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Mathematics Course Descriptions
The Definition of IAI GECC Mathematics
All courses listed require at least satisfactory
completion of intermediate algebra and geometry as prerequisites. To fulfill the Illinois Transferable General Education Core Curriculum (IAI Gen. Ed.) mathematics requirement, students are
expected to complete satisfactorily 1 to 2 courses (3 to 6 semester
credit hours) as follows:
M1 900: College-level Calculus (3-5 semester credits)
RETIRED [effective Fall 2004]
NOTICE:
The panel has decided to retire M1 900. Each course under M1 900 will now be identified separately with the following IAI Codes:
M1 900-1: Calculus I
M1 900-2: Calculus II
M1 900-3: Calculus III
M1 900-B: Business Calculus
A college-level calculus course. Policies on acceptance of AP credit vary among academic programs and from institution to institution, so AP credit toward the GECC or major requirements is not guaranteed. In general, a score of 3 or higher on the AP Calculus exam may be considered as equivalent to successful completion of courses approved for M1 900.
Prerequisite: C or better in college algebra.
M1 900-1: College-level Calculus I (4-5 semester credits)
Topics include (but are not limited to) the following: limits and continuity; definition of derivative: rate of change, slope; derivatives of polynomial and rational functions; the chain rule; implicit differentials; approximation by differentials; higher order derivatives; Rolle’s Theorem: mean value theorem; applications of the derivative; anti-derivative; the definite integral; the fundamental theorem of calculus; area, volume, other applications of the integral; the calculus of the trigonometric functions; logarithmic and exponential functions; techniques of integration, including numerical methods; indeterminate forms: L'Hôpital's rule; improper integrals; sequences and series, convergence tests, Taylor series; functions of more than one variable, partial derivatives; the differential, directional derivatives, gradients; double and triple integrals: evaluation and applications. Prerequisite for Calculus I: College Algebra and Trigonometry with grades of C or better or Elementary Functions with a grade of C or better.
M1 900-2: College-level Calculus II (3-5 semester credits)
Topics include (but are not limited to) the following: limits and continuity; definition of derivative: rate of change, slope; derivatives of polynomial and rational functions; the chain rule; implicit differentials; approximation by differentials; higher order derivatives; Rolle’s Theorem: mean value theorem; applications of the derivative; anti-derivative; the definite integral; the fundamental theorem of calculus; area, volume, other applications of the integral; the calculus of the trigonometric functions; logarithmic and exponential functions; techniques of integration, including numerical methods; indeterminate forms: L'Hôpital's rule; improper integrals; sequences and series, convergence tests, Taylor series; functions of more than one variable, partial derivatives; the differential, directional derivatives, gradients; double and triple integrals: evaluation and applications. Prerequisite for Calculus II: Calculus I or equivalent with a grade of C or better.
M1 900-3: College-level Calculus III (3-5 semester credits)
Topics include (but are not limited to) the following: limits and continuity; definition of derivative: rate of change, slope; derivatives of polynomial and rational functions; the chain rule; implicit differentials; approximation by differentials; higher order derivatives; Rolle’s Theorem: mean value theorem; applications of the derivative; anti-derivative; the definite integral; the fundamental theorem of calculus; area, volume, other applications of the integral; the calculus of the trigonometric functions; logarithmic and exponential functions; techniques of integration, including numerical methods; indeterminate forms: L'Hôpital's rule; improper integrals; sequences and series, convergence tests, Taylor series; functions of more than one variable, partial derivatives; the differential, directional derivatives, gradients; double and triple integrals: evaluation and applications. Prerequisite for Calculus III: Calculus II or equivalent of C or better.
M1 900-B: Calculus for Business and Social Sciences (3-5 semester credits)
This course is designed specifically for students in business and the social sciences
and does not count toward a major or minor in mathematics. It may be taken before
or after a course in finite mathematics. The course emphasizes application of
the basic concepts of calculus rather than proofs. Topics include curve sketching
and recognition of curves, techniques of differentiation applied to polynomial,
rational, exponential, and logarithmic functions, maxima and minima of a function
of one or more variables, partial derivatives, LaGrange multipliers, and elementary
techniques of integration. Application to the worlds of business and social science
should be stressed throughout the course. Prerequisite: College Algebra with a
grade of C or better.
