applying maths to a range of problems that prepare them for work and life. Ready-to-use tasks can be accessed via your VLE to cover Level 1 and Level 2 functional skills.
About this resource
• Set functional skills homework with easy access to the digital edition available for your VLE • Develop problem solving skills with 40 totally new and inspiring topics, some familiar and some unfamiliar, grouped into three sections: beginner, improver, advanced • Build, apply and secure the functional and process skills that are integral to the 2010 GCSE Maths Specifications • Challenge students at all levels with open questions that can be approached in different ways • Encourage discussion and collaboration between students to encourage team work and responsibility • Make mathematics relevant and useful, with scenarios such as Coastguard Search and Rescue, and Investigating Design and Cost in Tea Bag Production • Promote self-assessment with 'How did you find these tasks?' questions at the end of each topic • Answers and guidance are given in the separate Teacher's Pack ISBN 978-0-00-741007-1 |
Description
For courses in mathematics for retail merchandising.
Written by experienced retailers, this text introduces students to the essential principles and techniques of merchandising mathematics, and explains how to apply them in solving everyday retail merchandising problems. Instructor- and student-friendly, it features clear and concise explanations of key concepts, followed by problems, case studies, spreadsheets, and summary problems using realistic industry figures. Most chapters lend themselves to spreadsheet use, and skeletal spreadsheets are provided to instructors. This edition is extensively updated to reflect current trends, and to discuss careers from the viewpoint of working professionals. It adds 20+ new case studies that encourage students to use analytic skills, and link content to realistic retail challenges. This edition also contains a focused discussion of profitability measures, and an extended discussion of assortment planning.
Table of Contents
1. Introduction
2. Basic Merchandising Mathematics
3. Profitability
4. Cost of Merchandise Sold
5. Markup as a Merchandising Tool
6. Retail Pricing for Profit
7. Inventory Valuation
8. The Dollar Merchandise Plan
9. Open-to-Buy and Assortment Planning |
Maple for OSU ECE
Getting started with Maple
Note: This document was written under the HPUX operating system,
which is now deprecated with the department. To the best of our
knowledge, the basics presented here continue to hold on other
installations, but if you note an issue with what is presented
and what you are seeing with your own experiences, please send a
note to site.
This document covers these subjects
What is Maple?:
Maple is a tool for symbolic mathematical calculation. Maple can
do expand, simplify, and factor algebraic expressions, integrate
and differentiate, and solve linear and differential equations or
systems of equations. Maple works symbolically rather than with
numerical approximations, which means that if you ask it for the
integral of sin(x) with respect to x it will give you -cos(x).
Maple can also plot functions.
Here are a few very simple examples:
Expression
Maple Command
Maple Output
the integral of sin(x)
with respect to x
int(cos(x),x);
sin(x)
the sum of 2 to -kth power
for k=0 to infinity
sum('1/(2^k)', 'k'=0..infinity);
2
the derivative of
the log of x squared
diff(log(x^2),x);
2/x
the solution of
x*x - 3x + 2 = 0
solve(x^2-3*x+2=0);
2,1
Starting Maple:
Sit down at one of the Unix systems in DL557 and log in.
Using the mouse, position the cursor on the background, away from
any of the windows. The mouse cursor will change to X.
Press and hold the right mouse button to bring up the Root
Menu. The cursor will change to an arrow while you are
holding the right button. Slide the arrow down to the menu entry
Design tools. The Design tools menu
will appear. Slide the arrow to the right until it is on the
Design tools menu, then down until it is on the
entry Maple. Now release the button.
The outline of a rectangle will appear on the screen. This will
be the Maple window, as soon as you've told the computer where
you want it. Using the mouse, position this outline anywhere you
like on the screen. When you like the position of the box, click
the left mouse button. The outline will fill in. The window will
say Maple V Release 3 in the title bar on top. Below
the title bar is a menu bar (you can access the menus by clicking
the left mouse button on one of the menu labels) and below the
menu bar are three buttons you can use to stop or pause Maple's
calculations. The large area in the middle of the window is where
you type Maple commands, and where Maple will display most of its
results. It contains the Maple prompt, which looks like this:
>
You can also start up maple from a shell prompt, by typing:
Plotting on the HPs:
To bring up a simple plot, type the following command in the
Maple window:
Don't leave out the semicolon (;) at the end of
the line - Maple needs it to know that you've typed a complete
expression. The outline of a new window will soon appear on
the screen. Place it by clicking the left mouse button, and the
new window will appear, titled Maple V 2D and
showing a plot of this function.
Maple can also do three dimensional plots---try the commands:
How to print:
To get a printed copy of the plot, you first need to create a
file containing a Postscript version of the plot. To do this,
move the mouse cursor onto the word File which
appears in the top left corner of the plot window. Do this in the
plot window, not in the main Maple window. Click and hold the
left mouse button, and slide the cursor down to select the
Print option, then slide the cursor right and select
the Postscript option. A small window will pop up,
asking you to confirm the name for the file to be created. Change
the name if you like, then select Confirm.
Now go to one of your xterm windows and you can
print the file with the lp command. If you accepted
Maple's default file name, the command to do this would be:
Be sure that you are in the correct directory for this! If Maple
was started from the mouse menu, the file will be saved in your
top level home directory. Otherwise, it will be saved in the
directory from which you started Maple.
To remove a plot window, select Exit from the
File menu in the plot window, or hold down the
<Alt> key and type x in the plot
window.
Using Maple's on-line help facilities:
Maple has extensive built-in help facilities, which you can get
at in several ways. One way is through the Help menu
in the upper right corner of the Maple window. Under this menu
you'll find the Help Browser, which lets you select
help by category, and the Keyword Search, which lets
you search the entire set of help files for a particular word or
topic.
You can also look at help files by using the help command
(?) at the Maple prompt. Follow the question mark
with the name of a command for which you need help, and Maple
will give you an appropriate help window. Here are some ways to
use the help command:
?intro
?library
?index
?index,category
?topic
?topic,subtopic
- Introduction to Maple
- Maple library functions and procedures
- List of all help categories
- List of help files on specific topics
- Explanation of a specific topic
- Explanation of a subtopic under a topic
Learning more about Maple:
Maple is a very powerful tool, and you'll have to do some reading
before becoming proficient at it. You can learn all you need to
by browsing through the on-line help and experimenting, but
fortunately this is not the only way. There is a very good
tutorial introduction to Maple in the book:
How to quit Maple:
Select Exit from the File menu. Or,
hold down the <Alt> key and type
x in the Maple window. Or, type quit in
the Maple window. |
Maths Year 11
Year 11 is a very busy year at CHSG in the Mathematics Faculty! For 2012-13 there will be three opportunities for students to sit a GCSE in Mathematics; in November, March and in June 2013. Revision for the GCSE exams starts almost immediately from the beginning of Year 11, working towards either a Mock exam in November or the early-entry GCSE itself for a select few students. The majority of girls will sit the final GCSE in March 2013, with an option to re-sit in June if they are close to the next grade up. Students will be given many revision materials over the course of year 11, but one they have access to already is
Areas studied
Number & Problem Solving
Algebra
Geometry & Measures
Data Handling/Statistics
Skills
During GCSE Mathematics students will be taught skills that enable them to function in other subjects and in everyday life. In particular, students will be taught how to present and analyse data accurately, they will be shown how to calculate percentages quickly and efficiently in their heads and also how and when it is appropriate to use their calculators. They will study and learn how to convert between widely used measures including metric and imperial measures, and they will also learn how to problem solve and how to present their findings in a meaningful way. They will also learn to use algebra and geometry to generalize and to solve problems. The skills learnt during GCSE Mathematics prepare students for life after Year 11 and for those pupils that wish to continue studying the subject post-16 and take A level Mathematics, their GCSE studies will have prepared them for the rigours, as well as the beauty, of the subject.
Setting
Students are set according to their potential, based on prior results in tests and teacher assessments. We are combining both types of assessment to provide a rounded view of individual student understanding so that they are placed in the group that will best meet their Mathematical needs. They are also set challenging yet achievable targets based upon their last exam result. Students will be in classes of no more than 30 students, and in lower ability groups, sometimes less than 15 per class. There will be opportunities throughout the year for pupils to move groups, according to their progress. Teachers will discuss movements at Mathematics Faculty meetings and decide if a move is in the best interest of the student.
Homework
Students will be set one piece of homework a week. Homework may be from the MyMaths website, which is marked automatically and immediately online, with a written piece of work lat east once a fortnight. Both pieces will be designed to extend or consolidate class work, or will be revision work. Students should get written feedback from their teacher on their homework once a fortnight. In year 11, students will be given past papers to complete in the Spring term in preparation for their GCSE exam.
Assessment & Reporting
Students are assessed using a variety of methods with homework and class work being an important part of this. They will have a formal exam at the end of Year 9 and Year 10 to look at progress from previous years. There will also be interim reports throughout the year, as well as an annual full report according to the whole school timetable. Parents can contact class teachers at any time to get an update on their daughter's progress.
How parents can help
Ensuring that students come equipped to their lessons – students will need their own geometry set and a calculator for both class work and homework
Checking that students are completing homework tasks to the best of their ability and encouraging them to seek support in plenty of time if they are struggling
Giving opportunities to work out how much change you should get in a shop, or to estimate shopping bills – it's a good mental Maths workout!
In Year 11, students are given a MathsWatch revision CD Rom – please encourage them to use it and ask them to show you how it works, its just like having a private tutor at home, but for free!
All pupils have access to MyMaths – they can revise or study independently at any time to complement their studies. It has a GCSE Statistics section too.
Most importantly, be positive about Mathematics at home – students that hear positive things about the subject at home are more likely to develop a positive attitude to it themselves!
GCSE Revision - February 2012
All year 11 students that are to take the GCSE examination on Monday 5th March please find below revision lists for your information and attention. |
256 October 10 & 14, 2008Mathematical Induction (Rosen 4.1) Mathematical induction is a form of proof that is used to prove statements of the following structure: n Z+ P (n), where P (n) is some statement about the positive integer n. A
Mathematics 256, Final Exam 9:00 a.m.12:00 noon, December 18, 2008The nal exam will be comprehensive. Approximately 40% of the exam will cover discrete mathematics and 60% will cover linear algebra. Your nal exam score may replace one of the two tes
Euclids Algorithm and Solving Congruences Mathematics 100 A September 22, 2006Denition. The greatest common divisor of two natural numbers a and b, written gcd(a, b), is the largest natural number that divides both a and b. Middle School Algorithm.
36243_1_p1-2912/8/97 8:39 AM Page 23MORE ABOUT FUNCTION PARAMETERSDefault Values for Parameters in FunctionsProblem. We wish to construct a function that will evaluate any real-valued polynomial function of degree 4 or less for a given real val
36243_2_p31-3412/8/97 8:42 AMPage 3136243AdamsPRECEAPPENDIX 2 JA ACS11/17/97pg 31CODES OF ETHICSThe PART OF THE PICTURE: Ethics and Computing section in Chapter 1 noted that professional societies have adopted and instituted codes
14.4 The STL list<T> Class Template114.4 The STL list<T> Class TemplateIn our description of the C+ Standard Template Library in Section 10.6 of the text, we saw that it provides a variety of other storage containers besides vector<T> and that o
15.4 An Introduction to Trees1TREES IN STLThe Standard Template Library does not provide any templates with Tree in their name. However, some of its containers - the set<T>, map<T1, T2> , multiset<T>, and multmap<T1, T2> templates - are generall
10.2 C-Style Arrays1VALARRAYSAn important use of arrays is in vector processing and other numeric computation in science and engineering. In mathematics the term vector refers to a sequence (one-dimensional array) of real values on which various
15.3 Recursion Revisited1EXAMPLE: DRY BONES!The Old Testament book of Ezekiel is a book of vivid images that chronicle the siege of Jerusalem by the Babylonians and the subsequent forced relocation (known as the exile) of the Israelites followin
10.7 An Overview of the Standard Template Library1STL Iterators. The Standard Template Library provides a rich variety of containers:vector list deque stack queue priority_gueue map and multimapset and multiset The elements of a vector<T> can
5.5 Case Study: Decoding Phone Numbers15.5 Case Study: Decoding Phone NumbersPROBLEMTo dial a telephone number, we use the telephones keypad to enter a sequence of digits. For a long-distance call, the telephone system must divide this number i
1.3 Case Study: Revenue Calculation11.3 Case Study: Revenue CalculationPROBLEMSam Splicer installs coaxial cable for the Metro Cable Company. For each installation, there is a basic service charge of $25.00 and an additional charge of $2.00 for
7.7 Case Study: Calculating Depreciation17.7 Case Study: Calculating DepreciationPROBLEMDepreciation is a decrease in the value over time of some asset due to wear and tear, decay, declining price, and so on. For example, suppose that a company
1From Paraconsistent Logic to Universal LogicJean-Yves Bziau"The undetermined is the structure of everything" AnaximanderAbstract During these last years I have been developed a general theory of logics that I have called Universal Logic. In t |
This text is designed to help teachers work with beginning ESL students in grades 5 to 12. It provides lessons and activities that will develop the students' vocabulary, English usage, and mathematical understanding. A balance of high-interest activities,
Some probability problems are so difficult that they stump the smartest mathematicians. But even the hardest of these problems can often be solved with a computer and a Monte Carlo simulation, in which a random-number generator simulates a physical process, such as a million rolls of a pair of dice. This is what Digital Dice is all about: how to get numerical answers to difficult probability problems without having to solve complicated mathematical equations.Popular-math writer Paul Nahin challenges readers to solve twenty-one difficult but fun problems, from determining the odds of coin-flipping games to figuring out the behavior of elevators. Problems build from relatively easy (deciding whether a dishwasher who breaks most of the dishes at a restaurant during a given week is clumsy or just the victim of randomness) to the very difficult (tackling branching processes of the kind that had to be solved by Manhattan Project mathematician Stanislaw Ulam). In his characteristic style, Nahin brings the problems to life with interesting and odd historical anecdotes. Readers learn, for example, not just how to determine the optimal stopping point in any selection process but that astronomer Johannes Kepler selected his second wife by interviewing eleven women.The book shows readers how to write elementary computer codes using any common programming language, and provides solutions and line-by-line walk-throughs of a MATLAB code for each problem.Digital Dice will appeal to anyone who enjoys popular math or computer science.
