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University of Northern Colorado, School of
Mathematical Sciences |
Course:
Math 124 Ð College
Algebra
Credit: 4 units
Course Description: Prerequisite is high
school Algebra II, or intermediate algebra with a grade of ÒCÓ or better and
ACT-Math at an appropriate level, or the equivalent. Topics include linear,
quadratic, exponential and logarithmic functions; matrices; theory of
equations.
Course Objectives:
The primary objective of the course is to develop understanding of the
techniques involved in algebraic problem solving. The course is designed to
fulfill the liberal arts core mathematics requirement and to prepare students
to take calculus (note that a pre-calculus or trigonometry course may also be
necessary before calculus, depending on the calculus course) and/or statistics,
should they decide to continue to study mathematics. Liberal Arts Core, Area 2,
expectations met by Math 124:
¯
The student
will demonstrate proficiency in the use of algebra to structure their
understanding of and investigate questions in the world around them.
¯
The student
will demonstrate proficiency in treating algebraic content at an appropriate
level.
¯
The student
will demonstrate competence in the use of numerical, graphical, and functional
representations of algebra topics.
¯
The student
will demonstrate the ability to interpret data, analyze graphical information,
and communicate solutions in written and oral form.
¯
The student
will demonstrate proficiency in the use of algebra to formulate and solve
problems.
¯ The student will demonstrate proficiency in using technology such as handheld calculators and computers to support their use of algebra.
Special
Needs: Students who
believe they may need accommodations in this class are encouraged to contact
the Disability Support Services, (970) 351-2289, as soon as possible to ensure
that accommodations are implemented in a timely fashion.
Course
Content
Major
Study Units (not
necessarily taught in the order given):
¯
Set theory:
notation, subsets of real numbers and properties of real numbers; summation and
series notation and use.
¯ Algebraic manipulations: including working
with exponents, radicals, polynomial operations, factoring and algebraic
fractions.
¯ Solving equations and systems of
equations: linear, quadratic, equations involving radicals, equations in
quadratic form and equations involving absolute value.
¯ Formulas: including formula evaluation
and solving for any variable in multivariate representations.
¯ Problem analysis: word problem
applications and generating solutions using equations.
¯ Inequalities: first-degree inequalities,
higher degree inequalities and inequalities involving absolute value.
¯ Functions: recognize, graph, model, and
apply: linear, rational, absolute value, polynomial, exponential, and
logarithmic functions; inequalities in two variables; inverse functions.
¯ Representation: work with function notation, graphical, and tabular representations; graphical, tabular, verbal, and formulaic representations of inverse functions.
Instructional
Strategies: There are
three major instructional strategies in teaching the course Ð an emphasis on
effective writing about mathematics, appropriate use of technology, and the
rule of three:
¯ Written assignments in the course will result in at least
1100 words of prose writing related to mathematical situations. These written
assignments may have one (or more) of the following forms:
-
one or more project reports,
- homework
assignments that include short essay answer explanatory responses in addition
to brief written justification for application and exploration problems,
-
exam questions that require explanation and/or justification, in full sentences,
of solutions.
¯ Technology, in particular a scientific or graphing
calculator along with its manual (or an equivalent computer or web-based
program), are used to help each student think about and analyze mathematics. In
addition to the traditional use as a simple calculational tool, students may
also master the graphing and basic programming capabilities of calculators in
order to better visualize models and estimate solutions.
¯ The semiotic "rule of three" means that concepts, symbols, and words
are investigated for each topic. The most common interpretation of the rule of
three in algebra is to have students explore the geometric/graphical,
numeric/tabular, and functional views for topics.
Methods of Evaluation: Assessment of student
learning is accomplished through at least two in-class examinations, regular
homework or quizzes on which substantive feedback is given to students, and a
comprehensive final exam. Additional in-class or web-based activities are
likely to be included in formative or summative assessments of student
progress. One or two projects that result in summative reports can take the
place of some, but not all, home, class, and quiz work. Lab sessions on a
computer or using graphing calculators that illustrate the topics discussed in
class are necessary. Assessment of technological mastery will be made through
quizzes, class activities, projects, or short essay assignments.
Bibliography
Coburn, J. (2006). College
Algebra. New York:
McGraw-Hill. (COURSE TEXTBOOK)
COMAP project (1994). For
all practical purposes: introduction to contemporary mathematics, Freeman and Co., New York.
Giordano, F., W. P. Fox, and
M. Weir (1997) An Introduction to Mathematical Modeling, Brooks/Cole.
Hoffman, P. (1988). Archimedes'
Revenge, Fawcett.
Ifrah, Georges (2000). The
Universal History of Numbers,
Wiley & Sons.
Prepared by S. Hauk, 8/24/04; Rev. 7/15/05sh; 7/15/06sh/7/25/07sh.
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Addendum on content for Coburn (2006): |
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Topics/sections to be
taught and assessed (i.e., must be covered) |
Suggested additional sections (i.e., might be covered) |
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1.1 through 1.5 |
Review: R.A, R.1 |
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2.1 through 2.5 |
2.6, R.2 |
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3.1 through 3.8 (all of Chapter 3) |
R.3 |
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4.1 through 4.5 |
4.6, 4.7, R.4, R.5 |
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5.1 through 5.5 |
5.6, R.6 |
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6.1 through 6.3, 6.5, AND partial fractions in 6.8 |
6.4, 6.6, 6.7, rest of 6.8 |
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7.1 AND 7.5 |
7.2, 7.3, 7.4, |
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8.1 |
8.2, 8.3, 8.4, 8.5, 8.6, 8.7 |