M1 900-O: Calculus (other) (3-5 semester credits)
Courses in this category meet the basic description of a college-level calculus course and includes the concepts of differentiation and integration as appropriate. Courses such as a Short Course in Calculus, Non-Technical Calculus, and others are assigned here. Such courses do not fulfill the description of any course in the standard calculus sequence or the description of a calculus course for business and social science. Prerequisite: college algebra or equivalent with a grade of “C” or better.
M1 901: Quantitative Literacy (3-4 semester credits)
Develops conceptual understanding, problem-solving, decision-making and analytic
skills dealing with quantities and their magnitudes and interrelationships, using
calculators and personal computers as tools. Includes: representing and analyzing
data through such statistical measures as central tendency, dispersion, normal
and chi-square distributions, and correlation and regression to test hypotheses
(maximum of one-third of course); using logical statements and arguments in a
real-world context; estimating, approximating and judging the reasonableness of
answers; graphing and using polynomial functions and systems of equations and
inequalities in the interpretation and solutions of problems; and selecting and
using appropriate approaches and tools in formulating and solving real-world problems.
Prerequisite: C or better in intermediate algebra and geometry.
M1 902: General Education Statistics (3-4 semester credits)
Focuses on mathematical reasoning and the solving of real-life problems, rather
than on routine skills and appreciation. Descriptive methods (frequency distributions,
graphing and measures of location and variation), basic probability theory (sample
spaces, counting, factorials, combinations, permutations, and probability laws),
probability distributions (normal distributions and normal curve, binomial distribution,
and random samples and sampling techniques), statistical inference (estimation,
hypothesis testing, t-test, and chi-square test, and errors), correlation and
regression, and f-test and analysis of variance. Prerequisite: C or better in
intermediate algebra and geometry.
M1 903: Mathematics for Elementary Teaching I and II (3-4 semester credits)
Focuses on mathematical reasoning and problem solving, by using calculators and
microcomputers in problem solving. Topics are selected from: sets, functions and
logic, whole numbers, integers, rational numbers, irrational numbers and the real
number system (e.g., number theory, probability, statistics, measurement and non-metric
geometry). The two-course sequence meets the requirements for state certification
in elementary teaching. Fulfills the Illinois Transferable General Education Core
Curriculum (iTransfer Gen. Ed.) requirement only for students seeking state certification
as elementary teachers or special education teachers. Prerequisite: C or better
in intermediate algebra and geometry.
M1 904: General Education Mathematics (3-4 semester credits)
Focuses on mathematical reasoning and the solving of real-life problems, rather
than on routine skills and appreciation. Three or 4 topics are studied in depth,
with at least 3 chosen from the following list: geometry, counting techniques
and probability, graph theory, logic/set theory, mathematical modeling, mathematics
of finance, game theory, linear programming and statistics. The use of calculators
and computers are strongly encouraged. Prerequisite: C or better in intermediate
algebra and geometry.
M1 905: Discrete Mathematics (3 semester credits)
Introduction to analysis of finite collections and mathematical foundations of sequential machines, computer system design, data structures and algorithms. Includes: sets, counting, recursion, graph theory, trees, nets, Boolean algebra, automata, and formal grammars and languages. Prerequisite: C or better in college algebra.
M1 906: Finite Mathematics (3-4 semester credits)
Emphasis on concepts and applications, rather than mathematical structures. Form A (designed especially for students
in business, economics, Social Sciences and Life Sciences, with applications drawn from these fields) includes such
topics as: vectors, determinants, matrices and matrix algebra; systems of linear equations and matrices; systems of
inequalities and linear programming; simplex method, set theory, logic and Boolean algebra; counting and probability
theory; stochastic processes; game theory; Markov chain methods; mathematical modeling; and the mathematics of
finance. Form B: matrix algebra; systems of linear equations and matrices; determinants; vectors in 2-space and
3-space; vector spaces; eigenvalues and eigenvectors. Prerequisite: C or better in college algebra.
M1 907: Elementary Mathematical Modeling (3-4 semester credits)
Focuses on mathematical reasoning through the active participations of students
in building a knowledge base of numeric, geometric, and algebraic models. Integrates
the use of graphing calculators and personal computers. Includes inductive and
deductive reasoning, mathematical proof, mathematical modeling in problem solving,
and limitations therein. Topics may include: sequences and series in modeling,
variables and functions, graphical, tabular, and formulaic representation of
algebraic functions, algebraic functions in modeling logarithmic scales, logarithmic
functions and exponential functions in modeling. Prerequisite: C or better in
both intermediate algebra and geometry.
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