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Stirling CalculusStudents will learn to graph rational equations and conic sections such as parabolas, ellipses, hyperbolas and more. They will be able to translate and classify these conic sections based on both their graphs and their equations. The course will provide a structured introduction to logarithmic ...Thank you for your consideration. Physics is different things to different people. As a body of knowledge, it's the collection of experimentally verifiable ideas about how the objective world works. |
There are many graph-drawing programs, but doing it well is harder than it may seem. The traditional approach is to restrict users to considering only explicit functions of the form y=f(x) and to graph them by "joining the dots", but this approach can give inaccurate results and is unnecessarily limiting. Students of algebra should be free to explore the broader class of relations, including inequalities like (x^2+y^2)^2<12*(x^2-y^2).
Hydrix has developed a graphing engine that can quickly and accurately graph a broad range of algebraic relations. Additionally it can identify and display regions where the relation is undefined. The graphing engine has been designed specifically for embedding within handheld calculators, using efficient algorithms and compact data structures that perform well within the processor and memory constraints of a low-power device.
For more information, please consult our white paper available here. It contains a detailed analysis of the problem and the various algorithms used to try to solve it. Traditionally, those solutions were either not suited for embedded environment or somewhat inaccurate. |
Introduction
These Guidelines are intended to provide a resource for teachers of Junior Certificate mathematics. In particular they are designed to support the revised Junior Certificate syllabuses (introduced in September 2000) during the first cycle of implementation: that is, until the end of the academic year 2002/2003.
The current draft version of the Guidelines can be updated after 2003 to reflect the experience and wisdom of teachers who have taught the new syllabuses during their introductory period.
The document aims to address a variety of questions that may be asked about the syllabuses. Questions can be grouped under the headings "why", "what" and "how". The opening sections of the Guidelines focus especially on providing answers to questions of "why" type. Section 1 describes the background to and reasons for the revision of the mathematics syllabuses; Section 2, dealing with the specification of aims and objectives, emphasises the rationale and principles underlying their design; and Section 3, on syllabus content, outlines reasons for including specific topics. These sections also address issues of "what" type. For example, Section 3 highlights the changes that were made from the preceding syllabuses and the differences that may be expected in student knowledge and attitude at entry to the junior cycle following the introduction of the revised Primary School Curriculum. In Section 4, "how" questions are considered: how the work might be organised in the school or classroom, and how specific topics might be taught. This section describes some of the insights and practice of experienced teachers who have "made it work" in Irish classrooms. Against this exposition of where the learning of mathematics should be going and how it might get there, Section 5, on assessment, indicates ways in which information can be obtained on whether or not the students have arrived at the intended goals. A number of appendices provide reference material.
Thus, the different parts of the Guidelines are likely to be used in different ways. The initial parts offer a general orientation and invite reflection on the purposes of mathematics education in the junior cycle. The central sections provide a resource for the day-to-day work of mathematics teaching: a compendium of ideas, to which teachers may turn when they wish to improve the quality or vary the style of learning in their classrooms. The section dealing with assessment is likely to be of special interest to those preparing students for state examinations, but its brief is wider, with the focus being on formative as well as summative assessment. Altogether, it is hoped that the emphasis on meaningful and enjoyable learning will enrich the quality and enhance the effectiveness of our students' mathematics education.
The Guidelines are designed to support the teaching of mathematics in the junior cycle in such a way as to meet a wide range of learning needs. However, students with a mild general learning disability often face particular challenges in the area of mathematics. Additional guidelines for teachers of students with a mild general learning disability have been drawn up, and provide a further resource for all teachers of mathematics.
Many people too many to mention individually have contributed to the Guidelines. A special tribute must be paid to the teachers who provided the "lesson ideas" which form a key part of the document and also to those who made inputs to other sections. The engagement of so many people from outside the course committee, as well as of committee members, is a welcome feature of the process leading to the production of the draft Guidelines document. It represents a significant advance in the sharing of mathematics teaching methodologies at national level. As indicated above, the intention is that even more members of the mathematics education community will contribute their ideas over the period of operation of the draft Guidelines. The final version can then provide a resource that reflects as much good practice as possible in mathematics teaching in Ireland.
Context of the Changes
1.1 HISTORY OF THE SYLLABUSES
DEVELOPMENT OF THE JUNIOR CYCLE SYLLABUSES
The development of the current syllabuses can be traced back to the sixties: that period of great change in mathematics courses world-wide. The changes were driven by a philosophy of mathematics that had transformed the subject at university level and was then starting to penetrate school systems. It was characterised by emphasis on structure and rigour. Starting from sets, the whole edifice of mathematics could be built up logically, via relations and in particular functions; the structure laws (such as those we know as the commutative, associative and distributive properties) were golden threads tying the different parts of mathematics together. As a summary of the mathematics of the day, it was splendidly conceived and realised by the famous Bourbaki group in France; but it was devised as a state-of-the art summary of the discipline of mathematics, not as an introduction to the subject for young learners. Nonetheless, many countries embraced the philosophy or at least its outcome, revised subject-matter and rigorous presentation with great enthusiasm. In Ireland, teachers attended seminars given by mathematicians; the early years of the Irish Mathematics Teachers' Association were enlivened by discussions of the new material.
The first changes in the mathematics syllabuses in this period took place in the senior cycle; new Leaving Certificate syllabuses were introduced in 1964, for first examination in 1966. Meanwhile, thoroughly "modern" syllabuses were being prepared for the junior cycle. They were introduced in 1966, for first examination in 1969, and were provided at two levels: "Higher" and "Lower". (Prior to 1966, two levels had also been offered, but the less demanding of the two had been available only to girls.) These revisions brought in some topics which we now take for granted, such as sets and statistics, as well as a few, such as number bases, which have not stood the test of time. The new syllabuses also addressed a problem in their predecessors: students were finding difficulty with the (comparatively) traditional presentation of formal geometry difficulty, it can be said, shared by students in many other countries; so Papy's system, based on couples and transformations of the plane, was introduced alongside the existing version. For the examinations, papers clearly delineated by topic arithmetic, algebra and geometry were replaced by two papers in which a more integrated approach was taken, in keeping with the "modern" vision of mathematics.
The syllabuses introduced in 1966 ran for seven years. In 1973, revised versions were implemented in order to deal with some aspects that were causing difficulty. Two main alterations were made. First, the hybrid system of geometry was replaced by one entirely in the style of Papy. Secondly, the examination papers were redesigned so that the first section on each consisted of several compulsory multiple-choice items, effectively spanning the entire content relevant to the paper in question. The revised syllabuses were even more strongly Bourbakiste in character than their predecessors, with the ideas of set and function being intended to unify very many aspects of the syllabuses. However, it was hoped that emphasis would be given to arithmetic calculation and algebraic manipulation, which were felt to have suffered some neglect in the first rush of enthusiasm for the modern topics.
The size of the cohort taking the Intermediate Certificate increased in the 1970s. The rather abstract and formal nature of "modern" mathematics was not suitable for all the cohort, and further revisions were needed. In the early eighties, therefore, it was decided to introduce a third syllabus, geared to the needs of the less able. Also, some amendments were made to the former Higher and Lower level syllabuses. The package of three syllabuses, then called Syllabuses A, B and C, was introduced in 1987, for first examination in 1990. In the examination papers for Syllabuses A and B, question 1 took on the role of examining all topics in the relevant half of the syllabus, but the multiple-choice format was dropped in favour of the short-answer one that was already in use at Leaving Certificate level. A very limited choice was offered for the remaining questions (of traditional "long answer" format). For Syllabus C, a single paper with twenty short-answer questions was introduced.
The unified Junior Certificate programme was introduced in 1989. As the Intermediate Certificate mathematics syllabuses had been revised so recently, they were adopted as Junior Certificate syllabuses without further consideration (except that Syllabuses A, B and C were duly renamed the Higher, Ordinary and Foundation level syllabuses). Consequently, there was no opportunity to review the syllabuses thoroughly or to give due consideration to an appropriate philosophy and style for junior cycle mathematics in the 1990s and the new millennium.
The focus so far has been on syllabus content, and has indicated that the revolution in mathematics education in the 1960s has been followed by gradual evolution. Accompanying methodology received comparatively little attention in the ongoing debates. Choice of teaching method is not prescribed at national level; it is the domain of the teacher, the professional in the classroom. However, pointers could be given as to what was deemed appropriate, and the Preambles to the syllabuses introduced in 1973 and 1987 referred to the importance of understanding, the need for practical experience and the use of appropriate contexts. Now, with the increase in student retention and in view of the challenges posed by the information age, greater emphasis on methodology has become a matter of priority.
RECENT CHANGES AT OTHER LEVELS IN THE SYSTEM
To set the scene properly for the current revision of the Junior Certificate syllabuses, it is necessary to look also at what precedes and follows them in the students' education: the Primary School Curriculum and Leaving Certificate syllabuses.
The Leaving Certificate syllabuses were revised in the early 1990s. The revised syllabuses had to follow suitably from the then current Junior Certificate syllabuses, to fit into the existing senior cycle framework, and also to meet the needs of the world beyond school. This imposed some limitations on the scope of the revision. However, content was thoroughly critiqued for current relevance and suitability, some topics being discarded and a limited number of new ones being introduced. For the new Foundation level syllabus brought in as the Ordinary Alternative syllabus in 1990, and amended slightly and designated as being at Foundation level in 1995 some recommendations were made with respect to methodology. They emphasised the particular need for concrete approaches to concepts and for careful sequencing of techniques so that students could find meaning and experience success in their work. Much of the work was built round the use of calculators, which were treated as learning tools rather than just computational aids.
The introduction of calculators is also a feature of the revised Primary School Curriculum which was published in 1999. The revision was the first to be undertaken since the introduction of the radically restructured Primary School Curriculum in 1971. The revised curriculum is being implemented on a phased basis, with the mathematics element scheduled for introduction in 2002. As is the case for the second level syllabuses, the revolution of the earlier period has been followed by evolution. The 1971 curriculum emphasised discovery learning, and this has led to considerable use of concrete materials and activity methods in junior classes. The revised Primary School Curriculum focuses to a greater extent on problem-solving and on the need for students to encounter concepts in contexts to which they can relate. Students emerging from the revised curriculum should be more likely than their predecessors to look for meaning in their mathematics and less likely to see the subject almost totally in terms of the rapid performance of techniques. They may be more used to active learning, in which they have to construct meaning and understanding for themselves, rather than passively receiving information from their teachers. The detailed changes in content and emphasis likely to affect second level mathematics are outlined in Section 3.4.
1.2 DEVELOPMENT OF THE REVISED SYLLABUSES
EVALUATIONS OF THE 1987 SYLLABUSES
Under the jurisdiction of the NCCA, the mathematics (junior cycle) course committee was first convened in November 1990, and was asked to analyse the impact of the new junior cycle mathematics syllabus. A somewhat similar brief was given in 1992, coinciding with a wider review: that of the first examination of syllabuses introduced at the inception of the Junior Certificate in 1989. The committee produced a report in response to each request. Among the difficulties identified in one or both of these reports were
the length of the Higher level syllabus (which had actually been shortened in 1987, but the restricted choice in the examination meant that greater coverage was required than before)
aspects of the geometry syllabus, especially at Higher level
the proscription of calculators in the examinations, and consequently their restricted use as learning tools and computational aids in the classroom
design of the Higher and Ordinary level examination papers (the restricted choice being endorsed, but the absence of aims and objectives giving problems in specifying criteria for question design and for formulation of marking schemes).
Both reports included favourable comments on the appropriateness of the Foundation level syllabus newly introduced at that stage for most of the students who were taking it.
BRIEF FOR THE REVISIONS
In Autumn 1994, the course committee was asked to critique the Junior Certificate mathematics syllabuses, this time with a view to introducing some amendments if required. Because of the amount of change that had taken, and was taking, place in the junior cycle in other subject areas, it was specified that the outcomes of the reviewwould build on current syllabus provision and examinationapproaches rather than leading to a root and branchchange of either. Thus, once more, the syllabuses were to berevised rather than fundamentally redesigned. The review was to take into account
the work being done by the NCCA with respect to the curriculum for the upper end of the primary school
the earlier reviews carried out by the committee
changing patterns of examination papers over recent years
analysis of examination results since 1990.
The following tasks were set out for the committee:
To identify the major issues of concern regarding the existing syllabuses in their design, implementation and assessment;
To address the issues surrounding Foundation level mathematics;
To draft an appropriate statement of aims and objectives for each of the three syllabuses in line with Junior Certificate practice;
To prepare Guidelines to assist in improving the teaching of mathematics.
EXECUTION OF THE TASKS
The committee had already identified the main issues, as described above. Consultation with the constituencies, for example at meetings of the Irish Mathematics Teachers' Association, tended to confirm that these were indeed the areas of chief concern to mathematics teachers. Chief Examiners' reports and international studies involving Ireland provided further insights. Altogether, the information pointed to strengths of Irish mathematics education such as its sense of purpose and focus and the very good performance of the best students but also to weaknesses, for example with respect to students' basic skills and understanding in some key areas of the curriculum, their communication skills and their ability to apply knowledge in realistic contexts. Consequent changes eventually made to the syllabuses and proposed for the examinations are outlined in Sections 3.3 and 5.4 of this document.
Further consideration of the Foundation level syllabus led to endorsement of its main thrust and its appropriateness for many students at the weaker end of the mathematical ability spectrum. Against this background of general approval, however, the committee recognised some difficulties, both with the syllabus content and with the format of the Junior Certificate examination. Changes were needed to enrich the content and improve the standing of the syllabus and to give students more opportunity to show what they had learnt. The problem of students following the Foundation level syllabus, or taking the examination, when they are capable of working at the Ordinary level, also needed to be addressed. Again, consequent changes are described elsewhere in these Guidelines (see Sections 3.3 and 5.4).
FROM INTENTION TO IMPLEMENTATION
The course committee duly presented the final draft of the syllabus to the NCCA Council, and this was approved by Council in May 1998. Later in the same year, the Minister for Education and Science announced his decision to implement the syllabus. It was introduced into schools in Autumn 2000 for first examination in 2003.
Introduction of the syllabus is being accompanied by incareer development for teachers of mathematics. This has been planned so as to focus, not only on the changes in syllabus content, but also on the types of teachingmethodology that might facilitate achievement of the aims and objectives of the revised syllabus. These Guidelines are intended to complement the in-career development sessions. They can also support further study involving teachers or groups of teachers throughout the country.
Aims, Objectives and Principles of Syllabus Design
2.1 INTRODUCTION
One of the tasks given to the Course Committee was to write suitable aims and objectives for Junior Certificate mathematics. Accordingly, aims and generalobjectives are specified in the Introduction to the syllabus document. They apply to all three syllabuses. To augment these broad aims and general objectives appropriately, each syllabus is introduced by a further specification of its purpose, by means of
a rationale, describing the target group of students, the general scope and style of the syllabus, and aspects deserving particular emphasis in order to tailor the syllabus to the students' needs
a statement of level-specific aims, highlighting aspects of the aims that are of particular relevance for the target group
a listing of assessment objectives: a subset of the general objectives, to be interpreted in the light of the levelspecific aims and hence suitably for the ability levels, developmental stages and learning styles of the different groups of students.
Sections 2.2 to 2.4 of the Guidelines discuss these features and set them in context. Against this background, Section 2.5 outlines certain principles that guided and constrained design of the syllabuses to meet the aims.
2.2 AIMS FOR JUNIOR CERTIFICATE MATHEMATICS
The aims formulated for Junior Certificate mathematics are derived from those specified for the current Leaving Certificate syllabuses, with appropriate alterations to suit the junior rather than the senior cycle of second level education. The Leaving Certificate aims were based on those specified in the booklet Mathematics Education:Primary and Junior Cycle Post-Primary produced by the Curriculum and Examinations Board in 1985. In the absence of a specific formulation for the Junior Certificate, these were taken as the best approximation to contemporary thinking about mathematics education in Ireland.
The syllabus document presents a common set of aims for the three syllabuses (Higher, Ordinary and Foundation level). They can be summarised and explained as follows.
It is intended that mathematics education should:
A) Contribute to the personal development of the students.
This aim is chiefly concerned with the students' feelings of worth as a result of finding meaning and interest, as well as achieving success, in mathematics.
B) Help to provide them with the mathematical knowledge, skills and understanding needed for continuing their education, and eventually for life and work.
This aim focuses on what the students will be able to do with their mathematics in the future: hence, on their ability to recognise the power of mathematics and to apply it appropriately.
Section 3.5 of this document describes one vision (not the only possible one) of how these aims might be addressed in the different content areas.
2.3 GENERAL OBJECTIVES FOR JUNIOR CERTIFICATE MATHEMATICS
The aspirational aims need to be translated into more specific objectives which, typically, specify what students should be able to do at the end of the junior cycle. As with the aims, the general objectives are modelled on those for the current Leaving Certificate syllabuses, notably in this case the most recently formulated set produced for Foundation level.
The objectives listed in the syllabus document can be summarised and explained as follows.
A. Students should be able to recall basic facts.
That is, they should have fundamental information readily available for use. Such information is not necessarily an end in itself; rather, it can support (and enhance) understanding and aid application.
B. They should be equipped with the competencies needed for mathematical activities.
Hence, they should be able to perform the basic skills and carry out the routine algorithms that are involved in "doing sums" (or other exercises), and be able to use appropriate equipment (such as calculators and geometrical instruments) and they should also know when to do so. This kind of "knowing how" is called instrumental understanding: understanding that leads to getting something done.
C. They should have an overall picture of mathematics as a system that makes sense.
This involves understanding individual concepts and conceptual structures, and also seeing the subject as a logical discipline and an integrated whole. In general, this objective is concerned with "knowing why", or so-called relational understanding.
D. They should be able to apply their knowledge.
Thus, they should be able to use mathematics (and perhaps also to recognise uses beyond their own scope to employ) hence seeing that it is a powerful tool with many areas of applicability.
E. The students should be able to analyse information, including information presented in unfamiliar contexts.
In particular, this provides the basis for exploring and solving extended or non-standard problems.
F. They should be able to create mathematics for themselves.
Naturally, we do not expect the students to discover or invent significant new results; but they may make informed guesses and then critique and debate these guesses. This may help them to feel personally involved in, and even to attain a measure of ownership of, some of the mathematics they encounter.
G. They should have developed the necessary psychomotor skills to attain the above objectives.
Thus, for example, the students should be enabled to present their mathematics in an orderly way, including constructions and other diagrams where relevant, and to operate a calculator or calculator software.
H. They should be able to communicate mathematics, both verbally and in writing.
Thus, they should be able to describe their mathematical procedures and insights and explain their arguments in their own words; and they should be able to present their working and reasoning in written form.
I. They should appreciate mathematics.
For some students, appreciation may come first only from carrying out familiar procedures efficiently and "getting things right". However, this can provide the confidence that leads to enjoyable recognition of mathematics in the environment and to its successful application to areas of common or everyday experience. The challenge of problems, puzzles and games provides another source of enjoyment. Aesthetic appreciation may arise, for instance, from the study of mathematical patterns (those occurring in nature as well as those produced by human endeavour), and the best students may be helped towards identifying the more abstract beauty of form and structure.
J. They should be aware of the history of mathematics.
The history of mathematics can provide a human face for the subject, as regards both the personalities involved and the models provided for seeing mathematics as a lively and evolving subject.
It is important to note that the objectives, like the aims, are common to all the Junior Certificate syllabuses (Higher, Ordinary, and Foundation level). However, they are intended to be interpreted appropriately at the different levels, and indeed for different students, bearing in mind their abilities, stages of development, and learning styles. This is particularly relevant for assessment purposes, as discussed in Section 5. It leads to the formulation of level-specific aims and their application to assessment objectives, discussed in Section 2.4.
2.4 RATIONALE, LEVEL-SPECIFIC AIMS AND ASSESSMENT OBJECTIVES
The aims and objectives together provide a framework for all the syllabuses. However, the fact that there are three different syllabuses reflects the varying provision that has to be made for those with different needs. Each syllabus has its own rationale, spelled out in the syllabus document. Key phrases in the three rationales are juxtaposed in the following table in order to highlight the intended thrust of each syllabus.
RATIONALE FOR THE HIGHER LEVEL
RATIONALE FOR THE ORDINARY LEVEL
RATIONALE FOR THE FOUNDATION LEVEL
[This] is geared to the needs of students of above average mathematical ability.... However, not all students ... are ... future users of academic mathematics.
[This] is geared to the needs of students of average mathematical ability.
[This] is geared to the needs of students who are unready for or unsuited by the mathematics of the Ordinary [level syllabus].
For the target group, particular emphasis can be placed on the development of powers of abstraction and generalisation and on an introduction to the idea of proof.
For the target group, particular emphasis can be placed on the development of mathematics as a body of knowledge and skills that makes sense and that can be used in many different ways hence, as an efficient system for the solution of problems and provision of answers.
For the target group, particular emphasis can be placed on promoting students' confidence in themselves (confidence that they can do mathematics) and in the subject (confidence that mathematics makes sense).