This adaptation of an earlier work by the authors is a graduate text and professional reference on the fundamentals of graph theory. It covers the theory of graphs, its applications to computer networks and the theory of graph algorithms. Also includes exercises and an updated bibliography.
A thorough and highly accessible resource for analysts in a broad range of social sciences. Optimization: Foundations and Applications presents a series of approaches to the challenges faced by analysts who must find the best way to accomplish particular objectives, usually with the added complication of constraints on the available choices. Award-winning educator Ronald E. Miller provides detailed coverage of both classical, calculus-based approaches and newer, computer-based iterative methods. Dr. Miller lays a solid foundation for both linear and nonlinear models and quickly moves on to discuss applications, including iterative methods for root-finding and for unconstrained maximization, approaches to the inequality constrained linear programming problem, and the complexities of inequality constrained maximization and minimization in nonlinear problems. Other important features include: More than 200 geometric interpretations of algebraic results, emphasizing the intuitive appeal of mathematics Classic results mixed with modern numerical methods to aid users of computer programs Extensive appendices containing mathematical details important for a thorough understanding of the topic With special emphasis on questions most frequently asked by those encountering this material for the first time, Optimization: Foundations and Applications is an extremely useful resource for professionals in such areas as mathematics, engineering, economics and business, regional science, geography, sociology, political science, management and decision sciences, public policy analysis, and numerous other social sciences. An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.
Uses a strong computational and truly interdisciplinary treatment to introduce applied inverse theory. The author created the Mollification Method as a means of dealing with ill-posed problems. Although the presentation focuses on problems with origins in mechanical engineering, many of the ideas and techniques can be easily applied to a broad range of situations.
New statistical methods and future directions of research in time series A Course in Time Series Analysis demonstrates how to build time series models for univariate and multivariate time series data. It brings together material previously available only in the professional literature and presents a unified view of the most advanced procedures available for time series model building. The authors begin with basic concepts in univariate time series, providing an up-to-date presentation of ARIMA models, including the Kalman filter, outlier analysis, automatic methods for building ARIMA models, and signal extraction. They then move on to advanced topics, focusing on heteroscedastic models, nonlinear time series models, Bayesian time series analysis, nonparametric time series analysis, and neural networks. Multivariate time series coverage includes presentations on vector ARMA models, cointegration, and multivariate linear systems. Special features include: Contributions from eleven of the world??'s leading figures in time series Shared balance between theory and application Exercise series sets Many real data examples Consistent style and clear, common notation in all contributions 60 helpful graphs and tables Requiring no previous knowledge of the subject, A Course in Time Series Analysis is an important reference and a highly useful resource for researchers and practitioners in statistics, economics, business, engineering, and environmental analysis. An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.
This book provides a grounded introduction to the fundamental concepts of mathematics, neuroscience and their combined use, thus providing the reader with a springboard to cutting-edge research topics and fostering a tighter integration of mathematics and neuroscience for future generations of students. The book alternates between mathematical chapters, introducing important concepts and numerical methods, and neurobiological chapters, applying these concepts and methods to specific topics. It covers topics ranging from classical cellular biophysics and proceeding up to systems level neuroscience. Starting at an introductory mathematical level, presuming no more than calculus through elementary differential equations, the level will build up as increasingly complex techniques are introduced and combined with earlier ones. Each chapter includes a comprehensive series of exercises with solutions, taken from the set developed by the authors in their course lectures. MATLAB code is included for each computational figure, to allow the reader to reproduce them. Biographical notes referring the reader to more specialized literature and additional mathematical material that may be needed either to deepen the reader's understanding or to introduce basic concepts for less mathematically inclined readers completes each chapter.A very didactic and systematic introduction to mathematical concepts of importance for the analysis of data and the formulation of concepts based on experimental data in neuroscienceProvides introductions to linear algebra, ordinary and partial differential equations, Fourier transforms, probabilities and stochastic processesIntroduces numerical methods used to implement algorithms related to each mathematical conceptIllustrates numerical methods by applying them to specific topics inneuroscience, including Hodgkin-Huxley equations, probabilities to describe stochastic release, stochastic processes to describe noise in neurons, Fourier transforms to desc Sec
Mathematics is often thought of as the coldest expression of pure reason. But few subjects provoke hotter emotions—and inspire more love and hatred—than mathematics. And although math is frequently idealized as floating above the messiness of human life, its story is nothing if not human; often, it is all too human. Loving and Hating Mathematics is about the hidden human, emotional, and social forces that shape mathematics and affect the experiences of students and mathematicians. Written in a lively, accessible style, and filled with gripping stories and anecdotes, Loving and Hating Mathematics brings home the intense pleasures and pains of mathematical life.These stories challenge many myths, including the notions that mathematics is a solitary pursuit and a "young man's game," the belief that mathematicians are emotionally different from other people, and even the idea that to be a great mathematician it helps to be a little bit crazy. Reuben Hersh and Vera John-Steiner tell stories of lives in math from their very beginnings through old age, including accounts of teaching and mentoring, friendships and rivalries, love affairs and marriages, and the experiences of women and minorities in a field that has traditionally been unfriendly to both. Included here are also stories of people for whom mathematics has been an immense solace during times of crisis, war, and even imprisonment—as well as of those rare individuals driven to insanity and even murder by an obsession with math.This is a book for anyone who wants to understand why the most rational of human endeavors is at the same time one of the most emotional.
A perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight.In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out—from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft—indeed, brilliant—instructions on stripping away irrelevancies and going straight to the heart of the problem.In this best-selling classic, George Pólya revealed how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out—from building a bridge to winning a game of anagrams. Generations of readers have relished Pólya's deft instructions on stripping away irrelevancies and going straight to the heart of a problem. How to Solve It popularized heuristics, the art and science of discovery and invention. It has been in print continuously since 1945 and has been translated into twenty-three different languages.P—he taught until he was ninety—and maintained a strong interest in pedagogical matters throughout his long career. In addition to How to Solve It, he published a two-volume work on the topic of problem solving, Mathematics of Plausible Reasoning, also with Princeton.Pólya is one of the most frequently quoted mathematicians, and the following statements from How to Solve It make clear why: "My method to overcome a difficulty is to go around it." "Geometry is the science of correct reasoning on incorrect figures." "In order to solve this differential equation you look at it till
Leonhard Euler's polyhedron formula describes the structure of many objects—from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon molecules. Yet Euler's formula is so simple it can be explained to a child. Euler's Gem tells the illuminating story of this indispensable mathematical idea.From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V-E+F=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler's formula. Using wonderful examples and numerous illustrations, Richeson presents the formula's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map.Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, Euler's Gem will fascinate every mathematics enthusiast.
An undergraduate textbook devoted exclusively to relationships between mathematics and art, Viewpoints is ideally suited for math-for-liberal-arts courses and mathematics courses for fine arts majors. The textbook contains a wide variety of classroom-tested activities and problems, a series of essays by contemporary artists written especially for the book, and a plethora of pedagogical and learning opportunities for instructors and students.Viewpoints focuses on two mathematical areas: perspective related to drawing man-made forms and fractal geometry related to drawing natural forms. Investigating facets of the three-dimensional world in order to understand mathematical concepts behind the art, the textbook explores art topics including comic, anamorphic, and classical art, as well as photography, while presenting such mathematical ideas as proportion, ratio, self-similarity, exponents, and logarithms. Straightforward problems and rewarding solutions empower students to make accurate, sophisticated drawings. Personal essays and short biographies by contemporary artists are interspersed between chapters and are accompanied by images of their work. These fine artists—who include mathematicians and scientists—examine how mathematics influences their art. Accessible to students of all levels, Viewpoints encourages experimentation and collaboration, and captures the essence of artistic and mathematical creation and discovery.Classroom-tested activities and problem solvingAccessible problems that move beyond regular art school curriculumMultiple solutions of varying difficulty and applicabilityAppropriate for students of all mathematics and art levelsOriginal and exclusive essays by contemporary artistsSolutions manual (available only to teachers)
The Handbook Philosophy of Technology and Engineering Sciences addresses numerous issues in the emerging field of the philosophy of those sciences that are involved in the technological process of designing, developing and making of new technical artifact
Computational science is a quickly emerging field at the intersection of the sciences, computer science, and mathematics because much scientific investigation now involves computing as well as theory and experiment. However, limited educational materials exist in this field. Introduction to Computational Science fills this void with a flexible, readable textbook that assumes only a background in high school algebra and enables instructors to follow tailored pathways through the material. It is the first textbook designed specifically for an introductory course in the computational science and engineering curriculum.The text embraces two major approaches to computational science problems: System dynamics models with their global views of major systems that change with time; and cellular automaton simulations with their local views of how individuals affect individuals. While the text is generic, an extensive author-generated Web-site contains tutorials and files in a variety of software packages to accompany the text.Generic software approach in the textWeb site with tutorials and files in a variety of software packagesEngaging examples, exercises, and projects that explore scienceAdditional, substantial projects for students to develop individually or in teamsConsistent application of the modeling processQuick review questions and answersProjects for students to develop individually or in teamsReference sections for most modules, as well as a glossaryOnline instructor's manual with a test bank and solutions |
Oxford GCSE Maths for Edexcel: Higher Homework VLE Pack
Oxford GCSE Maths for Edexcel has a unique 4-book approach that will make learning much more focused and effective and help your results zoom ahead. Student Books that target four different levels are designed to make learning simpler, more targeted, and therefore more successful. Written by practising teachers and examiners to make sure it really works, the course provides a range of targeted components, including Teacher Guides and unique OxBox CD-ROMs, as well as these flexible-use VLE Packs to provide homework material targeting the four levels. This pack is for Higher level students, and targets grades B-D, comprising the pages of the Higher Homework Book for you to save, display, network, print or use with your students exactly as you choose. |
Comprehensive ...
Practical Problems in Mathematics for Welders, 5E, takes the same straightforward and practical approach to mathematics that made previous editions so highly effective, and combines it with the latest procedures and practices in the welding industry. With this comprehensive, instructional book, read...
Gain the math skills you need to succeed in the electrical trade with this new edition of Practical Problems in Mathematics for Electricians. Using the same straightforward writing style and simple, step-by-step explanations that made previous editions so reader-friendly, the eighth edition includes...
This widely used text/workbook teaches the practical mathematics essential to the building construction and carpentry trades. The book features short units that begin with a brief explanation of an important math principle followed by straightforward explanations and examples that are worked out in ...
This fully updated edition of Practical Problems in Mathematics for Drafting and CAD features contemporary drafting problems, CAD drawings, and industry applications and practices-essential information designed to enhance the math skills of students concentrating their studies in the field of drafti...
Success in the electronics field requires a substantial background in mathematics. This updated book is written to provide beginning students with these needed skills. Practical, easy-to-understand problems help prepare students for the types of problems that professional electronic technicians fa...
This book covers a variety of topics in mathematics as they relate to industrial technologies including manufacturing, electricity/electronics, graphics, communication, transportation, industrial management, materials and related science principles. Organized by topics, the main objective is to dev... |
Excel 2010 Workbook for Dummies
Reinforce your understanding of Excel with these Workbook exercises
Excel is the world's most popular number-crunching program, and For Dummies books are the most popular guides to Excel
The Workbook approach offers practical application, with more than 100 exercises to work through and plenty of step-by-step guidance
This guide covers the new features of Excel 2010, includes a section on creating graphic displays of information, and offers ideas for financial planners
Also provides exercises on using formulas and functions, managing and securing data, and performing data analysis
A companion CD-ROM includes screen shots and practice materials
Excel 2010 Workbook For Dummies helps you get comfortable with Excel so you can take advantage of all it has to offer.
Note: CD-ROM/DVD and other supplementary materials are not included as part of eBook file.
Hands-on practice in solving quantum physics problems. Quantum Physics is the study of the behavior of matter and energy at the molecular, atomic, nuclear, and even smaller microscopic levels. Like ...
