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Synopses & Reviews
Publisher Comments:
Maple V Mathematics Learning Guide is the fully revised introductory documentation for Maple V Release 5. It shows how to use Maple V as a calculator with instant access to hundreds of high-level math routines and as a programming language for more demanding or specialized tasks. Topics include the basic data types and statements in the Maple V language. The book serves as a tutorial introduction and explains the difference between numeric computation and symbolic computation, illustrating how both are used in Maple V Release 5. Extensive how-to examples are presented throughout the text to show how common types of calculations can be easily expressed in Maple. Graphics examples are used to illustrate the way in which 2D and 3D graphics can aid in understanding the behaviour of | 677.169 | 1 |
9780471707080
ISBN:
0471707082
Edition: 1 Pub Date: 2009 Publisher: Wiley
Summary: This text offers a fresh approach to algebra that focuses on teaching readers how to truly understand the principles, rather than viewing them merely as tools for other forms of mathematics. It relies on a storyline to form the backbone of the chapters and make the material more engaging.
William G. McCallum is the author of Algebra: Form and Function, published 2009 under ISBN 9780471707080 and 0471707082. ...Two hundred eighty one Algebra: Form and Function textbooks are available for sale on ValoreBooks.com, sixty five used from the cheapest price of $9.35, or buy new starting at $158.19 | 677.169 | 1 |
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Targeted Math | Formulas
This lesson plan is one of 12 that were created for teachers to use with their students who need to brush up on their math skills in order to pass the 2002 GED® Math Test. To see all 12 lesson plans, go to Targeted Math Instruction for the 2002 GED® Test.
Formulas describe the constant (unchanging) relationship between two or more values. For example, "π" is the constant relationship between the diameter and circumference of a circle. Math formulas express relationships by using variables. If we know a value for every variable but one, we can substitute values in place of the variables we know, and solve for the unknown value. These formulas are printed in the GED® test booklet. This lesson should take approximately 2 hours to complete, if all components are utilized | 677.169 | 1 |
MERLOT Search - category=2548&sort.property=overallRating
A search of MERLOT materialsCopyright 1997-2015 MERLOT. All rights reserved.Wed, 7 Oct 2015 00:19:56 PDTWed, 7 Oct 2015 00:19:56 PDTMERLOT Search - category=2548&sort.property=overallRating
4434Graph Theory Lessons
The applets contain topics typically found in undergraduate graph theory and discrete structures classes like null graphs, the handshaking lemma, isomorphism, complete graphs, subgraphs, regular graphs, platonic graphs, adjacency matrices, graph coloring, bipartite graphs, simple circuits, Euler and Hamilton circuits, trees, unions and sums of graphs, complements of graphs, line graphs, spanning trees, plane graphs, shortest paths, minimal spanning trees. The applet utilizes Petersen software written by the author. Peterson can draw, edit and manipulate simple graphs, examine properties of the graphs, and demonstrate them using computer animation.Sat, 24 Sep 2005 00:00:00 -0700Discrete Math Resources
This site consists of examples, exercises, games, and other learning activities associated with the textbook, Discrete Mathematics: Mathematical Reasoning and Proof with Puzzles, Patterns and Games by Doug Ensley and Winston Crawley. Requires Adobe Flash player.Tue, 27 Jan 2009 19:07:46 -0800Graph Theory: Trees
This applet is part of a larger collection of lessons on graph theory. The focus of this particular applet is Trees. The user will explore full binary, ternary and n-ary trees, the relationship of parent and child, and depth-first and breadth-first traversal.Sat, 6 May 2006 00:00:00 -0700Euler Circuits, Hamilton Circuits, Directed Graphs
This applet is a component of a larger site on Graph Theory. It introduces Euler Circuits and Hamilton Circuits and provides opportunities to investigate their properties using Peterson software.Sat, 6 May 2006 00:00:00 -0700Graph Theory: Spanning Trees
This applet is part of a larger collection of lessons on graph theory. The focus of this particular applet is on Spanning Trees. The user will explore depth first and breadth first methods of developing spanning trees from a connected graph.Sat, 6 May 2006 00:00:00 -0700Graph Theory Tutorials
This is a series of short interactive tutorials introducing the basic concepts of graph theory. There is not a great deal of theory here, but enough will be taught to wet your appetite for more!Fri, 2 Jun 2006 00:00:00 -0700Integer Optimization and the Network Models
It covers integer and network optimization with numerical examples and applicationsSun, 15 Feb 2004 00:00:00 -0800'Lies, Damn Lies, and Statistics': A Critical Assessment of Preferential Attachment-type Network Models of the Internet
This video was recorded at 4th European Conference on Complex Systems. Basic Question: Do the available Internet-related connectivity measurements and their analysis support the sort of claims that can be found in the existing complex networks literature? Key Issues: What about data hygiene? What about statistical rigor? What about model validation? Author discusses some of the main problems and challenges associated with measuring, inferring, and modeling various types of Internet-related connectivity structures. To this end, he uses some known examples to illustrate the need to understand the process by which Internet connectivity measurements are obtained, explore the sensitivity of inferred graph properties to known ambiguities in the data, be more critical with respect to the dominant, preferential attachmenttype network modeling paradigm, and be more serious/ambitious when it comes to model validation. Ignoring any of these issues is bound to produce results that are best described by the well-known aphorism "lies, damned lies, and statistics."Sun, 8 Feb 2015 21:11:25 -0800A Century of Graph Theory
This video was recorded at Predavanja, seminarji in srečanja na Fakulteti za matematiko in fiziko. Graph theory has changed completely from the late-19th century to the late 20th century, from a collection of mainly recreational problems to a well-developed mainstream area of mathematics. In this talk I outline its development over this period, both chronologically and thematically.Sun, 8 Feb 2015 21:38:06 -0800A Polynomial-time Metric for Outerplanar Graphs (Extended Abstract)
This video was recorded at 5th International Workshop on Mining and Learning with Graphs (MLG), Firenze 2007. In the chemoinformatics context, graphs have become very popular for the representation of molecules. However, a lot of algorithms handling graphs are computationally very expensive. In this paper we focus on outerplanar graphs, a class of graphs that is able to represent the majority of molecules. We define a metric on outerplanar graphs that is based on finding a maximum common subgraph and we present an algorithm that runs in polynomial time. Having an efficiently computable metric on molecules can improve the virtual screening of molecular databases significantly.Tue, 10 Feb 2015 13:24:05 -0800 | 677.169 | 1 |
al Introduction and Historical Perspective
Mathematics has become essential and pervasive in the U.S. workplace, arid pro-
jections indicate that its use will expand, as will the need for more workers with a
knowledge of college-level mathematics. However, socioeconomic and demographic
projections as well as circumstances within the college and university mathematical
sciences system suggest that an adequate supply of appropriately educated workers is
not forthcoming. Development of mathematical talent will be impeded by the low
general interest in mathematics as a college major; the relatively small numbers of
minorities and women studying and practicing mathematics; a shortage of qualified
faculty to deal with huge enrollments in low-level courses and students with widely
varying levels of preparation; and the difficulty of maintaining the vitality of the mathe-
matical sciences faculty.
The MS 2000 Project and the Scope of This Report
Because a healthy flow of mathematical talent is
important for the nation's welfare, the National Research
Council initiated in 1986 the project Mathematical Sci-
ences in the Year 2000 (MS 2000) to assess the status of
college and university mathematical scier~ces and to design
a plan for revitalization and renewal. This report describes
the circumstances and issues surrounding the people in-
volved in the mathematical sciences, principally students
and teachers. The description is not complete because
comprehensive data are not available, but most data that
are relevant and available are included and are adequate to
describe the circumstances in the mathematical sciences.
Two additional descriptive reports~ne on curriculum
and the other on resources-are forthcoming,. Together
these three reports will form the basis for the the MS 2000
Committee's final report, which will contain recommen-
dations for actions to achieve revitalization and renewal of
the college and university mathematical sciences enter-
pr~se.
This report is concerned with all students of collegiate
mathematics. However, mathematics majors have a spe-
cial role to play because they are the source of the new
faculty members necessary to renew and sustain the sys-
tem. And increases in the need for mathematics in the
workplace in turn fuel a need for more academically skilled
workers. A dramatic demonstration of this need is the
'For the purposes of this report the discipline referred to as the "mathematical sciences'' includes mathematics, applied mathematics. and statistics.
A broader definition is generally used in the taxonomy of scientific disciplines. For a discussion of the mathematical sciences research community
see Reneu ing U.S. Mathematics s: Critical Resou' ~ e fo'- the Future (National Academy Press. Washington. D.C.. 1984). pp. 77-85. Computer science
is not a branch of the mathematical sciences. but its close ties with mathematics. both intellectually and administratively, have significantly affected
college and university mathematical sciences over the past two decades. This report does not attempt to describe circumstances in computer science,
but references tO computer science are necessary because of these ties and their effects.
A Challenge of Numbers
doubling of the number of scientists and engineers in a
single decade (Figure 1.1~.
Understanding students and teachers in the mathe-
matical sciences who they are, what they learn and teach,
and how they use what they learn-requires understanding
the vast and diverse system in which they work. The
mathematical sciences programs in U.S. colleges and
universities account for nearly logo of all collegiate teach-
ing in the United States and nearly 3097c of all collegiate
teaching in the natural sciences and engineering. Eac
term, approximately 3 million students are taught by more
than 40,000 full-time and part-time faculty members and
8,000 graduate teaching assistants in 2,500 institutions. To
better understand this system and how current circum-
stances evolved, a review of events of the past 30 years is
helpful.
Three Roller Coaster Decades
For centuries, mathematics has been recognized as
interesting,, challenging,, and essential for the support of
science and engineering. Within this century, mathematics
has become much more broadly applicable and important.
Giant strides toward reco;,nition of its significance were
made during World War II. After World War II, U.S.
mathematicians branched out, studyin;, and developing
(in thousands)
4000 · .
3 000 r
2000
1000
1 976
-
11~ Engineers
· Scientists
1986
FIGURE 1.1 Total number of scientists and engineers.
SOURCE: National Science Board (NSB, 19871.
2
new areas in many directions very successfully. This
period of innovation and the concurrent expansion of
college and university mathematics programs positioned
mathematics as a key participant in the nation's emphasis
on science spurred on by the 1957 launch of Sputnik. Thus
began three decades of extraordinary change-a decade of
expansion, followed by a decade of adjustment and depres-
sion, followed by a decade of partial recovery.
The decade following Sputnik's launch was one of
expansion for U.S. mathematics. Statistics became more
widely recognized as a distinct discipline and began to
flourish. Then as now, to a slightly lesser extent most
of the research in mathematics and statistics was per-
formed in universities. College enrollments increased,
faculties expanded, and positions were plentiful. The
number of bachelor's degrees in mathematics awarded
annually tripled, and the number of graduate degrees
increased fivefold in this decade. Support for specialized
research programs, which was available from federal
agencies for individuals, was ideally suited to the mathe-
matical research mode.
In the late 1 960s, immediately following the dramatic
expansion of science and mathematics programs, the na-
tion's interest and attention shifted to social issues. Al-
though more students continued to enter colle ,e as access
to higher education expanded significantly, many came
without adequate preparation for college mathematics and
with questions about the relevance of learning any. Over
the 20-year period from 1965 to 1985, college enrollments
doubled, and mathematical sciences enrollments more
than kept pace. However, most of the increase in mathe-
matics enrollments was at the lower levels, with remedial
enrollments in high school mathematics taught in college
leading the way.
The surge in the numbers of decrees awarded in the
mathematical sciences in the late 1960s and early 1970s
and the lack of establi shed employment markets for mathe-
maticians outside of academe created more degree holders
than there were jobs, especially at the doctoral level; in
addition, part of the response to increased enrollments in
mathematics courses was to let student-faculty ratios in-
crease. A depressed employment market resulted that
Introduction and Historical Perspective
fasted nearly a decade, into the early 1980s. To some extent
this depression was spread across all science and engineer
ing fields. Statistics was an exception, with some modest White Males
increases in degrees granted and a better nonacademic 74%
employment market.
College and university mathematical sciences facul
ties were changing. Increasing responsibilities for teach
ing precalculus and high-school-level courses, the predic
tion that college enrollments would soon decline, and the
perception that mathematics Ph.D.s were plentiful changed
employment practices on college faculties. The changes
included the creation of positions with heavy teaching
loads for full-time faculty and the use of more part-time and
temporary teachers. Many faculty members had little time
and motivation for personal scholarship; some lapsed into
inactivity. Teaching introductory algebra and calculus to
students majoring, in other areas became more widespread
and restricted the independent growth of mathematics and
mathematicians. Some faculty members did not teach
what they thought about their research- and also had
little enthusiasm or latitude to think about what they taught.
These forces reduced the attention to curriculum develop
ment and redo. In response to nationally articulated
goals in the mid-1960s, the fraction of Ph.D.s on mathe
matical sciences faculties had increased significantly to
nearly 80% in four-year institutions, but a seeming mis
match between training and duties prompted a reversal of
this effort. In particular, new doctoral degree holders,
educated for research, were mismatched with the teaching
positions available. Consequently, both teaching and
research suffered.
In research universities, graduate students, plentiful in
the 1960s, assumed a large share of the teaching responsi
bilities. Inflation on a weak mathematics employment
market and better opportunities in other areas such as
computer science spread quickly among U.S. students, and
the numbers choosing mathematics as a major area of study
began to decline. This decline was partially offset at the
graduate level by increases in the number of non-U.S.
students that, combined with the significant decline in the
number of U.S. students enrolled in mathematics, changed
/ _
~-
_ ~
- _ ~
White Females
19%
Non-White Males
5%
Non-White Females
1%
FIGURE 1.2 Ph.D. degrees in mathematics, 1986-1987.
SOURCE: American Mathematical Society (AMS, 1987~.
to nearly one of two in 1988. This trend, coupled with the
heavy teaching burden carried by graduate students, cre-
ated teaching problems across the country.
Factors other than the poor employment market also
reduced the number of mathematical sciences majors. One
factor was the predominance of white middle-class males
in the study and practice of mathematics. Relatively few
women and minorities were choosing mathematically based
careers and curricula, although more women, more blacks,
and more Hispanics were entering college. The fraction of
bachelor's degrees earned by women did increase-from
about one-third of the total in the mid- 1 960s to almost one-
half by 1 98~but the increase was smaller at the master's
level and smaller still at the doctoral level (Figure 1.21.
That comparatively few blacks and Hispanics choose
mathematically based careers has continued to be the case.
The number of Native Americans choosing such careers is
small but does reflect approximately this aroup's share of
the total U.S. population, while Asian-Americans continue
to show a preference for these careers.
In the 1960s and 1970s, little attention was given to
creating employment opportunities for mathematical sci-
entists in the nonacademic workplace. Academic employ-
ment in a research environment was the dominant destina-
tion for degree holders in mathematics, and these opportu-
nities had diminished. Thus, not only were there rough
transitions to the workplace for those with bachelor's and
master's degrees, but Ph.D.s, too, were not suitably matched
the non-U.S. representation from about one of five in 1970 with the teaching jobs that were available in colleges.
3
A Challenge of Numbers
Mathematical sciences enrollments in introductory
and remedial courses continued to increase in the 1970s,
fueled by added mathematics requirements in the curricula
of fields such as business and by shifts to majors that
required more mathematics. This development reflected
an increasing need for mathematics in the workplace, both
for professionals in other areas and for mathematical
scientists. Mathematics was emerging as more important
in professional education, achieving a new prominence
that complemented its centuries-long role in human intel-
lectual development. Problem-solvina ability and adapta-
bility dominated the requirements of new jobs. Said
another way, liberal arts education especially mathemat-
ics education was becoming closer to professional edu-
cation. However, the nonacademic employment market
for mathematical scientists continued to be poorly under-
stood and was invisible to many.
Departments across the country met the increased
enrollments of the 1 970s with a variety of types of faculty
members and the same traditional courses, mostly because
they were busy and lacked resources (Figure 1.31. Many
temporary and part-time teachers were hired on an ad hoc
basis tenn after term. Thus began a dismantling of the
buildup to a high fraction of faculty with Ph.D.s that had
just been achieved. The responsibilities of departments
became more diverse and more difficult to carry out
(thousands)
2.000
1.500
1 .000
Advanced
_., ~:~ I, I: ,. ~ , ,: :' ''lo .... :'::': ::'
O:. ~ ~ ~ . ~ . ~ .: ~ :: :. I- . ~ . ~ ..~ .: ... , ~, : ~. ::. I.: :, ~ I. ~ : ~.. ~: ..~. .,
' 'a 1 1 111 111 :1
965
1970 1975 1980 1985
FIGURE 1.3 Left: Total undergraduate enrollments in mathematical sciences departments. Right: Mathematical sciences
faculty at colleges and universities. SOURCE: Conference Board of the Mathematical Sciences (CBMS, 1987).
because of heavier involvement in coordinating activities,
fewer experienced and involved teachers, large remedial
and placement problems' and fewer mathematics majors.
No other collegiate discipline teaches as many students
with such widely differing levels of preparation as does
mathematics, and most of the students are expected to use
the mathematics in subsequent courses. An overwhelming
combination of problems of collegiate teaching-unmoti-
vated and underprepared students, unenthusiastic teachers,
language problems in the classroom, outdated and irrele-
vant curricula and courses, large classes, heavy teaching
loads, too few resources, and little use of modern technol-
ogy-came together in the 1 970s and resonated in mathe-
matics classrooms across the United States.
By the early 1980s, the number of degrees awarded
annually in the mathematical sciences had fallen by nearly
50% at all three levels (Figure 1.41. Occurring simultane-
ously with the decline in the numbers of degrees awarded
were increases in enrollments and in reliance on part-time
faculty. Belatedly, institutions decided that the high mathe-
matical sciences enrollments would persist, and they began
to employ regular faculty members. By this time there
were too few U.S. citizens among the new doctoral degree
holders to meet the demand; indeed, there were overall
shortages of candidates. There were (and are) no surplus
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ . . Hi. ~ .
pUU1b U1 Illa~l~rnaucal sciences tn.~.s no large number
40,000
30.000
20.000
1 0~000
o
1970
1980 1985
Introduction and Historical Perspective
BOX 1.1 Computer Science
Computer science has developed since World War I} from roots in mathematics and electrical engineering.
It has become a separate academic discipline within the past two decades and has developed its own sources of
students and federal fundin;, for research. (See the 1984 David Report (NRC, 1984) for a fuller analysis.)
Computer science is not considered to be a part of the mathematical sciences, and that is the position taken
throu Shout this report. However, older reports on the mathematical sciences may include computer science data,
and computer science and mathematics continue to be administered by the same unit in most colleges and
universities (see Box 3.3~. Because of these historical, administrative, and intellectual ties, the emergence and
rapid growth of the discipline of computer science have had a significant effect on the mathematical sciences. At
points in this report some of these effects are conjectured, but only the effects of computer science on the
mathematical sciences are considered. No attempt is made to describe the conditions in computer science.
Nevertheless, the grouping of computer science with the mathematical sciences in many college and university
departments and the dual teaching roles of many faculty members are facts.
The 1985 CBMS Survey (Box 3.3) concluded that in four-year colleges and universities, half (49%) of all
computer science course sections were taught in departments with mathematics and the other half (51 Tic) in com-
puter science departments. (This breakdown did not include courses in computing, taught by many units in busi-
ness and engineering, for example.) Thus approximately 270,000 students enrolled in computer science courses
were taught in mathematics departments in fall 1985. This compares to estimated enrollments of 1,827,000 in
mathematics and statistics courses in these departments in fall ~ 985. Thus approximately 13% of the teaching, in
these departments was in computer science (the 1985 Annual AMS Survey results give an estimate of 10% rather
than Who, but the 1984 Annual AMS Survey yielded 12% see Box 3.2~.
In two-year colleges in 1985, approximately 10% of the 1 million students enrolled per term were enrolled
in computing and data processing.
The 1985 CBMS Survey listed 27,500 bachelor's degrees awarded by departments of 'mathematics" and 400
awarded by departments of statistics in the period July 1984 to June 1985. Of these 27,500 degrees, 40% were
awarded in computer science (8,700) or jointly with computer science (2,5003.
The 1985 CBMS Survey reported that of the 3,750 Ph.D.s on the nation's full-time computer science faculty,
41 % had their doctorates in mathematics. Of the 2,200 Ph.D.s on the part-time computer science faculty, 61 % had
their doctorates in mathematics. Of the total full-time computer science faculty, 35% had their highest decrees in
mathematics, and of the total part-time computer science faculty, 42% had their highest degree in mathematics.
Of the 5,650 members of the full-time computer science faculty, 2,O50 were employed by 'mathematics'-
departments. Of the 5,350 members of the part-time computer science faculty, 3350 were employed by
'mathematics" departments. This translated to 3,150 full-time equivalents (FTE) offaculty members teaching one-
half of the computer science sections in "mathematics" departments and 4,250 FTE of faculty members teaching
the other half in computer science departments. It is noted that computer science departments are concentrated
in the universities where teaching loads are lower.
s
A Challenge of Numbers
of postdoctoral positions and no candidates from other
disciplines who fit the faculty needs. Ad hoc hiring
practices continued, partly because of a lack of suitable
candidates for regular faculty positions.
From another perspective, by 1970 a large infrastruc-
ture of mathematical sciences graduate study and research
had been established across the country and was spread
through more than lSO universities. Success in research
was clearly the principal criterion for respect within this
community, and the research environment was clearly the
best in the world. However, federal support formathemati-
cal sciences research became less available, as did other
governmental and institutional support (NRC, 1984), and
the employment market was very depressed. There were
many discouraged faculty members and persons seeking
faculty positions. Many defected to other areas. By 1980,
the mathematical sciences infrastructure was clearly weak-
ening.
During the 1970s and continuing until the present,
many departments' programs, especially at four-year col-
leges, contained a mixture of mathematics, statistics, and
computer science. Planning, was confounded further by
conflicting trends within these three disciplines. Computer
science was booming, statistics was growing steadily, and
mathematics was struggling to adjust to a depressed em
00000
0000
000 ~
he..
1~^
00
1950 1956 1962 1968 1974 1980 1986
o
Coo ~
Too 00
° 04C.°0°
c, ~ .e
,~ ,G, ~
Bachelor's
Master's
FIGURE 1.4 Mathematical sciences degrees awarded
SOURCE: National Center for Education Statistics (NCES,
198Sa).
ployment market, fewer majors, and huge enrollments in
introductory courses.