A balance must be struck, therefore, between challenging the most able students and encouraging those who are developing a little more slowly.
[It] ... must start where these students are, offering mathematics that is meaningful and accessible to them at their present stage of development. It should also provide for the gradual introduction of more abstract ideas.
[It] must therefore help the students to construct a clearer knowledge of, and to develop improved skills in, basic mathematics, and to develop an awareness of its usefulness.
In the light of these rationales, level-specific aims emphasise the various skills in ways that, hopefully, are appropriate to the levels of development of the target groups. The table opposite presents the aims for the three levels, as set out in the syllabus document.
SPECIFIC AIMS FOR HIGHER LEVEL
SPECIFIC AIMS FOR ORDINARY LEVEL
SPECIFIC AIMS FOR FOUNDATION LEVEL
[This] is intended to provide students with
a firm understanding of mathematical concepts and relationships
confidence and competence in basic skills
the ability to formulate and solve problems
an introduction to the idea of proof and to the role of logical argument in building up a mathematical system
a developing appreciation of the power and beauty of mathematics and of the manner in which it provides a useful and efficient system for the formulation and solution of problems.
[This] is intended to provide students with
an understanding of mathematical concepts and of their relationships
confidence and competence in basic skills
the ability to solve problems
an introduction to the idea of logical argument
appreciation both of the intrinsic interest of mathematics and of its usefulness and efficiency for formulating and solving problems.
[This] is intended to provide students with
an understanding of basic mathematical concepts and relationships
confidence and competence in basic skills
the ability to solve simple problems
experience of following clear arguments and of citing evidence to support their own ideas
appreciation of mathematics both as an enjoyable activity through which they experience success and as a useful body of knowledge and skills.
Against this background, objectives can be specified for assessment leading to certification as part of the Junior Certificate. Mathematics to date in the Junior Certificate has been assessed solely by a terminal examination; consideration of alternative forms of assessment was outside the scope of the current revision. This has a considerable effect on what can be assessed for certification purposes a point taken up more fully in Section 5 of this document.
The assessment objectives are objectives A, B, C, D(dealing with knowledge, understanding andapplication), G (dealing with psychomotor skills) and H(dealing with communication). These objectives, while the same for all three syllabuses, are to be interpreted in the context of the level-specific aims as described above. Further illustration is provided in Section 5.
2.5 PRINCIPLES OF SYLLABUS DESIGN
The aims and objectives are important determinants of syllabus content; but so also is the context in which the syllabuses are implemented. The most attractive syllabuses are doomed to failure if they cannot be translated into action in the classroom. With this in mind, several principles were specified in order to guide the syllabus design. They are particularly important for understanding the inclusion, exclusion, form of presentation, or intended sequencing of certain topics. The principles are displayed (in "boxes") overleaf.
A. The mathematics syllabuses should provide continuation from and development of the primary school curriculum, and should lead to appropriate syllabuses in the senior cycle.
Hence, the syllabuses should take account of the varied backgrounds, likely learning styles, potential for development, and future needs of the students entering second level education. Moreover, for the cohort of students proceeding from each junior cycle syllabus into the senior cycle, there should be clear avenues of progression.
B. The syllabuses should be implementable in the present circumstances and flexible as regards future development.
They should therefore be teachable, learnable and adaptable.
The points regarding teachability, learnability and adaptability can be considered in turn.
(a) The syllabuses should be teachable, in that it should be possible to implement them with the resources available.
The syllabuses should be teachable in the time normally allocated to a subject in the Junior Certificate programme.
Requirements as regards equipment should not go beyond that normally found in, or easily acquired by, Irish schools.
The aims and style of the syllabuses should be ones that teachers support and can address with confidence, and the material should in general be familiar.
(b) The syllabuses should be learnable, by virtue of being appropriate to the different cohorts of students for whom they are designed.
Each syllabus should start where the students in its target group are at the time, should move appropriately from the concrete to or towards the abstract, and should proceed to suitable levels of difficulty.
The approaches used should accommodate the widest possible range of abilities and learning styles.
They should cater for the interests and needs of all groups in the population.
The materials and methods should be such that students are motivated to learn.
(c) The syllabuses should be adaptable designed so that they can serve present needs and also can evolve in future.
C. The mathematics they contain should be sound, important and interesting.
In order to cater for the differing interests of students and teachers, a broad range of appropriate aspects of mathematics should be included. Where possible the mathematics should be applicable, and the applications should be such that they can be made clear to the students (now, rather than in some undefined future) and can be addressed, at least to some extent, within the course. |
The user reviews the coordinate system and basic geometry terms associated with the coordinate plane. After viewing examples of graphing objects, users can interactively test their understanding of th... More: lessons, discussions, ratings, reviews,...
The user reviews the slope and y-intercept of a line and learns how to graph a linear equation. After viewing examples, users can interactively practice determining the linear equation for each line |
Although the skills in sections of this curriculum supplement are
presented sequentially, they are not intended to be taught in
isolation or necessarily in order. In particular, most existing GED
materials for math instruction organize content in a sequential manner
(i.e., whole numbers, fractions, decimals), even though this does not
reflect current research regarding acquisition of math skills. GED
students often have a wide range of math skills and each student
should be individually assessed.
Similarly, emphasis should be placed on the student using reading
and writing processes to lead to higher-order thinking such as
application, analysis, synthesis, and evaluation. This focus on
abstract reasoning and problem solving considers the adult world and
stresses the workplace, a global perspective, and the emergence of new
technologies. The key concepts listed in this curriculum supplement
are provided as a guide and are not all-inclusive.
The GED tests, in addition to measuring the integrated and
comprehensive skills of each subtest, are primarily a multiple choice
reading test. Examinees must be able to comprehend and draw inferences
from written and graphic materials. This curriculum supplement should
be used by teachers for students who demonstrate a reading competence
comparable to that of a senior high school student. It is important to
remember that the test is normed on high school seniors. Please note
that mathematics concepts and basic reading and writing skills are
covered in other sections of this document. |
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Section 7.8: 3-D Band Diagrams and Tensor Effective Mass Band diagrams characterize the effect of the crystal geometry on the behavior of the electrons within the semiconductor. We discuss 3-D bands and the tensor form of the effective mass. The band
Section A1.4: The Divergence The divergence of a vector field describes how ! much a vector field diverges away from a point r or a volume. Two vector fields with nonzero divergence appear in Figure A1.4.1. The field on the left of the figure resembl
Section 7.8: Introduction to Matter and Light as Systems Previous sections and chapters discuss the Hamiltonian for free particles and free fields. Particles interacting with a potential cannot be considered as free. Likewise, EM fields interacting w
Section 8.7: Dopant Ionization Statistics This section derives the Fermi function for dopants in order to determine the occupation as a function of temperature. We will want to know the suitable range of temperatures for which the dopants remain ioni
Chapter 2: Graphical Solutions to Partial Differential EquationsThe present chapter explores the solution to first and second-order partial differential equations using characteristic equations and graphical techniques. The analysis is limited to a
Section 3.10: Dispersion in Waveguides The rate at which light propagates along a waveguide depends on the frequency of the wave and upon the construction of the waveguide. We discuss intermodal and intramodal dispersion and how they limit the bandwi
Section 6.2: The Crystal, Lattice, Atomic Basis and Miller Notation A crystal consists of a single atom or a group of atoms arranged as a periodic array. The mathematical construction, the lattice, gives the array its periodic nature. Bravais lattice
Section A1.5: The Curl Figure A1.5.1 shows the typical picture for a vector field with nonzero curl. The curl of a vector field measures how much of the field curls around a point. Applying the curl operator Curl = to a field with only radial compo
Section 3.6: Electromagnetic Scattering and Transfer Matrix Theory Many emitters and detectors use multiple optical elements as part of the device structure. For example, the vertical cavity lasers (VCSELs) use multiple layers of dissimilar optical m
Section 8.8: The pn-Junction at Equilibrium The notes in this section sketch the physical principles involved with establishing a pn junction. Topic 8.8: Introductory Concepts The PN junction forms when p-type and n-type semiconductors come into suff
Synchronized ComputationsData Parallel ComputationsIn a data parallel computation, the same operation is performed on different data elements simultaneously; i.e., in parallel. Particularly convenient because: Ease of programming (essentially only |
PEMDAS: A Method for Remembering Order of Operations This video demonstrates solving a problem involving order of operations using PEMDAS as a memory technique. The problem appears on a white board and is solved step-by-step as a narrator explains the steps. ( 1:13) Author(s): No creator set
Finding the Domain of a Function - Problem 3 of 4 This video is a continuation and presents a more challenging example problem that demonstrates how to find the domain of a function that involves a polynomial inequality. (3:11) Author(s): No creator set
screencastfilmpje: Pomp je geld in de pomp, de oorzaak van de stijgende olieprijzen in 2011
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Michael Buckley: 2011 National Book Festival Michael Buckley appears at the 2011 National Book Festival.
Speaker Biography: Michael Buckley is the author of two New York Times best-selling series for children: "The Sisters Grimm," a "Today" show Al Roker Book Club pick, and "NERDS." He has also written and developed shows for the Cartoon Network, Nickelodeon and Discovery Channel. Author(s): No creator set
The Quiet People: A Memoir Kelle Groom reads from a manuscript in progress, which is a memoir incorporating private and public history in a lyrically structured narrative that examines contemporary concerns through the lens of the author's Finnish, Irish, and Wampanoag ancestors in Massachusetts. The title references ancestors who left little written record, which challenges Groom to make their lives visible and discover how her life connects to their earlier struggles.
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of University Toronto at Scarborough
Department of Computer & Mathematical Sciences
MAT A23S
Winter 2012
Assignment #7
You are expected to work on this assignment prior to your tutorial in the
week of March 12th . You may ask questions about this assignment in that
tutorial.
In your tutorial in the week of March 19th you will be asked to write a quiz
based on this assignment and assignments 6 and 7 Toronto at ScarboroughDepartment of Computer & Mathematical SciencesMAT A23SWinter 2012Assignment #8You are expected to work on this assignment prior to your tutorial in theweek of March 21st . You may ask questions about this assignme
University of Toronto at ScarboroughDepartment of Computer & Mathematical SciencesMAT A23SWinter 2012Assignment #9You are expected to work on this assignment prior to your tutorial in theweek of March 26th . You may ask questions about this assignme
University of Toronto at ScarboroughDepartment of Computer & Mathematical SciencesMAT A23SWinter 2012Assignment 10You are expected to work on this assignment prior to your tutorial in theweek of April 2nd. You may ask questions about this assignment
MATA23 Solution 10 Solution 10 1) Read the lectures and the book to find the answers. 2) Section 5.2 c = -2a. d = -c+d so that c = 2d and d = -a. There are no more restrictionexcept that C be invertible. We take a =
Lecture 9: Gaze Control &Spatial Constancy1Introduction: the schedule2SAQTBDOverview Six kinds of eye movements Six eye muscles Eye movements are three-dimensional The motor circuits for saccades lie in thebrain stem! Cerebral control of sacc
JaneAustenGlossary: Characteraparticipant or an actor in astoryworld whynot just say people?Character Variants People Animalsspeaking as people Animals acting as animals Objects (The Titanic and the Iceberg) Cyborgs, robots, living particles
Narratorsand NarrationGlossary: Narrative (JamesPhelan)narrative can be fruitfully understood as arhetorical act: somebody telling somebody else onsome occasion and for some purpose(s) thatsomething has happened.Pride and Prejudice (I: 1)It is a
Critical ThinkingAbout NarrativeStoryworldsa global mental model of thesituations and events being recountedThe world we enter when we enter astoryPossible Worlds.There is a God.There is no God.There is justice.There is no justice.The world is
Part A [5 points]1)Enter the letter from the list of properties on the right for each of the following logicstatements:AND(A,1) = Aa.b.c.d.e.f._fA (B C) = (A B) (A C)_eAND(A, B) = AND(B, A)_b2)A3a)b)c)d)e)f)ANDNANDXORORNORNOT
Good afternoon Dear Sir or MadamI would appreciate if you could please help me with the following questions.Question 11Answer thefollowing questionsusing theinformation below:Trustme VehicalRental Corporationhas twodepartments, CarRental and Tr
Apple CaseDo you consider the introduction of the iPhone a blue oceanstrategy? Please, justify your answerFirst of all, we will introduce the blue ocean strategy, how it differs from moretraditional strategies. Then by studying the case of the iPhone,
P age |1Dustin NagyBrenda BakerThomas RowellNatalie J. EdwardsBUSN 2043/2/2011AmazonThe case study summarizes Amazon.com, one of the leading internet marketingcompanies today. Amazon was founded by Jeffery Bezos in 1995. Bezos started his company
Name: Sandrine FaltasID: 900 09 0591The Middle East is one of the rich arenas in the world in terms of natural resources. However, it lackssome sort of knowledge, experience and external communications. Each country in the Middle East is limitedwith b
Name: Sandrine FaltasID# 900090591Essay #3Composition TopicsGenderGrandmothers and older generations did suffer dramatically in their lives. Theywere too afraid to alter their status, so they gave up and accepted their lives as it was.Finally, the
surpriseddazzled.1forcedcompelled.2Ever lastingperennial.3Has to do with placegeographical.4Has to do with timechronological.5Liberation, freedomemancipation.6Too muchoverwhelmingly.7edgeverge.8difficultwayward.9painanguish.10
Name: SandrineFaltasID# 900090591Essay #2Composition TopicsEducationBased on international statistics, giving birth to a girl has ahigher probability than giving birth to a boy. In other words,girls form 51% of human population while boys form 49%.
Sandrine Faltas900 090 591RHET 102-32Essay 2 draft 1Y Motawy13 May 2010Are You Breathing? Breathing is key to our energy and is of great importanceto consider. You are breathing all time regardless your health state although difficultylevels vary.
Sandrine Faltas900 090 591RHET 102-32Essay 1 draft 1Y Motawy8 Mar 2010Sex EducationYoung children starting from 12 to adulthood pass through a new stage in thecognitive development, according to the Psychiatrist Piaget. This stage is called thefo
Sandrine Faltas900090591Econ 224Assignment 1Feudal Europe in the 10th and 11th centuries differed to a great extent in theirpolitical, social and economic structures from Feudal Europe in 1450-1500. In youropinion, what are the advantages and disadv
1Chapter 1The Demand for Audit and Other Assurance ServicesReview Questions1-1The relationship among audit services, attestation services, and assuranceservices is reflected in Figure 1-3 on page 13 of the text. An assurance service isan independent
Sandrine FaltasAssignment #1Part 1:Platos famous writing, the Apology is an exception of not being written fully in adialogue form. It is about that Socrates is defending himself from the accusation of being theman who corrupts the youth by making th
Chapter 3Audit ReportsReview Questions3-1Auditor's reports are important to users of financial statements becausethey inform users of the auditor's opinion as to whether or not the statements arefairly stated or whether no conclusion can be made wit
1Chapter 4Legal LiabilityReview Questions4-1Several factors that have affected the increased number of lawsuits againstCPAs are:1. The growing awareness of the responsibilities of public accountants onthe part of users of financial statements.2. A
1Chapter 6Audit Responsibilities and ObjectivesReview Questions6-1 The objective of the audit of financial statements by the independentauditor is the expression of an opinion on the fairness with which the financialstatements present financial posit
1Chapter 11Fraud AuditingReview Questions11-1Fraudulent financial reporting is an intentional misstatement or omissionof amounts or disclosures with the intent to deceive users. Two examples offraudulent financial reporting are accelerating the timi
Maie Mubasher900081143AuditingAssignment # 11-6Examples of evidence that the internal revenue agent will use in the auditingof the Jones Companys tax return include documentation. The auditor canuse cash receipts, bank statements and invoices. Expe
DepartmentofElectricalandComputerEngineering,GeorgeMasonUniversityECE445ComputerOrganizationSpring20122) Number SystemsDecimalBinaryOctalHexadecimala)23.12510111.00127.10017.2000b)19.62510011.10123.50013.Ac)55.645110111.1067.51237.A5 |
The course offers intermediate content to students preparing for four-year or technical college experiences. The course includes laws of exponents, complex numbers, matrices, relations, functions, and equations-including linear, quadratic, exponential, radical, absolute value, and rational. Most students should have completed Algebra I, and Geometry. Algebra II will take a more in depth approach to major concepts by studying relationships, analyzing functions, and systems in detail using higher order thinking skills. More complex analyses of concepts will be a vital part of the course.
Instructional Philosophy
Instructional Approach
As teachers, we, the math department, want to provide the very best education and learning experience for the students in our classes. We, the math department, believe the teacher should work with the students in the classroom.
A Typical Day in the Classroom
The class will begin each day with a "bell-ringer" assignment which will be completed in the first 5 minutes of the class. The teacher will then review homework completed the day before. The class will then learn the new material for the day using a variety of activities. The later part of class will have a review of what was learned and the start of home work.
Teaching Strategies
We will be using a variety of teaching strategies in the classroom. The following strategies will be used: lecture, group work, presentations, modeling, computer labs, writing assignments and many more. Graphing calculators will be utilized throughout the course in instruction and assessment.
Classroom Design
The classroom design will change according to the strategy of teaching. Some designs include: u-shape, row, and cluster.
Student Participation
The student is expected to take part in the class, doing the assigned work, paying attention, asking and answering questions. You can expect to have assignments every class period. Use your time wisely in class so that if you do have time to get started in class, you can acquire help. Homework/Class work will be checked daily and will be graded on a completion basis. Therefore, you should at least attempt each problem. If you have no idea how to do a problem, you should copy the problem and directions that go with it and then move on to the next problem. If you leave a problem blank, you will not receive credit for it.
Expectations
Students are expected to follow school rules as outlined in the handbook. In addition, we, the math department, expect the following:
Be on time. You must be in your seat when the tardy bell rings.
Be fully prepared for class.
Sharpen pencils and take care of any other business of such a manner before the tardy bell rings. Class will start immediately after the bell.
Have your book, notebook, paper, and pencil for class everyday.
Complete all assignments given.
Be kind, courteous, and respectful of others.
Keep your hands and feet to yourself.
Do not talk while other are talking, disrupt class, talk excessively, or make unnecessary comments.
Give your undivided attention to this class for the entire 90 minutes you are in class.
No food or drinks allowed (with the exception of water in a closed container).
Course Goals/Power Standards
The course goals and power standards may be assessed by teacher observation, daily class work/homework, quizzes, projects, and tests.
Set Theory
Exponential and Logarithmic Functions
Applications of Linear Equations and Inequalities Functions
Rational Expressions , Functions, and Equations
Quadratic Functions
Conic Sections
Quadratic Inequalities
Sequences
Polynomials and their graphs
Series
Radicals and Rational Exponents
Using a Handheld Graphing Calculator
Writing Assignments
Major Assignments
Major unit tests/assessments will be given every five to seven school days. Some tests will be cumulative, some will not. Test formats will vary and will include multiple choice, short answer, free response, and essays.
Assessment and Grading
Students will be graded on the basis of classroom participation, homework, class work, tests/assessments. Major assessments (tests) will count sixty percent and minor assessments (classwork/homework/participation) will count forty percent. Students will not be allowed to retakes tests but are required to complete test corrections which will count as a minor grade. The final exam will count 20% of the final grade. Each quarter will count 40% of the final grade. (First Quarter: 40%, Second Quarter: 40%, Exam: 20%)
Grading Scale: A: 93-100 B: 85-92 C: 77-84 D: 70-76 F: 69 and below
General Information
As we begin each unit, students will be given an overview of what we will be covering and a general time line. Students will know when their tests will be well in advance of the assigned date of the tests. Homework will be assigned everyday with very few exceptions. Great study help, including the entire textbook, can be found at |
Algebasics
Kelowna teacher, Sharon Affeld, told me about Algebasics – an online mathematics instructional resource that takes a middle school, high school or adult learner through the basics of algebra. The material is divided into sixteen sections, which begin with, "the basics," and includes a section on applying algebra to real-world situations. You'll need audio to get the full value of this site! |
Cognitive Tutor Algebra I Screen Shots
Algebra I Screenshot
This screen shot shows the some of the multiple representations available in the lessons. Here we see a graph, a data table, and a word problem.
Interactive Example
This screen shows an Interactive Example. Students can use these example problems to learn the basics of how to solve the problem type, and can refer back to it while they work. Numbered "breadcrumbs" allow the student to see the various steps of solving a problem in the correct order.
Hints
Hints are contextual and oriented towards helping the student to solve key steps in the problem.
Just-In-Time Hint
The immediate feedback of our Just-In-Time hints enables the student to self-correct and leads to more effective learning and applying of the mathematics.
Skillometer
As a student becomes more proficient in a skill, the bars on the Skillometer increase in length and turn gold, indicating mastery. |
Math 105 Overview
Textbook: Data, Functions, and Graphs
Functions Modeling Change: A Preparation for Calculus, University of Michigan Custom Edition
Connally, Hughes-Hallett, Gleason, et. al., 2012. ISBN: 978-1-1184-6184-6
There is also an eBook version available at
Graphing Calculator: TI-84 is recommended. Other graphing calculators may be substituted, but if you have a graphing calculator other than the
TI-84, you will be responsible for knowing how
to operate it on your own. (Calculators with a QWERTY keyboard are not acceptable.)
