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# IAI General Education Math Course Descriptions

**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 CalculusA 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)
**

T

• 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 and inverse 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 including cylindrical and 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.

**
Last Update 03/24/2023 -
**

**M1900-2: College-level Calculus II **
**(3-5 semester credits)
**

T

• 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 and inverse 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 including cylindrical and 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.

**
Last Update 03/24/2023 -
**

**M1900-3: College-level Calculus III (3-5 semester credits)
**

T

• 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 and inverse 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 including cylindrical and 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.

**
Last Update 03/24/2023 -
**

**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 involving maxima and minima of functions in more than one variable; 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 to 4-5 semester credit hours from 3-5 semester credits on Jan. 1, 2017.

Revised information in description regarding partial derivatives and applications – Spring 2021 – 04/23/2021 – effective Fall 2021

**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.

**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 technology as a tool. Selecting and using appropriate approaches and tools in formulating and solving real-world problems and estimating/approximating and judging the reasonableness of answers should be integrated throughout the course.

**The course must include all of the following topics: **

- Representing and analyzing data through statistical measures such as central tendency, dispersion, normal distributions, chi-square distributions, and/or correlation and regression to test hypotheses (maximum of one-third of course);
- Using logical statements and arguments in a real-world context;
- Applying techniques such as graphing functions, systems of equations, and systems of inequalities in the interpretation and solutions of problems.

Prerequisite: A student in this course should be college-ready in mathematics as assessed by local institutions (for example: Intermediate Algebra with a C or better, placement, co-requisite course, multiple measures, transitional mathematics competencies, PMGE, or professional organization recommendations, etc.).

Full Revision – Fall 2019 – 10/18/2019, Effective Spring 2020.

Prior Revisions: Prerequisite Revised – Fall 2017/10-27-2017 – Effective Spring 2018, Tweaked Fall 2016 - Effective Spring 2017

**M1902: General Education Statistics (3-4 semester credits)
**

This course focuses on statistical reasoning and the solving of problems using real-world data rather than on computational skills. **The use of technology-based computations (more advanced than a basic scientific calculator, such as graphing calculators with a statistical package, spreadsheets, or statistical computing software) is required with an emphasis on interpretation and evaluation of statistical results. **Topics must include data collection processes (observational studies, experimental design, sampling techniques, bias), descriptive methods using quantitative and qualitative data, bivariate data, correlation, and leastsquares regression, basic probability theory, probability distributions (normal distributions and normal curve, binomial distribution), confidence intervals and hypothesis tests using p-values. Prerequisite: A student in this course should be college-ready in mathematics as assessed by local institutions (for example: Intermediate Algebra with a C or better, placement, co-requisite course, multiple measures, transitional mathematics competencies, PMGE, or professional organization recommendations, etc.). 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 Ml 902.Feb 2016

*Panel rephrased the technology requirements of this course in Fall 2018 due confusion in course review during the semester. The Fall 2018 tweaks are effecting Spring 2019. The primary Spring 2018 change was to add some technology wording. This wording was refined. See the *
**bolded**
* section of the description. *

**M1903: Mathematics for Elementary Teaching I and II (3-4 semester credits)
**

Focuses on mathematical reasoning and 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.

*
Please Note: The IAI approval goes on the second course of the sequence; however representative syllabi for both courses must be included within the course submission of the "Mathematics for Elementary Teaching II." Do not submit the first course as a separate submission.*

**Minor revision to description (removal of “by using calculators and microcomputers in problem-solving”) – Spring 2021 – 04/21/2021 – effective fall 2021.**

**M1904: General Education Mathematics **
**(3-4 semester credits)
**Focuses on mathematical reasoning and the solving of real-life problems and appreciation, rather than on routine skills. Three or four topics are studied in depth, with at least three chosen from the following list:

· geometry

· counting techniques and probability (both are required for this topic)

· graph theory

· logic and set theory (both are required for this topic)

· mathematical modeling

· mathematics of finance

· game theory

· linear programming, including the simplex method

· statistics

· voting and apportionment (both are required for this topic)

The use of calculators and computers are strongly encouraged. Prerequisite: A student in this course should be college-ready in mathematics as assessed by local institutions (for example: Intermediate Algebra with a C or better, placement, co-requisite course, multiple measures, transitional mathematics competencies, PMGE, or professional organization recommendations, etc.).

Last Revision: Panel added "including the simplex method" to the description - Spring 2023 - 03/24/2023

Topics clarified – Spring 2022 – 03/11/2022 – Effective Fall 2022

Prerequisite Revised – Fall 2017/10-27-2017 – Effective Spring 2018

Tweaked Spring 2018 – 03/09/2018 – effective Fall 2018

**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 - 03/24/2017Credit 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.

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 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 Revised – Fall 2017/10-27-2017 – Effective Spring 2018

Tweaked Fall 2016 - Effective Spring 2017

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