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Mathematics Course Descriptions

The Definition of IAI GECC Mathematics

All courses listed require at least satisfactory completion (a āCā or better) of intermediate algebra and geometry as prerequisites. For M1-901, M1-902, M1-904, and M1-907, satisfactory completion (a āCā or better) of Preparatory Mathematics for General Education (PMGE) may be used to meet the intermediate algebra requirement. To fulfill the Illinois Transferable General Education Core Curriculum (IAI Gen. Ed.) mathematics requirement, students are expected to complete satisfactorily 1 course (3 to 5 semester credits) as follows:

### M1900 : 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.

### M1900-1 : College-level Calculus I

**(4-5 semester credits)****The following description is for the full Calculus sequence (M1900-1, M1900-2, M1900-3): **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 differentiation; approximation by differentials; higher-order derivatives; Rolle's Theorem and mean value theorem; applications of the derivative; antiderivatives; 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, substitution, integration by parts, trigonometric substitution, and partial fractions; indeterminate forms and L'Hôpital's rule; improper integrals; sequences and series, convergence tests, Taylor series; parametric equations; polar coordinates and equations; vectors in 2 and 3 dimensions, vector operations; lines and planes in space; surfaces, quadric surfaces; functions of more than one variable, partial derivatives; the differential, directional derivatives, gradients; double and triple integrals, evaluation and applications; cylindrical and spherical coordinates. Prerequisite for Calculus I: College Algebra and Trigonometry with grades of C or better, or Precalculus with a grade of C or better. *The panel has compared the IAI GECC M1 900-1 descriptor against the AP Calculus AB and BC exams and determined there is not a match. ***Feb 2016**

*>>>Note: When three courses are required to convey the necessary skills in calculus to mathematics majors, it is highly advised that students complete the entire sequence at a single institution. Course content may vary widely among institutions depending on the credits assigned to each course, and completing the sequence at a single institution is the best way to assure that neither credit nor content is lost in transfer.*

*Last Updated April 2016 - **Wording adopted by GECC Mathematics panel from Mathematics major panel recommendations.*

### M1900-2 : College-level Calculus II

**(3-5 semester credits)****The following description is for the full Calculus sequence (M1900-1, M1900-2, M1900-3): **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 differentiation; approximation by differentials; higher-order derivatives; Rolle's Theorem and mean value theorem; applications of the derivative; antiderivatives; 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, substitution, integration by parts, trigonometric substitution, and partial fractions; indeterminate forms and L'Hôpital's rule; improper integrals; sequences and series, convergence tests, Taylor series; parametric equations; polar coordinates and equations; vectors in 2 and 3 dimensions, vector operations; lines and planes in space; surfaces, quadric surfaces; functions of more than one variable, partial derivatives; the differential, directional derivatives, gradients; double and triple integrals, evaluation and applications; cylindrical and spherical coordinates. Prerequisite for Calculus I: College Algebra and Trigonometry with grades of C or better, or Precalculus with a grade of C or better. *The panel has compared the IAI GECC M1 900-2 descriptor against the AP Calculus AB and BC exams and determined there is not a match. ***Feb 2016**

*>>>Note: When three courses are required to convey the necessary skills in calculus to mathematics majors, it is highly advised that students complete the entire sequence at a single institution. Course content may vary widely among institutions depending on the credits assigned to each course, and completing the sequence at a single institution is the best way to assure that neither credit nor content is lost in transfer.*

*Last Updated April 2016 - **Wording adopted by GECC Mathematics panel from Mathematics major panel recommendations.*

### M1900-3 : College-level Calculus III

**(3-5 semester credits)****The following description is for the full Calculus sequence (M1900-1, M1900-2, M1900-3): **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 differentiation; approximation by differentials; higher-order derivatives; Rolle's Theorem and mean value theorem; applications of the derivative; antiderivatives; 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, substitution, integration by parts, trigonometric substitution, and partial fractions; indeterminate forms and L'Hôpital's rule; improper integrals; sequences and series, convergence tests, Taylor series; parametric equations; polar coordinates and equations; vectors in 2 and 3 dimensions, vector operations; lines and planes in space; surfaces, quadric surfaces; functions of more than one variable, partial derivatives; the differential, directional derivatives, gradients; double and triple integrals, evaluation and applications; cylindrical and spherical coordinates. Prerequisite for Calculus I: College Algebra and Trigonometry with grades of C or better, or Precalculus with a grade of C or better. *The panel has compared the IAI GECC M1 900-3 descriptor against the AP Calculus AB and BC exams and determined there is not a match. ***Feb 2016**