Student Body:
Largely first year students
Background and Goals:
Math 105 serves both as a preparatory class to the
calculus sequences and as a terminal course for students
who need only this level of mathematics.
Students who understand the material in 105
are fully prepared for Math 115.
Content:
This course presents the concepts of precalculus from four points of view:
geometric (graphs), numeric (tables), symbolic (formulas), and written
(verbal descriptions). The emphasis is on the mathematical modeling
of real-life problems using linear, polynomial, exponential, logarithmic,
and trigonometric functions. Students develop their reading,
writing, and questioning skills in an interactive classroom setting. |
Overview: The focus of this lesson is linear and exponential growth. Students in a 1st or 2nd year Algebra course are given a scenario about two different contribution plans for a child's college savings within non-interest bearing savings accounts. Students will build models of each savings plan and make predictions about the growth of each account. By comparing and contrasting the two plans, students will gain an understanding of how quickly a value can grow exponentially.
Lesson Objectives
Curriculum Context
Systems Thinking Concepts
Students will be able to:
increase their ability to make accurate predictions regarding linear and exponential growth
determine the rate of change (patterns of growth) for both linear and exponential growth
compare and contrast linear and exponential growth
build computer models that demonstrate linear and exponential growth
state differences between the graphs of linear and exponential growth
demonstrate their understanding of why exponential growth increases so rapidly
This lesson focuses on these curricular benchmarks:
Recognize, describe, create and analyze patterns.
Show an understanding of exponential and linear functions by identifying rates of change.
Use and create tables, graphs, and symbols to describe relationships and to solve problems.
Explain how change in one quantity results in a change in another using graphs, tables, symbols and words.
Reinforcing feedback Accumulation
Click hereto go to definition search.You may search for concepts or tools. |
Program Model B' Pacing Guide
Blended Model for High School Mathematics
Traditionally, high school mathematics has been compartmentalized into separate
courses for Algebra I, Geometry, and Algebra II. In the Ohio Academic Content Standards,
however, the algebra and geometry standards appear side-by-side through all the
grades, along with standards for number, measurement, and data analysis. This model
is designed to blend all five standards in a two-year program that exploits connections
among those different branches of mathematics.
In the first year, the primary focus of the course is linear mathematics, with non-linear
topics emphasized in the second year. The entry point each year is through the first
two levels of the data analysis standard, namely identifying a problem to be investigated
and collecting data. With that introduction, students should understand the advantage
gained by applying algebraic and geometric tools in solving these problems. The
second year concludes with an in-depth study that involves the analysis and interpretation
of data both linear and non-linear. This should provide students with an opportunity
to consolidate concepts and skills in number, algebra, and geometry that they have
acquired over the two years and use them to solve realistic problems.
The model assumes that students will be engaged with rich problems in each course.
This experience is essential to assuring that students understand the mathematics
fully and that they develop creative problem solving and reasoning skills. Students
should also be expected to communicate mathematical ideas using formal mathematical
language.
Model B' is an adaptation of Model B that allows additional time for students who are preparing
for postsecondary education in programs that do not include calculus. This adaptation prepares
students for OGT requirements by the end of the second year course and meets the Ohio Board of
Regents expectations for students to be prepared for a non-remedial college mathematics course
by the end of the third year course an in-depth study
of functions not considered earlier and then moves toTopics in this course include applications of algebra and trigonometry for students not planning to take calculus.
Fourth Year, Option 1, Course Description
The course includes systems of equations, exponential and logarithmic functions, infinite series and trigonometry |
may Algebra 2. In this course, the student will begin exploring radical functions, rational exponents, as well as exponential and logarithmic functions. Then the student will study rational functions, quadratic relations, and conic sections. Finally, the student will review sequences, series, probability, and statistics while expanding his previous knowledge of using distributions and conditional probability.
Throughout the course the student will be introduced to many problem-solving strategies, exposed to various technologies, and taught test-taking strategies. |
I recommend the Algebra Buster to students who need help with fractions, equations and algebra. The program is a great tool! Not only does it give you the answers but it also shows you how and why you come up with those answers. Ive shown my students how to use the program during some of our lessons. A couple of them even bought the program to help them out with their algebra homework. Brian Cook, CO
Just when I thought I couldn't find the program to do the job, I found Algebra Buster and my algebra problems were gone! Thank you. Rebecca Silva, OR
I just finished using Algebra Buster for the first time. I just had to let you know how satisfied I am with how easy and powerful it is. Excellent product. Keep up the good work. Dora Greenwood, PA
OK here is what I like: much friendlier interface, coverage of functions, trig. better graphing, wizards. However, still no word problems, pre-calc, calc. (Please tell me that you are working on it - who is going to do my homework when I am past College Algebra?!? Mark Fedor, MI
I just received your update, I am so happy I hooked up with you, its been the best thing for me and my learning. I love your program, thanks07-08 :
partial fractions solver
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Quadratic equations can be solved by graphing, using the quadratic formula, completing the square, and factoring. |
View of /trunk/webwork2/courses.dist/modelCourse/templates/setOrientation/prob06.pg
1 DOCUMENT(); # This should be the first executable line in the problem.
2 3 loadMacros(
4 "PGstandard.pl",
5 "MathObjects.pl",
6 "PGunion.pl",
7 "parserOrientation.pl",
8 "PGcourse.pl",
9 );
10 11 12 $showPartialCorrectAnswers = 1;
13 14 Context("Numeric")->variables->are(y=>'Real'); $y = Formula('y');
15 Context("Numeric")->variables->are(x=>'Real'); $x = Formula('x');
16 Context()->flags->set(limits=>[0,2]);
17 18 TEXT(beginproblem());
19 Title("Using Parentheses Effectively");
20 21 ##############################################
22 23 BEGIN_TEXT
24 25 One of the hardest parts about using parentheses is making sure that
26 they match up correctly. Here are a couple of hints to help you with
27 this:
28 29 $PAR
30 END_TEXT
31 32 $BRACES = HTML('{}','\char123\char125');
33 34 BEGIN_TEXT
35 36 \{BeginParList("UL")\}
37 38 $ITEM
39 Several types of parentheses are allowed: \{student "()"\},
40 \{student "[]"\}, and \{student $BRACES\}. When you need to nest
41 parentheses inside other parentheses, try using a different type for
42 each so that you can see more easily which ones match up.
43 $ITEMSEP
44 45 $ITEM
46 When you type a left parenthesis, type the corresponding right
47 parenthesis at the same time, then position your cursor between them and
48 type the expression that goes inside. This can save you a
49 lot of time hunting for mismatched parentheses.
50 $ITEMSEP
51 52 $ITEM
53 When you have a complicated answer, type a template for
54 the structure of your result first. For example, suppose that you are
55 planning to enter the fraction
56 \[\frac{2x^2-5}{(x+1)(3x^{3x} - 22)}.\]
57 A good way to start would be to type in \{student "()/[()*()]"\}.
58 This shows a template of one number divided by the product of two
59 other numbers. (Note that \{student "()/()*()"\} would not be a good
60 way to start; do you see why?) Now when you fill in the expressions, you
61 will be sure your parentheses balance correctly.
62 $PAR
63 64 Although $WW understands that numbers written next to each other are
65 meant to be multiplied (so you do not have to use \{student "*"\} to
66 indicate multiplication if you don't want to), it is often useful for
67 you to include the \{student "*"\} anyway, as it helps you keep track
68 of the structure of your answer.
69 $PAR
70 71 $ITEM
72 To see how $WW is interpreting what you type, enter your answer and
73 then click the ${LQ}Preview Answers$RQ button, which is next to the
74 ${LQ}Submit Answers$RQ button below. $WW will show you what it thinks
75 you entered (the preview appears in your answer area at the top of the
76 page). Previewing your answer does not submit it for credit; that only
77 happens when you press the ${LQ}Submit Answers$RQ button.
78 $ITEMSEP
79 80 $ITEM
81 When division or exponentiation are involved, it is a good idea to
82 use parentheses even in simple situations, rather than relying on the
83 order of operations. For example, 1/2x and (1/2)x both mean the same
84 thing (first divide 1 by 2, then multiply the result by x), but the
85 second makes it easier to see what is going on. Likewise, use
86 parentheses to clarify expressions involving exponentiation. Type
87 \{student "(e${CARET}x)${CARET}2"\} if you mean \((e^x)^2\), and type
88 \{student "e${CARET}(x${CARET}2)"\} if you mean \(e^{(x^2)}\).
89 90 \{EndParList("UL")\}
91 92 $PAR
93 $HR
94 $PAR
95 96 Now enter the following functions:
97 98 $BBLOCKQUOTE
99 100 \{@ExampleDefaults = (ans_rule_len => 50, ans_rule_height => 1);
101 BeginExamples\}
102 103 \{BeginExample(QA(($x**(2*$x-1))/(($x**2-$x)*(3*$x+5))))\}
104 Start with the template \{student "[x${CARET}()]/[()*()]"\}.
105 \{EndExample\}
106 \{ExampleRule\}
107 108 \{BeginExample(QA((($y+3)*($y**3+$y+1))/((2*$y**2-2)*(5*$y+4))))\}
109 Start by putting in an appropriate template. This means that you
110 should begin by looking at the function and thinking about how many
111 pieces are used to construct it and how those pieces are related.
112 Once you have entered your answer, try using the ${LQ}Preview$RQ button
113 to see how $WW is interpreting your answer.
114 \{EndExample\}
115 \{ExampleRule\}
116 117 \{BeginExample(QA((($x+1)/($x-2))**4))\}
118 Start by putting in an appropriate template.
119 \{EndExample\}
120 121 \{EndExamples\}
122 123 $EBLOCKQUOTE
124 125 END_TEXT
126 127 ##############################################
128 129 ENDDOCUMENT(); # This should be the last executable line in the problem. |
Lessons that require a teacher, horrifically dull examples, and forbidding language are all hurdles that homeschoolers must survive when looking at math curriculum...or do we? This applauded geometry curriculum was written specifically for homeschoolers; it doesn't presuppose a teacher constantly at the student's side, so it's very clear about instructions and employs an easy conversational style of writing. Illustrations, examples and graphs have a hand drawn look to them, and problems often use engaging real life illustrations. Not only is the textbook well done, but there are audiovisual lecture, practice, and solution CDs for every chapter, homework and test problem (though Teaching Textbooks Geometry does not feature automated grading). Definitions, theories and more have their own reference portion in the back of the text.
All together, this kit includes:
A 768 page spiral bound softcover textbook
164 page test book with answer key
1 test solution CD
6 homework solution CDs with step by step explanations for every problem |
2 years later, I understand this answer might not be helpful to you, lamdbafunctor, but for all of the other undergrads who come here and will see this, I believe Boyce and DiPrima's "Elementary Differential Equations and Boundary Value Problems" is exactly what you are looking for. The initial 4 chapter sequence this book follows (First order linear and nonlinear -> Second order linear and nonlinear -> Higher order linear and nonlinear) allows you to see the basic fundamentals being extended to more and more general cases and with very terse yet thorough and meaningful explanations through the entire way, it was a joy to read. From what I saw, it was almost like the book was written explicitly for self-study, as there is very little assumed detail. Many engineers find the downside to this book to be the almost complete lack of real-world modeling examples and such, and my response to them is that the purpose of Boyce/DiPrima is to gain a firm grounding in theory, while the purpose of other books like Edwards/Penney is to gain a firm grounding in physical/real-world applications. I am currently finishing up my first semester in Honors Diff Eq sophomore year, and I owe it almost entirely to this book. |
Our users:
I will be more confident when I face my algebra exam. Kenneth Schneider, WV
I really like your software. I was struggling with fractions. I had the questions and the answers but couldnt figure how to get from one to other. Your software shows how the problems are solved and that was the answer for me. Thanks. Dr. Stephen Wordell, KA
The Algebrator could replace teachers, sometime in the future. It is more detailed and more patient than my current math teacher. I, personally, understand algebra better. Thank you for creating it! Barbara, LA
As a mother who is both a research scientist and a company president (we do early ADME Tox analyses for the drug-discovery industry), I am very concerned about my daughters math education. Your algebra software was tremendously helpful for her. Its patient, full explanations were nearly what one would get with a professional tutor, but far more convenient and, needless to say, less expensive |
Geometry Quick Study Guide (BlackBerry) description
Boost Your grades with this illustrated quick-study guide.
Boost Your grades with this illustrated quick-study guide. You will use it from college to graduate school and beyond. Intended for everyone interested in Math and Science, particularly high school and undergraduate students.
Here are some key features of "Geometry Quick Study Guide (BlackBerry)":
· Clear and concise explanations
· Difficult concepts are explained in simple terms
· Illustrated with graphs and diagrams
· Search for the words or phrases |
Sample chapters for download
About the book
This aim of this Guide is to help students prepare for the Mathematical Studies
SL final examinations. The Guide has four distinct sections:
the first part covers Topics 2-8 in the course. Each topic begins with a
concise summary of key facts and concepts followed by a set of practice
questions. Each set of practice questions comprises at least 25 'short
questions' and 8 'long questions'.
the second part comprises five specimen examinations. Each examination is
divided into Paper 1 and Paper 2 questions. Each Paper 1 has 15 questions to be
completed within 90 minutes; each Paper 2 has 5 questions also to be completed
within 90 minutes.
the third part provides the fully worked solutions to all the practice
questions.
the fourth part provides a detailed marks scheme for each paper in the
specimen examinations.
Good examination techniques come from good examination preparation and
practice. We hope this Guide will help you succeed. |
Math
Math
Mathematics
Students are required to earn three math credits as part of their graduation requirements. The usual sequence of math courses for college-bound students, particularly those students with interests in science, mathematics, engineering, law, and medicine, is Algebra I, Geometry, Algebra II, Introductory Analysis, and Calculus. Exceptions to this order must be cleared by the administration. The minimal high school math sequence is Algebra I, Basic Geometry, and two of the Integrated Math courses. Algebra I, Basic Geometry, and Algebra II will fulfill the college entrance requirements for those students who are more interested in the humanities. Graphing or scientific calculators are required for some math courses. Calculators with QWERTY keyboard are not permitted.
Algebra I is a course in the language and methods of algebraic expressions and sentences and the first college-preparatory course in mathematics. Students will gain skill and precision in simplifying and solving equations and inequalities in one variable. Analysis of familiar situations and translation of their components to mathematical language is emphasized along with signed numbers, factoring, simplifying radical expressions, graphing on coordinate planes and solving systems of equations.
This course covers all of the topics in Algebra I – Modules A and B, but the course is taught over two semesters rather than one. There is special emphasis on hands-on learning and organizational skills.
This course covers all of the topics in Algebra I – Modules C and D, but the course is taught over two semesters rather than one. There is special emphasis on hands-on learning and organizational skills.
This course is designed for college-bound students. This course improves upon and extends the skills and concepts from Algebra I and stresses verbal precision and applications. The concept of function is introduced with emphasis on linear, quadratic, and logarithmic functions.
This course covers all of the topics taught in Algebra II, plus a thorough discussion and analysis of trigonometry. Graphing calculators are used to enhance the curriculum. This course moves more rapidly and is more challenging than regular Algebra II; it is designed for students planning a career in mathematics, engineering, physics, etc. Computer projects may be included.
Basic Geometry is a course for students who have a need or desire for more mathematics, but who do not require a rigorous approach as presented in regular geometry. This course presents all of the theorems and properties of plane geometry, but does not go into detailed presentation of each theorem or each proof.
This course is open to seniors only. Calculus is designed for students interested in mathematics, science and engineering. It covers a major part of the differential calculus. Applications will be stressed. Graphing calculators are used to enhance the curriculum. Computer projects may be included.
This course covers the topics of regular calculus, but also includes integral calculus. This course prepares students to take the Advanced Placement Exam for Calculus AB for which college credit may be awarded. Computer projects may be included.
Computer Science ½ credit Prerequisite: Algebra I
This course provides an introduction to fundamental computer concepts and elementary programming techniques. It involves the study of the programming language C++. The course is particularly valuable to students interested in engineering, science, research, and computer programming. The NCAA Clearinghouse will not count this course as a mathematics credit.
This is a course in traditional Euclidean geometry enhanced with some work with three dimensions, as well as integrating the uses of algebra in problem solving. The primary focus is on practicing and understanding deductive logic through proofs of theorems and exercises.
This course is designed and recommended for students who desire to reinforce and expand their knowledge of algebra fundamentals while working toward their graduation requirements in mathematics. Together with Integrated Math 211 reinforce and expand their knowledge of geometry fundamentals while working toward their graduation requirements in mathematics. Together with Integrated Math 111 work toward their graduation requirement in mathematics and already have mastered the competencies necessary for passing the Ohio Graduation Mathematics Test. It may serve as a stand-alone course or as a stepping-stone toward Algebra II.
This course is specifically designed for college-bound students. The course concepts include but are not limited to trigonometry, complex numbers, relation, functions, vectors, polar equations, conic sections and detailed use of graphing calculators to explore these concepts with deeper understanding.
This course is designed for students who have completed the study of trigonometry. It is a thorough course in the detailed study of all types of functions. Trigonometric ideas are used throughout the course. Computer projects may be included.
Probability and Statistics ½ Credit Prerequisite: Algebra I
This semester course emphasizes introductory statistics more than probability. Content includes proper sampling methods, methods for organizing data, calculation of measures of central tendency and measures of dispersion (variability), and finally how predictions can be made. Many areas of study in college require an introductory statistics course; this course would give students a strong base for entering a collegiate level statistics course. It is of particular interest to students who wish to learn to read and interpret statistical data. |
MULTIPLY your chances of understanding DISCRETE MATHEMATICS. If you're interested in learning the fundamentals of discrete mathematics but can't seem to get your brain to function, then here's your solution. Add this easy-to-follow guide to the equation and calculate how quickly you learn the essential concepts. Written by award-winningThe "Handbook of Typography for the Mathematical Sciences" explains how to use TeX, LaTeX and AMS TeX during the typesetting process so that readers can take a more active role in ensuring that their work is properly represented in print. more...
Here's the perfect self-teaching guide to help anyone master differential equations--... more...
This text explores the many transformations that the mathematical proof has undergone from its inception to its versatile, present-day use, considering the advent of high-speed computing machines. Though there are many truths to be discovered in this book, by the end it is clear that there is no formalized approach or standard method of discovery to...Introduces geometric measure theory through the notion of currents. This book provides background for the student and discusses techniques that are applicable to complex geometry, partial differential equations, harmonic analysis, differential geometry, and many other parts of mathematics. more... |
Mathematica is a feature-rich, high-level programming language which has historically been used by engineers. This book unpacks Mathematica for programmers, building insights into programming style via real world syntax, real world examples, and extensive parallels to other languages.
Starting from first principles, this book covers all of the foundational material needed to develop a clear understanding of the Mathematica language, with a practical emphasis on solving problems. Concrete examples throughout the text demonstrate how Mathematica language, can be used to solve problems in science, engineering, economics/finance, computational linguistics, geoscience, bioinformatics, and a range of other fields.
Modeling is practiced in engineering and all physical sciences. Many specialized texts exist - written at a high level - that cover this subject. However, students and even professionals often experience difficulties in setting up and solving even the simplest of models. This can be attributed to three difficulties: the proper choice of model, the absence of precise solutions, and the necessity to make suitable simplifying assumptions and approximations inspanidual or enterprise solutions
This textbook takes a broad yet thorough approach to mechanics, aimed at bridging the gap between classical analytic and modern differential geometric approaches to the subject. Developed by the author from 35 years of teaching experience, the presentation is designed to give students an overview of the many different models used through the history of the field—from Newton to Lagrange—while also painting a clear picture of the most modern developments.
Mathematica - a program designed to perform calculations for the preparation of interactive documents and programming. This tool is used in scientific research, engineering analysis and simulation for training in technical schools.
This book teaches how to use Mathematica to solve a wide variety of problems in mathematics and physics. It is based on the lecture notes of a course taught at the University of Illinois at Chicago to advanced undergrad and graduate students.
Mathematica is the tool of choice across the technical world for everything from simple calculations to large-scale computations, programming, or presenting. Throughout industry, government, and education, two million people - from students to Nobel Laureates - use Mathematica to achieve more. |
Physics: Fundamentals and Problem Solving for the iPad #physicsed #edtech
I'm thrilled to announce that Physics: Fundamentals and Problem Solving has been released for the iPad today. This book, which is for the iPad only, is an algebra-based physics book featuring hundreds of worked-out problems, video mini-lessons, and other interactive elements designed for the introductory physics student.
This entry was posted by admin on June 21, 2012 at 1:20 pm, and is filed under APlusPhysics. Follow any responses to this post through RSS 2.0.You can skip to the end and leave a response. Pinging is currently not allowed. |
(3) . . . gain knowledge and skills to formalize their ideas and express them with a full mathematical rigour.
Content:: (1) Systems of Linear Equations.