Computer science was emerging as a separate aca-
demic discipline. Many computer science programs had
been formed within mathematical sciences departments,
and the number of majors and the course enrollments were
rising rapidly. Since there were far too few people with
academic degrees in computer science to fill the available
faculty positions and because of computer science's close
connections to mathematics, many mathematics faculty
members were able to cross over to computer science. And
students who once might have been mathematics majors
began to choose computer science as a major. By 1988
separate computer science departments had been estab-
lished in most large universities, but in smaller institutions
the hybrid department was still the rule. Approximately
half of all computer science enrollments continue to be in
these combined departments, thus competing for faculty
time and energy and the interest of the students (see BOX
1.1~.
While much of the ferment over the past two decades
also affected other academic disciplines, especially the
sciences and engineering, the impact on the mathematical
sciences was more extreme. The declines in the numbers
of mathematics degrees awarded were relatively larger,
and the declines in the numbers of majors in other science
and engineering disciplines turned around much more
quickly in the early 1980s. Mathematics has been the
slowest field to recover although there has been some
recovery-one reason being the close ties between mathe-
matics and academe. No other science or engineering
discipline depends as heavily on academic employment for
its graduates, especially those with doctorates, as does
Doctorate mathematics. Consequently the health of the mathemati-
cal sciences enterprise is very closely tied to the health of
education, especially higher education.
By 1982 a number of serious problems posing a risk to
the general health of mathematics had become apparent.
The numbers of degrees awarded were near the lowest;
course enrollments were the highest, with the heaviest
concentration at the lower levels; teaching loads had in-
creased dramatically; federal support for research was at a
Introduction and Historical Perspective
BOX 1.2 Sources of Data
Several sources of data were used to compile this report. The main sources include:
· American Mathematical Society (AMS);
· Conference Board of the Mathematical Sciences (CBMS);
· National Center for Education Statistics (NCES) of the Department of Education;
· National Research Council (NRC); and
· National Science Foundation (NSF).
In general, the mathematical professional societies' (AMS and CI3MS) data relate only to the field of mathe-
matical sciences and do not allow any comparisons across fields. When field comparisons are made, the sources
of data are usually the NRC, NSF, or NCES. Inconsistencies do arise, partly because of different survey
populations. For instance, some data on mathematical sciences include data on computer science. Where possible
in this report, mathematical sciences data have been separated from computer science data. It is not feasible to
reconcile or explain all the differences Analysis of data in detail reveals differences that cannot be reconciled,
but the implications of these differences appear to be minor. Nevertheless, the different sources have beers found
to be consistent enough to depict the general circumstances in the mathematical sciences enterprise.
The tables in the text are numbered consecutively within each chapter, as are the figures (mostly graphs).
Tables giving the data used to construct the figures presented in this report are included in the report's appendix
and are numbered to correspond to the relevant text chapter rather than to a particular text figure or table. For
example, Table A4.3 is the third table in Appendix Tables that contains data for Chapter4, while Table 4.3 is simply
the third table in the text of Chapter 4. The sources of the information shown in the tables and figures are given
according, to the standard referencing system used throughout the report.
very low point, especially in core areas of mathematics;
and faculty morale was frequently low. Responding to the
expansion of the previous two decades and the associated
problems had talcen most of the faculty time and energy.
During that period, whole new areas of mathematical
sciences had developed, including operations research,
discrete mathematics, mathematical biology, statistical
design and analysis, and nonlinear dynamical systems. In
fact, the term "mathematical sciences" itself had become a
part of the taxonomy of science. In spite of these new
developments in the mathematical sciences, new applica-
tions, and new opportunities for using technological ad-
vancements, the teaching of mathematics had essentially
not changed. Both the curricular content and its delivery
had remained static. Mathematical sciences departments
were not able to simultaneously cope with enoImous
instructional loads, maintain excellence in faculty scholar-
ship, and allocate resources to innovations or even known
improvements. The forces at work were too diverse and
too disparate.
National Efforts Toward Renewal
In 1982 the mathematical sciences community began
to address these problems on a national level. In 1984 the
National Research Council (NRC) published Renewing
U.S. Mathematics: Critical Resource for the Future (re-
ferred to as the David Report; NRC, 1984), documenting
7
A Challenge of Numbers
the weakening of federal support for research in the mathe-
matical sciences. That report was the first of a series of
efforts within the NRC and in professional societies to
assess the health of the mathematical sciences and to
design a plan for renewal. The NRC project Mathematical
Sciences in the Year 2000 (MS 2000), of which this report
BOX 1.3 Statistics
The discipline of statistics is included in this
report as a part of the mathematical sciences, pnnci-
pally because statistics has an intellectual base in
mathematics, mathematics students are the principal
source of statistics graduate students, and significant
federal funding for academic research that develops
fundamental statistical concepts and methods comes
from the "mathematical sciences" units of federal
agencies (NRC, 1984~.
Degree programs in statistics are mostly gradu-
ate degree programs. The number of students en-
rolled in statistics and the number of undergraduate
statistics majors are much smaller than the analo-
gous numbers for mathematics. In major universi-
ties, statistics usually constitutes a separate aca-
demic department, but in other institutions statistics
is likely to be taught in the same unit as mathematics
(see Box 3.3~. In addition, statistics courses are
taught in a variety of administrative units, including
business, engineering, medical sciences, and social
sciences.
Partly because of the close administrative and
intellectual ties between statistics and mathematics,
much of the data on statistics in colleges and univer-
sities in this report is a;,gre~,ated with analogous data
on mathematics. Some disag~regation is possible
and has been done when possible in this report.
However, in general, the data are dominated by those
for mathematics, and caution must be used in draw-
ing conclusions about statistics from the aggregated
data.
8
is a part, was initiated in 1986. MS 2000 is an effort to
assess the state of college and university mathematical
sciences and to design a national agenda for revitalization
and renewal. The events of the past three decades, detailed
here, lend urgency to this effort. A major step in broaden-
ing the audience for this message and including all of
mathematics education was taken by the NRC in publishing
Everybody Counts early in 1989 (NRC, 1989~. The issues
and implications identified in this report and the two
additional descriptive reports on curriculum and resources
will assist the MS 2000 Committee in presentin;, an a ,enda
that will ensure a healthy flow of mathematical talent into
the next century.
Contents of This Report
Fundamentally this report concerns students and teach-
ers. The events and forces described above indicate the
complexity of this simple-sounding enterprise and how the
current predicaments have developed. Box 1.2 describes
the sources of the data used to compile this report and
explains the relationship between the text tables and fi ,-
ures and the additional data presented in the report's
Appendix Tables. Box 1.3 details characteristics of the
statistics component of college and university mathemati-
cal sciences and describes the the context in which infor-
mation in that area is provided. Chapter 2 describes in
broad strokes the larger communities of the U.S. labor
force and higher education, which both encompass the
mathematical sciences enterprise. Chapter 3 describes the
major components of, trends in, and utilization of college
and university mathematical sciences. Chapter 4 focuses
on mathematical sciences majors, both undergraduate and
graduate. Chapter 5 describes mathematical scientists in
the workplace; colleges and universities are a principal
topic, since academe is still the dominant employer of
mathematical scientists. That situation, however, is chang-
in=. The increased use in various professions of the mathe-
matical sciences adds to their traditionally important uses
in everyday life, civic activities, and our rich intellectual
culture.
A Challenge of Numbers describes the circumstances and issues centered on people in the mathematical sciences, principally students and teachers at U.S. colleges and universities. A healthy flow of mathematical talent is crucial not only to the future of U.S. mathematics but also as a keystone supporting a technological workforce. Trends in the mathematical sciences' most valuable resource--its people--are presented narratively, graphically, and numerically as an information base for policymakers and for those interested in the people in this not very visible, but critical profession | 677.169 | 1 |
Ordering Information
QuickList
This 2-line display scientific calculator combines statistics and advanced scientific functions and is a durable and affordable calculator for the classroom. The 2-line display helps students explore math and science concepts in the classroom. It is ideal for algebra, geometry, trigonometry, and statistics as well as general math and science. | 677.169 | 1 |
9780871508676
ISBN:
0871508672
Edition: 2 Publisher: Brooks/Cole
Summary: This outstanding text starts off using vectors and the geometric approach, featuring a computational emphasis. The authors provide students with easy-to-read explanations, examples, proofs, and procedures. Elementary Linear Algebra can be used in both a matrix-oriented course, or a more traditionally structured course.
Ships From:Sand Springs, OKShipping:Standard, ExpeditedComments:2nd edition. Book is in good shape, no scribbles, highlighting or underlining, a little general w... [more] [less]
2nd edition. Book is in good shape, no scribbles, highlighting or underlining, a little general wear, little bit of a tear inside, from a smoke-free environment. Items are typ [more]
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ISBN-13:9780871508676
ISBN:0871508672
Edition:2nd
Publisher:Brooks/Cole
Valore Books is the best place for cheap Elementary Linear Algebra - Stewart M. Venit - Mass Market Paperback - 2nd ed rentals, or used and new condition books available to purchase and have shipped quickly. | 677.169 | 1 |
Introduces students to both traditional economic views and their progressive critique. This book offers a discussion of economic history and the history of economic thought, including the ideas of Karl...
Maths for Economics provides a solid foundation in mathematical principles and methods used in economics, beginning by revisiting basic skills in arithmetic, algebra and equation solving and slowly building to... | 677.169 | 1 |
102 Combinatorial Problems From the Training of the USA Imo Team
9780817643171
ISBN:
0817643176
Publisher: Birkhauser Boston
Summary: "Andreescu's 51 'introductory problems' and 51 'advanced problems,' all novel, would nicely supplement any university course in combinatorics or discrete mathematics. This volume contains detailed solutions, sometimes multiple solutions, for all the problems, and some solutions offer additional twists for further thought . . . "'"CHOICE102 Combinatorial Problems consists of carefully selected problems that have been ...used in the training and testing of the USA International Mathematical Olympiad (IMO) team. The text provides in-depth enrichment in the important areas of combinatorics by systematically reorganizing and enhancing problem-solving tactics and strategies. The book gradually builds combinatorial skills and techniques and not only broadens the student's view of mathematics, but is also excellent for training teachers.
Andreescu, Titu is the author of 102 Combinatorial Problems From the Training of the USA Imo Team, published under ISBN 9780817643171 and 0817643176. Two hundred twenty six 102 Combinatorial Problems From the Training of the USA Imo Team textbooks are available for sale on ValoreBooks.com, fifty four used from the cheapest price of $32.02, or buy new starting at $47.66 | 677.169 | 1 |
Can someone point me to site that would help me in using Mathematica 5.2 for Students for purpose of calculations related to Systhems theory. I'm having trouble with several topics... for example doing InverseLaplaceTransform of function: | 677.169 | 1 |
Essential Calculus, 2nd Edition | 9781133112297
Author(s): Stewart book is for instructors who think that most calculus textbooks are too long. In writing the book, James Stewart asked himself: What is essential for a three-semester calculus course for scientists and engineers? ESSENTIAL CALCULUS, Second Edition, offers a concise approach to teaching calculus that focuses on major concepts, and supports those concepts with precise definitions, patient explanations, and carefully graded problems. The book is only 900 pages--two-thirds the size of Stewart's other calculus texts, and yet it contains almost all of the same topics. The author achieved this relative brevity primarily by condensing the exposition and by putting some of the features on the book's website, Despite the more compact size, the book has a modern flavor, covering technology and incorporating material to promote conceptual understanding, though not as prominently as in Stewart's other books. ESSENTIAL CALCULUS features the same attention to detail, eye for innovation, and meticulous accuracy that have made Stewart's textbooks the best-selling calculus texts in the world. | 677.169 | 1 |
This is a text on elementary multivariable calculus, designed for students who have completed courses in single-variable calculus. The traditional topics are covered: basic vector algebra; lines,... More > planes and surfaces; vector-valued functions; functions of 2 or 3 variables; partial derivatives; optimization; multiple integrals; line and surface integrals.
The book also includes discussion of numerical methods: Newton's method for optimization, and the Monte Carlo method for evaluating multiple integrals. There is a section dealing with applications to probability. Appendices include a proof of the right-hand rule for the cross product, and a short tutorial on using Gnuplot for graphing functions of 2 variables.
There are 420 exercises in the book. Answers to selected exercises are included.< Less
This is a text on elementary trigonometry, designed for students who have completed courses in high-school algebra and geometry. Though designed for college students, it could also be used in high... More > schools. The traditional topics are covered, but a more geometrical approach is taken than usual. Also, some numerical methods (e.g. the secant method for solving trigonometric equations) are discussed. A brief tutorial on using Gnuplot to graph trigonometric functions is | 677.169 | 1 |
Elementary Linear Algebra
9780534951900
ISBN:
0534951902
Edition: 4 Pub Date: 1995 Publisher: Brooks Cole
Summary: This outstanding text starts off using vectors and the geometric approach, featuring a computational emphasis. The authors provide students with easy-to-read explanations, examples, proofs, and procedures. Elementary Linear Algebra can be used in both a matrix-oriented course, or a more traditionally structured course.
Stewart Venit is the author of Elementary Linear Algebra, published 1995 under ISBN 978053...4951900 and 0534951902. One hundred twenty eight Elementary Linear Algebra textbooks are available for sale on ValoreBooks.com, twenty used from the cheapest price of $3.90, or buy new starting at $39 | 677.169 | 1 |
Teaching Mathematics in ATE Programs
A working draft of resources and reports from an NSF-sponsored project intended to strengthen the role of mathematics in Advanced Technological Education (ATE) programs. Intended as a resource for ATE faculty and members of the mathematical community. Comments are welcome by e-mail to the project directors:
Susan L. Forman or
Lynn A. Steen.
ATE projects enable teachers and students to look at the world differently. Most mathematics teachers have little experience either using or teaching the kind of mathematical applications that are embedded in ATE projects. So while working on ATE projects, matheamatics faculty become students again: to teach in these programs, they need to acquire new vocabulary, learn new methods, and struggle with new concepts. Through this effort they experience education once again through the eyes of their students. Likewise, ATE students become teachers: as students work in teams to solve real problems, they discover the benefits of learning from each other.
The project approach of ATE programs creates other pedagogical opportunities as well. In traditional mathematics courses dominated by homework and tests, teachers learn more about their students' weaknesses than about their strengths, more about what they can't do than about what they can do. In contrast, students working on ATE projects have much more opportunity to demonstrate their strengths--and more opportunities to work around (or remedy) their weaknesses.
Notwithstanding these opportunities for creative pedagogy, many students in ATE programs find that their mathematical experiences remain as they had been in traditional courses, even as other parts of their program adopt more project-oriented, student-active, exploratory characteristics. In this section we examine some of the distinctive pedagogical challenges posed by mathematics in ATE programs.
Worksheets
Since all students need help learning how to approach complex problems, ATE curriculum developers and instructors generally provide stepping stones that bridge the gap between students' prior experience with narrow exercises and the ATE requirement of working through broad projects. The most common means of providing this help is a worksheet that lays out a precise plan in a succession of small steps with clear instructions for completing each step. Worksheets can be especially helpful as an aid for enabling students with spotty mathematical backgrounds to successfully complete large-scale projects. With worksheets, virtually any conscientious student can complete the required work, and everyone involved--teacher and student--feels greater confidence that challenge of problem-solving has been met.
Unfortunately, few students learn much lasting or important mathematics from worksheets. Worksheets violate most of the pedagogical principles espoused by the mathematics standards. Far too many worksheets offer little more than rote instruction for solving a particular problem or operating particular software. Students who complete worksheets may have solved the problem yet still not have learned anything about problem solving. Often, they don't even have a comprehensive understanding of the particular problem they have just solved.
The challenge of helping students move from simple, one-step problems to cognitively complex multi-step endeavors is significant, but worksheets are rarely an ideal strategy.
Highlighting Mathematics
Although mathematicians often focus on formal proof as an essential aspect of mathematics, in real life careful reasoning is more important than formal proof. Effective ATE programs help students learn how to make a persuasive case for the analysis they have performed. Learning how to make decisions based on evidence and how to convince others of the soundness of one's own work is not only essential training for successful employment, but is also very good practice for understanding formal proofs which a student may encounter in subsequent mathematics courses. ATE students need not only to learn to reason, but they also to recognize how reasoning in applied contexts compares with reasoning in mathematical contexts.
More generally, since ATE curricula are often unconventional when measured against traditional academic programs, students need at some point to recognize and be able to describe what they have learned using the conventional language of mathematics. Otherwise they begin to think that their friends in traditional courses are learning all the "right stuff" while they are not. ATE students need not only to solve problems but also to learn proper names for mathematical objects and procedures; to distinguish among guessing, conjecturing, solving, and proving; and to understand the the map of mathematics. Reaching this kind of mathematical closure is an important objective for any ATE program.
Authentic Problems
Mathematics problems that students encounter tend to come in three flavors: pure, applied, and authentic. Pureproblems--the majority found in school classrooms--present mathematics naked, without clothing or context. What is 25% of 73? Solve 3x + 7 = 15. What is the area of a triangle with sides 3, 5, and 7? Even though problems such as these represent the core of mathematics and are essential to any uses of mathematics, they fail to pique the interest of many students.
In response to demands for more relevance, publishers fill textbooks also with so-called appliedproblems that situate mathematical questions in some context, real or imagined:
If 8 men can do a job in 12 days, how long it will take to complete the job if two men quit?
Stephen had $24.09 in his pocket. If he spends $10.60 on a book and $3.30 on a snack, how much does he have left?
Most of these problems are contrived, and students know it. Rarely do they represent a plausible problem, and even when they do it is unlikely that a person would use school mathematics as the means to solve it. (Stephen would probably take the remaining money out of his pocket and count it.)
Authenticproblems, in contrast, arise naturally in work (e.g., controlling processes on assembly lines, laying out new manufacturing facilities, preparing yield maps of a farmer's fields) and in ordinary living (e.g., understanding amounts withheld from a paycheck, planning to buy a car or redecorate a room). Because authentic problems are rooted in context, they rarely survive transplantation to generic mathematics classrooms. Since they can be properly experienced only in an environment that is hospitable to their defining context, they are rarely encountered in traditional classrooms. Even for instructors strongly committed to authenticity, finding and employing natural contexts remains a nearly insurmountable obstacle.
ATE programs can help with the problem of authenticity. Workplace settings connected with the ATE goal can be used to motivate, illustrate, and teach mathematics. For example:
Data from the manufacuture of silicon wafers (for computer chips) can be used to introduce formal logic, sets, Venn diagrams, logic gates, and finite fields.
Data from fast food chains on nutrition and sales (gathered from corporate reports found on the Internet) can support a project in which students analyse issues surounding the selection of a fast food chain for their campus.
Federal guidelines from the Americans with Disabilities Act (ADA) provide an opportunity for students to experience practical trigonometry by checking campus wheelchair ramps.
Global geography and climate (e.g., surveying, navigation, land use, heat islands, urbanization) can be used to introduce geometry in thee-dimensional contexts.
Flow charts, decision trees, pie charts, coded maps, and business charts can be used to introduce mathematical ideas in the vocabulary of the typical workplace and with the authenticity of real data.
Transfer of Learning
An important practical and political impediment to ATE programs is the well known difficulty of transferring mathematical skills and knowledge from one context to another. Many parents and policy leaders oppose applied and vocationally oriented programs such as ATE because of a belief that skills learned in such programs will be applicable to only one type of job. They are well aware that today's students must be prepared to change both jobs and even careers several times throughout their working lifetimes. Moreover, mathematics is seen as a subject that is supposed to be useful in many fields, so the idea of teaching it in the specific context of a single ATE applicaiton strikes many as problematic.
Educators also complain about students' lack of ability to use in new contexts skills learned in other settings. For example, science students fail to recognize in a biology class equations they learned to solve in their mathematics class. Agriculture students fail to recognize patterns in data that they learned about, albeit abstractly, in their statistics course. Students everywhere persist in believing that the mathematics they learn is of little use since they fail to recognize it when it arises outside of mathematics class.
Those who teach mathematics as part of the ATE program can aid transfer of learing by introducing students to the same mathematical concept in a different context. This approach, more self-conscious about the problem of transfer of learning, helps many students recognize that mathematical tools are meant to be used, and can be used in more than one context. But it requires an unusually high degree of coordination between the mathematics program and the ATE program--coordination that is often impeded by turf issues or articulation restrictions.
Supported by the Advanced Technological Education (ATE) program at the National Science Foundation. Opinions and information on this site are those of the authors and do not represent the views of either the ATE program or the National Science Foundation. | 677.169 | 1 |
Summary: STUDY GUIDE FOR 3C
K. GRACE KENNEDY
Spring 2009
Contents
1. Introduction 1
1.1. When we can find a solution explicitly. 2
1.2. When you don't or can't find a solution explicitly: Qualitative
Analysis of the Solutions. 4
1.3. Applications 4
2. Systems of Differential Equations 5
2.1. Phase Diagrams 5
2.2. Linear Algebra 6
3. Review 7
4. Study tips 7
Please keep in mind that this is up to date as of Thursday May 7th. Anything
covered in class or section between now and the midterm is fair game.
If you find any errors in content or formating or if there is something that I have
left off, please send me an email and let me know. I hope this helps!
Do not walk into the exam without a thorough understanding of the following
information: | 677.169 | 1 |
AP Central
Professional mathematics organizations, such as the National Council of Teachers of Mathematics, the Mathematical Association of America, and the Mathematical Sciences Education Board of the National Academy of Sciences, have strongly endorsed the use of calculators in mathematics instruction and testing.
The use of a graphing calculator in AP Calculus is considered an integral part of the course. Teachers should be using this technology on a regular basis with students so that students become adept at using their graphing calculators.
The Development Committee Perspective
The AP Calculus Development Committee understands that new calculators and computers, capable of enhancing the teaching of calculus, continue to be developed. There are two main concerns that The Committee considers when deciding what level of technology should be required for the exams: equity issues and teacher development. The Committee can develop exams that are appropriate for any given level of technology, but it cannot develop exams that are fair to all students if the spread in the capabilities of the technology is too wide. The use of graphing calculators was introduced in 1994-95, and the course description was revised in 1997-98 to reflect significant changes in calculus instruction. The AP Calculus Development Committee recognizes the large burden placed on AP teachers to incorporate these changes into their courses.