Geometry is one of the oldest mathematical subjects in history. Unfortunately, few geometry study guides offer clear explanations, causing many people to get tripped up or lost when trying to solve a ... |
Essay: Use of Mathematics in Daily Life – College Studies
Mathematics is probably one of the most feared subjects among students in high school and college. The very nature of the subject involving complex manipulation of equations using a full range of key mathematical operations such as addition, subtraction, multiplication and division, is something that students do not like doing. Mathematics is a subject that involves logic and everything in it is based on logical applications. For instance, we can never claim that 2+2 can ever be equal to 5 as it is 4, so coming back to the main point; mathematics is something that is based on pure facts and what is tangible. There is no room for errors and false assumptions in mathematics. However, despite it being so unpopular it is vital for everyday living. We like it or not but the use of mathematical functions are always there in our day to day living unconsciously.
During Shopping
When we go to malls we make purchases of particular household or other kinds of items. We use mathematics when we exchange these items for certain amount of money. Therefore, we have to make calculations orally as how much a particular item is worth, how much amount do we need to pay, in case we pay more than the specified price of the item how much change we will receive. We perform all these calculations unconsciously but what we are doing is basically using mathematical functions. |
Linear Algebra by BookMan Publishing A fuzzy algebraic structure is a function ƒÝ : A "_ [0, 1], where A is any algebraic structure with two binary operations, 'ƒx' and '"P', and [0, 1] is the closed interval, and ƒÝ satisfies the following conditions
ƒÝ(x ƒx .. Buy! Amazon, |
Grade Descriptors
Thorough knowledge and understanding; successfully applied mathematical principles in a sophisticated and accurate manner in a wide variety of contexts.
Successful application of mathematical principles to solve a range of challenging problems. Clear integration of knowledge, understanding and skills from different areas. Comprehensive responses containing all necessary detail.
Thorough knowledge and comprehensive understanding of the syllabus.
B
Broad knowledge and understanding, although some responses lacked detail or contained minor errors.
Broad knowledge and understanding; applied mathematical principles in a variety of contexts, although some responses lacked detail or contained minor errors.
Successful application of mathematical principles to solve a variety of problems. Some integration of knowledge, understanding and skills from different areas. Some responses lacked necessary detail or contained minor errors.
Broad knowledge and understanding, although some responses lacked detail or contained minor errors.
C
Satisfactory knowledge and understanding of the syllabus; satisfactory application of mathematical processes in performing routine tasks. Some responses lacked detail; some significant errors.
Satisfactory knowledge and understanding of the syllabus; applied mathematical principles and processes in performing routine tasks to a satisfactory level, although some responses lacked detail; several significant errors.
Satisfactory application of mathematical principles to solve some problems. Satisfactory integration of knowledge, understanding and skills from different areas, when given some direction.
Satisfactory knowledge and understanding of the syllabus; satisfactory application of mathematical processes in performing routine tasks. Some responses lacked detail; some significant errors.
D
Basic knowledge of the syllabus and limited understanding of mathematical principles; attempted to carry out mathematical processes in straightforward contexts, but many significant errors.
Basic knowledge of the syllabus and limited understanding of mathematical principles; attempted to apply mathematical principles in straightforward contexts; many significant errors.
Limited application of mathematical principles to solve problems.
Basic knowledge of the syllabus and limited understanding of mathematical principles; attempted to carry out mathematical processes in straightforward contexts, but many significant errors.
E
Very limited knowledge of the syllabus; difficulty carrying out mathematical processes at a basic level.
Very limited knowledge of the syllabus; difficulty applying mathematical principles even at a basic level.
Limited application of mathematical principles to solve even the most basic problems.
Very limited knowledge of the syllabus; difficulty carrying out mathematical processes at a basic level. |
Basic Multivariable Calculus - 93 edition
Summary: Basic Multivariable Calculus helps students make the difficult transition to advanced calculus by focusing exclusively on topics traditionally covered in the third-semester course in the calculus of functions of several variables. The concepts of vector calculus are clearly and accurately explained, with an emphasis on developing students' intuitive understanding and computational technique.
Only first year calculus required--all necessary linear al...show moregebra is explained
Incorporates wide range of physical applications, dozens of graphics, and a large number of exercises
Volume and Cavalieri's Principle The Double Integral over a Rectangle The Double Integral over Regions The Triple Integral Change of a Variable, Cylindrical and Spherical Coordinates Applications of Multiple Integrals
6. Integrals over Curves and Surfaces
Line Integrals Parametrized Surfaces Area of a Surface Surface Integrals |
Long description International MetricProduct details
Publisher:
Brooks/Cole
ISBN:
9780495383628
Publication date:
February 2008
Length:
254mm
Width:
224mm
Thickness:
48mm
Weight:
2421g
Edition:
6th international ed
Pages:
1344
Table of contents
1. Functions and Models. Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. New Functions from Old Functions. Graphing Calculators and Computers. Principles of Problem Solving. 2. Limits. The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. Continuity. 3. Derivatives. Derivatives and Rates of Change. Writing Project: Early Methods for Finding Tangents. The Derivative as a Function. Differentiation Formulas. Applied Project: Building a Better Roller Coaster. Derivatives of Trigonometric Functions. The Chain Rule. Applied Project: Where Should a Pilot Start Descent?. Imlicit Differentiation. Rates of Change in the Natural and Social Sciences. Related Rates. Linear Approximations and Differentials. Laboratory Project: Taylor Polynomials. 4. Applications of Differentiation. Maximum and Minimum Values. Applied Project: The Calculus of Rainbows. The Mean Value Theorem. How Derivatives Affect the Shape of a Graph. Limits at Infinity |
7
Hello, in this blog I am going to look back on all of the topics we have covered so far in this semester which are: real numbers, order of operations, evaluating, translating, solving 1-step equations, solving 2-step equations, solving literal equations, CLT, exponents, and distributive property. I feel that I get real numbers really well, but sometimes I can get a little confused, but not a lot. Order of operations, evaluating, exponents, and distributive property all come easy to me really good! For the rest of them they are kind of confusing to me, but I understand them in the end. Yes, I have been thinking about semester exams, what I think about them is I am nervous like everyone else is because I don't want to fail them and do bad. Exams always get me nervous because I don't want to do bad on them and then have them bring my grades down. Three things that I could start doing now to help get ready for exams is start studying, get all of the papers needed to study for the exams, and just prepare myself.
Thanks for listening! |
FUGP - Fungraph - Graphs of mathematical functions - 5 types of graphs:- Single - Piecewise - Parametric - Pola and Multiple - Print and copy graph into clipboard - 15 preset examples - Easy to use - User's manual in PDF format - At home or in the classroom, FunGraph is suitable both for learning and for teaching. |
Shimon Even's Graph Algorithms, published in 1979, was a seminal introductory book on algorithms read by everyone engaged in the field. This thoroughly revised second edition, with a foreword by Richard M. Karp and notes by Andrew V. Goldberg, continues the exceptional presentation from the first edition and explains algorithms in a formal but simple language with a direct and intuitive presentation.
The book begins by covering basic material, including graphs and shortest paths, trees, depth-first-search and breadth-first search. The main part of the book is devoted to network flows and applications of network flows, and it ends with chapters on planar graphs and testing graph planarity.
show more show less
Paths in graphs
Trees
Depth-first search
Ordered trees
Flow in networks
Applications of network flow techniques
Planar graphs
Testing graph planarity
Shimon Even (1935ndash;2004) was a pioneering researcher on graph algorithms and cryptography. He was a highly influential educator who played a major role in establishing computer science education in Israel at the Weizmann Institute and the Technion. He served as a source of professional inspiration and as a role model for generations of students and researchers. He is the author of Algorithmic Combinatorics (1973) and Graph Algorithms (1979).
List price:
$90.00
Edition:
2nd 2011
Publisher:
Cambridge University Press
Binding:
Trade Cloth
Pages:
202 |
Discrete Transition to Advanced Mathematics
9780534405182
ISBN:
0534405185
Publisher: Thomson Learning
Summary: As the title indicates, this text is intended for courses aimed at bridging the gap between lower level mathematics and advanced mathematics. The transition to advanced mathematics presented is discrete since continuous functions are not studied. The text provides a careful introduction to techniques for writing proofs and a logical development of topics based on intuitive understanding of concepts. The authors utili...ze a clear writing style and a wealth of examples to develop an understanding of discrete mathematics and critical thinking skills. Including more topics than can be covered in one semester, the text offers innovative material throughout, particularly in the last three chapters (e.g. Fibonacci Numbers and Pascal's Triangle). This allows flexibility for the instructor and the ability to teach a deeper, richer course |
Some senior teachers groan
over the fact that the rigor of geometric proofs, which is very useful to
train the students in logical thinking, is no longer in the current curriculum.
The introduction of computer software into the curriculum always invites fear
among the teachers of the loss of students' basic mathematical ability. For
example, with the introduction of calculators, some teachers complained that
students might lose their sense of estimates for basic operations on simple
numbers. The same reasoning extends to the use of computer in education: with
the use of GSP, would the rigor of training in logical training and the students'
ability to solve geometry problems be affected?
Hoehn (1997) gave sample activities of exploring
worksheets that could be done with GSP. He suggested that activities that
involve the proof of theorems on geometry could be done with the software.
It is implied that more abstract results on geometry can be taught by focusing
on improving students' spatial ability. Hoehn further suggested that students
could be asked to attempt to generalize existing theorems and state and verify
their conjectures. All this is in line with our new Problem-Solving Approach
in the syllabus (Ministry of Education, 2000).
As Leong & Lim (2003) pointed out, the key
features that make the software GSP suitable for teaching transformation geometry
are
(a) it enables objects to be transformed on the screen;
(b) it allows easy measurement of distances, angles and
areas;
(c) it has the click-and-drag feature that enables users
to experiment different cases
(d) it allows animations of motion to be done.
Here the above features will be made use of
to enable the teaching of concepts of mechanics more visual than rigorous
proofs. |
WELCOME to the Mathematics Department at Highland Park Senior High School!
Mathematics is the study of quantity, structure, space and change. It developed, through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the study of the shapes and motions of physical objects.
Please click on the following links for course offerings, helpful resources and a directory of department faculty. |
Using And Understanding Mathematics A Quantitative Reasoning Approach
9780321458209
ISBN:
0321458206
Edition: 4 Pub Date: 2007 Publisher: Addison-Wesley
Summary: Most students taking this course do so to fulfill a requirement, but the true benefit of the course is learning how to use and understand mathematics in daily life. This quantitative reasoning text is written expressly for those students, providing them with the mathematical reasoning and quantitative literacy skills they'll need to make good decisions throughout their lives. Common-sense applications of mathematics ...engage students while underscoring the practical, essential uses of math |
This
course is a continuation of Analytic Geometry and Calculus II,
extending the skills of differentiation and integration by learning new
techniques and working with partial derivatives and double and triple
integrals. Other major topics include cylindrical and spherical
coordinates, quadric surfaces, vector functions, vector analysis,
Green''s theorem and Stoke''s theorem.
GENERAL EDUCATION APPLICABILITY
CSU GE Area B: Physical and its Life Forms(mark all that apply) = B4 - Mathematics/Quantitative Thinking;
UC Transfer Course:
CSU Transfer Course:
STUDENT LEARNING OUTCOMES Upon completion of the course, the student will be able to
Use the Cartesian, polar, cylindrical, and spherical coordinate systems effectively.
Use scalar and vector products in applications.
Use vector-valued functions to describe motion in space.
Extend the concepts of derivatives, differentials, and integrals to include multiple independent variables.
Solve simple differential equations of the first and second order.
REQUISITES
Prerequisite:
MATH C152A. Partial Differentiation
1. Functions of two or more variables
a. Limits
b. Continuity
c. Geometric interpretation
d. Derivatives
2. Tangent planes and normal lines
3. The directional derivative
4. The gradient
5. The chain rule
6. Linearization and differentials
7. Maximum-Minimum problems
a. Use of derivatives for extreme values
b. Lagrange multipliers
c. Methods of least squares
8. Higher order derivatives
B. Multiple Integrals
1. Functions of two or more variables
a. Plane area
b. Volume
c. Center of mass
d. Moments of inertia
e. Polar coordinates
f. Surface area
2. Triple Integrals
a. Volume
b. Center of mass
c. Moments of inertia
d. Cylindrical coordinates
e. Spherical coordinates
C. Vectors and Parametric Equations
1. Parametric Equations in Kinematics
2. Parametric Equations in Analytic Geometry
3. Vectors in two dimensions
a. The i and j components
b. Vector algebra
c.
Unit and Zero
Vectors
4. Space Coordinates
a. Cartesian
b. Cylindrical
c. Spherical
5. Vectors in Space
6. Scalar Product of Two Vectors
a. Algebraic properties
b. Orthogonal vectors
c. Vector projection
7. Vector Product of Two Vectors
a. Algebraic properties
b. Area
8. Equations of Lines and Planes
9. Product of Three or More Vectors
10. Cylinders
11. Quadric Surfaces
D. Vector Functions and Their Derivatives
1. Derivative of a Vector Function
2. Velocity and Acceleration
3. Tangential Vectors
4. Curvature and Normal Vectors
5. Differentiation of Products of Vectors
6. Polar and Cylindrical Coordinates
E. Multi-Dimensional Vector Analysis
1. Vector fields
2. Surface integrals
3. Line integrals
4. Green's Theorem
5. Stokes' Theorem
METHODS OF INSTRUCTION--Course instructional methods may include but are not limited to
Discussion;
Lecture;
Other Methods: A. lecture and discussion of all course concepts.