(2) Matrices.
(3) Determinants
(4) Vector Spaces
(5) Inner Product Spaces.
(6) Linear Transformations.
(7) Eigenvalues and Eigenvectors.
Course Philosophy and Procedure: Just keep this simple principle in mind:
If you are not enjoying this course, if the work is not fun, then something most be wrong. Talk to me right away! This course involves a lot of concepts that easily translate into fairly straightforward (but sometimes lengthy) calculations. Geometry, i.e., visualization is essential. There are also some topics that involve a greater level of abstraction yet there will be plenty of exercises available to check and enhance your understanding of those concepts.
You will find that the concepts learned in this course can be applied to many problems in Mathematics and Science.
You should plan to reserve a significant amount of time to study for this course. The material is easy, but the nature of the exercises is such that they are going to be time consuming. Being focused is of utmost importance. Don't rush in doing the problems!
Grading will consist of three exams (two during the semester and the
final exam) worth 100 points each. The homework and chapter projects will total to 200 points.
My grading scale is
A=90%, AB=87%, B=80%, BC=77%, C=70%, CD=67%, D=60%.
Final Exam: Thursday, May 11, 3:00 - 5:00.
Americans with Disability Act:: If you are a person with a disability and require any auxiliary aids, services or other accommodations for this class, please see me and Wayne Wojciechowski in Murphy Center Room 320 (796- 3085) within ten days to discuss your accommodation needs. |
Plane Algebraic Curves
Aims
The aim of the module is to introduce and study algebraic curves in the real plane, the complex plane and the complex projective plane. [Such curves are defined by a polynomial equation and the course involves an interplay between the geometry of the curves and the algebra of polynomials.]
Learning objectives
At the end of the module you should be familiar with and able to carry out operations related to curves in the complex affine plane and in the complex projective plane.
Syllabus
the construction of the projective plane defined by a field;
the curve in the affine plane corresponding to a polynomial in two variables;
the curve in the projective plane corresponding to a homogeneous polynomial; |
Mathematics in Education
FindGraph is a graphing, curve-fitting, and digitizing tool for engineers, scientists and business. Discover the model that best describes your data. FindGraph is a comprehensive graphing, curve fitting, and digitizing tool. FindGraph offers 12...
Easy CurveFit - A very easy tool to fit curve includes linear and nonlinear. Easy CurveFit - A very easy tool to fit curve includes linear and nonlinear. Easy CurveFit is a very easy tool to fit curve. Only three steps you should do, and...
Crocodile Mathematics is user-friendly mathematical modeling software for secondary school geometry and numeracy. Crocodile Mathematics is user-friendly mathematical modeling software for secondary school geometry and numeracy. Using this...
A powerful mathematical expressions editor. A powerful mathematical expressions editor. Formulator is aware of presentation and semantics face of mathematics, and so it allows not only to visually edit, but also to calculate simple Content MathML...
Description: This script provides a GUI-based approach to stopping and starting the Folding@home service for Intel Mac users who already have fah6 installed and configured correctly. Description: This script provides a GUI-based approach to...
An antenna design and electronics/electrical tool package. An antenna design and electronics/electrical tool package. It takes you step by step through the design of the following types of antennas:- Dipole- Fat Dipole- Yagi- J-Pole- Super J-Pole-...
A&G Grapher is a powerful graphing application that allows you to draw any 2D and 3D mathematical equation. A&G Grapher is a powerful graphing application that allows you to draw any 2D and 3D mathematical equation. It can be used by...
A problem analyzer is now available. A problem analyzer is now available. It generates an simple report with of statisics and information about the optimization problem and relevant warnings about the problem formulation are included. A solution...
Timez Attack is an educational game that kids can use to practice the multiplication tables. Timez Attack is an educational game that kids can use to practice the multiplication tables. You will help the character you have chosen (a male or...
This simple demo allows the user to experiment with a wide variety of 2-dimensional triangle groups. This simple demo allows the user to experiment with a wide variety of 2-dimensional triangle groups. In the process the users gains a direct...
Calclipse™ is a math tool written in Java™. Calclipse™ is a math tool written in Java™. Calclipse comprises a scripting framework containing a software library for evaluating mathematical expressions. The Calclipse...
Although a large number of tools for the three-dimensional visualization of molecular structures exists, it often proved convenient to tailor a visualization tool specifically for a certain purpose. Although a large number of tools for the...
Realzone Table is a simple and truly useful utility that will help you study, learn, and double-check your mathematical tables. Realzone Table is a simple and truly useful utility that will help you study, learn, and double-check your mathematical...
A native OSX application for viewing analog and digital simulation waveforms from VCD files as well as transaction level modeling (TLM) traces. A native OSX application for viewing analog and digital simulation waveforms from VCD files as well as...
A minimalistic tool for molecular phylogenetics able to recover phylogenies from nucleotide sequences. A minimalistic tool for molecular phylogenetics able to recover phylogenies from nucleotide sequences. PhyloCoco uses the likelihood or the...
An antenna analysis program. An antenna analysis program. Any type of antenna may be analyzed. The physical design of the antenna is entered (such as the lengths of wires and elements). For a given frequency, the feedpoint impedance is calculated,...
POLYMATH Educational is a computational system that has been created for educational or professional purpose. POLYMATH Educational is a computational system that has been created for educational or professional purpose. Polymath Educational...
Bell Curve is a very useful and small windows application wich serves to help senior students to understand the curve mechanism and introduce them to the Normal Curve. Bell Curve is a very useful and small windows application wich serves to help...
This is a product which can be found most useful by scientists, engineers, professors, and students. This is a product which can be found most useful by scientists, engineers, professors, and students. This calculator follows classical approach...
Partial Derivatives is a simple program that finds approximate numerical values for the 1st and 2nd order partial derivatives of a function at a given point. Partial Derivatives is a simple program that finds approximate numerical values for the... |
Math trainer soft/freeware
Hey, does anyone knwo of a program that can train you in different basic fields of mathematics, and preferrably keep track of performance statistics, so pin-pointing individual weaknesses would be easier?
I would find this kind of a program very useful and more motivating than simply going through problems in books. |
PARKSIDE HIGH SCHOOL MATHEMATICS DEPARTMENT
PARKSIDE HIGH SCHOOL MATHEMATICS DEPARTMENT
Course Title: MAT1L
Course Description:
This course emphasizes further development of mathematical knowledge and skills to prepare students
for success in their everyday lives, in the workplace, and in the Grade 11 workplace course.
This course is organized in 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 skills,
and to continue developing their skills in reading, writing, and oral language through relevant and
practical math activities.
Course Level: Level 1 MAT2L
Course Description:
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 Grade 11 Mathematics Workplace
Preparation course.
This course is organized in three strands related to money sense, measurement, and proportional
reasoning. In all strands, the focus is on strengthening and extending key foundational mathematical
concepts and skills by solving authentic, everyday problems.
Students have opportunities to extend their mathematical literacy and problem solving skills, and to
continue developing their skills in reading, writing, and oral language through relevant and practical math
activities.
Course Level: Level 23E
Course Description:
This course enables students to broaden their understanding of mathematics as it applies in the
workplace and daily life. Students will solve problems associated with earning money, paying taxes, and
making purchases; apply calculations of simple and compound interest in saving, investing, and
borrowing; and calculate the costs of transportation and travel in a variety of situations. Students will
consolidate their mathematical skills as they solve problems and communicate their thinking.
Course Level: Level 34E
Course Description:
This course enables students to broaden their understanding of mathematics as it is applied in important
areas of daily living. Students will use statistics in investigating questions of interest and apply principles
of probability in familiar situations. The students will also investigate accommodation costs and create
household budgets; solve problems involving estimation and measurement.
Course Level: Level 41P
Course Description:
This course enables students to develop an 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 relations, and will determine the connections between the
representations. They will also explore certain relationships that emerge from the measurement of three-
dimensional figures and two-dimensional shapes. Students will consolidate their mathematical skills as
they solve problems and communicate their thinking.
Course Level: Level 1 70% EQAO: 10% Culminating Activity & Final Exam:2P
Course Description:
This course enables students to consolidate their understanding of linear relations 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 relations. Students will investigate
similar triangles, the trigonometry of right triangles, and the measurement of three-dimensional figures.
Students will consolidate their mathematical skills as they solve problems and communicate their
thinking.
Course Level: Level 2 MBF3C
Course Description:
This course enables students to broaden their understanding of mathematics as a problem-solving in the
real world. Students will extend their understanding of quadratic relations; investigate situations
involving exponential growth; solve problems involving compound interest; solve financial problems
connected with vehicle ownership; develop their ability to reason by collecting, analysing, and evaluating
data involving one variable; connect probability and statistics; and solve problems in geometry and
trigonometry. Students will consolidate their mathematical skills as they solve problems and
communicate their thinking.
Course Level: Level 3 MAP4C
Course Description:
This course enables students to broaden their understanding of real-world applications of mathematics.
Students will analyse data using statistical methods; solve problems involving application of geometry
and trigonometry; solve financial problems connected with annuities, budgets, and renting or owning
accommodations; 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, human services, and for certain skilled trades.
Course Level: Level 41D
Course Description:
This course enables students to develop an understanding of mathematical concepts related to algebra,
analytic geometry, and measurement and geometry through investigation, 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 linear
relation. They will also explore relationships that emerge from the measurement of three-dimensional
figures and two-dimensional shapes. Students will reason mathematically and communicate their
thinking as they solve multi-step problems.
Course Level: Level 1 EQAO: worth 10% Final Exam: worth2D
Course Description:
This course enables students to broaden their understanding of relationships and extend their problem-
solving algebraic skills through investigation, effective use of technology and abstract reasoning. Students
will explore quadratic relations 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 and communicate their thinking as they solve multi-step problems.
Course Level: Level 2F3M
Course Description:
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
real-world situations. Students will represent functions numerically, graphically, and algebraically; simply
expressions; solve equations; and solve problems relating to applications. Students will reason
mathematically and communicate their thinking as they solve multi-step problems.
Course Level: Level 3, University/CollegeCR3U
Course Description:
This course introduces the mathematical concept of the function by extending students' experiences with
linear and quadratic relations. Students will investigate properties of discrete and continuous functions,
including trigonometric and exponential functions; represent the functions numerically, algebraically, and
graphically; solve problems involving applications of functions; investigate inverse functions; and develop
facility in determining equivalent algebraic expressions. Students will reason mathematically and
communicate their thinking as they solve multi-step problems.
Course Level: Level 3 MDM4U
Course Description:
This course broadens students' understanding of mathematics as it relates to managing data. Students
will apply methods for organizing and analysing large amounts of information; solve problems involving
probability and statistics; and carry out a culminating investigation that integrates statistical concepts and
skills. Students will also refine their use of mathematical processes necessary for success in senior
mathematics. Students planning to enter university programs in business, social sciences, and the
humanities will find this course of particular interest.
Course Level: Level 4, University Preparation
Course Evaluation:
(a) Regular tests or assignments based on work done to date Project: 15% Final Exam: worth 15 MHF4U
Course Description:
This course extends students' experience with functions. Students will investigate the properties of
polynomial, rational, logarithmic, and trigonometric functions; develop techniques for combining
functions; broaden their understanding of rates of change; and develop facility in applying these concepts
and skills. Students will also refine their use of their use of the mathematical processes necessary for
success in senior mathematics. This course is intended both for students taking the Calculus and Vectors
course as a prerequisite for university program and for those wishing to consolidate their understanding
of mathematics before proceeding to any one of a variety of university programsV4U
Course Description:
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, sinusoidal, exponential, rational, and radical
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 choose to pursue careers in fields such as science, engineering,
economics, and some areas of business, including those students who will be required to take a university
level calculus, linear algebra, or physics course |
What is WeBWorK ?
WeBWorK is an open-source web based homework system for math and sciences courses. WeBWorK is supported by the MAA (Mathematical association of America) and the NSA (National Science Foundation) and comes with a NPL (National Problem Library) of over 20,000 homework problems. Webwork can be used for college algebra, discrete mathematics, probability and statistics, single and multivariable calculus, differential equations, linear algebra and complex analysis. |
Homeschool Features
Learn Algebra naturally
Believe it or not, Algebra isn't just about solving meaningless problems that aren't related to anything; it's about asking interesting questions and exploring new ideas. And, with a unique pedagogical approach, this online algebra book will help you to see mathematics as a connected set of ideas, each flowing into the next. To achieve this, we begin each chapter with a question related to the real world — a question that we can only answer after developing some new mathematical tools. Throughout the chapter you explore the question and see where it leads you, highlighting connections along the way. Never again will you think of algebra as being a hodgepodge of random rules and formulas without any meaningful context!
Currently we're "beta testing" the site, meaning that you can sign up and have full access for FREE. Once the beta period is over, we'll let you know and you'll have the opportunity to become a member for just $30. This one-time fee would give you unlimited access to the homework system and your personalized book |
Welcome
Welcome to CPM Educational Program,
an educational non-profit organization dedicated to improving grades 6-12 mathematics instruction. CPM offers professional development and curriculum materials. We invite you to learn more about the CPM mathematics program by clicking the "Learn about CPM" link at left. The other sections offer support materials for teachers, parents and students.
Headlines
CPM to offer Integrated I-III
CPM will develop an Integrated series based on the Appendix A pathway. Click here for full details.
Middle School acceleration pathways now available
The timelines, pacing guides and tables of contents for acceleration to take algebra in 8th grade are now available here.
CPM offers regional conferences for Summer 2013
CPM releases Common Core series, Core Connections
Click on "Learn About CPM" at left to see tables of contents and sample chapters.
For an eBook preview, click here.
News
New curriculum and technical support available
Three CPM mentor teachers are now available to help parents, students and teachers who have questions about the CPM program. This support is primarily for questions about using the program, its technology and the website. To use CPM's support service, go to to see the available services. Follow the prompts to get help. Note that this service is not a "homework helpline." That support is at
CPM now offers a new series of textbooks to meet the grade 6-8 and high school CCSS content and practice standards: Core Connections, Courses 1 - 3 and Core Connections Algebra 1 & 2 and Geometry. Learn how this series as well as the original Connections series of CPM textbooks are fully aligned with the CCSS Content and Mathematical Practice Standards. CPM can also provide professional development centered around embedding the eight CCSS Mathematical Practices into your current lessons and current textbook from any publisher. Start moving on the path to the CCSS today!
Parent e-book licenses are now available!
Parents may purchase a one-year e-book license of their student's book for $10 by calling CPM and using a credit card. See order form for a complete list of available one-year licenses. Contact CPM at (209) 745-2055.
Sample Problem
Core Connections Geometry : 3-35.
GEORGE WASHINGTON'S NOSE
On her way to visit Horace Mann University, Casey stopped by Mount Rushmore in South Dakota. The park ranger gave a talk that described the history of the monument and provided some interesting facts. Casey could
not believe that the carving of George Washington's face is 60 feet tall from his chin to the top of his head!
However, when a tourist asked about the length of Washington's nose, the ranger was stumped! Casey came to her rescue by measuring, calculating and getting an answer. How did Casey get an answer?
Your Task: Figure out the length of George Washington's nose on the monument. Work with your team to come up with a strategy. Show all measurements and calculations on your paper with clear labels so anyone could understand your work.
DISCUSSION POINTS
What is this question asking you to find?
How can you use similarity to solve this problem?
Is there something in this room that you can use to compare to the monument?
What parts do you need to compare?
Do you have any math tools that can help you gather information? |
FL Students
Course Name:
Liberal Arts Mathematics
Course Code:
1208300
Honors Course Code:
AP Course Code:
Description:
The total weight of two beluga whales and three orca whales is 36,000 pounds. The weight of each whale could be determined with just one additional fact. The Liberal Arts Math course provides all the math tools needed to answer this weighty question. The setting for this course is an amusement park with animals, rides, and games. The students' job is to apply what they learn to dozens of real-world scenarios. .
Equations, geometric relationships, and statistical probabilities can sometimes be dull, but not in this class! The park guide (teacher) takes each student on a grand tour of problems and puzzles that show how things work and how mathematics provides valuable tools for everyday living.
Students should come ready to reinforce and grow their existing algebra and geometry skills to learn complex algebraic and geometric concepts they will need needed for further study of mathematics.
Note: This course does not meet the academic core requirement for math for entry into the State University System of Florida or eligibility requirements for some Bright Futures Scholarships.
Access the site link below to view |
News
Key Stage 5 Mathematics
Why choose Mathematics A/AS Level?
'The highest form of pure thought is in mathematics.' (Plato)
Mathematics A Level will help your understanding of mathematics and mathematical processes. It can make sense of 'real world' problems and help develop your ability to analyse and refine a model that describes a real life situation. It can boost your confidence and self-esteem and give you great satisfaction when you crack a problem. Mathematics can help you communicate effectively, both with written work and through discussing concepts with others. You can acquire new IT skills through the use of graphical calculators and graphing computer packages. But perhaps most importantly, you will study an enjoyable and rewarding subject that is both relevant and useful to your life and your future career.
Your modules
Post 16 Mathematics is divided into two parts: Core and Applied.
Core Maths, to some extent, builds on topics covered in GCSE Maths including geometry with co-ordinates, sequences, trigonometry and vectors. It also introduces the new topic of calculus, which involves gradients of curves and areas under curves.
Applied Maths is divided into two areas: Statistics and Mechanics. Statistics is the study of the use of data, how to set up appropriate models for sets of data, estimating values in a population by using a sample and probability. Mechanics is the study of forces and of movement.
On your marks...
Year 12
Raw Score Max Mark
UMS
Examination
Core 1
75
100
1.5hr Non-Calc
Core 2
75
100
1.5hr Calc
Statistics 1
75
100
1.5hr Calc
Year 13
Core 3
75
100
1.5hr Calc
Core 4
75
100
1.5hr Calc
Mechanics 1
75
100
1.5hr Calc
To Put this in Perspective... overall in your A Level if you achieve an A overall and you average 90% in your A2 modules.
We follow the Edexcel ( scheme of learning. Click on the following link to access more information on the scheme of learning, formula booklet and support materials:
Who takes this course?
What skills will I learn?
All sorts of skills, relevant to your life and the other subjects that you study:
Logical reasoning
You will be able to tackle problems mathematically and analyse and refine models that you produce
Communication skills, both through written and oral explanations
IT skills will improve as you use computer software and graphical calculators
Increased responsibility for your own learning and gain a deeper understanding of mathematical problems.
What could this lead to in the future?
Mathematics is one of those subjects that can fit in with many things you may want to do in the future. It is especially vital if you want to study a Mathematics, Physics, Chemistry or Engineering based course at Higher Education.
How will this fit into my life?
Students who take Mathematics often also study from a wide range of subjects such as Geography, Biology and Business Studies and allows you to gain a non-arts/humanities qualification.
What do I do now?
Talk to your Mathematics teacher and get some advice as to whether the course could be right for you. Making an appointment to see your school careers advisor is also a good idea. |
Fall 2007
Text :An Introduction to Optimization, 2rd
Edition, by Chong and Zak
Overview:Optimization is the process of finding the maximum or minimum value of
a function.In both Calculus 9A and
Multivariable Calculus 10A, you have already had a brief introduction to
optimizing one variable and multivariable functions.The tools at hand were first and second
derivatives.In this course we will
review the skills you learned in multivariable calculus using the language of
linear algebra.Then we will forge ahead
and learn about linear programming and the simplex method for maximizing linear
functions on polyhedra.Knowing and being comfortable with linear
algebra is a must in this course.
Course
Meetings: The course lectures will be held in Sproul Hall 2340 on Mondays, Wednesdays and Fridays at
11:10 am-12 pm.Discussion sessions will
be held on Thursday (7:10 am) with Jenn Burke (003)
or (7:40 am) with Tiff Troutman (002).You are expected to attend both the lectures and the discussion sessions
as per Math Department decree.
Tips
for Success: * Come to class!It is amazing how much you can learn by being
attentive in class. * Collaborative learning is encouraged but remember only YOU will be taking the quizzes and exams...
* Like all mathematics, Optimization is not a spectator sport; you will
learn only by doing! You will find that a consistent effort will be
rewarded. * Be organized. Have a notebook or binder for Linear Algebra
alone to keep your class notes, homework, quizzes and exams in order.
* No question you have should be left unanswered. Ask your questions in
class, discussion session or take advantage of office hours.
Homework (100 points): Homework will be assigned every Wednesday and will be collected during
the next week's discussion session.No late homework will be accepted.Homework will not be graded
unless it is written in order and labeled appropriately.An answer alone will get 0 points.Make sure to justify every answer.Your lowest homework score will be dropped
and the remaining homework will be averaged to get a score out of 100.
Quizzes (100 points): At least once every week there will be a short quiz given at the
beginning of each lecture testing you on the definitions and theory that you
learned from last class.You may use
your notes.Quizzes will only last 5
minutes so make sure that your notes are organized and that you arrive on time
for class.There may also be a quiz at
the end of discussion with one problem similar to the homework problems
assigned during the previous week.You
may not use your notes for this quiz.The in class quizzes will be worth 3 points each, the lowest three will
be dropped and the remaining will be averaged to obtain a score out of 50
points.The discussion quizzes will be
worth 10 points each, there will be at least 6, and I will keep only the top 5
scores for a total of 50 points.