Over time, the range of capabilities of graphing calculators has increased significantly. Some calculators are much more powerful than first-generation graphing calculators and may include symbolic algebra features. Other graphing calculators are, by design, intended for students studying mathematics at lower levels than calculus. Therefore, The Committee has found it necessary to make certain requirements of the technology that will help ensure that all students have sufficient computational tools for the AP Calculus Exams. Exam restrictions should not be interpreted as restrictions on classroom activities. The Committee will continue to monitor the developments of technology and will reassess the testing policy regularly.
Technology Restrictions on the Exams Unacceptable machines, models and features include the following: Non-graphing scientific calculators, portable/handheld computers, laptops, electronic writing pads, pocket organizers; models with QWERTY (i.e., typewriter) keypads as part of hardware or software (e.g., TI-92 Plus, Voyage 200); models with pen-input/stylus/touch-screen capability (e.g., Palm, PDAs, Casio ClassPad); models with wireless or Bluetooth capability; models with paper tapes; models that "talk" or make noise; models that require an electrical outlet; models that can access the Internet; models that have cell phone capability or audio/video recording capability; models that have a digital audio/video player; models that have a camera or scanning capability. In addition, the use of hardware peripherals with an approved calculator is not permitted.
Test administrators are required to check calculators before the exam. Therefore, it is important for each student to have an approved calculator. Students should be thoroughly familiar with the operation of the calculators they plan to use on the exam. Calculators may not be shared, and communication between calculators is prohibited during the exam. Students may bring to the exam one or two (but no more than two) graphing calculators from the current List of Graphing Calculators.
Calculator memories will not be cleared. Students are allowed to bring to the exam calculators containing whatever programs they want.
Students must not use calculator memories to take test materials out of the room. Students should be warned that their scores will be invalidated if they attempt to remove test materials from the room by any method.
For results obtained using one of the four required calculator capabilities listed above, students are required to write the setup (e.g., the equation being solved, or the derivative or definite integral being evaluated) that leads to the solution, along with the result produced by the calculator. For example, if the student is asked to find the area of a region, the student is expected to show a definite integral (i.e., the setup) and the answer. The student need not compute the antiderivative; the calculator may be used to calculate the value of the definite integral without further explanation. For solutions obtained using a calculator capability other than one of the four required ones, students must also show the mathematical steps that lead to the answer; a calculator result is not sufficient. For example, if the student is asked to find a relative minimum value of a function, the student is expected to use calculus and show the mathematical steps that lead to the answer. It is not sufficient to graph the function or use a built-in minimum folder.
When a student is asked to justify an answer, the justification must include mathematical reasons, not merely calculator results. Functions, graphs, tables, or other objects that are used in a justification should be clearly identified.
Exploration Versus Mathematical Solution
A graphing calculator is a powerful tool for exploration, but students must be cautioned that exploration is not a mathematical solution. Exploration with a graphing calculator can lead a student toward an analytical solution, and after a solution is found, a graphing calculator can often be used to check the reasonableness of the solution.
Note: As on previous AP Calculus Exams, a decimal answer must be correct to three decimal places unless otherwise indicated. Students should be cautioned against rounding values in intermediate steps before a final calculation is made. Students should also be aware that there are limitations inherent in graphing calculator technology; for example, answers obtained by tracing along a graph to find roots or points of intersection might not produce the required accuracy.
Graphing Calculator Capabilities for the Exams
The committee develops exams based on the assumption that all students have access to four basic calculator capabilities used extensively in calculus. A graphing calculator appropriate for use on the exams is expected to have the built-in capability to:
plot the graph of a function within an arbitrary viewing window
find the zeros of functions (solve equations numerically)
numerically calculate the derivative of a function
numerically calculate the value of a definite integral
One or more of these capabilities should provide the sufficient computational tools for successful development of a solution to any exam question that requires the use of a calculator. Care is taken to ensure that the exam questions do not favor students who use graphing calculators with more extensive built-in features.
If a student wishes to use a calculator not on the list, then the AP teacher must contact ETS (609 771-7300) prior to April 1 of the testing year to receive written permission for the student to use the calculator on the AP Exams.
The College Board neither endorses, controls the content of, nor reviews the external Web sites included on this page. Please note that following links to external Web sites will open a new browser window. If you discover a bad link, let us know by sending mail to apctechsupport@collegeboard.org. | 677.169 | 1 |
Practical Approach to Arithmetic And Algebra for College Students
9780759352230
ISBN:
0759352232
Publisher: CENGAGE Learning Custom Publishing
Summary: Dr. Jerry Kornbluth earned his B.S. at Bowling Green State University and his MBA and PhD from Hofstra University. He retired from Nassau Community College after 35 years of teaching math and statistics, reaching rank of full professor in 1979 and awarded the rank of Professor Emeritus in 2001. Kornbluth also was an adjunct professor at La Guarida Community College and Queensborough Community College for 32 years. He... has worked with school districts throughout New York City and Long Island as well as federal agencies as a consultant on statistics related projects. Kornbluth is currently the Assistant Vice President of Academics at Interboro Institute.
Green, Edward L. is the author of Practical Approach to Arithmetic And Algebra for College Students, published under ISBN 9780759352230 and 0759352232. Three Practical Approach to Arithmetic And Algebra for College Students textbooks are available for sale on ValoreBooks.com, two used from the cheapest price of $0.24, or buy new starting at $31.75.[read more] | 677.169 | 1 |
An Logo-animated helicopter can be used to investigate the concepts of variables, and of reflections and y as a function of x on the coordinate grid. The first Logo animation of a helicopter flying ba... More: lessons, discussions, ratings, reviews,...
This is an extended Logo investigation of probabilities and of modeling real-life situations: that of a 1 and 1 shooter in basketball, and the expected probabilities arising from past performance. More: lessons, discussions, ratings, reviews,...
This problem could be used in varying degrees with 6th graders through high school. It encourages students to use good problem-solving heuristics. Logo is used to extend this problem and to encourage ... More: lessons, discussions, ratings, reviews,...
As part of an Honors project, a pre-service teacher relates how she worked with three seventh grade students to see if the balance applets would give students a deeper understanding of algebraic equat... More: lessons, discussions, ratings, reviews,...
This mathlet allows you to solve simple linear equations through the use of a balance beam. Unit blocks (representing 1s) and X-boxes (for the unknown, X), are placed on the pans of a balance beam. More: lessons, discussions, ratings, reviews,...
The user reviews definitions of important algebra terms. After viewing further explanations and some examples, users can interactively test their understanding of the definitions of important algebra... More: lessons, discussions, ratings, reviews,...
The user reviews like terms and how to group like terms together in expressions. After viewing examples, users can interactively practice matching expressions on one side with expressions on the othe... More: lessons, discussions, ratings, reviews,...
The user reads about the definition of an equation, the use of variables, and how to write an equation from a sentence. Examples are given as well as an online quiz to practice the skill of matching a | 677.169 | 1 |
Enter your mobile number or email address below and we'll send you a link to download the free Kindle App. Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required.
Tough Test Questions? Missed Lectures? Not Enough Time?
Fortunately, there's Schaum's. This all-in-one-package includes more than 500 fully solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 25 detailed videos featuring math instructors who explain how to solve the most commonly tested problems--it's just like having your own virtual tutor! You'll find everything you need to build confidence, skills, and knowledge for the highest score possible.
More Helpful tables and illustrations increase your understanding of the subject at hand. | 677.169 | 1 |
97805216307Mathematical Explorations with MATLAB
Mathematical Explorations with MATLAB examines the mathematics most frequently encountered in first-year university courses. A key feature of the book is its use of MATLAB, a popular and powerful software package. The book's emphasis is on understanding and investigating the mathematics by putting the mathematical tools into practice in a wide variety of modeling situations. Even readers who have no prior experience with MATLAB will gain fluency. The book covers a wide range of material: matrices, whole numbers, complex numbers, geometry of curves and families of lines, data analysis, random numbers and simulations, and differential equations from the basic mathematics. These lessons are applied to a rich variety of investigations and modeling problems, from sequences of real numbers to cafeteria queues, from card shuffling to models of fish growth. All extras to the standard MATLAB package are supplied on the World Wide Web. | 677.169 | 1 |
Precalculus
Browse related Subjects ...
Read More introduces a unit circle approach to trigonometry and includes a chapter on limits to provide students with a solid foundation for calculus concepts. The large number of pedagogical devices employed in this text will guide a student through the course. Integrated throughout the text, students and instructors will find Explore-Discuss boxes which encourage students to think critically about mathematical concepts. In each section, the worked examples are followed by matched problems that reinforce the concept being taught. In addition, the text contains an abundance of exercises and applications that will convince students that math is useful. There is a MathZone site featuring algorithmic exercises, videos, and other resources that accompanies the text.
Read Less
Fair. 0073519510 All Supplemental Materials Not Included. -used book-book appears to be recovered-has some used book stickers-free tracking number with every order. book may have some writing or highlighting, or used book stickers on front or back
Fair. 0073519510 0073519510 | 677.169 | 1 |
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About the book:
A proven motivator for readers of diverse mathematical backgrounds, this book explores mathematics within the context of real life using understandable, realistic applications consistent with the abilities of any reader. Graphing techniques are emphasized, including a thorough discussion of polynomial, rational, exponential, and logarithmic functions and conics. Includes Case Studies; New design that utilizes multiple colors to enhance accessibility; Multiple source applications; Numerous graduated examples and exercises; Discussion, writing, and research problems; Important formulas, theorems, definitions, and objectives; and more. For anyone interested in algebra and trigonometry.
Hardcover, ISBN 0130914657 Publisher: Pearson, 200130914657 Publisher: Prentice Hall, 2001 Used - Good, Usually ships in 1-2 business days, Book has a small amount of wear visible on the binding, cover, pages. Selection as wide as the Mississippi.
Hardcover, ISBN 0130914657 Publisher: Prentice Hall, 2001 Used - Acceptable, Usually ships in 1-2 business days, 0130914657 Publisher: Prentice Hall, 200130914657 Publisher: Prentice Hall, 2001 | 677.169 | 1 |
This is a short eBook that describes how to get free high school Algebra 1 help online without having to spend any money, buy anything, join any free trials, or anything like that. Free High School Algebra 1 Help Online | Algebra 1 Help.org.
A short ebook explaining a simple way to subtract integers for people who have trouble subtracting integers. This uses a method based on simply changing a subtraction problem to an addition problem based on helping people with algebra. How to Subtract Integers Without Getting Confused | Algebra 1 Help.org | 677.169 | 1 |
Find a Merrimack MathIn general to join a PhD program a student should pass at least three branches of math namely, Analysis, Geometry and Algebra. Analysis include real and complex analysis (advanced calculus is part of analysis) Algebra include abstract algebra ( group theory, ring theory, field theory etc ). Geom... have built lasers, taught how to make holograms and helped design robots. In my work I had to design and perform tests or experiments where the results would be used in the real world. It is also necessary to be able to explain to others, including non-scientists what you did and why. | 677.169 | 1 |
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Written for undergraduate students in mathematics, engineering, and science programs, this book provides an introduction to basic terminology and concepts found in mathematical studies of wave phenomena. The book is divided into three parts: an introduction to one-dimensional waves and their visualization, traveling and standing waves, and waves arising from conservation laws. MATLAB functions are presented to animate solutions of examples in the book | 677.169 | 1 |
course involves students taking turn giving lectures on geometry topics. Subjects such as Gauss maps, minimal surfaces and manifolds and geodesics were covered in the lectures. Course materials include lecture...
This course, presented by MIT and taught by Professor Alar Toomre, provides an introduction to numerical analysis. The material looks at the basic techniques for the efficient numerical solution of problems in science... | 677.169 | 1 |
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MTH 149: Functional Math for Elementary Teachers II
This course is the second in a two-course sequence presenting the mathematical concepts and problem-solving techniques necessary for success in a teaching career at the elementary school level. It is not a course solely for math teachers; rather it provides the general mathematical background for teachers of all subjects. Topics include probability, an introduction to statistics, introductory geometry, congruence and similarity and measurement concepts | 677.169 | 1 |
This book presents an alternative way of constructing multi-frontal direct solver algorithms for mesh-based computations. The construction of the solver algorithm is based on the additional available knowledge concerning the structure of the computational mesh. The alternative method presented in…
Models, Methods, and Analysis with MATLAB® and MPI, Second Edition
This text is designed for mathematical modeling courses that teach programming with MATLAB®. Many examples show how to apply a model, select a numerical method, implement computer simulations, and assess the ensuing results. By using MATLAB code in a practical way instead of as a "black box,"…
The Cauchy Transform, Potential Theory and Conformal Mapping explores the most central result in all of classical function theory, the Cauchy integral formula, in a new and novel way based on an advance made by Kerzman and Stein in 1976.
The book provides a fast track to understanding the Riemann…
A Powerful Methodology for Solving All Types of Differential Equations
Decomposition Analysis Method in Linear and Non-Linear Differential Equations explains how the Adomian decomposition method can solve differential equations for the series solutions of fundamental problems in physics,…
Line Integral Methods for Conservative Problems explains the numerical solution of differential equations within the framework of geometric integration, a branch of numerical analysis that devises numerical methods able to reproduce (in the discrete solution) relevant geometric properties of the…
Methods and Applications, Second Edition
Numerical Analysis for Engineers: Methods and Applications demonstrates the power of numerical methods in the context of solving complex engineering and scientific problems. The book helps to prepare future engineers and assists practicing engineers in understanding the fundamentals of numerical…
Optimization algorithms are critical tools for engineers, but difficult to use since none of them are universal in application. This introductery text builds up the knowledge set, from the basics, so that engineering students can understand the processes that govern optimization processes.…
A concise introduction
Computational Economics: A concise introduction is a comprehensive textbook designed to help students move from the traditional and comparative static analysis of economic models, to a modern and dynamic computational study. The ability to equate an economic problem, to formulate it into a…
Methods for Computer Vision, Machine Learning, and Graphics
Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook…
Teach Your Students Both the Mathematics of Numerical Methods and the Art of Computer Programming
Introduction to Computational Linear Algebra presents classroom-tested material on computational linear algebra and its application to numerical solutions of partial and ordinary differential equations…
A Practical Guide to Geometric Regulation for Distributed Parameter Systems provides an introduction to geometric control design methodologies for asymptotic tracking and disturbance rejection of infinite-dimensional systems. The book also introduces several new control algorithms inspired by… | 677.169 | 1 |
Product Overview
This booklet, produced in conjunction with the Mathematical Association of America, features 20 two-page profiles of people who use math to help instructors answer the question: "What''s math good for anyway?"
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Physical
Dimensions
(in Inches) 9.25H x 6.25L x 0.25T
From the Publisher
Editors Note
This booklet, produced in conjunction with the Mathematical Association of America, features 20 two-page profiles of people who use math to help instructors answer the question: "What's math good for anyway?" | 677.169 | 1 |
The first edition of this book sold more than 100,000 copies-Discrete Mathematics and its Applications, Seventh Edition, is intended for one- or two-term introductory discrete mathematics courses taken by students from a wide variety of majors, including computer science, mathematics, and engineering. This renowned best-selling text, which has been used at over 500 institutions around the world, gives a focused introduction to the primary themes in a discrete mathematics course and demonstrates the relevance and practicality of discrete mathematics to a wide a wide variety of real-world applications…from computer science to data networking, to psychology, to chemistry, to engineering, to linguistics, to biology, to business, and to many other important fields.
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science.
New Senior Mathematics Extension 1 for Years 11&12 covers all aspects of the Extension 1 Mathematics course for Year 11&12. We've completely updated the series for today's classrooms, continuing the much-loved approach to deliver mathematical rigour with challenging student questions.
Users discover the many ways in which mathematics is relevant to their lives with MATHEMATICS: A PRACTICAL ODYSSEY, 7E and its accompanying online resources. They master problem-solving skills in such areas as calculating interest and understanding voting systems and come to recognize the relevance of mathematics and to appreciate its human aspect." | 677.169 | 1 |
2Math Principles for Food Service Occupations
Math Principles for Food Service Occupations
Summary
MATH PRINCIPLES FOR FOOD SERVICE OCCUPATIONS, 6E stresses the direct relevance of math skills in the food service industry while teaching the basic math principles that affect everything from basic recipe preparation to managing food and labor costs in a restaurant operation. All the mathematical problems and concepts presented are explained in a simplified, logical, step-by-step manner. New to this edition, illustrations in full color add visual appeal to the text and help culinary students to master important concepts. Now in its 6th edition, this book demonstrates the importance of understanding and using math concepts to effectively make money in this demanding business. Part 1 explains how to use the calculator. Part 2 reviews basic math fundamentals. The following parts address math essentials and cost controls in food preparation and math essentials in food service record keeping, while the last part of the book concentrates on managerial math. New topics to this 6th edition include controlling beverage costs; clarifying and explaining the difference between fluid ounces and avoirdupois ounces; and an entire new section on yield testing and how to conduct these tests. There are new methods using helpful memory devices and acronyms to help readers remember procedures and formulas, such as BLT, NO, and the Big Ounce. New strategies and charts are also shown and explained on how to use purchases in order to control food and beverage costs and how transfers affect food and beverage costs. In addition, sections have been added on how to control costs using food (or liquor, or labor) cost percentage guidelines. The content in MATH PRINCIPLES FOR FOOD SERVICE OCCUPATIONS, 6E meets the required knowledge and competencies for business and math skills as required by the American Culinary Federation. | 677.169 | 1 |
Understanding Intermediate Algebra A Course for College Students (with CD-ROM, Make the Grade, students grasp the "why" of algebra through patient explanations, Hirsch and Goodman gradually build students' confidence without sacrificing rigor. To help students move beyond the "how" of algebra (computational proficiency) to the "why" (conceptual understanding), the authors introduce topics at an elementary level and return to them at increasing levels of complexity. Their gradual introduction of concepts, rules, and definitions through a wealth of illustrative examples - both numerical and algebraic-helps students compare and contrast related ideas and understand the sometimes subtle distinctions among a variety of situations. This author team carefully prepares students to succeed in higher level mathematics. | 677.169 | 1 |
My son has had some experience with algebra in 7th grade public school. I bought Saxon Math Algebra 1/2 and found it to be extremely dry and hard for us to follow. I used a Spectrum Algebra workbook ($12 at B&N), which I found to be an effective temporary solution until we found LifePac math.
The LifePac math curriculum works well for my son. We use YouTube videos for instruction from time to time, but usually a quick glance of the newly introduced step is enough for him to grasp the lesson. Some sections have a lot of practice problems, so I let him do the odd number problems and only the even if he needs more practice. We started doing the first half (ex. 1-5 of 10 problems), but the problems sometimes increase in difficulty towards the end of the practice section. I love the teacher's manual because it shows all of the work. I am a humble mouthpiece when it comes to math instruction. With this teacher's manual, i can write out all the steps and let my son break them down for me.
Ballistic tip:
My son doesnt like to 'show work,' so I bought a dry erase board at the dollar store and he'll show me his work on that without messing up his paper. He shows his work on chapter tests, but not on daily assignments. If he misses a practice question, i have him show his work on the dry erase board and he finds his mistake rather quickly.
Excellent as a primary math book, and the teacher's guide has all the ideas you would need for anything "extra", based on the student's needs. Combining the Grade 9 with the Grade 10 Lifepac Math is also an excellent idea, depending on your classes motivation and progress.
This is my first time to use the Lifepac curriculum and I must say I am very pleased with it. The lessons are very easy to understand. I have ordered this for a refresher for my daughter over the summer. I will most likely be using this curriculum for all of her subjects in the fall.
Very detail material. Make sure your student comprehends the pre-algebra first before doing this. In the beginning it's easy, as you go further it gets harder but has good examples to go by and explanations | 677.169 | 1 |
Tagged Questions
Abstract algebra is the subject area of mathematics that studies algebraic structures such as groups, rings, fields, modules, vector spaces, and algebras. It is heavily used in several programming related fields, such as cryptography. Any math questions on this site should be programming related. | 677.169 | 1 |
book is relatively short, about 200 pages, organized into seven chapters. The first chapter sets the scope and objectives and contains a note on notation. The next chapter contains the fundamental concepts that are the key to the presentation and the authors' philosophy on numerical methods. Chapters 4–6 treat elliptic (Poisson's equation), parabolic (the diffusion equation), and hyperbolic partial differential equations, respectively. The last chapter shows the solutions of certain cases with singularities and nonlinear behavior. The boundary element method is briefly discussed in chapter 4; the method of characteristics is discussed in chapter 6. | 677.169 | 1 |
Master Algebra Lite
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Description
This is for students in High School/College learning algebra. If you are a beginner in algebra you might be thinking X+Y=XY, Is not it? But it's not.
The beauty of algebra is, it deals with variables, expressions & equations. You will come to know various formulas.
For example if you know (a+b)^3= a^3+b^3+3a^2b+3ab^2.
You can calculate any number to the powers 2,3,4…in a fraction of seconds.
In the above equation a ,b are variables. So you can calculate (1.034)^3 also using that formula. Just feed a=1& b=.034
IMathPractice Algebra's 3 steps method of teaching has sections like Tutorial, Practice Skills, Practice Test & Algebra Challenge. Under tutorial it teaches you.
Numbers
Types of Number like real number, integer, negative number, complex number
Addition, Subtraction, Multiplication & Division of Real Number
Addition, Subtraction, Multiplication & Division of Negative Number
Addition, Subtraction, Multiplication & Division of Complex Number
Properties of Number | 677.169 | 1 |
Later in the chapter we'll present a step method that you should employ on
every Problem Solving question you face. However, since different problems call
for different approaches, one of the steps, "Plan the Attack," is open-ended and
calls for you to choose the most effective approach to the problem at hand. So
before we get to the step method itself, we'll first demonstrate a standard
approach, as well as a few alternative approaches that may come in handy in
particular situations. Each approach discussed in this section represents a
different way to use the math concepts you reviewed in the previous chapter.
We'll cover the following:
Standard Applications of Math Concepts
Alternative Approaches for Special Cases
Standard Applications of Math Concepts
There's no need to make things more complicated than they need to be;
some questions require nothing more than straightforward applications of the
concepts you learned in chapter 2. This doesn't necessarily mean that such
questions will be easy, since some of the concepts themselves can be
complex, and the test makers occasionally complicate matters by sprinkling
traps among the choices. Easier questions often require the application of a
single concept, while harder questions may involve multiple concepts. Some
may even require you to draw your own diagram when none is given. Regardless
of the difficulty level, the standard application approach is the same:
Scope out the situation, decide on what concept or concepts are being
tested, and then use what you know about those concepts to answer the
question before looking at the choices. If you've done your work well, the
answer you get will be among the choices on the screen, and you'll click it
and move on.