B. demonstration of developing proofs and solving application problems.
C. reading textbooks and journals to see presentations different than those of the instructor.
D. assignments and quizzes
E. the use of computational and other types of mathematical software
OUT OF CLASS ASSIGNMENTS: Out of class assignments may include but are not limited to
A. Reading assignments.
B. Bi-weekly homework assignments.
METHODS OF EVALUATION: Assessment of student performance may include but is not limited to
A. tests on course content, to include solving equations as well as demonstration of specific skills B. quizzes (in-class and take-home) to include solving equations as well as demonstration of specific skills C. group work to analyze and solve application problems
TEXTS, READINGS, AND MATERIALS: Instructional materials may include but are not limited to |
Math 171: Math for Elementary Educators I
Common Course Numbering
This course was previously known (prior to Summer 2010) as Math 121; only the course number and title have changed.
Course Description
Math 171 is intended for prospective and current elementary school teachers. The course examines problem-solving techniques and mathematics related to topics taught at the K–8 level. Topics include number theory, set theory, functions and the use of technology.
Who should take this course?
Prospective and current elementary school teachers. You should consult the planning sheet for your program and consult an advisor to determine if this course is appropriate for you.
Who is eligible to take this course?
The prerequisite for this course is Math 90 or Math 95 with a grade of 2.0 or higher. Students new to EdCC with an appropriately high Accuplacer score may also take Math 171.
Is this course transferable?
This course may transfer to certain universities if the student enrolls in a teacher-preparation program; consult an advisor or see the Transfer Center to determine transferability.
What textbook is used for this course?
The tenth edition of Reconceptualizing Mathematics for Elementary School Teachers by Judith Sowder, Larry Sowder and Susan Nickerson. |
Calculus Latin, calculus, a small stone used for counting of calculus. Cal broadly called mathematical analysis. Calculus has widespread applications in science, economics, and engineering and can solve many problems for which algebra alone is insufficient.
In American mathematics education, precalculus or Algebra 3 in some areas, an advanced form of secondary school algebra, is a foundational mathematical discipline. It is also called Introduction to Analysis. In many schools, precalculus is actually two separate courses: Algebra and Trigonometry. Precalculus prepares students for calculus the same way as pre algebra prepares students for Algebra I. While pre algebra A lower level class might focus on topics used in a wider selection of higher mathematical areas, such as matrices which are used in business.
With the same design and feature sets as the market leading Precalculus, 8/e, this addition to the Larson Precalculus series provides both students and instructors with sound, consistently structured explanations of the mathematical concepts. Designed for a two-term course, this text contains the features that have made Precalculus a complete solution for both students and instructors: interesting applications, cutting-edge design, and innovative technology combined with an abundance of carefully written exercises. In addition to a brief algebra review and the core precalculus topics, PRECALCULUS WITH LIMITS covers analytic geometry in three dimensions and introduces concepts covered in calculus.
This market-leading text continues to provide both students and instructors with sound, consistently structured explanations of the mathematical concepts. Designed for a one- or two-term course that prepares students to study calculus, the new Eighth Edition retains the features that have made PRECALCULUS a complete solution for both students and instructors: interesting applications, cutting-edge design, and innovative technology combined with an abundance of carefully written exercises.
Traditionally studied after Algebra II, this mathematical field covers advanced algebra, trigonometry, exponents, logarithms, and much more. These interrelated topics are essential for solving calculus problems, and by themselves are powerful methods for describing the real world, permeating all areas of science and every branch of mathematics. Little wonder, then, that precalculus is a core course in high schools throughout the country and an important review subject in college. Unfortunately, many students struggle in precalculus because they fail to see the links between different topics—between one approach to finding an answer and a startlingly different, often miraculously simpler, technique. As a result, they lose out on the enjoyment and fascination of mastering an amazingly useful tool box of problem-solving strategies. And even if you're not planning to take calculus, understanding the fundamentals of precalculus can give you a versatile set of skills that can be applied to a wide range of fields—from computer science and engineering to business and health care. Mathematics Describing the Real World: Precalculus and Trigonometry is your unrivaled introduction to this crucial subject, taught by award-winning Professor Bruce Edwards of the University of Florida. Professor Edwards is coauthor of one of the most widely used textbooks on precalculus and an expert in getting students over the trouble spots of this challenging phase of their mathematics education.
Full of relevant and current real-world applications, Stefan Waner and Steven Costenoble's FINITE MATHEMATICS AND FINITE MATHEMATICS AND APPLIED CALCULUS, Fifth Edition connects with all types of teaching and learning styles. Resources like the accompanying website allow the text to support a range of course formats, from traditional lectures to strictly online courses.
This textbook has been in constant use since 1980, and this edition represents the first major revision of this text since the second edition. It was time to select, make hard choices of material, polish, refine, and fill in where needed. Much has been rewritten to be even cleaner and clearer, new features have been introduced, and some peripheral topics have been removed.
Finite Mathematics and Calculus with Applications, Ninth Edition, by Lial, Greenwell, and Ritchey, is our most applied text to date, making the math relevant and accessible for students of business, life science, and social sciences. Current applications, many using real data, are incorporated in numerous forms throughout the book, preparing students for success in their professional careers. With this edition, students will find new ways to get involved with the material, such as "Your Turn" exercises and "Apply It" vignettes that encourage active participation.
Clear provides calculator examples, including specific keystrokes that show you how to use various graphing calculators to solve problems more quickly. Perhaps most important-this book effectively prepares you for further courses in mathematics.Designed for the two-semester Applied Calculus course, this graphing calculator-dependent text uses an innovative approach that includes real-life applications and technology such as graphing utilities and Excel spreadsheets to help students learn mathematical skills that they will draw on in their lives and careers. |
Maple is a comprehensive general purpose computer algebra system which
can do symbolic and numerical calculations and has facilities for 2- and
3-dimensional graphical output. Calculus courses may be structured
so that Maple can be used as a tool that will help you gain a complete
understanding of the material discussed. You will discover that the
capability of Maple goes well beyond the realm of calculus; it is a
tool that is used more and more in education and scientific research
in mathematics and engineering.
This chapter is a brief introduction to the use of Maple
in the environment that you will discover at Stony Brook. It is not exhaustive
and its sole purpose is to guide you through the first steps
needed to start using this tool. Once you become familiar with the basics
of Maple and can appreciate its advantages, we encourage you to
experiment with it, not only to learn mathematics in more detail but also to
help you in other courses and your own research. More advanced
documentation is available on line, in the computer lab, and in the library.
Maple runs on many different types of computers and operating systems.
For example, you might use Maple from a Sun workstation running
Solaris (a flavor of Unix) in the computer lab, from a Windows
computer in the library, and from a Macintosh at home. Maple behaves
similarly on all of them; we will usually point it out when we use
something specific to one type of computer. |
This online course comes from the Open Learning Initiative (OLI) by Carnegie Mellon. "The course includes self-guiding materials and activities, and is ideal for independent learners, or instructors trying out this course package."
"The equations, variable definitions, etc. Students are free to make as many entries as they want in order to solve a problem. After they make each entry, they receive immediate feedback on its correctness. They can also ask why an entry (e.g., an equation) is wrong, and they can request hints on what to do next in order to solve the problem. Their score on a problem can be based mostly on the entries made while deriving the answer, and not just on the answer itself."
Primary Audience:
High School, |
Product Description
This program is a review of Linear inequalities. That's right, not everything in this world is equal. Linear inequalities are like linear equations'except they are different and this program will tell you how and why! Topics include: Linear Inequalities, Graphing Liner Inequalities, Systems of Liner Inequalities.Includes a DVD plus a CD-ROM with teacher's guide, quizzes, graphic organizers and classroom activities. Teaching Systems programs are optimized for classroom use and include "Full Public Performance Rights". Grades 8-12. 26 |
Normal 0 false false false MicrosoftInternetExplorer4 Algebra: A Combined Approachis intended for a 2-semester sequence ofIntroductoryandIntermediate Algebrawhere students get a solid foundation in algebra, including exposure to functions, which prepares them for success in College Algebra or their next math course. Prealgebra Review; Real Numbers and Introduction to Algebra; Equations, Inequalities, and Problem Solving; Graphing Equations and Inequalities; Systems of Equations; Exponents and Polynomials; Factoring Polynomials; Rational Expressions; Graphs and Functions; Systems of Equations and Inequalities, and Variation; Rational Exponents, Radicals and Complex Numbers; Quadratic Equations and Functions; Exponential and Logarithmic Functions; Conic Sections For all readers interested in algebra.
Table of Contents
Tools to Help Students Succeed
xi
Additional Resources to Help You Succeed
xiii
Preface
xv
Applications Index
xxv
Prealgebra Review
1
(1)
Factors and the Least Common Multiple
2
(7)
Fractions
9
(10)
Decimals and Percents
19
Group Activity: Interpreting Survey Results
28
(1)
Vocabulary Check
29
(1)
Highlights
29
(3)
Review
32
(2)
Test
34
Real Numbers and Introduction to Algebra
1
(88)
Tips for Success in Mathematics
2
(6)
Symbols and Sets of Numbers
8
(11)
Exponents, Order of Operations, and Variable Expressions
19
(10)
Adding Real Numbers
29
(9)
Subtracting Real Numbers
38
(10)
Integrated Review---Operations on Real Numbers
46
(2)
Multiplying and Dividing Real Numbers
48
(12)
Properties of Real Numbers
60
(8)
Simplifying Expressions
68
(21)
Chapter 1 Group Activity: Magic Squares
77
(1)
Chapter 1 Vocabulary Check
78
(1)
Chapter 1 Highlights
78
(5)
Chapter 1 Review
83
(4)
Chapter 1 Test
87
(2)
Equations, Inequalities, and Problem Solving
89
(89)
The Addition Property of Equality
90
(9)
The Multiplication Property of Equality
99
(9)
Further Solving Linear Equations
108
(10)
Integrated Review---Solving Linear Equations
116
(2)
An Introduction to Problem Solving
118
(12)
Formulas and Problem Solving
130
(12)
Percent and Mixture Problem Solving
142
(12)
Solving Linear Inequalities
154
(24)
Chapter 2 Group Activity: Investigating Averages
164
(1)
Chapter 2 Vocabulary Check
165
(1)
Chapter 2 Highlights
165
(3)
Chapter 2 Review
168
(5)
Chapter 2 Test
173
(2)
Cumulative Review
175
(3)
Graphing Equations and Inequalities
178
(89)
Reading Graphs and the Rectangular Coordinate System
179
(15)
Graphing Linear Equations
194
(11)
Intercepts
205
(10)
Slope and Rate of Change
215
(18)
Integrated Review---Summary on Linear Equations
231
(2)
Equations of Lines
233
(10)
Graphing Linear Inequalities in Two Variables
243
(24)
Chapter 3 Group Activity: Finding a Linear Model
252
(1)
Chapter 3 Vocabulary Check
253
(1)
Chapter 3 Highlights
253
(4)
Chapter 3 Review
257
(6)
Chapter 3 Test
263
(2)
Cumulative Review
265
(2)
Systems of Equations
267
(49)
Solving Systems of Linear Equations by Graphing
268
(10)
Solving Systems of Linear Equations by Substitution
278
(8)
Solving Systems of Linear Equations by Addition
286
(8)
Integrated Review---Summary on Solving Systems of Equations
293
(1)
Systems of Linear Equations and Problem Solving
294
(22)
Chapter 4 Group Activity: Break-Even Point
305
(1)
Chapter 4 Vocabulary Check
306
(1)
Chapter 4 Highlights
306
(3)
Chapter 4 Review
309
(3)
Chapter 4 Test
312
(2)
Cumulative Review
314
(2)
Exponents and Polynomials
316
(76)
Exponents
317
(12)
Negative Exponents and Scientific Notation
329
(9)
Introduction to Polynomials
338
(10)
Adding and Subtracting Polynomials
348
(7)
Multiplying Polynomials
355
(7)
Special Products
362
(9)
Integrated Review---Exponents and Operations on Polynomials
369
(2)
Dividing Polynomials
371
(21)
Chapter 5 Group Activity: Modeling with Polynomials
378
(1)
Chapter 5 Vocabulary Check
379
(1)
Chapter 5 Highlights
379
(3)
Chapter 5 Review
382
(5)
Chapter 5 Test
387
(2)
Cumulative Review
389
(3)
Factoring Polynomials
392
(70)
The Greatest Common Factor
393
(10)
Factoring Trinomials of the Form x2 + bx + c
403
(7)
Factoring Trinomials of the Form ax2 + bx + c
410
(7)
Factoring Trinomials of the Form ax2 + bx + c by Grouping
417
(4)
Factoring by Special Products
421
(10)
Integrated Review---Choosing a Factoring Strategy
429
(2)
Solving Quadratic Equations by Factoring
431
(9)
Quadratic Equations and Problem Solving
440
(22)
Chapter 6 Group Activity
449
(1)
Chapter 6 Vocabulary Check
450
(1)
Chapter 6 Highlights
450
(3)
Chapter 6 Review
453
(4)
Chapter 6 Test
457
(2)
Cumulative Review
459
(3)
Rational Expressions
462
(82)
Simplifying Rational Expressions
463
(10)
Multiplying and Dividing Rational Expressions
473
(9)
Adding and Subtracting Rational Expressions with the Same Denominator and Least Common Denominators
482
(9)
Adding and Subtracting Rational Expressions with Different Denominators
491
(8)
Solving Equations Containing Rational Expressions
499
(9)
Integrated Review---Summary on Rational Exprssions
506
(2)
Proportions and Problem Solving with Rational Equations
508
(15)
Simplifying Complex Fractions
523
(21)
Chapter 7 Group Activity: Fast-Growing Careers
529
(1)
Chapter 7 Vocabulary Check
530
(1)
Chapter 7 Highlights
530
(5)
Chapter 7 Review
535
(4)
Chapter 7 Test
539
(2)
Cumulative Review
541
(3)
Graphs and Functions
544
(61)
Review of Equations of Lines and Writing Parallel and Perpendicular Lines |
As the impact of technology on our society continues to broaden, a foundation in and facility with mathematics will become increasingly necessary. For that reason, the Mathematics Department strongly recommends that each student complete four years of high school mathematics regardless of his or her plans after graduation. Success in mathematics courses depends upon the mastery of skills, understanding of basic concepts, proper placement and
adequate motivation. Homework is an essential element in all mathematics courses. It is expected that all students will spend sufficient time on the homework assignments not only to complete the homework but also to gain the necessary practice, skills and understanding of the material. It is beneficial for students to purchase their own scientific calculator so that they may become familiar with its functions.