Exams
(300 points): I will give one midterm (100 points) and a
final (200 points). Please bring your ID to each exam.There are no make up exams. If a test is missed, notify me as soon as possibleon
the day of the exam. For the midterms only, if you
have a legitimate and documented excuse, your grade will be
recalculated without that test.The
Midterm is tentatively scheduled on Friday, October 26.The Final is on Wednesday, December 13, from
8-11 am.
Grades:
General guidelines for letter grades
(subject to change; but they won't get any more strict): 90-100% - A; 80-89% -
B; 70-79% - C; 60-69% - D; below 60% - F. In assigning Final Grades for
the course, I will compare your grade on all course work (including the Final)and your grade on
the Final Exam.You will receive the
better of the two grades.
Calculator
Policy: It is the Math Department's policy to forbid the use of
calculators on both exams and quizzes. |
The Second Edition of this popular textbook provides a highly accessible introduction to the numerical solution of linear algebraic problems. Readers gain a solid theoretical foundation for all the methods discussed in the text and learn to write FORTRAN90 and MATLAB(r) programs to solve problems. This new edition is enhanced with new material and pedagogical tools, reflecting the author's hands-on teaching experience, including:
A new chapter covering modern supercomputing and parallel programming
Fifty percent more examples and exercises that help clarify theory and demonstrate real-world applications
MATLAB(r) versions of all the FORTRAN90 programs
An appendix with answers to selected problems
The book starts with basic definitions and results from linear algebra that are used as a foundation for later chapters. The following four chapters present and analyze direct and iterative methods for the solution of linear systems of equations, linear least-squares problems, linear eigenvalue problems, and linear programming problems. Next, a chapter is devoted to the fast Fourier transform, a topic not often covered by comparable texts. The final chapter features a practical introduction to writing computational linear algebra software to run on today's vector and parallel supercomputers.
Highlighted are double-precision FORTRAN90 subroutines that solve the problems presented in the text. The subroutines are carefully documented and readable, allowing students to follow the program logic from start to finish. MATLAB(r) versions of the codes are listed in an appendix. Machine-readable copies of the FORTRAN90 and MATLAB(r) codes can be downloaded from the text's accompanying Web site.
With its clear style and emphasis on problem solving, this is a superior textbook for upper-level undergraduates and graduate students.
Details
ISBN: 9780471742135
Publisher: John Wiley & Sons, Ltd.
Imprint: Wiley-Interscience
Date: Sept 2005
Creators
Author: Granville Sewell
Reviews
"This robust text is well worth an evaluation for anyone interested in teaching such topics. If this book or a subset of its content were used, students would undoubtedly benefit from the tutelage it offers." - SIAM Review, Vol 50, Issue 4, 2008 |
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. |
Problem Solving
9780759342644
0759342644
Summary: Problem Solving provides students with a general approach and strategies to solve problems in real life. The text is easy to read and geared mainly for students who dislike math. Problems throughout the book range from easy to difficult, and require minimal mathematical experience. While possessing knowledge is one important requirement to solving problems, there are many others. Problem Solving focuses on providing ...strategies to help students become proactive, successful, and confident problem solversProblem Solving provides students with a general approach and strategies to solve problems in real life. The text is easy to read and geared mainly for students who dislike m [more]
Problem Solving provides students with a general approach and strategies to solve problems in real life. The text is easy to read and geared mainly for students who dislike math. Problems throughout the book range from easy to difficult, and require |
What can you do to help students learn the advanced math that is required in so much of today's industries and technologies? What helpful insights come from cognitive science, comparative anthropology, and educational psychology? |
Newton's Method
To use this method
to approximate a solution to an equation, first put your equation in
the form
.
Understand how to
visualize Newton's Method iterations geometrically.
Realize that on
some problems the choice of your initial "guess" is critical.
Keep lots of
digits in your intermediate results!
Newton's Method
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture. |
Welcome
Looking ahead to the fall, here are
some skills that you will need to master in order to be successful
in your math courses this year. These review packets reflect review
work from previous years, and it is expected that you can solve
these problems accurately and with proficiency. If you find some
areas more challenging than others, please invest the time to review
thoroughly and explore additional resources to help you prepare. We
look forward to working with you!
The Math Department at Tappan Zee High School seeks to inspire
and empower students to become diligent problem solvers, critical
thinkers, and responsible learners. Our curriculum is designed to
challenge students to master algebraic, geometric, and trigonometric
skills and apply this knowledge to real world situations and higher
level mathematics. Our Faculty strives to prepare students to
become independent thinkers by encouraging creativity, by teaching
students to read, write, and think using the language of mathematics,
and by nurturing each student to rise to meet their individual goals.
Area of Focus
Classroom Behavior Expectation
Respect for oneself and one's classmates as well as adult staff should be
the priority classroom rule. Participation in activities with respect for
answering and asking questions in appropriate classroom fashion should be
demonstrated on a daily basis.
Appropriate classroom protocol is to be reinforced and immediate intervention
and consequences should result. Expectations upon arrival to class will
include a "Do Now" question for the students to answer. In addition notebooks
and all learning tools should be accessible. The notes for the day and the
homework assignment should be readily accessible for the teachers view. When
the student follows the correct protocol the student will attain positive points
for his/her class participation grade.
Homework Policy
Homework is given on a daily basis and is reviewed by the teacher or adult staff
member in the classroom. The homework should be completed in the same fashion the
regents exams are credited, which includes complete work shown. Just recording
answers is inappropriate and unacceptable. If a student is absent, a legitimate
readmit will be necessary to credit the homework assignments as well as the option
to take a "make up test or examination".
Attendance/Absence Policy
School Policy regarding lateness to class and absence from class will apply to all
math classes. The consequences will have an effect on the students overall class grade.
When a legal lateness or absence is shown the student will have a three (3) day period
to make up the assignments and/or test missed during their absence. If the student is
not excused the three (3) day make up policy does not go into effect. Students are also
encouraged to get telephone numbers from classmates and to have their texts available
at home to complete assignments.
Grading Policy
Grades in the math department are made up of test, homework, class participation, projects and problem sets. |
Mathematics Knowledge Study Guide for McGraw-Hill's ASVAB
The ASVAB Mathematics Knowledge test measures your ability to solve problems using concepts taught in high school math courses. These concepts include various topics in algebra, probability, and geometry. You'll need to know about solving equations, setting up ratios and proportions, graphing on a coordinate plane, determining the probability of a given event, identifying plane and solid geometric figures, and calculating perimeter, area, and volume.
It is important that you do well on the Mathematics Knowledge test because it is one of the four ASVAB tests that are used to calculate the AFQT—your military entrance score. That's why it pays to spend time reviewing topics in algebra, probability, and geometry and tackling plenty of sample ASVAB Mathematics Knowledge questions.
The following pages offer a quick but important overview of the basic algebra and probability that you need to know if you are to score well on the ASVAB. Make sure that you carefully review and test yourself on every topic covered in this section. Also make sure that you learn how to use all of the problem-solving methods presented in the examples. Chapter 13 will provide a similar review of basic concepts and problem-solving methods in geometry. If you master the core information presented in these two chapters, you will be able to answer ASVAB Mathematics Knowledge questions with relative ease. |
Environmental mathematics seeks to marry the most pressing challenge of our time with the most powerful technology of our time - mathematics. This book does this at an elementary level and demonstrates a wide variety of significant environmental applications that can be explored without resorting to calculus. Environmental mathematics in the classroom includes several chapters accessible enough to be a text in a general education course, or to enrich an elementary algebra course. Ground-level ozone, pollution and water use, preservation of whales, mathematical economics, the movement of clouds over a mountain range, at least one population model and a smorgasbord of 'newspaper mathematics' can be studied at this level and would form a stimulating course. It would prepare future teachers not only to learn basic mathematics, but to understand how they can integrate it into other topics that will intrigue students [via] |
Welcome to Algebra 1! Every student in the state is required to take this course in order to graduate from high school. We will cover all basic algebra topics: data analysis, solving equations, graphing lines, simplifying expressions, and exponents. These topics will be applied to real-world situations. I look forward to working with each one of you! |
Discrete Mathematics
The widespread use of computers and the rapid growth in computer science have led to a new emphasis on discrete mathematics, a discipline which deals with calculations involving a finite number of steps. This book provides a well-structured introduction to discrete mathematics, taking a self-contained approach that requires no ancillary knowledge of mathematics, avoids unnecessary abstraction, and incorporates a wide rage of topics, including graph theory, combinatorics, number theory, coding theory, combinatorial optimization, and abstract algebra.
Amply illustrated with examples and exercises.
show more show less
Numbers And Counting
Integers
Functions and counting
Principles of counting
Subsets and designs
Partition, classification, and distribution
Modular arithmetic
Graphs And Algorithms
Algorithms and their efficiency
Graphs
Trees, sorting, and searching
Bipartite graphs and matching problems
Digraphs, networks, and flows
Recursive techniques
Algebraic Methods
Groups
Groups of permutations
Rings, fields, and polynomials
Finite fields and some applications
Error-correcting codes
Generating functions
Partitions of a positive integer
Symmetry and counting
Table of Contents provided by Publisher. All Rights Reserved.
List price:
$32.50
Edition:
1985
Publisher:
Oxford University Press, Incorporated
Binding:
Trade Cloth
Pages:
400
Size:
6.38" wide x 9.50" long x 1.31" tall
Weight:
2.07 |
I'm so glad I found this group!! Today I was helping my little brother with his math homework (a.k.a. I was doing it for him) and when we were done I was so disappointed. I wanted to do more! And I'm not being challenged enough in my math class at school :(
(I'm in 8th grade, but I take 9th grade advanced math. It's still too easy! I think it's a problem with the teacher.)
I learned slope-intercept first... and then they taught me point slope and I haven't really gone back to thinking of it as slope-intercept when I use that at the origin. I wonder if it's better to start with specific cases and then generalize or to learn the general method and then apply it in specific cases...
Hi! I'm more of an applied math person myself and I like differential equations more than I like discrete (though number theory was fun). That said, analysis was one of my favorite classes last semester!
I can access JSTOR, but only at work and I don't go back there until Monday. I'm really sorry. :¬( Feel free to contact me, though, if I can help in the future. (That goes for everyone, not just Lexie.) |
Algebra
There are 366 different Starters of The Day, many to
choose from. You will find in the left column below some starters on the topic of AlgebraStudents begin their study of algebra by investigating number patterns. Later they construct and express in symbolic form and use simple formulae involving one or two operations. They use brackets and apply algebra to real word problems.
Do you have any comments? It is always useful to receive
feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world.
Click here to enter your comments. |
Matt's Tutoring Blog very beginning -- the diagnostic test, of all things! -- of... Introduction (page 23) to Manhattan's Strategy Guides for the...
The most lasting way to improve your vocabulary is to learn new words (1) in context (by looking up unknown words when you read and keeping a journal of their definitions) and (2) in thematic groups -- NOT by memorizing huge lists of unrelated words. These are some of the resources I use with my students; feel free to comment to add your own favorite vocabulary book!
Most students taking the SAT, GRE, or GMAT know their algebra fairly well, but many find they can't complete all the problems in the allowed time. Why? It's NOT because those students are just naturally slow: it's because they're doing more work than they need to! It's not their speed but their very approach --- the very way they conceive of the process of problem-solving --- that's flawed. To ace the math sections of standardized tests, you have to learn how to attack problems in new ways so that you get the right answers by doing as little work as possible! (Part of the reason so many students...
Many first-year calculus students fall into a common trap: they tend to make bad assumptions about how functions behave. In particular, they tend to think all functions are "nice," in the sense of easy to draw and understand -- because most of the pictures their teachers draw in school to illustrate examples tend to be of nice, familiar functions they are comfortable working with, like polynomials. But functions, in general, are extremely unwieldy, and to truly master differential calculus, you have to learn to be on guard against making simplifying assumptions: what we often imagine to be the...
Of the vast amount of math taught in high school, combinatorics is usually the most baffling for students. In my ten years of teaching, I've never had a student who felt totally confident about counting problems -- I myself didn't feel I really understood them until I went to college! -- and the most typical reaction to them is immediate fear or frustration: students often give up as soon as they see one, before they even attempt a solution. Why? Probably because many high school math teachers don't do a good job of explaining the basic concepts with concrete examples; instead, they often present...
Many of my students preparing for the SAT, GRE, and GMAT have decent algebraic intuition when it comes to EQUATIONS, but most are much weaker when it comes to INEQUALITIES.
On the one hand, this is entirely natural: inequalities capture less information than equations -- they establish merely a relation between two quantities, rather than their equivalence -- so they are inherently trickier to think about. But on the other hand, it's crucial to have a very solid grasp of how inequalities work to do well on the SAT, GRE, and especially the GMAT (which tends to love data sufficiency questions...
Many of my students preparing for the GRE or GMAT have decent algebraic skills, but most have trouble with statistical reasoning --- for a variety of reasons. Some have never had statistics; others have been away from it for years. In either case, it's crucial to get up to speed on the basics!
To get a sense of how prepared you are for some of the more challenging statistics questions on the GRE and GMAT, check out the following worksheet I've developed. When you work with me, you'll gain exactly the skills you need to ace these and similar problems --- you'll learn to complete this entire...
Matt L.
Matt L.
passed a background check on
2/20/2013. You may run an updated background check on
Matt
once you send an email. |
Book details
Book description
The books in this bite-sized new series contain no complicated
techniques or tricky materials, making them ideal for the busy, the
time-pressured or the merely curious. Mathematics Made Easy is a short,
simple and to-the-point guide to mathematics. In just 96 pages, the
reader will learn all the basics, from addition and subtraction to
fractions and decimals. Ideal for the busy, the time-pressured or the
merely curious, Mathematics Made Easy is a quick, no-effort way to break
into this fascinating topic. Alan Graham has lectured in Mathematics
Education at the Open University for over 30 years. His particular
interest is statistics and he has written a number of books and OU
course units in this field. He is also the author of Teach Yourself
Basic Mathematics. |
Course Description: An investigation of topics, including the history of mathematics, number systems, geometry, logic, probability, and statistics. There is an emphasis throughout on problem solving. Recommended for general education requirements, B.S. degree.
(a) ... understand culture as an evolving set of world views with diverse historical roots that provides a framework for guiding, expressing, and interpreting human behavior.
(b) ... demonstrate knowledge of the signs and symbols of another culture.
(c) ... participate in activity that broadens their customary way of thinking.
Aesthetic Skills: The students will ...
(a) ... develop an aesthetic sensitivity.
It is also worth mentioning the NCTM (National Council of Teachers of Mathematics) "standards" for mathematics education, because they are also a list of some overall goals we strive for in this course:
The students shall develop an appreciation of mathematics, its history and its applications.
The students shall become confident in their own ability to do mathematics.
(c) ... explore linear and exponential growth functions, including the use of logarithms, and be able to compare these two growth models.
(d) ... explore a few major concepts of Euclidean Geometry, focusing especially on the axiomatic-deductive nature of this mathematical system.
(e) ... develop an ability to use deductive reasoning, in the context of the rules of logic and syllogisms.
(f) ... explore the basics of probability.
(g) ... learn descriptive statistics, including making the connection between probability and the normal distribution table.
(h) ... learn the basics of financial mathematics, including working with the formulas for compound interest, annuities, and loan amortizations.
(i) ... solve a variety of problems throughout the course which will require the application of several topics addressed during the course.
Communication Skills: The students will ...
(a) ... write a mathematical autobiography.
(b) ... collect a portfolio of their work during the course and write a reflection paper.
(c) ... do group work (labs and practice exams), involving both written and oral communication.
(d) ... turn in written solutions to occasional problems.
Life Value Skills: The students will ...
(a) ... develop an appreciation for the intellectual honesty of deductive reasoning.
(b) ... understand the need to do one's own work, to honestly challenge oneself to master the material.
Cultural Skills: The students will ...
(a) ... explore a number of different numeration systems used by other cultures, such as the early Egyptian and the Mayan peoples.
(b) ... develop an appreciation for the work of the Arab and Asian cultures in developing algebra during the European "Dark Ages".
(c) ... explore the contribution of the Greeks, especially in the areas of Logic and Geometry.
Aesthetic Skills: The students will ...
(a) ... develop an appreciation for the austere intellectual beauty of deductive reasoning.
(b) ... develop an appreciation for mathematical eleganceThere will be a few assignments not generally included in a mathematics course, but which will, I hope, make your experience in this class more well-rounded than in a typical algebra course. These include the following:
MATHEMATICAL AUTOBIOGRAPHY: Due: Monday, September 16 87% or more, "B" = 80% or more, "BC" = 77% or more, "C" = 70% or more, "CD" = 67% or more, and "D" = 60% or more. We will probably end up with about 800 possible points. My advice is simple: if you wish to earn a decent grade, make sure that you keep up with your work and that you turn in ALL the papers which are to be graded. I find that the surest way to receive less than a "C" is to make sure you miss some classes and fail to turn in all your work!
ATTENDANCE POLICIES: Attendance is important in this class. There is really never a "good day" to miss because we will either be covering new material or working in groups on some problems. I will not formally reduce your grade for poor attendance, but I will take attendance throughout the course so that I can apply the 2-day rule when we take those practice exams (see above). I can also tell you that poor attendance is one of the best ways to hurt you overall chances of success - third floor, Murphy Center. The book publisher, Prentice-Hall, has provided a set of CDs that contain lectures for each chapter in the text, covering the main key ideas in that chapter. I will put this set of CDs on reserve in the library; you might want to consider watching some of these lectures, especially if you are having trouble with some material. These CDs should run in the CD-drive of any computer.
I also want you to consider coming to see me if you have a problem with some material. Sometimes we can resolve in a few minutes a difficulty that can cause problems for weeks. I don't resent your coming – it's part of my job! I want your success as much as you do.
BLACKBOARD: I'm not sure how much I will be using "Blackboard" but I will enter you into the system and it will give us a resource, at least for web sites that might be interesting and useful group-mates. Please feel free to come to my office to discuss problems you might be having. Please feel free to go visit the learning center for tutoring help if necessary |
Number
The students will develop an algebraic expression from geometric representations and ultimately graph quadratic equations with understanding. The students will also develop a better understanding of algebraic expressions by comparing with geometric, tabular, and graphical representationsThis lesson unit is intended to help teachers assess how well students are able to solve quadratics in one variable. In particular, the lesson will help teachers identify and help students who have the following difficulties: making sense of a real life situation and deciding on the math to apply to the problem; solving quadratic equations by taking square roots, completing the square, using the quadratic formula, and factoring; and interpreting results in the context of a real life situation. |
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
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Chemistry 112B: Organic Chemistry Winter 2008 Professor Rebecca Braslau Assigned Homework Problems The following problems are required, and must be turned in. Problems are to b e done without looking at the answers as much as possible, then corrected
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Overview
Working through the practice problems in this book and then consulting the detailed solutions will help you understand not only what the correct answer is, but why it is correct and the most efficient way to arrive at the answer.
More About
This Book
Overview
Working through the practice problems in this book and then consulting the detailed solutions will help you understand not only what the correct answer is, but why it is correct and the most efficient way to arrive at the |
Encyclopedia of Mathematics & Society
Published by Salem Press
Presents articles showing the math behind our daily lives. Explains how and why math works, and allows readers to better understand how disciplines such as algebra, geometry, calculus, and others affect what we do every day |
This applet encompasses five different applets on different topics and at different levels. (The user can access each topic via Course Activity tab.) The first activity consists of a simple function grapher that graphs a pre-defined function from a large collection of functions and two user-defined functions. (Very easy zoom-in and zoom-out functionality that can be used to illustrate local linearity.) The second activity provides an interactive illustration of the Mean Value Theorem. The third part shows the Newton's method in action. The fourth activity shows Riemann sums and several numerical integration methods, including the midpoint and the trapezoid rules. Finally, the last activity demonstrates the definite integral in terms of areas. All activities are interactive: the user chooses a function, an interval, a starting point, the number of divisions, etc. depending on the activity. |
Binomial Expansion
Introduction and Summary
This chapter deals with binomial expansion; that is, with writing expressions of
the form
(a + b)n
as the sum of several monomials.
Prior to the discussion of binomial expansion, this chapter will present
Pascal's Triangle. Pascal's Triangle is a triangle in which each row has
one more entry than the preceding row, each row begins and ends with "1," and
the interior elements are found by adding the adjacent elements in the preceding
row. Section one will display part of Pascal's Triangle, and will provide a
formula for finding any element of any row in the triangle.
Pascal's Triangle is essential to the discussion of binomial expansion because,
as it turns out, the numbers in Pascal's Triangle are the coefficients of the
monomials in the expansion of
(a + b)n
. The monomials also have other
properties, which can be summed up in the Binomial Theorem. This theorem is
presented in section two. Using this theorem, we will be able to write out any
expansion of any binomial.