Let's look at a few examples spanning various difficulty levels. We'll
take a look at single-concept questions based around one particular math
concept, and multiple-concept questions that require you to make use of
numerous bits of math knowledge to arrive at the answer. As you'll see,
we've bolded all our Math 101 concepts as they come up to make it easier for
you to navigate through our explanations.
Single-Concept Questions
Here's an example of the most basic kind of Problem Solving
question you'll see:
What is the value of x
if 3x – 27 = 33?
(A)
2
(B)
11
(C)
20
(D)
27
(E)
35
The math concept in play here is equations with one
variable, something you likely remember from junior high school.
There's nothing to do here but apply the concept: First isolate the
variable by adding 27 to both sides to get 3x = 60, and
then divide both sides by 3 to get x = 20, choice
C. No doubt the test makers include 2 among the answer
choices to trap people who accidentally subtracted 27 from both sides,
yielding 3x = 6 and x = 2. 11, choice
B, is what you get if you divide one number in the
problem (33) by another (3), and 27, choice D, appears in
the problem itself. Assuming you didn't fall for any of these traps,
there's not much to it: Just apply a single, fairly basic concept
directly to the problem to pick up the point.
Not all single-concept questions are necessarily so
straightforward, however, especially as you get on in the section. Try
this one on for size:
At a local golf club, 75 members
attend weekday lessons, 12 members attend weekend
lessons, and 4 members attend both weekday and
weekend lessons. If 10 members of the club do not
attend any lessons, how many members are in the
club?
(A)
65
(B)
75
(C)
82
(D)
93
(E)
101
There's only one concept in play here, but if you don't know it,
you're in for a very tough time. You need the formula for group
problems with two groups: group 1 + group 2 – both + neither = total. This is a formula you probably didn't learn in junior high or
high school, or most likely forgot even if you did. You probably won't
see a question like this early in the section, but if you're doing well,
the CAT's going to challenge you and start spitting out questions from
the harder end of the question pool. In any case, it's really only
testing whether you've done your homework and memorized the formula.
If you did, then you'd be in great shape, since the math itself is
not particularly difficult: If we let group 1 be the 75
members who attend weekday lessons and let group 2 be
the 12 members who attend weekend lessons, we get: 75 + 12 – 4 + 10 =
total. Solving for total gives 93, choice
D. Notice how choice B, 75, is a number
contained in the problem, while choice E, 101, is what you
get if you mistakenly add 4 instead of subtract it.
Multiple-Concept Questions
Some Problem Solving questions require you to pull together two or
more choice tidbits from your arsenal of essential math concepts. One of
the most common examples of a multiple-concept question involves
geometric formulas that generate equations that need to be solved
arithmetically and/or algebraically. Here's an example:
If AB =
BC and x = 60,
what is the length of CE in
rectangle ACDE?
(A)
4
(B)
(C)
(D)
8
(E)
12
This is a bit more involved than a typical single-concept question
because there are a number of geometry concepts you need to know and
some genuine opportunities to slip up on the arithmetic end too. It's a
mish-mash problem to boot, involving three triangles and a rectangle, so
if you don't know the special and exciting properties of these geometric
figures, you're pretty much sunk right there. If you do, then you should
be able to at least formulate the correct equation for line
EC, but then you still have to crunch the numbers to
solve it. Let's see what a solid effort on this question might look
like.
First, you're best off redrawing the diagram on your scratch
paper, since you wouldn't want to keep all the information you're going
to add to it in your head. Since AB and
BC are equal, ∠BAC and
∠BCA must be equal since the angles in a triangle
opposite from equal sides are equal (concept
1). Since the third angle labeled x equals
60°, ∠BAC and ∠BCA together must total
120° because the three angles of a triangle add up to 180°
(concept 2). Since we determined that
∠BAC and ∠BCA are equal, they both
must be 60°. Notice anything now? A triangle with three equal
angles is an equilateral triangle (concept
3). Since all three sides in an equilateral triangle are
equal (concept 4), AB =
BC = AC = 4. Since
ACDE is a rectangle, and opposite sides of a
rectangle are equal (concept 5),
AC = ED = 4. By now your sketch should
look like this:
Now that we have two sides of right triangle ECD,
we have everything we need to figure out the length of
EC, thanks to the Pythagorean theorem: x2 +
y2 =
z2
where x and y are the sides and
z is the hypotenuse (concept 6).
Substituting 4 and 8 as the sides and EC as the
hypotenuse gives us:
(EC)2 =
42 + 82
For convenience, we'll denote all of the ensuing
arithmetic, including simplifying the radical,
as concept 7:
Voila!—choice B. Check out the
traps: 4 (A) is a number calculated along the way; 8
(D) is a number given in the problem; and 12
(E) is what you get if you add the two known sides of
triangle ECD together.
Notice that no fewer than seven math concepts made their way into
this problem—none of them particularly earth-shattering or treacherous,
mind you, but still adding up to a medium-level challenge with plenty of
potential pitfalls.
Alternative Approaches for Special Cases
The standard "do question, look for answer" approach is all well and
good in many cases, but some questions call out for alternative approaches.
When the question contains variables in the answer choices, making up
numbers and substituting them into the problem is often very effective.
Conversely, when the answer choices contain actual numbers, you may benefit
from simply plugging them into the given situation to see which one works,
instead of hacking through some difficult arithmetic or algebra. Let's take
a look at each of these strategies, one by one.
Making Up Numbers
Which of the following problems would you rather be faced with on
test day?
Question 1: If x apples cost
y cents, how much will z apples
cost in dollars?
Question 2: If 5 apples cost 50 cents, how much will 10 apples
cost in dollars?
If you're like most people, question 2 looks much easier, and you
probably wouldn't have much trouble solving it: If you double the number
of apples, you double the number of cents. One hundred cents equals one
dollar. Done.
The difference between question 1 and question 2 is simple. We
replaced the variables in question 1 with some made-up numbers, thus
creating the easier question 2. So, if you see x, y, m,
n, or any other variables in both the question and the answer
choices, see if you can avoid using complicated algebra by making up
numbers and inserting them into the problem. You don't want to just make
up any old numbers, however—you want numbers that will simplify the
problem. Use the following guidelines:
Pick easy numbers. Although you could choose
582.97 as a value, you definitely wouldn't be making the problem any
easier. Stick to relatively small, whole numbers whenever possible.
Avoid 0, 1, and any numbers used in the problem.
The numbers 0 and 1 have unique properties that may skew the results
when used for this technique, so don't substitute either of those
into the problem. (We'll give you the exact opposite advice in the
Quantitative Comparisons chapter, since in those questions the
special properties of 0 and 1 come in handy.) Also, since the test
makers sometimes use numbers from the question to construct
distractors, you may get yourself into trouble by selecting those as
well. If, for example, the problem contains the expression
3a + 5, don't use 3 or 5. You shouldn't have
any trouble avoiding the few numbers used in the question itself,
just for good measure.
Choose different numbers for different variables.
For example, if the problem contains the variables
m and n, you wouldn't want to
choose 2 for both. Instead, you might choose 2 for
m and 3 for n.
Pay attention to units. If a problem involves a
change in units (such as minutes to hours, pennies to dollars, feet
to yards, and so on), choose a number that works well for both
units. For example, 120 would be a good choice for a vari- able
representing minutes, since 120 minutes is easily converted into 2
hours.
Obey the rules of the problem. Occasionally, the
problem may include specific requirements for variables. For
example, if the problem says that x must be
negative, you can't make up a positive value for x.
Save dependent variables for last. If the value
of one variable is determined by the value of one or more other
variables, make up numbers for those other variables first. That
will automatically determine the value of the variable that depends
on the value of the others. For example, if the problem states that
a = b + c,
a is dependent on b and
c. Choose values for b and
c first, and the value of a
will then simply emerge as the sum of b and
c.
Once you've selected your values, an actual number will emerge
when you work the problem out with the numbers you've selected. All you
need to do then is check which answer choice contains an expression that
yields the same value when you make the same substitutions. This will
make more sense in the context of an example, so let's apply the
strategy to the following question.
A gear makes r
rotations in m minutes. If it
rotates at a constant speed, how many rotations will
the gear make in h hours?
(A)
(B)
(C)
(D)
(E)
Sure, you could crunch through this algebraically, and if that
floats your boat, great. However, if you're among those who get a
headache from just looking at questions like this, making up numbers may
be just the way to go. Here's how.
The variables in this problem are r, m, and h. We can make up
whatever values we'd like for these, as long as the values we choose
make it easy to work the problem. For r, the number of rotations, let's
choose something small, like 3. For m, the number of minutes, we should
choose a value that will make it easy to convert to hours: 120 works
well, since 120 minutes is the same as 2 hours. Finally, for h, we
should choose something small again. Remember that we need to choose a
different value for each variable, so let's use 4. Now that we have our
numbers, simply plug them into the situation:
A gear makes 3 rotations in
120 minutes. If it rotates at a constant speed, how
many rotations will the gear make in 4 hours?
Okay, much better—that's something we can sink our teeth into. 120
minutes is the same as 2 hours, during which time the gear rotates 3
times. If it rotates 3 times in 2 hours, how many times will it rotate
in 4 hours? That's just twice as much time, so it will make twice as
many rotations: 2 × 3 = 6, and so 6 is what we get when we substitute
our values into the problem. Now we have to find the answer choice
that's equal to 6 when the same values are substituted for its
variables. Just work your way down the list, using 3 for
r, 120 for m, and 4 for
h:
A: That's not 6, the answer we
seek, so move on.
B: Yup—this is exactly what we're
looking for, so B is correct. If you're sure of your work,
there's no need to even continue with the choices; you'd just
click B and move on to the next question. For practice,
though, let's see how the other three pan out:
C: Way too big.
D: Way too small.
E: Four times bigger than what
we're after. Just what we thought: B is the only choice
that matches the number we derived from our made-up numbers, so B
gets the point.
You'll get more practice with this strategy as we go forward.
Let's now move on to our other specialty technique, an exercise in role
reversal that we call . . .
Working Backward
When the question includes an equation (or a word problem that can
be translated into an equation), and the answer choices contain
relatively simple numbers, then it may be possible to plug the choices
into the equation to see which one works. Working backward from the
choices in this manner may help you avoid setting up or solving
complicated equations and can save you time as well because of a neat
wrinkle of this technique: Since the choices in math questions are
usually written in either ascending or descending order, you can start
with the middle choice, choice C, and either get the answer
immediately or at least eliminate three choices for the price of one.
Here's how.
Let's say the answer choices are in ascending order. If you start
by plugging in C, then even if that choice doesn't work,
you can use the outcome to determine whether you need to plug in a
smaller or larger number. If you need a smaller number, then D
and E are out of the question, and you can go right
to test choice A or B. If instead you need a
larger number, chop A and B and try D
or E. Notice another nice feature: When you plug in
for the second time, that choice will either work or leave only one
choice standing. If you follow this alternative approach, you shouldn't
ever have to check more than two choices.
As always, math strategies make the most sense in the context of
examples, so we'll demonstrate using the following question.
A classroom contains 31 chairs,
each of which has either a cushion or a hard back.
If the room has five more cushion chairs than
hard-backed chairs, how many cushion chairs does it
contain?
(A)
10
(B)
13
(C)
16
(D)
18
(E)
21
Now if you happen to be an algebra whiz, you'd go ahead and use
the information to set up a pair of simultaneous equations to solve the
problem. However, you may find it easier to work backward instead. Since
the choices are in ascending order, we'll start with the middle one and
pretend it's correct. If it really is correct, then
plugging it into the problem's scenario will cause all the numbers to
work out, so let's see if it does.
The question is looking for the number of cushion chairs, which
for the moment we're assuming to be 16. We can bounce that number off
the information in the beginning of the second sentence (5 more cushion
chairs than hard chairs) to determine that with 16 cushion chairs, there
would have to be 11 hard chairs. Now all we have to do is check whether
this scenario matches the information in the first sentence. Would that
give us 31 chairs total? Nope: 16 + 11 = 27, so the numbers don't jibe.
That tells us three things: Choice C isn't correct,
choice B isn't correct, and choice A isn't
correct. We can knock out A and B along
with C because they're both smaller than
C, and if the number in C isn't big enough to
get us to our required 31 chairs, A and B
ain't gonna cut it either.
Now let's try D—if it works, it's correct, and if it
doesn't, we can select E without even trying it out: 18
cushion chairs means 18 – 5 = 13 hard chairs and 18 + 13 = 31 chairs
total. That matches the information in the question, so D
is correct. Note that you could have worked the numbers the other
way: If there are 31 chairs total, and we assume there are 18 cushion
chairs, then there would have to be 13 hard chairs. That matches the
information in the second sentence that requires 5 more cushion chairs
than hard ones. Either way you slice it, the number 18 fits the bill
when plugged back into the situation, and we didn't have to bother with
creating and solving simultaneous equations.
Use your judgment as to when to work backward. If there are
numbers in the answer choices, then consider it, but don't do it if the
numbers are unwieldy, such as complex fractions. One of the skills that
the best math test takers possess is the ability to determine the most
effective way to work through the problems. We've shown you standard
applications and a few powerful alternatives. Now let's assimilate what
you've learned into the general step method you'll use for all Problem
Solving questions. | 677.169 | 1 |
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The fun and friendly guide to really understanding math U Can: Basic Math & Pre-Algebra For Dummies is the fun, friendly guide to making sense of math. It walks you through the "how" and "why" to help you master the crucial operations that underpin every math class you'll ever take. With no-nonsense lessons, step-by-step instructions, practical... more...
Conquer Algebra I with these key lessons, practice problems, and easy-to-follow examples. Algebra can be challenging. But you no longer need to be vexed by variables. With U Can, studying the key concepts from your class just got easier than ever before. Simply open this book to find help on all the topics in your Algebra I class. You'll get... more... | 677.169 | 1 |
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When the answer at the back of the book is simply not enough, then you need the Student Solutions Manual. With fully worked-out solutions to all odd-numbered text problems, the Student Solutions Manual lets you "learn by example" and see the mathematical steps required to reach a solution. Worked-out problems included in the Solutions Manual are carefully selected from the textbook as representative of each section's exercise sets so you can follow-along and study more effectively. The Student Solutions Manual is simply the fastest way to see your mistakes, improve learning, and get better grades.
Most Helpful Customer Reviews
I'm 38 and am a home schooler and to get back into math mode, I chose this book. I did every odd problem and some of the systhesis problems. You will learn the material if you take the time. I spent around 14 or 15 months to get through the book. The program is excersises and review. Constant review is huge plus. I recommend you get the solutions manual from addison wesley. I've just started Marv's et.al.. Precalculus book and then will go onto calculus. I'm enjoying the math. Much more then in high school. My son and I sit down and learn together. He says "get your book" and lets do math. The key to his desire to do math is because he see's his dad doing it. I've seen many other books and this tops them all.
This book is not all you get. The book itself is great. But the additional FREE helps which come with the book assure that even the most inept math student can learn algebra. These helps consist of, but are not limited to:1) free tutoring via phone,email,& fax; 2)free practice problems via internet website. Other supplemental materials consist of: Videotapes, Tutorial Software, and a solutions manual. These are all available for the student. I haven't even mentioned the benefits that a classroom teacher has through the Instructor Supplements. These consist of a Test Bank/Instructor's Guide, extra practice problems, mtls for transparencies, video tape index, and several tools for the computer users: test generator, test grader,on-line course management and testing. In other words, this is a great resource for teachers also. I am in the processing of trying to purchase it for my school.
I have tutored math for over 20 years and Bittenger's book is one of the best I have ever seen for taking pre-algebra students from the basics to the complex. His examples are clearly laid out, easy to follow, and they lay a solid foundation for higher math learning. This book's concepts will definitely help high school students prepare for the SATs.
This is a used book in great condition. I first ordered it and received the wrong book, so had to go back and reorder the book again, but finally received the correct book. I am very happy with the price and condition of the book. I will order more college books from Amazon rather than spend a ton of money at the book store on campus. Even my college instructor recommended the class go on-line to Amazon and order used books because they were so much cheaper and usually in good condition.
This is the answer portion of a two book set plus an online MML site that compiles a portion this piece of education if you choose to rent or purchase the spiral version of the authors' series of books to complete this course. The price of the text is a little pricey but then maybe not when you consider you are getting two classes worth of teaching for the price of one. From that point of view this is a pretty cheap text and workbook combo. You can rent a spiral bound that requires you to get info from the MML site which you find you have no access code for. Ratings state the company willing to refund but if you ordered this manual of answers and you need the book, may I suggest you do not rent or buy the spiral edition. Look for a used book in good enough condition to get you through the courses and be done with it! | 677.169 | 1 |
Essential Info
Instructor Resources
Foundations of Mathematical Economics
Overview
This book provides a comprehensive introduction to the mathematical foundations of economics, from basic set theory to fixed point theorems and constrained optimization. Rather than simply offer a collection of problem-solving techniques, the book emphasizes the unifying mathematical principles that underlie economics. Features include an extended presentation of separation theorems and their applications, an account of constraint qualification in constrained optimization, and an introduction to monotone comparative statics. These topics are developed by way of more than 800 exercises. The book is designed to be used as a graduate text, a resource for self-study, and a reference for the professional economist.
About the Author
Michael Carter is Visiting Professor at the University of Hohenheim, Germany.
Endorsements
"This book extends the study of evolutionary dynamics to extensive form games, shifting seamlessly between biological foundations, mathematical tools and economic applications. It will be an essential resource for anyone interested in the evolutionary foundations of behavior." —Larry Samuelson, Department of Economics, University of Wisconsin, Madison
"Michael Carter's lucid exposition of a wide range of mathematical tools is essential reading for graduate students of economics. His marvelous collection of up-to-date examples perfectly complements his exposition of the theory." —Martin J. Osborne, Department of Economics, University of Toronto | 677.169 | 1 |
Algebra 1, Student Edition CCSSPrepare students for 21st century success with...- Seamlessly integrated print, digital, and interactive content that connects with students anytime and on any device.- Complete alignment with the Common Core State Standards- Support and resources for tailoring instruction to all levels of learners.- Built-in, frequent assessments that monitor student understanding and progress to ensure all students master concepts. Includes Print Student Edition | 677.169 | 1 |
A computer algebra system (CAS) is a software program that facilitates symbolic mathematics. The core functionality of a CAS is manipulation of mathematical expressions in symbolic form.
more from Wikipedia
Integral equation
In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign. There is a close connection between differential and integral equations, and some problems may be formulated either way. See, for example, Maxwell's equations.
more from Wikipedia
Analytic geometry
Analytic geometry, or analytical geometry has two different meanings in mathematics. The modern and advanced meaning refers to the geometry of analytic varieties. This article focuses on the classical and elementary meaning. In classical mathematics, analytic geometry, also known as coordinate geometry, or Cartesian geometry, is the study of geometry using a coordinate system and the principles of algebra and analysis.
more from Wikipedia | 677.169 | 1 |
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This activity and lesson is a great introduction to solving systems of equations. The site has links to tons of additional helpful material. #algebra #mathactivities
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These foldable notes are great for use in interactive notebooks!FactContents:- Teacher instructions for assembling the foldable notes- Foldable- Answer key for examplesCCSS A-SSECheck out these factoring activities: ... | 677.169 | 1 |
...
Show More succeeded with tens of thousands of college students, regardless of their math experience or affinity for the subject. With Business Calculus Demystified, you learn at your own pace. You get explanations that make differentiation and integration -- the main concepts of calculus -- understandable and interesting. This unique self-teaching guide reinforces learning, builds your confidence and skill, and continuously demonstrates your mastery of topics with a wealth of practice problems and detailed solutions throughout, multiple-choice quizzes at the end of each chapter, and a "final exam" that tests your total understanding of business calculus. Learn business calculus for the real world! This self-teaching course conquers confusion with clarity and ease. Get ready to: Get a solid foundation right from the start with a review of algebra Master one idea per section -- develop complete, comfortable understanding of a topic before proceeding to the next Find a well-explained definition of the derivative and its properties; instantaneous rates of change; the power, product, quotient, and chain rules; and layering different formulas Learn methods for maximizing revenue and profit... minimizing cost... and solving other optimizing problems See how to use calculus to sketch graphs Understand implicit differentiation, rational functions, exponents, and logarithm functions -- learn how to use log properties to simplify differentiation Painlessly learn integration formulas and techniques and applications of the integral Take a "final exam" and grade it yourself! Who says business calculus has to be boring? Business Calculus Demystified is a lively and entertaining way to master this essential math subject00
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Help
The goal of Making Mathematics is to provide high school students and teachers with the materials and mentorship necessary for engaging in a mathematical research experience.
Mathematical research can be described as the process through which an open-ended mathematical problem is investigated.
It can be fun, stimulating, rewarding, and quite challenging.
At Making Mathematics, students and teachers are paired with professional research mathematicians who guide the research process.
Our open-ended, mentored projects provide a very different experience than the school projects students are most often asked to participate in.
We encourage teachers, parents, mentors, and students to engage in this creative process. Through its ups and downs, we
hope you'll learn not only about mathematics but also that persistence and engaging the challenge are their own reward.
During summer 2000, the Making Mathematics Web site contains a limited number of prototype materials.
During autumn 2000, we will be pilot testing and refining these materials, as well as adding additional resources.
Our summer 2000 offerings include one complete project, The Simplex Lock.
The project provides warm-up exercises, hints, teaching notes, resources, extensions, and results so that students, teachers, and mentors can peruse a full spectrum of materials.
We have also included a sample of student work for this project.
(While results and student work are available to all Web site visitors during summer 2000, in the future these materials will be visible only to teachers and mentors who register with our site.
Registration will be initiated during autumn 2000.)
In coming months, we will also offer general teaching advice and lesson plans.
These curricular materials can be used to create a strand on doing research within a standard secondary mathematics course.
They can also be used as an elective devoted to mathematical research, or as stand-alone materials for working individually.
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The Making Mathematics Web site requires that your Web browser allow the use of "cookies".
A "cookie" is a marker that is shared between your computer and our Web site so that we can present automated features to you.
(For example, our menus and application forms depend upon cookies to display appropriate options for you.)
Our cookies are perfectly safe, and they are erased from your computer when you close or quit your Web browser.
If you see a request to "allow cookies" when you access our Web site, please click "yes" to enjoy the full resources of Making Mathematics.