Department Announcements
Math Winners- WPI
Mass Academy of Arts and Sciences Teacher Appreciation Day
Grafton teachers were recognized at a ceremony at the Mass Academy of Arts and Sciences. |
The math program at TJ is unique. The decision to come to TJ includes the acceptance of the math program as it has been developed. At all levels it exceeds the basic requirements of similar advanced courses. There is an emphasis on problem solving and the use of technology throughout the program. Data analysis units in the Algebra 2 – Trigonometry program are taught in support of the science program, recursion is taught in support of the Computer Science program, etc.
This year all incoming freshmen will be asked to take a math diagnostic assessment. This assessment will be delivered online and will provide valuable information about your strengths and weaknesses in math. The diagnostic test will not be used to bar you from moving ahead in math, nor will it be used to allow you to accelerate. Instead, we will give you detailed feedback on your readiness for your first TJ mathematics experience, and will give you some opportunities for additional support if you need it. More information about the diagnostic will be available on the registration nights.
Here are some Frequently Asked Questions about the math at TJ:
Which calculator should I have? The Geometry, Advanced Algebra 2 – Trigonometry and Precalculus programs have been developed with the assumption that students will be using the
TI-84 or a similar calculator. Students enrolled in Geometry and Algebra 2 – Trigonometry will be required to take the state-mandated Standards of Learning test in May. These tests do not allow the use of calculators beyond the capability of the TI-84, therefore students may not use more advanced calculators (i.e. TI-89) in classes below Precalculus.
Which courses can I take in summer school? The only approved Summer School math course is Advanced Geometry offered at TJ. No other online courses or other summer school courses meet the requirements of TJ courses. You may also take Trigonometry through the
FCPS Online Campus if you have completed an Algebra 2 Honors course without trig. (see below)
Which class should I take next year? If you are currently in Algebra 1 Honors, you will enroll in Advanced Geometry for the upcoming school year. You may wish to take Summer School Advanced Geometry at TJ. If you are currently in Geometry Honors, you will enroll in Advanced Algebra 2/Trigonometry for the upcoming school year. If you are currently in Algebra 2-Trig Honors, you will enroll in Precalculus Honors. If you are enrolled in any course higher than Algebra 2, please consult with the Math-CS division or a guidance counselor about which math course to sign up for.
My Algebra 2 class didn't include Trig. What should I do? To satisfy the Trig requirement, you have two options: (1) Take the ½ credit Trigonometry course offered through the
FCPS Online Campus this summer, or (2) study the material on your own during the summer and take a placement test on Friday, August 24 proving your mastery (you must earn an 84% in order to prove mastery). If you wish to attempt the placement test, please go to the Math-CS website and download and complete the Trig Placement Form, which must be returned to Mrs. Allard by August 1. You will also find information on the website about the Trig topics that you are responsible for.
Is there anything else I need to do to prepare for higher level math courses? If you are entering TJ in Precalculus Honors or higher, you have not had the opportunity to study data analysis and will need these skills in your science classes. You must complete the Data Analysis Packets A and B. Go to go to the Math-CS website and download the packets. Complete them before September. The packets will not be collected but you are accountable for the information. You may ask your math teacher next year for help if needed.
I want to skip a math class. Do you have placement tests? We strongly encourage you to take Precalculus with us. Many students find adjustment to high school demanding and time-consuming. It is important that you are successful in all of your courses next year, and attempting a college level course during your freshman year can be daunting. With those words of advice in mind, however, the only course that we allow placement out of is Precalculus (which for most students occurs after they have been with us for at least one year). In order to attempt the test you must meet the following criteria:
earned A's in Algebra 1 and Geometry
currently have an A average (94% or above) in your Advanced Algebra 2 – Trigonometry class
demonstrate a strong interest in mathematics (eg., be an involved, active and successful member of your school's math team and/or a successful American Math Competitions participant and/or have participated in an enrichment mathematics program outside of school)
The placement test will be administered on Friday, August 24. A score of 90% must be earned in order to place out of Precalculus and into BC Calculus. You will earn placement, not credit so you are committing yourself to an additional upper level math course. Approximately 30% of those students who attempt the placement test are successful, and the proportion of rising ninth graders is lower. It is extremely difficult to master an entire year of math over the summer. If you wish to attempt this and meet the criteria above, go to the Math-CS website for the PreCalc Placement Form and more information. Request forms are due to Mrs. Allard on or before June 22. You must enroll in Precalculus for next year. Once a student passes the placement test, his/her counselor is notified that a schedule change is required and the student will then be enrolled in BC Calculus. |
Advances on Fractional Inequalities use primarily the Caputo fractional derivative, as the most important in applications, and presents the first fractional differentiation inequalities of Opial type which involves the balanced fractional derivatives. The book continues with right and mixed fractional differentiation Ostrowski inequalities in the univariate
Students can gain a thorough understanding of differential and integral calculus with this powerful study tool. They'll also find the related analytic geometry much easier. The clear review of algebra and geometry in this edition will make calculus easier for students who wish to strengthen their knowledge in these areas. Updated to meet the emphasis... more...
Your INTEGRAL tool for mastering ADVANCED CALCULUS. Interested in going further in calculus but don't where to begin? No problem! With Advanced Calculus Demystified , there's no limit to how much you will learn. Beginning with an overview of functions of multiple variables and their graphs, this book covers the fundamentals, without spending... more...
In its largest aspect, the calculus functions as a celestial measuring tape, able to order the infinite expanse of the universe. Time and space are given names, points, and limits; seemingly intractable problems of motion, growth, and form are reduced to answerable questions. Calculus was humanity's first attempt to represent the world and perhaps... more...
This book is a detailed study of Gottfried Wilhelm Leibniz's creation of calculus from 1673 to the 1680s. We examine and analyze the mathematics in several of his early manuscripts as well as various articles published in the Acta Eruditorum. It studies some of the other lesser known "calculi" Leibniz created such as the Analysis Situs,... more...
Silvestre FranAois Lacroix (Paris, 1765 - ibid., 1843) was a most influential mathematical book author. His most famous work is the three-volume TraitA(c) du calcul diffA(c)rentiel et du calcul intA(c)gral (1797-1800; 2nd ed. 1810-1819) a" an encyclopedic appraisal of 18th-century calculus which remained the standard reference on the subject through... more... |
Dojo Toolkit Graphing Calculator Project Readme
Author: Jason Hays
Trac ID: jason_hays22
Contents:
Expressions
Variables, Functions, and uninitializing variables
toFrac in GraphPro
Numbers and bases
Graphing equations
Substitutes for hard to type characters
Making Functions
Decimal points, commas, and semicolons in different languages
Important mathematical functions
---------------Expressions----------------
The calculator has the ability to simplify a valid expression.
With Augmented Mathematical Syntax, users are allowed to use nonstandard operators in their expressions. Those operators include ^, !, and radical.
^ is used for exponentiation.
It is a binary operator, which means it needs a number on both the left and right side (like multiplication and division)
2^5 is an example of valid use of ^, and represents two to the power of five.
! is used for factorial.
It supports numbers that are not whole numbers through the use of the gamma function. It uses the number on its left side. Both 2! and 2.6! are examples of valid input in America. (2,6! is valid in some nations)
radicals can be used for either square root or various other roots.
to use it as a square root sign, there should only be a number on its right. If you put a number on the left as well, then it will use that number as the root.
To evaluate an expression, type in a valid expression, such as 2*(10+5), into the input box. If you are using GraphPro, then it is the smaller text box.
After you have chosen an expression, press Enter on either your keyboard or on the lower right of the calculator.
If it did not evaluate, make sure you correctly closed your parentheses.
In the Standard calculator, the answer will appear in the input box, in GraphPro, the answer will appear in the larger text box above.
On the keyboard, you can navigate through your previous inputs with the up and down arrow keys.
If you enter an operator when the textbox is empty or highlighted (like *) then Ans* should appear. That means the answer you got before will be multiplied by whatever you input next.
So try Ans*3. Whenever you start the calculator, Ans is set to zero.
--------------Variables, Functions, and uninitializing variables----------------
A variable is basically something that stores a value. If you saw Ans in the previous example, you've also seen a variable.
If you want to store your own number somewhere, you'll need to use the = operator.
Valid variable and function names include cannot start with numbers, do not include spaces, but can start with the alphabet (a-z or A-Z) and can have numbers within the names "var1" is a valid name
Input "myVar = 2" into the textbox and press "Enter." You've just saved a variable. Now if you ever type myVar into an expression, 2 will appear (unless you change it to something else).
Variables are best used to store Ans. Ans is overridden whenever you evaluate an expression, so it is good to store the value of Ans somewhere else before it is overridden.
If you want a variable (like myVar) to become empty, or undefined, you just need to set it equal to undefined.
Now try "myVar = undefined" Now myVar is no longer defined.
Functions are very useful for finding answers and gathering data.
You can use functions by inputting their name and their arguments.
For this example, I'll be using the functions named "sqrt" and "pow"
sqrt is a function with one argument. That argument has a name too, its name is 'x.' x is a very common name amongst built in functions
So, let's run a function. Input "sqrt" then input a left parenthesis (all arguments of a function go within parentheses). Now type a value for x, like 2.
Now close the parentheses with the right parenthesis. If you used 2, you should have "sqrt(2)" in the text box. If you press enter, you should get the square root of 2 back from the calculator.
Now for "pow" it has two arguments 'x' and 'y'
Type in "pow(" and pick a value for 'x' (I am picking 2 again)
but now, you need to separate the value you gave x with a list separator. Depending on your location, it is either a comma or a semicolon. I'm in America, and I use commas.
by this point, I have "pow(2,"
Now we need a value for 'y' (I'm using 3). Put a ')' and now I have 'pow(2,3)'
Press Enter, and, following my example, you should get 8
In this calculator, there are several ways to input arguments.
You've already seen the first way, just input numbers in a specific order based on the names.
The second way is with an arbitrary order, and storage.
With 'pow' I can input "pow(y=3, x=2)" and get the exact answer as before. x and y will retain their assigned values, so you will need to set them to undefined it you want to try the next way.
The third way is to let the calculator ask you for the values. Input "pow()" If the values have been assigned globally, then it will use those values, but otherwise, it will ask for values of x and y. They will not be stored globally this way.
I'll go ahead and mention that because of the way the calculator parses, underscores should not be used to name a variable like _#_ (where # is an integer of any length)
---------------toFrac()----------------
toFrac is a function that takes one parameter, x, and converts it to a fraction for you. It is only in GraphPro, not the Standard mode.
It will try to simplify pi, square roots, and rational numbers where the denominator is less than a set bound (100 right now).
Immediately after the calculator starts, toFrac may seen slow, but it just needs to finish loading when the calculator starts. After that, it will respond without delay.
For an example, input "toFrac(.5)" or (,5 for some). It will return "1/2"
For a more complicated example, input "toFrac(atan(1))" to get back "pi/4" (atan is also known as "arc tangent" or "inverse tangent")
--------------Numbers and bases----------------
This calculator supports multiple bases, and not only that, but non integer versions of multiple bases.
What is a base? Well, the numbers you know and love are base 10. That means that you count to all of the numbers up until 10 before you move on to add to the tenths place.
So, what about base 2? All of the numbers up until 2 are 0 and 1. If you want to type a base 2 number into the calculator, simply input "0b" (meaning base 2) followed by some number of 1's and 0's. 0b101 is 5 in base 10
Hexadecimal is 0x, and octal is 0o, but i won't go into too much detail on those here.
If you want an arbitrary integer base, type the number in the correct base, insert '#' and put the radix on the end. ".1#3" is the same as 1/3 in base 10
Because there is not yet cause for it, you cannot have a base that is not a whole number.
--------------Graphing Equations----------------
First thing is first, in GraphPro only, the "Graph" button in the top left corner opens the Graph Window
So, now you should see a single text box adjacent to "y="
Type the right side of the equation using 'x' as the independent variable.
"sin(x)" for example. To Graph it, make sure the checkbox to the left of the equation is selected, and press the Draw Selected button.