Binomial expansion has other uses besides those in algebra II. It is used in
statistics to calculate the binomial distribution. This allows statisticians to
determine the probability of a given number of favorable outcomes in a repeated
number of trials. Binomial expansion is also interesting from a mathematical
point of view--it gives mathematicians insight into the properties of
polynomials. |
Hey guys, so I suggested to start threads about discussions for courses, since they kinda get lost in the other forums.
How is this course going for you guys so far? Any advice from people who took it? I have an 84 after the first unit of piecewise/polynomial functions.
This is a thread for the discussion about grade 12 Advanced Functions(AP and Non AP). General discussions about the course, specific questions, studying guides, strategies etc can all be posted here.
Here is the Ontario Curriculum for this course: 1. Characteristics and Transformations 2. Polynomial and Rational Functions 3. Trigonometric functions and identities 4. Exponential and Logarithmic Functions 5. Combinations of functions and rate of change start. This course has been going pretty well so far. The graphing part kind of takes me long on the tests, so I can never finish them, but graphing is so important in this course.
We did polynomial functions, piecewise functions, and now we are on rates of change. I don't know what the easiest units are, but I know trig will be an average killer!Ur so true about MHF being the easiest of all three grade 12 math, haven't take calculus, but I have data and adv functions this semester. Adv functions like soo easy where in data, I find it quite hard and my teacher said its normal lol
If data management is taught as it should be, the application and extension of concepts should be harder than advanced functions.
At my school, MDM4U is the credit that we get for IB Math Studies, which is basically math for people who 1. are just bad at math OR 2. don't need math for university but need to take a math course to get their IB diploma. Needless to say, it's a super easy course.
At my school, Data Management is easily the easiest 4U math course. It's pretty much designed for students who need a 4U math credit but aren't particularly good at math.
Same at my school. No one I know thinks advanced functions is easier than data.
I dont actually need data, but i took it cuz i thought it's easy. Then i realize that was a mistake....i only have a 91% in data whereas 99% in advanced functions.
Wow, so you're saying you could have chosen another five courses to beat that mark in data? That's incredible. If not, it wouldn't necessarily be a 'mistake'.
yeh I already took CHI4U, BBB4M, CLN4U and they all beat my mark in data, plus English and MHF4U, there're 5 courses in total. Im positive i can get a high 90s in BAT4M next semester. Therefore, yeh i shouldn't have taken data....Hi, I'm taking Data Management right now. We learned permutations and combinations. Now we're learning statstics. I'm wondering if there's any way to improve my mark?
Getting an 83 in this course. The class average is 45% because the teacher is always putting at least one hardcore thinking question that is ten marks. Our school usually does well on the math contests, so I hope it will go well. I'm quite happy with my mark though, considering how hard she was. I just wish I didn't make careless mistakes on the tests. Losing 4 marks on questions because you got mixed up with speed and velocity or didn't know the definition or calculated the rate of change for 3 months instead of 2 months can cost a lot when the test is out of 35 |
Why Choose MathMedia?
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Product Description
What are your specific needs? Do you have students with a variety of ability levels?
Do you have students with "holes" in their background?
Would you like to supplement your classroom teaching?
Do you have adult students preparing for the TABE or GED?
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Math Course Offerings
Students must have earned 1 credit in algebra and 1 credit in geometry in order to receive math credit for accounting.
Algebra I Sequence I Prerequisite: A good proficiency with arithmetic or passing grade in General Math.
This course is designed to aid students' transition from middle school math to algebra. It provides an in-depth presentation of skills, concepts, and problem-solving processes needed to help students become successful in algebra. Topics covered in this course will be the same as the first semester of Algebra I.
Algebra I Sequence II Prerequisite: Grade of C or better in Algebra I Seq I.
Topics covered in this course will be the same as the second semester of Algebra I. Units of study will include analyzing linear functions, systems of equations, inequalities, polynomials, number lines.
The field of real numbers is developed with emphasis on the set of rational numbers. Other topics include linear equations, data analysis, functional analysis and operations on polynomials and rational expressions as well as applications of these topics to problem-solving.
Introduction to Algebra II Prerequisite: A passing grade in Algebra I and a passing grade in geometry class or passing Algebra I Seq I, Algebra I Seq II, and a Geometry Class.
This course reviews and expands on the concepts taught in Algebra I. Topics are presented from a "hands-on" perspective with use of graphing calculators and an emphasis on real-world problems. Certain topics are covered in less detail than in the conventional Algebra II course.
Algebra II Prerequisite: A minimum grade of C in Algebra I and Academic Geometry.
Algebra II expands on skills introduced in Algebra I with a serious study of functions and graphs. The course reviews topics and presents new topics by applying them in mathematical modeling problems and performance activities.
This course involves an intense study of important algebraic topics and techniques with special emphasis on functions, graphs and their properties. Linear, quadratic, higher degree polynomial, rational, algebraic, exponential and logarithmic functions receive serious study as do matrices and determinants.
This course covers basic topics such as measure, angles, triangles, and parallel lines. These and other topics are examined from an informal perspective which is based on application of concepts rather than formal proofs.
Calculus - Honors Prerequisite: A minimum grade of C in Academic Precalculus or a passing grade in Honors Precalculus. A good working knowledge of the graphing calculator is required.
The focus of the course is the study of functions, limits, derivatives and antiderivatives. There is an emphasis on applications to business, physics and medicine.
Calculus - Advanced Placement Prerequisite: A minimum grade of B in Honors Precalculus or teacher recommendation. A good working knowledge of the following background areas is expected: algebra, geometry, functional analysis, trigonometry and use of the graphing calculators.
The course subject matter includes work in analystic geometry, limits and functions, and is designed to prepare students for the AB level AP Calculus exam.
CAPT Math - Core (1/2 year, 1/2 credit) Prerequisite: Students must have taken the math portion of the CAPT test and scored at the "Basic: Level 2" or "Below Basic: Level 1)
The goal of this course is to increase students' ability to develop math problem-solving strategies, communicate ideas mathematically and estimate or compute an answer to a problem.
Consumer Mathematics Prerequisite: A course in algebra or algebra I sequence I, and Applied Geometry or Geometry.
This 9th Grade course is for those not enrolled in a college-preparatory program. The course focuses on basic arithmetic content.
Geometry Prerequisite: A minimum grade of C in Algebra I.
The subject matter includes the study of angles, line segments, parallel lines, polygons, circles, prisms, and other common solids. The structure of plane geometry is emphasized and developed using reasoning patterns and proof.
Geometry - Honors Prerequisite: A final grade of A or A+ in Algebra I
The course develops logical reasoning and spacial/visual skills using inquiry-based teaching methods for the self-directed learner. The subject matter includes concepts of proof and applications of Euclidean Geometry.
This course introduces the C++ programming language. Basic program structures, syntax, data types and data storage will be examined. No prior programming experience is required but the student should have good basic computer skills.
Precalculus Prerequisite: A minimum grade of C in Algebra II. A good working knowledge of a graphing calculator is required. Introduction to Algebra is NOT a prerequisite for this course.
Trigonometry and analytic geometry are covered in this course. Elementary functions such as polynomial, exponential, logarithmic and circular are emphasized in Academic Precalculus.
Precalculus - Honors Prerequisite: A minimum grade of C in Algebra II - Honors. A good working knowledge of a graphic calculator is required.
This course studies trigonometry and its applications, sequences and series, and the conic sections. Other topics include vectors, limits and polar coordinates.
Probability and Statistics Prerequisite or Corequisite: Algebra II. A good working knowledge of a graphic calculator is recommended.
The student will study means of analyzing and presenting data. Topics include rules of probability, binomial functions, the normal distribution, linear correlation and linear regression.
Statistics - Advanced Placement Prerequisite: Algebra II and a good working knowledge of a graphing calculator.
The course introduces students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. Students will be exposed to four broad conceptual themes: exploring data, planning a study, anticipating patterns, and statistical inference. Students who enroll in this course will be expected to thake the AP Exam in Statistics. |
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Twelfth graders explore differential equations. In this calculus activity, 12th graders explore Euler's Methods of solving differential equations. Students use the symbolic capacity of the TI-89 to compare Euler's Method of numeric solutions to a graphical solution.
Twelfth graders solve problems using differential equations. In this Calculus lesson, 12th graders analyze data regarding the spread of a flu virus. Students use the symbolic capacity of the TI-89 to develop a model and analyze the spread of the disease.
In this differential equations worksheet, students solve systems of simultaneous differential equations using linear algebra. This six-page worksheet contains approximately six problems, with explanations and examples.
Students identify and familiarize themself with the features and capabilities of the TI-92 Plus calculator. They also find symbolic solutions of differential
equations and general solutions or to find particular solutions of initial-value and boundary-value problems. Finally, students use TRACE to find numerical values for this phase-plane graph.
Twelfth graders investigate differential equations. In this calculus lesson, 12th graders are presented with a step-by-step illustrated review of the process used in solving differential equations and an application problem. Students solve differential equations and application of differential equations.
Students investigate differential equations and slope fields. In this differential equations and slope fields lesson, students determine how much time can pass before a cup of coffee is safe to drink. Students use a differential equation to solve the problem algebraically. Students create a slope field to represent the time at which it is safe to drink the coffee.
In this A.P. Calculus activity, students complete a sixteen question test covering trigonometric integration, area under a curve, differential equations, and slope fields. Some of the problems are multiple choice, while others are free-response. |
Synopsis
This eBook comprehensively introduces the student to graphs. It encompasses linear co-ordinate systems, linear equations and graphs, quadratic equations and graphs, cubic equations and graphs, reciprocal equations and graphs, distance time graphs and conversion graphs. This eBook is part of our range of Grades 6, 7 & 8 maths eBooks that are aligned with the North American maths curriculum. Our Grades 6, 7 & 8 maths eBooks comprise three principle sections. These are, notably: •Number and Algebra •Geometry and Measures •Handling Data In addition, there exists a Publications Guide. Our maths eBooks are produced such as that as well as a Publications Guide, and three principle publications corresponding to the principle sections (Number and Algebra, Geometry and Measures and Handling Data) there are individual modules produced within each principle section which are published as eBooks. Graphs is a module within the Number and Algebra principle section our Grades 6, 7 & 8 publications. It is one module out of a total of seven modules in that principle section, the others being: •Factors, Prime Numbers and Directed Numbers •Fractions, Percentages and Ratio •Decimal •Indices and Standard Index Form •Algebra •Number Patterns and Sequences
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eBook Information
ISBN: 97814764414 |
College Geometry : Using The Geometer's Sketchpad - 12 edition
Summary: From two authors who embrace technology in the classroom and value the role of collaborative learning comes College Geometry Using The Geometer's Sketchpad. The book's truly discovery-based approach guides readers to learn geometry through explorations of topics ranging from triangles and circles to transformational, taxicab, and hyperbolic geometries. In the process, readers hone their understanding of geometry and their ability to write rigorous mathematical proofs.
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Each of our math seminars is designed as an intensive six day course with 39 hours of instruction time and is offered either in the summer or winter break. As of today we have offered the following mathematics seminars: |
book contains over 100 challenging problems for pupils aged 11-15, taken from the hugely popular UK Junior Mathematical Olympiad. There are also sixty additional problems in a similar style. The second section of the book consists of detailed comments and hints, while the third section gives outline solutions. These high quality, more challenging problems will provide an excellent and invaluable resource for all mathematics teachers.Book DescriptionThis book contains over 100 challenging problems for pupils aged 11-15, taken from the hugely popular UK Junior Mathematical Olympiad. There a
Contains the report and proceeddings of the inaugural programme of the African Leadership Forum. The book's main theme is the challenge of development: development of economies, of education facilities and agricultural infrastructures. |
MATH 2431
This is an archive of the Common Course Outlines prior to fall 2011. The current Common Course Outlines can be found at Credit Hours 4 Course Title Calculus I Prerequisite(s) MATH 1113 with a grade of "C" or better or placement by examination Corequisite(s)None Specified Catalog Description
This course includes the study of the derivative and its applications, limits and continuity, anti-differentiation, the definite integral, and the Fundamental Theorem of Calculus. Algebraic, trigonometric, exponential, and logarithmic functions are studied.
Expected Educational Results
As a result of completing this course, the student will be able to: 1. Investigate limits using algebraic, graphical, and numerical techniques. 2. Investigate derivatives using the definition, differentiation techniques, and graphs. The classes of functions studied include algebraic, trigonometric, inverse trigonometric, exponential, logarithmic, hyperbolic and implicit. 3. Apply the derivative as a rate of change, optimize functions, use Newton's Method, and sketch curves. 4. Define the definite integral and use Riemann sums to approximate definite integrals. 5. State and apply the Fundamental Theorem of Calculus. 6. Graph and use parametric equations.
General Education Outcomes
I. This course addresses the general education outcome relating to communication by providing additional support as follows: A. Students improve their listening skills by taking part in general class discussions and in small group activities. B. Students improve their reading skills by reading and discussing the text and other materials. Reading mathematics requires skills somewhat different from those used in reading materials for other courses in that students are expected to read highly technical material. C. Unit tests, examinations, and other assignments provide opportunities for students to practice and improve mathematical writing skills. Mathematics has a specialized vocabulary that students are expected to use correctly. II. This course addresses the general education outcome of demonstrating effective individual and group problem-solving and critical-thinking skills as follows: A. Students must apply mathematical concepts to non-template problems and situations. B. In applications, students must analyze problems, often through the use of multiple representations, develop or select an appropriate mathematical model, utilize the model, and interpret results. III. This course addresses the general education outcome of using mathematical concepts to interpret, understand, and communicate quantitative data as follows: A. Students must demonstrate proficiency in problem-solving skills by solving application problems relating to rates of change and optimization problems. B. Students must sketch and interpret graphs using concepts such as limits, continuity, derivatives, increasing and decreasing, local extrema, concavity, and points of inflection. C. Students must be able to approximate definite integrals using numerical techniques, including situations in which only numerical data from the function is available. IV. This course addresses the general education outcome of locating, organizing, and analyzing information through appropriate computer applications (including hand-held graphing calculators). As a result of taking this course, the student should be able to use technology to: A. sketch graphs, create tables of values, and approximate limits of functions. B. implement Newton's method to approximate zeros, critical values, and potential points of inflection of functions. C. approximate local extrema and approximate where a function is increasing, decreasing, concave upward, and concave downward. D. approximate the value of the derivative at a point. E. approximate Riemann sums. F. approximate definite integrals using Simpson's rule or a built-in integration feature. V. This course addresses the general education outcome of using scientific inquiry by using techniques of Calculus including integration or differentiation to apply scientific inquiry to problem solving.
Course Content
1. The Derivative 2. Techniques for Finding Derivatives 3. Applications of the Derivative 4. The Definite Integral ENTRY LEVEL COMPETENCIES Students should have successfully completed Math 1113 or an equivalent course prior to enrolling in Math 2431. ASSESSMENT OF EXPECTED EDUCATIONAL RESULTS I. COURSE GRADE The course grade will be determined by the individual instructor using a variety of evaluation methods such as tests, quizzes, projects, homework, and writing assignments. These methods will include the appropriate use of graphing calculators or PC software as required in the course. A comprehensive final examination is required which must count at least one-fourth and no more than one-third of the course grade. The final examination will include items that require the student to demonstrate ability in problem solving and critical thinking as evidenced by detailed, worked-out solutions. II. COLLEGE WIDE ASSESSMENT
This course will be assessed according to the college wide/mathematics department schedule. The assessment instrument will include a set of appropriate questions to be a portion of the final exam for all students taking the course. An out of class project may be an assessment instrument as well.
Assessment of Outcome Objectives
The Calculus Committee or a special assessment committee appointed by the Chair of the Math, Computer Science, and Engineering Executive Committee, will accumulate and analyze the results of the assessment and determine implications for curriculum changes. The committee will prepare a report for the Academic Group summarizing its finding. |
material in this user-friendly text is presented as simply as possible to ensure that students will gain a solid understanding of statistical procedures and analysis. The goal of this book is to demystify and present statistics in a clear, cohesive manner. The student is presented with...
For introductory-level courses in Technical Mathematics. This tried-and-true text from Allyn Washington, the pioneer of the basic technical mathematics course, now includes a fully developed MyMathLab program that may be packaged with every text, providing students with unlimited pract... |
This book offers a wide-ranging introduction to algebraic geometry along classical lines. It consists of lectures on topics in classical algebraic geometry, including the basic properties of projective algebraic varieties, linear systems of hypersurfaces, algebraic curves (with special emphasis on rational curves), linear series on algebraic curves, Cremona transformations, rational surfaces, and notable examples of special varieties like the Segre, Grassmann, and Veronese varieties. An integral part and special feature of the presentation is the inclusion of many exercises, not easy to find in the literature and almost all with complete solutions. The text is aimed at students in the last two years of an undergraduate program in mathematics. It contains some rather advanced topics suitable for specialized courses at the advanced undergraduate or beginning graduate level, as well as interesting topics for a senior thesis. The prerequisites have been deliberately limited to basic elements of projective geometry and abstract algebra. Thus, for example, some knowledge of the geometry of subspaces and properties of fields is assumed. The book will be welcomed by teachers and students of algebraic geometry who are seeking a clear and panoramic path leading from the basic facts about linear subspaces, conics and quadrics to a systematic discussion of classical algebraic varieties and the tools needed to study them. The text provides a solid foundation for approaching more advanced and abstract literature.
Both fractal geometry and dynamical systems have a long history of development and have provided fertile ground for many great mathematicians and much deep and important mathematics. These two areas ...
This book contains a compilation of papers presented at the II International Conference on Environmental, Industrial and Applied Microbiology (BioMicroWorld2007) held in Seville, Spain on 28 November ...
Schubert varieties and degeneracy loci have a long history in mathematics, starting from questions about loci of matrices with given ranks. These notes, from a summer school in Thurnau, aim to give ...
Differential geometry began as the study of curves and surfaces using the methods of calculus. In time, the notions of curve and surface were generalized along with associated notions such as length, ... |
The Review Quiz will include the following information sheet,
which consists of all the formulas listed as ``Equations
introduced in this unit'' for Units 1 and 2. You should
understand the meaning of these equations, but you need not
memorize them. |
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This subsite of Mathematics Tutorials and Problems (with applets) (see ) is divided into Interactive Tutorials, Calculus Problems, and Calculus Questions, Answers and Solutions. Here the user will find applets with guided exercises and many examples and worked out problems applicable to the first year of Calculus.
Learning Goals:
To provide tutorials in various areas of mathematics, including pre-calculus, calculus, geometry and statistics.
Target Student Population:
Undergraduate students taking Calculus.
Prerequisite Knowledge or Skills:
Basic algebra.
Type of Material:
This material is designed as tutorials, but many of the applets could also be used as simulations.
Recommended Uses:
This material is designed as tutorials but many of the applets could also be used in classroom demonstrations.
Technical Requirements:
A Java-enabled Web browser.
Evaluation and Observation
Content Quality
Rating:
Strengths:
This site is divided into Interactive Tutorials, Calculus Problems, and Calculus Questions, Answers and Solutions.
1. Interactive Tutorials
There are 15 tutorials. Each one consists of an applet accompanied by a brief discussion of the math concept, an explanation of how to use the applet, and a series of guided exercises. The intent of the guided exercises is to provide the student with a more in-depth understanding of the concept rather than to solve a particular problem. For example in the Concavity of Polynomial Functions tutorial, the student is guided to discover that the first derivative is increasing in an interval where the function is concave up, thus explaining why f ''(x) > 0 corresponds to concave up on the graph. Topics covered in the Interactive Tutorials include derivatives, concavity, Mean Value Theorem, Runge Kutta Method, Riemann Sums, the natural logarithm, and Fourier Series.
2. Calculus Problems
There are 13 problem areas, but some of areas contain more than one problem. Each of these is a typical calculus textbook problem. For example, one asks for the dimensions of the base of a pyramid that minimizes the surface area for a given volume. Another problem is that of finding all points on a polynomial with horizontal tangent. Graphs, diagrams, and detailed solutions are provided. The problems in this section are limited to differential Calculus.
3. Calculus Questions, Answers and Solutions
This section deals with examples that are quite similar to the "Calculus Problems" discussed above. Nearly 50 topics are listed, and each topic contains two or three examples (worked-out exercises). Many are typical textbook problems, like find the derivative of the inverse of a given function or use implicit differentiation to find dy/dx for a given implicitly defined function. The areas of Calculus covered include differential, integral, and ordinary differential equations.
Concerns:
None.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
This site should be quite effective for students seeking help in the first year of calculus or introductory ordinary differential equations. While some of the more sophisticated interactive tutorials that use experimentation and discovery may require the aid of an instructor, the majority of the material should be quite accessible to most Calculus students. The math concepts are well-explained, the solutions are quite detailed and thorough, and ample instructions are provided for operating the Java applets. The site should also be quite useful for classroom demonstrations.
Concerns:
None.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
Most of the Java applets are intuitive and easy to use. There is quite adequate instruction provided for the technical aspects throughout the site, and the problems and solutions are well-explained. Even in the non-interactive parts, one finds a great number of illustrative graphs.