Adobe Acrobat Reader
We offer many materials on our Web site in two formats:
HTML (HyperText Markup Language)
You can see these documents directly in your Web browser. (They are "plain" Web documents.)
PDF (Portable Document Format)
To see these documents, you must have Adobe Acrobat Reader installed on your computer. PDF documents display and print mathematics more crisply than HTML documents, and they include pagination. If you want to create handouts, use the PDF version of our documents.
Adobe Acrobat Reader is free, and installing and using the software is relatively easy. Many new computers come with Adobe Acrobat Reader already installed. You can read more about Adobe Acrobat Reader and download it if necessary at the following Adobe Web sites.
Macintosh users:
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Students
If you are a student who wishes to participate in Making Mathematics, you have several alternatives.
You can speak to your mathematics teacher and ask to include Making Mathematics research projects as part of your classroom work.
If your teacher agrees to participate, he or she can contact us at the addresses below.
Alternatively, if you are a student who wishes to work with us directly (no teacher involved), you can also contact us at the same addresses.
You should note, however that if you are under 13 years of age, your parents must send a separate email or letter approving of your participation.
We will contact you parents to verify their consent. | 677.169 | 1 |
I am teaching myself mathematics using textbooks and I'm currently studying the UK a-level syllabus (I think in the USA this is equivalent to pre-college algebra & calculus). Two resources I have found invaluable for this are this website ( and Wolfram Alpha ( I am very grateful that with those tools, I have managed to understand any questions/doubts I have had so far.
Can anyone recommended other valuable resources for the self-taught student of mathematics at this basic level?
1 Answer
1
Yes, this site as well as wolfram|alpha are both excellent resources for teaching yourself math!
In addition, I would suggest looking at this site. It provides tons of great math videos, if you are like me and too lazy to read your book sometimes. :) KhanAcademy is also good, but I do prefer the latter. If you can afford it, perhaps you should consider getting into an online class? That way you get more resources and a professor to directly speak to. Not to mention, most math jobs require that you show some accreditation (e.g. a degree). Not exactly sure about your situation, but thought I would mention it. Best of luck!
Thanks @Mr_CryptoPrime, patrickjmt.com looks excellent. I study computer science at university but have always only just "got by" with any mathematical understanding. So I am re-studying maths up to pre-university level. Actually I quite enjoy it now and I hope to continue into more advanced topics, so online classes may be a great idea. Thanks again!
–
Danny KingApr 12 '11 at 9:12
Cool, I am in my second semester of college, double majoring in applied mathematics and computer science. Ironically, I am failing my algorithms and discrete math class. :( I think I just over did it. Just a couple grand (at minimum wage) and 5 months of my life, oh well...lol I have taken college algebra, pre-calc, calc I online (and plan doing calc. II this summer). They have worked out fairly well I suppose. Much easier than driving all the way up to the University (an hour away). Nice to meet you!
–
Mr_CryptoPrimeApr 12 '11 at 9:21
Nice to meet you too, good luck with the course!
–
Danny KingApr 12 '11 at 10:59 | 677.169 | 1 |
This powerful problem-solver gives you 2,000 problems in discrete mathematics, fully solved step-by-step! From Schaum's, the originator of the solved-problem guide, and students' favorite with over 30 million study guides sold and this solution-packed timesaver helps you master every type of problem you will face on your tests, from simple questions on set theory to complex Boolean algebra, logic gates, and the use of propositional calculus. Go directly to the answers you need with a complete index. Compatible with any classroom text, Schaum's "2000 Solved Problems in Discrete Mathematics" is so complete it's the perfect tool for graduate or professional exam prep!
Back cover copy
Master discrete mathematics with Schaum'sNthe high-performance solved-problem guide. It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams! Students love Schaum's Solved Problem Guides because they produce results. Each year, thousands of students improve their test scores and final grades with these indispensable guides. Get the edge on your classmates. Use Schaum's! If you don't have a lot of time but want to excel in class, use this book to: Brush up before tests; Study quickly and more effectively; Learn the best strategies for solving tough problems in step-by-step detail. Review what you've learned in class by solving thousands of relevant problems that test your skill. Compatible with any classroom text, SchaumOs Solved Problem Guides let you practice at your own pace and remind you of all the important problem-solving techniques you need to rememberNfast! And SchaumOs are so complete, theyOre perfect for preparing for graduate or professional exams. Inside you will find: 2000 solved problems with complete solutionsNthe largest selection of solved problems yet published in discrete mathematics; A superb index to help you quickly locate the types of problems you want to solve; Problems like those you'll find on your exams; Techniques for choosing the correct approach to problems. If you want top grades and thorough understanding of discrete mathematics, this powerful study tool is the best tutor you can have! Chapters include: Set Theory; Relations; Functions; Vectors and Matrices; Graph Theory; Planar Graphs and Trees; Directed Graphs and Binary Trees; Combinatorial Analysis; Algebraic Systems; Languages, Grammars, Automata; OrderedSets and Lattices; Propositional Calculus; Boolean Algebra; Logic Gates. | 677.169 | 1 |
MathCast: Trigonometry
De Relentless Entertainment
Descrição
In most Colleges and Universities a course in Trigonometry is offered after a student has completed College Algebra and before the student goes on to Calculus. Trigonometry is a very important part of our daily lives. Every time you get into an automobile you experience the transformation of angular velocity to linear velocity that gets you to your destination. Every time you take a trip by air ; Vectors help you get there! Would you believe that your lawn mower blade is turning at the equivalent of approximately 120 miles per hour ( about 190 Kilometers per hour). Sadly, I encounter students in my Calculus classes who had not taken Trig, or not taken it seriously, and they pay a heavy price!
This set of videos is designed to cover all the major topics in Trigonometry in small segments, which you can stop and re-play at any time until you get it!
Our assumption is that you have successfully completed a College Algebra course and are continuing your career in mathematics, science or engineering.
We start this course with the basic definition of an angle and develop the basic principles of Trig. We discuss angular measurement in degrees and radians, angular velocity, basic trig functions, sine, cosine and tangent functions and their reciprocals cosecant, secant and cotangent. We show you how to plot these functions. We introduce Trig Identities and strategies to prove them. The course also covers Inverse Trig Function, Solving Triangles using the Laws of Sines and Cosines and how to solve a variety of trig problems. The course also covers the Complex Plane, Polar Co-ordinates and Parametric Functions.
Math is not a spectator sport! To get really good at it you must work problems to re-enforce your understanding. To that end we have includes numerous examples of how to solve various problems
The topics presented in Trigonometry include, but are not limited to, Angles, angular measure in radians and degrees, how to graph the various trig functions, trig identities and how to prove them, Inverse Trig Functions, Vectors, the complex and polar planes, parametric equations and more. | 677.169 | 1 |
A Source Book in Mathematics
A Source Book in Mathematics
A Source Book in Mathematics
Excerpt
The purpose of a source book is to supply teachers and students with a selection of excerpts from the works of the makers of the subject considered. The purpose of supplying such excerpts is to stimulate the study of the various branches of this subjects--in the present case, the subject of mathematics. By knowing the beginnings of these branches, the reader is encouraged to follow the growth of the science, to see how it has developed, to appreciate more clearly its present status, and thus to see its future possibilities.
It need hardly be said that the preparation of a source book has many difficulties. In this particular case, one of these lies in the fact that the general plan allows for no sources before the advent of printing or after the close of the nineteenth century. On the one hand, this eliminates most of mathematics before the invention of the calculus and modern geometry; while on the other hand, it excludes all recent activities in this field. The latter fact is not of great consequence for the large majority of readers, but the former is more serious for all who seek the sources of elementary mathematics. It is to be hoped that the success of the series will permit of a volume devoted to this important phase of the development of the science.
In the selection of material in the four and a half centuries closing with the year 1900, it is desirable to touch upon a wide range of interests. In no other way can any source book be made to meet the needs, the interests, and the tastes of a wide range of readers. To make selections from the field, however, is to neglect many more sources than can possibly be selected. It would be an easy thing for anyone to name a hundred excerpts that he would wish to see, and to eliminate selections in which he has no . . . | 677.169 | 1 |
Course description:
The first few weeks will be spent quickly covering the foundations of elementary number theory: divisibility, congruences, prime numbers, and so on, some of which might already be familiar to you. Emphasis will be on a level of mastery sufficient for you to teach the material. Once we have this foundation, we will move on to roots of polynomial congruences, arithmetic and multiplicative functions, binary quadratic forms, and parametrizing Pythagorean triples. The two most important topics of the course are primitive roots and quadratic reciprocity. Topics that might also be covered include simple Diophantine equations, Diophantine approximation, and continued fractions.
Course textbook:An Introduction to the Theory of Numbers, by Niven, Zuckerman, and Montgomery, 5th edition (required). We will cover roughly the following sections:
Notes to undergraduates: For all practical purposes, MATH 437 is an honours course! It treats roughly the same material as MATH 312 and 313 combined, and will take nearly twice as much work as either of those classes. Note that a student cannot have credit for both MATH 312 and MATH 437, nor for both MATH 313 and MATH 437. To enroll in MATH 437, an undergraduate student must have already taken, or be taking simultaneously, one of MATH 320 or MATH 322.
The word "elementary" in the title does not mean the course isn't difficult; rather it means that the course doesn't use techniques from real or complex analysis or from abstract algebra. The course will not require any particular background in number theory. What is required is "mathematical sophistication", which certainly includes being able to understand and write proofs. Be forewarned that this course will be taught at the level of a graduate course. Honours students typically will be well-equipped to succeed in this course.
Evaluation: The course mark will be based on (approximately) weekly homework assignments (65% of the final mark; the lowest homework score will automatically be ignored), engaged participation in in-class group problem sessions (10% of the final mark), and one final exam (25% of the final mark) whose date and location are still to be determined. The final exam will be a typical closed-book exam, with problems very much like the homework problems (indeed, there will probably be significant inclusion of actual homework/discussion problems on the final exam). In the case of extreme disparity between homework/discussion marks and exam marks, the instructor may use his discretion in assigning a final course mark.
Your homework will be marked on correctness, completeness, rigor, and elegance. A correct answer will not earn full marks unless it is completely justified, in a rigorous manner, and written in a logical sequence that is easy to follow and confirm. I plan on being pedantic about completeness of solutions (for example, if you invoke Euler's theorem to assert that aφ(q) ≡ 1 (mod q), you need to explicity acknowledge the fact that a must be relatively prime to q). Part of the goal of this course is to provide training and practice at writing proofs with sufficient rigor to be accepted by research journals.
You are very welcome to come by my office hours and ask questions about the lecture material, homework/discussion problems, clarity of style in proof writing, or related mathematical content. If office hours conflict with your schedule, you may make an appointment with me via email; you are also welcome to just drop by my office and see if I'm there—about half the time, I'll be free to talk right then. Students are allowed to consult one another concerning the homework problems, but your submitted solutions must be written by you in your own words. If two students submit virtually identical answers to a question, both can be found guilty of plagiarism.
No handouts will be distributed in class. All homework assignments and any other course materials will be posted on this course web page below. Homework solutions must be prepared in LaTeX and submitted to me in PDF format via email; please add your name to the filename before submitting your homework (for example, GregMartin-homework1.pdf). I will supply LaTeX templates with each assignment. All homeworks are due before the beginning of class (9:59 AM) on the indicated days.
Homework #0: due Monday, September 14. Download both the TeX file and the PDF file.
Unless otherwise announced, the in-class group problem sessions will take place the lecture after each assignment is due—so Wednesday, September 16; Wednesday, September 23, and so on through Monday, November 30. (Hopefully there will be no exceptions to this rule, so that you can easily predict when the group problem sessions will be.)
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and last modified on Nov. 23, 2015.
This page's URL is:
This page, and all files on this server linked from it, are ęGreg Martin and are not to be copied, used, or revised without explicit written permission from the copyright owner. (Some manuscripts have had their copyright assigned to the journals in which they are published). | 677.169 | 1 |
Course Content and Outcome Guide for ABE 0782 Effective Fall 2015
Course Number:
ABE 0782
Course Title:
Fundamentals of Mathematics
Credit Hours:
0
Lecture Hours:
0
Lecture/Lab Hours:
0
Lab Hours:
0
Special Fee:
Course Description
Use whole numbers, fractions and decimals to write, manipulate, interpret and solve application and formula problems. Concepts will be introduces numerically, graphically, and symbolically, in oral and written form. Placement into RD 80 or higher. CASAS score of 221 or higher. Prerequisites: Placement below MTH 20.
Intended Outcomes for the course
1. Creatively and confidently use mathematical and other problem solving strategies to formulate problems, to solve problems using multiple approaches, and to interpret results.
2. Meet the prerequisites for further math course work.
3. Choose and perform accurate arithmetic operations in a variety of situations with and without a calculator.
4. Present results numerically, symbolically, and graphically in written and oral form.
5. Estimate and compute personal needs relating to life skills through mathematics.
6. Solve problems and make decisions using multiple and effective strategies.
Outcome Assessment Strategies
Take CASAS math pre and progress test and improve one level or pass the GED if not college bound
Pass at least one real-world application activity (Capstone)
Pass at least five in-class examinations - Whole numbers, fractions and decimals testing without calculator. No more than 50% of any test can be multiple choice
Complete at least two or more of the following measures: At least one written explanation of a mathematical concept, take-home examinations, Graded homework, Quizzes, Group projects, In-class activities, Attendance, Portfolios, Individual projects, Individual student conference, Service learning
Course Content (Themes, Concepts, Issues and Skills)
Themes:
Life (e.g. family and citizen) and employability (i.e. worker) planning
Life-long learning
Goal setting
Critical thinking skills
Team work
Concepts:
Time management (attendance and completing tasks)
Social skills (communication and diversity)
Issues:
Confidence building
Communication styles
Employability attributes
Access to resources for students success
Math anxiety
Skills:
1.0 Basic Arithmetic Facts
1.1 Solve numerical and application problems with whole numbers
1.2 Perform order of operations accurately using whole numbers
1.3 Develop skills in estimation and number sense
1.4 Master fraction and decimal vocabulary
1.5 Solve numerical and application problems with fractions and decimals
1.6 Round a given number to a specified place
1.7 Arrange numbers in numerical order
1.8 Perform order of operations accurately using fractions and decimals | 677.169 | 1 |
This book aims first to prove the local Langlands conjecture for GL n over a p-adic field and, second, to identify the action of the decomposition group at a prime of bad reduction on the l-adic cohomology of the "simple" Shimura varieties. These two problems go hand in hand. The results represent a major advance in algebraic number theory, finally... more...
A successful presentation of the fundamental concepts of number theory and computer programming Bridging an existing gap between mathematics and programming, Elementary Number Theory with Programming provides a unique introduction to elementary number theory with fundamental coverage of computer programming. Written by highly-qualified experts... more...
Ideal for a first course in number theory, this lively, engaging text requires only a familiarity with elementary algebra and the properties of real numbers. Author Underwood Dudley, who has written a series of popular mathematics books, maintains that the best way to learn mathematics is by solving problems. In keeping with this philosophy, the text... more...
Self-contained and comprehensive, this elementary introduction to real and functional analysis is readily accessible to those with background in advanced calculus. It covers basic concepts and introductory principles in set theory, metric spaces, topological and linear spaces, linear functionals and linear operators, and much more. 350 problems. 1970... more...
The theory of uniform distribution began with Hermann Weyl's celebrated paper of 1916. In later decades, the theory moved beyond its roots in diophantine approximations to provide common ground for topics as diverse as number theory, probability theory, functional analysis, and topological algebra. This book summarizes the theory's development from... more...
"A very stimulating book ... in a class by itself." ? American Mathematical Monthly Advanced students, mathematicians and number theorists will welcome this stimulating treatment of advanced number theory, which approaches the complex topic of algebraic number theory from a historical standpoint, taking pains to show the reader how concepts, definitions... more... | 677.169 | 1 |
MATRICES TUTORIAL
Introduction
A matrix is a rectangular array of entries or elements, which
can be variables, constants, functions, etc. A matrix is denoted by an
uppercase letter, sometimes with a subscript which denotes the number of
rows by the number of columns in the matrix. For example, Am×n
denotes a matrix with the name A, which has m rows and n columns. The
entries in a matrix are denoted by the name of the matrix in lowercase,
with subscripts which identify which row and column the entry is from.
The entries in our above example would be denoted in the form aij,
which would mean that the entry is in row i,column j. For example, an entry denoted as a23 would be in the
second row, in the third column (counting from the upper left, of
course.) The entries in the matrix are usually enclosed in rounded
brackets, although they may also be enclosed in square brackets. The
following are examples of matrices:
There are some special types of matrices. A square matrix has
the same number of rows as columns, and is usually denoted Anxn.
A diagonal matrixis a square matrix with entries only
along the diagonal, with all others being zero. A diagonal matrix whose diagonal
entries are all 1 is called an identity matrix. The identity
matrix is denoted In, or simply I. The zero matrix
Om×n is an matrix with m rows and n columns of all zeroes.
Given two matrices A and B, they are considered equal (A=B) if they
are the same size, with the exact same entries in the same locations in
the matrices.
Matrix Operations
Addition
Addition of matrices is very similar to addition of vectors. In fact,
a vector can generally be considered as a one column matrix, with n
rows corresponding to the n dimensions of the vector. In order to
add matrices, they must be the same size, that is, they must have an
equal number of rows, and an equal number of columns. We then add
matching elements as shown below,
Scalar Multiplication
Scalar multiplication of matrices is also similar to scalar
multiplication of vectors. The
scalar is multiplied by each element of the matrix, giving us a new matrix
of the same size. Examples are shown below,
Matrix subtraction, similar to vector subtraction, can be performed by multiplying the
matrix to be subtracted by the scalar -1, and then adding it. So, A - B = A + (-B) = (-B) + A.
So like adding matrices, subtracting matrices requires them to be the same size, and
then operating on the elements of the matrices.
Matrix Multiplication
Two matrices can also be multiplied to find their product. In order to multiply two matrices,
the number of columns in the first matrix must equal the number of rows in the second matrix. So
if we have A2×3 and B3×4, then the product AB exists, while
the product BA does not. This is one of the most important things to remember about matrix multiplication.
Matrix multiplication is not commutative. That is, AB ≠ BA. Even when both products exist, they
do not have to be (and are not usually) equal. Additional properties of matrix multiplication are shown below.
Matrix multiplication involves multiplying entries along the rows of the first matrix with entries
along the columns of the second matrix. For example, to find the entry in the first row and first column
of the product, AB, we would take entries from the first row of A with the first column from B.
We take the first entry in that row, and multiply (regular multiplication of real numbers) it
with the first entry in the column in the second matrix. We do that with each entry in the row/column,
and add them together. So, entry abij = ai1b1j + ai2b
2j + ... + aimbmj. This seems complicated, but it is fairly easy
to see visually. We continue this process for each entry in the product matrix, multiplying
respective rows in A by columns in B. So, if the size of A is m×n, and the size of B is n×p, then
the size of the product AB is m×p. We show this process below:
Matrix multiplication can also be written in exponent form. This requires that we have a square matrix.
Like real number multiplication and exponents, An means that we multiply A together n times.
So A2 = AA, A5 = AAAAA, and so on. We should note, however, that unlike
real number multiplication, A2 = 0 does not imply that A = 0. The
same is true for higher exponents.
Linear Combinations/Linear Independence of Matrices
Similar to the case with vectors, we can have linear combinations of matrices. In order to have
linear combination of matrices, they must be the same size to allow for addition and subtraction. If
a matrix A is a linear combination of matrices B and C, then there exist scalars j, k such
that A = jB + kC. A set of matrices is said to be linearly dependent if any one of them
can be expressed as the linear combination of the others. Equivalently, they are linearly dependent
if there exists a linear combination of the matrices in the set using nonzero scalars which gives the zero matrix. Otherwise,
the matrices are linearly independent.
Transpose of a Matrix
The transpose of a matrix A, denoted AT, is obtained by swapping rows for columns and vice versa
in A. So the rows of A become the columns, and the columns become the rows. An example is shown below.
A square matrix is called symmetric if AT = A. Some properties of the transpose are:
1) (AT)T = A
2) (A + B)T = AT + BT
3) (kA)T = k(AT), where k is a scalar
4) (AB)T = BTAT
5) (Ar)T = (AT)r, where r is a nonnegative integer
Please note the following theorems. The first is proved in the text, the second is
proved in the sample problems for this section:
Theorem: If A is a square matrix, A + AT is symmetric Theorem: For any matrix A, AAT and ATA are symmetric.
Inverse of a Matrix
Similar to the way that a real number multiplied by its reciprocal fraction gives us 1, we can
sometimes get an inverse to a square matrix, so when a square matrix A is multiplied by its inverse
denoted A-1, we get the identity matrix I.
Please note that only square matrices can be inverted, and only some of those that meet a certain
property. That certain property is that the determinant of the matrix must be nonzero. Determinants
are explained more in the next section, but for 2x2 matrices, determinants and inverses are easy to find.
The inverse (if it exists) has the following properties:
1) AA-1 = A-1A = I
2) If A is invertible, A-1 is unique.
3) (A-1)-1 = A
4) (cA)-1 = (1/c)A-1, where c is a nonzero scalar
5) (AB)-1 = B-1A-1, where A, B are the same size
6) (AT)-1 = (A-1)T
7) (An)-1 = (A-1)n, where n is a nonnegative integer
8) A-n = (A-1)n = (An)-1, where n is a positive integer
We can easily find the inverse (if it exists) of a 2x2 matrix using the following formula:
Using the idea of inverses, we can use it to solve systems. Let A be a square coefficient matrix (size n×n)
of a system of linear equations. Then if A is invertible, the system Ax = b has a unique solution
by multiplying both sides of the equation by A-1, that is, x = A-1b, where
b is a vector in Rn.
Elementary matrices
Elementary matrices are square matrices that can be obtained from the identity matrix by
performing elementary row operations, for example, each of these is an elementary matrix:
Elementary matrices are always invertible, and their inverse is of the same form. Also, if E is an
elementary matrix obtained by performing an elementary row operation on I, then the product EA, where
the number of rows in n is the same the number of rows and columns of E, gives the same result as performing
that elementary row operation on A. Finally, we can state the following theorem from the text (where
you can also find the proof):
The fundamental theorem of invertible matrices, version 1:
Where A is a square matrix of size n×n, the following are equivalent:
1) A is invertible
2) Ax = b has a unique solution for every b in Rn
3) Ax = 0 has only the trivial solution
4) rref(A) = I
5) A can be expressed as the product of elementary matrices.