You can change the color in the color tab. By default, it is black. Under window options, you can change the window size and x/y boundaries
Let's add a second function. Go to the Add Function button, select the mode you want, and press Create. Another input box will appear.
If you selected x= as the Mode, then y is the independent variable for the line (an example is "x=sin(y)").
If you want to erase, check the checkboxes you want to erase, and press "Erase Selected"
And similarly, Delete Selected will delete the chosen functions
"Close" will terminate the Graph Window completely
---------------Substitutes for hard to type characters---------------
Some characters are not simple to add in for keyboard users, so there are substitutes that are much easier to add into the text box.
pi or PI can be used in place of the special character for it.
For epsilon, eps or E can be used.
radical has replacement functions. sqrt(x) or pow(x,y) can be used instead.
--------------Making Functions-----------------
My favorite part. Before we start, I'll mention that Augmented Mathematical Syntax is allowed in the Function Generator (yay).
Ok, now the bad news: to prevent some security issues, keywords new and delete are forbidden.
Sorry, it is a math calculator, not a game container; not that that would be so bad, but it is to keep it from being used for some evil purposes.
Ok, onto function making. Most JavaScript arithmetic is supported here, but, some syntax was overlapping mathematical syntax, so ++Variable no longer increases the contents of Variable because of ++1, but Variable++ does increase it (same deal with --)
Strings have incredibly limited support. Objects have near zero support
So, let's make a Function:
Press the "Func" button. A Function Window should pop up.
Enter a name into the "functionName" box. (it must follow the name guidelines in the variables section) I'm putting myFunc
Enter the variables you want into the arguments box (I'll put "x,y" so I have two arguments x and y)
Now enter the giant text box.
Type "return " and then the expression you want to give to the calculator. I'm putting "return x*2 + y/2"
Then press Save. Now your function should appear in the functionName list and you can call it in the Calculator.
If you want to Delete a function you made, select it in the function Name list, and then press Delete.
If you altered a previously saved function (and haven't saved over the old one) you can reset the text back to its original state with the Reset button.
Clear will empty out all of the text boxes in the Function Window
Close terminates the Function Window
---------------Decimal points, commas, and semicolons in different languages----------------
In America, 3.5 is three and one half. Comma is used to separate function parameters and list members.
In some nations, 3,5 is three and one half. In lists, ;'s are used to separate its members.
So, when you evaluate expressions, 3,5 will be valid, but in the function generator, some ambiguous texts prevent me from allowing the conversion of that format to JavaScript. So I cannot parse it in the Function Generator.
And here is my example:
var i = 3,5;
b = 2;
I cannot discern whether the semicolon between i and b are list separators or the JavaScript character for end the line. b could be intended as a global variable, and i is a local variable, but I don't know that. So language conversion isn't supported in Function Making.
--------------Important mathematical Functions---------------
Here is a list of functions you may find useful and their variable arguments:
sqrt(x) returns the square root of x
x is in radians for all trig functions
sin(x) returns the sine of x
asin(x) returns the arc sine of x
cos(x) returns the cosine of x
acos(x) returns the arc cosine of x
tan(x) returns the tangent of x
atan(x) returns the arc tangent of x
atan2(y, x) returns the arc tangent of y and x
Round(x) returns the rounded integer form of x
Int(x) Cuts off the decimal digits of x
Ceil(x) If x has decimal digits, get the next highest integer
ln(x) return the natural log of x
log(x) return log base 10 of x
pow(x, y) return x to the power of y
permutations(n, r) get the permutations for n choose r
P(n, r) see permutations
combinations(n, r) get the combinations for n choose r
C(n, r) see combinations
toRadix(number, baseOut) convert a number to a different base (baseOut)
toBin(number) convert number to a binary number
toOct(number) convert number to an octal number
toHex(number) convert number to a hexadecimal number |
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05/14/09EP 471 Homework #7: Parabolic PDEs Due: Thursday, May 8th, 2008Each problem is equally weighted; I'd suggest using Matlab's pdepe utility for both problems. (1) At the end of Exercise 19, I mentioned some modifications to the transient sl
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Direction to the Air National Guard Base: 1) 2) 3) 4) We are starting at 1513 University Ave. We are going to 3110 Mitchell St. Use Mapquest or other to get directions We will leave here (meet on the south side of ME in cars, ready to go) at 9:45 AM |
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Here's a real-world instructional activity using a business simulation. Two business accounts are used to find slope and intercept functions. The class graphs and interprets the information to find a break even point. There are plenty of worksheets and assessments included in this instructional activity.
High schoolers graph exponential equations and solve application problems using exponential functions. They re-enact a story about a peasant worker whose payment for services is rice grains doubled on a checker board. They place M & Ms on a checkerboard and mark the number on a graph. They double the number for each space on the board and create a graph of the data.
Young scholars analyze graphs and determine their general shape. In this calculus lesson, students solve functions by taking the derivative, sketch tangent lines and estimate the slope of the line using the derivative. They graph and analyze their answersAre you working on the distance formula? Derive the distance formula and help your learners by showing them the logic behind the distance formula. This practical video should help conceptual understanding and is appropriate for in-class or at-home use.
Play ball! High schoolers explore the concept of quadratic equations through modeling how shooting a basketball can be expressed as a quadratic function. They impose a coordinate grid on the path of a shooting basketball and determine points to model the data. Additionally, they enter data into lists and perform a quadratic regression on the data.
Twelfth graders investigate the derivative of a function. For this calculus lesson, 12th graders explore the derivatives of sine, cosine, natural log, and natural exponential functions. The lesson promotes the idea of the derivative as a function and uses numerical and graphical investigations to form conjectures about common derivative formulas.
Examine the concept of functions using real-world data. Phone bills, postage rates, and airline schedules are analyzed by plotting data and drawing lines that fit the data. Predictions are made that extrapolate or interpolate the data. |
THE NEMETH CODE TUTORIAL FOR THE BRAILLE LITE
The Problem
For individuals who cannot read print symbols, the study of
mathematics poses an extreme challenge. In order for a person who
reads braille to succeed in the study of mathematics, a necessary
condition is mastery of the Nemeth Code, a complex braille code
used to display braille equivalents of print math symbols found
in all fields of mathematics. Unfortunately, many teachers of
students with visual disabilities are ill prepared to provide
effective instruction in this braille code. Therefore, legions of
academically able blind students cannot read or write the Nemeth
Code, and are forced to listen to the contents of math
instructional materials and attempt to carry out mathematical
operations mentally. It is virtually impossible to achieve
mathematical literacy through this ill-advised approach.
The inability to master the concepts underpinning the study of
mathematics is a decades-long stumbling block which will
constrain the individual in many aspects of life, limiting
educational and vocational choices, as well as potential earning
capacity. To rectify this untenable situation, the staff of
Research and Development Institute is engaged in the development
of a tutorial which will provide an effective, independent method
for blind students to study the Nemeth Code. This groundbreaking
effort, never before attempted by any other group, holds the
promise of providing a solution to the intractable problem of
mathematical illiteracy among blind students.
The Braille Lite
The interactive Nemeth Code Tutorial has been designed to be
used with the Braille Lite, a hand-held computer specifically
designed for use by blind persons which combines synthetic speech
and a 20 or 40 cell electronic refreshable braille display. The
device is small and lightweight, and operates on standard
household current or a rechargeable nickel-cadmium battery which
provides thirty hours of operation between charges. The braille
display is designed to show braille symbols in a series of cells.
Each cell is composed of eight tiny pins, housed in small holes,
which "pop up" when stimulated electronically. As the Braille
Lite sends signals to each cell, the appropriate pins move up
slightly out of their holes, tactually perceivable by the braille
reader. To move to the next set of braille symbols after reading
a line of braille cells, a key is pressed and the next set of
braille symbols appears instantaneously. Following this
procedure, the reader can move forward and backward through a
file. The Braille Lite also has speech capability, enabling the
user to simultaneously listen to information and read braille.
This marriage of synthetic speech and refreshable braille is the
most expeditious combination for a tactile reader to learn the
code of braille mathematics.
The Tutorial
Special delimiters have been programmed into the software to
cause the Braille Lite to speak Nemeth Code correctly,
distinguishing mathematical notation from the code used in
literary braille. This is the capability of the software which
makes it extraordinarily valuable to the learner. No other device
exists that speaks braille mathematics correctly, enabling the
learner to compare spoken Nemeth Code symbols to their display on
the electronic braille array. This makes learning to read and
write the symbols remarkably efficient.
The tutorial content is divided into lessons which include
basic concepts initially, and progressively more sophisticated
notation in successive lessons. The scope of the notation
includes that which is found in all mathematics courses up to and
including calculus. Lesson material can be heard by the learner
as well as read on the braille display. Each lesson contains
explanatory material describing the rules governing various
topics within the Nemeth Code and examples of Nemeth Code
expressions. Following the explanatory section of each lesson,
three sets of interactive exercises are presented to the learner,
providing immediate feedback; this is a major strength of this
tutorial. In the first exercise set, the learner is presented
with spoken mathematics notation which is to be brailled. After
the "judge" command is invoked, the Braille Lite announces the
number of errors, and marks the first error by raising two pins
below it on the braille display. The learner is then given
limitless opportunities to correct those errors. There is also a
command which can be used to toggle between the incorrect and the
correct answer, providing the opportunity for direct
comparison.
The second set of exercises emphasizes reading of Nemeth Code
symbols. The learner is instructed to read braille shown on the
display. The "judge" command causes the Braille Lite to speak the
displayed symbols, either one symbol at a time or one line at a
time, enabling the learner to compare the correct spoken
equivalent to his or her answer.
Proofreading exercises are presented in the third set, where
correct spoken symbols are supplied along with a display of
braille symbols which contain errors. The learner is instructed
to find and correct the errors. The 'judge" command can be
invoked to indicate errors. A "show answer" function enables the
learner to toggle the braille display between the correct answer
and the answer which contains errors. |
Our middle school math program has 3 levels: honors, average, and 6th grade math. All students study pre-algebra topics in 6th grade. This includes exemplars, geometry topics and ISAT test preparation.
In 7th grade, a majority of students (all honors and regular levels) begin algebra 1. Half of the algebra curriculum is taught in 7th grade and the remaining algebra 1 curriculum is taught in 8th grade. These students then enter into geometry classes as freshmen in high school.
The 7th grade (honors and pre algebra) Algebra 1 curriculum includes: properties of real numbers, solving linear equations and inequalities, and graphing in the x-y coordinate plane, some geometry, as well as ISAT test preparation and an introduction to the use of the graphing calculator.
Students that do not take algebra in 7th grade continue with a general middle school math program in 7th and 8th grades. Their curriculum includes the study of fractions, decimals, signed numbers, percents, and selected geometry topics and ISAT test preparation. |
Topology is a major branch of modern mathematics. Topology is often described as rubber sheet geometry. In geometry objects are considered rigid with fixed distances and angles, but in topology distances and angles can be deformed. In topology objects are treated as if they are made out of rubber, capable of being deformed.
Objects are allowed to be bent, stretched or shrunk but not allowed to be ripped apart or cut.
For example, in topology a coffee mug and a doughnut are the same! This kind of equivalence is cleverly illustrated by the following animated gif written by Lucas V. Barbosa.
In this course we will develop the mathematical framework to understand some of these ideas.
The authors of our textbook write:
Topology
is generally considered to be one of the three linchpins of modern
abstract mathematics (along with analysis and algebra). In the early
history of topology, results were primarily motivated by investigations
of real-world problems. Then, after the formal foundation for topology
was established in the first part of the twentieth century, the
emphasis turned to its abstract development. However, within the past
few decades there has been a significant increase in the applications
of topology to fields as diverse as economics, engineering, chemistry,
medicine, and cosmology.
When
your instructor was a student (in the middle of the last century)
topologists never talked about applications – it is exciting to see the
range of applications that have been found for this abstract subject.
Because we have limited class time, our emphasis will be an
introduction to the theory of point-set topology (text chapters 0-7).
Students may wish to pursue some of these applications for individual
projects.
Course Objectives
Most of the work you will need to do in this class will require reading the textbook and solving homework exercises (these will focus on creating and explaining mathematical arguments). I
expect you to work collaboratively with other students and I hope you
will talk to me about any exercises you are unsure about (either face
to face or via email). I will try to give sufficient lead time to make
this possible. Although I encourage you to work with others, I want
you to write up your solutions individually.
In
addition to reading your homework exercises and talking with you in
class, I'd like you to take a few minutes each weekend to send me a
brief update on how things are going (an email journal).
I won't grade these critically but I hope they will give me some
guidance on how things are progressing and I will record that you have
sent them.
After we've worked through some preliminary definitions, I'd like you to think about possible topics for an individual project.
There are many topics in the textbook that I will not have time to
discuss in class and you might want to choose one of these. (We'll
start putting together a list of topics and scheduling presentations
after the first six weeks.) An individual project should include a
15-20 minute presentation to the class and a short writeup (3-5 pages).
Both the midterm and the final exam will include take-home as well as in-class questions. |
amount of math in materials science/engineering?
amount of math in materials science/engineering?