Concerns:
Initially, some of the applets would not work in Firefox. After upgrading Java and then re-installing the upgrade, these difficulties seem to be resolved. Internet Explorer played all the applets without a hitch.
There is an apparent font problem in rendering some of the pages in FireFox. In particular, the arrow symbols in limits appear correctly on some pages but not on others. No such difficulties occurred with Internet Explorer.
Also, this site would definitely benefit from a hyperlinked subject index that can make navigation a lot easier. |
meth... read moreMathematics and the Imagination by Edward Kasner, James Newman With wit and clarity, the authors progress from simple arithmetic to calculus and non-Euclidean geometry. Their subjects: geometry, plane and fancy; puzzles that made mathematical history; tantalizing paradoxes; more. Includes 169 figures.
The World of Mathematics, Vol. 1 by James R. Newman Vol. 1 of a monumental 4-volume set includes a general survey of mathematics; historical and biographical information on prominent mathematicians throughout history; material on arithmetic, numbers and the art of counting, more.
The World of Mathematics, Vol. 2 by James R. Newman Vol. 2 of a monumental 4-volume set covers mathematics and the physical world, mathematics and social science, and the laws of chance, with non-technical essays by eminent mathematicians, economists, scientists, and others.
The World of Mathematics, Vol. 3 by James R. Newman Vol. 3 of a monumental 4-volume set covers such topics as statistics and the design of experiments, group theory, the mathematics of infinity, the unreasonableness of mathematics, the vocabulary of mathematics, and more.
The World of Mathematics, Vol. 4 by James R. Newman Vol. 4 of a monumental 4-volume set covers such topics as mathematical machines, mathematics in warfare, a mathematical theory of art, mathematics of the good, mathematics in literature, mathematics and music, and amusements.A Long Way from Euclid by Constance Reid Lively guide by a prominent historian focuses on the role of Euclid's Elements in subsequent mathematical developments. Elementary algebra and plane geometry are sole prerequisites. 80 drawings. 1963A Bridge to Advanced Mathematics by Dennis Sentilles This helpful "bridge" book offers students the foundations they need to understand advanced mathematics. The two-part treatment provides basic tools and covers sets, relations, functions, mathematical proofs and reasoning, more. 1975 edition.
Discovering Mathematics: The Art of Investigation by A. Gardiner With puzzles involving coins, postage stamps, and other commonplace items, readers are challenged to explain perplexing mathematical phenomena. Simple methods are employed to capture the essentials of mathematical discovery. Solutions.
Lectures on Elementary Mathematics by Joseph Louis Lagrange One of the 18th century's greatest mathematicians delivered these lectures at a training school for teachers. An exemplar among elementary expositions, they combine original ideas and elegant expression. 1898 edition.
Mathematics and the Physical World by Morris Kline Stimulating account of development of mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations, and non-Euclidean geometries. Also describes how math is used in optics, astronomy, and other phenomena.
The Nature of Mathematics by Philip E. B. Jourdain Anyone interested in mathematics will appreciate this survey, which explores the distinction between the body of knowledge known as mathematics and the methods used in its discovery. 1913A Source Book in Mathematics by David Eugene Smith The writings of Newton, Leibniz, Pascal, Riemann, Bernoulli, and others in a comprehensive selection of 125 treatises dating from the Renaissance to the late 19th century — most unavailable elsewhere.
Product Description:
methods into a collection of well-defined theorems about limits, continuity, series, derivatives, and integrals. Beginning with a survey of the characteristic 19th-century view of analysis, the book proceeds to an examination of the 18th-century concept of calculus and focuses on the innovative methods of Cauchy and his contemporaries in refining existing methods into the basis of rigorous calculus. 1981 |
Find an Alviso Algebra 2Math that uses letters and symbols to represent values and their relations, especially for solving equations. It is also the study of relations and operations. A set of words within a language that are familiar to an individual The set of rules that govern the composition of clauses, phrases, and words in any natural language.
...Students should not have a goal of pleasing their parents or merely getting a good grade. True
I have a PhD in Computer Science and Masters in Mathematics from Vanderbilt University. With graduate degrees in Computer Science and Mathematics, I am more than qualified to help students in a wide range of mathematics and computing subjects. I have experience both as a university instructor and ... |
Calculus AB: First-Time (math 1247)
AB Calculus first timers is intended for those individuals who have not taught AP* Calculus or have been teaching AP* Calculus for less than three years. The course will review concepts of Calculus while focusing on the requirements for students to be successful on the Calculus AB exam. Much of the week will be spent looking at previous AP* exams and working the problems so that participants will get a sense of how the scoring works and how to help students earn the maximum number of points. The course will focus on the rule of four, looking at Calculus from numerical, graphical, algebraic, and verbal perspectives.
Rose Gundacker taught AP* Calculus, both AB and BC, at Rosemount High School for 20 years before retiring in 2008. Since then she has continued teaching part-time either at St. Olaf College or the University of St. Thomas. Her experience with the AP* program goes back to 1998 when she started as a reader. After 6 years as a reader, Rose spent 6 years as a table leader and then 2 years as both a table leader and a member of a question team. Last year was her first year as a question leader and she will continue in this role for the 2013 Reading. Rose Gundacker has been an AP* consultant since 2000 and has presented summer workshops and one-day workshops at various sites throughout the Midwest |
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Seeing Math™ has developed interactive software tools to clarify key mathematical ideas in middle and high school mathematics. Each interactive provides a real-time connection between representations of the mathematics (symbolic, graphical, etc.), so that changes in one representation instantly cause changes in the other. The eight applets include: Qualitative Grapher, Piecewise Linear Grapher, Linear Transformer, Function Analyzer, Quadratic Transformer, System Solver, Plop It!, and Proportioner.
Learning Goals:
To illustrate and reinforce key mathematical ideas for teachers and students of algebra. To accelerate learning and enhance comprehension of difficult concepts.
Target Student Population:
Middle school and high school students; beginning college students can also benefit
Prerequisite Knowledge or Skills:
General knowledge of functions, equations, and graphs; mean, median and mode
Type of Material:
Interactive Java applet
Recommended Uses:
Classroom demo; student exploration or enrichment
Technical Requirements:
Java-enabled Web browser
Evaluation and Observation
Content Quality
Rating:
Strengths:
The applets are well-designed and implemented. Each includes a detailed Sample Activity, and all but the Quantitative Grapher include a User Guide and a sample Warm Up activity. Some also include a section on Frequently Asked Questions.
Concerns:
None
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
The materials are well-written and the applets are effective. As noted by the authors, the applets are designed to illustrate and reinforce key mathematical ideas for teachers and students of algebra. Seeing immediate feedback to changes in parameters is most informative and can easily be related to textbook and/or classroom presentations. The Linear and Quadratic Transformers, in particular, allows students to analyze the nature of their respective functions. A nice feature is that they allow linear and quadratic functions to be entered and manipulated in multiple forms (e.g., polynomial, vertex, and root forms for a quadratic functions). Plop It! provides a nice analysis of mean, median and mode. The Warm Ups and Sample Activities are quite extensive and provide ready-to-use examples for both teachers and students.
Concerns:
The System Solver and Proportioner applets are somewhat complicated and their goals and effectiveness are not immediately obvious from the applet interface; their user guides are necessary in order to make effective use of the applets.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
The applets may be downloaded for use offline.
The User Guides open in new windows and are thus easy to use while running the interactive applets.
The FAQ sections are designed to address known issues in usage.
No technical difficulties were encountered in the use of this site
Concerns:
Some of the applets are a bit complicated and their interfaces are not immediately obvious (viz., System Solver and Proportioner); however, the user guides are thorough and complete. |
Embroidered Math
In this lesson, students are introduced to basic graph theory and Euler circuits. They stitch paths and circuits to create their own graphs. Students also problem solve as they design a route that creates the same pattern on the front and back of a canvas.
Learning Objectives
Students will:
Define and draw vertex/edge graphs
Describe Euler paths and Euler circuits
Determine whether or not graphs have Euler paths and circuits
Sketch graphs that have Euler paths and circuits
Stitch the Euler circuit, considering the stitches on each side of the fabric to be distinct edges
Materials
Instructional Plan
Ask, "When I say graph, what do you think of?" [Expected answers include coordinate graphs, bar graphs, pie graphs, data collections, grids, slope-intercept.] Show the Graph Theory overhead. Tell students that in graph theory, a graph is a collection of points, called vertices, and the edges that connect them. Note that edges do not have to be straight; the only requirement is that they have vertices as their endpoints. Mention that multiple edges can connect the same two vertices and an edge can connect a vertex to itself.
Discuss how a graph on paper can be a model of a real-world situation. For example, the vertices of a graph might represent houses, and the edges might represent streets. Ask students for other situations that might be modeled by graphs. [Airports and routes, cell phone signals and towers, assignment of class sections to rooms.]
Pass out the Graph Theory activity sheet. Explain that graphs can be used to find the most efficient way to carry out a task. For example, a road striper (the machine that paints lines down the middle of a road) or a street cleaner might want to travel along each street in a town exactly once. By drawing a graph that includes streets as edges and intersections as vertices, the driver can use a graph to determine the optimal path for the job. A path that starts at a vertex and traces each edge exactly once is called an Euler path, named after the mathematician Leonhard Euler (pronounced oil‑er). An Euler path that starts and ends at the same vertex is called an Euler circuit.
Have students trace paths on the graphs and decide if each graph has an Euler path or circuit. Then, students should draw their own paths. Encourage students to look for patterns and try to draw a conclusion about what graph features make it possible to trace an Euler path or circuit. If students are not ready to draw a conclusion, they will be able to return to the activity sheet later in the lesson.
Needlework
Distribute dot paper to each student. Have students draw an Euler circuit on the dot paper, using the dots as vertices. Distribute sewing needles and thread to each student. Explain that they are going to use stitches to trace their circuits. Help students thread their needles, if necessary. Then, tape the loose end of the thread to the back of the paper near the starting point. Have students push the needle through the starting point and then make a stitch by pushing the needle through at the next vertex and repeating until all edges have been traced, either on the front or the back of the paper. Students can use their stitching to verify that they have not traced any edges more than once. Below are some examples of circuits that have been stitched.
Blackwork
Have students look at the front and the back of the dot paper on which they stitched their designs. They should note that the design is different on the front and the back. Blackwork embroidery creates the same image on the front and back sides of the canvas. Remind students that their canvas is dot paper. Show students Blackwork 1 overhead. Explain that they are going to trace a path that, when stitched, creates the same image on the front and the back. You will track whether the stitches are on the front or the back of the paper by recording it in the appropriate column. Note that stitches alternate between front and back, depending on where the needle begins. The beginning and ending vertex for each stitch is recorded in parentheses. The first letter is where the stitch begins, and the second letter is where it ends. When the stitches are listed in order, the ending vertex of one stitch should be the same as the beginning vertex of the next stitch. While analyzing the stitches listed, trace them on the graph above, using different colors for front and back stitches. In the end, each edge will have be been traced in two colors, indicating that the image would be the same on the front and the back of the canvas. Students may also want to draw this pattern on their own dot paper and stitch the pattern to see better how it works.
Show the Blackwork 2 overhead. Explain that some designs are much more complicated and require many more stitches. In these designs, the stitches are numbered. The T indicates that the stitch is made on the first trip around the pattern, and a B indicates that it is made on the return trip. As you trace the stitches, again use two colors to indicate the stitches on the front or the back. Have students help you problem solve about where to begin each stitch so that the back image will look identical to the front image. Again, when you are finished, each edge should be traced in two colors.
Show the Blackwork 3 overhead. Again, the numbered stitches can be traced in two colors, with color designating whether the stitch is on the front or the back of the canvas. The T stitches are made between the starting point and the turn around, and the B stitches are made after the turn around and on the way to the finish. Ask students why they think this design is called "Journey and Side Trips." Discuss the efficiency of the stitching pattern; there are very few stitches required between the turn around and the finish.
Wrap-Up
Since we actually stitch on both sides of the canvas, every edge on the front will have a matching edge on the back. Explain that the degree of a vertex is the number of edges that connect to it. Ask, "Why will every vertex have an even degree?" [Each time an edge passes through the front, there is also one on the back. The total degree will always be a multiple of two.] Have students return to the Graph Theory Answer Sheet and complete the last two questions.
Questions for Students
What conditions describe a graph that has an Euler path?
[No more than two vertices may have an odd degree.]
What conditions describe a graph that has an Euler circuit?
[All vertices must have an even degree.]
Why does the double-sided needlework always have an Euler circuit?
[Every time the needle enters the fabric, or paper, it must also come out. Therefore, every vertex must have an even degree.]
In the overhead examples, the circuit is completed by alternating stitches on the top and bottom and then turning back and reversing the procedure. When can a circuit be stitched continuously, without changing directions?
[The original pattern must have an odd number of stitches.]
Assessment Options
Have students draw a graph without an Euler circuit and explain why it does not have an Euler circuit.
Pass out a sketch of the Koenigsberg bridge problem, a famous problem where seven bridges connect the banks of a river with two islands in the river. Have students represent it as a graph and explain why it has no solution.
Ask students to write a journal entry explaining how the needlework contributed to their understanding of the graphs.
Extensions
Research applications of Euler graphs, such as the Chinese Postman Problem, which involves finding the most efficient way for a postman to traverse every street in a neighborhood.
Research Hamiltonian graphs, which are graphs that pass through every vertex exactly once, without restrictions on how many times an edge is traversed. One example that students may consider is the Traveling Salesman Problem, where a salesman wants to travel the shortest distance while visiting each customer on his route. Note that Euler graphs focus on traversing every edge, while Hamiltonian graphs focus on visiting every vertex.
Research isomorphic graphs, which are graphs where corresponding vertices are connected to corresponding edges. Also consider planar graphs, which are isomorphic to a graph where none of the edges appear to intersect.
Teacher Reflection
Did the needlework enhance student understanding of the graph concepts?
Were you able to use the needlework tasks to differentiate instruction among your students?
Were concepts presented too abstractly? too concretely? How would you change them?
Were students able to come up with potential applications for edge/vertex graphs |
Description: This handbook has been designed to provide scientific investigators with a comprehensive and self-contained summary of the mathematical functions that arise in physical and engineering problems. 125 worksheets have been developed as general-purpose tools that illustrate a variety of useful Mathcad techniques and are compatible with Mathcad 14 and 15. [Mathcad 14 or 15 is required.]
This 1972 book is a compendium of mathematical formulas, tables, and graphs. It contains a very complete table of analytical integrals, differential equations, and numerical series; and includes tables of trigonometric and hyperbolic functions, tables for numerical integration, rules for differentiation and integration, and techniques for point interpolation and function approximation. Additionally, the book devotes an entire section to mathematical and physical constants as fractions and powers of Pi, e, and prime numbers; and discusses statistics by presenting combinatorial analysis and probability functions. The coverage is extensive. In its more than 1000 pages, almost all mathematical areas are treated.
125 worksheets have been developed as general-purpose tools that illustrate a variety of useful Mathcad techniques and are compatible with Mathcad 14 and 15.
[Mathcad 14 or 15 is required.] |
This Interactive Online Mathematics Dictionary was developed for use by middle school mathematics students as well as the parents and teachers of middle school mathematics students. The language of the definitions attempts to be consistent with middle school levels of rigor. The examples, links, tests help to elaborate on the definitions. Although developed as a separate project, it was incorporated into the InterMath Project and has been adopted by the Georgia Department of Education.
Project InterMath was funded by the National Science Foundation as a collaborative effort of the Department of Mathematics Education and the Learning and Performance Support Laboratory (LPSL) and the CEISMC group at the Georgia Institute of Technology. InterMath is a professional development effort designed to support teachers in becoming better mathematics educators. It focuses on building teachers' mathematical content knowledge through mathematical investigations that are supported by technology. InterMath includes a workshop component and materials to support instructors. |
Maths Standards Unit C5: Mostly Calculus
Maths activities, games and work sheets. KS5, A Level. Core 1 - Differentiation. Finding Stationary Points of Cubic Functions Students make connections between quadratic and cubic functions, their derivatives and graphs. They analyse solutions to problems. This is part of the "Mostly Calculus" set o More…f materials from Standards unit: Improving learning in mathematics.
Classification
Reviews (1)
This is a great resource for Core 1, it is basically a card sort with equations, derivatives and graphs. You could use this as an informal assessment to see how much the students had understood the topic so far, ot you may want to just use it as a plenary to check understanding. Thank you for sharing. |
CAROL SCHWAB @ webster university - math&computer science
Introduction to DPGraph software
What is DPGraph?
Over one million mathematicians, physicists, teachers, and students use DPGraph.
The world's most powerful software for math and physics visualization. Create beautiful, interactive, dynamic, photorealistic 2D, 3D, 4D, 5D, 6D, 7D and 8D graphs. Includes hundreds of examples contributed by users from around the world. Used for algebra, geometry, trigonometry and general physics, through multivariable calculus, field theory, quantum mechanics and gravitation. Use time and color as extra dimensions (to create motion or encode momentum, for example). Use the scrollbar to vary parameters in realtime, to slice through graphs, or to vary transparency. Programmed entirely in assembly language for maximum speed. Graph functions, equations, conic sections, planes, spheres, toruses, parametric curves and surfaces, implicit equalities and inequalities, volume intersections, volumes of integration, vector fields, surfaces of revolution, equipotential surfaces, and much more, in rectangular, polar, cylindrical, or spherical coordinates.
To download DPGraph, click on the Access DPGraph link. Follow the instructions.
*For Windows XP, 2000, NT, and 98 Operating Systems only!
Sample DPGraphs to download
Click on the name of graph icon below to download/open the .DPG file. Once downloaded, start DPGraph and OPEN the file by navigating to its location.
You can set DPGraph's parameters to do 2D graphs, too. This graph lets you use DPGraph's scrollbar to change the variables A, B, and C to explore the classic sine curve y=a sin(bx+c) using GRAPH3D((Y = A*SIN(B*X+C), X=0, Y=0)).
2D Level Curves
As with 3D, DPGraph can display 2D level curves. This is handy for viewing everything from complex variable conformal maps to the characteristic curves of partial differential equations. Here's a snapshot from a movie of equipotential lines "flowing" along streamlines from the source on the right to the sink on the left. You can use DPGraph's scrollbar to adjust A (the distance of the source or the sink from the origin) and C (the strength of the source or the sink from the origin).
Slice
One way to make a graph move is to use DPGraph's scrollbar to slice through it in the x, y, or z directions in real time. Here's a movie of the slicer sweeping through the previous level surfaces, showing what the inside of the graph looks like. |
0618372210
9780618372218 to mathematics, along with the integration of graphing calculators and Excel spreadsheet explorations, exposes students to the tools they will encounter in future careers.A wealth of pedagogy includes the following distinctive features: detailed Worked-out Examples with Annotations help students through more challenging concepts; Practice Problems are offered to help students check their understanding of concepts presented in the examples; Section Summaries briefly restate essential formulas and key concepts; Chapter Summary with Hints and Suggestions unify chapter themes, give specific reminders, and reference problems in the review exercises suitable for a practice test; and Cumulative Review Exercises appear at the end of groups of chapters to reinforce previously learned concepts and skills. «Show less... Show more»
Rent Finite Mathematics 2nd Edition today, or search our site for other Berresford |
Can anyone suggest a linear algebra textbook?
Can anyone suggest a linear algebra textbook?
I've seen loads of "what is the best Linear Algebra" threads but none quite match what I'm looking for. I'm currently using David Lay's Linear Algebra and its Applications, and I find the book readable, but strange.
He changes notations quite often and sometimes I have to try to figure out what he's talking about because his notations are different yet again. Also, his examples are not really illustrative of anything significant, are but simple calculations and step-by-step guides to how to solve problems.
I also find that it is not conceptually cohesive. I'm taking a summer course in Linear Algebra right now and it introduced a lot of terminology: "This is called x" but doesn't make it relevant what x actually signifies. As I progressed in math I found that a lot of the "jargon" are actually very meaningful, and I'm not getting that here, and the pace at which we're going only ensures that one day my ADHD brain will bet bowled over by all the terms. Maybe I'm missing the point, but I don't think he ties together concepts well.
I read a lot of good reviews on Shilov's book but also that it's not good for first-timers and wouldn't really be compatible with the course I'm taking- my professor pretty much lectures straight out of the book. Is there a good textbook that is more conceptual, but still accessible?
Hey Rubicon, welcome to the physics forums!
I have read a bit of Lay's book, and am not a big fan of it. My favorite book on linear algebra is Axler's Linear Algebra Done Right. It provides plenty of motivation for the subject, and uses a clean, operator-theory approach that doesn't needlessly bring up matrices and determinants when they are not needed.
However, it is a pretty abstract treatment, in the classic theorem, proof, theorem, proof,... style. Are you looking for something with more physical or intuitive examples?
Can anyone suggest a linear algebra textbook?