The Gauss-Jordan Method of Finding the Inverse
In order to find the inverse of matrices larger that 2x2, we need a better method. If A is invertible and
of size n×n, then we can find the matrix by the following method:
1) Set up a matrix [A|I], a n×2n matrix where the left half is A and the right half is the identity matrix size n.
2) Perform elementary row operations to reduce the left side to the identity matrix, while also performing those
same operations on the right side.
3) If A is invertible, when the left side is reduced to the identity matrix, the right side will be A-1. If
the left side cannot be reduced to I, then A is not invertible. | 677.169 | 1 |
modules/show.full.php on line 335Mathematical modelling and computer simulations are an essential part of the analytical toolset used by earth scientists. Computer simulations based on mathematical models are routinely used to study geophysical, environmental, and geological processes in many areas of work and research from geophysics to petroleum engineering and from hydrology to environmental fluid dynamics. Author Xin-She Yang has carefully selected the topics which will be of most value to students. Dr. Yang has recognized the need to be careful in his examples while being comprehensive enough to include important topics and popular algorithms. The book is designed to be 'theorem-free' while balancing formality and practicality. Using worked examples and tackling each problem in a step-by-step manner, the text is especially suitable for more advanced students of this aspect of earth sciences. The coverage and level, for instance in the calculus of variation and pattern formation, will be of interest to mathematicians. | 677.169 | 1 |
For electrical or computer engineering students or anyone with a passing interest, this site presents a very good overview of digital logic. The basics of both combinational and sequential logic are discussed, and the design of specific components such as counters and shift registers are also illustrated. A particularly interesting section is devoted to the inner workings of logic gates, which is...
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Integrated Arithmetic and Basic Algebra
9780321442550
ISBN:
0321442555
Pub Date: 2007 Publisher: Addison-Wesley
Summary: A combination of a basic mathematics or prealgebra text and an introductory algebra text, this work provides an integrated presentation of the material for these courses in a way that is beneficial to students.
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Mathematical language
Introduction
When we try to use ordinary language to explore mathematics, the words involved may not have a precise meaning, or may have more than one meaning. Many words have meanings that evolve as people adapt their understanding of them to accord with new experiences and new ideas. At any given time, one person's interpretation of language may differ from another person's interpretation, and this can lead to misunderstandings and confusion.
In mathematics we try to avoid these difficulties by expressing our thoughts in terms of well-defined mathematical objects. These objects can be anything from numbers and geometrical shapes to more complicated objects, usually constructed from numbers, points and functions. We discuss these objects using precise language which should be interpreted in the same way by everyone. In this unit we introduce the basic mathematical language needed to express a range of mathematical concepts.
Please note that this unit is presented through a series of downloadable PDF files.
This unit is an adapted extract from the Open University course Pure mathematics
(M208) [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)]
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Originally published: Tuesday, 28th June 2011
Last updated on: Monday, 25 | 677.169 | 1 |
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namatad:TheMaybe, but everyone should be forced to take Probability and Stats in college.
Grand_Moff_Joseph:A huge part of the problem is that math isn't being taught correctly, even by the (many) good teachers out there. I spent far too much time in math classes working on the "theory", the "whys" of math, and little time on the practical application thereof.
For example: No one (and I mean NO ONE) cares "why" 2+2=4, or "why" limits and log functions work the way that they do. Why are spending half of a test writing proofs for these concepts? We should be using those tests to apply the ideas to problems, and find reality-based ways to solve them.
Also, while I understand the pervasiveness of calculators and computers today (my TI83 got me through Trig and Calc), calculators need to stay out of the classroom until at least high school. I'm not a math whiz, but I can make change in my head. When the power went out in the WalMart I worked at in College, half of the cashiers had to use their phones to calculate change amounts because they couldn't do it manually.
I think there might be some value to introducing them earlier, mostly because the students will be introduced to calculators and computers at an early age regardless of how the school approaches it. There's no harm in showing students how use tools properly.
The fact that this is even a debate is proof that we're completely farked as a country. How the hell can the US compete with non-derpy countries if we can't understand the most basic of abstract mathematics?
Seriously, people. We must teach it because it's hard....even though it really isn't.
EngineerBoy TheseIf you can't explain it simply, you don't understand it well enough. If you can't explain it at all, you probably teach high school.
I think that we have been trying to find "easier" ways to teach math for over 40 years
Evidence is that for the most part, the easier ways are failures.
The key to being good at math is the same as being good at reading. You have to do it and do it and do it and do it. In other words, those old fashioned work books that were full of excercise problems are the way to go. Teach the concept, show some sample problems, have the students do 20 problems over night. Check their work, if they don't have the idea, find common threads in the lack of understanding, assign 50 more problems designed to address the problems. Check them the next day, if they have it, go to the next concept.
The other problem is that many teachers, especially at the elementary level, don't really understand math well enough to understand whether their students get it or not, much less why they don't get itALL classes which will never be needed are a waste. DUH composition? complete waste. philosophy? complete waste. bioethics? complete waste.
Babwa Wawa:I went into that article thinking you could get rid of algebra if you replaced it with something more relevant like statistics.
The nation would be much better off if everyone had a basic understanding of stats.
That's funny... I was just having a discussion maybe 2 days ago about the reasoning behind why stats isn't a required part of a high school education. Not necessarily a whole semester of stats, but all the basics. I even discussed a single semester of algebra and stats combined. Advanced material from either one of them is all but useless to most students, but the basics learned from both carry on to a number of things in the job market that are not science related.
The problem is with convincing kids that mad mathz skillz are important- you've got to remember, these are little idiots with - as a matter of course - no properly developed concept of what the future holds for them. In more traditional societies and in the developing world, it's easy: The motivation is "because your parents want you to" or "because learning as much as you can will get you out of this place". In the US and elsewhere in the West, it's harder: You have to convince them that they will need these skills in the future.
buckler:namMeat is $2.99/lb. Last week it was 15% less, and you could afford 3 pounds. How much money did you have last week.
And that's elementary algebra - I don't think anyone here is arguing that you don't need that level of education. Certainly the author didn't argue that. The question is whether people need to actually master abstract algebra in order to graduate HS.
Ah, so this is an argument about degrees of algebra.
man, I hate useless word problems like this one. There has *got* to be a better way to get this same point across in a useful manner. I mean, are there any situations when I wouldn't know I had $7.62 last week, but I would know the relative difference in price and the amount I bought? That is sooo... backwards.
I guess, you could make it like a detective story: "A detective is investigating a robbery and the suspect was seen leaving the supermarket and throwing away the receipt, which would have his finger prints. There are 4 receipts, but they only indicate the price spent/item. The clerk doesn't remember the price of the meat, but does remember that the suspect bought 3 pounds of beef, currently $3.99, which cost 15% less the day on the crime. Which receipt has the suspect's fingerprints?"
That's probably too long and complicated, but at least more interesting.
buckler:buckler: namatad: why do tards complain about things that they dont like, but think that others should take topics that they think are important.
Review your own posts, then attempt to answer your own question.
...or do I have a hook in my mouth at this point?
LOL no .... my complaint is that these people want to change the things that they hate, but think their stuff is perfect. Literature classes exist to employ literature students. why are the rest of us punished to employ them??
EngineerBoy:The problem, in my opinion, is not with Algrebra, but with math education in this country, starting from grade school on. In college I had many classes in common with Education majors, and with virtual unanimity they complained about how hard it was to pass basic college math courses, and that what they taught wasn't necessary in life. Several of then went on to become math teachers, because that's what was hiring.
TheseIn my opinion the solution is to make teaching a respectably paid vocation, such that it will attract people who could easily get work in the business sector, but might choose to become teachers if it didn't mean settling for a life of extraordinarily limited earning potential.
Babwa Wawa:slayer199: AsI disagree - a university degree should (but usually doesn't) indicate a person with a well-rounded education.
Allowing people to focus exclusively on their degree is job training, not university education. You end up wit scientists who can't write, and historians who can't analyze data.
no you dont. there are no scientists that cant write. writing is a huge component of being a scientist. historians should be analyzing history, not data anyway. people that like learning will do so no matter what. It is not a university's job to "round me" it is their job to provide specialized high tech training with resources I cant find elsewhere. I can buy lit books and biographies on my own thanks.
namatad:buckler: namThanks. I'm working on about three things plus Farking at the moment. My sarcasm meter alarm didn't go off to alert me. Back to the shop for it, I guessI hated math, became an English major, got out into the real world, and landed my first job in banking. That evolved into analytics, performance tracking, and statistical analysis & modeling. I use algebra every day. I'm damn glad I received the broad, liberal education that included algebra, stats, logic and computer science.
I'm one of the few in my part of the corporation who is a solid writer. Probably the only one who both understands the complex issues discussed and is capable of communicating effectively. Job security rocks...
/the math is there to teach you how to effectively approach abstract and uncomfortable challenges...pretty useful, in general...
wingedkat:downstairs: As a completely random example, but something that irks me personally... so many people cannot uderstand crime statistics. Not even to the point of understanding that per capita must be applied to any number, or its generally meaningless. Of course thats basic division, not even algebra.
Yeah, they do teach algebra abysmally in most places. After all, the understanding of when to apply basic division is something generally gained by learning algebra (or should be, at least).
I think two big changes need to be made:
1. Math majors shouldn't teach math. 2. Algebra, geometry, etc needs to be taught along with all the basics way back in grade school. Algebra especially is basically just math grammar, nothing that should be pulled out and made a big deal of.
To be in compliance with NCLB and the CRCT, it already is being taught in the lower grades. It's being taught like crap, but it's being taught. Most kids memorize stuff just long enough to pass and then have to re-learn it the next time around, while the kids that get it are bored beyond belief. My fifth grader and second grader were actually working the same friggin problems at one point, because the fifth grade teacher really liked the worksheet the second grade teacher created.
Brian Erst writes: "Just make the coming generation of fembots user-programmable in a way that requires good math and logic skills. You will very quickly have a generation of mathematical and programming geniuses."
LordOfThePings:Lord Dimwit: My high school honors (!) geometry teacher told me that pi is an irrational number because we can't measure it because we can't draw a perfect circle. If we could draw a perfect circle, the exact value of pi would be known.
Duuuuude! Your teacher ever share the bong?
And just to be clear, I mean that she thought that pi was irrational because every time we measure a circle, our measurements are slightly off. She thought there was a finite decimal expansion of pi, we just hadn't discovered it yet.
rumpelstiltskin:No shiat. That's because you aren't supposed to learn the algorithms; you're supposed to learn how abstraction and reasoning lead to the algorithms. We don't need any more people in the workforce who are experts in applying the quadratic formula, but that simply isn't the point. Mathematical reasoning in workplaces takes the form of abstraction and identification of relationships between abstractions. These are the skills you are supposed to begin to develop in high school "algebra" and geometry. And if you can't, you should be a barrista or some kind of clerk. You have no business making decisions. Or you could be a political science professor, who's work depends heavily on numbers he doesn't understand. You could do that, too.
Well said. And the author is an idiot for thinking you can teach stats without any math background... unless one is a social scientist who likes playing with numbers without understanding how methodologies work. I know plenty of social scientists who love playing with quantitative models, but when you ask basic questions about their logic and causality, everything falls apart.
Mmm, no. Here's the thing: an alarmingly large proportion of the middle school kids I've encountered in the past while have often come in with huge gaps in their math abilities, often operating several years behind where they should be.
It should be noted that a BSc-Math degree doesn't qualify one to start an elementary certification program under typical state NCLB standards. You would need an extra year or so of general arts credits beyond your degree to qualify. Basically, you'd have to hybrid into the equivalent of a BA (Math). Math majors generally certify at middle or high school.
The converse is not true. One or two math credits are sufficient for an Arts or History major.
Worse, most teacher college professors appear to have been drawn from the huge pool of English/History majors. You're very lucky if you have a math or science background professor who can teach that aspect of education to the elementary school teacher candidatesThat sounds a lot like the last time I tried to calculate the precise value of infinity using a scratch pad, a tape measure and the end off of a serial cable.. and three days later discovered that there were two tabs stuck together, apparently.
buckler:I am terrible at math. I tried and tried in school, but I just couldn't wrap my head around it. My brain just isn't wired that way. However, I excel when it comes to language and interpretive arts, and I did very well in visual arts. Aside from the occasional grammar-Nazi snark here, I don't put down those who don't do well in English or related fields, because I know my own limits when it comes to math. I had a roommate who admitted he never learned to read, and I helped tutor him until he had at least the basic skills.
The important thing for me is that I was necessarily exposed to both fields. I found I did well in one, and not so much the other; I would expect to find that there are those who excel in math, but maybe not so much in language skills. I don't value them less that anyone else. Indeed, these people are vital in the STEM fields, which our country needs people in now more than ever. This guy's thesis is bunkum.
PERFECT!! And this is what school should be all about. Finding the things which one is good at and then being educated in those things. People with no interest in ... botany, wouldnt disrupt the class. those interested in band, would do band.
the only reason that you would need to take other classes is to get enough exposure to determine interest in the first place.
Learning math is really learning problem solving, the numbers are almost irrelevant. When I taught prep for the GMATand GRE I found the students who couldn't do math were the students who could never solve any of the verbal problems they didn't immediately know. They seemed to lack the ability to break down a question and figure out how to solve it.
Kimothy:Their definitely not using trig or calculus, unless they pursued careers that use those things.
My brother cannot understand the different between growth at a slower rate and shrinking. This impacts his ability to understand all manner of social and economic issues. Even if you don't solve trig and calculus problems everyday, mastering those concepts allows you to better understand the world around you. | 677.169 | 1 |
According to the author, "It is by no means a comprehensive guide to all the mathematics an engineer might encounter during...
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According to the author, "It is by no means a comprehensive guide to all the mathematics an engineer might encounter during the course of his or her degree. The aim is more to highlight and explain some areas commonly found difficult, such as calculus, and to ease the transition from school level to university level mathematics, where sometimes the subject matter is similar, but the emphasis is usually different. The early sections on functions and single variable calculus are in this spirit. The later sections on multivariate calculus, differential equations and complex functions are more typically found on a first or second year undergraduate course, depending upon the university. The necessary linear algebra for multivariate calculus is also outlined. More advanced topics which have been omitted, but which you will certainly come across, are partial differential equations, Fourier transforms and Laplace transforms Essential Engineering Mathematics to your Bookmark Collection or Course ePortfolio
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This free, online textbook "introduces engineering techniques and practices to high school students. This book is designed...
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This free, online textbook "introduces engineering techniques and practices to high school students. This book is designed for a broad range of student abilities and does not require significant math or science prerequisites: An Introduction for High School to your Bookmark Collection or Course ePortfolio
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According to the United States Agency for International Development, 20 million people in developing countries require...
see more environments, social stigmas against the disabled, and manufacturing constraints, and then applying sound scientific/engineering knowledge to develop appropriate technical solutions. Multidisciplinary student teams will conduct term-long projects on topics such as hardware design, manufacturing optimization, biomechanics modeling, and business plan development. Theory will further be connected to real-world implementation during guest lectures by MIT faculty, Third-World community partners, and U.S. wheelchair organizations. This class is made possible by an MIT Alumni Sponsored Funding Opportunities grant with additional support from the National Collegiate Inventors and Innovators Alliance, the MIT Public Service Center, and the MIT Edgerton Center; special thanks to CustomInk784 Wheelchair Design in Developing Countries to your Bookmark Collection or Course ePortfolio
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LEGO® robotics uses LEGO®s as a fun tool to explore robotics, mechanical systems, electronics, and programming. This seminar...
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LEGO® robotics uses LEGO®s as a fun tool to explore robotics, mechanical systems, electronics, and programming. This seminar is primarily a lab experience which provides students with resources to design, build, and program functional robots constructed from LEGO®s and a few other parts such as motors and sensors293 Lego Robotics to your Bookmark Collection or Course ePortfolio
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This course is aimed at the aspiring planning practitioner, policy-maker, or industry decision-maker with an interest in...
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This course is aimed at the aspiring planning practitioner, policy-maker, or industry decision-maker with an interest in urban transportation and environmental issues in Latin America. The course will focus on current transport-related themes confronting many cities in the region, including: rapid motorization and suburbanization and subsequent impacts on transportation infrastructure and quality of life; public sector management and improvement of privately-owned and operated transit systems; and, transportation air pollution problems and potential solutions. The course will be geared towards interactive problem-solving, taking advantage of students' skills and experiences in: institutional analysis, policy analysis, and project and program evaluation and implementation. Detailed knowledge of transportation planning is not required; instead, the course will attempt to place the general practitioner into a specific transportation public policy situation and draw from her skills to devise real solutions. To fulfill this problem-solving orientation, the course will be divided into two parts. Part I of the course will consist of a series of lectures on the principal issues surrounding transportation in the developing world (including motorization, fiscal pressures, urban sprawl), concepts of sustainability as they relate to urban transportation, regional strategic planning approaches, and transportation policy and technology options and examples of successful implementation. After these lectures, Part II of the course will be dedicated to the two case studies, where students will apply the knowledge gained in Part I to develop strategic solutions to the transport-land use-environment challenges in two different cities43J / ESD.935 Urban Transportation, Land Use, and the Environment to your Bookmark Collection or Course ePortfolio
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21W.783 is a series of seminars focusing on common writing problems faced by professional engineers and scientists....
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Engineering Cultures China consists of multimedia learning modules and other supporting materials that examine the historical...
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Engineering Cultures China consists of multimedia learning modules and other supporting materials that examine the historical development and contemporary state of engineering education and the engineering profession in mainland China. Developed by a team led by Prof. Brent Jesiek (Purdue University), the content builds on the Engineering Cultures instructional model, originally developed by Profs. Gary Downey (Virginia Tech) and Juan Lucena (Colorado School of Mines). These modules can help students take the first step toward enhancing their ability to practice effectively as global technical professionals, in China Cultures China to your Bookmark Collection or Course ePortfolio
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Mathematics
It is the goal of the mathematics department that every student will develop a competence in fundamental mathematical processes and a foundation for logical thinking. In accordance with the National Council of Teachers of Mathematics Standards, an emphasis is placed on problem-solving techniques. TI-84 Plus graphing calculators are introduced in Algebra I and used extensively beginning in the second year of algebra. In our highly technological society all young women must increase their mathematical sophistication so that their future career options will be kept open.
The study of mathematics is required through the junior year and strongly recommended for senior year. Every student must complete two years of algebra and a year of geometry. The mathematics department places a student in the course and level most appropriate to her aptitude and preparation. Placement in all math classes is based on departmental recommendation and is determined by a student's overall academic performance as well as a good aptitude for mathematical reasoning and active learning.
Courses in this department:
Math
Algebra I
Credit: 1 (if taken in 9th grade or above)
Students entering this class are expected to have already studied positive and negative numbers, the basic properties of numbers, and simple equations. The course covers all topics of elementary algebra, including verbal problems, factoring, graphing of linear equations, radicals, solving linear and quadratic equations, and linear systems.
Honors Algebra I
Credit: 1 (if taken in 9th grade or above)
This course is for students who have a strong background in arithmetic facts and skills and in elementary algebra, including positive and negative numbers, the basic properties of numbers, and simple equations. They must have demonstrated a good aptitude for mathematical reasoning. The course covers all topics of elementary algebra, including verbal problems, factoring, algebraic fractions, graphing of linear functions, radicals, solving linear and quadratic equations, systems of equations, variations, and the quadratic formula.
Geometry
Credit: 1
This course is for students who had had a full year of elementary algebra. Plane geometry relationships are developed as part of a logical system, and the student learns to write short proofs based on these relations. Algebraic and numerical applications are provided, and units on right triangle trigonometry, three-dimensional figures, and coordinate geometry are included.
Honors Geometry
Credit: 1
This course is for students who have a strong mathematical background, good insight, and solid problem solving skills. Plane geometry relationships will be explored in depth with algebraic and numerical applications provided. Units on congruence, similarity, polygons, right triangles, trigonometry, circles, plane and solid figures, and coordinate geometry will be included.
Algebra II
Credit: 1
This course is for students who have had a full year of elementary algebra. The year consists of a review and extension of Algebra I topics including inequalities, linear equations, operations with polynomials, and application of algebraic skills through verbal problems. Additional topics include functions, complex numbers, and quadratics graphs.
Honors Algebra II
Credit: 1
This course is for students who have a strong background in elementary algebra, including systems of equations, radicals, and quadratics. They must have demonstrated a good aptitude for mathematical reasoning. This course begins with an extension of Algebra I topics and continues with the study of complex numbers, quadratic functions, rational and polynomial functions, rational and polynomial functions, exponents, radicals and logarithms.
Trigonometry
Credit: 1
This course consists of a review of advanced algebraic topics as well as an exploration of basic trigonometry. The algebraic topics include quadratic functions and their applications, composite and inverse functions, exponents, radicals and logarithms. The study of trigonometry consists of right triangle and general triangle relationships and applications, the unit circle, and sine and cosine graphs.
Precalculus
Credit: 1
This course is for students who have a strong background in advanced algebraic topics. The transition from a focus on algebraic skill building and processes to that of their application and conceptual analysis is a challenging one that students must make in this challenging course. Students are expected to be quite proficient with a graphing calculator and to extract information from the textbook effectively in order to make connections and to contribute to class discussions and discoveries. Topics reviewed and studied consist of various functions (including compositions, inverse, polynomial, rational, exponential and logarithmic) and trigonometry.
Honors Precalculus
Credit: 1
This course is for students who have a strong background in advanced algebraic topics and have demonstrated a good aptitude for mathematical reasoning and intellectual curiosity. The transition from a focus on algebraic skill building and processes to that of their application and conceptual analysis is a challenging one that students must make in this challenging course. Precise arithmetic and algebraic skills are essential to ensure accurate data for proper analysis and to attain a strong level of command and understanding of the concepts studied. Students are expected to be quite proficient with a graphing calculator and to extract information from the textbook effectively in order to make connections and to contribute to class discussions and discoveries. Topics reviewed and studied consist of several types of functions (including compositions, inverse, polynomial, rational, exponential, logarithmic and circular) and an introduction to limits.
Honors Calculus
Prerequisite: Precalculus or Honors Precalculus Credit: 1
This course is a survey of topics in Calculus from limits and continuity to basic differentiation. It is an opportunity for students to integrate ideas from algebra and geometry to do analytical applications of trigonometry, rational functions, compositions and logarithmic functions. It is a course geared toward deeper understanding of the material but without the focus being on preparing for the AP exam. Students enrolled in this course will not be permitted to take the AP Calculus exam.