Hi, I was just looking over the "course calendar" for a materials science/engineering program at the University of Toronto ( I find it strange that there is only ONE required math course throughout all 4 years. I know that there is some physics involved with materials science, so how much math is generally "required" in this field? will there be algebra? the expectations only seem to be a course in calculus, but I'm pretty sure that I'll need more than that. thanksthanks. to clarify, by algebra, I meant linear algebra.. et c. I don't know "college algebra" is supposed to be but linear algebra is usually taken after or concurrently with calculus
amount of math in materials science/engineering?
Hello,
I am a materials science/engineering major (along with a double major in physics) at a major research university in the US. For MSE I had to take calc I, calc II, calc III (sometimes called multivariable), diff. eq., linear algebra and a stat class.
You need differential equations for things like solid state diffusion (you need it for all of physics really); you need calc III for stuff like thermo and magnetic properties; you need lin. alg. for analyzing crystal lattices as well as quantum mechanics which materials scientists DO NEED TO BE PROFICIENT WITH. And you need the others in order to learn the above subjects, they're the base.
I would encourage you to take as much math as possible; I would also encourage you to double major or minor in physics or chem. Every time I tell a mat sci prof my major, they say something to the effect of "I wish I had done something like that." Materials science is getting evermore fundamental. And physics or chemistry will give you an advantage.
thanks, it was precisely the information I was looking for. I'm taking spivak-style calculus courses and a more theoretical linear algebra course right now. I really like it, but is it necessary? should I look at the more computational side of math rather than the proof/theoretical side of math? I've heard some people say "if you need calculus for physics, spivak isn't your book" - I'm thinking if this applies. |
Preface
Preface
This is an introductory textbook on optimization—that is, on mathematical programming—intended for undergraduates and graduate students in management or engineering. The principal coverage includes linear programming, nonlinear programming, integer programming, and heuristic programming; and the emphasis is on model building using Excel and Solver.
The emphasis on model building (rather than algorithms) is one of the features that makes this book distinctive. Most textbooks devote more space to algorithmic details than to formulation principles. These days, however, it is not necessary to know a great deal about algorithms in order to apply optimization tools, especially when relying on the spreadsheet as a solution platform.
The emphasis on spreadsheets is another feature that makes this book distinctive. Few textbooks devoted to optimization pay much attention to spreadsheet implementation of optimization principles, and most books that emphasize model building ignore spreadsheets entirely. Thus, someone looking for a spreadsheet-based treatment would otherwise have to use a textbook that was designed for some other purpose, like a survey of management science topics, rather than one devoted to optimization. |
This training is the first of a two-part program. The course will help anyone within the extrusion industry looking to expand or fine-tune his or her math skills.
Topics start with the basics of using whole Numbers, negative numbers, and decimals; then continues on to refining the use of a calculator. Addition, subtraction, multiplication and division are reviewed before learning the benefits of rounding numbers and using significant figures. Finally, formulas, equations, and order of operations is definedIntroduction
Whole Numbers and Negative Numbers
Decimals
Using a Calculator
Addition
Subtraction
Multiplication
Division
Rounding Numbers
Significant Figures
Formulas, Equations & the Order of Operations
Conclusion
Intended Learning Outcomes
Upon successful completion of this course you will be better prepared to:
Identify whole numbers.
Define how decimals are represented and used worldwide.
Associate the buttons of calculators with their respective functions.
Perform addition.
Perform subtraction.
Perform multiplication.
Perform division.
Choose procedures for rounding numbers to appropriate place value.
Identify the number of digits within a calculation that have certainty |
Find a Glendale, CA ScienceIt also makes a world of difference in how you approach everyday problems from managing money to measuring ingredients in the kitchen. Algebra 2 builds on the topics explored in Algebra 1. These topics include: real and imaginary numbers, inequalities, exponents, polynomials, equations, graphs, linear equations, functions and more. |
All the key areas of the SAT of Mathematics are covered in this iTooch SAT Math app including Numbers and Operations, Algebra, Geometry and Statistics. Short and helpful chapter summaries review key facts and over 1,400 example problems give students plenty of practice so that the methodology of working through problems is clear. Thanks to this app, future exposure to complex SAT math structures should seem less daunting.
This app allows you to cover a spectrum of problems; you can make sure you've got the basics covered and stretch yourself with some of the more difficult questions. Real-world problems are used in many cases, so that the importance of learning these skills is clear. It can be used to help students prepare for the SAT and/or review high-school level math concepts in general in a fun and interactive way.
Apps automatically sync in the background in order to load new activities whenever an Internet connection is available.
Meet the SAT Math Team:
Hannah Kirk
SAT Math author, Hannah Kirk, is a British mathematics graduate with a professional background in research. She holds a BSc Economics and Mathematics from the University of the West of England and an MSc Econometrics from the University of Manchester. Her research interests revolve around international development issues. Hannah has experience as a private tutor of mathematics for pupils undertaking the equivalent high school graduation exam in England.
Eileen Heyes
SAT Math editor, Eileen Heyes has a BA in journalism from California State University, Long Beach. She wrote and edited at newspapers for 30 years while trying to decide what she wanted to be when she grew up. She is the author of three nonfiction books for teens and two mysteries for children. In learning the storytelling craft, she has studied screenwriting and improv, earned a certificate in Documentary Arts, and volunteered in the street cast of a Renaissance Faire. She takes it all back into the classroom as a writer-in-residence with the United Arts Council of Wake County, North Carolina. Originally from Los Angeles, she now lives in Raleigh with her brilliant husband and one of her two interesting, articulate sons. |
MATERIALS NEEDED FOR CLASS 1. Notebook. (3 ring binder with paper)
2. Pencil for quizzes/tests. (pen may be used for notes/worksheets)
3. Textbook with book cover.
4. Graphing calculator. (TI-83+ or TI-84+ recommended)
GRADING SCALE 95-100 A 93-94 A-
91-92 B+
87-90 B
85-86 B-
83-84 C+
79-82 C
77-78 C-
75-76 D+
72-74 D
70-71 D-
0-69 F ATTENDANCE Absences: If you are absent, please get assignments by one of the following methods:
1. asking me when you return to school.
2. calling a reliable friend from class.
3. checking the Milwaukee Lutheran website
If you are absent for a long period of time, please contact the school so that assignments can be sent home. You are required to make up the missing work. When you get back, you need to make arrangements with me to get the work completed. If an absence is due to a field trip, vacation or other school activities, you must get assignments ahead of time and make arrangements for missing quizzes or tests ahead of time. Tardies: You must be completely in the classroom by the end of the tone. Please get seated immediately.
HOW TO BE SUCCESSFUL 1. Take notes (in a notebook) during class. Copy sample problems from the board and try them as we go through them in class. Do the assignments in your notebook. If you have trouble with the assignment problems, come in and get extra help. All worksheets must be completed! Everyone must complete a notebook for the first two chapters and submit these at the end of the chapter. 2. Use all given class time to begin your practice problems. 3. Take announced quizzes. 4. Take Chapter Tests.
a. Chapter tests are cumulative. The last cumulative chapter test of the semester will be the final exam.
5. Complete all projects.
a. Projects will be given to show application to real life situations. These projects are intended to extend your learning and to allow you to utilize skills beyond mathematics.
b. Projects may be turned in early for a preliminary check(s) and then corrected.
c. Additional information will be given prior to beginning a project.
NOTE: All students will be required to complete and submit a notebook for the first two chapters. After that, any student whose average falls below a C- (77%) will be required to complete and submit all homework/notes in an organized notebook.
ON-LINE GRADES To access grades go to the Milwaukee Lutheran website. Daily work will be posted within 2-3 days. Quizzes/Tests will be posted within 1 week.
MISCELLANEOUS Cheating Policy: You will receive a zero along with the person who gave you the answers or work and will be referred through the disciplinary cycle.
Extra Help:Hours 3 and 8 (with a pass from me)
before school (7:35-7:50 Mondays; 7:20-7:50 Tuesdays, Wednesdays, Fridays)
before school (7:30-8:30 on Student Help Thursdays)
after school (3:06-3:35 ) (except when coaching)
Passes:Given for emergencies only! (must have planner and school ID)
Classroom R's:Responsibility and Respect
You are responsible for your education. Others, like myself, are here to guide and help you. Please respect the right of others wanting to learn. |
Pre-Algebra is the link between basic math and Algebra. We will be studying positive and negative integers, and learning how to solve equations for unknown variables. Get ready and buckle up... it's going to be one heck of a ride! |
Description
A Concise Introduction to Matlab is a simple, concise book designed to cover all the major capabilities of MATLAB that are useful for beginning students. Thorough coverage of Function handles, Anonymous functions, and Subfunctions. In addition, key applications including plotting, programming, statistics and model building are also all covered.
MATLAB is presently a globally available standard computational tool for engineers and scientists. The terminology, syntax, and the use of the programming language are well defined and the organization of the material makes it easy to locate information and navigate through the textbook Concise Introduction to Matlab |
Metadata
Name:
Solving Linear Equations and Inequalities: Further Techniques in Equation Solving
ID:
m21992
Language:
English
(en)
Summary:
This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr.
In this chapter, the emphasis is on the mechanics of equation solving, which clearly explains how to isolate a variable. The goal is to help the student feel more comfortable with solving applied problems. Ample opportunity is provided for the student to practice translating words to symbols, which is an important part of the "Five-Step Method" of solving applied problems (discussed in modules ((Reference)) and ((Reference))).
Objectives of this module: be comfortable with combining techniques in equation solving, be able to recognize identities and contradictions. |
• Understands culture as an evolving set of world views with diverse historical roots that provides a framework for guiding, expressing, and interpreting human behavior.
• Demonstrates knowledge of the signs and symbols of another culture.
• Participates in activity that broadens the student's customary way of thinking.
5. Aesthetic Skills:
• Develops an aesthetic sensitivity
Mathematics Program Course-level Outcomes:
As part of the assessment process, I also list here the specific student outcomes desired for math majors in this course. Even though we want to use this list to help us assess the success of the mathematics program, to judge how well we are doing what we think we are doing, these outcomes are also important for those of you who are not math majors.
Content
¨ Students will understand the concepts three-dimensional space, vectors, multivariable functions and their derivatives, multiple integration and their applications.
Reasoning
¨ Students will be able to reason deductively to prove the truth or falsity of a conjecture (Outcome 2.2)
Problem Solving
¨ Students will apply calculus techniques to novel or non-routine problems (Outcome 3.1)
¨ Students will demonstrate the ability to solve a problem in multiple ways (Outcome 3.2)
Technology
¨ Students will use a calculator for basic computation and for graphing functions with an appropriate viewing window and scale (Outcome 4.1)
¨ Students will demonstrate an understanding of the limitations of a calculator (Outcome 4.2)
¨ Students will use DERIVE (CAS software) to solve problems (Outcome 4.3)
Communication
¨ Students will use mathematical notation and language to accurately and appropriately write solutions to problems (Outcome 5.1)
Additional comments:
From a most general perspective, the student should see growth in his/her mathematical maturity. The three-semester sequence of calculus courses form the foundation of any serious study of mathematics or other mathematically-oriented disciplines and this course is the capstone of that sequence.
Course Content Outline:
The student will study three-dimensional space and vectors, lines, planes and general surfaces.
The student will study derivatives and partial derivatives of functions in 3D space.
The student will study the concept and process of multiple integration, and explore a variety of applications of such processes.
COURSE PHILOSOPHY AND PROCEDURES:
I am a firm believer in the notion that you as the student must be actively engaged in the learning process and that this is best accomplished by your DOING mathematics. My job here is not to somehow convince you that I know how to do the mathematics included in the course, but to help guide YOU through the material; I am to be a "guide on the side, NOT a sage on the stage". I may not always say things in the way which best leads to your full comprehension, but I will try to do so and I ask that you try to see your learning as something YOU DO rather than as something I do TO you. PLEASE feel free to come see me to discuss questions or concerns you may have during the course; I will not bite! PLEASE ask questions in class if you have them; the only dumb question is the one you fail to ask!
Let me therefore urge you to make it a regular part of your day to try working the HOMEWORK problems. There will never be enough time for us to go through every listed problem in class, and it is unrealistic to think that you will be able to find the time to work through every listed problem, but you should at least spend some time thinking about virtually every problem, and working the more interesting or challenging to completion. The daily HomeworkIn general, I think students can benefit greatly by WORKING TOGETHER on problems. While there is some danger of the "blind leading the blind" syndrome, or of students deceiving themselves into thinking they understand the material better than they actually do, for the most part grappling with ideas and trying to explain them to another student or learning to listen to others explain an idea is a wonderful way to see that you really do understand the material. In class we will spend an occasional day working on a group "lab", and we sill also typically have a group "practice exam" before the individual exams, and I also encourage you to find a "learning group" outside of class.
I will be asking you to assemble a PORTFOLIO. The portfolio will be collected at the end of the semester, on Friday 10 December. This "portfolio" should be a representative collection of your work during the semester, and should include 5 problems, written up in a finished form, along with a brief discussion of why you chose to include that particular problem. These problems should represent work you are proud of, or problems that brought you to a breakthrough point. This portfolio of your work will be worth 40 points, 8 points per problem. Presumably you will hand in 5 sheets of paper, each of which will include a nicely organized solution to the problem, which might be from homework, or from a lab or worksheet, of from an exam, along with that reflection mentioned above.