Thanks for the responses. Generally I like more intuitive examples. For some reason I have a hard time translating between theory and reality and physical examples always make me think of more variables than are relevant in the problem. I'm not very good at applied math and generally appreciate a more theoretical approach. I always "see" better when the examples are just points and lines, and when I think about things, even in other subjects such as history, I tend to see forces and light blots and colors. |
My son used the Saxon Algebra 1/2 for grades 8 and 9. He studied the first half of the book for 8th grade and the second half of the book for 9th grade. It all depends on what pace you keep. This worked for us as it kept him from feeling so rushed. He was able to take his time to get a good grasp on the concepts involved, getting a good foundation for higher math.
answered 1 year ago
by
mom of 4
Georgia
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0out of0found this answer helpful.
answer 3
I all depends on what you used in the eighth grade yr. If you used Saxon algebra .5 then you would want to use Saxon Algebra 1. There are also Math workbooks in other curriculums. For instance I used Key to algebra for my oldest son, who is now going to the 12th grade. He has a different learning style than my two younger children. I suggest that you go to a homeschool store and spend the day looking at curriculum. and write down three or four that you think would work, if the store has a return policy get the ones you think might work and spend a week pouring over them and you will figure out which one will work best and return the others. :) Happy hunting!
As a general rule Algebra 1 is recommended for grade 9. Since every student is different, we recommend administering a "Saxon Placement Exam". Select the "Homeschool" tab at the top of our web page, then select the "Saxon" tab located under the main tabs. You will find the link to the free PDF test document there. |
Gary Rockswold teaches algebra in context, answering the question, "Why am I learning this?" By experiencing math through applications, students see how it fits into their lives, and they become motivated to succeed. Rockswold focus on conceptual understanding helps students make connections between the concepts and as a result, students see the bigger picture of math and are prepared for future courses.
Introduction to Functions and Graphs; Linear Functions and Equations; Quadratic Functions and Equations; More Nonlinear Functions and Equations; Exponential and Logarithmic Functions; Trigonometric Functions; Trigonometric Identities and Equations; Further Topics in Trigonometry; Systems of Equations and Inequalities; Conic Sections; Further Topics in Algebra |
CS 1050 Section B Sample Final ExamProve that if x is a rational number, then x 2 is an irrational number. You may p use the fact that 2 is irrational. 5 points: Prove that 1 + 2 + 3 + + n is divisible by n if and only if n is odd. 10 points: Wh
Graduate Teaching Workshop - Grading GuidelinesIdris Hsi, last updated August 30, 2000IntroductionGrading is usually the primary responsibility of a Teaching Assistant. As such, it will take up the most time, not just in the process of grading bu
Bump Mapping Explained by Group 8 - http:/ Summary Bump mapping is a texturing technique developed by Blinn in 1978. Essentially, bump mapping allows for wrinkling eects to be applied to surfaces in a cost-ecient manner. The nec
CS3451 TEST 2 practice problems FALL 20061. What is the area of the polygon with vertices (in order along the boundary) (0, 5), (5, 2), (10, 1) and (-2, -3)? 2. Let's say you are given a hexagon in the plane. You draw intervals inside the hexagon. 6520: Computational ComplexityProblem Set 1 Due March 4, 2008 Problem 1Give a Karp reduction from CLIQUE to SAT.Problem 2Let Quadratic be the problem of deciding whether a given system of quadratic multivariate polynomial equations with integ |
Survey of Mathematics With Applications
9780321112507
ISBN:
0321112504
Edition: 7 Pub Date: 2004 Publisher: Addison-Wesley
Summary: The sixth edition of this best-selling text balances solid mathematical coverage with a comprehensive overview of mathematical ideas as they relate to varied disciplines. This book provides an appreciation of mathematics, highlighting mathematical history, applications of mathematics to the arts and sciences across cultures, and introduces students to the uses of technology in mathematics. Exercise sets are now organ...ized into Concept/Writing, Practice the Skills, Problem Solving, Challenge Problems/Group Activities, Research Activities. An updated Consumer Math section including updated material on sources of credit and mutual funds. Motivational, chapter-opening material demonstrates connections between math and various other disciplines. KEY MARKET For those who require a general overview of mathematics, especially in the fields of elementary education, the social sciences, business, nursing and allied health fields |
Normal 0 false false false MicrosoftInternetExplorer4 The goal ofElementary Algebra: Concepts and Applications,7e is to help todayrs"s students learn and retain mathematical concepts by preparing them for the transition from "skills-oriented" elementaryConcept Reinforcementexercises, Student Notes that help students avoid common mistakes, and Study Summaries that highlight the most important concepts and terminology from each chapter. For all readers interested in elementary algebra.
Table of Contents
Introduction to Algebraic Expressions
Introduction to Algebra
2
(11)
The Commutative, Associative, and Distributive Laws
13
(7)
Fraction Notation
20
(10)
Positive and Negative Real Numbers
30
(9)
Addition of Real Numbers
39
(7)
Subtraction of Real Numbers
46
(8)
Multiplication and Division of Real Numbers
54
(9)
Exponential Notation and Order of Operations
63
(17)
Study Summary
74
(1)
Review Exercises
75
(3)
Test
78
(2)
Equations, Inequalities, and Problem Solving
Solving Equations
80
(9)
Using the Principles Together
89
(8)
Formulas
97
(7)
Applications with Percent
104
(10)
Problem Solving
114
(13)
Solving Inequalities
127
(8)
Solving Applications with Inequalities
135
(13)
Study Summary
143
(1)
Review Exercises
144
(2)
Test
146
(2)
Introduction to Graphing
Reading Graphs, Plotting Points, and Scaling Graphs
148
(11)
Graphing Linear Equations
159
(10)
Graphing and Intercepts
169
(8)
Rates
177
(10)
Slope
187
(14)
Slope--Intercept Form
201
(8)
Point--Slope Form
209
(17)
Study Summary
219
(1)
Review Exercises
219
(3)
Test
222
(1)
Cumulative Review: Chapters 1--3
223
(3)
Polynomials
Exponents and Their Properties
226
(9)
Polynomials
235
(9)
Addition and Subtraction of Polynomials
244
(9)
Multiplication of Polynomials
253
(8)
Special Products
261
(9)
Polynomials in Several Variables
270
(9)
Division of Polynomials
279
(5)
Negative Exponents and Scientific Notation
284
(16)
Study Summary
294
(1)
Review Exercises
295
(3)
Test
298
(2)
Polynomials and Factoring
Introduction to Factoring
300
(8)
Factoring Trinomials of the Type x2 + bx + c
308
(9)
Factoring Trinomials of the Type ax2 + bx + c
317
(9)
Factoring Perfect-Square Trinomials and Differences of Squares
326
(8)
Factoring: A General Strategy
334
(6)
Solving Quadratic Equations by Factoring
340
(8)
Solving Applications
348
(16)
Study Summary
359
(1)
Review Exercises
360
(1)
Test
361
(3)
Rational Expressions and Equations
Rational Expressions
364
(7)
Multiplication and Division
371
(6)
Addition, Subtraction, and Least Common Denominators
377
(10)
Addition and Subtraction with Unlike Denominators
387
(9)
Complex Rational Expressions
396
(6)
Solving Rational Equations
402
(8)
Applications Using Rational Equations and Proportions
410
(20)
Study Summary
423
(1)
Review Exercises
424
(2)
Test
426
(1)
Cumulative Review: Chapters 1--6
427
(3)
Systems and More Graphing
Systems of Equations and Graphing
430
(7)
Systems of Equations and Substitution
437
(7)
Systems of Equations and Elimination
444
(9)
More Applications Using Systems
453
(11)
Linear Inequalities in Two Variables
464
(5)
Systems of Linear Inequalities
469
(3)
Direct and Inverse Variation
472
(12)
Study Summary
479
(1)
Review Exercises
480
(2)
Test
482
(2)
Radical Expressions and Equations
Introduction to Square Roots and Radical Expressions
484
(8)
Multiplying and Simplifying Radical Expressions
492
(6)
Quotients Involving Square Roots
498
(5)
Radical Expressions with Several Terms
503
(5)
Radical Equations
508
(7)
Applications Using Right Triangles
515
(8)
Higher Roots and Rational Exponents
523
(11)
Study Summary
529
(1)
Review Exercises
530
(2)
Test
532
(2)
Quadratic Equations
Solving Quadratic Equations: The Principle of Square Roots
534
(6)
Solving Quadratic Equations: Completing the Square
540
(6)
The Quadratic Formula and Applications
546
(10)
Formulas and Equations
556
(6)
Complex Numbers as Solutions of Quadratic Equations
562
(4)
Graphs of Quadratic Equations
566
(6)
Functions
572
(19)
Study Summary
583
(1)
Review Exercises
584
(2)
Test
586
(1)
Cumulative Review: Chapters 1--9
587
(4)
Appendix A: Factoring Sums or Differences of Cubes
591
(3)
Appendix B: Mean, Median, and Mode
594
(4)
Appendix C: Sets
598
(5)
Table 1: Fraction and Decimal Equivalents
603
(1)
Table 2: Squares and Square Roots with Approximations to Three Decimal Places |
Summary of Courses Available
Because individual students have different needs, interests and abilities, there are four different courses in mathematics. These courses are designed for different types of students: those who wish to study mathematics in depth, either as a subject in its own right or to pursue their interests in areas
related to mathematics; those who wish to gain a degree of understanding and competence better to understand their approach to other subjects; and those who may not as yet be aware how mathematics may be relevant to their studies and in their daily lives. Each course is designed to meet the needs of a particular group of students. Therefore, great care should be taken to select the course that is most appropriate for an individual student. In making this selection, individual students should be advised to take account of the following types
of factor.
Their own abilities in mathematics and the type of mathematics in which they can be successful.
Their own interest in mathematics, and those particular areas of the subject that may hold the most interest for them
Their other choices of subjects within the framework of the DP
Their academic plans, in particular the subjects they wish to study in future.
Their choice of career
Teachers assist with the selection process and offer advice to students about how to choose the most appropriate course from the three mathematics courses available.
Mathematics Higher Level
This course caters for students with a good background in mathematics who are competent in a range of analytical and technical skills. The majority of these students will be expecting to include mathematics as a major component of their university studies, either as a subject in its own right or within courses such as physics, engineering and technology. Others may take this subject because they have a strong interest in mathematics and enjoy meeting its challenges and engaging with its problems.
Mathematics Standard Level: Methods
This course caters for students who already possess knowledge of basic mathematical concepts, and who are equipped with the skills needed to apply simple mathematical techniques correctly. The majority of these students will expect to need a sound mathematical background as they prepare for future studies in subjects such as chemistry, economics, psychology and business administration.
Mathematics Standard Level: Studies
This course is available at SL |
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
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How to use Powerpoint Matthew StoneDo formatting on the master Get the master view with View>MasterGet rid of the master view with View>NormalAvoid formatting individual slidesDo color with a color scheme Right panel Slide design > Color S
Learning in GamesRakesh V. VohraNorthwestern UniversityThe notion of an equilibrium in a game attracts criticism in much the same way that corpses attract flies. The objections are three: 1) The Presumption of Unreasonable Rationality 2 |
MathDL Partners
Loci. This online publication is presented by the Mathematical Association of America (MAA). It is contained within MathDL. Locicarries on the tradition of three earlier online publications, the Journal of Online Mathematics and its Applications, Digital Classroom Resources and Convergence.
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The Developmental Mathematics Collectioncontains resources for the community college educator who teaches basic arithmetic through intermediate algebra. Educators will find student activities, topic teaching plans, innovative curricula and course sequences, as well as research syntheses on pedagogy and learning.
PlanetMath is an online mathematics community, featuring an encyclopedia with over 5,500 entries defining approximately 10,000 concepts. There are also forums for asking and answering questions, and collections of free electronic books, papers, and other expositions. The site is maintained entirely by volunteers.
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The Connected Curriculum Project (CCP) at Duke is primarily a collection of modules for use in courses from precalculus to linear algebra, differential equations, and engineering mathematics. Most modules use CAS worksheets. Maple and Mathematica versions exist for all, Mathcad and Matlab versions for some.
iLumina Digital Library, based at the University of North Carolina at Wilmington, contains materials for Chemistry, Biology, Computer Science, and Mathematics.
Demos With Positive Impact features short materials that can be used in a classroom presentation. The demos use a range of technology from animated gifs to java applets.
causeweb.org is the web site for the Consortium for the Advancement of Undergraduate Statistics Education (CAUSE). Their resources include lecture examples, laboratories, datasets, analysis tools, multimedia, and more.
The National Curve Bank began as a resource to display representations of two- and three-dimensional curves. It has expanded to include many more types of resources. Materials include animations, historical notes, java applets, Mathematica code, and more.
TheNSDL Middle School Portal was begun by the Eisenhower National Clearinghouse. It contains tracks for science, technology, and mathematics. |
Hotmath and Texas Instruments Work Together
Free Movies
Hotmath.com provides free Getting Started Movies to help Prealgebra, Algebra 1, and Geometry students become familiar with TI graphing calculators.
Free Exercises
Hotmath.com provides free Practice Exercises, to help
students learn TI graphing calculators at their own pace. These are correlated
to the chapter topics in Prealgebra, Algebra 1, and Geometry textbooks.
Math Homework Help
Hotmath.com offers homework support for over 300 math textbooks. We display keystroke solutions to the graphing calculator problems in selected textbooks from Glencoe, Key Curriculum Press, and McDougal Littell. |
MAKE IT MATH
MAKE IT MATH ALGEBRA STUDENT BOOK
Provide instruction and practice for the range of math skills students need to succeed on standardized tests and in everyday life. Each Student Book offers easy-to-follow instructions for basic math...
Overview - MAKE IT MATH ALGEBRA STUDENT BOOK
Provide instruction and practice for the range of math skills students need to succeed on standardized tests and in everyday life. Each Student Book offers easy-to-follow instructions for basic math concepts. Thousands of practice problems include multiple choice, open response, and answer grid. Students learn how to use a calculator, fill in standard and coordinate test grids, and use other math concepts, such as estimation, to solve different types of math problem. Lessons provide techniques to help students solve single-step and multi-step problems. The 190-page Teacher's Resource Guide includes answer keys to all 9 student books, diagnostic tests, and test answer keys. For Grades 6-10. |
Book Description: Your guide to a higher score on the Praxis II?: Mathematics Content Knowledge Test (0061)Why CliffsTestPrep Guides?Go with the name you know and trustGet the information you need--fast!Written by test-prep specialistsAbout the contents:Introduction* Overview of the exam* How to use this book* Proven study strategies and test-taking tipsPart I: Subject Review* Focused review of all exam topics: arithmetic and basic algebra, geometry, trigonometry, analytic geometry, functions and their graphs, calculus, probability and statistics, discrete mathematics, linear algebra, computer science, and mathematical reasoning and modeling* Reviews cover basic terminology and principles, relevant laws, formulas, theorems, algorithms, and morePart II: 3 Full-Length Practice Examinations* Like the actual exam, each practice exam includes 50 multiple-choice questions* Complete with answers and explanations for all questionsTest Prep-Essentials from the Experts at CliffsNotes? |
We emphasize that the structure of solutions to linear systems applies not only to systems of linear ODEs but also to systems of linear algebraic equations and systems of linear integral equations.
Phase planes, qualitative analysis of linear systems and stability are introduced after analytic solutions and enhanced with MATLAB and MAPLE demonstrations and assignments.
The operator method and Laplace transforms are covered. Then we proceed to systems of nonlinear differential equations, including linearization, Hopf bifurcation, limit cycles, Lorentz equations, and chaos in chemical systems.
To better understand chaos, we also introduce chaos in discrete systems. |
Mathematical Application In Agriculture - 2nd edition
Summary: Get the specialized math skills you need to be successful in today's farming industry with MATHEMATICAL APPLICATIONS IN AGRICULTURE, 2nd Edition. Invaluable in any area of agriculture-from livestock and dairy production to horticulture and agronomy--this easy to follow book gives you steps by step instructions on how to address problems in the field using math and logic skills. Clearly written and thoughtfully organized, the stand-alone chapters on mathematics involved in crop produc...show moretion, livestock production, and financial management allow you to focus on those topics specific to your area while useful graphics, case studies, examples, and sample problems to help you hone your critical thinking skills and master the |
Introduction to Matlab 7 for Engineers
9780072548181
ISBN:
0072548185
Edition: 2 Pub Date: 2004 Publisher: McGraw-Hill
Summary: This is a simple, concise book designed to be useful for beginners and to be kept as a reference. 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. The text covers all the major cap...abilities of MATLAB that are useful for beginning students. An instructor's manual and other web resources are available |
Discrete Math
Discrete mathematics is a branch of math that deals with structures having specific values, as opposed to continuously varying values. There are analogies in signal processing to digital and analog signals, and in science to quantum and classical modeling of atomic and molecular systems. Discrete math is naturally extended, through computer programming algorithms, to analysis of complex infrastructure systems like telecommunication routing, utility distribution, highway and traffic pattern studies, and many others.
Any course in discrete math will cover the following topics:
logic and proofs
sets, functions, sequences and sums
algorithms, integers, and matrices
induction and recursion
mathematical induction
counting
discrete probability
advanced counting techniques
relations
graphs
trees
boolean algebra
modeling computation
A fabulous resource for discrete mathematics can be found at the online forum Science Direct, where refereed journal articles are available, although not for free. This is the real deal, where the latest research is being done in the field.
To fulfill our mission of educating students, our online tutoring centers are standing by 24/7, ready to assist students who need extra practice in discrete math. |
This
course provides the student with a good foundation in differential and
integral calculus with emphasis on both skills and applications. Topics
covered include functions; limits; derivatives of polynomial,
trigonometric, parametric, and implicit functions; applications of
differentiation; the indefinite integral; the definite integral;
applications of the definite integral.
Apply the integral in finding the center of mass in one and two dimensions.
Apply the derivative or integral in solving distance, velocity, and acceleration problems.
Solve first order differential equations with initial conditions.
REQUISITES
Prerequisite:
MATH C141
MATH C142
DETAILED TOPICAL OUTLINE:
Lecture:
The Mathematics Department has adopted the following best practices for teaching this course:offering
or awarding extra-credit is forbidden, the allowance of multiple
attempts at exams is forbidden, and an approved on-site proctor for
online course exams is required.
A. Preliminary Concepts
1. Rectangular Coordinates
a. Slope of a Line
i.
Parallel Lines
ii.
Perpendicular Lines
b. Equations of Lines
c. Distance
2. Functions
a. Domain and Range
b. Graphs
c. Absolute Value
d. Composite Functions
3. Derivative of a Function
a. Definition - using the delta X process
b. Average and Instantaneous Rate of Change
c. Slope of a Curve
d. Velocity
4. Limits
a. Definition - epsilon and delta notation
b. Limit at a point
c. Limit as x
d. Continuity
e. Asymptotes of rational functions
B. Differentiation
1. Derivative of a Polynomial
2. Power Rule
3. Product Rule
4. Quotient Rule
5. Implicit Differentiation
6. Chain Rule
7. Differentials and Linear Approximations
8. Derivatives of the Trigonometric Functions
9. Higher Order Derivatives
a. Polynomial Functions
b. Implicit Functions
Applications of Differentiation
1. Curve Sketching
a. Sign of first derivative – increasing and decreasing
b. Sign of second derivative - concavity
c. Relative maxima, minima
d. Points of inflection
2. Velocity and Acceleration
3. Related Rates
4. Maxima, Minima Problems
5. Newton's Method (Newton-Raphson)
6. Equations of Lines Tangent and Normal to a Curve
7. Mean Value Theorem
8. Rolle's Theorem
Integration
1. Indefinite Integral
a. Anti-differentiation
b. Of the form c du, u du, du+dv
c. Integrals of the Trigonometric Functions
2. Applications of the Indefinite Integral
a. Solutions to Simple Differential Equations with Initial Conditions
b. Velocity and Position
c. Equation of a Family of Curves
3. Numerical Methods for the Definite Integral
a. Circumscribed Rectangles
b. Inscribed Rectangles
c. Trapezoidal Method
d. Simpson's Method
4. The Fundamental Theorem of Integral Calculus
a. Evaluation of Definite Integrals
b. Substitution Method Applied to Definite Integrals
Applications of the Definite Integral
1. Area Under a Curve
2. Area Between two Curves
3. Volume of a Body of Revolution
a. Cylindrical Shell Method
b. Disk Method
c. Washer Method
4. Length of a Plane Curve
5. Moments and Center of Mass
METHODS OF INSTRUCTION--Course instructional methods may include but are not limited to
Demonstration;
Discussion;
Lecture;
Other Methods: • Lecture and discussion of all course concepts.
• Demonstration of developing proofs and solving application problems.
• Reading textbooks and journals to see presentations different than those of the instructor.
• Assignments and quizzes.
• 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 |
Department of Economics, Business School
College of Social Sciences
Details
Module description
Quantitative Methods provides an introduction to some of the techniques employed in economic analysis. The course starts with an introduction to elementary algebra and proceeds to show how economic problems can be formulated and solved algebraically. The emphasis is on practical application rather than on the study of mathematics for its own sake. |
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