Advanced Calculus
The methods and techniques of differential and integral calculus are developed and applied to algebraic, trigonometric, logarithmic and exponential functions. Students are required to use a graphing calculator.
Applications of Advanced Mathematics
Open to Grades: 11-12, and Sophomores with Approval of Instructor Prerequisite: Completion of Precalculus Credit: 1
Students will focus on a "problem" they identify in our society or a global issue that interests them. The problem could be based in nature, culture, society, current events, historical events, or even based in human behavior. As a class we will collect data related to the topic and use statistical methods and advanced applied mathematics to interpret and communicate findings, make recommendations, and draw conclusions. Collaboration with another field of study is inevitable but will be determined by what the students decide to study. Alongside gathering data, students will also learn and research the facts surrounding their proposed problem. The underlying goal of the course would be to learn how to use mathematics to both interpret facts and communicate ideas persuasively.
Introduction to Computer Science
Open to Grades: 10-12 Spring Semester Credit: .5
This course focuses and engages the entire discipline of computer science. By demystifying computer hardware and how it works, using computer software and exploring design and implementation, problem solving and developing software, and understanding how computers, people and society interoperate in this course, we will look to build quantitative reasoning skills and a basis for future survival and exploration in our advancing world.
Advanced Computer Science
Open to Grades: 11-12, and Sophomores with Approval of Instructor Credit: 1
Advanced Computer Science aims to introduce students to a broad array of concepts in Computer Science. Students will use the Java programming language to explore complex problem solving, algorithm design and implementation, writing programs from scratch, and building on what others have given us. Topics include Data Structures, Loops, Arrays, Searching and Sorting, Formal Logic, Decision Processing, and much more. | 677.169 | 1 |
Web Codes
Prentice Hall Connected Mathematics 2 (CMP2)
Features and Benefits
NSF funded. CMP2 has been classroom tested for five years as part of a new NSF grant prior to publication to ensure student success with the materials.
Problem-centered, research-based approach. The same problem-centered, research-based approach proven successful with students as the original; content is developmentally appropriate for middle-school students.
Embeds important mathematical concepts in interesting problems. Students learn important mathematical ideas in the context of interesting, interconnected problems. This exploration leads to understanding and the development of higher-order thinking skills and problem-solving strategies.
Accessible to all levels of students. CMP2 is an effective combination of content and methodology designed to foster more "a-ha!" moments, regardless of a student's skill level or learning style.
New technology to support learning! CMP2 now comes with updated technology to support teachers and students. Support is provided for digital presentations and StudentEXPRESS™ provides an interactive version of the textbook, with built-in homework help! | 677.169 | 1 |
Math Resources
Math Mechanixs® is an award winning easy to use general purpose math software program compatible with Microsoft Windows®. It is ideal for students, teachers, engineers and scientists or anyone requiring an easy to use PC based mathematical software program. It will also do so much more than your calculator. Math Mechanixs was created with the belief that computers were made to solve mathematical problems. Our goal is to make math software available to everyone.
Math Software Description
Math Mechanixs is not a training aid or a spreadsheet program. It works using a Math Editor (as opposed to a Text Editor) allowing you to type the mathematical expressions similar to the way you would write them on a piece of paper. The software uses a multiple document interface so that you can work on multiple solutions simultaneously. There is a full feature scientific calculator combined with an integrated variables and functions list window so that you can easily track your defined variables and functions.
Stunning Color Graphs
You can easily create large 2D and 3D full color graphs that are nothing less than "Stunning". With Math Mechanixs, 2D and 3D graphing of data and functions is easy. Our graphing utility allows you to label data points, as well as zoom, rotate and translate the graph. For more information see our graphing page or check out our screen shots page for examples of our 2D and 3D graphics. There is also Tutorials available that will help you quickly learn how to create various types of 2D and 3D graphs in Math Mechanixs.
Function Library and Solver
The math software also provides an extensive function library containing over 280 embedded functions which includes general math, trigonometric, chemistry, geometric, statistical, and numerous random number generators following a variety of statistical distribution and many other function categories. The library is also completely extendable by the user. Math Mechanixs also includes a Function Solver graphical interface that allows you to quickly obtain a solution, to any function, by only entering the input parameters.
Calculus
The Math Mechanixs Calculus Utility contains a numerical integration module capable of performing single, double, and triple integration. You can easily compute the integral of almost any mathematical function. This utility also includes a numerical differentiation module which is capable of performing single, double and triple differentials. You can easily plot the differentiation curve to locate maxima and minima with the click of a button. This utility is currently available for download in the latest release.
Root Finding
Released in version 1.3.0.1 is a Math Tools utility which includes a Root Finding tool. This utility will find the real roots of mathematical expressions and functions plus complex roots of polynomials. The Root Finder allows you to easily graph your function or expression in order to visualize the zero crossings (i.e. roots) making it easier to focus on roots within specific thresholds of your function or to verify your results.
Curve Fitting
The Curve Fitting Utility released in version 1.4.0.1 will allow you to easily perform linear and non-linear regression analysis using an nth order polynomial. This tool is perhaps one of the most useful tools available in Math Mechanixs. Data modeling has wide reaching applications in Manufacturing, Quality Control and Six Sigma, Process Engineering and many other scientific and engineering fields. Please periodically visit this website and watch for new releases of Math Mechanixs.
Quick Graph
Quick Graph Utility is another Math Tools utility which promises to make 2D graphing of mathematical expressions as easy as 1, 2, 3. It couldn't be easier, simply enter your mathematical expression, select or enter the x-axis variable, enter the range and number of points, and press the graph button. Your graph will intantly appear... Ok, so maybe it is more like 1, 2, 3, 4... but we still guarantee that this utility will make graphing so simple, a baby can do it!
Matrices
The Matrix Utility (released in version 1.5) is also part of the Math Mechanixs Math Tools utility and can be used to perform common matrix mathematics and linear equation solving. The new utility can be used to solve matrix problems with matrices as large as 10 x 10. The utility supports matrix addition, subtraction, multiplication, scalar multiplication, inverse, transpose, cofactor, adjugate, trace, rank, LU decomposition and determinants. Math Mechanixs makes matrix math simple, compare the ease or our GUI against your graphing calculator and its tiny 2 X 2 display!
Statistical Plotting
The Statistical Plotting Utility, released with version 1.5.0.3, allows you to easily build Hytograms and Pareto Charts from manually entered data or from imported data loaded from ASCII Text or CSV files.You can easily select from two chart types, hystogram or pareto, plus you can either let Math Mechanixs compute the optimal frequency interval or you can explicitly set the number of frequency intervals to use in creating your plot.
Integrated Help System
Math Mechanixs has a completely integrated help system which also includes select video tutorials which will greatly reduce the time it takes to learn how to use the software. To find the help topic associated with a particular feature of the software using the integrated help, simply click on the help button assocated with the feature and get instant help or click the context sensitive help button from the main tool bar and then click on any point where you would like help.
Math Mechanixs Pricing and Licensing
Math Mechanixs Lite is available FREE with our compliments. The Lite version includes the Math Editor, the Scientific Calculator, 2D/3D Graphing, and the user extendable Function Library with over 280 predefined functions. However, if you enjoy using the more advanced features of Math Mechanixs Professional, we kindly ask that you register the software after your 30 day evaluation period has ended. For more information on pricing, please visit our pricing and licensing page. | 677.169 | 1 |
Book summary: This text places mathematics into a real-world setting. Concepts are developed through the "Rule of Four - Numeric, Analytic, Graphic, and Verbal". Graphing utilities are integrated as a tool while the focus is on the mathematics. Emphasizing problem-solving skills, this book introduces new concepts in the context of physical situations to illustrate how algebra can solve them. It provides analytical, graphical, and numerical approaches to major topics, and includes the use of Polya problem-solving strategies. By frequently identifying Polya strategies used in the exposition, the book offers readers a number of examples of how each stragey can be used effectively. The use of graphing calculators is incorporated where appropriate, as well as discussions of the advantages and limitations of technology. | 677.169 | 1 |
The fun and friendly guide to really understanding math U Can: Basic Math & Pre-Algebra For Dummies is the fun, friendly guide to making sense of math. It walks you through the "how" and "why" to help you master the crucial operations that underpin every math class you'll ever take. With no-nonsense lessons, step-by-step instructions, practical... more...
Have you ever found yourself saying, ?I?m never going to pass the math pre-service exam!? This statement, and many others like it, led the authors to discover exactly how to crack the math pre-service exam test code and students are reaping all the benefits. How to Pass the Pre-Service Mathematics Test for Teachers is the result of years of researching... more...
This volume casts light on new and interesting relationships between mathematics, imagination, and culture, from the connections between modern art and mathematics to mathematical models and their influence on modern and contemporary art. more...
This self-contained monograph explores a new theory centered around boolean representations of simplicial complexes leading to a new class of complexes featuring matroids as central to the theory. The book illustrates these new tools to study the classical theory of matroids as well as their important geometric connections. Moreover, many geometric... more...
Being taught by a great teacher is one of the great privileges of life. Teach Now! is an exciting new series that opens up the secrets of great teachers and, step-by-step, helps trainees to build the skills and confidence they need to become first-rate classroom practitioners. Written by a highly-skilled practitioner, this practical, classroom-focused... more...
In this new text, Steven Givant?the author of several acclaimed books, including works co-authored with Paul Halmos and Alfred Tarski?develops three theories of duality for Boolean algebras with operators. Givant addresses the two most recognized dualities (one algebraic and the other topological) and introduces a third duality, best understood as... more...
How do you make mathematics relevant and exciting to young children? How can mathematics and literacy be combined in a meaningful way? How can stories inspire the teaching and learning of mathematics? This book explores the exciting ways in which story can be used as a flexible resource to facilitate children?s mathematical thinking. It looks at... more... | 677.169 | 1 |
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About the book:
This concise "Teach Yourself" text provides a thorough, practical grounding in the fundamental principles of trigonometry, which any reader can apply to his or her own field. The text explores the use of calculators and contains worked examples and exercises (with answers) within each chapter.
Softcover, ISBN 0844200425 Publisher: Teach Yourself | 677.169 | 1 |
New Unit: Bits and Pieces III provides experiences in building algorithms for the four basic operations with decimals New resource: CMP Strategies for English Language Learners Video Tutors available on-line Academic vocabulary support added in each Student Unit
In Covering and Surrounding, you will explore areas and perimeters of figures. Attention is given especially to quadrilaterals and triangles. You will also explore surface area and volume of rectangular prisms.
The book takes an approach that will make students extend their work with linear relations and explore important non-linear relationships. The book has a collection of units that will guide the students throughoutGeometry is focused, organized, and easy to follow. The program shows your students how to read, write, and understand the unique language of mathematics, so that they are prepared for every type of problem-solving and assessment situation | 677.169 | 1 |
Details about Intermediate Algebra:
Larson IS student success. INTERMEDIATE ALGEBRA owes its success to the hallmark features for which the Larson team is known: learning by example, a straightforward and accessible writing style, emphasis on visualization through the use of graphs to reinforce algebraic and numeric solutions and to interpret data, and comprehensive exercise sets. These pedagogical features are carefully coordinated to ensure that students are better able to make connections between mathematical concepts and understand the content. With a bright, appealing design, the new Fifth Edition builds on the Larson tradition of guided learning by incorporating a comprehensive range of student success materials to help develop students' proficiency and conceptual understanding of algebra. The text also continues coverage and integration of geometry in examples and exercises.
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Rent Intermediate Algebra 5th edition today, or search our site for Ron textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by CENGAGE Learning. | 677.169 | 1 |
Beginning Algebra
This course is designed to cover the topics found in a year long high school algebra course. The course builds on the skills begun in pre-algebra to lay a foundation for mathematical problem solving.
You will read, define and apply algebraic and functional vocabulary and symbols; evaluate and perform algebraic operations on rational, radical, and polynomial expressions; set up and solve word problems involving linear, quadratic and rational expressions; and construct and graph linear equations given appropriate information. | 677.169 | 1 |
The Dugopolski series in developmental mathematics has helped thousands of students succeed in their developmental math courses. Algebra for College Students,
"synopsis" may belong to another edition of this title.
About the Author:
Mark Dugopolski was born and raised in Menominee, Michigan. He received a degree in mathematics education from Michigan State University and then taught high school mathematics in the Chicago area. While teaching high school, he received a master's degree in mathematics from Northern Illinois University. He then entered a doctoral program in mathematics at the University of Illinois in Champaign, where he earned his doctorate in topology in 1977. He was then appointed to the faculty at Southeastern Louisiana University, where he now holds the position of professor of mathematics. He has taught high school and college mathematics for over 30 years. He is a member of the MAA, the AMS, and the AMATYC. He has written many articles and mathematics textbooks. He has a wife and two daughters. When he is not working, he enjoys hiking, bicycling, jogging, tennis, fishing, and motorcycling.
Book Description McGraw-Hill Science/Engineering/Math, 2011. Book Condition: New. Brand New, Unread Copy in Perfect Condition. A+ Customer Service! Summary: The Dugopolski series in developmental mathematics has helped thousands of students succeed in their developmental math courses."Algebra for College Students, " Bookseller Inventory # ABE_book_new_0073384348
Book Description McGraw-Hill Education. Hardcover. Book Condition: New. 0073384348 AtAGlance Books -- Orders ship next business day, with tracking numbers, from our warehouse in upstate NY. This book is in brand new condition. Bookseller Inventory # 9780073384344N | 677.169 | 1 |
"Why don't they let us use calculators here?!"
The above question is asked by nearly every single freshman at Johns Hopkins. I'm going to attempt to explain to you why calculators are forbidden on exams and generally discouraged for use in most math classes here and at other institutions of higher education.
"What's with Hopkins?"
Almost anybody involved in higher education beyond the community college level anywhere in the world would agree that learning mathematics should have nothing to do with using calculators. At one community college where I taught, I and my colleagues were forced by administrators to integrate calculator use into our lesson plans despite our objections.
Calculators certainly have their place. When I'm adding the scores on your final exam, I'm going to be typing them into my trusty TI. I don't trust myself to add long lists of numbers by hand accurately. When I'm finished with a long and difficult problem, I often check the answer on my calculator or computer to see if I've messed anything up.
"What's wrong with calculators anyway?"
They lie.
The calculator is a machine. It doesn't know anything about mathematics. A smart engineer has programmed it to give some pretty good answers to some math questions, but these are usually approximations, and, in the strictest sense, very often incorrect.
For example, once you've become acquainted with elementary manipulation of exponents in algebra, you, a human, can tell that 20x×30x=600x so 20x×30x – 600x=0.
Look at what calculators think the graph of 0 looks like when you write it as above:
Asking for something to be done for you is not the same as doing it yourself.
Depending on a machine to do your intellectual work is not just degrading, it also limits your understanding. If you want to do any kind of science from Engineering to Biology to being a practicing physician, you're going to have to understand mathematics. Understanding comes from doing.
You need to be able to recognize when they err and possibly supply an alternative answer yourself!
Your graphing calculator is a precision instrument that will probably not have a real bug for years to come. But, if you only learn how to do math with a calculator, you're going to have to depend on whatever machine happens to be around when you're doing your job. That machine might not be as dependable:
"Why do they want me to be good at calculating stuff by hand? It's so tedious."
Math teachers don't want you to be fast accurate human replacements for calculators. Most teachers consider it their responsibility to craft test questions and exercises in such a way that the arithmetic involved doesn't invite too many errors. Limiting calculator usage in class is to help you learn mathematics, not learn fast arithmetic.
"But I don't know a bunch of elementary arithmetic!"
Ask me anything.
Please ask me about any aspect of mathematics that's escaping you. You can come by my office anytime. Don't have shame about anything. Teaching you is my job. Understanding your coursework is your job. I mean it. If you can't add 1/3 to 1/2 ask me how! | 677.169 | 1 |
text is intended for the Foundations of Higher Math bridge course taken by prospective math majors following completion of the mainstream Calculus sequence, and is designed to help students develop the abstract mathematical thinking skills necessary for success in later upper-level majors math courses. As lower-level courses such as Calculus rely more exclusively on computational problems to service students in the sciences and engineering, math majors increasingly need clearer guidance and more rigorous practice in proof technique to adequately prepare themselves for the advanced math curriculum. With their friendly writing style Bob Dumas and John McCarthy teach students how to organize and structure their mathematical thoughts, how to read and manipulate abstract definitions, and how to prove or refute proofs by effectively evaluating them. Its wealth of exercises give students the practice they need, and its rich array of topics give instructors the flexibility they desire to cater coverage to the needs of their school's majors curriculum.
This text is part of the Walter Rudin Student Series in Advanced MathematicsGood fundamental material is in this book, but the index is absolutely useless! I've never before seen a text where nearly everything I look up in the index is not on the page it says! Good book for a read, but if you use this book for a course, where key concepts must be looked up for review, you'll be left out to dry most of the time. Note to authors and publishers: fix the index!
I liked the conversational tone of this book. The wacky index wasn't great, but I didn't use the index too much anyways. Some of the theorems and proofs could definitely have been written better (like those in chapter 7 (?)--the ones with the Euclidean algorithm). Overall, it was a very useful book. | 677.169 | 1 |
Descriptions du produit
Présentation de l'éditeur
Both simple and accessible, Maths in Minutes is a visually led introduction to 200 key mathematical ideas. Each concept is quick and easy to remember, described by means of an easy-to-understand picture and a maximum 200-word explanation. Concepts span all of the key areas of mathematics, including Fundamentals of Mathematics, Sets and Numbers, Geometry, Equations, Limits, Functions and Calculus, Vectors and Algebra, Complex Numbers, Combinatorics, Number Theory, Metrics and Measures and Topology.
Below title of this tiny (5" square) paperback it says "200 Key Concepts Explained in an Instant," and on the back cover, it claims to be "The quickest possible way to learn about everything from prime numbers to polynomial equations." What it actually contains, largely, are brief dictionary definitions that really do nothing to explain concepts. If you know enough math to understand the definitions,you really don't need this book.
Example: The section on vector functions begins "Vectors whose components are functions, describing a relationship between two or more variables, are vector functions. To study these relationships, the components can be differentiated or integrated like real functions."
Now that's perfectly clear IF you already know what a function is, what a vector is, what the components of a vector are, what differentiation is, and what integration is. And if you know all these things, you've probably already had a basic introduction to vector functions.
There are a few simple introductory pieces on the number line, what a square and a square root are, and the kinds of different triangles, and then it jumps into topics like homologies, the fundamental theorem of algebra, set theory, symmetries and so forth. As a reference for students of math, it's far too sketchy, and as an introduction to mathematical concepts for non-mathematicians it's far too opaque. There are better books for both groups of readers.
4 internautes sur 4 ont trouvé ce commentaire utile
4.0 étoiles sur 5An enjoyable little book30 octobre 2013
Par Aaron C. Brown - Publié sur Amazon.com
Format:Broché
Like the other reviewers, I got this from Amazon Vine instead of the advertised Math in 100 Key Breakthroughs. However unlike them, I enjoyed this book. I understand the criticisms that it is too superficial for a mathematician and too obscure for someone with no mathematical training, but I think it fills a useful intermediate niche.
Each of the 200 2-page spreads (usually words on one page, illustration on the other) is interesting in its own right with mathematical, historical and visual information skillfully intertwined. I found that the level was just right to remind me of ideas, sort of like looking through pictures you took on a vacation in order to relive it. In a few cases, it inspired me to dive a bit deeper.
How does this compare to browsing through Wolfram? It's not as detailed, and of course you don't have the hyperlinks. But it's more fun, due to the high quality presentation and editing, and you can do it without electricity (during the daytime, anyway, or by candlelight at night). I carried it around for a few days and read some pages while waiting for the subway and during boring meetings. I found it entertaining, stimulating and a bit educational. I recommend it.
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4.0 étoiles sur 5Interesting assortment, but only for the interested2 décembre 2013
Par J. Leeman - Publié sur Amazon.com
Format:Broché
First I will say that I really enjoyed this little book. That being said I am an avid reader of math texts, math history, etc so the subject matter was immediately interesting to me. I am slightly worried that the average reader that was looking for some quick facts may feel a bit overwhelmed at times. Unlike many books of this style, this volume is meant to be read straight through, with concepts building on previous topics. This is necessary by the nature of math, but don't expect to turn to a random page and fully grasp it unless you've had some formal math training.
The tone of the book is generally light and easy to read. Occasionally the proofy language of rigorous math drifts in, but is easy to follow and meant to get the reader thinking mathematically. It's very hard to cram so much information into short 2-page blurbs, so some things fall through the cracks. This book starts at the beginning (numbers) and goes into fields such as combinatorics that most people won't know anything about at first. Overall if you are interested in mathematics and want to expand your math knowledge, trivia, and vocabulary this is a fun and quick read.
I just received this book in error (the correct Amazon Vine title I was supposed to receive was "Math in 100 Key Breakthroughs"). I have no idea what the quality of the "100 breakthroughs" book is, because I haven't gotten it, but the author is different from this "Maths in Minutes" book.
Don't waste ANY money on this book! All it is, is a rather poorly written miniature "dictionary of math", and is useless for most people, whether they're interested in math or not. It claims to "explain" 200 key concepts in math, in an instant, but it is not an explanation of any math concept. It is merely a 5" x 5" (by 1 inch thick) dictionary, describing (not really explaining) math terms, and absolutely nothing more.
3.0 étoiles sur 5Bathroom reading for math geeks30 décembre 2013
Par Knits in Tardis - Publié sur Amazon.com
Format:Broché
Does that sound insulting? I promise that it is only defensive, as I live as the sole outsider in a household of math geeks. (Darn that lib'ral arts education!) This is a fun book, if it's more or less your area of interest. For the rest of us, it gets to be pretty rough slogging after page 90 or so (of 400 some total), even considering that the topics are all just a few (tiny) pages in length. For me, if I ever am forced to retake high school calculus -- which would have to be due to some unforseeable and really utterly unfathomable twist of fate -- I'll be grabbing this book as an extended cheat sheet. But not as a primary source -- it's definitely Cliff Notes.