I use a rather traditional GRADING SCALE: A = 90% (or better), AB = 87%, B = 80%, BC = 77%, C = 70%, CD = 67%, D = 60%. I do try to come up with a mix of points so that exams are not weighted too heavily; about half the points during the semester will come from individual, in-class exams - the rest will come from group labs, take-home problems, group practice exams, and portfolios.
It is rarely much of a problem at the level of a calculus course, but it remains important that students turn in work in a timely manner, so that they do not get behind. Consequently, LATE ASSIGNMENTS will be penalized 20% of the possible points for each class period late, up to a maximum of three periods.
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Product Description:
strass, Zermelo, Bernstein, Dedekind, and other mathematicians. It analyzes concepts and principles, offering numerous examples. An emphasis on fundamentals makes the presentation easily comprehensible to students acquainted with college-level algebra. Starting with the rudiments of set theory--including first classifications, subsets, sums, intersection of sets, and nonenumerable sets--the text advances to arbitrary sets and their cardinal numbers, exploring extensions of number concepts, equivalence of sets, and sums and products of two and many cardinal numbers. Additional topics include ordered sets and their order types and well-ordered sets and their ordinal numbers. Particular focus is placed upon addition and multiplication of ordinal numbers, transfinite induction, products and powers of ordinal numbers, well-ordering theorem, and the well-ordering of cardinal and ordinal |
maple1
Course: MATH 291, Fall 2009 School: Rutgers Rating:
Word Count: 1154
Document Preview ask you to hit the "enter" key (new line) with the request RET. Now, please, log in to eden and get a prompt in an x-window. Then type xmaple & RET The system should respond with a Maple screen on your display. There are standard ways for you to move or resize the screen, and various Maple-specific command possibilities. Maple is a huge program with a great many capabilities. We'll just explore a few of them. Right now I'd like you to move your mouse into the Maple window. You should see this, which is the command line: >| The symbol for your cursor is | and it is currently at an input line, indicated by the > sign. Please type 3+2 RET Maple did nothing with your input you only get another input line, and a complaint message from Maple! Move your cursor back (with the arrow keys or the mouse) to the first input line, and then move the cursor to the the end of the line. The input line should look like > 3 + 2| Then continue your typing with a semicolon followed by a return: ; RET Something should happen. You should get 5 and a new input line. You can move your cursor up and down. Now move your cursor back to your new input line. Type 17*3; RET and see what the result is. At the next input line type %+5; RET and explain the result. What do you think the meaning of the symbol % is? Now type the following to learn what ^ means. 2^3; RET But . . . I made a mistake! I wanted you to calculate the 300th power of 2. Please do the following: move your cursor back to the input line with 2^3 and position it in the following place: > 2^3|; and now type 00 and immediately hit RET. What happened? Please compute 3300 in the same fashion by moving your cursor and changing the input line. (Hint: position your cursor after the 2, type backspace, and then type 3.) What are the first 5 and last 5 decimal digits of this number? A little more: please type (look carefully here I'm asking for a colon, not a semicolon!) 5+6: RET You should immediately get another input line. Type (for example) %+7; and deduce what Maple does when an input line ends with a : (that is, a colon). Note that computations might and do occur which have results that are huge and silly to print out if you don't need them -- 2^(2^(2^(2^2))), for example. Try that sometime on your own, please, with ";" rather than a ":" and see what happens (hah!). Onward: please type 20; RET and see the result. Go back with your cursor and put a space between the 2 and the 0 and hit RET. What's the result? Now let's try 2*3+7; RET and observe that Maple follows the usual rules of precedence. Can you put parentheses in so that Maple will compute two times the sum of three plus seven instead? Remember to hit RET after you make the alterations. You should have gotten 20 as your answer, of course. If you did not make an error inserting the parentheses, go back and take one out (create an intentional error!) and then hit RET. What happens? haven't You broken anything. Let's keep exploring. Please get a new input line and try these commands in succession to learn how to do more arithmetic and to explore more features of Maple. OVER
... you can't break the program, so explore!
... you can't break the program, so explore!
... you can't break the program, so explore!
... you can't break the program, so explore!
2/3; RET Maple computes "exactly" and can do some (fourth grade?) arithmetic: %*300; RET Now try sqrt(2); RET and now %^2; RET so Maple knows the "meaning" of fractions and square roots or at least how to manipulate them. And now try (remember, if you mess up with a parenthesis or something else, just go back and do it again nothing is broken!): (sqrt(2)-1)^5; RET This result is puzzling. Sometimes Maple is lazy. Let's urge it to work by writing expand(%); RET That's better. But what if we want or need decimal approximations? Try evalf(sqrt(2)); RET Parentheses need to be matched always a source of anxiety as more and more complex expressions and commands are typed. What if we want more digits of 2? We can coax evalf to do this with more informed use. To see how, type help(evalf); RET Another screen should pop up. When I use Maple I tend to need a lot of help so the help screens accumulate on my display. You can "click" them on and off, and eliminate them entirely (click on the upper left or right corners of the screen to see how). Read the evalf screen until you can figure out how to get the first 100 digits (after the decimal point) of 2. I usually skip down to the examples on any help screen first, because they are usually relevant to my questions! What is the one-hundredth digit after the decimal point? Can you tell me the three-hundredth digit after the decimal point of 171/3 ? Use lots of parentheses, even in exponents, to inform Maple clearly what you want. Now try 1400/24; RET and we learn that Maple knows how to factor integers automatically. Can you get Maple to factor your social security number? How would you find a factoring command in Maple? If the first thing you try with the help command doesn't work, look at the references on the SEE ALSO line and check one of them. We can go on to try some algebra. But notice that you can stop your Maple session at any time in a variety of ways. One way that is polite to the system and also simple for you is to type quit RET and your Maple window will disappear, and you can exit the program by clicking on the File button. Of course all of your work will also have vanished, but at some other time you can explore various possibilities of saving what you've done.
Disclaimer! Non-advertisement!! Important information!!! Symbolic manipulation programs such as Maple are increasingly available. Mathematica and Derive are other programs with the same capability. There are many special purpose programs in science, engineering, and mathematics which have extensive "intelligence" to analyze models. We're considering Maple here because Rutgers has a site license for this program. It is generally available on Rutgers systems. The specific instructions won't be the same from program to program, but many of the same ideas will be present. Students should expect to have a machine do tiresome or elaborate symbolic computations as well as numerical comput you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!640:291:01Part II: playing with algebra on Maple9/15/2002Maple's mos
. you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!640:291:01Part III: playing with calculus on Maple9/15/2002The basic
. you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!640:291:01Part IV: playing with graphs on Maple9/15/2002The graphing
DisclaimerThis site makes available conceptual plans that can be helpful in developing building layouts and selecting equipment for various agricultural applications. These plans do not necessarily represent the most current technology or constructi
UNDER
FACTS AND FIGURES 2000 - 2001Office of Institutional Research and PlanningMichael F. Middaugh, Assistant Vice President for Institutional Research and Planning Dale W. Trusheim, Associate Director of Institutional Research and Planning Karen W. Bau
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Introduction to RDownloadingFor your home/office computer, you can get binaries (ready-to-run) for R by going to http:/ clicking on CRAN and picking one of "mirror" websites to download from, click on Windows, base, R-2.2.1-win32.
Latin square design The Latin square design is for a situation in which there are two extraneous sources of variation. If the rows and columns of a square are thought of as levels of the the two extraneous variables, then in a Latin square each treat
Using SPSS to Perform a Chi-Square Goodness-of-fit Test The data set consists of two variables: one indicates the categories, and the other the counts for each category. First step: Select Data Weight Cases. A box pops up with a list of the input var
reak the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, soNew users may read this side before starting. Please don't read the other side until later. It m
reak the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so640:192:01Part I: playing with arithmetic on maple9/1/2005What you should type will be in
reak the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so640:192:01Part II: playing with algebra on maple9/1/2005The most attractive feature of map
reak the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so640:192:01Part III: playing with calculus on maple9/1/2005The basic calculus commands do d
reak the program, so explore!. you can't break the program, so explore!. you can't break the program, so explore!. you can't break the program, so640:192:01Part IV: playing with graphs on maple9/1/2005The graphing capabilities of maple
This version prepared 6/30/200356 Lecture 14 / : IntermezzoBIRTHDAY TIME!Suppose you have a crowd of people. When will two of them share a birthday?* Probabilistic answer This question is studied in almost every elementary probability text.
This version prepared 6/30/200338Lecture 9: Probably .9.1 Vocabulary A real-world experiment has various outcomes. The collection of all possible outcomes is called the sample space. This vocabulary discussion will be accompanied by two simple e
September 15, 2003ALIENS!Due Thursday, September 18 Background assumptions We imagine an alien language which has only three words: 40% of the words are 1111111. Abbreviate this word with A. It is seven bits long. 30% of the words are 00000. Abb |
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for space; classification of the elementary configurations of space according to their behavior under transformation of rectangular coordinates; and derivative manifolds. The second section, on geometric transformations, examines affine and projective transformations; higher point transformations; transformations with change of space element; and the theory of the imaginary. The text concludes with a systematic discussion of geometry and its foundations. 1939 edition. 141 |
I learned graph theory from John Kennedy and Christopher Hanusa, the former an extremely well respected graph theorist and the latter a rising young combinatorialist.There'scombinatorialfree,as far as I know. The second edition is more comprehensive and up-to-date,butup-to-date,but it's more of a problem course and therefore more difficult.Jonathandifficult.Jonathan Gross and Jay Yellen's Graph Theory With Applications is the best textbook there is on graph theory PERIOD.RigorousPERIOD.Rigorous and as comprehensive as it gets.Thegets.The section on topological graph theory is particularly good.(Igood.(I HATE thiertheir combinatorics text-it'stext–it's a hodgepodge text that's nowhere near as well written and organized.)
There are several other good books. Chartrand et.alet.al isn't as comprehensive as Gross and Yellen,butYellen,but quite good and in the same spirit. Douglas West's book is considered by many to be the preeminent graph theory text. I own it-it'sit–it's pretty good,butgood,but not as careful and comprehensive as Gross and Yellen. If you can get a cheap copy,bycopy,by all means,getWest-butmeans,getWest–but if you're gonna end up spending THAtTHAT much money,mightmoney,might as well go a little more and get the FarrariFerrari.
There's my 2 cents for what it's worth.
I learned graph theory from John Kennedy and Christopher Hanusa, the former an extremely well respected graph theorist and the latter a rising young combinatorial far as I know. The second edition is more comprehensive and up-to-date,but it's more of a problem course and therefore more difficult.Jonathan Gross and Jay Yellen's Graph Theory With Applications is the best textbook there is on graph theory PERIOD.Rigorous and as comprehensive as it gets.The section on topological graph theory is particularly good.(I HATE thier combinatorics text-it's a hodgepodge text that's nowhere near as well written and organized.)
There are several other good books. Chartrand et.al isn't as comprehensive as Gross and Yellen,but quite good and in the same spirit. Douglas West's book is considered by many to be the preeminent graph theory text. I own it-it's pretty good,but not as careful and comprehensive as Gross and Yellen. If you can get a cheap copy,by all means,get West-but if you're gonna end up spending THAt much money,might as well go a little more and get the Farrari.
There's my 2 cents for what it's worth. |
Brings together ideas from PDE theory, General Relativity and Astrophysics
Valuable resource for advanced undergraduates, graduates and researchers in fields such as numerical relativity and cosmology which are currently very active
A graduate level text on a subject which brings together several areas of mathematics and physics: partial differential equations, differential geometry and general relativity. It explains the basics of the theory of partial differential equations in a form accessible to physicists and the basics of general relativity in a form accessible to mathematicians. In recent years the theory of partial differential equations has come to play an ever more important role in research on general relativity. This is partly due to the growth of the field of numerical
relativity, stimulated in turn by work on gravitational wave detection, but also due to an increased interest in general relativity among pure mathematicians working in the areas of partial differential equations and Riemannian geometry, who have realized the exceptional richness of the interactions between geometry and analysis which arise. This book provides the background for those wishing to learn about these topics. It treats key themes in general relativity including matter models and symmetry classes and gives an introduction to relevant aspects of the most important classes of partial differential equations, including ordinary differential equations, and material on functional analysis. These elements are brought together to discuss a variety of important examples in the field of
mathematical relativity, including asymptotically flat spacetimes, which are used to describe isolated systems, and spatially compact spacetimes, which are of importance in cosmology |
Math
8:
This course will use the Prentice Hall Course 3 Mathematics book
(Copyright 2004). It covers a vast amount of mathematics including,
but not limited to: Real numbers/integers and algebraic expressions,
equations and inequalities, graphing linear and nonlinear equations,
proportions, percents/decimals/fractions their relationships and
applications, exponents and powers, area, surface area, and volume,
probability, as well as other various algebraic relationships. Calculators
are provided for in class use. It is recommended that students have a
scientific calculator at home to complete assignments.
Algebra: This course
will use the Prentice Hall Algebra 1 book
(Copyright 2007). It covers solving/graphing equations and
inequalities, solving and applying proportions, graphs and functions,
systems of equations and inequalities, exponents and exponential functions,
polynomials and factoring, quadratic equations and functions, radical
expressions and equations, rational expressions and functions, as well as
other algebraic related topics. Graphing calculators (Texas Instruments TI
83-Plus) will be used for data analysis and enforcing concepts. It is
recommended that students have a scientific calculator at home to complete
assignments. |
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