*>>>Note: When three courses are required to convey the necessary skills in calculus to mathematics majors, it is highly advised that students complete the entire sequence at a single institution. Course content may vary widely among institutions depending on the credits assigned to each course, and completing the sequence at a single institution is the best way to assure that neither credit nor content is lost in transfer.*

*Last Updated April 2016 - **Wording adopted by GECC Mathematics panel from Mathematics major panel recommendations.*

### M1900-B : Calculus for Business and Social Sciences

**(4-5 semester credits)**This calculus course is designed specifically for students in business and the social sciences and does not count toward a major or minor in mathematics. It emphasizes applications of the basic concepts of calculus rather than proofs. Topics must include limits; techniques of differentiation applied to polynomial, rational, exponential, and logarithmic functions; partial derivatives and applications; maxima and minima of functions; and elementary techniques of integration including substitution and integration by parts. Business and social science applications are stressed throughout the course. Prerequisite: College Algebra with a grade of C or better. *The panel has compared the IAI GECC M1 900-B descriptor against the AP Calculus AB and BC exams and determined there is not a match. Feb 2016*

**IMPORTANT SPECIAL NOTE:** * This course's credit hours increased from 3-5 semester credit hours to 4-5 semester credit hours on Jan. 1, 2017.*

### M1900-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. *Policies on the 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. A score of 3 or higher on the AP Calculus AB or BC exam may be considered as equivalent to successful completion of postsecondary courses approved for IAI GECC M1 900-0. Feb 2016*

### M1901 : 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: Intermediate Algebra or PMGE with a grade of “C” or better. **The GECC Mathematics panel will support the pilot of the co-requisite model from 2016 to 2019. During the ****3 year**** co-requisite pilot, the GECC Mathematics panel will allow the co-requisite to serve as the prerequisite for M1901, M1902, M1904, and M1907.** *The panel has compared the IAI GECC M1 901 descriptor against the AP Calculus AB and BC exams and determined there is not a match. ***Feb 2016**

Tweaked Fall 2016

### M1902 : 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: Prerequisite: Intermediate Algebra or PMGE with a grade of “C” or better. **The GECC Mathematics panel will support the pilot of the co-requisite model from 2016 to 2019. During the ****3 year**** co-requisite pilot, the GECC Mathematics panel will allow the co-requisite to serve as the prerequisite for M1901, M1902, M1904, and M1907.** *Policies on the 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. A score of 3 or higher on the AP Statistics exam may be considered as equivalent to successful completion of postsecondary courses approved for IAI GECC M1 902.***Feb 2016**

Tweaked Fall 2016

### M1903 : 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.

### M1904 : 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: Intermediate Algebra or PMGE with a grade of “C” or better. **The GECC Mathematics panel will support the pilot of the co-requisite model from 2016 to 2019. During the ****3 year**** co-requisite pilot, the GECC Mathematics panel will allow the co-requisite to serve as the prerequisite for M1901, M1902, M1904, and M1907.**

Tweaked Fall 2016

### M1905 : Discrete Mathematics

**(3-4 semester credits)**Introduction to analysis of finite collections and mathematical foundations of sequential machines, computer system design, data structures and algorithms. Includes a minimum of 6 of the following: sets, counting, recursion, graph theory, trees, nets, Boolean algebra, automata, and formal grammars and languages. Prerequisite: C or better in college algebra.

**Description Revised Spring 2017 - 03/24/2017**

Credit hours revised 04/15/2016 - effective 01/01/2017

### M1906 : 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) must include the following topics: systems of linear equations and matrices; linear programming; counting and probability theory. Other possible additional topics include: vectors; determinants; systems of inequalities; simplex method; set theory; logic and Boolean algebra; 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.

Reviewed and revised Fall 2016 - 10/21/2016

### M1907 : 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 technology such as graphing calculators or personal computers. Includes inductive and deductive reasoning, mathematical modeling in problem solving, and limitations therein. Topics must include a minimum of 6 of the following topics: mathematical proof, sequences and series in modeling, variables and functions, graphical, tabular, and formulaic representation of algebraic functions, algebraic functions in modeling logarithmic scales, and logarithmic and exponential functions in modeling. Prerequisite: Intermediate Algebra or PMGE with a grade of “C” or better. **The GECC Mathematics panel will support the pilot of the co-requisite model from 2016 to 2019. During the 3 year co-requisite pilot, the GECC Mathematics panel will allow the co-requisite to serve as the prerequisite for M1901, M1902, M1904, and M1907.**

**Revised Spring 2017 – 03/24/2017**