So, not entirely a fit for math-adverse-ish pragmatists, or those who would wish to learn mathematical concepts in detail. That said, if you've already started shopping for next Xmas, this one's worth considering as a stocking stuffer for your favorite math geek. | 677.169 | 1 |
This field guide contains a quick look at the functions commonly encountered in single variable calculus, with exercises for each topic: linear, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise functions. Also algebraic operations on functions, function composition, and general types of functions.
Links to selected sites, projects, and graphing calculator explorations designed to foster understanding of the family of functions known as exponential functions, useful in such applications as population growth, compound interest, radioactive decay, and value depreciation, where the rate of change is either continuously decreasing or continuously increasing.
A unit that uses functions to connect mathematical concepts to weather and climate. The first section discusses concepts relevant to climate, weather, and the atmosphere. Topics such as the earth's energy budget, clouds and cloud formation, winds and the wind system, and the effect of the corolis force on wind direction are discussed; this section can be used as a reference source for a lesson ... | 677.169 | 1 |
Written by the author, this manual offers step-by-step solutions for all odd-numbered text exercises as well as Chapter and Cumulative tests. In addition to Chapter and Cumulative tests, the manual also provides practice tests and practice test answers.
Designed to build a strong foundation in precalculus, this premier text for a reform-oriented course encourages students to develop a firm grasp of the underlying mathematical concepts while using algebra as a tool for solving real-life problems. The comprehensive text presentation invites discovery and exploration, while the integrated technology and consistent problem-solving strategies help the student develop strong precalculus skills.
In the Third Edition, we have revised and improved upon many text features designed for this purpose. Our pedagogical approach includes presenting solutions to examples from multiple perspectives-algebraic, graphic, and numeric. The side-by-side format allows students to see that a problem can be solved in more than one way, and to compare the accuracy of the solution methods.
This new precalculus textbook focuses on making the mathematics accessible, supporting student success, and offering teachers flexible teaching options. It thoroughly covers the topics of a traditional precalculus text with the addition of two new chapters. Chapter 11 encompasses analytic geometry in three dimensions and Chapter 12 introduces students to the key calculus topics, including limits, the tangent line problem, and the area problem.
If you shoot an arrow into the air, its height above the ground depends on the number of seconds since you released it. In this chapter you will learn ways to express quantitatively the relationship between to variables such as height and time. You will deepen what you have learned in previous courses about functions and the particular relationships that they describe for example, how height depends on time.
In this new ADVANTAGE SERIES version of David Cohen's PRECALCULUS: WITH UNIT CIRCLE TRIGONOMETRY, THIRD EDITION, Cohen continues to offer a book that is accessible to the student through a careful progression and presentation of concepts, rich problem sets and examples to help explain and motivate concepts, and continual guidance through the challenging work needed to master concepts and skills. This book is identical to PRECALCULUS: A PROBLEMS-ORIENTED APPROACH, Fifth Edition with the exception of the first four chapters on trigonometry. As part of the ADVANTAGE SERIES, this new version will offer all the quality content you've come to expect from Cohen sold to your students at a significantly lower price.
PRECISION MACHINING TECHNOLOGY has been carefully written to align with the National Institute of Metalworking Skills (NIMS) Machining Level I Standard and to support achievement of NIMS credentials. This new text carries NIMS' exclusive endorsement and recommendation for use in NIMS-accredited Machining Level I Programs. It's the ideal way to introduce students to the excitement of today's machine tool industry and provide a solid understanding of fundamental and intermediate machining skills needed for successful 21st Century careers. With an emphasis on safety throughout, PRECISION MACHINING TECHNOLOGY offers a fresh view of the role of modern machining in today's economic environment. The text covers such topics as the basics of hand tools, job planning, benchwork, layout operations, drill press, milling and grinding processes, and CNC. The companion Workbook/Shop Manual contains helpful review material to ensure that readers have mastered key concepts and provides guided practice operations and projects on a wide range of machine tools that will enhance their NIMS credentialing success.
This book owes its existence to a need felt, we believe, by many people who are trying to teach European prehistory, for an elementary textbook suitable for students taking their first course in the subject with little or no previous experience in archeology.
Galaxy Zack blasts back to the past in this outer space chapter book adventure!A baby pterosaur can't find his way home, so it's up to the Nebulon Navigators to return him to the Prehistoric Planet. And when Zack's dad is invited on the journey, Zack finds a way to go along too! But as they blast off on the super shuttle, they hear a strange noise. Is it the pterosaur, crying for his mama? No, it's...Zack's dog, Luna, who has snuck onto the shuttle! When the shuttle lands, Zack can't believe his eyes: The Prehistoric Planet is full of creatures that he's only read about in books. Zack and the team of navigators head out in search of the pterosaur's mother--and end up in the middle of an amazing adventure. With easy-to-read language and illustrations on almost every page, the Galaxy Zack chapter books are perfect for beginning readers.
This textbook traces the history of Black people in America, from the time of first colonization to today. It describes slavery, the role of African-Americans in the Revolutionary War, the status of free Blacks in the Antebellum south, the abolition movement, the Civil War, emancipation, Reconstruction, the Harlem Renaissance, the role of Blacks in World War II, the civil rights and Black Power movements, and the lives of Black people in contemporary American society. Illustrations and profiles of prominent figures support the narrative. A companion CD-ROM contains speeches, songs, stories and poetry. The authors teach at Michigan State university and South Carolina State University.
Prentice Hall Algebra 1 is focused, organized, and easy to follow. The program shows your students how to read, write, and understand the unique language of mathematics, so that they are prepared for every type of problem-solving and assessment situation.
Applications are handled by creating mathematical models of phenomena in the real world. Students must select a kind of function that fits a given situation, and derive an equation that suits the information in the problem. The equation is then used to predict values of y when x is given or values of x when y is given. Sometimes students must use the results of their work to make interpretations about the real world, such as what "slope" means, or why there cannot be people as small as in Gulliver's Travels. The problems require the students to use many mathematical concepts in the same problem. This is in contrast to the traditional "word problems" of elementary algebra, in which the same one concept is used in many problems.
There are many features built into the daily lessons of this text that will help you learn the important concepts and skills you will need to be successful in this course. There are numerous Exercises in each lesson to give you the practice you need to learn. Practice Multiple Choice exercises are included in the lesson to help you prepare for success on your state test. The text also contains Error Analysis, Test Prep exercises, Critical Thinking exercises, Challenge exercises, etc | 677.169 | 1 |
Sunday, February 3, 2013
Mathematics notes algebra,trigonometry,calculas
Mathematics notes
Mathematics notes provided by online teachers include almost all content related to mathematics. There are three portion for these mathematics first portion is about the algebra and content related to algebra. The second portion is of trigonometry and content related to trigonometry The third portion is calculus and content related to calculus. These notes include chapter wise content of mathematics.
Mathematics notes for trigonometry portion
Mathematics notes for trigonometry portion include content about the Fundamentals of Trigonometry,Trigonometric Identities Sum and Difference of Angles,Application of Trigonometry,Inverse Trigonometric Functions,Solution of Trigonometric Equations.
Mathematics notes for calculus portion
Mathematics notes for calculus portion include content about the Functions and Limits,Differentiation,Integration,linear inequalities and linear programming(like Coordination system, distance formula , Ratio formula , Translation and rotations axes. Then we feather discuss the equations of straight lines, slop of the line etc),conics section(like circle, elips , parabola and about the hyperbola etc ),vectors(like introduction of vectors then introduction of vector space , scalar product of two vectors, vector product of two vectors, scalar triple product of vectors etc).
Note
These notes are specially for class 11 and of class 12 (Intermediate level) standard. Mathematics notes covers all syllabus of Fsc pre engineering part 1 and Fsc pre engineering of part 2. It is also for F.A part 1 and F.A part 2 with mathematics subject. And for intermediate with computer science (ICS) part 1 and for Intermediate with computer science (ICS) part 2. These notes cover all chapter of first year student and for the second year student. | 677.169 | 1 |
S. S. M. Precalculus
9780495382874
ISBN:
0495382876
Edition: 11 Pub Date: 2007 Publisher: Cengage Learning
Summary: Check your work-and your understanding-with this manual, which provides solutions for all of the odd-numbered exercises in the text. You will also find strategies for solving additional exercises and many helpful hints and warnings.
Cole, Matt is the author of S. S. M. Precalculus, published 2007 under ISBN 9780495382874 and 0495382876. Twenty five S. S. M. Precalculus textbooks are available for sale on Val...oreBooks.com, three used from the cheapest price of $8.46, or buy new starting at $102.36 | 677.169 | 1 |
Maths is everywhere, often where we least expect it. Award-winning professor Steven Strogatz acts as our guide as he takes us on a tour of numbers that - unbeknownst to the most of us - form a fascinating and integral part of our everyday lives. In The Joy of X , Strogatz explains the great ideas of maths - from negative numbers to calculus, fat tails... more...
The irresistibly engaging book that "enlarges one's wonder at Tammet's mind and his all-embracing vision of the world as grounded in numbers." --Oliver Sacks, MD THINKING IN NUMBERS is the book that Daniel Tammet, mathematical savant and bestselling author, was born to write. In Tammet's world, numbers are beautiful and mathematics illuminates... more...
All the math basics you'll ever need! It's not too late to learn practical math skills! You may not need to use quadratic equations very often, but math does play a large part in everyday life. On any given day, you'll need to know how long a drive will take, what to tip a waiter, how large a rug to buy, and how to calculate a discount. With The... more...
This text embodies at advanced and postgraduate level the professional and technical experience of two experienced mathematicians. It covers a wide range of applications relevant in many areas, including actuarial science, communications, engineering, finance, gambling, house purchase, lotteries, management, operational research, pursuit and search.... more...
Why do weather forecasters get it wrong? What are the best tactics for playing"Who Wants to be a Millionaire?"and"The Weakest Link"? And what is the link between a tin of baked beans and a men's urinal? These and many other questions are answered in this book. It is for anyone wanting to remind themselves - or discover for the first time - that maths... more...
Solutions manual to accompany Logic and Discrete Mathematics: A Concise Introduction This book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, presenting material that has been tested and refined by the authors in university courses taught over more... more...
This e-book gives the reader information on research in mathematics, and how the use of math Manipulatives can improve math performance. Differentiated learning is a way to modify the traditional curriculum in order to address the learning styles of other students. The book takes a look at mathematics education around the world, and compares it to... more...
Build your students' knowledge and understanding so that they can confidently reason, interpret, communicate mathematically and apply their mathematical skills to solve problems within mathematics and wider contexts; with resources developed specifically for the OCR GCSE 2015 specification by mathematics subject specialists experienced in teaching... more... | 677.169 | 1 |
Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODEs) deal with functions of one variable, which can often be thought of as time.
Topics include: Solution of first-order ODE's by analytical, graphical...
This math lesson from Illuminations helps students understand rational functions. The material uses the real-world problem. Students will write rational functions that model problem situations and use rational functions to solve those problems. Questions for students are included. The lesson is intended for grades 9-12 and should require 2 class periods to complete.
This lesson from Illuminations asks students to use graphs, tables, number lines, verbal descriptions, and symbols to represent the domain of various functions. The material allows students to examine and utilize connections between a function?s symbolic representation, a function?s graphical representation, and a function?s domain. The lesson is intended for grades 9-12 and should require 1 cla...
This unit from Illuminations focuses on collecting data and using technology to find functions to describe the data collected. Students will learn to use a calculator to find the curve of best fit for a set of data and demonstrate an understanding of how modifying parameters changes the graphs of functions by writing equations for those functions. The unit includes two lessons intended for grades... | 677.169 | 1 |
Casio FX-115ES Scientific Calculator
Casio FX-115ES Scientific Calculator - Casio FX-115ES Scientific Calculator is an advanced solar-powered scientific calculator which can perform metric calculations instantly. This is a scientific calculator with a 2-line textbook display which can produce the results and formulas that are seen exactly as in textbooks. The Casio FX-115ES Scientific Calculator can perform around 279 functions which include all the major mathematical formulas, square roots and fractions. The Casio FX-115ES Scientific Calculator is user-friendly and easy to handle, when compared to other scientific calculators. These Casio calculators have a wide range of applications in the fields of engineering, physics and statistics. These Casio calculators are mostly used for measurement conversions and estimations.
Casio's latest and most advanced scientific calculator features new Natural Textbook Display and improved math functionality. The FX-115ES Plus is designed to be the perfect choice for high school and college students learning general math, trigonometry, statistics, algebra I and II, calculus, engineering or physics | 677.169 | 1 |
Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for). | 677.169 | 1 |
Comment: Book is in good condition and fulfilled by Amazon. Signs of previous use but spine it tight and book is clean. This book CGP Study Guide explains everything students need to know for Key Stage Three Maths - all fully up-to-date for the new curriculum from September 2014 onwards. It's ideal for students working at a higher level (it covers what would have been called Levels 5-8 in the pre-2014 curriculum). Every topic is explained with clear, friendly notes and worked examples, and there's a range of practice questions to test the crucial skills. We've also included a digital Online Edition of the whole book to read on a PC, Mac or tablet - just use the unique code printed at the front of the book to access it. For extra practice, a matching KS3 Maths Workbook is also available (9781841460383Somehow CGP manage to produce guides which contain all the hard facts kids need for their exams, but which present them in a friendly, digestible format accessible to both children and adults. This comprehensive guide includes sections on numbers, algebra, shapes and statistics, presented with the usual CGP humour and cartoons. It is useful both as a reference book (when are shapes congruent and similar? What are the 8 simple rules of geometry?) and as a work-your-way through-it revision guide. Conclusion: everything you need for revising (and learning) KS3 maths.
My son was having problems in maths due to lessons missed after illness. I had very little knowledge of modern secondary level maths so this book was perfect to help us both to tackle some tricky new topics.
my 13 year old daughter was falling behind in her maths so i approached her maths teacher who recommended this book. we bought it for her and 4 weeks later she scored a 7C and secured her place in the top maths set for year 8. well worth every penny. i highly recommend this book.
I purchased this book roughly 6-7 weeks before the actual mathematics exam, thinking that it was too late to revise the majority of the year 9 curriculm. But I found it simple, fun and easy to understand because of its unique teaching methods. For instance it had useful pictures, strange jokes and questions at the end of each chapter to test your knowledge. All of which proved to be extremely helpful, due to the amount of time I had to revise.
A really good book that is worth reading it helps with your maths and covers all the catagories studied through Key Stage Three. With funny jokes and pictures it really makes Maths come to life, a brilliant read!!!
CGP books are absolutely fantastic for learning KS3 maths; I thoroughly recommend them for your first choice of guidebooks. There are 4 chapters, `Numbers Mostly' `Algebra' `Shapes' & `Statistics and Probability'. These are split into sections which explain all of the different parts - in amazing detail. CGP tell you everything you need to know and then test you at the end of the section; about 40 in-depth questions that will test your revision knowledge as far as it will go, and the answers are at the back of the book. You will find this book covers most topics, so this is a great buy.
I have purchased this for my daughter as she struggles with maths a little and after a. Opulent of pages read she understood maths more, this book is written to make you understand maths in a better or easier way as my daughter found out by using this, I would defiantly recommend to someone who struggles with maths. | 677.169 | 1 |
Whether they had any interest in mathematics in high school, students often discover a new appreciation for the field at Sarah Lawrence College. In our courses—which reveal the inherent elegance of mathematics as a reflection of the world and how it works—abstract concepts literally come to life. That vitality further emerges as faculty members adapt course content to fit student needs, emphasizing the historical context and philosophical underpinnings behind ideas and theories. By practicing rigorous logic, creative problem solving, and abstract thought in small seminar discussions, students cultivate habits of mind that they can apply to every interest. With well-developed, rational thinking and problem-solving skills, many students continue their studies in mathematics, computer science, philosophy, medicine, law, or business; others go into a range of careers in fields such as insurance, technology, defense, and industry.
Courses
Mathematics
Intermediate—Spring
Many laws governing physical and natural phenomena and, of late, a growing number of theories describing social phenomena are expressed in terms of the rates of change (derivatives) of interrelated variables. Differential equations, the branch of mathematics that explores these important relationships, provides a collection of tools and techniques fundamental to advanced study in engineering, physics, economics, and applied mathematics. The investigation of such equations and their applications will be the focus of this second half of the Multivariable Modeling two-course sequence. Conference work will involve a concentrated investigation of one application of multivariable mathematics.
Faculty
Open—Spring
Warfare, elections, auctions, labor-management negotiations, inheritance disputes, even divorce—these and many other conflicts can be successfully understood and studied as games. A game, in the parlance of social scientists and mathematicians, is any situation involving two or more participants (players) capable of rationally choosing among a set of possible actions (strategies) that lead to some final result (outcome) of typically unequal value (payoff or utility) to the players. Game theory is the interdisciplinary study of conflict, whose primary goal is the answer to the single, simply stated but surprisingly complex question: What is the best way to "play"? Although the principles of game theory have been widely applied throughout the social and natural sciences, the greatest impact has been felt in the fields of economics, political science and biology. This course represents a survey of basic techniques and principles. Of primary interest will be the applications of the theory to real-world conflicts of historical or current interest.
Faculty
Related Disciplines
Intermediate—Fall
Rarely is a quantity of interest (tomorrow's temperature, unemployment rates across Europe, the cost of a spring break flight to Denver) a simple function of just one other variable. Reality, for better or worse, is mathematically multivariable. This course provides an introduction to an array of topics and tools used in the mathematical analysis of multivariable functions. The intertwined theories of vectors, functions, and matrices will be the central theme of exploration in this first semester of the Multivariable Modeling two-course sequence. Specific topics to be covered include the algebra and geometry of vectors in two, three, and higher dimensions; dot and cross products and their applications; equations of lines and planes in higher dimensions; solutions to systems of linear equations using Gaussian elimination; theory and applications of determinants, inverses, and eigenvectors; volumes of solids in three dimension via integration; and spherical and cylindrical coordinate systems. Conference work will involve a concentrated investigation of one application of multivariable mathematics.
Faculty
Open—Fall
An introduction to the concepts, techniques, and reasoning central to the understanding of data, this lecture course focuses on the fundamental ideas of statistical analysis used to gain insight into diverse areas of human interest. The use, abuse, and misuse of statistics will be the central focus of the course. Topics of exploration will include the core statistical topics in the areas of experimental study design, sampling theory, data analysis, and statistical inference. Applications will be drawn from current events, business, psychology, politics, medicine, and other areas of the natural and social sciences. Spreadsheet statistical software will be introduced and used extensively in this course, but no prior experience with the software is assumed. Conference work will involve working in a small group to conceive and execute a small-scale research study. This seminar is an invaluable course for anybody planning to pursue graduate work and/or research in the natural sciences or social sciences. No college-level mathematical knowledge is required.
Faculty
Related Disciplines
Open—Spring
Our existence lies in a perpetual state of change. An apple falls from a tree. Clouds move across expansive farmland blocking out the sun for days. Meanwhile, satellites zip around the Earth, transmitting and receiving signals to our cell phones. The calculus was invented to develop a language to accurately describe and study the change that we see. The ancient Greeks began a detailed study of change but were scared to wrestle with the infinite, so it was not until the 17th century that Isaac Newton and Gottfried Leibniz, among others, tamed the infinite and gave birth to this extremely successful branch of mathematics. Though just a few hundred years old, the calculus has become an indispensable research tool in both the natural and social sciences. Our study begins with the central concept of the limit and proceeds to explore the dual of differentiation and integration. Numerous applications of the theory will be examined. For conference work,
Faculty
Open—Fall
This course continues the thread of mathematical inquiry, following an initial study of the dual topics of differentiation and integration (see Calculus I course description). Topics to be explored in this course include the calculus of exponential and logarithmic functions, applications of integration theory to geometry, alternative coordinate systems, and power series representations of functions. For conference work The theory of limits, differentiation, and integration will be briefly reviewed at the beginning of the term.
Faculty
Advanced— mathematics research, and we will discuss the questions that motivate its various branches, including geometric, algebraic, and differential topology. Conference work will be allocated to clarifying course ideas and exploring additional mathematical topics.
Faculty
Intermediate— DisciplinesIntermediate—Fall
This course covers the major developments that comprise modern physics—the paradigm shifts from the classical, Newtonian models covered in the introductory study of mechanics and electromagnetism. Topics to be covered include Einstein's special and general theories of relativity, wave-particle duality, Schrodinger's equation, and the mathematical and conceptual bases of quantum mechanics. Emphasis will be on mathematical models and problem solving, in addition to conceptual understanding. Seminars will include a mixture of discussion and mathematical problem solving. | 677.169 | 1 |
This online course includes elements from an undergraduate seminar on mathematical problem solving. The material will help students develop their mathematical and problem solving skills. A few topics that are covered include probability, generating mathematical functions and polynomials. Course materials include student assignments and solutions. MIT presents OpenCourseWare as free educational...
This page, presented by MIT and made available online via the university's Open Courseware site, presents a series of materials on biological engineering. Topics include introduction to biological engineering design, systems microbiology, computation for biological engineers and molecular principles of biomaterials. Materials are at both the undergraduate and graduate school levels....
This course involves students taking turn giving lectures on geometry topics. Subjects such as Gauss maps, minimal surfaces and manifolds and geodesics were covered in the lectures. Course materials include lecture notes as well as student projects and examples. MIT presents OpenCourseWare as free educational material online. No registration or enrollment is required to use the materials. | 677.169 | 1 |
Lessons Introductory to the Modern Higher Algebra (Classic Reprint)
Overview
Excerpt from Lessons Introductory to the Modern Higher Algebra Invariants, quite a new department of Algebra has been created; and there is no part of Mathematics in which an able mathematician, who had turned his attention to other subjects some twenty years ago, would find more difficulty in reading a memoir of the present day, and would more feel the want of an elementary guide to inform him of the meaning of the terms employed, and to establish the truth of the theorems assumed to be known.
With respect to the use of new words I have tried to steer a middle course. In this part of Algebra combinations of ideas require to be frequently spoken of which were not of important use in the older Algebra. This has made it necessary to employ some new words, in order to avoid an intolerable amount of circumlocution. But feeling that every strange term makes the science more repulsive to a beginner, I have generally preferred the use of a periphrasis to the introduction of a new word which I was not likely often to have occasion to employ | 677.169 | 1 |
Math and Meds for the Nurse / Edition 1
Using a programmed ratio proportion approach, this new book provides essential aides in learning and reviewing basic math and calculations of drugs and solutions. Its five units include: mathematics review, measuring systems and abbreviations, oral and parenteral medications, intravenous medications and fluids, and applications and review. It includes drug labels…
See more details below | 677.169 | 1 |
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